Foreword

Welcome to Tonc, a guide to Game Boy Advance programming originally published in 2004.

You are reading a new, revamped version of it, powered by mdbook and now maintained by the community.

Work In Progress notice

We recently finished the porting of this book. Improvements ongoing, if you spot any problems please feel free to ask for help or get involved!

Contributing

This book is open source, released under the CC-BY-NC-SA license. Everyone is welcome to help, provide feedback and propose additions or improvements. The git repository is hosted at github.com/gbadev-org/tonc, where you can learn more about how you can help, find detailed contribution guidelines and procedures, file Issues and send Pull Requests.

More resources about GBA development can be found at gbadev.net. There is also a Discord chat dedicated to the gbadev community.

Authors

Jasper “cearn” Vijn is the original author, creating and maintaining Tonc till 2013.

exelotl, avivace, PinoBatch, copyrat90, LunarLambda, gwilymk, mtthgn, and djedditt ported the contents to markdown and migrated the underlying rendering technology to mdbook.

Using this document

In the top navigation bar, you will find a series of icons.

By clicking on the icon you will toggle an interactive table of contents to navigate the document. You can also use and keys on your keyboard to go to the following and previous page.

The lets you choose among 6 different themes and color schemes to please your reading experience, including the classic Tonc theme.

You can search anywhere by pressing s on your keyboard or clicking the icon.

The icon allows you to suggest an edit on the current page by directly opening the source file in the git repository.


This document version was produced from git commit 414ee6 (2024-03-24 19:45:05 +0100 ).

Introduction

Organisation

TONC consists of three components: a text section (the actual tutorial), an examples repo with all the source code & makefiles of the various demos, and a library called libtonc which holds all the useful/reusable code introduced throughout the tutorial.

Previously these were all distributed as zip files, but times have changed and now they exist in separate git repositories. They will now be explained in more detail:

Tonc text

The text section, which you’re reading now, covers the principles of GBA programming in detail. The focus here is not so much on how to get something done, but how things actually work, and why it’s done the way it’s done. After that the how often comes naturally. Every chapter has one of more demonstrations of the covered theory, and a brief discussion of the demo itself.

Please, do not make the mistake of only reading the demo discussion: to properly understand how things work you need to read the text in full. While there are optional parts, and whole pages of boring text that seem to have little to do with actual GBA coding, they are there for a reason, usually there’s extra conceptual information or gotchas.

At first, the text part had only very little code in it, because I figured the demo code would be at hand and flicking between them would not be annoying. Well, I’ve realized that I figured wrong and am in the process of including more of the code into these pages; maybe not quite enough to copy-paste and get a clean compile, but enough to go with the explanations of the demos.

The main language will be C, and a smidgeon of assembly. These are the two main languages used in GBA programming even though there are others around. Since the basics of programming are independent of language, it should be possible to adapt them for your chosen language easily.

GBA programming is done close to the hardware, so I hope you know your pointers, hexadecimal numbers and boolean algebra/bit-operations. There’s also a fair amount of math here, mostly vector and matrix stuff so I hope your linear algebra is up to speed. Lastly, I am assuming your intellectual capacities exceed those of a random lab monkey, so I won’t elaborate on what I consider trivial matters too much.

Aside from the introduction and appendices, the text is divided into 3 parts. First there’s ‘basics’, which explains the absolute essentials for getting anything done. This includes setting up the development environment, basic use of graphics and buttons. It also contains text on what it means to do low level programming and programming efficiently; items that in my view you’d better learn sooner rather than later. The second part covers most of the other items of the GBA like special graphic effects, timers and interrupts. The final section covers more advanced items that uses elements from all chapters. This includes writing text (yes, that’s an advanced topic on the GBA), mode 7 graphics and a chapter on ARM assembly.

The Markdown source for the text is all available on GitHub, so please feel free to contribute if you find a typo or something that can be improved.

Tonc code (libtonc & examples)

The source code to all the demos mentioned in the text can be found in the libtonc-examples repository. Like the text, the examples themselves are divided into 3 parts: basic, extended and advanced. There is also a lab directory with a few interesting projects, but which might not be quite ready. Still interesting to look at, though.

The language we’ll be using is C with a dash of assembly (but not C++). I am working under the assumption that you are familiar with this language. If not, go learn it first because I’m not going to show you; this is not a C course. I do have some links to C tutorials in the references.

Unlike some older GBA tutorials, tonc uses makefiles instead of batch scripts to build the example projects, because they’re just Plain Better™. How to use these will be explained in the next chapter, but if you just wanted to check out the pre-compiled example ROMs, those are still available here: tonc-bin.zip.

The examples depend on libtonc, a library containing all the important #defines and functions introduced throughout the tutorial. This also includes text writers for all video modes, BIOS routines, a pretty advanced interrupt dispatcher, safe and fast memory copy and fill routines and much more. Historically libtonc was included alongside the examples, but nowadays it comes with devkitARM, so you don’t have to download it yourself.

Statement of Purpose

I wrote Tonc for two reasons. Firstly, as a way to organize my own thoughts. You often see things in a different light when you write things down and learn from that experience. Secondly, there is a lot of very bad information in other tutorials out there (the only exceptions I know of are the new PERN and Deku’s sound tutorial. Yes, I am aware of how that sounds, but unfortunately it happens to be true. A number of examples:

  • Only very basic information given, sometimes even incorrect info.
  • Strong focus on bitmap modes, which are hardly ever used for serious GBA programming.
  • Bad programming habits. Adding code/data to projects by #including the files, Using ancient toolchains, non-optimal compiler settings and data-types, and inefficient (sometimes very inefficient) code.

If you are new and have followed the other tutorials, everything will seem to work fine, so what’s the problem? Well, that’s part of the problem actually. Everything will seem fine, until you start bigger projects, at which time you’ll find hidden errors and that slow code really bogs things down and you’ll have unlearn all the bad habits you picked up and redo everything from the start. The GBA is one of the few platforms where efficient coding still means something, and sometimes all it takes is a change of datatype or compiler switch. These things are better done right from the start.

I’ve tried to go for completeness first, simplicity second. As a certain wild-haired scientist once said: “Make things as simple as possible, but no simpler.” This means things can seem a little technical at times, but that’s only because things are pretty technical at times, and there’s no sense in pretending they’re not.

In short, Tonc is not “GBA Programming for Dummies”, never was, never will be. There’s far too much of stuff for Dummies already anyway. If you consider yourself a dummy (and I do mean dummy, not newbie), maybe Tonc isn’t the right place. If you’re serious about learning GBA programming, however, accept no substitute.

Terminology and Notation

I’m a physicist by training which means that I know my math and its notational conventions. I use both quite often in Tonc, as well as a number of html-tag conventions. To make sure we’re all on the same page here’s a list:

Type notation example
bit n in a foo foo{n} REG_DISPCNT{4} (active page bit)
code <code> tag sx
command/file <tt> tag vid.h
matrix bold, uppercase P
memory hex + code 0400:002eh
new term bold, italic charblock
variable italics x
vector bold, lowercase v

I also use some non-ASCII symbols that may not show up properly depending on how old your browser is. These are:

symboldescription
α, β, γ Greek letters
approximately
½ one half
¼ one quarter
¾ three quarters
greater or equal
double-sided arrow
is in (an interval)
⟨ ⟩ ‘bra’ & ‘ket’
right arrow
² superscript 2
× times

I also make liberal use of shorthand for primitive C types like char and int and such. These are typedefs that better indicate the size of the variable that’s used. Since this is very important in console programming, they’re quite common. Anyway, here’s a list.

base type alt name unsigned signed volatile
char byte u8 s8 vu8 / vs8
short halfword u16 s16 vu16 / vs16
int word u32 s32 vu32 / vs32

Finally, there are a number of different notations for hex that I will switch between, depending on the situation. The C notation (‘0x’ prefix, 0x0400) is common for normal numbers, but I’ll also use the assembly affix at times (‘h’, 0400:0000h). The colon here is merely for ease of reading. It’s hard to tell the number of zeros without it.

Register names and descriptions

Getting the GBA to do things often involves the use of the so-called IO registers. Certain bits at certain addresses of memory can be used as switches for the various effects that the GBA is capable of. Each register is aliased as a normal variable, and you need to set/clear bits using bit operations. We’ll get to where these registers are and what bit does what later; right now I want to show you how I will present these, and refer to them in the text.

Each register (or register-like address) is mapped to a dereferenced pointer, usually 16bits long. For example, the display status register is

#define  REG_DISPSTAT *(u16*)0x04000004     

Every time I introduce a register I will give an overview of the bits like this:

REG_DISPSTAT @ 0400:0004h
F E D C B A 9 8 7 6543210
VcT - VcI HbI VbI VcS HbS VbS

The table lists the register’s name (REG_DISPSTAT, its address (0400:0000h) and the individual bits or bitfields. Sometimes, bits or entire registers are read- or write-only. Read-only is indicated with a red overbar (as used here). Write-only uses a blue underbar. After it will be a list that describes the various bits, and also gives the #define or #defines I use for that bit:

bitsnamedefinedescription
0 VbS DSTAT_IN_VBL VBlank status, read only. Will be set inside VBlank, clear in VDraw.
other fields
8-F VcT DSTAT_VCT# VCount trigger value. If the current scanline is at this value, bit 2 is set and an interrupt is fired if requested.

The full list of REG_DISPSTAT can be found here. The #defines are usually specific to tonc, by the way. Each site and API has its own terminology here. This is possible because it’s not the names that are important, but the numbers they stand for. That goes for the names of the registers themselves too, of course. One last point on the #defines: some of the ones listed have a hash (‘#’) affix. This is a shorthand notation to indicate that that field has foo_SHIFT and foo_MASK #defines, and a foo() macro. For example, the display register has an 8-bit trigger VCount field, which has ‘DSTAT_VCT#’ listed in the define column. This means that the following three things exist in the tonc headers:

#define DSTAT_VCT_MASK      0xFF00
#define DSTAT_VCT_SHIFT          8
#define DSTAT_VCT(_n)       ((_n)<<DSTAT_VCT_SHIFT)

Lastly, as shorthand for a specific bit in a register, I will use accolades. The number will be a hexadecimal number. For example, REG_DISPCNT{0} is the VBlank status bit (VbS above), and REG_DISPCNT{8-F} would be the whole byte for the VCount trigger.

On errors, suggestions

As much as we (cearn and the gbadev.net community) have tried to weed out things like spelling/grammar errors and broken links, it’s surely possible some have slipped by. If you find some, please raise an issue (or even better, make a pull request) on the GitHub repo. Of course, if things are unclear or *gasp* incorrect, or if you have suggestions, we’d like to know that as well! You can also reach us on Discord / IRC or the Forums.

And, of course:

This distribution is provided as is, without warranty of any kind. I cannot be held liable for any damage arising out of the use or inability to use this distribution. Code has been tested on emulator and real hardware as well as I could, but I can’t guarantee 100% correctness. Both text and code may be modified at any time. Check in once in a while to see if anything’s changed. There is also a log in the appendices.

OK that’s it. Have fun.

Jasper Vijn (jakvijn at gmail dot com) and the gbadev.net community

1. GBA Hardware

Meet the GBA

The Nintendo Game Boy Advance (GBA) is a portable games console. As if you didn’t know already. The CPU is a 32-bit ARM7tdmi chip running at 16.78 MHz. It has a number of distinct memory areas (like work RAM, IO and video memory) which we will look into shortly. The games are stored on Game Paks, consisting of ROM for code and data, and fairly often some RAM for saving game info. The GBA has a 240x160 LCD screen capable of displaying 32768 colors (15 bits).

Unfortunately, the screen is not back-lit, which made a lot of people very angry and has generally been regarded as a bad move. So, in 2003 Nintendo launched the GBA SP, a sort of GBA 2.0, which features a fold-up screen reminiscent of the old Game & Watch games (remember those? You do? Boy, you are old! (For the record, I still have mine too :) )). Then came the final GBA version, the Game Boy Micro, a very, very small GBA which easily fits in everyone’s pockets. The differences the GBA, GBA-SP and Micro are mainly cosmetic, though, they’re the same thing from a programming point of view.

The original Game Boy took the world by storm in 1989. Not bad for a monochrome handheld console, eh? Later the Game Boy Color was released which finally put some color on the aging machine, but it was still very much a simple Game Boy. The true successor was the GBA, released in 2001. The GBA is backward compatible with the Game Boy, so you can play all the old GB games as well.

In terms of capabilities the GBA is a lot like the Super NES (SNES): 15-bit color, multiple background layers and hardware rotation and scaling. And shoulder buttons, of course. A cynic might look at the enormous amount of SNES ports and say that the GBA is a SNES, only portable. This is true, but you can hardly call that a bad thing.

original GBA
Fig 1.1: original GBA.
GBA-SP
Fig 1.2: GBA-SP.

GBA specs and capabilities

Below is a list of the specifications and capabilities of the GBA. This is not a full list, but these are the most important things you need to know.

  • Video
  • Sound
    • 6 channels total
    • 4 tone generators from the original Game Boy: 2 square wave, 1 general wave and one noise generator.
    • 2 ‘DirectSound’ channels for playing samples and music.
  • Miscellaneous
    • 10 buttons (or keys): 4-way directional pad, Select/Start, fire buttons A/B, shoulder buttons L/R.
    • 14 hardware interrupts.
    • 4-player multiplayer mode via a multiboot cable.
    • Optional infrared, solar and gyroscopic interfaces. Other interfaces have also been made by some.
    • Main programming platforms: C/C++ and assembly, though there are tools for Pascal, Forth, Lua and others as well. Easy to start with, yet hard to truly master.

From a programming point of view, the GBA (or any other console for that matter) is totally different from a PC. There is no operating system, no messing with drivers and hardware incompatibilities; it’s bits as far as the eye can see. Well, PCs are also just bits, but that’s several layers down; on consoles it’s just you, the CPU and memory. Basically, it’s the Real Programmer’s dream.

To get anything done, you use memory-mapped IO. Specific areas of memory are mapped directly to hardware functions. In the first demo, for example, we will write the number 0x0403 to memory address 0400:0000h. This tells the GBA to enable background 2 and set the graphics mode to 3. What this actually means is, of course, what this tutorial is for :).

CPU

As said, the GBA runs on a ARM7tdmi RISC chip at 16.78 MHz (224 cycles/second). It is a 32-bit chip that can run on two different instruction sets. First, there’s is ARM code, which is a set of 32-bit instructions. Then there’s Thumb, which uses 16-bit instructions. Thumb instructions are a subset of the ARM instruction set; since the instructions are shorter, the code can be smaller, but their power is also reduced. It is recommended that normal code be Thumb code in ROM, and for time-critical code to be ARM code and put in IWRAM. Since all tonc-demos are still rather simple, most (but not all) code is Thumb code.

For more information on the CPU, go to www.arm.com or to the assembly chapter

Memory Sections

This section lists the various memory areas. It’s basically a summary of the GBATEK section on memory.

area start end length port-size description
System ROM 0000:0000 0000:03FF 16 KB 32 bit Bios memory. You can execute it, but not read it (i.o.w, touch, don't look)
EWRAM 0200:0000h 0203:FFFFh 256 KB 16 bit External work RAM. Is available for your code and data. If you're using a multiboot cable, this is where the downloaded code goes and execution starts (normally execution starts at ROM). Due to the 16-bit port, you want this section's code to be Thumb code.
IWRAM 0300:0000h 0300:7FFFh 32 KB 32 bit This is also available for code and data. The 32-bit bus and the fact it's embedded in the CPU make this the fastest memory section. The 32-bit bus means that ARM instructions can be loded at once, so put your ARM code here.
IO RAM 0400:0000h 0400:03FFh 1 KB 32 bit Memory-mapped IO registers. These have nothing to do with the CPU registers you use in assembly so the name can be a bit confusing. Don't blame me for that. This section is where you control graphics, sound, buttons and other features.
PAL RAM 0500:0000h 0500:03FFh 1 KB 16 bit Memory for two palettes contaning 256 entries of 15-bit colors each. The first is for backgrounds, the second for sprites.
VRAM 0600:0000h 0601:7FFFh 96 KB 16 bit Video RAM. This is where the data used for backgrounds and sprites are stored. The interpretation of this data depends on a number of things, including video mode and background and sprite settings.
OAM 0700:0000h 0700:03FFh 1 KB 32 bit Object Attribute Memory. This is where you control the sprites.
PAK ROM 0800:0000h var var 16 bit Game Pak ROM. This is where the game is located and execution starts, except when you're running from a multiboot cable. This size is variable, but the limit is 32 MB. It's a 16-bit bus, so Thumb code is preferable over ARM code here.
Cart RAM 0E00:0000h var var 8 bit This is where saved data is stored. Cart RAM can be in the form of SRAM, Flash ROM or EEPROM. Programatically they all do the same thing: store data. The total size is variable, but 64 KB is a good indication.

The various RAM sections (apart from Cart RAM) are zeroed at start-up by BIOS. The areas you will deal with them most are IO, PAL, VRAM and OAM. For simple games and demos it will usually suffice to load your graphics data into PAL and VRAM at the start use IO and OAM to take care of the actual interaction. The layout of these two sections is quite complex and almost impossible to figure out on your own (almost, because emulator builders obviously have done just that). With this in mind, reference sheets like GBATEK and the CowBite Spec are unmissable documents. In theory this is all you need to get you started, but in practice using one or more tutorials (such as this one) with example code will save a lot of headaches.

2. Setting up a development environment

Introduction

Unless you want to punch in the instructions in binary in a hex editor, you’ll need a development environment to turn human readable code into machine code. This chapter will show you how to set up the necessary components and use them to compile Tonc’s examples.

By the end you should have:

  • A text editor
  • A GBA emulator (mGBA)
  • A cross-compiler toolchain (devkitARM)
  • Libraries used for GBA programming (libtonc in particular)
  • The examples which accompany this tutorial

Some command-line skills required

To compile a GBA game, you’ll need a basic undestanding of the command-line. If this is unfamiliar to you, the following Unix command-line tutorial may be helpful.

If you’re on Windows, you should use the MSYS2 terminal which comes with devkitARM. On other OS’s, the built-in terminal should be perfectly adequate.

Choosing a text editor

A decent text editor is essential for programming. At the bare minimum you’ll want something that supports syntax highlighting and gives you control over indentation and line endings. That means notepad.exe sadly won’t cut it.

There are many options, and you may already have a favourite. But in case you don’t, here are some suggestions:

  • Visual Studio Code - a popular and featureful editor that works on Linux, Windows & Mac

  • Kate - another powerful editor, a bit lighter and fully open-source

  • Geany - runs well on low-end machines and is still very extensible via plugins

  • Notepad++ - a lightweight and widely-loved choice on Windows

Once you’ve chosen an editor and gotten comfortable with it, you can move onto the next section.


Fig 2.1: Editing a file in VS Code.

In many editors it’s possible to set a hotkey (usually F5 or Ctrl+Enter) to compile and run your code. This can be an effective workflow, but for the purposes of this tutorial we’ll use the command-line, because it’s essential to know what’s going on under the hood.

Likewise, code-completion and error highlighting are also valuable features which you may want to spend time setting up, but are outside the scope of this chapter.

Installing a GBA emulator

Needless to say, you’ll need a way to actually run your GBA programs. Testing on real hardware from time to time is highly recommended (and part of the fun), but for everyday development you’ll want something more convenient. That’s where emulators come in.

At the time of writing, the most suitable emulator for GBA development is mGBA. It’s highly accurate and has features for developers such as memory viewers, debug logging, and a GDB server for step debugging, all of which will make your life a lot easier when things go wrong (and they will)!


Fig 2.2: A GBA ROM running inside mGBA

Other emulators which you might want to use are: NanoBoyAdvance and SkyEmu, which are both cycle accurate and effectively the closest you can get to playing on real hardware without actually doing so.

Finally no$gba (debug version) is a somewhat older and less accurate Windows-only GBA emulator, but has some unique debugging features you won’t find elsewhere. Namely a visual debugger, performance profiler, CPU usage meters, and memory access checking which can catch buffer overflows and such. If you can get it working, it’s an invaluable tool!

Installing devkitARM

devkitARM has been the standard toolchain for GBA homebrew for many years. It is provided by a team called devkitPro (dkP), though informally the tools are often referred to as devkitPro too (much to the maintainers’ lament).

To install devkitARM, visit the devkitPro Getting Started page and follow the instructions for your OS.

Do not use spaces in paths

devkitARM uses make for building projects, which doesn’t cope well with spaces in paths (such as My Documents). The reason for this is that make uses spaces as a separator between command-line options, but unlike e.g. shell scripts, it doesn’t provide an adequate form of quoting/escaping, especially not when working with lists of filenames.

Windows tips

If you are on Windows, there is a GUI installer which downloads and installs the components automatically. Be sure to select “GBA Development” during installation, as shown in fig 2.3.


Fig 2.3: Installing devkitARM with the GBA packages on Windows.

Linux & Mac tips

If you are using Linux or Mac, after following the instructions on dkP’s Getting Started page, you should install the gba-dev package group via dkp-pacman in your terminal (or just pacman if you use Arch Linux). To do this, run the following command:

sudo dkp-pacman -S gba-dev

When asked which packages to install (“Enter a selection (default=all):”) you should simply hit Enter to install everything in the entire gba-dev group.

Obtaining Tonc’s example code

This tutorial comes with a full set of examples to demonstrate the concepts taught in each chapter.

Additionally, libtonc is the GBA programming library that accompanies Tonc, and is necessary to compile the examples. In the past, libtonc had to be downloaded separately and placed where your projects could find it. But nowadays it comes included as part of devkitARM. As long as you selected the gba-dev packages during installation, you already have libtonc.

The bad news is devkitARM doesn’t include the Tonc examples, so you still have to download those yourself. You can get them via “Code -> Download Zip” on the repository page, or by using git in your terminal:

git clone https://github.com/gbadev-org/libtonc-examples

toolbox.h vs libtonc

In the early chapters, we’ll be building our own library called toolbox.h which replicates parts of libtonc for educational purposes. But for real-world usage, sticking to a more featureful, tried-and-tested library (such as libtonc itself) should be preferred.

Compiling the examples

To test your installation, let’s try building one of the examples.

In the terminal, navigate to the directory where one of the examples is located (let’s say, the hello example) and run make:

cd libtonc-examples/basic/hello
make

When invoked, make will build the project by following the rules in the file called ‘Makefile’ in the current working directory. Assuming this was successful, a .gba file will be produced, which you can run in your emulator of choice:


Fig 2.4: One of the Tonc examples running in mGBA.

If you’ve gotten this far, congratulations! You are now ready to start writing your own GBA programs.

You can move onto the next chapter, or keep reading for more details.

Setting environment variables

If you get an error such as Please set DEVKITPRO in your environment, it means your environment variables aren’t set properly. The solution to this differs between machines, but usually you want to edit a file called .bashrc in your home directory, and add the following lines to it:

export DEVKITPRO=/opt/devkitpro
export DEVKITARM=/opt/devkitpro/devkitARM
export DEVKITPPC=/opt/devkitpro/devkitPPC

export PATH=$DEVKITARM/bin:$DEVKITPRO/tools/bin:$PATH  # optional

The last line adds the compiler and related tools to your PATH environment variable, allowing you to use them directly in your terminal.

This is optional, because the example makefiles also set PATH during the build process. But having the tools on hand is useful, and required if you want to follow along in the next section.

After editing .bashrc, you will have to close and reopen your terminal to apply the changes. Or you can run source ~/.bashrc to persist these changes in the current shell.

Manual steps to build a GBA ROM

We’ve just seen how to compile a GBA program via make. Copying the makefile and using it for your own projects is absolutely encouraged! That said, it’s valuable to know what’s happening under the hood.

Converting your C/C++/asm sources into a valid GBA ROM involves 4 steps, which can be seen in the output from running make:

$ make
hello.c               # <--- invoke the compiler
linking cartridge     # <--- invoke the linker
built ... hello.gba   # <--- elf stripped
ROM fixed!            # <--- header fixed

The steps are as follows:

  1. Compile/assemble the sources. We turn the human readable C or C++ files (.c/.cpp) or assembly files (.s/.asm) to a binary format known as object files (.o). There is one object file for each source file.

    The tool for this is called arm-none-eabi-gcc. Actually, this is just a front-end for the real compiler, but that’s just details. The arm-none-eabi- here is a prefix which means this version of GCC produces machine code for bare-metal ARM platforms; other target platforms have different prefixes. Note that C++ uses g++ instead of gcc.

  2. Link the object files. After that, the separate object files are linked into a single executable ELF file. Any precompiled code libraries (.a) you may have specified are linked at this stage too.

    You can actually compile and link at the same time, but it is good practice to keep them separate: serious projects usually contain multiple source files and you don’t want to have to wait for the whole world to recompile when you only changed one. This becomes even more important when you start adding data (graphics, music, etc).

    Again, arm-none-eabi-gcc is used for invoking the linker, although the actual linker is called arm-none-eabi-ld.

  3. Strip to raw binary. The ELF file still contains debug data and can’t actually be read by the GBA (though many emulators will accept it). arm-none-eabi-objcopy removes the debug data and makes sure the GBA will accept it. Well, almost.

  4. Fix the header. Each GBA game has a header with a checksum to make sure it’s a valid GBA ROM. The linking step makes room for one, but leaves it blank, so we have to use a tool like DarkFader’s gbafix to fix the header. This tool comes with devkitARM, so you don’t have to download it separately.

You can of course run all these commands in the terminal yourself without a makefile, provided the dkP tools are in your PATH.

Let’s try it with the example named first - this is the easiest one to compile because it doesn’t depend on any libraries.

cd libtonc-examples/basic/first/source

# Compile first.c to first.o
arm-none-eabi-gcc -mthumb -c first.c

# Link first.o (and standard libs) to first.elf
arm-none-eabi-gcc -specs=gba.specs -mthumb first.o -o first.elf

# Strip to binary-only
arm-none-eabi-objcopy -O binary first.elf first.gba

# Fix header
gbafix first.gba

There you have it - a GBA program compiled from scratch! Well… we can always go deeper but this is probably a good place to stop for now. x)

There are various options passed to the tools here that may not be immediately obvious. These are explained in the makefile appendix if you’re interested.

Avoid batch files for compiling

You may be tempted to stick all these commands into a batch file or shell script, and use that to compile your project. This is simple, but not recommended.

The reason becomes apparent as soon as your project has more than one source file: if you make an edit to a single file, you shouldn’t have to recompile all of the sources, only the one that changed. A build system such as make is smart enough to realise this, whereas simple shell scripts are not.

When you get to the point where your project has dozens of source files, this makes a big difference!

Alternative toolchains

The advantage of devkitARM is that it provides a consistent environment for compiling GBA homebrew on Windows, Mac and Linux. However, if you’re feeling adventurous there are other good options available nowadays:

  • gba-toolchain - uses the CMake build system instead of Makefiles
  • meson-gba - uses the Meson build system instead of Makefiles
  • gba-bootstrap - the bare minimum needed to compile a GBA program. In other words, roll your own toolchain, with the hard bits done for you.

Why would you want to use these? They might be easier to install (many Linux distros offer their own builds of arm-none-eabi-gcc and related packages, which is essentially the same thing devkitARM provides), or you could be using a machine for which devkitARM is not available (such as a Raspberry Pi). Or perhaps you just want a better build system than makefiles.

Tonc assumes you’re using devkitARM, but most of the information is relevant no matter which toolchain you’re using.

Avoid ‘devkitAdvance’

You may encounter a toolchain called devkitAdvance. This is an ancient toolchain which hasn’t been updated since 2003. By using it, you will be missing out on two decades worth of compiler improvements and optimisations. If somebody recommends this to you, run away!

3. My first GBA demo

Finally, your first GBA program

Now that you have your development environment ready, it’s time to take a look at a simple GBA program. For this we will use the code from the C-file first.c. The plan at this point is not full understanding; the plan is to get something to compile and get something running. The code will be discussed in this chapter, but what it all means will be covered in later chapters.

// First demo. You are not expected to understand it 
// (don't spend too much time trying and read on).
// But if you do understand (as a newbie): wow!

int main()
{
    *(unsigned int*)0x04000000 = 0x0403;

    ((unsigned short*)0x06000000)[120+80*240] = 0x001F;
    ((unsigned short*)0x06000000)[136+80*240] = 0x03E0;
    ((unsigned short*)0x06000000)[120+96*240] = 0x7C00;

    while(1);

    return 0;
}

Don’t worry about the code just yet, there’s time for that later. And don’t leave yet, I’ll give a nicer version later on. All that matters for now is that you’re able to compile and run it.

picture of the first demo

Fig 3.1: picture of the first demo

As explained in the previous chapter, you can run make in your terminal to build the project. Under the hood this does the following:

  • compile first.c to first.o,
  • link the list of object files (currently only first.o) to first.elf,
  • translate first.elf to first.gba by stripping all excess ELF information,
  • fix the header so that the GBA will accept it.

After the makefile has run, you should have a file called first.gba. If you don’t, there’s a problem with your setup because the code sure isn’t wrong! Go back to make sure you didn’t miss anything - but if you’re still having trouble, feel free to stop by on Discord / IRC or the Forums, there’s a good chance someone will be able to help!

If you do find yourself with a GBA executable, run it on hardware or your emulator of choice and you should get a red, a green, and a blue pixel at positions (120, 80), (136, 80) and (120, 96), respectively.

Now, for the code itself…

Huh?

If you’re somewhat confused by it, you wouldn’t be alone. I expect that unless you already know a thing or two about GBA programming or have experience with low-level programming from other platforms, the code will be a total mystery. If you’re proficient enough in C you may have some idea what’s making the three pixels appear, but I admit that it is very hard to see.

And that was kind of my point actually. If one were to hand this in for a test at a programming class, you would fail so hard. And if not, the professors should be fired. While the code show above does work, the fact that it’s almost unreadable makes it bad code. Writing good code is not only about getting results, it’s also about making sure other people can understand what’s happening without too much trouble.

The code of first.c also serves another purpose, namely as a reminder that GBA programming is very low-level. You interact directly with the memory, and not through multiple layers of abstraction brought by APIs. To be able to do that means you have to really understand how computers work, which all programmers should know at least to some degree. There are APIs (for lack of a better word) like HAM that take care of the lowest levels, which definitely has its merits as it allows you to deal with more important stuff like actual game programming, but on the other hand it hides a lot of details – details that sometimes are better left in the open.

Those who want a better, more intelligible, version of the previous code can skip the next section and move on to the second first demo. The warped minds who can’t just let it go and want to have an explanation right now (for the record, I count myself among them), here’s what’s going on.

Explanation of the code

This is a quick and dirty explanation of the earlier code. Those previously mentioned warped minds for whom this section is intended will probably prefer it that way. A more detailed discussion will be given later.

As I said, GBA programming is low-level programming and sometimes goes right down to the bit. The 0x04000000 and 0x06000000 are parts of the accessible memory sections. These numbers themselves don’t mean much, by the way; they just refer to different sections. There aren’t really 0x02000000 between these two sections. As you can see in the memory map, these two sections are for the IO registers and VRAM, respectively.

To work with these sections in C, we have to make pointers out of them, which is what the ‘unsigned int*’ and ‘unsigned short*’ do. The types used here are almost arbitrary; almost, because some of them are more convenient than others. For example, the GBA has a number of different video modes, and in modes 3 and 5 VRAM is used to store 16-bit colors, so in that case casting it to halfword pointers is a good idea. Again, it is not required to do so, and in some cases different people will use different types of pointers. If you’re using someone else’s code, be sure to note the datatypes of the pointers used, not just the names.

The word at 0400:0000 contains the main bits for the display control. By writing 0x0403 into it, we tell the GBA to use video mode 3 and activate background 2. What this actually means will be explained in the video and bitmap mode chapters.

In mode 3, VRAM is a 16-bit bitmap; when we make a halfword pointer for it, each entry is a pixel. This bitmap itself is the same size as the screen (240x160) and because of the way bitmaps and C matrices work, by using something of the form ‘array[y*width + x]’ are the contents of coordinates (x, y) on screen. That gives us our 3 pixel locations. We fill these with three 16-bit numbers that happen to be full red, green and blue in 5.5.5 BGR format. Or is that RGB, I always forget. In any case, that’s what makes the pixels appear. After that there is one more important line, which is the infinite loop. Normally, infinite loops are things to be avoided, but in this case what happens after main() returns is rather undefined because there’s little to return to, so it’s best to avoid that possibility.

And that’s about it. While the Spartan purity of the code does appeal to a part of me, I will stress again that this is not the right way to program in C. Save the raw numbers for assembly please.

Your second first GBA program

So, let’s start over again and do it right this time. Or at least more right than before. There are a number of simple ways to improve the legibility of the code. Here is the list of things we’ll do.

  • First and foremost is the use of named literals, that is to say #defined names for the constants. The numbers that went into the display control will get proper names, as will the colors that we plotted.
  • We’ll also use #define for the memory mapping: the display control and VRAM will then work more like normal variables.
  • We’ll also create some typedefs, both for ease of use and to indicate conceptual types. For instance, a 16-bit color is essentially a halfword like any other, but if you typedef it as, say, COLOR, everyone will know that it’s not a normal halfword, but has something to do with colors.
  • Finally, instead of plotting pixels with an array access, which could still mean anything, well use a subroutine for it instead.

Naturally, this will expand the total lines of code a bit. Quite a bit, in fact. But it is well worth it. The code is actually a two-parter. The actual code, the thing that has all the functionality of the first demo, can be found in second.c. All the items discussed above, the typedefs, #defines and inlines, are put in toolbox.h.

// toolbox.h: 
//
// === NOTES ===
// * This is a _small_ set of typedefs, #defines and inlines that can 
//   be found in libtonc, and might not represent the 
//   final forms.


#ifndef TOOLBOX_H
#define TOOLBOX_H

// === (from tonc_types.h) ============================================

typedef unsigned char   u8;
typedef unsigned short  u16;
typedef unsigned int    u32;

typedef u16 COLOR;

#define INLINE static inline

// === (from tonc_memmap.h) ===========================================

#define MEM_IO      0x04000000
#define MEM_VRAM    0x06000000

#define REG_DISPCNT     *((volatile u32*)(MEM_IO+0x0000))

// === (from tonc_memdef.h) ===========================================

// --- REG_DISPCNT defines ---
#define DCNT_MODE0     0x0000
#define DCNT_MODE1      0x0001
#define DCNT_MODE2      0x0002
#define DCNT_MODE3      0x0003
#define DCNT_MODE4      0x0004
#define DCNT_MODE5      0x0005
// layers
#define DCNT_BG0        0x0100
#define DCNT_BG1        0x0200
#define DCNT_BG2        0x0400
#define DCNT_BG3        0x0800
#define DCNT_OBJ        0x1000


// === (from tonc_video.h) ============================================

#define SCREEN_WIDTH   240
#define SCREEN_HEIGHT  160

#define vid_mem     ((u16*)MEM_VRAM)

INLINE void m3_plot(int x, int y, COLOR clr)
{   vid_mem[y*SCREEN_WIDTH+x]= clr;    }

#define CLR_BLACK   0x0000
#define CLR_RED     0x001F
#define CLR_LIME    0x03E0
#define CLR_YELLOW  0x03FF
#define CLR_BLUE    0x7C00
#define CLR_MAG     0x7C1F
#define CLR_CYAN    0x7FE0
#define CLR_WHITE   0x7FFF


INLINE COLOR RGB15(u32 red, u32 green, u32 blue)
{   return red | (green<<5) | (blue<<10);   }

#endif // TOOLBOX_H
#include "toolbox.h"

int main()
{
    REG_DISPCNT= DCNT_MODE3 | DCNT_BG2;

    m3_plot( 120, 80, RGB15(31, 0, 0) );    // or CLR_RED
    m3_plot( 136, 80, RGB15( 0,31, 0) );    // or CLR_LIME
    m3_plot( 120, 96, RGB15( 0, 0,31) );    // or CLR_BLUE

    while(1);

    return 0;
}

As you can see, the number of lines in toolbox.h is actually much larger than that of the real code. This may seem like a bit of a waste now, but this is only because it’s such a small demo. None of the contents of toolbox.h is actually compiled, so there is no cost in terms of memory use. In fact, if it did it wouldn’t belong in a header file, but that’s a discussion I’ll go into another time. Right now, let’s see what we actually have in toolbox.h

The toolbox

Types and typedefs

First of all, we create some shorthand notations of commonly used types. No matter what anyone says, brevity is a virtue. For example, unsigned types are very common and writing out the full names (e.g, ‘unsigned short’) serves little purpose. The shorthand ‘u16’ is just much more convenient. Besides convenience, it also gives better information on the size of the variable, which is also of great importance here.

I’ve also added a conceptual typedef. While it’s true that, in principle, an int is an int no matter what it’s used for, it is helpful if you can tell what its supposed use is from its type. In this case, I have a COLOR alias for u16 when I want to indicate a particular halfword contains color information.

Memory map defines

To be able to work directly specific addresses in memory, you’ll have to cast them to pointers or arrays and work with those. In this demo’s case, the addresses we’re interested in are 0600:0000 (VRAM) and 0400:0000 (the display control register). In the first demo I did the casts manually, but it’s better to use names for them so that you don’t have to remember all the numbers and also because nobody else would have any clue to what’s going on.

For the IO registers I’m using the official names, which are recognized by all parties. The display control is known as REG_DISPCNT, and is defined as the word at 0400:0000. Note that neither the name nor the type are set in stone: you could as easily have called it “BOO” and even used a halfword pointer. The full list of register #defines can be found in libtonc’s regs.h.

For those who aren’t as familiar with pointers as you should (boy, are you gonna be in trouble :P), here is the structure of the REG_DISPCNT #define. I’m using vu32 as a typedef for ‘volatile u32’ here.

#define REG_DISPCNT *((volatile u32*)(MEM_IO+0x0000)) 
code type description
MEM_IO+0x0000 Address MEM_IO=0x04000000, so this is address 0400:0000
(vu32*)0x04000000 pointer A pointer to an unsigned int of the volatile persuasion (ignore this last part for now)
*(vu32*)0x04000000 ‘variable’ By dereferencing the pointer (the ‘*’ unary operator), we access the contents of the pointer. Id est, the whole thing becomes usable as a variable.

So for all intents and purposes, REG_DISPCNT is a variable just like any other. You can assign values to it, read its contents, perform bit operations on it and so forth. Which is good, because that’s just the way we want to use that register.

A similar procedure is carried out for VRAM, only this is still in its pointer form in the end. Because of that, vid_mem works as an array, not a variable. Again, this is exactly how we want things. Please be careful with the definition, though: all the parentheses there are required! Because of the operator precedence between casts and arrays, leaving out the outer parentheses pair gives compilation errors.

IO register and their bits

The IO registers (not to be confused with the CPU registers) are a collection of switches in the form of bitfields that control various operations of the GBA. The IO registers can be found in the 0400:0000 range of memory, and are usually clumped into words or halfwords according to personal preference. To get anything done, you have to set specific bits of the IO registers. While you can try to remember all the numerical values of these bits, it’s more convenient to use #defines instead.

The toolbox header lists a number of the #defines I use for REG_DISPCNT. The full list can be found in vid.h of libtonc, and the register itself is described in the video chapter. For now, we only need DCNT_MODE3 and DCNT_BG2. The former sets the video mode to mode 3, which is simplest of the 3 available bitmap modes, and the latter activates background 2. Out of a total of four, bg 2 is the only one available in the bitmap modes and you have to switch it on if you want anything to show up. You have to admit that these names are a lot more descriptive than 0x0003 and 0x0400, right?

I’ve also added a list of useful color defines, even though I’m not using them in second.c. They may or may not be useful in the future, though, so it’s good to have them around.

Creating the register #defines is probably the biggest part of header files. As a rough estimate, there are 100 registers with 16 bits each, so that would be 1600 #defines. That’s a lot. The exact number may be smaller, but it is still large. Because the names of the #defines in and of themselves aren’t important, you can expect different naming schemes for different people. I am partial to my own set of names, other older GBA coders may use PERN’s names and more recent ones may use libgba’s, which comes with devkitARM. Take your pick.

Macros and inline functions

You can also create #defines that work a little like functions. These are called macros. I’m not using them here, but there are plenty to be found in libtonc’s headers. Like all #defines, macros are part of the preprocessor, not the compiler, which means that the debugger never sees them and they can have many hidden errors in them. For that reason, they have been depreciated in favor of inline functions. They have all the benefits of macros (i.e., integrated into the functions that call them so that they’re fast), but are still function-like in syntax and resolved at compile time. At least that’s the theory, in practice they’re not quite as speedy as macros, but often preferable anyway.

One inline function I’m using is m3_plot(), which, as you may have guessed, is used to plot pixels in mode 3. In mode 3, VRAM is just a matrix of 16bit colors, so all we have to do to plot a pixel is enter a halfword in the right array element. m3_plot() looks exactly like a normal function, but because the ‘static inline’ in front of it makes it an inline function. Note that inlining is only a recommendation to the compiler, not a commandment, and it only works if optimizations are switched on.

// Mode 3 plotter as macro ...
#define M3_PLOT(x, y, clr)   vid_mem[(y)*SCREEN_WIDTH+(x)]=(clr)

// and as an inline function
static inline void m3_plot(int x, int y, COLOR clr)
{   vid_mem[y*SCREEN_WIDTH+x]= clr;  }

The second inline function is RGB15(), which creates a 16bit color from any given red, green and blue values. The GBA uses 16bit colors for its graphics – or actually 15bit colors in a 5.5.5 BGR format. That’s 32 shades of red in the first (lowest) 5 bits, 32 greens in bits 5 to 9, and 32 blues in 10-14. The RGB15() inline takes care of all the shifting and masking to make that happen.

The working code

Making use of the contents of toolbox.h makes the code of the demo much more understandable.

The first line in main() sets a few bits in the display control, commonly known as REG_DISPCNT. I use DCNT_MODE3 to set the video mode to mode 3, and activate background 2 with DCNT_BG2. This translates to 0x0403 as before, but this method gives a better indication of what’s happening than entering the raw number. Using a variable-like #define instead of the raw dereferenced pointer is also preferable; especially as the latter is sure to wig out people new to C.

So how do I know what bit does what to create the #defines in the first place? Simple, I looked them up in GBATEK, the essential reference to GBA programming. For every IO register I use in these pages I’ll give a description of the bits and a list of #defines as they’re defined in libtonc. The formats for these descriptions were given in the preface, and the table for REG_DISPCNT can be found in the video chapter.

Actually plotting the pixels is now done with the inline function m3_plot(), which is formatted much the same way as every kind of pixel plotter in existence: 2 coordinates and the color. Much better than raw memory access, even though it works exactly the same way. The colors themselves are now created with an inline too: RGB15 takes 3 numbers for the red, green and blue components and ties them together to form a valid 16-bit color.

Finally, there is an endless loop to prevent the program from ever ending. But aren’t endless loops bad? Well usually yes, but not here. Remember what happens when PC programs end: control is kicked back to the operating system. Well, we don’t have an operating system. So what happens after main() returns is undefined. It is possible to see what happens by looking at a file called ctrs0.S, which comes with your dev-kit, but that’s not a thing for beginners so at the moment my advice is to simply not let it happen. Ergo, endless loop. For the record, there are better ways of stopping GBA programs, but this one’s the easiest. And now we’ve reached the end of the demo.

Better, no?

And that is what proper code looks like. As a basic rule, try to avoid raw numbers: nobody except you will know what they mean, and after a while you may forget them yourself as well. Typedefs (and enums and structs) can work wonders in structuring code, so can subroutines (functions, inline functions and macros). Basically, every time you notice you are repeating yourself (copy&paste coding), it might be time to think about creating some subs to replace that code.

These are just a few basic guidelines. If you need more, you can find some more here, for example. Google is your friend. Now, if you’ve followed any classes on C, you should already know these things. If not, you have been cheated. Books and tutorials may sometimes skip these topics, so it may be necessary to browse around for more guidelines on programming styles. That’s all they are, by the way: guidelines. While the rules are usually sensible, there’s no need to get fascist about them. Sometimes the rules won’t quite work for your situation; in that case feel free to break them. But please keep in mind that these guidelines have been written for a reason: more often than not you will benefit from following them.

First demo v3?

There are many ways that lead to Rome. You’ve already seen two ways of coding that essentially do the same thing, though one was easily superior. But sometimes things aren’t so clear cut. In many cases, there are a number of equally valid ways of programming. The obvious example is the names you give your identifiers. No one’s forcing you to a particular set of names because it’s not the names that are important, it’s what they stand for. Another point of contention is whether you use macros, functions, arrays or what not for dealing with the memory map. In most cases, there’s no difference in the compiled code.

The code below shows yet another way of plotting the 3 pixels. In this case, I am using the color #defines rather than the RGB inline, but more importantly I’m using an array typedef M3LINE with which I can map VRAM as a matrix so that each pixel is represented by a matrix element. Yes, you can do that, and in some way it’s even better than using an inline or macro because you’re not limited to just setting pixels; getting, masking and what not are all perfectly possible with a matrix, but if you were to go the subroutine way, you’d have to create more for each type of action.

As you can see, there’s all kinds of ways of getting something done, and some are more practical than others. Which one is appropriate for your situation is pretty much up to you; it’s just part of software design.

#include "toolbox.h"

// extra stuff, also in tonc_video.h
#define M3_WIDTH    SCREEN_WIDTH
// typedef for a whole mode3 line
typedef COLOR       M3LINE[M3_WIDTH];
// m3_mem is a matrix; m3_mem[y][x] is pixel (x,y)
#define m3_mem    ((M3LINE*)MEM_VRAM)

int main()
{
    REG_DISPCNT= DCNT_MODE3 | DCNT_BG2;

    m3_mem[80][120]= CLR_RED;
    m3_mem[80][136]= CLR_LIME;
    m3_mem[96][120]= CLR_BLUE;

    while(1);
    return 0;
}

General notes on GBA programming

Console programming is substantially different from PC programming, especially for something like the GBA. There is no operating system, no complex API to learn, it’s just you against the memory. You need to have intimate knowledge of the GBA memory sections to make things work, and good pointer and bit-operation skills are a must. Also remember that you don’t have a 2GHz CPU, half a gig of RAM and a GPU that can do a gazillion polygons per second. It’s just a 16 MHz CPU with 96kB video memory. And no floating point support or even hardware division. These are all things you need to be aware of when designing your GBA software.

Another thing that you need to remember is that the GBA has a tendency to do things just a tiny bit different than you may expect. The primary example of this is the matrix used for affine transformations like rotation and scaling. All of the popular tutorials give the wrong matrix for a rotation-scale transformation, even though the reference documents give the correct description of each element. Other good examples are the end result of trying to write a single byte to VRAM, the fact that bits for key-states are actually set when the button’s unpressed instead of the other way around, or what the timer register REG_TMxD really does.

I’ve tried to be complete in my explanations of all these things, but I’m positive I’ve missed a thing or two. If you encounter problems, you’re probably not the first one. There are plenty of FAQs and forums where you can find the solution. If that fails, it never hurts to ask. If any of my information is incorrect or incomplete, please don’t hesitate to tell me.

GBA Good/bad practices

For some reason, there are a lot of bad programming practices among the GBA development community. The main reason for this is probably that people just copy-paste from tutorial code, most of which use these practices. Here’s a short list of things to avoid, and things to adopt.

  • Don’t believe everything you read. Bottom line: people make mistakes. Sometimes, the information that is given is incorrect or incomplete. Sometimes the code doesn’t work; sometimes it does, but it’s inefficient or inconsistent or just contains practices that will come back to bite you later on. This is true for most (if not all) older tutorials. Don’t automatically assume you’re doing it wrong: there is a chance it’s the source material.

    Unfortunately, if you’re new to programming you might not recognize the bad and adopt the standards exhibited by some sources. Do not learn C programming from GBA tutorials! I’d almost extent that suggestion to on-line tutorials in general, especially short ones. Books are usually more accurate and provide a better insight into the material. (But again, not always.)

  • RTFAQ / RTFR. Read the gbadev forum FAQ. Should go without saying. It covers a lot of common problems. Additionally, read the fuckin reference, by which I mean GBATEK, which covers just about everything.

  • Makefiles are good. Many tutorials use batchfiles for building projects. This is a very easy method, I agree, but in the long run, it’s very inefficient, Windows only and is prone to maintainability problems. Makefiles are better for Real World projects, even though there may be a hurdle setting them up initially. Fortunately, you don’t have to worry about it that much, because DevkitPro comes with a template makefile/project (see ${DEVKITPRO}/examples/gba/template) where all you need to do is say in which directories the source/header/data files are kept. The makefiles I use for the advanced and lab projects are an adaptation of these.

  • Thumb-code is good. The standard sections for code (ROM and EWRAM) have 16bit buses. ARM instructions will clog the bus and can seriously slow down performance. Thumb instructions fit better here. Thumb code is often smaller too. Note that because of the 32bit bus of IWRAM, there is no penalty for ARM code there.

  • Enabling interworking, optimizations and warnings are good. Interworking (-mthumb-interwork) allows you to use switch between ARM and Thumb code; you may want this if you have a few high-performance routines in ARM/IWRAM that you want to call from ROM code. Optimizations (-O#) make GCC not be an idiot when compiling C into machine code (I’m serious: without them the output is attrociously bad in every way). It produces faster code, and usually smaller as well. Warnings -Wall should be enabled because you will do stupid things that will produce compilable output, but won’t do what you expected. Warnings are reminders that something funky may be going on.

  • 32bit variables are good. Every CPU has a ‘native’ datatype, also known as the word, or in C-speak, the int. Generally speaking, the CPU is better equipped to deal with that datatype than any other. The GBA is called a 32bit machine because the CPU’s native datatype is 32-bit. The instruction sets are optimised for word-sized chunks. It likes words, so you’d better feed it words unless you have no other choice.

    In a very real way, the 32bit integer is the only datatype the GBA has. The rest are essentially emulated, which carries a small performance penatly (2 extra shift instructions for bytes and halfwords). Do not use u8 or u16 for loop-indices for example, doing so can cut the speed of a loop in half! (The belief that using smaller types means lower memory-use only holds for aggregates and maybe globals; for local variables it actually costs memory). Likewise, if you have memory to copy or fill, using words can be about twice as fast as halfwords. Just be careful when casting, because an ARM CPU is very picky when it comes to alignment.

  • Data in header files is bad, very bad. I’ll go in a little detail about it when talking about data. And see also here and here.

Those are points where other GBA tutorials often err. It’s not an exclusive list, but the main points are there I think. There are also a few things on (C) programming in general that I’d like to mention here.

  • Know the language; know the system. It should go without saying that if you’re programming in a certain language or on a certain system, you should know a little (and preferably a lot) about both. However, I have seen a good deal of code that was problematic simply because the author apparently didn’t know much about either. As I said in the beginning of this section, the GBA has a few interesting quirks that you need to know about when programming for it. That, of course, is what Tonc is all about. Some things stem from lack of C skills – the ‘int’-thing is an example of this. Another very common problem is correct memory and pointer use, something that I will cover a little later and also in the section on data. With C, you have different kinds of datatypes, pointers, the preprocessor and bit-operators at your disposal. Learn what they do and how to use them effectively.

  • Think first, code later. Don’t open up an editor, type some code and hope it works correctly. It won’t. How can it, if you haven’t even defined what ‘correctly’ means? Think of what you want to do first, then what you need to get it done and then try to implement it.

    A lot of programming (for me anyway) is not done in a text editor at all. For example, for anything involving math (which can include graphics as well), it’s better to make a diagram of the situation. I have pages of diagrams and equations for the affine transformation and mode 7, just to see what what going on. Pen and paper are your friends here.

  • Learn to generalize and simplify. This is actually not about programming, but problem-solving in general. Specific problems are often special cases of more general problems. For example, 2D math is a subset of multi-dimensional math; vector analysis and transformations such as rotations and scaling are parts of linear algebra. If you know the general solution, you can always (well, often, at any rate) work down to the specific case. However, what is often taught (in school, but in universities as well) are the specific solutions, not the general ones. While using the special case solutions are often faster in use, they won’t work at all if the case is just a little different than the example in the book. If you’d learned the general solution – better yet, how to arrive at the general solution – you’d stand a much better change of solving the task at hand.

    A related issue is simplification. For example, if you have long expressions in a set of equations (or algorithms), you can group them to together under a new name. This means less writing, less writing and a lower risk of making a mistake somewhere.

  • Learn basic optimization strategies. By this I don’t mean that you should know every trick in the book, but there are a few things that you can use in writing code that can speed things up (sometimes even significantly) without cost to readbility and maintainability. In fact, sometimes the code actually becomes easier to read because of it. A few examples:

    • Use a better algorithm. Okay, so this one may not always be simple, but it’s still very true.
    • Use ints. The int is loosely defined as the native datatype. Processors tend to perform better when they deal with their native datatype.
    • Use temporary variables for common expressions. If you use a long expression more than a few times, consider dumping it in a temp. This means less writing for you, and less reading for everyone. It can also make your code faster because you don’t need to evaluate the entire expression all the time. This is especially true for global variables, which have to be reloaded after each function-call because the values may have changed.
    • Use pointers. Pointers have the reputation of being dangerous, but they’re a very powerful tool if used correctly. Pointer arithmetic is usually faster than indexing because it’s closer to hardware, and by assigning temp pointers to deeply nested structure expressions (see above), you can gratly reduce the length of the expressions, which makes things easier on the compiler and the reader alike.
    • Precalculate. This is related to the previous two points. If you have a loop in which things don’t depend on the loop-variable, precalculate that part before the loop. Also, to avoid (complex) calculations, you could dump the data in a Look-up Table and simply grab a value from there.
    • Avoid branches. Things that redirect program flow (ifs, loops, switches) generally cost more than other operations such as arithmetic. Sometimes it’s possible to effectively do the branch with arithmetic (for example, (int)x>>1 gives −1 or 0, depending on the sign of x) There are many more optimization techniques, of course. Wikipedia has a nice overview, and you can find pages discussing particular techniques here[b0rked] and there. Some of these techniques will be done by the compiler anyway, but not always.
  • Learn to optimize later. Also known as “premature optimization is the root of all evil”. Optimization should be done in the final stages, when most code is in pace and you can actually tell where optimization is necessary (if it’s necessary at all). However, this does not mean you should actually strive for the slowest solution in the early phases. Often there is a cleaner and/or faster (sometimes even much faster) algorithm then the trivial one, which will come to you with just a small amount of thought. This isn’t optimization, it’s simply a matter of not being stupid. A few of the points mentioned above fall in this category.

  • There are always exceptions. There is no programming guideline that doesn’t have its exception. Except maybe this one.

I’ll leave it at that for now. Entire books have been written on how to code efficiently. Resources are available on the well as well: search for things like “optimization”, “coding standards” or “coding guidelines” should give you more than enough. Also look up Design Pattern and Anti-pattern. Also fun are books and sites that show how not to code. Sometimes these are even more useful. Worse than Failure is one of these (in particular the codeSOD category); The programming section of Computer stupidities is also nice. If you want to see why the use of global variables is generally discouraged, do a search for ‘alpha’ in the latter page.

A few examples of good/bad practices

Here are a few examples of code that, while functional, could be improved in terms of speed, amount of code and/or maintainability.

Ints versus non-ints

Above, I noted that use of non-ints can be problematic. Because this bad habit is particularly common under GBA and NDS code (both homebrew and commercial), I’d like to show you an example of this.

// Force a number into range [min, max>
#define CLAMP(x, min, max)   \
    ( (x)>=(max) ? ((max)-1) : ( ((x)<(min)) ? (min) : (x) ) )

// Change brightness of a palette (kinda) (70)
void pal_brightness(u16 *pal, u16 size, s8 bright)
{
    u16 ii;
    s8 r, g, b;

    for(ii=0; ii<size; ii++)
    {
        r= (pal[ii]    )&31;
        g= (pal[ii] >>5)&31;
        b= (pal[ii]>>10)&31;

        r += bright;    r= CLAMP(r, 0, 32);
        g += bright;    g= CLAMP(g, 0, 32);
        b += bright;    b= CLAMP(b, 0, 32);

        pal[ii]= r |(g<<5) | (b<<10);
    }
}

This routine brightens or darkens a palette by adding a brightness-factor to the color components, each of which is then clamped to the range [0,31⟩ to avoid funky errors. The basic algorithm is sound, even the implementation is, IMHO, pretty good. What isn’t good, however is the datatypes used. Using s8 and u16 here adds an extra shift-pair practically every time any variable is used! The loop itself compiles to about 90 Thumb instructions. In contrast, when using ints for everything except pal the loop is only 45 instructions long. Of course the increase in size means an increase in time as well: the int-only version is 78% faster than the one given above. To repeat that: the code has doubled in size and slowed down by 78% just by using the wrong datatype!

I’ll admit that this example is particularly nasty because there is a lot of arithmetic in it. Most functions would incur a smaller penalty. However, there is no reason for losing that performance in the first place. There is no benefit of using s8 and u16; it does not increase redability – all it does is cause bloat and slow-down. Use 32-bit variables when you can, the others only when you have to.

Now, before this becomes another goto issue, non-ints do have their place. Variables can be divided into two groups: worker variables (things in registers) and memory variables. Local variables and function parameters are worker variables. These should be 32-bit. Items that are in memory (arrays, globals, structs, and what not) could benefit from being as small as possible. Of course, memory variables still have to be loaded into registers before you can do anything with them. An explicit local variable may be useful here, but it depends on the case at hand.

Pointer problems

One of the most common mistakes GBA neophytes make is mixing up array/pointer sizes when copying data. Data is data, but you can access it in different ways. For example, here’s code that copies bitmap-data from an array into VRAM.

// An array representing a 240x160@16 bitmap, converted 
// to an array by some graphics conversion tool.
const u8 fooBitmap[240*160*2]= 
{
    // Maaaaany, many lines of data.
}

int main()
{
    REG_DISPCNT= DCNT_MODE3 | DCNT_BG2;

    // Copy 240x160 pixels to VRAM (ORLY?)
    int ii;
    for(ii=0; ii<240*160; ii++)
        vid_mem[ii]= fooBitmap[ii];

    return 0;
}

The fooBitmap array represents some bitmap. In order to display that bitmap on the screen, you need to copy its data into VRAM. That’s simple enough: we have vid_mem from before, and we can copy from fooBitmap to VRAM by copying elements using a simple for-loop.

However, it’s not quite as simple as that. vid_mem is an u16 array; so defined because in mode 3 each pixel is an 16-bit color. But fooBitmap is a byte-array: two elements of this array represent one color, and copying bytes-to-halfwords leaves the top-byte of each pixel empty, giving a very skewed result. Such a source-destination is incredibly common, partly because people don’t know how pointers and arrays represent memory, but also because they don’t pay attention to the datatype.

Here’s a version that would work:

// An array representing a 240x160@16 bitmap, converted 
// to an array by some graphics conversion tool.
const u8 fooBitmap[240*160*2]= 
{
    // Maaaaany, many lines of data.
}

int main()
{
    REG_DISPCNT= DCNT_MODE3 | DCNT_BG2;

    u16 *src= (u16*)fooBitmap;  // Cast source to u16-array

    // Copy 240x160 pixels to VRAM (YARLY!)
    int ii;
    for(ii=0; ii<240*160; ii++)
        vid_mem[ii]= src[ii];

    return 0;
}

By ensuring the source and destinations are of the same type, the copying leaves no gaps. Note that the underlying data hasn’t changed – only how it’s used. There are actually a lot more things you need to know about how to use data and memory, which will be covered in a later chapter.

Simplification

Consider the following function (basically taken from the Rinkworks site mentioned earlier):

int foo(int x)
{
    switch(x)
    {
    case 1: return 1;
    case 2: return 2;
    case 3: return 3;
    case 4: return 4;
    case 5: return 5;
    case 6: return 6;
    case 7: return 7;
    }
    return 0;
}

What this function does is this: if x is between 1 and 7, return that number, otherwise return 0. The thing to note is that the case-value and the return code are the same, so instead of the switch-block you could have just returned x.

int foo(int x)
{
    if(x >= 1 && x <= 7)
        return x;
    else
       return 0;
}

Simplifications like this often present themselves if you just think about what you’re doing for a little while, rather than just entering code. Now, this would should be rather obvious, but more difficult switch-blocks can often be replaces by something like this as well. For example, if there is a simple mathematical relation between the input and the return value (some addition or multiplication, for example), you can just use that relation. Even if there is not such a simple relation, there can be possibilities. If you’re returning constants, you could put those constants in a table and use x as an index.

The above is a simplification in terms of the algorithm used. Another kind of simplification is in readability. Of course, everybody has their own ideas about what’s readable. Personally, I prefer to keep my statements short, especially in the place where the action happens. The next function is an example of bounding circle collision detection. Basically, you have two circles at points p1 = (x1y1) and p2 = (x2y2) and radii r1 and r2. The distance between these two points can be calculated with the Pythagorean theorem. If this distance is smaller than the sum of the two radii, the circles overlap. A function that checks whether the player sprite hits any of the enemy sprites could look something like this:

// Some basic structs and a sprite array.
// #defines for sprite-indices and amounts omitted.
typedef struct { int x, y; } POINT;

typedef struct
{
    POINT position;
    int radius;
} TSprite;

TSprite gSprites[SPRITE_MAX];

// Collision function.

int player_collision()
{
    int ii;

    for(ii=0; ii<ENEMY_MAX; ii++)
    {
        // Test for hit between player and enemy ii
        if( (gSprites[ENEMY_ID+ii].position.x - gSprites[PLAYER_ID].position.x) *
            (gSprites[ENEMY_ID+ii].position.x - gSprites[PLAYER_ID].position.x) +
            (gSprites[ENEMY_ID+ii].position.y - gSprites[PLAYER_ID].position.y) *
            (gSprites[ENEMY_ID+ii].position.y - gSprites[PLAYER_ID].position.y) < 
            (gSprites[ENEMY_ID+ii].radius + gSprites[PLAYER_ID].radius) *
            (gSprites[ENEMY_ID+ii].radius + gSprites[PLAYER_ID].radius) )
        {
            return 1;
        }
    }

    // Not hit
    return 0;
}

Personally, I have a hard time reading what actually goes on inside the if-statement there. Because the expression is 6 lines long, I actually have to sit down and parse what it actually does, and hope that the parentheses are all correct, etc. Now, note that a number of things are used multiple times here: the gSprites accesses (6× for the player, 6× for the enemy) and then the positions as well. These can all be accessed with less code by using pointers and other local variables. Also, the player’s attributes are loop invariant (they don’t change during the loop), so they can be loaded outside the loop.

int player_collision()
{
    int ii; 
    int r1= gSprites[PLAYER_ID].radius, r2, dx, dy;
    POINT *pt1= &gSprites[PLAYER_ID].position, *pt2;
    TSprite *enemy= &gSprites[ENEMY_ID];

    for(ii=0; ii<ENEMY_MAX; ii++)
    {
        r2= enemy[ii].radius;
        pt2= &enemy[ii].position;
        dx= pt2->x - pt1->x;
        dy= pt2->y - pt1->y;
        
        // Test for hit between player and enemy ii
        if( dx*dx + dy*dy < (r1+r2)*(r1+r2) )
            return 1;
    }

    // Not hit
    return 0;
}

There may not have been a real change in the number of lines, but the lines themselves are shorter and easier to read. Also, instead of a 6-line if-expression, it now fits on a single line and you can actually see what it does. Personally, I’d call that a win.

Testing your code on a real GBA

If you’re just starting GBA programming, chances are you’re using the emulators that are out there, and will be content with those. However, if you look through the forums you’ll see many people urging you to test on hardware regularly. They are absolutely right.

Now, it isn’t that the emulators are bad. On the contrary, in fact; the most popular emulators have things like tile, map and memory viewers that are essential to debugging. An emulator like VBA is very, very good, but not quite perfect. Take the Tonc demos, for example: they run the same on VBA as on a real GBA in all cases … mostly. For one thing, timing is a real issue on most of them (the exception here is no$gba, which I’ve never seen off the mark by more than 2%, usually a lot less). Also, in a few rare occasions (like in cbb_demo and win_demo) there were small but important differences between GBA and emulator outputs, and if you’ve never tested on the real thing, you’d never know.

One other thing that is very different is the colors. Since it’s not back-lit the GBA screen is much darker than a PC monitor. Or maybe that’s just my room ;). Also, on an emulator you have the luxury of scaling your view; the real GBA is always 3“ screen. There’s world of difference, trust me on this. Take that first.gba example I showed above: the pixels are so tiny it’s almost impossible to see on a real GBA! Even an 8x8 tile is pretty small. Also, the use of a keyboard in an emu is nothing like holding a real GBA in your hands.

And, of course, the whole idea of creating something that works on a console has an air of coolness that defies description. Well, almost anyway. The word is progasm. Says it all really, doesn’t it?

Multiboot & linkers

OK, so now you know you should test on hardware, how do you do it? After all, you can’t exactly plug a GBA into your PC like a USB memory stick or a printer? Well, yes you can … with the right equipment. The two most common ways are a multiboot cable or a flash linker.

Flash Card & Linker

A flash card is a GBA cart with a difference: it is completely rewritable. There are a number of different sets available: different sized carts (64Mbit to 1024Mbit), USB or Parallel port versions; sets that use a separate linker (where you have to take the cart out of the GBA, write to it, and reinsert) or ones that write directly to the cart or transfer through the multiboot port. Ideally you’d use one of these. However, they can be rather pricy ($60 - $200 (and up?)) and generally only available through online stores, which also means shipping and taxes and such.

Multimedia cards

A solution that’s becoming more and more popular is using standard multimedia cards (eg. SD, CompactFlash) and an adapter like GBAMP and SuperCard. Memory cards can be very cheap (like $10) and bought in most electronics stores; the adapters are genereally $25 and up.

SuperCard vs waitstates

There is one small technical problem with SuperCards: they use slow memory that doesn’t support 3/1 ROM waitstates. This is a faster setting than the default 4/2 and anything that uses the former simply won’t run. This shouldn’t be a problem with most homebrew things, but a handful of binaries will fail and you wouldn’t be able to make use of the speed-up yourself either.

Multiboot cable

The other way is a multiboot cable. This is a cable that plugs into the GBA multiboot port (like multiplayer games do) and one of the PC ports, usually the parallel port. These are a lot cheaper than a flash kit. You can even build one yourself :)! You can find the instructions and necessary software to build an Xboo communication cable on www.devkitpro.org, which works like a charm. Basically all you need to do is connect one end of the link cable to a male parallel port cable. If you shop around you should be able to get all you need for as little as $5.

But, like always, there’s no such thing as a free lunch. What happens in a multiboot game is that the code is written to EWRAM. That’s how you can use one cart in a multiplayer game. The multiboot cable is the same thing, only with the PC as the host. The trouble is that EWRAM is only 256kb in size; you won’t be able to fit an entire game on it. And, of course, it runs always through your computer, so unless you have a laptop, forget about taking it outside to show off to your friends.


Fig 3.2: efa flash card.

Fig 3.3: SuperCard, compact flash version.

Fig 3.4: xboo multiboot cable.

Compiling for real hardware

This is almost the same as for emulators. The only real things you have to worry about are a) that you can only use the binary after the objcopy treatment, and b) that you need to have a valid GBA header, which it usually doesn’t. If the intro screen shows “Game Boy” as normal, but the “Nintendo” at the bottom is garbled, you have a bad header. To get a valid header, use a program called gbafix.exe. This is originally by darkfader, but you can also find it at www.devkitpro.org. I already mentioned the extra steps for a multiboot game earlier.

Flash kits usually come with software that can take care of all this stuff for you (or so I’m told, I don’t have one). The Xboo zip-file also has a little app that sends your binary to the GBA.

4. Introduction to GBA Graphics

General introduction

The GBA has an LCD screen that is 240 pixels wide, 160 pixels high and is capable of displaying 32768 (15 bit) colors. The refresh rate is just shy of 60 frames per second (59.73 Hz). The GBA has 5 independent layers that can contain graphics: 4 backgrounds and one sprite layer and is capable of some special effects that include blending two layers and mosaic and, of course, rotation and scaling.

Whereas sound and joypad functionality have to make do with only a few measly registers, the video system has a great deal of memory at its disposal (relatively speaking). Apart from a multitude of registers in I/O memory, there’s the 96kb of video memory (starting at 0600:0000h), palette memory (0500:0000h) and OAM memory (0700:0000h).

Draw and blank periods

As said, the entire GBA screen is refreshed every 60th of a second, but there’s more to it than that. After a scanline has been drawn (the HDraw period, 240 pixels), there is a pause (HBlank, 68 pixels) before it starts drawing the next scanline. Likewise, after the 160 scanlines (VDraw) is a 68 scanline blank (VBlank) before it starts over again. To avoid tearing, positional data is usually updated at the VBlank. This is why most games run at 60 or 30 fps. (FYI, syncing at the VBlank is also why we in PAL countries often had slower games: PAL TVs run (ran) at 50Hz, hence only 50 fps instead of 60, hence a 17% slower game if nobody bothered to account for it. Few companies ever did :( ).

Both the CowBite Spec and GBATEK give you some interesting details about the timings of the display. A full screen refresh takes exactly 280896 cycles, divided by the clock speed gives a framerate of 59.73. From the Draw/Blank periods given above you can see that there are 4 cycles per pixel, and 1232 cycles per scanline. You can find a summary of timing details in table 4.1.



Fig 4.1: vdraw, vblank and hblank periods.
Table 4.1: Display timing details
subject length cycles
pixel 1 4
HDraw 240px 960
HBlank 68px 272
scanline Hdraw+Hbl 1232
VDraw 160*scanline197120
VBlank 68*scanline 83776
refresh VDraw+Vbl 280896

Colors and palettes

The GBA is capable of displaying 16bit colors in a 5.5.5 format. That means 5 bits for red, 5 for green and 5 for blue; the leftover bit is unused. Basically, the bit-pattern looks like this: “xbbbbbgggggrrrrr”. There are a number of defines and macros in color.h that will make dealing with color easier.

Now, as for palettes…

<rant>
Guys, the word here is “palette”! One ‘l’, two ‘t’s and an ‘e’ at the end. It is not a “pallet”, which is “a low, portable platform, usually double-faced, on which materials are stacked for storage or transportation, as in a warehouse”, nor is it a “pallette”, meaning “a plate protecting the armpit, in a suit of armor”. The word “pallete”, its most common variant, isn’t even in the dictionary, thus not even worth considering. It’s “palette”, people, “palette”.
</rant>

Anyhoo, the GBA has two palettes, one for sprites (objects) and one for backgrounds. Both palettes contain 256 entries of 16bit colors (512 bytes, each). The background palette starts at 0500:0000h, immediately followed by the sprite palette at 0500:0200h. Sprites and backgrounds can use these palettes in two ways: as a single palette with 256 colors (8 bits per pixel); or as 16 sub-palettes or palette banks of 16 colors (4 bits per pixel).

One final thing about palettes: index 0 is the transparency index. In paletted modes, pixels with a value of 0 will be transparent.

Bitmaps, backgrounds and sprites

All things considered, the GBA knows 3 types of graphics representations: bitmaps, tiled backgrounds and sprites. The bitmap and tiled background (also simply known as background) types affect how the whole screen is built up and as such cannot both be activated at the same time.
In bitmap mode, video memory works just like a w×h bitmap. To plot a pixel at location (x,y), go to location y*w+x and fill in the color. Note that you cannot build up a screen-full of individual pixels each frame on the GBA, there are simply too many of them.

Tiled backgrounds work completely different. First, you store 8x8 pixel tiles in one part of video memory. Then, in another part, you build up a tile-map, which contains indices that tells the GBA which tiles go into the image you see on the screen. To build a screen you’d only need a 30x20 map of numbers and the hardware takes care of drawing the tiles that these numbers point to. This way, you can update an entire screen each frame. There are very few games that do not rely on this graphics type.

Finally, we have sprites. Sprites are small (8x8 to 64x64 pixels) graphical objects that can be transformed independently from each other and can be used in conjunction with either bitmap or background types.

Prefer tile modes over bitmap modes

In almost all types of games, the tile modes will be more suitable. Most other tutorials focus on bitmap modes, but that’s only because they are easier on beginners, not because of their practical value for games. The vast majority of commercial games use tile modes; that should tell you something.

Those are the three basic graphical types, though other classifications also spring to mind. For example, the bitmap and tiled backgrounds types, since they’re mutually exclusive and use the entire screen, constitute the background-types. Also, it so happens that the tiles of tiled backgrounds and the sprites have the same memory layout (namely, in groups of 8x8 pixel tiles). This makes tiled backgrounds and sprites the tiled-types.

Display registers: REG_DISPCNT, REG_DISPSTAT and REG_VCOUNT

There are three I/O registers that you will encounter when doing anything graphical: the display control REG_DISPCNT (0400:0000h), the display status REG_DISPSTAT (0400:0004h) and the scanline counter REG_VCOUNT (0400:0006h). Those names are simply defines to the memory locations and can, in principle, be chosen at will. However, we will use the names as they appear in the Pern Project, which are the most common.

The REG_DISPCNT register is the primary control of the screen. The bit-layout of this register and their meanings can be found in the following table. This is the general format I will use for registers or register-like sections. The details of the format have already been explained in the preface.

REG_DISPCNT @ 0400:0000h
FEDCBA98 765432 1 0
OW W1 W0 Obj BG3 BG2 BG1 BG0 FB OM HB PS GB Mode
bitsnamedefinedescription
0-2 Mode DCNT_MODEx. DCNT_MODE# Sets video mode. 0, 1, 2 are tiled modes; 3, 4, 5 are bitmap modes.
3 GB DCNT_GB Is set if cartridge is a GBC game. Read-only.
4 PS DCNT_PAGE Page select. Modes 4 and 5 can use page flipping for smoother animation. This bit selects the displayed page (and allowing the other one to be drawn on without artifacts).
5 HB DCNT_OAM_HBL Allows access to OAM in an HBlank. OAM is normally locked in VDraw. Will reduce the amount of sprite pixels rendered per line.
6 OM DCNT_OBJ_1D Object mapping mode. Tile memory can be seen as a 32x32 matrix of tiles. When sprites are composed of multiple tiles high, this bit tells whether the next row of tiles lies beneath the previous, in correspondence with the matrix structure (2D mapping, OM=0), or right next to it, so that memory is arranged as an array of sprites (1D mapping OM=1). More on this in the sprite chapter.
7 FB DCNT_BLANK Force a screen blank.
8-B BG0-BG3, Obj DCNT_BGx, DCNT_OBJ. DCNT_LAYER# Enables rendering of the corresponding background and sprites.
D-F W0-OW DCNT_WINx, DCNT_WINOBJ Enables the use of windows 0, 1 and Object window, respectively. Windows can be used to mask out certain areas (like the lamp did in Zelda:LTTP).

Setting the display control is probably the first thing you’ll be doing. For simple demos, you can just set it once and leave it at that, though switching between the video-modes can have some interesting results.

Now the other two registers I mentioned, REG_DISPSTAT and REG_VCOUNT. The latter tells you the scanline that is currently being worked on. Note that this counter keeps going into the VBlank as well, so it counts to 227 before starting at 0 again. The former gives you information about the Draw/Blank status and is used to set display interrupts. You can also do some really cool stuff with the interrupts that you can enable here. For one thing, the HBlank interrupt is used in creating Mode 7 graphics, and you want to know how that works, don’t you?

REG_DISPSTAT @ 0400:0004h
F E D C B A 9 8 7 6543210
VcT - VcI HbI VbI VcS HbS VbS
bitsnamedefinedescription
0VbS DSTAT_IN_VBL VBlank status, read only. Will be set inside VBlank, clear in VDraw.
1 HbS DSTAT_IN_HBL HBlank status, read only. Will be set inside HBlank.
2 VcS DSTAT_IN_VCT VCount trigger status. Set if the current scanline matches the scanline trigger ( REG_VCOUNT == REG_DISPSTAT{8-F} )
3 VbI DSTAT_VBL_IRQ VBlank interrupt request. If set, an interrupt will be fired at VBlank.
4 HbI DSTAT_HBL_IRQ HBlank interrupt request.
5 VcI DSTAT_VCT_IRQ VCount interrupt request. Fires interrupt if current scanline matches trigger value.
8-F VcT DSTAT_VCT# VCount trigger value. If the current scanline is at this value, bit 2 is set and an interrupt is fired if requested.

REG_VCOUNT @ 0400:0006h (read-only)
F E D C B A 9 8 7 6 5 4 3 2 1 0
- Vc
bitsnamedescription
0-7 Vc Vertical count. Range is [0,227]

Vsyncing part I, the busy-wait loop

As said, use the VBlank as a timing mechanism and to update the game data. This is called vsync (vertical syncronisation). There are a number of ways to vsync. The two most common methods use a while loop and check REG_VCOUNT or REG_DISPSTAT. For example, since the VBlank starts at scanline 160, you could see when REG_VCOUNT goes beyond this value.

#define REG_VCOUNT *(u16*)0x04000006

void vid_vsync()
{    while(REG_VCOUNT < 160);   }

Unfortunately, there are a few problems with this code.

First of all, if you’re simply doing an empty while loop to wait for 160, the compiler may try to get smart, notice that the loop doesn’t change REG_VCOUNT and put its value in a register for easy reference. Since there is a good chance that that value will be below 160 at some point, you have a nice little infinite loop on your hand. To prevent this, use the keyword volatile (see regs.h).

Second, in small demos simply waiting for the VBlank isn’t enough; you may still be in that VBlank when you call vid_sync() again, which will be blazed through immediately. That does not sync to 60 fps. To do this, you first have to wait until the next VDraw. This makes our vid_sync look a little like this:

#define REG_VCOUNT *(vu16*)0x04000006

void vid_vsync()
{
    while(REG_VCOUNT >= 160);   // wait till VDraw
    while(REG_VCOUNT < 160);    // wait till VBlank
}

This will always wait until the start of the next VBlank occurs. And REG_VCOUNT is now volatile (the “vu16” is typedefed as a volatile unsigned (16bit) short. I’ll be using a lot of this kind of shorthand, so get used to it). That’s one way to do it. Another is checking the last bit in the display status register, REG_DISPSTAT{0}.

So we’re done here, right? Errm … no, not exactly. While it’s true that you now have an easy way to vsync, it’s also a very poor one. While you’re in the while loop, you’re still burning CPU cycles. Which, of course, costs battery power. And since you’re doing absolutely nothing inside that while-loop, you’re not just using it, you’re actually wasting battery power. Moreover, since you will probably make only small games at first, you’ll be wasting a LOT of battery power. The recommended way to vsync is putting the CPU in low-power mode when you’re done and then use interrupts to bring it back to life again. You can read about the procedure here, but since you have to know how to use interrupts and BIOS calls, you might want to wait a while.

5. The Bitmap modes (mode 3, 4, 5)

Introduction

In this chapter, we’ll look at the bitmap modes. Bitmap modes are a good place to start because there is a one to one relation between the contents of memory and the pixels on the screen. The essentials of all the bitmap modes will be discussed briefly, with a closer look at what you can do in mode 3 as an example. We’ll also see a bit of page flipping (mode 4), which allows for smoother animation.

The chapter will close with a section on how to deal with data and computer memory in general. Because GBA programming is very close to the hardware, you need to know these things. If you’ve been programming (in C or assembly) for a long time and have already gained a good understanding on data, datatypes and memory you can probably skip it; for the rest of you, I would strongly urge to read it, because it is very important for all the chapters to come.

Bitmap 101

a 24x24 bitmap of Link.
Fig 5.1: Link (24x24 bitmap).

In fig 5.1 you can find a bitmap of one of the game characters that made Nintendo great. This is probably how most people think of bitmaps: a grid of colored pixels. In order to use bitmaps in a program we need to know how they’re arranged in memory. For that we use fig 5.2 (below); this is a zoomed out version of fig 5.1, with a pixel grid imposed over it and some numbers.

A bitmap is little more than a w×h matrix of colors (or color-indices), where w is the number of columns (the width) and h the number of rows (the height). A particular pixel can be referred to with a coordinate pair: (xy). By the way, the y-axis of the GBA points down, not up. So pixel (0, 0) is in the top-left corner. In memory, the lines of the bitmap are laid out sequentially, so that the following rule holds: in a w×h bitmap, the pixel (x, y) is the (w×y + x)-th pixel. This is true for all C matrices, by the way.

Fig 5.2 shows how this works. This is a w=24 by h=24 bitmap, at 8bpp (8 Bits Per Pixel (=1 byte)). The numbers in yellow indicate the memory locations; you can count them for yourself if you don’t believe me. The first pixel, (0, 0), can be found at location 0. The last pixel of the first row (23, 0) is at w−1 (=23 in this case). The first pixel of the second row (0, 1) is at w (=24) etc, etc, till the last pixel at w×h−1.

Note, however, that when you use another bitdepth, the addresses change too. For example, at 16bpp (2 bytes per pixel), you’d need to multiply the pixel-number by 2. Or use another datatype for your array. The general formula is left as an exercise for the reader.

Usually it’s not actually the width (i.e., the number of pixels in a row) that’s important, but the pitch. The pitch is defined as the number of bytes in a scanline. For 8bpp images the pitch and width will usually be the same, but for, say, 16bpp images (2 bytes per pixel) the pitch is the width times two. There’s another catch: memory alignment. Alignment will be covered in a later section, but the upshot is that systems generally have a ‘preferred’ type size and can better deal with data if the addresses are a multiple of that type size. This is why scanlines in some bitmap file formats are always aligned to 32-bit boundaries.

The GBA bitmap modes

Video modes 3, 4 and 5 are the bitmap modes. To use them, put 3, 4 or 5 in the lowest bits of REG_DISPCNT and enable BG2. You may wonder why we start with mode 3, rather than mode 0. The reason for this is that bitmaps are a lot easier to come to terms with than tilemaps. And this is the only reason. The truth of the matter is that the bitmap modes are just too slow to be used for most conventional GBA games. I can’t give an exact figure, but if someone told me 90% or more of GBA games used tile modes and not bitmap modes, I wouldn’t be surprised. The only time when bitmap modes would be beneficial would be either for very static screens (introductory demos) or very dynamic screens (3D games like Star Fox or Doom).

The bitmap modes have the following characteristics:

Table 5.1: Bitmap mode characteristics
modewidthheightbppsize page-flip
3 240 160 16 1× 12C00h No
4 240 160 8 2× 9600h Yes
5 160 128 16 2× A000h Yes

What width, height and bpp mean should be clear by now; the size that the bitmap requires is simply width × height × bpp/8. Page flipping may need some more explanation, but first we’ll look at some examples of mode 3 graphics.

Drawing primitives in mode 3

We’ve already seen how to plot pixels, now it’s time for some lines and rectangles. Horizontal lines are nearly trivial: because the pixels are in adjacent memory, all you need is a simple loop from the starting x to the final x. Vertical lines are nearly as easy: while the pixels aren’t right next to each other, they do have a fixed offset between them, namely the pitch. So again a simple loop is all you need. Rectangles are essentially multiple horizontal lines, so those are easy as well.

Diagonal lines are a little trickier, for a number of reasons. Diagonal lines have a slope that indicates how many horizontal steps you need to take before moving to the next scanline. That would only work if the absolute value were lower than one, otherwise you’d get gaps between pixels. For higher slopes, you need to increment vertically, and plot horizontally.

Another point is how to make the routine fast enough to be of real use. Fortunately, these things have all been figured out in the past already, so we’ll just use the results here. In this case, we’ll use a Bresenham Midpoint algorithm for the line drawing, modified to deal with horizontal and vertical lines separately. While I could explain what the routine does exactly, it is out of the scope of the chapter, really.

Two points I have ignored here are normalization and clipping. Normalization means making sure the routine runs in the right direction. For example, when implementing a line drawing routine that runs from x1 to x2 via an incrementing for loop, you’d best be sure that x2 is actually higher than x1 in the first place. Clipping means cutting the primitive down to fit inside the viewport. While this is a good thing to do, we will omit it because it can get really hairy to do it well.

The code below is an excerpt from toolbox.c from the m3_demo and contains functions for drawing lines, rectangles and frames on a 16bpp canvas, like in mode 3 and mode 5. dstBase is the base-pointer to the canvas and dstPitch is the pitch. The rest of the parameters should be obvious.

#include "toolbox.h"

//! Draw a line on a 16bpp canvas
void bmp16_line(int x1, int y1, int x2, int y2, u32 clr,
    void *dstBase, uint dstPitch)
{
    int ii, dx, dy, xstep, ystep, dd;
    u16 *dst= (u16*)(dstBase + y1*dstPitch + x1*2);
    dstPitch /= 2;

    // --- Normalization ---
    if(x1>x2)
    {   xstep= -1;  dx= x1-x2;  }
    else
    {   xstep= +1;  dx= x2-x1;  }

    if(y1>y2)
    {   ystep= -dstPitch;   dy= y1-y2;  }
    else
    {   ystep= +dstPitch;   dy= y2-y1;  }


    // --- Drawing ---

    if(dy == 0)         // Horizontal
    {
        for(ii=0; ii<=dx; ii++)
            dst[ii*xstep]= clr;
    }
    else if(dx == 0)    // Vertical
    {
        for(ii=0; ii<=dy; ii++)
            dst[ii*ystep]= clr;
    }
    else if(dx>=dy)     // Diagonal, slope <= 1
    {
        dd= 2*dy - dx;

        for(ii=0; ii<=dx; ii++)
        {
            *dst= clr;
            if(dd >= 0)
            {   dd -= 2*dx; dst += ystep;  }

            dd += 2*dy;
            dst += xstep;
        }
    }
    else                // Diagonal, slope > 1
    {
        dd= 2*dx - dy;

        for(ii=0; ii<=dy; ii++)
        {
            *dst= clr;
            if(dd >= 0)
            {   dd -= 2*dy; dst += xstep;  }

            dd += 2*dx;
            dst += ystep;
        }
    }
}

//! Draw a rectangle on a 16bpp canvas
void bmp16_rect(int left, int top, int right, int bottom, u32 clr,
    void *dstBase, uint dstPitch)
{
    int ix, iy;

    uint width= right-left, height= bottom-top;
    u16 *dst= (u16*)(dstBase+top*dstPitch + left*2);
    dstPitch /= 2;

    // --- Draw ---
    for(iy=0; iy<height; iy++)
        for(ix=0; ix<width; ix++)
            dst[iy*dstPitch + ix]= clr;
}

//! Draw a frame on a 16bpp canvas
void bmp16_frame(int left, int top, int right, int bottom, u32 clr,
    void *dstBase, uint dstPitch)
{
    // Frame is RB exclusive
    right--;
    bottom--;

    bmp16_line(left,  top,   right,  top,    clr, dstBase, dstPitch);
    bmp16_line(left,  bottom, right, bottom, clr, dstBase, dstPitch);

    bmp16_line(left,  top,   left,   bottom, clr, dstBase, dstPitch);
    bmp16_line(right, top,   right,  bottom, clr, dstBase, dstPitch);
}

These functions are very general: they will work for anything that has 16-bit colors. That said, it may be annoying to have to add the canvas pointer and pitch all the time, so you could create an interface layer specifically for mode 3 and mode 5. The ones for mode 3 would look something like this:

typedef u16 COLOR;

#define vid_mem         ((COLOR*)MEM_VRAM)

#define M3_WIDTH        240


// === PROTOTYPES =====================================================

INLINE void m3_plot(int x, int y, COLOR clr);
INLINE void m3_line(int x1, int y1, int x2, int y2, COLOR clr);
INLINE void m3_rect(int left, int top, int right, int bottom, COLOR clr);
INLINE void m3_frame(int left, int top, int right, int bottom, COLOR clr);


// === INLINES ========================================================

//! Plot a single \a clr colored pixel in mode 3 at (\a x, \a y).
INLINE void m3_plot(int x, int y, COLOR clr)
{
    vid_mem[y*M3_WIDTH+x]= clr; 
}

//! Draw a \a clr colored line in mode 3.
INLINE void m3_line(int x1, int y1, int x2, int y2, COLOR clr)
{
    bmp16_line(x1, y1, x2, y2, clr, vid_mem, M3_WIDTH*2);
}

//! Draw a \a clr colored rectangle in mode 3.
INLINE void m3_rect(int left, int top, int right, int bottom, COLOR clr)
{
    bmp16_rect(left, top, right, bottom, clr, vid_mem, M3_WIDTH*2);
}

//! Draw a \a clr colored frame in mode 3.
INLINE void m3_frame(int left, int top, int right, int bottom, COLOR clr)
{
    bmp16_frame(left, top, right, bottom, clr, vid_mem, M3_WIDTH*2);
}

Finally, there is a m3_fill() function, that fills the entire mode 3 canvas with a single color.

//! Fill the mode 3 background with color \a clr.
void m3_fill(COLOR clr)
{
    int ii;
    u32 *dst= (u32*)vid_mem;
    u32 wd= (clr<<16) | clr;

    for(ii=0; ii<M3_SIZE/4; ii++)
        *dst++= wd;
}
mode3 screen Fig 5.3: drawing in mode 3.

Now, note what I’m doing here: instead of treating VRAM as an array of 16-bit values which are appropriate for 16bpp colors, I’m using a 32-bit pointer and filling VRAM with a 32-bit variable containing two colors. When filling large chunks of memory, it makes no difference if I fill it in N 16-bit chunks, or ½N 32-bit chunks. However, because you only use half the number of iterations in the latter case, it’s roughly twice as fast. In C, it’s perfectly legal to do something like this (provided that strict aliasing is satisfied) and often actually useful. This is why it’s important to know the principles of data and memory. Also note that I’m using pointer arithmetic here instead of array indices. While the compiler generally make the conversion itself, doing it manually is still often a little faster. (When in doubt, read the assembly language that GCC generates.)

While this method is already twice as fast as the ‘normal’ method, there are actually much faster methods as well. We will meet these later, when we stop using separate toolkit files and start using libtonc, the code library for tonc. Tonclib contains the functions described above (only faster), as well as 8bpp variations of the bmp16_ routines and interfaces for mode 4 and mode 5.

Below you can find the main code for m3_demo, which uses the m3_ functions to draw some items on the screen. Technically, it’s bad form to use this many magic numbers, but for demonstration purposes it should be okay. The result can be seen in fig 5.3.

#include "toolbox.h"

int main()
{
    int ii, jj;

    REG_DISPCNT= DCNT_MODE3 | DCNT_BG2;

    // Fill screen with grey color
    m3_fill(RGB15(12, 12, 14));

    // Rectangles:
    m3_rect( 12,  8, 108,  72, CLR_RED);
    m3_rect(108, 72, 132,  88, CLR_LIME);
    m3_rect(132, 88, 228, 152, CLR_BLUE);

    // Rectangle frames
    m3_frame(132,  8, 228,  72, CLR_CYAN);
    m3_frame(109, 73, 131,  87, CLR_BLACK);
    m3_frame( 12, 88, 108, 152, CLR_YELLOW);

    // Lines in top right frame
    for(ii=0; ii<=8; ii++)
    {
        jj= 3*ii+7;
        m3_line(132+11*ii, 9, 226, 12+7*ii, RGB15(jj, 0, jj));
        m3_line(226-11*ii,70, 133, 69-7*ii, RGB15(jj, 0, jj));
    }

    // Lines in bottom left frame
    for(ii=0; ii<=8; ii++)
    {
        jj= 3*ii+7;
        m3_line(15+11*ii, 88, 104-11*ii, 150, RGB15(0, jj, jj));
    }

    while(1);

    return 0;
}

A dash of mode 4

Mode 4 is another bitmap mode. It also has a 240×160 frame-buffer, but instead of 16bpp pixels it uses 8bpp pixels. These 8 bits are a palette index to the background palette located at 0500:0000. The color you’ll see on screen is the color found in the palette at that location.

Pixels of a bitdepth of 8 mean you can only have 256 colors at a time (instead of 32768 in the case of 15bpp), but there are benefits as well. For one, you can manipulate the colors of many pixels by simply changing the color in the palette. An 8bpp frame-buffer also takes up half as much memory as a 16bpp buffer. Not only is it faster to fill (well, in principle anyway), but there is now also room for a second buffer to allow page flipping. Why that’s useful will be covered in a minute.

There is, however, one major downsize to using mode 4, which stems from a hardware limitation. With 8-bit pixels, it’d make sense to map VRAM as an array of bytes. This would be fine if it weren’t for the rather annoying fact that VRAM does not allow byte-writes! Now, because this is a very important point, let me repeat that: You cannot write to VRAM in byte-sized chunks!!!. Byte reads are ok, but writes have to be done in 16-bit or 32-bit chunks. If you do write in bytes to VRAM, the halfword you’re accessing will end up with that byte duplicated into both the lower and upper bytes: you’re setting two pixels at once. Note that this no-byte-write rule also extends to palette memory and OAM, but there it doesn’t cause trouble because you won’t be using that as bytes anyway.

So how to plot single-pixels then? Well, you have to read the whole halfword you’re trying to access, mask off the bits you don’t want to overwrite, insert your pixels and then write it back. In code:

#define M4_WIDTH    240     // Width in mode 4
u16 *vid_page= vid_mem;     // Point to current frame buffer

INLINE void m4_plot(int x, int y, u8 clrid)
{
    u16 *dst= &vid_page[(y*M4_WIDTH+x)/2];  // Division by 2 due to u8/u16 pointer mismatch!
    if(x&1)
        *dst= (*dst& 0xFF) | (clrid<<8);    // odd pixel
    else
        *dst= (*dst&~0xFF) |  clrid;        // even pixel
}

As you can see, it’s a little more complicated than m3_plot(). It takes a lot longer to run as well. Still, once you have a pixel plotter, you can create other rendering routines with ease. The basic code for drawing lines, rectangles, circles and the like are pretty much independent of how pixels are formatted. For example, drawing a rectangle is basically plotting pixels in a double loop.

void generic_rect(int left, int top, int right, int bottom, COLOR clr)
{
    int ix, iy;
    for(iy=top; iy<bottom; iy++)
        for(ix=left; ix<right; ix++)
            generic_plot(ix, iy, clr);
}

This is the generic template for a rectangle drawing routine. As long as you have a functional pixel plotter, you’re in business. However, business will be very slow in mode 4, because of the complicated form of the plotter. In all likelihood, it’ll be so slow to make it useless for games. There is a way out, though. The reason m4_plot() is slow is because you have to take care not to overwrite the other pixel. However, when you’re drawing a horizontal line (basically the ix loop here), chances are that you’ll have to give that other pixel the same color anyway, so you needn’t bother with read-mask-write stuff except at the edges. The implementation of this faster (much faster) line algorithm and subsequently rectangle drawer is left as an exercise for the reader. Or you can seek out tonc_bmp8.c in libtonc.

VRAM vs. byte writes

You cannot write individual bytes into VRAM (or the palette or OAM for that matter). Halfwords or words only, please. If you want to write single bytes, you have to read the full (half)word, insert the byte, and put it back.

Please don’t skip this note, and make yourself aware of the full ramifications of this. Errors due to pointer-type mismatches are very easy to make, and you may be writing to VRAM as bytes more often than you think.

Generic vs. specific rendering routines

Every kind of graphics surface needs its own pixel plotter. In principle, more complicated (multi-pixel) shapes are surface independent. For example, a line routine follows the same algorithm, but simply uses a different plotter for drawing pixels. These generic forms are great in terms of re-usability and maintainability, but can be disastrous when it comes to speed. Creating surface-specific renderers may be extra work, but can on occasion save you up to a factor of 100 in speed.

Complications of bitmap modes

While I could go on to discuss more complicated matters, such as drawing rectangles and blits and text, there’s very little reason to do so at this junction. As I said before, the bitmap modes are useful to learn some basic functionality, but for most practical purposes, you’re better off with tiled modes.

The primary issue is speed. Even simple primitives such as the ones shown here can take a lot of time, especially if you’re not careful in your implementation. For example, a full mode 3 screen-wipe would take about 60% of a VBlank at best! In bad implementations of a screen-wipe, like doing it with a rectangle drawer that calls a non-inline pixel-plotting function, could take as much as 10 frames. And then you still have to draw all your backgrounds and sprites and do the game logic. The phrase ‘crawling horror’ somehow springs to mind at the thought of this.

Aside from that, bitmap modes can use only one background and have no hardware scrolling to speak of. Also, though this is jumping the gun a bit, it overlaps the memory that contains the sprite tiles, which starts at 0601:0000h. For that reason, you will only be able to use sprite-tiles 512 to 1023 when in modes 3-5.

Page flipping can alleviate some of these items, but that’s not available in mode 3. It is in mode 5, but that uses only a small portion of the screen, so gaming with only that looks awkward. As for mode 4, well, that’s one of those places where you will really see what programming close to the hardware means: it doesn’t allow you to write to VRAM in byte-sized chunks! The only way to have a single-pixel resolution is to combine 2 adjacent pixels and write those, which costs a lot of extra time.

So basically, use the bitmap modes for testing and/or static images, but not much else unless you know the tilemodes can’t do what you want.

Bitmap modes are not for gaming

Do not get too comfortable with bitmap modes. Though they’re nice for gbadev introductory sections because they are easier to work with than tile modes, and they have advantages for 3D games, they are not suitable for most types of games because the GBA simply can’t push pixels fast enough. Tinker with them to get a feel for IO registers and the like, then move on.

Page flipping

Page flipping procedure
Fig 5.4: Page flipping procedure. No data is copied, only the ‘display’ and ‘write’ pointers are swapped.

Page flipping is a technique that eliminates nasty artifacts like tearing in animation. There are two things going on at the same time in an animation: placing the pixels on bitmap (writing), and drawing the bitmap on screen (displaying). Software takes care of writing, updating the positions of characters etc; hardware does the displaying: it simply takes the bitmap and copies it to the screen. The problem is that both these processes take time. What’s worse, they happen at the same time. And when the game state changes in mid draw, the bottom section will be of the current state, while the top section will represent the previous state. Needless to say, this is bad.

Enter page flipping. Instead of using one single bitmap to write and display, you use two. While one bitmap is displayed, you write all you need onto a second bitmap (the back-buffer). Then, when you’re finished, you tell the hardware to display that second bitmap and you can prepare the next frame on the first. No artifacts whatsoever.

While the procedure works great, there are some snares. For the first, consider this. Given are the pointers to the two pages page1 and page2. Right now, page1 is displayed and page2 is being prepared; so far so good. But when you switch to the second page, this only makes page2 the display-page; you have to make page1 the write-page yourself! The solution to this problem is simple: use a write-buffer pointer, but it can catch you off-guard if you’re new to this stuff.

The second problem concerns a little nasty in the age-old method of animation. The canonical animation does this. Frame1: draw object. Frame2: erase old object, draw object in new state. This doesn’t work for page flipping since Frame2 is written on an entirely different bitmap than Frame1, so trying to erase Frame1’s old object doesn’t. What you need to erase is the object from 2 frames ago. Again, easy solution, but you have be aware of the problem. (Of course, erasing the entire frame each time would work too, but who’s got the time?)

Pageflipping, not double buffering

Another method of smoother animation is double buffering: draw on a secondary buffer (the backbuffer) and copy it to the screen when finished. This is a fundamentally different technique than page flipping! Even though both use two buffers, in page flipping you don’t copy the backbuffer to the display buffer, you make backbuffer the display buffer.

What the GBA does is page flipping, so refer to it as such.

GBA page flipping

The second page of the GBA is located at location 0600:A000h. If you look at the size required for mode 3, you’ll see why it doesn’t have page-flipping capabilities: there’s no room for a second page. To set the GBA to display the second page, set REG_DISPCNT{4}. My page flipping function looks a little like this:

u16 *vid_flip()
{
    // toggle the write_buffer's page
    vid_page= (u16*)((u32)vid_page ^ VID_FLIP);
    REG_DISPCNT ^= DCNT_PAGE;            // update control register
    return vid_page;
}

The code is relatively straightforward. vid_page is the pointer that always points to the write-page. I had to pull a little casting trickery to get the XOR to work (C doesn’t like it when you try it on pointers). On the GBA, the steps for page flipping are perfectly xorrable operations. Sure, you could just put the equivalent in an if-else block, but where’s the fun in that :P?

Page flipping demo

What follows is the code (sans data) for the pageflip demo. The actual part concerned with page flipping is very small. In fact, the actual flip is merely a call to vid_flip() once every 60 frames = 1 second (point 3). We’ll also have to set the video mode to something that actually has pages to flip, which in this case is mode 4.

What we’ll have to do as well is load the data that will be displayed on these two pages. I’m using the standard C routine memcpy() for the copy, because that’s the standard way of copying things in C. While it’s faster than manual loops, it does come with a few snares that you need to be aware of before using it everywhere. Tonclib comes with faster and safer routines, but we’ll get to those when it’s time.

Loading a bitmap is very simple in theory, but the bitmap(s) I’m using are only 144×16 in size, while the VRAM page’s pitch is 240 pixels wide. This means that we’ll have to copy each scanline separately, which is done at point (1). Note that I’m copying frontBitmap to vid_mem_front and backBitmap to vid_mem_back, because those are the starting locations of the two pages.

Since these are mode 4 bitmaps, they’ll also need a palette. Both palettes use frontPal, but instead of using memcpy() to copy it to the background palette memory, I’m using a u32 array because … well, just because I guess.

Lastly, you can pause and unpause the demo by holding the Start Button.

#include <string.h>

#include <toolbox.h>
#include "page_pic.h"

void load_gfx()
{
    int ii;
    // (1) Because my bitmaps here don't fit the  screen size, 
    // I'll have to load them one scanlline at a time
    for(ii=0; ii<16; ii++)
    {
        memcpy(&vid_mem_front[ii*120], &frontBitmap[ii*144/4], 144);
        memcpy(&vid_mem_back[ii*120], &backBitmap[ii*144/4], 144);
    }

    // (2) You don't have to do everything with memcpy.
    // In fact, for small blocks it might be better if you didn't.
    // Just mind your types, though. No sense in copying from a 32-bit 
    // array to a 16-bit one.
    u32 *dst= (u32*)pal_bg_mem;
    for(ii=0; ii<8; ii++)
        dst[ii]= frontPal[ii];
}

int main()
{
    int ii=0;

    load_gfx();
    // Set video mode to 4 (8bpp, 2 pages)
    REG_DISPCNT= DCNT_MODE4 | DCNT_BG2;

    while(1)
    {
        while(KEY_DOWN_NOW(KEY_START)); // pause with start
        vid_vsync();

        // (3) Count 60 frames, then flip pages
        if(++ii == 60)
        {   
            ii=0;   
            vid_flip(); 
        }
    }
    return 0;
}
Flip A    Flip B
Fig 5.5: the page flipping demo switches between these two blocks.

On data and how to use it

This section is a little boring (ok, very boring) but it needs to be said. While books and tutorials on C may use data for whatever purpose, they often gloss over what data actually is at the lowest level, and how to deal with it correctly. As you’ll be dealing directly with hardware and memory here, it is important that you are aware of these items, preferably even understand them, so that they don’t bite you in the ass at some later point.

The first two subsections are about how to get graphics into your game, something that you’ll really need to know. After that I’ll discuss a few nasty and highly technical things that may or may not cause problems later on. These are optional and you can skip to the data-loading/interpreting demo at any time. That said, I urge you to read them anyway because they may save you a lot of debugging time.

Relax, it’s only 1s and 0s

When you get right down to it, everything on computers is merely a big mess of bits without any purpose by itself. It is the interaction between hardware and software that makes sequences of bits appear as valid executable code, a bitmap, music or whatever.

Yes, we have no files

This may be a good point to say a few words on data. Strictly speaking, everything is data, but in this case I’m referring to data that on PC games would be separate from the executable: graphics, music, maybe scripts and text-files and what not. This all works fine on a PC, but not so fine on the GBA because there is no file system. This means that you cannot use the standard file I/O routines (fscanf(), fread(), etc) to read the data, because there are no files to read them from.

All the game’s data has to be added directly to the binary. There are a number of ways to do this. The most common way is to convert the raw binary files to C-arrays, then compile those and link them to the project. Well, the most common among homebrewers is probably converting to C arrays and using #include on them, but that’s something that you should never do. Also popular are assembly arrays. These are a useful alternative to C arrays because a) they can’t be #included and b) because they bypass the compilation step and compilation of arrays is very intensive. Of course, you would have to know how to work with the assembler. Another nice thing about the assembler is that you can include binary files directly into them, eliminating the need for a converter. Lastly, while the GBA doesn’t have a native file system, you can always write your own. A common one is GBFS by the gbadev forum FAQ maintainer, tepples. Using a file system is actually the recommended method, but for now, I’ll stick to C arrays because they are the easiest to use.

Ahem. Actually, we do have files

There were no files in the past, but in July of 2006, Chishm gave us libfat, which is a FAT-like file system for GBA and Nintendo DS. It is distributed via devkitPro Updater as well, so chances are you have it already.

Where do my arrays go?

By default, arrays go into IWRAM. You know, the one that’s only 32 KiB long. Now, a mode 3 bitmap is 240×160×2 = 77 kB. Obviously, trying to put a 77 kB object into a 32 KiB section would fit nicely into the bad things category. To avoid this, put it in the read-only section (ROM), which is much larger. All you have to do for this is add the const keyword to the definition if you’re using C, or the .rodata directive in assembly. Note that for multiboot programs, ROM actually means EWRAM, which is only 256 KiB long. The latter would fit three mode 3 bitmaps; more would again be bad unless you use compression.

Note that what I said about arrays is true for all arrays, not just data arrays: if you want any kind of large array (like a backbuffer for mode 3), it would also default to and overfill IWRAM. But you can’t make it const because then you’d not be able to write on it. GCC has attributes that lets you choose where things are put – in EWRAM for instance. Here are the commonly seen #define macros for the attributes that can be used for specific section placement.

#define EWRAM_DATA __attribute__((section(".ewram")))
#define IWRAM_DATA __attribute__((section(".iwram")))
#define  EWRAM_BSS __attribute__((section(".sbss")))

#define EWRAM_CODE __attribute__((section(".ewram"), long_call))
#define IWRAM_CODE __attribute__((section(".iwram"), long_call))

Const is good

Data that you don’t expect to change in your game should be defined as constant data using the const keyword, lest it trashes your IWRAM.

Converted and const arrays in C++

There are two little snags that you can trip on if you’re using (converted) data arrays in C++. The first is that tools that generate the arrays will output C files, not C++ files. This is not a problem in itself because those files will be compiled just the same. What is a problem is that C++ uses something known as Name mangling to allow overloading and stuff like that. C doesn’t and as a result, the name that the C++ file looks for isn’t the same one as in the C file and you get undefined references. To fix this, use extern "C" in front or around the declarations of the stuff in the C files.

// This:

extern "C" const unsigned char C_array[];

// Or this:
extern "C"
{
const unsigned char C_array1[];
const unsigned char C_array2[];
}

Another problem with C++ is that const-arrays are considered static (local to the file that contains it) unless you add an external declaration to it. So if you just have const u8 foo[]= { etc } in a file, the array will be invisible to other files.The solution here would be to add the declaration inside the file itself as well.

// foo.cpp. Always have an external declaration 
// inside the file as well.

extern const unsigned char foo[];

const unsigned char foo[]=
{
    // data
};

Data conversion

It’s rather easy to write a tool that converts a binary file to a C or asm array. In fact, devkitARM comes with two that do just that: raw2c.exe and bin2s.exe. It also comes with the basic tools for gbfs by the way. But being able to attach binary files to your game is only part of the story. Consider a bitmap, for example. In principle, a bitmap is a binary file just like any other. There’s nothing inherently graphical about it, and it doesn’t magically appear as a bitmap whenever you use it by itself. Yes, when you double-click on it, an image viewer may pop up and display it, but that’s only because there’s some serious work by the OS going on underneath. Which we don’t have here.

Most files will follow a certain format to tell it what it is, and how to use it. For bitmaps, that usually means width, height, bitdepths and a few other fields as well. The point is that they’re not directly usable. You can’t just attach, say, a BMP file to your project and copy it to VRAM and think that everything will work out. No, you have to convert it to a GBA-usable format. Now, you can do this internally (on the GBA itself), or externally (on the PC and attach the converted data to the project). Because the latter is a much more efficient use of GBA resources, that is the usual procedure.

There are many conversion tools, one might almost say too many. Some are one-trick ponies: a single file-type to a single graphics mode for example. Some are very powerful and can handle multiple file-types, multiple files, different conversion modes with lots of options on the side, and compression. It should be obvious which are of the most value.

A good one is gfx2gba. This is a command-line tool so that it can be used in a makefile, but there is a GUI front-end for it as well. This tool has the Good Things I mentioned earlier, plus some map-exporting options and palette merging, but the input file must be 8-bit and I hear that while it does compress data, the array-size is still given as its uncompressed size for some unfortunate reason. This tool comes with the HAM installation, and is quite common, so definitely recommended. Unfortunately, there seems to be another tool with the same name. You’ll want the v0.13 version by Markus, not the other one.

Personally, I use Usenti, which is my own tool. This is a bitmap editor (paint program) with exporting options thrown in. It allows different file-types, different bitdepths, different output files, all modes, some map-exporting stuff, meta-tiling, compression and a few others. It may not be as powerful as big photo-editing tools as Photoshop, GIMP, Aseprite, and the like, but it gets the job done. If you’re still drawing your graphics with Microsoft Paint, please stop that and use this one instead. The exporter is also available separately in the form of the open source project called (win)grit, which comes in a command-line interface (grit) and a GUI (wingrit). As of January 2007, it is also part of the devkitPro distribution.

Bitmap conversion via CLI

There are many command-line interfaces available for graphics conversion, but to make them function you need the correct flags. Here are examples for gfx2gba and grit, converting a bitmap foo.bmp to a C array for modes 3, 4 and 5. This is just an example, because this is not the place for a full discussion on them. Look in their respective readme’s for more details.

# gfx2gba
# mode 3, 5 (C array; u16 foo_Bitmap[]; foo.raw.c)
    gfx2gba -fsrc -c32k foo.bmp
# mode 4 (C array u8 foo_Bitmap[], u16 master_Palette[]; foo.raw.c, mastel.pal.c)
    gfx2gba -fsrc -c256 foo.bmp
# grit
# mode 3, 5 (C array; u32 fooBitmap[]; foo.c foo.h)
    grit foo.bmp -gb -gB16
# mode 4 (C array; u32 fooBitmap[], u16 fooPal[]; foo.c foo.h)
    grit foo.bmp -gb -gB8
Table 5.2: Big endian vs little endian interpretation of byte-sequence 01h, 02h, 03h, 04h
big u32 0x01020304
big u16 0x0102 0x0304
u8 0x01 0x02 0x03 0x04
little u16 0x0201 0x0403
little u32 0x04030201

Below, you can see a partial listing of modes.c, which contains the bitmap and the palette used in the bm_modes demo discussed at the end of this section, as exported by Usenti. It is only a very small part of the file because at over 2700 lines it is way too long to display here, which wouldn’t serve much of a purpose anyway. Note that both are u32 arrays, rather than the u8 or u16 arrays you might encounter elsewhere. What you need to remember is that it doesn’t matter in what kind of an array you put the data: in memory it’ll come out the same anyway.

Well, that’s not quite true. Only with u32 arrays is proper data alignment guaranteed, which is a good thing. More importantly, you have to be careful with the byte-order of multi-byte types. This is called the endianness of types. In a little endian scheme, least significant bytes will go first and in a big endian, most significant bytes will go first. See table 2 for an example using 0x01, 0x02, 0x03 and 0x04. The GBA is a little endian machine, so the first word of the modesBitmap array, 0x7FE003E0 is the halfwords 0x03E0 (green) followed by 0x7FE0 (cyan). If you want more examples of this, open up VBA’s memory viewer and play around with the 8-bit, 16-bit and 32-bit settings.

The key point here: the data itself doesn’t change when you use different data-types for the arrays, only the way you represent it does. That was also the point of the bm_modes demo: it’s the same data in VRAM all the time; it’s just used in a different way.

//======================================================================
//
//  modes, 240x160@16, 
//  + bitmap not compressed
//  Total size: 76800 = 76800
//
//  Time-stamp: 2005-12-24, 18:13:22
//  Exported by Cearn's Usenti v1.7.1
//  (comments, kudos, flames to "daytshen@hotmail.com")
//
//======================================================================

const unsigned int modesBitmap[19200]=
{
    0x7FE003E0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,
    0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,
    0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,
    0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,
// ...
// over 2500 more lines like this
// ...
    0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,
    0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,
    0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,0x080F080F,
    0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,0x7FE07FE0,
};

const unsigned int modesPal[8]=
{
    0x7FE07C1F,0x03FF0505,0x03E00505,0x7C000000,0x0000080F,0x00000000,0x00000000,0x080F0000,
};

Those 2700 lines represent a 77 kB bitmap. One single bitmap. In all likelihood, you’ll need at least a couple of them to make anything worthwhile. Most games have lots of data in them, not only graphics but maps and sound and music as well. All this adds up to a huge amount of data, certainly too much for just EWRAM and maybe even for a full cart. That is why compression is also important. The GBA BIOS has decompression routines for bit-packing, run-length encoding, LZ77 and Huffman. Converters sometimes have the appropriate compressors for these routines, which can drastically shrink the amount of memory used. Usenti and (win)grit support these compressors. So does gfx2gba, which even has some more. A tool that just does compression on binary files (but does it very well) is GBACrusher. I won’t go into compression that much (or at all), but you can read up on the subject here.

Understanding data

It is vital that you understand what data is, how the different datatypes work. Preferably endianness and alignment too. Emulators and hex editors can help you with this. Once you have compilation working, just make a few random arrays and see what they look like in the VBA memory viewer for a while.

#include code or data considered harmful

Lines
Fig 5.6: even Bart knows …

Most non-trivial projects will have multiple files with code and data. The standard way of dealing with these is to compile these separately and then link the results to the final binary. This is the recommended strategy. However, most other tutorials and many of the example code you can find on the web do something else: a unity build. They #include everything into the main source file and compile that. This is not a recommended practice and should be avoided.

”But why not? It seems to work fine, and it’s so easy!”

Yes, it is easy; and it does seem to work. The main problem is that a unity build isn’t scalable. For small projects (a handful of files) you probably won’t notice, but as projects grow to hundreds and perhaps thousands of files, you will run into some very annoying problems. The main issue is what #include actually does. It copies the whole included file into the includer to form a single larger file. This leads to the following issues.

  • Massive files to compile. So, #include creates one big file. If you have a lot of stuff, you’ll have one very big file. This will cost large amounts of memory and slows down compilation. As the project grows, what starts as a compile time of a second can grow to several, then minutes and perhaps even hours.

    At some point, there was also the problem that the compiler couldn’t handle files exceeding 4 MB, putting a limit on how much you could #include in a C file. I’m not sure if this is still an issue.

  • Recompiling the world. The main problem is that when you #include everything, you need to recompile everything as well. If you make one change anywhere, no matter how small, causes everything to be compiled. For small projects (say, a handful of files), a full rebuild would take a few seconds so it’s not a problem. But larger projects can have hundreds or thousands of files, and the time is not measured in seconds, but in minutes or perhaps hours. Sure it’s a good excuse to go sword fighting, but terribly annoying if you want to do something productive.

  • Bloat. Even if your own code and data are relatively small in number, you’re probably using some code library for API functions. Normally, these are pre-compiled and only the functions used are linked into your binary. But if those worked by #include as well (in other words, if their creators had followed the practice I’m warning against), every function in that library would be included as well, including the ones you’re not using. This increases the filesize, and increases the problems mentioned above.

  • Undeclared identifiers, multiple definitions and circular dependencies. In a nutshell, C requires that you declare an identifier before it’s referenced, and it can only be defined once. The first point means that the order of inclusions starts to matter: if, say, fileB.c needs something from fileA.c, the latter needs to be included before the former to get a compile. The second means that you could only #include a file once in the whole project: if fileB.c and fileC.c both need stuff from fileA.c, you can’t #include it in them both because when they’re #included in main.c, fileA.c is effectively #included twice and the compiler will balk.

    These points can technically be overcome by being careful, such as using an include guard. But, again, when projects grow, things can get increasingly more difficult to keep track of which comes before what and why. There is, however, one point at which it will go wrong, namely when there are circular dependencies: fileB.c needs fileA.c and vice versa. Each file would require the other to go first, which simply isn’t possible because it’d cause multiple definitions.

  • Data alignment. I’ll get to what this means in a minute, but right now know that copy routines work better if the data is aligned to 32-bit boundaries (even for byte and halfword arrays). Some of them won’t even work properly if this isn’t the case. This is usually guaranteed if you compile separately, but if the arrays are #included and no steps have been taken to force alignment, you simply never know.

    It’s not much of a problem nowadays because most graphics converters force data alignment, but you still need to know about it. Because data alignment is a fairly esotheric concept, it’s next to impossible to track down unless you’re aware of the problems it can bring.

So please, do yourself a favor and do not #include every file you have into main.c or its counterpart in your project. Put function and variable definitions in separate source files to be compiled separately and linked later. The #include directive is only to be used for files with preprocessor directives, declarations, type definitions, and inline functions.

Proper build procedure

Separate compilation

So what do you do instead? Well, for starters keep all the code and data in separate source files. Compile these separately by invoking gcc on each file. This gives you a list of object files. These you then link together. In batch files, you’d need to add extra commands for each file, but a properly setup makefile uses a list of object files, and the makefile’s rules will then take care of the rest automatically. Using the makefile of the second demo as a reference, you’ll get something like this:

# partial makefile for using multiple source files
# some steps omitted for clarity

# 3 targets for compilation
OBJS    := foo.o bar.o boo.o

# link step: .o -> .elf
$(PROJ).elf : $(OBJS)
    $(LD) $^ $(LDFLAGS) -o $@

# compile step .c -> .o
$(OBJS) : %.o : %.c
    $(CC) -c $< $(CFLAGS) -o $@

The OBJS variable contains the names of three object files, which would be the targets of compiling foo.c, bar.c and boo.c. Remember, makefiles list rules by target, not by prerequisite. The compilation step uses a static pattern rule, which for each object file (.o) in OBJS compiles the source file (.c) file with the same title. This is what runs the compiler for our three source files. In the linking step, the automatic variable $^ expands to the prerequisites of the rule, which is the list of all object files, and this is how the files are all linked together. If you need more files, add them to the OBJS list.

Note that the devkitARM and tonc template files take care of these things automatically. Just put the source files into the right directory and you’re good to go.

Symbols, declarations and definitions

If you have been doing everything via #include, you should consider refactoring all of your stuff to separate source files. No, let me rephrase that, you need to do this because you’ll benefit from it in the end. If you’re already well in your project, this is going to suck because it’s boring and time consuming and most likely it’s not even going to work properly when you try the first build afterwards. I expect you’ll get a whole slew of errors, particularly these three:

  • `foo’ undeclared
  • redefinition of `foo’
  • multiple definition of `foo’

To understand what these mean, you need to know a little bit more about how C (and indeed programs) actually works.

As I said before, there aren’t really things like programs, bitmaps, sound on computers; it’s all just bits. Bits, bits and more bits. What makes a sequence of bits work as a program is the way it is fed to the CPU, VRAM, and other sections. Somewhere in the build process, there has to be a translation of all the C code to data and machine instructions. This, of course, is the compiler’s job.

But wait, there’s more. C allows you to compile each file separately, and then link them later into the actual program. This is a good idea, because it allows you to save time by only compiling the files that you have recently modified, as well as the use of code libraries, which are little more than a bunch of precompiled source files. If you’re not convinced that this is a good idea, consider what it would take without it. You’d have to have all the source code that you wanted to use (including for things like printf() and all the API code), and compile all those megabytes of source files each time. Sounds like fun? No, I didn’t think so either.

However, you need a little more bookkeeping to make this all work. Because everything is just bits, you’d need a way to find out where the function or data you want to use actually is. The contents of the compiled files (the object files) isn’t just raw binary, it contains symbols. This is just a word for the group of things that have actual binary information attached to them. Among other things, the object file keeps track of the symbol’s name, section, size, and where its content is in the object file. A function is a symbol, because it contains instructions. A variable is also a symbol, as is data for bitmaps, sound, maps et cetera. Preprocessor #defines, typedefs and struct/class declarations are not symbols, because they only don’t have actual content in them, but allow you to structure your code better.

The other bookkeeping note is that each source/object file is a separate entity. In principle, it knows nothing about the outside world. This makes sense because it limits the dependency on other files, but it does create a little problem when you want to make files work together. This is where declarations come in.

You may have noticed that C is pretty strict when it comes to names of stuff. Before you can use anything, it requires you to mention what it is beforehand. For example, if you use a function foo() in your code and you never defined its code, or even if you put it after the call to foo(), the compiler will complain that it doesn’t know what you’re talking about. That is, it will say that ‘`foo’ is undeclared’. You have to admit it has a right to stop there: how would it know how to use the thing if you never told it what it was?

The code snippet below gives an example of when a reference is and is not declared, and why it’s important to have a declaration. Function a() calls foo(), which is not known at the time, so an error is produced. Function b() also calls foo(), which is known at that time, but still gives an error because foo() just happens to require an integer as an argument. If the declaration wasn’t mandatory and the call in a() was allowed, foo() would have been processing the wrong kind of information at runtime. There are ways around such problems, of course, languages like PHP, VB and others work fine without mandatory declarations, but the cost for that is speed and possibly a lot more runtime errors.

//# C requires identifiers to be declared or defined before first use.

// ERROR: `foo' is undefined.
void a()
{
    foo();
}

// Definition of foo(). Now the system 'knows' what foo is.
void foo(int x)
{
   // code
}

// foo is known and used correctly: no errors.
void b()
{
    foo(42);
}

// foo is known but used incorrectly. Compiler issues error.
void c()
{
    foo();
}

Now back to our separate files, and the difference between declarations and definitions of symbols. A definition is something of actual content: it is what actually forms the symbol. Examples are the value(s) in variables, and the code in functions. A declaration is just an empty reference. It just says that there is something in the project with a particular name, and indicates how that something is supposed to be used: whether it’s a function or variable, what datatype, which arguments, that sort of things. This is how you can use symbols from other object files.

You should be familiar with what a definition looks like. A declaration looks very similar. The basic variable declaration is the variable name and attributes (type, const, section) preceded by extern. For functions, replace the code block by a semi-colon. You can also add extern there, but it’s not required.

// --------------------------------------------------------------------
// DECLARATIONS. Put these in source (.c) or header (.h) files.
// --------------------------------------------------------------------
extern int var;
extern const unsigned int data[256];
void foo(int x);


// --------------------------------------------------------------------
// DEFINITIONS. Put these in source (.c) only.
// --------------------------------------------------------------------

// uninitialized definition
int var;

// initialized definition
const unsigned int data[256]=
{
    // data
};

void foo(int x)
{
    // code
}

Now, a definition is also a declaration, but this does not work the other way. How can it, the declaration is supposed to be empty. The distinction is subtle, but it’s the reason you might get multiple definition errors when linking the files together. Think of what would happen if you have the definition of function foo() in multiple files. Each file itself would know what foo() is because definitions are also declarations, so it would pass the compilation stage. So now you have multiple object files, each containing a symbol called foo. But then you try to link them into one file. The linker sees different versions of foo, and stops because it doesn’t know which one you are actually trying to use. The moral here is that you can have as many declarations as you want, but there can be only one definition.

Another point I should raise is that the declaration defines how a symbol is to be dealt with, as it is the only point of reference if the definition is in another file. This means that, in theory, you could have a variable var defined as an int, but declared as a short, or even a function! While not exactly recommended, but it is an interesting item.

Lastly: the distinction of what should go in source files, and what in headers. Source files can actually contain anything, so that’s an easy one. Remember that they will contain everything after the preprocessor step anyway, because that’s what #include really does. So what matters is what you put in headers. The purpose of header files is to have a place for all the non-symbol stuff that you want to use in different source files. That means declarations, #defines, macros, typedefs, struct/class descriptions. It also means static inline functions, because these don’t form symbols either, but are integrated in the functions that call them.

Summary

All this stuff about separate compilation, declarations, and definitions is rather important for C programming, but the preceding text may be a little much to take in at once. So here is a summary of the most important points.

  • Symbols. Symbols are those parts of the code that form actual binary content in the final program. This includes functions, variables, data, but not preprocessor or type description stuff.
  • Declarations/definitions. A definition of a symbol is where the actual content is. A declaration just says that something of a certain name exists, but will be added to the project later. Multiple (identical) declarations may exist, but there can be only one definition in the project. Definitions are also declarations.
  • Source/object files are selfcontained entities. They contain the definitions of the symbols that are in the code, and a list of references to outside symbols, as indicated by the declarations.
  • Header files contain meta-data, not symbols. Header files cannot be compiled, but are intended contain the ‘glue’ that allow difference sources to work together (i.e., declarations) and stuff that makes writing the sources easier (like #defines and macros). They are meant to be included in multiple files, so they cannot create symbols because that would lead to multiple definitions.

Potential problems during compilation or linking:

  • `foo’ undeclared. Compiler error. The identifier foo is not known at this point. Check the spelling, or add the appropriate declaration or header file containing the declaration.
  • redefinition of `foo’. Compiler error. The identifier as a previous declaration or definition conflicting with the current one in the same file or included headers. Usually accompanied by a message of the previous definition.
  • multiple definition of ‘foo’. Linker error. The symbol name foo is shared by multiple object files. Replace all but one definitions of foo in the source files with the appropriate declarations. Usually accompanied with a message indicating the object file with the other definition(s).

Data alignment

Data alignment is about the ‘natural’ memory addresses of variables. It is often beneficial to have a variable of a certain length to start at an address divisible by that length. For example, a 32-bit variable likes to be put at addresses that are a multiple of 4. Processors themselves also have certain preferred alignments. Addressing will work faster if you stick to their native types and alignment (say, 32-bit everything for 32-bit CPUs). For PCs it is not required to do any of this, it’ll just run slower. For RISC systems, however, things must be aligned properly or data gets mangled.

In most cases, the compiler will align things for you. It will put all halfwords on even boundaries and words on quad-byte boundaries. As long as you stick to the normal programming rules, you can remain completely oblivious to this alignment stuff. Except that you won’t always stick to the rules. In fact, C is a language that allows you to break the rules whenever you feel like it. It trusts you to know what you’re doing. Whether that trust is always justified is another matter :P

The best example of breaking the rules is pointer casting. For example, most graphics converters will output the data as u16 arrays, so you can copy it to VRAM with a simple for loop. You can speed up copying by roughly 160% if you copy by words (32-bit) rather than halfwords (16-bit). Run the txt_se2 demo and see for yourself. All you have to do for this is one or two pointer casts, as shown here.

#define fooSize ...
const u16 fooData[]= { ... };

// copy via u16 array (the de facto standard)
u16 *dst= (u16*)vid_mem, *src= (u16*)fooData;
for(ii=0; ii<fooSize/2; ii++)
    dst[ii]= src[ii];

// copy via u32 array (mooch faster)
u32 *dst= (u32*)vid_mem, *src= (u32*)fooData;
for(ii=0; ii<fooSize/4; ii++)
     dst[ii]= src[ii];

Both these routines copy fooSize bytes from fooData to VRAM. Only the second version is much faster because there are half as many loop iterations and also because the ARM CPU is just better at dealing with 32-bit chunks. The only danger here is that while fooData will be halfword aligned, it need not be word aligned, which is a requirement for the second version. For those readers that think casts like this and mis-alignment only happen to other people, think again: the faster copy routines (memcpy(), CpuFastSet(), and DMA too) cast to word pointers implicitly. Use them (and you should) and you run the risk of misalignment.

There are many ways of ensuring proper alignment. The easiest way is to not mix converted data with the rest of your stuff. That is, don’t #include data-files. This should suffice. Another method is to convert to u32 arrays in the first place. In assembly files, you can control alignment by using the .p2align *n* directive, where n aligns to 2n bytes. C itself doesn’t allow manual alignment, but there is an extension for this in GCC: __attribute__(( aligned(4) )). Add that to the definition and it’ll be word aligned. This is often #defined as ALIGN4 in some headers. Files in GBFS are also always correctly aligned.

Struct alignment

One other area where alignment can cause problems is in struct definitions. Look at the following code. Here we have a struct named FOO consisting of one byte, b, one word w and one halfword h. So that’s 1+4+2=7 bytes for the struct right? Wrong. Because of the alignment requirement, w doesn’t immediately follow b but leaves 3 bytes of padding. When defining arrays of this type, you’ll also see that there are also two padding bytes after h, because otherwise later array entries would run into trouble.

// one byte, one word, one halfword. 7 byte struct? 
// Well let's see ...
struct FOO
{
     u8 b;
    u32 w;
    u16 h;
};

// Define a FOO array
struct FOO foos[4]= 
{
    { 0x10, 0x14131211, 0x1615 }, 
    { 0x20, 0x24232221, 0x2625 }, 
    { 0x30, 0x34333231, 0x3635 }, 
    { 0x40, 0x44434241, 0x4645 }, 
};

// In memory. 4x12 bytes.
// 10 00 00 00 | 11 12 13 14 | 15 16 00 00
// 20 00 00 00 | 21 22 23 24 | 25 26 00 00
// 30 00 00 00 | 31 32 33 34 | 35 36 00 00
// 40 00 00 00 | 41 42 43 44 | 45 46 00 00

The real size is actually 12 bytes. Not only is this almost twice the size, if you ever try to copy the array using a hard-coded 7 rather than sizeof(struct FOO), you completely mess it up. Take this lesson to heart. It’s a very easy mistake to make and difficult to detect after the fact. If you were unaware of this fact and you’ve already done some GBA coding, check your struct (or class) declarations now; chances are there are gaps that shouldn’t be there. Simply rearranging some of the members should suffice to make them fit better. Note that this is not specific to the GBA: structs on PCs may behave the same way, as I noticed when I was writing my TGA functions.

There are ways of forcing packing, using the ‘__attribute__((packed))’ attribute. If struct FOO had that, it really would be 7 bytes long. The downside of this is that the non-byte members could be mis-aligned, and the compiler emits code to put the value together byte for byte. This is very much slower than the non-packed version, so only use this attribute if you have no other choice. What happens with mis-aligned (half)words then I can’t tell you though, but I’m sure it’s not pretty.

Forcing alignment and packing

GCC has two attributes that allow you to force alignment of arrays, and remove member-alignment in structs.

// Useful macros
#define ALIGN(n)    __attribute__((aligned(n)))
#define PACKED      __attribute__((packed))

// force word alignment
const  u8 array[256] ALIGN(4) = {...};
typedef struct FOO {...} ALIGN(4) FOO;


// force struct packing
struct FOO {...} PACKED;

Devkits and struct alignment

As far as I’ve been able to tell, structs have always had word alignment. This was useful because it made copying structs faster. C allows you to copy structs with a single assignment, just like the standard data types. Because of the word-alignment, these copies are fast because GCC will make use of ARM’s block-copy instructions, which are much faster than copying member by member.

However, this does not seem to be true under devkitARM r19 (and presumably higher) anymore. The new rule seems to be that structs are aligned to their largest member. This does make more sense as a struct of two bytes would actually be two bytes long. However, it does mean that GCC will now call memcpy() for non-aligned structs. Apart from it being a function with quite a bit of overhead (i.e., it’s very slow if you want to copy a single small struct), it will actually fail to produce correct results in some cases. The problem is that low-length copies it will copy by the byte, which is something you cannot do for VRAM, OAM, or the palette. For example, objects that we’ll see later use a struct of four halfwords; using a struct copy there, something I am very fond of doing, screws up everything. The only way to make it work properly is to force word alignment on the struct.

// This doesn't work on devkitARM r19 anymore
typedef struct OBJ_ATTR 
{ 
    u16 attr0, attr1, attr2;
    s16 fill;
} OBJ_ATTR;

OBJ_ATTR a, b;
b= a;   // Fails because of memcpy

// Forcing alignment: this works properly again
typedef struct OBJ_ATTR 
{ 
    u16 attr0, attr1, attr2;
    s16 fill;
} ALIGN(4) OBJ_ATTR;

OBJ_ATTR a, b;
b= a;   // No memcpy == no fail and over 10 times faster

Forcing struct-alignment is a Good Thing

The rules for struct alignment have changed since devkitARM r19. Instead of being always word-aligned, they are now aligned as well as their members will allow. If this means they’re not necessarily word-aligned, then they will use memcpy() for struct copies, which is slow for small structs, and may even be wrong (see next section). If you want to be able to do struct copies fast and safe, either force alignment or cast to other datatypes.

Copying, memcpy() and sizeof

There are many different ways of copying data on this platform. Arrays, struct copies, standard copiers like memcpy(), and GBA specific routines like CpuFastSet() and DMA. All of these have their own strengths and weaknesses. All of them can be affected by misalignment and the no-byte-write rule. I discuss some of them in the txt_se2 demo.

I’ve chosen to use memcpy() in the early demos for a number of reasons. The main one is that it is part of the standard C library, meaning that C programmers should already be familiar with it. Secondly, it is somewhat optimized (see the txt_se2 demo for details). However, there are two potential pitfalls with the routine. The first is data alignment (yes, that again). If either the source or the destination is not word-aligned, you’re in trouble. Secondly, if the number of bytes is too small, you’re in trouble too.

Both of these have to do with the basic function of memcpy(), namely to be a fast byte copier. But as you know, you can’t copy single bytes to VRAM directly. Fortunately, it has an optimised mode that uses an unrolled word-copy loop if two conditions are satisfied:

  1. When both source and destinations are word aligned.
  2. When you are copying more than 16 bytes.

This is usually the case so I figured it’d be safe enough for the demos. There are also look-alikes in libtonc that do the same thing only better, namely memcpy16() and memcpy32(), but these are in assembly so I thought I wouldn’t lay them on you so soon. Highly recommended for later though.

On a related subject, there is also memset() for memory fills. Be careful with that one, because that will only work with bytes. Tonclib also includes 16- and 32-bit versions of this routine, but also in assembly.

The last thing I want to discuss is the sizeof() operator. In other tutorials you will see this being used to find the size in bytes of arrays, which is then used in memcpy(). It’s a good procedure but will not always work. First, sizeof() actually gives the size of the variable, which need not always be the array itself. For example, if you use it on a pointer to the array, it’ll give the size of the pointer and not of the array. The compiler never complains, but you might when hardly anything is copied. Secondly, sizeof() is an operator, not a function. It is resolved at compile-time, so it needs to be able to find the size at that time as well. To do this, either the declaration (in the header) should indicate the size, or the array definition (in the source file) should be visible.

Bottom line: you can use sizeof(), just pay attention to what you use it on.

Okay, that was the long and boring –yet necessary– section on data. Congratulations if you’ve managed to stay awake till this point, especially if you’ve actually understood all of it. It’s okay if you didn’t though, in most cases you won’t run into the problems discussed here. But just remember this section for if you do run into trouble when copying and you can’t find it in the code; it might save you a few hours of debugging.

Data interpretation demo

The bm_modes is an example of how the same data can result in different results depending on interpretation (in this case, modes 3, 4 and 5). In the code below, I make one copy into VRAM, and switch between the modes using Left and Right. The results can be seen in Fig 5.7a-c.

I’ve arranged the data of the bitmap in such a way that the name of the current mode can be read clearly, as well as indicated the mode’s boundaries in memory. Because the data intended for the other modes is still present, but not interpreted as intended, that part of the bitmap will look a little distorted. And that’s partly the point of the demo: when filling VRAM, you need to know how the GBA will use the data in it, and make sure it’ll be used. If the bitmap ends up being all garbled, this is the likely suspect; check the bitdepth, dimensions and format (linear, tiled, compressed, etc) and if something conflicts, fix it.

Now, sometimes this is not as easy as it sounds. The general procedure for graphics is to create it on the PC, then use an exporter tool to convert it to a raw binary format, then copy it to VRAM. If the exporter has been given the wrong options, or if it can’t handle the image in the first place, you’ll get garbage. This can happen with some of the older tools. In some cases, it’s the bitmap editor that is the culprit. For paletted images, a lot depends on the exact layout of the palette, and therefore it is vital that you have a bitmap editor that allows total control over the palette, and leaves it intact when saving. Microsoft Paint and Pyxel Edit for example do neither. Even very expensive photo editing tools don’t, so be careful.

For this image, I used <plug>my own bitmap editor Usenti</plug>, which not only has some nice palette control options, and tiling functions, but a built-in GBA graphics exporter as well. To make the background be the same color in all modes, the two bytes of the 16-bit background color of modes 3 and 5 had to serve as palette entries for mode 4, both using that 16-bit color again. In this case, the color is 0x080F, sort of a brownish color. The bytes are 8 and 15, so that’s the palette entries where the color goes too. Normally you don’t have to worry about switching bitdepths mid-game, but knowing how to read data like this is a useful debugging skill.

#include <string.h>
#include "toolbox.h"
#include "modes.h"

int main()
{
    int mode= 3;
    REG_DISPCNT= mode | DCNT_BG2;

    // Copy the data and palette to the right
    // addresses
    memcpy(vid_mem, modesBitmap, modesBitmapLen);
    memcpy(pal_bg_mem, modesPal, modesPalLen);

    while(1)
    {
        // Wait till VBlank before doing anything
        vid_vsync();

        // Check keys for mode change
        key_poll();
        if(key_hit(KEY_LEFT) && mode>3)
            mode--;
        else if(key_hit(KEY_RIGHT) && mode<5)
            mode++;

        // Change the mode
        REG_DISPCNT= mode | DCNT_BG2;
    }

    return 0;
}
mode3 screen Fig 5.7a: bm_modes in mode 3.
mode4 screen Fig 5.7b: bm_modes in mode 4.
mode5 screen Fig 5.7c: bm_modes in mode 5.
 

Conclusions

Now we’ve seen some of the basics of the GBA bitmap modes: the properties of modes 3, 4 and 5, page flipping, rudimentary drawing for mode 3 and one of the most important rules of VRAM interactions: you cannot write to VRAM in bytes. There is much more that can be said, of course. Bitmap graphics is a rich subject, but going into more detail right now may not be the best idea. For one, the bitmap modes are very rarely used in games anyway, but also because there are other things to talk about as well. Things like button input, which is what the next chapter is about.

This chapter also discussed a few things about handling data, a very important topic when you’re this close to the hardware. Datatypes matter, especially when accessing memory through pointers, and you need to be aware of the differences between them, and the opportunities and dangers of each. Even if you don’t remember every little detail in the data section, at least remember where to look when things go screwy.

Before continuing with further chapters, this may be a good time to do some experimenting with data: try changing the data arrays and see what happens. Look at the different data interpretations, different casts, and maybe some intentional errors as well, just to see what kinds of problems you might face at some point. It’s better to make mistakes early, while programs are still short and simple and you have less potential problems.

Or not, of course :P. Maybe it’s worth waiting a little longer with that; or at least until we’ve covered basic input, which allows for much more interesting things than just passive images.

6. The GBA buttons (a.k.a. keys)

Introduction

As you no doubt already know, the GBA has one 4-way directional pad (D-pad); two control buttons (Select and Start); two regular fire buttons (A and B) and two shoulder buttons (L and R), making a total of 10 keys. This is all you have in terms of user-GBA interaction, and for most purposes it is plenty. The principles of key-handling are pretty simple: you have one register with the keystates and you see which buttons are pressed based on whether its bits are set or cleared. I will cover this, but I’ll also give some more advanced functions that you will probably want to have at some point.

Keypad registers

The keypad register, REG_KEYINPUT

As said, the GBA has ten buttons, often referred to as keys. Their states can be found in the first 10 bits of the REG_KEYINPUT register at location 0400:0130h (a.k.a. REG_P1). The exact layout is shown below. I will refrain from giving a bit-by-bit description because it should be quite obvious. The names of the defined constants I use are “KEY_x”, where x is the name of the button, in caps.

REG_KEYINPUT @ 0400:0130h
F E D C B A 9 8 7 6 5 4 3 2 1 0
- L R down up left right start select B A

Checking whether a key is pressed (down) or not would be obvious, if it weren’t for one little detail: the bits are cleared when a key is down. So the default state of REG_KEYINPUT is 0x03FF, and not 0. As such, checking if key is down goes like this:

#define KEY_DOWN_NOW(key)  (~(REG_KEYINPUT) & key)

In case your bit-operation knowledge is a bit hazy (get it cleared up. Fast!), this first inverts REG_KEYINPUT to a more intuitive (and useful) ‘bit is set when down’ setting and then masks it with the key(s) you want to check. Note that key can in fact be a combination of multiple keys and the result will be the combination of keys that are actually down.

Key states are inverted

The key bits are low-active, meaning that they are cleared when a button is pressed and set when they’re not. This may be a little counter-intuitive, but that’s the way it is.

The key control register, REG_KEYCNT

Just about everything you will ever need in terms of key-handling can be done with REG_KEYINPUT. That said, you might like to know there is another key-register for some extra control. The register in question is REG_KEYCNT, the key control register. This register is used for keypad interrupts, much like REG_DISPSTAT was used for video interrupts. The layout is the same as for REG_KEYINPUT, except for the top two bits, see the table below. With REG_KEYCNT{14} you can enable the keypad interrupt. The conditions for raising this interrupt are determined by REG_KEYCNT{0-9}, which say what keys to watch out for and REG_KEYCNT{15}, which state the exact conditions. If this bit is clear, then any of the aforementioned keys will raise the interrupt; if set, then they must all be down for the interrupt to be raised. I wouldn’t be surprised if this is how you can reset most games by pressing Start+Select+B+A. Of course, to make use of this register you need to know how to work with interrupts first.


REG_KEYCNT @ 0400:0132h
F E D C B A 9 8 7 6 5 4 3 2 1 0
Op I - L R down up left right start select B A

bits name define description
0-9 keys KEY_x keys to check for raising a key interrupt.
EI KCNT_IRQ Enables keypad interrupt
F Op KCNT_OR, KCNT_AND Boolean operator used for determining whether to raise a key- interrupt or not. If clear, it uses an OR (raise if any of the keys of bits 0-9 are down); if set, it uses an AND (raise if all of those keys are down).

Beyond basic button states

While checking for the keystate with KEY_DOWN_NOW() is nice and simple, there are better and/or more preferable methods of key-state handling. I will discuss two (or three) of them here. First, synchronous keystates. This is just a fancy way of reading the key-state at a given point and using that variable, instead of repeated reads of REG_KEYINPUT when you process input. An outshoot of this is transitional states, where you track not only the current state, but also the previous one. This lets you test for changes in keystates, rather than just the keystates themselves.. Lastly, tribools: three-state variables (in this cases −1, 0 and +1) that can be used to simplify direction processing.

Synchronous and transitional key states

The use of KEY_DOWN_NOW() is a form of asynchronous key handling: you check the state at the time the code needs it. While it works, it’s not always the best approach. Firstly, it is less efficient in terms of code because the register is loaded and read every time it is necessary (it’s volatile, remember?). A secondary concern is that a simultaneous multi-button tap may not be registered as such because the code reading the button states are a little apart.

But those are just minor concerns; the main issue is that there’s just little you can really do with them. You can get the current state, but that’s it. As a simple example of why this is insufficient for games, consider (un)pausing a game. This is usually done by pressing Start, and then Start again for unpausing. That’s fine until you consider that the game runs faster than you can react (this is a basic fact of life; the only reason you can win games is because the game lets you. Deal), so the Start button will be down for multiple frames. With KEY_DOWN_NOW(), the game will pause and unpause during this time; the state of the game when you finally release the button is essentially random. Needless to say, this is a Bad Thing™.

Enter synchronous states. Simply read the state once, at the beginning of the frame for example, and use that as ‘the’ state for the whole frame. That takes care of the excess readings of REG_KEYINPUT, and potentially missed simultaneity. For tracking state changes, we also save the state of the previous frame. So at the very least, we need two variables and a function that updates them, and for good measure, some functions that check the states. Because these will be quite small, it makes sense to inline them as well.

// === (tonc_core.c) ==================================================
// Globals to hold the key state
u16 __key_curr=0, __key_prev=0;
// === (tonc_input.h) =================================================
extern u16 __key_curr, __key_prev;

#define KEY_A        0x0001
#define KEY_B        0x0002
#define KEY_SELECT   0x0004
#define KEY_START    0x0008
#define KEY_RIGHT    0x0010
#define KEY_LEFT     0x0020
#define KEY_UP       0x0040
#define KEY_DOWN     0x0080
#define KEY_R        0x0100
#define KEY_L        0x0200

#define KEY_MASK     0x03FF

// Polling function
INLINE void key_poll()
{
    __key_prev= __key_curr;
    __key_curr= ~REG_KEYINPUT & KEY_MASK;
}

// Basic state checks
INLINE u32 key_curr_state()         {   return __key_curr;          }
INLINE u32 key_prev_state()         {   return __key_prev;          }
INLINE u32 key_is_down(u32 key)     {   return  __key_curr & key;   }
INLINE u32 key_is_up(u32 key)       {   return ~__key_curr & key;   }
INLINE u32 key_was_down(u32 key)    {   return  __key_prev & key;   }
INLINE u32 key_was_up(u32 key)      {   return ~__key_prev & key;   }

The key states are stored in __key_curr and __key_prev. The function that updates them is key_poll(). Note that this function already inverts REG_KEYINPUT, so that the variables are active high, which makes later operations more intuitive. For example, to test whether A is currently down (pressed), just mask __key_curr with KEY_A, the bit for A. This is what key_is_down() does. While KEY_DOWN_NOW() gives (almost) the same answer, I would still recommend using key_is_down() instead.

Invert REG_KEYINPUT reads as soon as possible

The things that you might check the keystates for are simply easier in active-high settings. Therefore, it is a good idea to make the keystate variables work that way.

Transitional states

Back to the pause/unpause issue. The nasty behaviour KEY_DOWN_NOW() causes is known as key bounce. This is because the macro only checks the current state. What you need for proper (un)pausing is something that checks whether a key is going down, rather than just down: you need to check the transition. That’s where the previous state comes in. When a key is hit, i.e., the moment of it going down, it will be pressed in the current state, but not the one before. In other words, the keys that are ‘hit’ are down currently, and not before: __key_curr&~__key_prev. After that, checking for a particular key can be achieved with a simple mask as usual. This is done by key_hit().

That’s really all there is to it, and you can create similar functions to check for releases (before AND NOT now), if it is held (before AND now), et cetera. Again, it all seems so simple because the states were already inverted; when I first made these functions, I had a terrible time figuring out what the right bit-ops were because the active-low logic was throwing me off. Well okay, not really but it would have been easier if I had them inverted from the start.

// Transitional state checks.

// Key is changing state.
INLINE u32 key_transit(u32 key)
{   return ( __key_curr ^  __key_prev) & key;   }

// Key is held (down now and before).
INLINE u32 key_held(u32 key)
{   return ( __key_curr &  __key_prev) & key;  }

// Key is being hit (down now, but not before).
INLINE u32 key_hit(u32 key)
{   return ( __key_curr &~ __key_prev) & key;  }

Key is being released (up now but down before)
INLINE u32 key_released(u32 key)
{   return (~__key_curr &  __key_prev) & key;  }

Key tribool states

This is a little technique taken from the PA_Lib wiki. It isn’t so much about keys per se, but a shorthand in how you can use the functions, and you will have to make up for yourself whether what’s discussed in this subsection is right for you.

Imagine you have a game/demo/whatever in which you can move stuff around. To make a character move left and right, for example, you might do use something like this.

// variable x, speed dx
if(key_is_down(KEY_RIGHT))
    x += dx;
else if(key_is_down(KEY_LEFT))
    x -= dx;

Thing moves right, x increases; thing moves left, x decreases, simple enough. Works fine too. However, and this may just be my ifphobia acting up, it’s not very pretty code. So let’s see if we can find something smoother.

Take a look at what the code is actually doing. Depending on two choices, the variable is either increased (+), decreased (−), or unchanged (0). That’s a pretty good definition of a tribool, a variable with three possible states, in this case +1, 0 and −1. What I’m after is something that lets you use these states to do the following.

x += DX*key_tri_horz();

I suppose I could just wrap the ifs in this function, but I prefer to do it via bit operations. All I need to do for this is shift the bits for specific keys down, mask that with one, and subtract the results.

// === (tonc_core.h) ==================================================
// tribool: 1 if {plus} on, -1 if {minus} on, 0 if {plus}=={minus}
INLINE int bit_tribool(u32 x, int plus, int minus)
{   return ((x>>plus)&1) - ((x>>minus)&1);  }
// === (tonc_input.h) =================================================
enum eKeyIndex
{
    KI_A=0, KI_B, KI_SELECT, KI_START,
    KI_RIGHT, KI_LEFT, KI_UP, KI_DOWN,
    KI_R, KI_L, KI_MAX
};

// --- TRISTATES ---
INLINE int key_tri_horz()       // right/left : +/-
{   return bit_tribool(__key_curr, KI_RIGHT, KI_LEFT);  }

INLINE int key_tri_vert()       // down/up : +/-
{   return bit_tribool(__key_curr, KI_DOWN, KI_UP);     }

INLINE int key_tri_shoulder()   // R/L : +/-
{   return bit_tribool(__key_curr, KI_R, KI_L);         }

INLINE int key_tri_fire()       // B/A : -/+
{   return bit_tribool(__key_curr, KI_A, KI_B);         }

The inline function bit_tribool() creates a tribool value from any two bits in a number (register or otherwise). The rest of the functions listed here use the current keystate and the key-bits to create tribools for horizontal, vertical, shoulder and fire buttons; others can be creates with relative ease. These functions make the code look cleaner and are faster to boot. You will be seeing them quite often.

While the functions mentioned above only use __key_curr, it is easy to write code that uses other key-state types. For example, a right-left key_hit variant might look something like this:

// increase/decrease x on a right/left hit
x += DX*bit_tribool(key_hit(-1), KI_RIGHT, KI_LEFT);

It’s just a call to bit_tribool() with using key_hit() instead of __key_curr. In case you’re wondering what the “−1” is doing there, I just need it to get the full hit state. Remember that −1 is 0xFFFFFFFF in hex, in other words a full mask, which will be optimized out of the final code. You will see this use of tribools a couple of times as well.

A simple key demo

key_demo screenshot

Fig 6.1: key_demo screenshot, with L and B held.

The key_demo demo illustrates how these key functions can be used. It shows a mode 4 picture of a GBA (a 240x160 8bit bitmap); the colors change according to the button presses. The normal state is grey; when you press the key, it turns red; when you release it, it goes yellow; and as long as it’s held it’s green. Fig 6.1 shows this for the L and B buttons. Here’s the code that does the real work:

#include <string.h>

#include "toolbox.h"
#include "input.h"

#include "gba_pic.h"

#define BTN_PAL_ID  5
#define CLR_UP   RGB15(27,27,29)

int main()
{
    int ii;
    u32 btn;
    COLOR clr;
    int frame=0;

    memcpy(vid_mem, gba_picBitmap, gba_picBitmapLen);
    memcpy(pal_bg_mem, gba_picPal, gba_picPalLen);

    REG_DISPCNT= DCNT_MODE4 | DCNT_BG2;

    while(1)
    {
        vid_vsync();
        // slowing down polling to make the changes visible
        if((frame & 7) == 0)
            key_poll();
        // check state of each button
        for(ii=0; ii<KI_MAX; ii++)
        {
            clr=0;
            btn= 1<<ii;
            if(key_hit(btn))
                clr= CLR_RED;
            else if(key_released(btn))
                clr= CLR_YELLOW;
            else if(key_held(btn))
                clr= CLR_LIME;
            else
                clr= CLR_UP;
            pal_bg_mem[BTN_PAL_ID+ii]= clr;
        }
        frame++;
    }

    return 0;
}

BTN_PAL_ID is the starting index of the palette-part used for the buttons and CLR_UP is a shade of grey; the rest of the colors should be obvious. To make sure that you can actually see the changes in button colors I’m only polling the keys once every 8 frames. If I didn’t do that, you’ll hardly ever see a red or yellow button. (By the way, I don’t actually change the buttons’ colors, but only the palette color that that button’s pixels use; palette animation is a Good Thing™).

7. Sprite and background overview

Sprites and backgrounds introduction

Although you can make games based purely on the bitmap modes, you’ll find very few that do. The simple reason for this is that all graphics would be rendered by software. No matter how good your code is, that’s always going to be a slow process. Now, I’m not saying it can’t be done: there are several FPSs on the GBA (Wolfenstein and Doom for example). I am saying that unless you’re willing to optimize the crap out of your code, you’ll have a hard time doing it.

The vast majority uses the GBA’s hardware graphics, which come in the forms of sprites and tiled backgrounds (simply “background” or “bg” for short). As I said in the video introduction, a tiled background is composed of a matrix of tiles (hence the name) and each tile contains an index to an 8x8 pixel bitmap known as a tile. So what ends up on screen is a matrix of tiles. There are four of these backgrounds with sizes between 128x128 pixels (32x32 tiles) to 1024x1024 pixels (128x128 tiles). Sprites are smaller objects between 8x8 to 64x64 pixels in size. There are 128 of them and you can move them independently of each other. Like backgrounds, sprites are built out of tiles.

The hardware takes care of several other aspects of rendering besides mere raster blasting. For one thing, it uses color keying to exclude some pixels from showing up (i.e., these are transparent). Basically, if the tile’s pixel has a value of zero it is transparent. Furthermore, the hardware takes care of a number of other effects like flipping, alpha-blending and affine transformations like rotation and scaling.

The trick is setting up the process. There are three basic steps to be aware of: control, mapping and image data. The boundaries of these steps are a bit vague, but it helps to see it in this manner since it allows you to see sprites and backgrounds as two sides of the same coin. And unification is a Good Thing®. There are still differences, of course, but only in the details.

This page gives a broad overview of what I will talk about in the next couple of pages. Don’t worry if you don’t understand right away, that’s not really the point right now. Just let it seep into your brain, read the other pages and then you’ll see what I’m on about here.

Sprite and background control

The first step of rendering is control. Control covers things that act on the sprites or backgrounds as a whole, like activation of the things themselves, whether to use 16 or 256 color tiles, and effects like alpha-blending and transformations. First up is whether or not you want to use the things in the first place. This is done by setting the right bits in the display control register REG_DISPCNT. Once you’ve done that there are further control registers for backgrounds: the REG_BGxCNT registers (0400:0008h-0400:000Fh). For sprites there’s the Object Attribute Memory, or OAM, which can be found at 0700:0000h. Each of the 128 sprites has three so-called attributes (hence OAM) which covers both the control and mapping aspects of the sprites.

Sprite and background mapping

There’s a lot of grey area between control and mapping, but here goes. Mapping concerns everything about which tiles to use and where they go. As said, the screen appearance of both sprites and backgrounds are constructed of tiles, laid out side by side. You have to tell the GBA which tiles to blit to what position. Fig 7.1a-c (below) illustrates this. In fig 7.1b you see the tiles. Note that both sprites and backgrounds have their own set of tiles.

In fig 7.1c you see how these tiles are used. The background uses a tile-map, which works just like an ordinary paletted bitmap except that it’s a matrix of screenblock entries (with tile-indices) instead of pixels (containing color-indices). Excuse me, a what?!? Screenblock entry. Yes, I know the name is a bit silly. The thing is that you need keep a clear distinction between the entries in the map (the screenblock entries, SE for short) and the image-data (the actual tiles). Unfortunately, the term “tile” is often used for both. I’ll stick to tiles for the actual graphical information, and since the tile-map is stored in things called screenblocks, screenblock entries or SE for the map data. Anyway, each SE has its own tile-index. It also contains bits for horizontal and vertical flipping and, if it’s a 16-color background, an index for the palbank as well. In fig 7.1c, you only see the tile-index, though.

For sprites, it’s s a bit different, but the basic steps remain. You give one tile-index for the whole sprite; the GBA then figures out the other tiles to use by looking at the shape and size of the sprite and the sprite mapping-mode. I’ll explain what this means later; suffice to say that the mapping mode is either 1D or 2D, depending on REG_DISPCNT{6}. In this case, I’ve used 1D mapping, which states that the tiles that a sprite should use are consecutive. Like backgrounds, there’s additional flipping flags and palette-info for 16-color sprites. Unlike backgrounds, these work on the whole sprite, not just on one tile. Also, the component tiles of sprites are always adjoining, so you can see a sprite as a miniature tiled-background with some imagination.

What belongs to the mapping step as well is the affine transformation matrix, if any. With this 2x2 matrix you can rotate, scale or shear sprites or backgrounds. There seems to be a lot of confusion about how this works so I’ve written a detailed, mathematical description on how this thing works. Bottom line: the matrix maps from screen space to texture-space, and not the other way round. Though all the reference documents do state this in a roundabout way, almost every rotation-scale matrix I’ve seen so far is incorrect. If your code is based on PERN’s, chances are yours is too.

Example of both sprites and background
Fig 7.1a: 2 sprites on a background.
Tile usage
Fig 7.1c: tile usage by bgs and sprites. One tile per SE for bgs, and the top-left tile for sprites. Default tiles (with index 0 are omitted for clarity's sake.
The bg and sprite tiles
Fig 7.1b: background (above) and sprite (below) tiles.

Sprite and background image data

Image data is what the GBA actually uses to produce an image. This means two things: tiles and palettes.

Tiles

Sprites and backgrounds are composed of a matrix of smaller bitmaps called tiles. Your basic tile is an 8x8 bitmap. Tiles come in 4bpp (16 colors / 16 palettes) and 8bpp (256 colors / 1 palette) variants. In analogy to floating point numbers, I refer to these as s-tiles (single-size tile) and d-tiles (double-size tiles). An s-tile is 32 (20h) bytes long, a d-tile 64 (40h) bytes. The default type of tile is the 4bpp variant (the s-tile). If I talk about tiles without mentioning which type, it either doesn’t matter or it’s an s-tile. Just pay attention to the context.

There is sometimes a misunderstanding about what working in tiles really means. In tiled modes, VRAM is not a big bitmap out of which tiles are selected, but a collection of 8x8 pixel bitmaps (i.e., the tiles). It is important that you understand the differences between these two methods! Consider an 8x8 rectangle in a big bitmap, and an 8x8 tile. In the big bigmap, the data after the first 8 pixels contain the next 8 pixels of the same scanline; the next line of the ‘tile’ can be found further on. In tiled modes, the next scanline of the tile immediately follows the current line.

Basically, VRAM works as an 8×N·8 bitmap in the tiled modes. Because such a small width is impractical to work with, they’re usually presented as a wider bitmap anyway. An example is the VBA tile viewer, which displays char blocks as a 256x256 bitmap; I do something similar in fig 7.2a. It is important to remember that these do not accurately mimic the contents of VRAM; to reproduce the actual content of VRAM you’d need something like fig 7.2b, but, of course, no-one is insane enough to edit bitmaps in that manner. In all likelihood, you need a tool that can break up a bitmap into 8x8 chunks. Or restructure it to a bitmap with a width of 8 pixels, which in essence is the same thing.

As with all bitmaps, it is the programmer’s responsibility (that means you!) that the bit-depth of the tiles that sprites and backgrounds correspond to the bit-depth of the data in VRAM. If this is out of sync, something like fig 7.2a may appear as fig 7.2c. Something like this is likely to happen sooner or later, because all graphics need to be converted outside of the system before use; one misplaced conversion option is all it takes.

8 bpp tiles Fig 7.2a: 8bpp tiles.
8 bpp tiles as bitmap Fig 7.2b: 8bpp tiles as bitmap.
as before, but interpreted as 4 bpp Fig 7.2c: the data of fig 7.2a, interpreted as 4bpp data. If you see something like this (and you will), you now know why.

Tiled graphics considerations

Remember and understand the following points:

  1. The data of each tile are stored sequentially, with the next row of 8 pixels immediately following the previous row. VRAM is basically a big bitmap 8 pixels wide. Graphics converters should be able to convert bigger bitmaps into this format.
  2. As always, watch your bitdepth.

Tip for graphics converters

If you want to make your own conversion tools, here’s a little tip that’ll help you with tiles. Work in stages; do not go directly from a normal, linear bitmap to writing the data-file. Create a tiling function that takes a bitmap and arranges the tiles into a bitmap 1 tile wide and H tiles high. This can then be exported normally. If you allow for a variable tile-width (not hard-coding the 8-pixel width), you can use it for other purposes as well. For example, to create 16x16 sprites, first arrange with width=16, then with width=8.

Tile blocks (aka charblocks)

All the tiles are stored in charblocks. As much as I’d like them to be called tile-blocks because that’s what they’re blocks of, tradition has it that tiles are characters (not to be confused with the programming type of characters: an 8bit integer) and so the critters are called charblock. Each charblock is 16kb (4000h bytes) long, so there’s room for 512 (4000h/20h) s-tiles or 256 (4000h/40h) d-tiles. You can also consider charblocks to be matrices of tiles; 32x16 for s-tiles, 16x16 (or 32x8) for d-tiles. The whole 96kb of VRAM can be seen as 6 charblocks.

As said, there are 6 tile-blocks, that is 4 for backgrounds (0-3) and 2 for sprites (4-5). For tiled backgrounds, tile-counting starts at a given character base block (block for the character base, CBB for short), which are indicated by REG_BGxCNT{2-3}. Sprite tile-indexing always starts at the lower sprite block (block 4, starting at 0601:0000h).

It’d be nice if tile-indexing followed the same scheme for backgrounds and sprites, but it doesn’t. For sprites, numbering always follows s-tiles (20h offsets) even for d-tiles, but backgrounds stick to their indicated tile-size: 20h offsets in 4bpp mode, 40h offsets for 8bpp mode.

Bg vs sprite tile indexing

Sprites always have 32 bytes between tile indices, bg tile-indexing uses 32 or 64 byte offsets, depending on their set bitdepth.

Now, both regular backgrounds and sprites have 10 bits for tile indices. That means 1024 allowed indices. Since each charblock contains 512 s-tiles, you can access not only the base block, but also the one after that. And if your background is using d-tiles, you can actually access a total of four blocks! Now, since tiled backgrounds can start counting at any of the four background charblocks, you might be tempted to try to use the sprite charblocks (blocks 4 and 5) as well. On the emulators I’ve tested, this does indeed work. On a real GBA, however, it does not. This is one of the reasons why you need to test on real hardware. For more on this subject see the background tile subtleties and the cbb_demo.

Another thing you need to know about available charblocks is that in one of the bitmap modes, the bitmaps extend into the lower sprite block. For that reason, you can only use the higher sprite block (containing tiles 512 to 1023) in this case.

Thanks to the wonderful concept of typedefs, you can define types for tiles and charblocks so that you can quickly come up with the addresses of tiles by simple array-accesses. An alternative to this is using macros or inline functions to calculate the right addresses. In the end it hardly matters which method you choose, though. Of course, the typedef method allows the use of the sizeof operator, which can be quite handy when you need to copy a certain amount of tile. Also, struct-copies are faster than simple loops, and require less C-code too.

// tile 8x8@4bpp: 32bytes; 8 ints
typedef struct { u32 data[8];  } TILE, TILE4;
// d-tile: double-sized tile (8bpp)
typedef struct { u32 data[16]; } TILE8;
// tile block: 32x16 tiles, 16x16 d-tiles
typedef TILE  CHARBLOCK[512];
typedef TILE8 CHARBLOCK8[256];

#define tile_mem  ( (CHARBLOCK*)0x06000000)
#define tile8_mem ((CHARBLOCK8*)0x06000000)

//In code somewhere
TILE *ptr= &tile_mem[4][12];   // block 4 (== lower object block), tile 12

// Copy a tile from data to sprite-mem, tile 12
tile_mem[4][12] = *(TILE*)spriteData;

Palettes and tile colors

Sprites and backgrounds have separate palettes. The background palette goes first at 0500:0000h, immediately followed by the sprite palette (0500:0200h). Both palettes contain 256 entries of 15bit colors.

In 8-bit color mode, the pixel value in the tiles is palette-index for that pixel. In 4-bit color mode, the pixel value contains the lower nybble of the palette index; the high nybble is the palbank index, which can be found in either the sprite’s attributes, or the upper nybble of the tiles. If the pixel-value is 0, then that pixel won’t be rendered (i.e., will be transparent).

Because of 16-color mode and the transparency issue, it is essential that your bitmap editor leaves the palette intact. I know from personal experience that MS-Paint and the Visual C bitmap editor don’t, so you might want to use something else. Favorites among other GBA developers are Graphics Gale and GIMP. Of course, since I have my my own bitmap editor, I prefer to use that.

Summary

This is a short list of various attributes of sprites and backgrounds. It’s alright if you don’t understand it right away; I’ll explain in more detail in the following pages.

Subject Backgrounds Sprites
Number 4 (2 affine) 128 (32 affine)
Max size reg: 512x512
aff: 1024x1024
64x64
Control REG_BGxCNT OAM
Base tile block 0-3 4
Available tiles ids reg: 0-1023
aff: 0-255
modes 0-2: 0-1023
modes 3-5: 512-1023
Tile memory offsets Per tile size:
4bpp: start= base + id*32
8bpp: start= base + id*64
Always per 4bpp tile size:
start= base + id*32
Mapping reg: the full map is divided into map-blocks of 32×32 tegels. (banked map)
aff: one matrix of tegels, just like a normal bitmap (flat map)
If a sprite is m × n tiles in size:
1D mapping: the m*n successive tiles are used, starting at id
2D mapping: tile-blocks are 32×32 matrices; the used tiles are the n columns of the m rows of the matrix, starting at id.
Flipping Each tile can be flipped individually Flips the whole sprite
Palette 0500:0000h 0500:0200h

What’s in a name?

Well, since you are a programmer you should know the answer: plenty. If you disagree, visit the How To Write Unmaintanable Code website and look at a number of their entries. My naming scheme is a bit different from that of the GBA community. I don’t do this just because I feel like being contrary. I find some of the conventional names are incomplete, misleading and ambiguous. I feel little need, at least at present, to follow tradition simply because everyone else does. But you still need to know the traditional names, simply because everyone else does. So here’s a list of differences in names.

Subject Traditional Tonc
Sprite and bg image data tiles tiles
Tile-map entries tiles (can you feel the confusion?) screenblock entries / SE
Matrix for transformations Rot/Scale matrix affine matrix / P
Sprite types ?? vs Rot/Scale regular vs affine
Background types text vs rot regular vs affine
Depository for sprite tiles (0601:0000) OAMData (i.e., not the real OAM, which is at 0700:0000) tile_mem_obj
OAM (0700:0000) OAMData or OAMMem oam_mem

8. Regular sprites

Sprite introduction

a metroid. Fig 8.1. Metroid. Rawr.

According to Webster’s, a sprite is “an imaginary being or spirit, as a fairy, elf, or goblin”. Right, glad that’s cleared up. For games, though, when referring to a sprite one is usually talking about “a [small] animated object that can move freely from the background” (PERN). Primary examples are game characters, but status objects like scores and life bars are often sprites as well. Fig 8.1 on the right shows a sprite of everybody’s favorite vampire jellyfish, the metroid. I will use this sprite in the demo at the end of this chapter.

Sprites are a little trickier to use than a bitmap background, but not by much. You just have to pay a little more attention to what you’re doing. For starters, the graphics have to be grouped into 8×8 tiles; make sure your graphics converter can do that. Aside from the obvious actions such as enabling sprites in the display control and loading up the graphics and palette, you also have to set-up the attributes of the sprites correctly in OAM. Miss any of these steps and you’ll see nothing. These things and more will be covered in this chapter.

Essential Sprite Steps

There are 3 things that you have to do right to get sprites to show up:

  • Load the graphics and palette into object VRAM and palette.
  • Set attributes in OAM to use the appropriate tiles and set the right size.
  • Switch on objects in REG_DISPCNT, and set the mapping mode there too.

Sprites aren’t objects

Or something like that. I know it sounds weird, but the more I think about it, the more I realize that sprites and objects shouldn’t be considered interchangeable. The term ‘object’, is a hardware feature, controlled in OAM. Right now, I think that ‘sprite’ is more of a conceptual term, and should be reserved for actors, like playing characters, monsters, bullets, etc. These can in fact be built up of multiple hardware objects, or even use a background.

You could also thing of it in this way: objects are system entities linked to the console itself, and sprites are game entities, living in the game world. The difference may be subtle, but an important one.

This is merely my opinion, and I can’t say how right I am in this. Tonc still switches back and forth between the two words because it’s too late to do anything about it now. Mea culpa. I’d love to hear the opinion of others on the subject, so feel free to speak your mind if you want.

Sprite image data and mapping mode

Like I said in the sprite and background overview, sprites are composed of a number of 8×8-pixel mini-bitmaps called tiles, which come in two types: 4bpp (s-tiles, 32 bytes long) and 8bpp (d-tiles, 64 bytes long). The tiles available for sprites are stored in object VRAM, or OVRAM for short. OVRAM is 32 KiB long and is mapped out by the last two charblocks of tile_mem, which are also known as the lower (block 4, starting at 0601:0000h) and higher (block 5, 0601:4000h) sprite blocks. Counting always starts at the lower sprite-block and is always done in 32 byte offsets, meaning that sprite-tile #1 is at 0601:0020h, no matter what the bit depth is (see table 8.1). With 4000h bytes per charblock, a quick calculation will show you that there are 512 tiles in each charblock, giving a total range of 1024. However, since the bitmap modes extend into the lower sprite block, you can only use the higher sprite block (containing tiles 512 to 1023) in modes 3-5.

It may seem that calculating those tile addresses can be annoying, and it would be if you had to do it manually. That’s why I have mapped the whole of VRAM with a charblock/tile matrix called tile_mem, as discussed in the overview. Need tile #123 of OVRAM? That’d be tile_mem[4][123]. Need its address? Use the address operator: &tile_mem[4][123]. Quick, easy, safe.

Also, don’t forget that the sprites have their own palette which starts at 0500:0200h (right after the background palette). If you are certain you’ve loaded your tiles correctly but nothing shows up, it’s possible you filled the wrong palette.

Table 8.1: tile counting for sprites, always per 32 bytes. (You can use odd numbers for 8bpp tiles, but be sure you fill the VRAM accordingly.)
memory 0601:00000020 00400060 00800100 ...
4bpp tile 0 1 2 3 4 5  
8bpp tile 0 2 4 

Bitmap modes and Object VRAM

Only the higher sprite block is available for sprites in modes 3-5. Indexing still starts at the lower block, though, so the tile range is 512-1023.

The sprite mapping mode

Sprites aren’t limited to a single tile. In fact, most sprites are larger (see Table 8.3 for a list of the available sizes for GBA sprites). Larger sprites simply use multiple tiles, but this may present a problem. For backgrounds, you choose each tile explicitly with the tile-map. In the case of sprites, you have two options: 1D and 2D mapping. The default is 2D mapping, and you can switch to 1D mapping by setting REG_DISPCNT{6}.

How do these work? Consider the example sprite of fig 8.2a, showing the metroid of fig 8.1 divided into tiles. In 2D mapping, you’re interpreting the sprite charblocks as one big bitmap of 256×256 pixels and the sprite a rectangle out of that bitmap (still divided into tiles, of course). In this case, each tile-row of a sprite is at a 32-tile offset. This is shown in fig 8.2b. On the other hand, you can also consider the charblocks as one big array of tiles, and the tiles of every sprite are consecutive. This is shown in fig 8.2c. The numbers in fig 8.2a show the difference between 1D and 2D mapping. Assuming we start at tile 0, the red and cyan numbers follow 2D and 1D mapping, respectively.

From a GBA-programming viewpoint, it is easier to use 1D mapping, as you don’t have to worry about the offset of each tile-row when storing sprites. However, actually creating sprites is easier in 2D mode. I mean, do you really want to edit a bitmap tile by tile? That’s what I thought. Of course, it should be the exporting tool’s job to convert your sprites from 2D to 1D mapping for you. You can do this with Usenti too.

a metroid divided into tiles Fig 8.2a: zoomed out version of Fig 8.1, divided into tiles; colored numbers indicate mapping mode: red for 2D, cyan for 1D.
2d mapping Fig 8.2b: how fig 8.2a should be stored in memory when using 2D mapping.

1d mapping Fig 8.2c: how fig 8.2a should be stored in memory when using 1D mapping.

Object data conversion via CLI

Some command-line interfaces can tile bitmaps for use with objects (and tilemaps). In some cases, they can also convert images with multiple sprite-frames to a set of object tiles in 1D object mapping mode. If foo.bmp is a 64×16 bitmap with 4 16×16 objects, here’s how you can convert it to 8×8 4bpp tiles using gfx2gba and grit (flags for 1D mapping are given in brackets)

# gfx2gba
# 4x 16x16@4 objects (C array; u8 foo_Bitmap[], u16 master_Palette[]; foo.raw.c, master.pal.c)
    gfx2gba -fsrc -c16 -t8 [-T32] foo.bmp
# grit
# 4x 16x16@4 objects (C array; u32 fooTiles[], u16 fooPal[]; foo.c, foo.h)
    grit foo.bmp -gB4 [-Mw 2 -Mh 2]

Two notes on the 1D mapping flags here. First, gfx2gba can only meta-tile (-T) square objects; for something like 16×8 objects you’d need to do the 1D mapping yourself. Second, grit’s meta-tiling flags (-Mw and -Mh) can be anything, and use tile units, not pixels.

Size units: tiles vs pixels

The default unit for bitmap dimensions is of course the pixel, but in tiled graphics it is sometimes more useful to use tiles as the basic unit, that is, the pixel size divided by 8. This is especially true for backgrounds. In most cases the context will suffice to indicate which one is meant, but at times I will denote the units with a ‘p’ for pixels or ‘t’ for tiles. For example, a 64x64p sprite is the same as a 8×8t sprite.

Sprite control: Object Attribute Memory

Much unlike in the bitmap modes, you don’t have to draw the sprites yourself: the GBA has special hardware that does it for you. This can get the sprites on screen faster than you could ever achieve programmatically. There are still limits, though: there is a limit to the amount of sprite pixels you can cram in one scanline. About 960, if the fora are anything to go by.

So you don’t have to draw the sprites yourself; however, you do need to tell the GBA how you want them. This is what the Object Attribute Memory –OAM for short– is for. This starts at address 0700:0000h and is 1024 bytes long. You can find two types of structures in OAM: the OBJ_ATTR struct for regular sprite attributes, and the OBJ_AFFINE struct containing the transformation data. The definitions of these structures can be found below. Note that names may vary from site to site.

typedef struct tagOBJ_ATTR
{
    u16 attr0;
    u16 attr1;
    u16 attr2;
    s16 fill;
} ALIGN4 OBJ_ATTR;

typedef struct OBJ_AFFINE
{
    u16 fill0[3];
    s16 pa;
    u16 fill1[3];
    s16 pb;
    u16 fill2[3];
    s16 pc;
    u16 fill3[3];
    s16 pd;
} ALIGN4 OBJ_AFFINE;

There are a few interesting things about these structures. First, you see a lot of filler fields. Second, if you would take 4 OBJ_ATTR structures and lay them over one OBJ_AFFINE structure, as done in table 8.2, you’d see that the fillers of one would exactly cover the data of the other, and vice versa. This is no coincidence: OAM is in fact a weave of OBJ_ATTRs and OBJ_AFFINEs. Why would Nintendo use a weave instead of simply having one section of attributes and one for transform data? That’s a good question and deserves a good answer. When I have one, I’ll tell you (I’m guessing it’s a data-alignment thing). Also, note that the elements of the OBJ_AFFINE are signed shorts. I’ve gone through a world of hurt with the obj_aff code because I used u16 instead of s16. With 1024 bytes at our disposal, we have room for 128 OBJ_ATTR structures and 32 OBJ_AFFINEs. The rest of this file will explain regular sprites that only use OBJ_ATTR. I want to give the affine transformation matrix the full mathematical treatment it deserves and will save affine sprites for later.

Table 8.2: memory interlace of OBJ_ATTR and OBJ_AFFINE structures.
mem (u16)03478bcf
OBJ_ATTR 0 1 2 0 1 2  0 1 2 0 1 2 
OBJ_AFFINE  pa pb  pc pd

Force alignment on OBJ_ATTRs

As of devkitARM r19, there are new rules on struct alignments, which means that structs may not always be word aligned, and in the case of OBJ_ATTR structs (and others), means that struct copies like the one in oam_update() later on, will not only be slow, they may actually break. For that reason, I will force word-alignment on many of my structs with ALIGN4, which is a macro for __attribute__((aligned(4))). For more on this, see the section on data alignment.

Object attributes: OBJ_ATTR

The basic control for every sprite is the OBJ_ATTR structure. It consists of three 16-bit attributes for such qualities as size, shape, position, base tile and more. Each of the three attributes is covered below.

Attribute 0

The first attribute controls a great deal, but the most important parts are for the y coordinate, and the shape of the sprite. Also important are whether or not the sprite is transformable (an affine sprite), and whether the tiles are considered to have a bit depth of 4 (16 colors, 16 sub-palettes) or 8 (256 colors / 1 palette).

OBJ_ATTR.attr0
F EDCB A9 8 7 6 5 4 3 2 1 0
Sh CM Mos GM OM Y
bitsnamedefinedescription
0-7Y ATTR0_Y# Y coordinate. Marks the top of the sprite.
8-9OM ATTR0_REG, ATTR0_AFF, ATTR0_HIDE, ATTR0_AFF_DBL. ATTR0_MODE# (Affine) object mode. Use to hide the sprite or govern affine mode.
  • 00. Normal rendering.
  • 01. Sprite is an affine sprite, using affine matrix specified by attr1{9-D}
  • 10. Disables rendering (hides the sprite)
  • 11. Affine sprite using double rendering area. See affine sprites for more.
A-BGM ATTR0_BLEND, ATTR0_WIN. ATTR0_GFX# Gfx mode. Flags for special effects.
  • 00. Normal rendering.
  • 01. Enables alpha blending. Covered here.
  • 10. Object is part of the object window. The sprite itself isn't rendered, but serves as a mask for bgs and other sprites. (I think, haven't used it yet)
  • 11. Forbidden.
CMos ATTR0_MOSAIC Enables mosaic effect. Covered here.
DCM ATTR0_4BPP, ATTR0_8BPP Color mode. 16 colors (4bpp) if cleared; 256 colors (8bpp) if set.
E-FSh ATTR0_SQUARE, ATTR0_WIDE, ATTR0_TALL. ATTR0_SHAPE# Sprite shape. This and the sprite's size (attr1{E-F}) determines the sprite's real size, see table 8.4.

Two extra notes on attribute 0. First, attr0 contains the y coordinate; attr1 contains the x coordinate. For some reason I keep messing these two up; if you find your sprite is moving left when it should be moving up, this may be why. Second, the affine and gfx modes aren’t always named as such. In particular, attr0{9} is simply referred to as the double-size flag, even though it only works in that capacity if bit 8 is set too. If it isn’t, then it hides the sprite. I think that it’s actually taken out of the object rendering stage entirely leaving more time for the others, but I’m not 100% sure of that.

Table 8.3: GBA sprite sizes
shape\size 00 01 10 11
008×8 16×16 32×32 64×64
0116×8 32×8 32×16 64×32
108×16 8×32 16×32 32×64

Attribute 1

The primary parts of this attribute are the x coordinate and the size of the sprite. The role of bits 9 to 13 depend on whether or not this is a affine sprite (determined by attr0{8}). If it is, these bits specify which of the 32 OBJ_AFFINEs should be used. If not, they hold flipping flags.

OBJ_ATTR.attr1
F EDCB A 98 7 6 5 4 3 2 1 0
Sz VF HF - X
- AID -
bitsnamedefinedescription
0-8X ATTR1_X# X coordinate. Marks left of the sprite.
9-DAID ATTR1_AFF# Affine index. Specifies the OAM_AFF_ENTY this sprite uses. Valid only if the affine flag (attr0{8}) is set.
C-DHF, VF ATTR1_HFLIP, ATTR1_VFLIP. ATTR1_FLIP# Horizontal/vertical flipping flags. Used only if the affine flag (attr0) is clear; otherwise they're part of the affine index.
E-FSz ATTR1_SIZE# Sprite size. Kinda. Together with the shape bits (attr0{E-F}) these determine the sprite's real size, see table 8.3.

I’ll say it here too: attr0 contains y, attr1 contains x. Note that bits 12 and 13 have a double role as either flipping flags or affine index. And if you are wondering if you can still flip affine sprites, the answer is yes: simply use negative scales in the matrix.

Attribute 2

This attribute tells the GBA which tiles to display and its background priority. If it’s a 4bpp sprite, this is also the place to say what sub-palette should be used.

OBJ_ATTR.attr2
F E D CB A9 8 7 6 5 4 3 2 1 0
PB Pr TID
bitsname description
0-9TID ATTR2_ID# Base tile index of sprite. Note that in bitmap modes, this must be 512 or higher.
A-BPr ATTR2_PRIO# Priority. Higher priorities are drawn first (and therefore can be covered by later sprites and backgrounds). Sprites cover backgrounds of the same priority, and for sprites of the same priority, the higher OBJ_ATTRs are drawn first.
C-FPB ATTR2_PALBANK# Palette bank to use when in 16-color mode. Has no effect if the color mode flag (attr0{C}) is set.

Attribute 3

There is no attribute 3. Although the OBJ_ATTR struct does have a fourth halfword, this is only a filler. The memory in that filler actually belongs to the OBJ_AFFINEs. Nobody is to mistreat attr3 in any way … if there’s any affine sprite active.

OAM double buffering

You could write all your sprite data directly to the OAM at 0700:0000h, but that might not always be the best move. If it’s done during VDraw there’s the possibility of tearing. Even worse, you might change the sprite’s tile-index in mid-render so that the top is in one animation frame and the bottom is in another. Not a pretty sight. Actually, this isn’t something to worry about because you can’t update OAM during VDraw; it’s locked then. What’s often done is creating a separate buffer of OAM entries (also known as the object shadow) that can be modified at any time, and then copy that to the real OAM during VBlank. Here’s my take on this.

OBJ_ATTR obj_buffer[128];
OBJ_AFFINE *const obj_aff_buffer= (OBJ_AFFINE*)obj_buffer;

I’m using 128 now, but I suppose you could use a lower number if you don’t use all the sprites. Anyway, now you have a double buffer for both OBJ_ATTR and OBJ_AFFINE data, which is available at any given time. Just make sure you copy it to the real OAM when the time is right.

Bitfield macros (OAM or otherwise)

Setting and clearing individual bits is easy, but sometimes it’s not too convenient to do it all yourself. This is especially true for field of bits like positions or palette banks, which would involve long statements with masks and shifts if you want to do it nicely. To improve on this a little bit, I have a number of macros that may shorted the amount of actual code. There are essentially three classes of macros here, but before I go into that, I have to explain a little bit more about the hashed (foo‘#”) defines in the attribute lists above.

The hash means that for each of these, there will be three #defines with foo as their roots: foo_MASK, foo_SHIFT, and foo(_n). These give the bitmask, bitshift and a bitfield set macro for the corresponding type.

For example, the one attached to the tile index, ATTR2_ID#. The tile index field has 10 bits and starts at bit 0. The corresponding defines therefore are:

// The 'ATTR2_ID#' from the attr2 list means these 3 #defines exist
#define ATTR2_ID_MASK       0x03FF    
#define ATTR2_ID_SHIFT           0    
#define ATTR2_ID(n)        ((n)<<ATTR2_ID_SHIFT)

Most GBA libraries out there have #defines like these, albeit with different names. The actual macro isn’t 100% safe because it does no range checking, but it’s short and sweet. Now, as far as Tonc’s text is concerned, every time you see the hash in the define list for a register, it’ll have these three #defines to go with that name.

I also have a second batch of macros you can use for setting and getting specific fields, which use the mask and shift names explained above. I’ll admit the macros look horrible, but I assure you they make sense and can come in handy.

// bit field set and get routines
#define BF_PREP(x, name)         ( ((x)<<name##_SHIFT)& name##_MASK  )
#define BF_GET(x, name)          ( ((x) & name##_MASK)>> name##_SHIFT )
#define BF_SET(y, x, name)       (y = ((y)&~name##_MASK) | BF_PREP(x,name) )

#define BF_PREP2(x, name)        ( (x) & name##_MASK )
#define BF_GET2(y, name)         ( (y) & name##_MASK )
#define BF_SET2(y, x, name)      (y = ((y)&~name##_MASK) | BF_PREP2(x, name) )

Well, I did warn you. The name argument here is the foo from before. The preprocessor concatenation operator is use to create the full mask and shift names. Again using the tile-index as an example, these macros expand to the following:

// Create bitfield:
attr2 |= BF_PREP(id, ATTR0_SHAPE);
// becomes:
attr2 |= (id<<ATTR2_ID_SHIFT) & ATTR2_ID_MASK;

// Retrieve bitfield:
id= BF_GET(attr2, ATTR2_ID);
// becomes:
id= (attr2 & ATTR2_ID_MASK)>>ATTR2_ID_SHIFT;

// Insert bitfield:
BF_SET(attr2, id, ATTR2_ID);
// becomes:
attr2= (attr&~ATTR2_ID_MASK) | ((id<<ATTR2_ID_SHIFT) & ATTR2_ID_MASK);

BF_PREP() can be used to prepare a bitfield for later insertion or comparison. BF_GET() gets a bitfield from a value, and BF_SET() sets a bitfield in a variable, without disturbing the rest of the bits. This is basically how bitfields normally work, except that true bitfields cannot be combined with OR and such.

The macros with a ‘2’ in their names work in a similar way, but do not apply shifts. These can be useful when you have already shifted #defines like ATTR0_WIDE, which can’t use the other ones.

// Insert pre-shifted bitfield:
// BF_SET2(attr0, ATTR0_WIDE, ATTR0_SHAPE);
attr0= (attr0&~ATTR0_SHAPE_MASK) | (id & ATTR0_SHAPE_MASK);

Note that none of these three have anything GBA specific in them; they can be used on any platform.

Finally, what I call my build macros. These piece together the various bit-flags into a single number in an orderly fashion, similar to HAM’s tool macros. I haven’t used them that often yet, and I’m not forcing you to, but on occasion they are useful to have around especially near initialization time.

// Attribute 0
#define ATTR0_BUILD(y, shape, bpp, mode, mos, bld, win)             \
(                                                                   \
    ((y)&255) | (((mode)&3)<<8) | (((bld)&1)<<10) | (((win)&1)<<11) \
    | (((mos)&1)<<12) | (((bpp)&8)<<10) | (((shape)&3)<<14)         \
)

// Attribute 1, regular sprites
#define ATTR1_BUILD_R(x, size, hflip, vflip)         \
( ((x)&511) | (((hflip)&1)<<12) | (((vflip)&1)<<13) | (((size)&3)<<14) )

// Attribute 1, affine sprites
#define ATTR1_BUILD_A(x, size, aff_id)               \
( ((x)&511) | (((aff_id)&31)<<9) | (((size)&3)<<14) )

// Attribute 2
#define ATTR2_BUILD(id, pbank, prio)                 \
( ((id)&0x3FF) | (((pbank)&15)<<12) | (((prio)&3)<<10) )

Instead of doing ORring the bitflags together yourself, you can use these and perhaps save some typing. The order of arguments maybe annoying to remember for some, and the amount of safety checking may be a bit excessive (gee, ya think?!?), but if the numbers you give them are constants the operations are done at compile time so that’s okay, and sometimes they really can be helpful. Or not :P. Like I said, I’m not forcing you to use them; if you think they’re wretched pieces of code (and I admit they are) and don’t want to taint your program with them, that’s fine.

Note that with the exception of bpp, the arguments are all shifted by the macros, meaning that you should not use the #define flags from the lists, just small values like you’d use if they were separate variables rather than bits in a variable.

Demo time

Now, to actually use the bloody things. The code below is part of the obj_demo. It is the most complex I’ve shown yet, but if you take it one step at a time you’ll be fine. Essentially, this demo places the tiles of a boxed metroid in the VRAM allotted for objects and then lets you screw around with various OBJ_ATTR bits like position and flipping flags. The controls are as follows:

  • Control Pad
    Moves the sprite. Note that if you move far enough off-screen, it’ll come up on the other side.
  • A and B Buttons
    Flip the sprite horizontally or vertically, respectively.
  • Select Button
    Makes it glow. Well, makes it palette-swap, actually. Handy for damage-flashing.
  • Start Button
    Toggles between 1D and 2D mapping modes. Fig 8.2b and fig 8.2c should explain what happens. Since the sprite is in 1D mode, there’s really not much to see when you switch to 2D mapping, but I had a few buttons to spare, so I thought why not.
  • L and R Buttons
    Decreases or increase the starting tile, respectively. Again, I had a few keys to spare.
// Excerpt from toolbox.h

void oam_init(OBJ_ATTR *obj, uint count);
void oam_copy(OBJ_ATTR *dst, const OBJ_ATTR *src, uint count);

INLINE OBJ_ATTR *obj_set_attr(OBJ_ATTR *obj, u16 a0, u16 a1, u16 a2);
INLINE void obj_set_pos(OBJ_ATTR *obj, int x, int y);
INLINE void obj_hide(OBJ_ATTR *oatr);
INLINE void obj_unhide(OBJ_ATTR *obj, u16 mode);

// === INLINES ========================================================

//! Set the attributes of an object.
INLINE OBJ_ATTR *obj_set_attr(OBJ_ATTR *obj, u16 a0, u16 a1, u16 a2)
{
    obj->attr0= a0; obj->attr1= a1; obj->attr2= a2;
    return obj;
}

//! Set the position of \a obj
INLINE void obj_set_pos(OBJ_ATTR *obj, int x, int y)
{
    BF_SET(obj->attr0, y, ATTR0_Y);
    BF_SET(obj->attr1, x, ATTR1_X);
}

//! Hide an object.
INLINE void obj_hide(OBJ_ATTR *obj)
{   BF_SET2(obj->attr0, ATTR0_HIDE, ATTR0_MODE);        }

//! Unhide an object.
INLINE void obj_unhide(OBJ_ATTR *obj, u16 mode)
{   BF_SET2(obj->attr0, mode, ATTR0_MODE);          }
// toolbox.c

void oam_init(OBJ_ATTR *obj, uint count)
{
    u32 nn= count;
    u32 *dst= (u32*)obj;

    // Hide each object
    while(nn--)
    {
        *dst++= ATTR0_HIDE;
        *dst++= 0;
    }
    // init oam
    oam_copy(oam_mem, obj, count);
}

void oam_copy(OBJ_ATTR *dst, const OBJ_ATTR *src, uint count)
{

// NOTE: while struct-copying is the Right Thing to do here, 
//   there's a strange bug in DKP that sometimes makes it not work
//   If you see problems, just use the word-copy version.
#if 1
    while(count--)
        *dst++ = *src++;
#else
    u32 *dstw= (u32*)dst, *srcw= (u32*)src;
    while(count--)
    {
        *dstw++ = *srcw++;
        *dstw++ = *srcw++;
    }
#endif

}

This is the basic utility code for the demo, and contains most of the things you’d actually like to have functions for. Note that the inline functions make good use of the bitfield macros shown earlier; if I hadn’t done that, the code would be a good deal longer.

Another point that I need to make is that if I’d put everything into toolbox.h, the file would be pretty big, around 700 lines or so. And with future demos, it’d be a lot longer. With that in mind, I’ve started redistributing the contents a little: all the types go in types.h, everything to do with the memory map goes into memmap.h, all the register defines go into memdef.h and the input inlines and macros can be found in input.h. The rest is still in toolbox.h, but will find themselves redistributed in the end as well.

The two functions in toolbox.c need some more clarification as well I guess. In oam_init() I cast the objects to a word pointer and use that for setting things; again, this is simply because it’s a lot faster. Because it may be used to initialixe something other than the real OAM, I copy the initialized buffer to OAM just in case.

The other point concerns something of a very specific bug in the optimizer of the current compiler (devkitARM r19b). I expect this to be fixed in a later addition and the basic version here should work, but just in case it isn’t, set the #if expression to 0 if you see OAM get corrupted. If you must know, the problem seems to be struct copying of OBJ_ATTRs in a for loop. Yes, it’s that specific. Even though struct copying is legal and fast if they’re word aligned, it seems GCC gets confused with 8-byte blocks in loops and uses memcpy() for each struct anyway, something that wouldn’t work on OAM. Oh well.

#include <string.h>
#include "toolbox.h"
#include "metr.h"


OBJ_ATTR obj_buffer[128];
OBJ_AFFINE *obj_aff_buffer= (OBJ_AFFINE*)obj_buffer;

void obj_test()
{
    int x= 96, y= 32;
    u32 tid= 0, pb= 0;      // (3) tile id, pal-bank
    OBJ_ATTR *metr= &obj_buffer[0];

    obj_set_attr(metr, 
        ATTR0_SQUARE,              // Square, regular sprite
        ATTR1_SIZE_64,              // 64x64p, 
        ATTR2_PALBANK(pb) | tid);   // palbank 0, tile 0

    // (4) position sprite (redundant here; the _real_ position
    // is set further down
    obj_set_pos(metr, x, y);

    while(1)
    {
        vid_vsync();
        key_poll();

        // (5) Do various interesting things
        // move left/right
        x += 2*key_tri_horz();
        // move up/down
        y += 2*key_tri_vert();

        // increment/decrement starting tile with R/L
        tid += bit_tribool(key_hit(-1), KI_R, KI_L);

        // flip
        if(key_hit(KEY_A))  // horizontally
            metr->attr1 ^= ATTR1_HFLIP;
        if(key_hit(KEY_B))  // vertically
            metr->attr1 ^= ATTR1_VFLIP;

        // make it glow (via palette swapping)
        pb= key_is_down(KEY_SELECT) ? 1 : 0;

        // toggle mapping mode
        if(key_hit(KEY_START))
            REG_DISPCNT ^= DCNT_OBJ_1D;

        // Hey look, it's one of them build macros!
        metr->attr2= ATTR2_BUILD(tid, pb, 0);
        obj_set_pos(metr, x, y);

        oam_copy(oam_mem, obj_buffer, 1);   // (6) Update OAM (only one now)
    }
}

int main()
{
    // (1) Places the tiles of a 4bpp boxed metroid sprite 
    //   into LOW obj memory (cbb == 4)
    memcpy(&tile_mem[4][0], metr_boxTiles, metr_boxTilesLen);
    memcpy(pal_obj_mem, metrPal, metrPalLen);

    // (2) Initialize all sprites
    oam_init(obj_buffer, 128);
    REG_DISPCNT= DCNT_OBJ | DCNT_OBJ_1D;

    obj_test();

    while(1);

    return 0;
}

Setting up sprites

Before any sprites show up, there are three things you have to do, although not necessarily in this order. They are: copying sprite graphics to VRAM, setting up OAM to use these graphics, and enabling sprites in the display control, REG_DISPCNT.

Display control

Starting with the last one, you enable sprites by setting bit 12 of REG_DISPCNT. Usually you’ll also want to use 1D mapping, so set bit 6 as well. This is done at point (2) of the code.

Hiding all sprites

The other step performed here is a call to oam_init(). This isn’t strictly necessary, but a good idea nonetheless. What oam_init() does is hide all the sprites. Why is this a good idea? Well, because a fully zeroed out OAM does not mean the sprites are invisible. If you check the attributes you’ll see that this will mean that they’re all 8×8-pixel sprites, using tile 0 for their graphics, located at (0,0). If the first tile isn’t empty, you’ll start with 128 versions of that tile in the top-left corner, which looks rather strange. So, make sure they’re all invisible first. The demo also comes with obj_hide() and obj_unhide() functions, although they aren’t used here.

Loading sprite graphics

The first thing to do (point (1)) is to store the sprite graphics in object VRAM. As I’ve already said a few times now, these graphics should be stored as 8×8-pixel tiles, not as a flat bitmap. For example, my sprite here is 64×64p in size, so to store it I’ve had to convert this to 8×8 separate tiles first. If you do not do this, your sprites will look very strange indeed.

Exactly where you put these tiles is actually not all that relevant (apart from the obvious, like mapping mode, and tile alignment, of course). Object VRAM works as a texture pool and has nothing to do with the screen directly. You store the tiles that you want to be available there, and it is by manipulating the OAM attributes that the system knows which tiles you want to use and where you want them. There is no reason why sprite 0 couldn’t start at tile 42, or why multiple sprites couldn’t use the same tiles. This is also why OAMData, which is sometimes used for object VRAM, is such a misnomer: object VRAM has nothing to do with OAM. Nothing! If your headers use this name for 0601:0000, or even 0601:4000, change it. Please. And be careful where you put things in the bitmap modes, as you can’t use tiles 0-511 there.

As I said, loading the sprites happens at point (1) in the code. If you paid attention to the overview, you’ll remember that tile_mem[][] is a two dimensional array, mapping charblocks and 4-bit tiles. You’ll also remember that object VRAM is charblocks 4 and 5, so &tile_mem[4][0] points to the first tile in object VRAM. So I’m loading my boxed metroid into the first 64 tiles of object VRAM.

I am also loading its palette into the sprite palette. That’s sprite palette (0500:0200), not background palette. Load it to the wrong place and you won’t see anything.

Finding tile addresses

Use tile_mem or a macro to find the addresses to copy your tiles too, it’s much more readable and maintainable than calculating them manually. You should not have any hard-coded VRAM addresses in your code, ever.

OAMData

Headers from other sites sometimes #define OAMData as part of VRAM. It is not. Rename it.

Setting attributes

Lastly, I’ll set up one OBJ_ATTR so that it actually uses the metroid tiles. This is done at point (3), using the obj_set_attr() inline function. All it does is three assignments to the attributes of the first argument, by the way, nothing spectacular. This just saves typing doing it this way rather than three separate statements. With this particular call, I tell this sprite that it’s a 64×64 pixel (8×8 tile) sprite, and its starting tile is tid, which is 0. This means that it’ll use the 64 tiles, starting at tile 0.

Note that the sprite I’m setting is actually part of the OAM buffer, not the real OAM. This means that even after I set the attributes there, nothing happens yet. To finalize the sprite I need to update the real OAM, which is done by a call to oam_copy() (point (6)). This carries two arguments: an index and a count denoting how many sprites to update, and which sprite to start at. I also have obj_copy(), which only copies attributes 0, 1 and 2, but not 3! This is necessary when you start using affine sprites, which may be copied incorrectly otherwise.

The previous steps are enough to get the metroid sprite on-screen. The story doesn’t end there, of course. Here are a few things that you can do with sprites.

Sprite positioning

The first order of business is usually to place it at some position on screen, or even off screen. To do this you have to update the bits for the y and x positions in attributes 0 and 1, respectively. One mistake I often seem to make is fill x into attr0 and y into attr1, when it should be the other way around. If your sprite moves strangely, this might be why.

Note that these coordinates mark the top-left of the sprite. Also, the number of bits for the coordinates means we have 512 possible x-values and 256 y-values. The coordinate ranges wrap around, so you could also say that these are signed integers, with the ranges x ∈ [-256, 255] and y ∈ [-128, 127]. Yes, that would make the highest y-value smaller than the height of the screen, but thanks to the wrapping it all works out. Well, almost. Anyway, thanks to the 2s-complement nature of integers, simply masking the x and y values by 0x01FF and 0x00FF, respectively, will give proper 9- and 8-bit signed values. You can do this manually, or use the obj_set_pos() function used at point (4).

You might see code that clears the lower bits of the attributes and then directly ORRs in x and y. This is not a good idea, because negative values are actually represented by upper half of a datatype’s range. −1 for example is all bits set (0xFFFFFFFF). Without masking off the higher bits, negative values would overwrite the rest of the attribute bits, which would be bad.

Mask your coordinates

If you’re making a sprite positioning function or use someone else’s make sure you mask off the bits in x and y before you insert them into the attributes. If not, negative values will overwrite the whole attribute.

This is bad

obj->attr0= (obj->attr0 &~ 0x00FF) | (y);

This is good:

obj->attr0= (obj->attr0 &~ 0x00FF) | (y & 0x00FF);

Position variables and using tribools

Instead of using an OBJ_ATTR to store the sprite’s position, it is better to keep them in separate variables, in this case x and y. This avoids having to mask coordinate fields all the time, but more importantly, the positions can extend beyond the size of the screen. As most game worlds aren’t restricted to a single screen, this is an important point. Then, when the time is right, these are fed to oam_set_pos() to update the sprite.

Also, note the use of my tribool key functions to update the positions. Input processing often follows a pattern of “key X pressed: increment, key opposite of Y pressed, decrement” The tribool functions bring that kind of code down from four lines to one, which makes the code easier to read (once you get over the initial hurdle). For example, key_tri_horz() returns +1 if ‘right’ is pressed, −1 if ‘left’ is pressed, and 0 if neither or both are pressed. key_tri_vert() does something similar for vertical movement and the line with bit_tribool() function makes a variant using key_hit() and R and L to increment or decrement the tile index.

Other attrs

Sprite coordinates are only two of the many sprite attributes that can be controlled with via specific OAM bits, even while the sprite is already active. Some of the obvious ones are flipping or mirroring it, which can be done using A and B here. Or, if you’re using a 4bpp sprite, you can swap palettes so that all the colors change. Pressing Select in the demo switches from palette bank 0 to 1, which happens to have a grey to white gradient. Toggling between these palette banks quickly can make the sprite flash. You could also change the priorities in which the sprites are rendered, or toggle alpha blending, although I haven’t done those things here.

Now, these things don’t really change the overall image of the sprite. What you should realize though is that it is possible to do that. As I’ve already noted before, it’s not true that the contents of VRAM are the sprite, rather that a sprite uses parts of VRAM to show something, anything, on screen. You could, for example, change the starting tile tid that the sprite uses, which in this case can be done using L and R. Not only is this legal, it’s the standard practice for animation (although you can also overwrite VRAM for that – resetting the tile index is just faster). Understanding this is one of the points of moving from a user to a developer perspective: the user only sees the surface; the coder looks below it and sees what’s really going on.

And that’s it for regular sprites. Using multiple sprites isn’t much different – seen one, seen them all. Basic animation shouldn’t be problematic either, until you run out of VRAM to put them in. There are still a few regions left untouched like blending and mosaic, but I’ll deal with those later.

9. Regular tiled backgrounds

Tilemap introduction

Tilemaps are the bread and butter for the GBA. Almost every commercial GBA game makes use of tile modes, with the bitmap modes seen only in 3D-like games that use ray-tracing. Everything else uses tiled graphics.

The reason why tilemaps are so popular is that they’re implemented in hardware and require less space than bitmap graphics. Consider fig 9.1a. This is a 512 by 256 image, which even at 8bpp would take up 128 KiB of VRAM, and we simply don’t have that. If you were to make one big bitmap of a normal level in a game, you can easily get up to 1000×1000 pixels, which is just not practical. And then there’s the matter of scrolling through the level, which means updating all pixels each frame. Even when your scrolling code is fully optimized that’d take quite a bit of time.

Now, notice that there are many repeated elements in this image. The bitmap seems to be divided into groups of 16×16 pixels. These are the tiles. The list of unique tiles is the tileset, which is given in fig 9.1b. As you can see, there are only 16 unique tiles making up the image. To create the image from these tiles, we need a tilemap. The image is divided into a matrix of tiles. Each element in the matrix has a tile index which indicates which tile should be rendered there; the tilemap can be seen in fig 9.1c.

Suppose both the tileset and map used 8-bit entries, the sizes are 16×(16×16) = 4096 bytes for the tileset and 32×16 = 512 bytes for the tilemap. So that’s 4.5 KiB for the whole scene rather than the 128 KiB we had before; a size reduction of a factor of 28.

Brinstar map Fig 9.1a: image on screen.
The tile mapping process. Using the tileset of fig 9.1b, and the tile map of fig 9.1c, the end-result is fig 9.1a.
(meta)tileset for the map
Fig 9.1b: the tile set.
Superimposed tile-map
Fig 9.1c: the tile map (with the proper tiles as a backdrop).

That’s basically how tilemaps work. You don’t define the whole image, but group pixels together into tiles and describe the image in terms of those groups. In the fig 9.1, the tiles were 16×16 pixels, so the tilemap is 256 times smaller than the bitmap. The unique tiles are in the tileset, which can (and usually will) be larger than the tilemap. The size of the tileset can vary: if the bitmap is highly variable, you’ll probably have many unique tiles; if the graphics are nicely aligned to tile boundaries already (as it is here), the tileset will be small. This is why tile-engines often have a distinct look to them.

Tilemaps for the GBA

In the tiled video-modes (0, 1 and 2) you can have up to four backgrounds that display tilemaps. The size of the maps is set by the control registers and can be between 128×128 and 1024×1024 pixels. The size of each tile is always 8×8 pixels, so fig 9.1 isn’t quite the way it’d work on the GBA. Because accessing the tilemaps is done in units of tiles, the map sizes correspond to 16×16 to 128×128 tiles.

Both the tiles and tilemaps are stored in VRAM, which is divided into charblocks and screenblocks. The tileset is stored in the charblocks and the tilemap goes into the screenblocks. In the common vernacular, the word “tile” is used for both the graphical tiles and the entries of the tilemaps. Because this is somewhat confusing, I’ll use the term screen entry (SE for short) as the items in the screenblocks (i.e., the map entries) and restrict tiles to the tileset.

64 KiB of VRAM is set aside for tilemaps (0600:0000h-0600:FFFFh). This is used for both screenblocks and charblocks. You can choose which ones to use freely through the control registers, but be careful that they can overlap (see table 9.1). Each screenblock is 2048 (800h) bytes long, giving 32 screenblocks in total. All but the smallest backgrounds use multiple screenblocks for the full tilemap. Each charblock is 16 KiB (4000h bytes) long, giving four blocks overall.

Table 9.1: charblock and screenblock overlap.
Memory 0600:0000 0600:4000 0600:8000 0600:C000
charblock 0 1 2 3
screenblock 0 7 8 15 16 23 24 31

Tiles vs ‘tiles’

Both the entries of the tilemap and the data in the tileset are often referred to as ‘tiles’, which can make conversation confusing. I reserve the term ‘tile’ for the graphics, and ‘screen(block) entry’ or ‘map entry’ for the map’s contents.

Charblocks vs screenblocks

Charblocks and screenblocks use the same addresses in memory. Each charblock overlaps eight screenblocks. When loading data, make sure the tiles themselves don’t overwrite the map, or vice versa.

Size was one of the benefits of using tilemaps, speed was another. The rendering of tilemaps in done in hardware and if you’ve ever played PC games in hardware and software modes, you’ll know that hardware is good. Another nice point is that scrolling is done in hardware too. Instead of redrawing the whole scene, you just have to enter some coordinates in the right registers.

As I said in the overview, there are three stages to setting up a tiled background: control, mapping and image-data. I’ve already covered most of the image-data in the overview, as well as some of the control and mapping parts that are shared by sprites and backgrounds alike; this chapter covers only things specific to backgrounds in general and regular backgrounds in particular. I’m assuming you’ve read the overview.

Essential tilemap steps

  • Load the graphics: tiles into charblocks and colors in the background palette.
  • Load a map into one or more screenblocks.
  • Switch to the right mode in REG_DISPCNT and activate a background.
  • Initialize that background’s control register to use the right CBB, SBB and bitdepth.

Background control

Background types

Just like sprites, there are two types of tiled backgrounds: regular and affine; these are also known as text and rotation backgrounds, respectively. The type of the background depends of the video mode (see table 9.2). At their cores, both regular and affine backgrounds work the same way: you have tiles, a tile-map and a few control registers. But that’s where the similarity ends. Affine backgrounds use more and different registers than regular ones, and even the maps are formatted differently. This page only covers the regular backgrounds. I’ll leave the affine ones till after the page on the affine matrix.

Table 9.2: video modes and background type
mode BG0 BG1 BG2 BG3
0 reg reg reg reg
1 reg reg aff -
2 - - aff aff

Control registers

All backgrounds have 3 primary control registers. The primary control register is REG_BGxCNT, where x indicates the backgrounds 0 through 3. This register is where you say what the size of the tilemap is, and which charblock and screenblock it uses. The other two are the scrolling registers, REG_BGxHOFS and REG_BGxVOFS.

Each of these is a 16-bit register. REG_BG0CNT can be found at 0400:0008, with the other controls right behind it. The offsets are paired by background, forming coordinate pairs. These start at 0400:0010

Table 9.3: Background register addresses
Register length address
REG_BGxCNT 2 0400:0008h + 2·x
REG_BGxHOFS 2 0400:0010h + 4·x
REG_BGxVOFS 2 0400:0012h + 4·x

The description of REG_BGxCNT can be found below. Most of it is pretty standard, except for the size: there are actually two lists of possible sizes; one for regular maps and one for affine maps. The both use the same bits you may have to be careful that you’re using the right #defines.

REG_BGxCNT @ 0400:0008 + 2x
F ED C B A 9 8 765 43 21 0
Sz Wr SBB CM Mos - CBB Pr
bitsnamedefinedescription
0-1Pr BG_PRIO# Priority. Determines drawing order of backgrounds.
2-3CBB BG_CBB# Character Base Block. Sets the charblock that serves as the base for character/tile indexing. Values: 0-3.
6 Mos BG_MOSAIC Mosaic flag. Enables mosaic effect.
7 CM BG_4BPP, BG_8BPP Color Mode. 16 colors (4bpp) if cleared; 256 colors (8bpp) if set.
8-CSBB BG_SBB# Screen Base Block. Sets the screenblock that serves as the base for screen-entry/map indexing. Values: 0-31.
D Wr BG_WRAP Affine Wrapping flag. If set, affine background wrap around at their edges. Has no effect on regular backgrounds as they wrap around by default.
E-FSz BG_SIZE#, see below Background Size. Regular and affine backgrounds have different sizes available to them. The sizes, in tiles and in pixels, can be found in table 9.4.
Table 9.4a: regular bg sizes
Sz-flag define (tiles)(pixels)
00 BG_REG_32x32 32×32 256×256
01 BG_REG_64x32 64×32 512×256
10 BG_REG_32x64 32×64 256×512
11 BG_REG_64x64 64×64 512×512
Table 9.4b: affine bg sizes
Sz-flag define (tiles) (pixels)
00 BG_AFF_16x16 16×16 128×128
01 BG_AFF_32x32 32×32 256×256
10 BG_AFF_64x64 64×64 512×512
11 BG_AFF_128x128128×128 1024×1024

Each background has two 16-bit scrolling registers to offset the rendering (REG_BGxHOFS and REG_BGxVOFS). There are a number of interesting points about these. First, because regular backgrounds wrap around, the values are essentially modulo mapsize. This is not really relevant at the moment, but you can use this to your benefit once you get to more advanced tilemaps. Second, these registers are write-only! This is a little annoying, as it means that you can’t update the position by simply doing REG_BG0HOFS++ and the like.

And now the third part, which may be the most important, namely what the values actually do. The simplest way of looking at them is that they give the coordinates of the screen on the map. Read that again, carefully: it’s the position of the screen on the map. It is not the position of the map on the screen, which is how sprites work. The difference is only a minus sign, but even something as small as a sign change can wreak havoc on your calculations.

map-ofs-a
Fig 9.2: Scrolling offset dx sets is the position of the screen on the map. In this case, dx = (192, 64).

So, if you increase the scrolling values, you move the screen to the right, which corresponds to the map moving left on the screen. In mathematical terms, if you have map position p and screen position q, then the following is true:

(9.1) q + d x = p q = p d x

Direction of offset registers

The offset registers REG_BGxHOFS and REG_BGxVOFS indicate which map location is mapped to the top-left of the screen, meaning positive offsets scroll the map left and up. Watch your minus signs.

Offset registers are write only

The offset registers are write-only! That means that direct arithmetic like += will not work.

Useful types and #defines

Tonc’s code has several useful extra types and macros that can make life a little easier.

// === Additional types (tonc_types.h) ================================

//! Screen entry conceptual typedef
typedef u16 SCR_ENTRY;

//! Affine parameter struct for backgrounds, covered later
typedef struct BG_AFFINE
{
    s16 pa, pb;
    s16 pc, pd;
    s32 dx, dy;
} ALIGN4 BG_AFFINE;

//! Regular map offsets
typedef struct BG_POINT
{
    s16 x, y;
} ALIGN4 BG_POINT;

//! Screenblock struct
typedef SCR_ENTRY   SCREENBLOCK[1024];


// === Memory map #defines (tonc_memmap.h) ============================

//! Screen-entry mapping: se_mem[y][x] is SBB y, entry x
#define se_mem          ((SCREENBLOCK*)MEM_VRAM)

//! BG control register array: REG_BGCNT[x] is REG_BGxCNT
#define REG_BGCNT      ((vu16*)(REG_BASE+0x0008))

//! BG offset array: REG_BG_OFS[n].x/.y is REG_BGnHOFS / REG_BGnVOFS
#define REG_BG_OFS      ((BG_POINT*)(REG_BASE+0x0010))

//! BG affine params array
#define REG_BG_AFFINE   ((BG_AFFINE*)(REG_BASE+0x0000))

Strictly speaking, making a SCREEN_ENTRY typedef is not necessary, but makes its use clearer. se_mem works much like tile_mem: it maps out VRAM into screenblocks screen-entries, making finding a specific entry easier. The other typedefs are used to map out arrays for the background registers. For example, REG_BGCNT is an array that maps out all REG_BGxCNT registers. REG_BGCNT[0] is REG_BG0CNT, etc. The BG_POINT and BG_AFFINE types are used in similar fashions. Note that REG_BG_OFS still covers the same registers as REG_BGxHOFS and REG_BGxVOFS do, and the write-only-ness of them has not magically disappeared. The same goes for REG_BG_AFFINE, but that discussion will be saved for another time.

In theory, it is also useful create a sort of background API, with a struct with the temporaries for map positioning and functions for initializing and updating the registers and maps. However, most of tonc’s demos are not complex enough to warrant these things. With the types above, manipulating the necessary items is already simplified enough for now.

Regular background tile-maps

The screenblocks form a matrix of screen entries that describe the full image on the screen. In the example of fig 9.1, the tilemap entries just contained the tile index. The GBA screen entries bahave a little differently.

For regular tilemaps, each screen entry is 16-bits long. Besides the tile index, it contains flipping flags and a palette bank index for 4bpp / 16-color tiles. The exact layout can be found in “Screen entry format” below. The affine screen entries are only 8 bits wide and just contain an 8-bit tile index.

Screen entry format for regular backgrounds
F E D CBA9 8 7 6 5 4 3 2 1 0
PB VF HF TID
bitsnamedefinedescription
0-9TID SE_ID# Tile-index of the SE.
A-BHF, VF SE_HFLIP, SE_VFLIP. SE_FLIP# Horizontal/vertical flipping flags.
C-FPB SE_PALBANK# Palette bank to use when in 16-color mode. Has no effect for 256-color bgs (REG_BGxCNT{6} is set).

Map layout

VRAM contains 32 screenblocks to store the tilemaps in. Each screenblock is 800h bytes long, so you can fit 32×32 screen entries into it, which equals one 256×256 pixel map. The bigger maps simply use more than one screenblock. The screenblock index set in REG_BGxCNT is the screen base block which indicates the start of the tilemap.

Now, suppose you have a tilemap that’s tw×th tiles/SEs in size. You might expect that the screen entry at tile-coordinates (txty) could be found at SE-number n = tx+ty·tw, because that’s how matrices always work, right? Well, you’d be wrong. At least, you’d be partially wrong.

Within each screenblock the equation works, but the bigger backgrounds don’t simply use multiple screenblocks, they’re actually accessed as four separate maps. How this works can be seen in table 9.5: each numbered block is a contingent block in memory. This means that to get the SE-index you have to find out which screenblock you are in and then find the SE-number inside that screenblock.

Table 9.5: screenblock layout of regular backgrounds.
32×3264×3232×6464×64
0
01
0
1
01
23

This kind of nesting problem isn’t as hard as it looks. We know how many tiles fit in a screenblock, so to get the SBB-coordinates, all we have to do divide the tile-coords by the SBB width and height: sbx=tx/32 and sby=ty/32. The SBB-number can then be found with the standard matrix→array formula. To find the in-SBB SE-number, we have to use tx%32 and ty%32 to find the in-SBB coordinates, and then again the conversion from 2D coords to a single element. This is to be offset by the SBB-number tiles the size of an SBB to find the final number. The final form would be:

//! Get the screen entry index for a tile-coord pair
//  And yes, the div and mods will be converted by the compiler
uint se_index(uint tx, uint ty, uint pitch)
{
    uint sbb= (ty/32)*(pitch/32) + (tx/32);
    return sbb*1024 + (ty%32)*32 + tx%32;
}

The general formula is left as an exercise for the reader – one that is well worth the effort, in my view. This kind of process crops up in a number of places, like getting the offset for bitmap coordinates in tiles, and tile coords in 1D object mapping.

If all those operations make you queasy, there’s also a faster version specifically for a 2×2 arrangement. It starts with calculating the number as if it’s a 32×32t map. This will be incorrect for a 64t wide map, which we can correct for by adding 0x0400−0x20 (i.e., tiles/block − tiles per row). We need another full block correction is the size is 64×64t.

//! Get the screen entry index for a tile-coord pair.
/*! This is the fast (and possibly unsafe) way.
*   \param bgcnt    Control flags for this background (to find its size)
*/

uint se_index_fast(uint tx, uint ty, u16 bgcnt)
{
    uint n= tx + ty*32;
    if(tx >= 32)
        n += 0x03E0;
    if(ty >= 32 && (bgcnt&BG_REG_64x64)==BG_REG_64x64)
        n += 0x0400;
    return n;
}

I would like to remind you that n here is the SE-number, not the address. Since the size of a regular SE is 2 bytes, you need to multiply n by 2 for the address. (Unless, of course, you have a pointer/array of u16s, in which case n will work fine.) Also, this works for regular backgrounds only; affine backgrounds use a linear map structure, which makes this extra work unnecessary there. By the way, both the screen-entry and map layouts are different for affine backgrounds. For their formats, see the map format section of the affine background page.

Background tile subtleties

There are two additional things you need to be aware of when using tiles for tile-maps. The first concerns tile-numbering. For sprites, numbering went according to 4-bit tiles (s-tiles); for 8-bit tiles (d-tiles) you’d have use multiples of 2 (a bit like u16 addresses are always multiples of 2 in memory). In tile-maps, however, d-tiles are numbered by the d-tile. To put it in other words, for sprites, using index id indicates the same tile for both 4 and 8-bit tiles, namely the one that starts at id·20h. For tile-maps, however, it starts at id·20h for 4-bit tiles, but at id·40h for 8-bit tiles.

Table 9.6: tile counting for backgrounds, sticks to its bit-depth.
memory offset000h020h 040h060h 080h100h ...
4bpp tile 0 1 2 3 4 5 ...
8bpp tile 0 1 2...

The second concerns, well, also tile-numbering, but more how many tiles you can use. Each map entry for regular backgrounds has 10 bits for a tile index, so you can use up to 1024 tiles. However, a quick calculation shows that a charblock contains 4000h/20h= 512 s-tiles, or 4000h/40h= 256 d-tiles. So what’s the deal here? Well, the charblock index you set in REG_BGxCNT is actually only the block where tile-counting starts: its character base block. You can use the ones after it as well. Cool, huh? But wait, if you can access subsequent charblocks as well; does this mean that, if you set the base charblock to 3, you can use the sprite blocks (which are basically blocks 4 and 5) as well?

The answer is: yes. And NO!

Emulators from the early 2000s allow you to do this. However, a real GBA doesn’t. It does output something, though: the screen-entry will be used as tile-data itself, but in a manner that simply defies explanation. Trust me on this one, okay? Of the current tonc demos, this is one of the times that VBA gets it wrong.

Available tiles

For both 4bpp and 8bpp regular bgs, you can access 1024 tiles. The only caveat here is that you cannot access the tiles in the object charblocks even if the index would call for it.

Another thing you may be wondering is if you can use a particular screenblock that is within a currently used charblock. For example, is it allowed to have a background use charblock 0 and screenblock 1. Again, yes you can do this. This can be useful since you’re not likely to fill an entire charblock, so using its later screenblocks for your map data is a good idea. (A sign of True Hackerdom would be if you manage to use the same data for both tiles and SEs and still get a meaningful image (this last part is important). If you have done this, please let me know.)

Tilemap data conversion via CLI

A converter that can tile images (for objects), can also create a tileset for tilemaps, although there will likely be many redundant tiles. A few converters can also reduce the tileset to only the unique tiles, and provide the tilemap that goes with it. The Brinstar bitmap from fig 9.1 is a 512×256 image, which could be tiled to a 64×32 map with a 4bpp tileset reduced for uniqueness in tiles, including palette info and mirroring.

# gfx2gba
# (C array; u8 foo_Tiles[], u16 foo_Map[], 
# u16 master_Palette[]; foo.raw.c, foo.map.c, master.pal.c)
    gfx2gba -fsrc -c16 -t8 -m foo.bmp
# grit
# (C array; u32 fooTiles[], u16 fooMap[], u16 fooPal[]; foo.c, foo.h)
    grit foo.bmp -gB4 -mRtpf

Two notes on gfx2gba: First, it merges the palette to a single 16-color array, rearranging it in the process. Second, while it lists metamapping options in the readme, it actually doesn’t give a metamap and meta-tileset, it just formats the map into different blocks.

Tilemap demos

There are four demos in this chapter. The first one is brin_demo, which is very, very short and shows the basic steps of tile loading and scrolling. The next ones are called sbb_reg and cbb_demo, which are tech demos, illustrating the layout of multiple screenblocks and how tile indexing is done on 4bpp and 8bpp backgrounds. In both these cases, the map data is created manually because it’s more convenient to do so here, but using map-data created by map editors really isn’t that different.

Essential tilemap steps: brin_demo

As I’ve been using a 512×256 part of Brinstar throughout this chapter, I thought I might as well use it for a demo.

There are a few map editors out there that you can use. Two good ones are Nessie’s MapEd or Mappy, both of which have a number of interesting features. I have my own map editor, mirach, but it’s just a very basic thing. Some tutorials may point you to GBAMapEditor. Do not use this editor as it’s pretty buggy, leaving out half of the tilemaps sometimes. Tilemaps can be troublesome enough for beginners without having to worry about whether the map data is faulty.

In this cause, however, I haven’t used any editor at all. Some of the graphics converters can convert to a tileset+tilemap – it’s not the standard method, but for small maps it may well be easier. In this case I’ve used Usenti to do it, but grit and gfx2gba work just as well. Note that because the map here is 64×32 tiles, which requires splitting into screenblocks. In Usenti this is called the ‘sbb’ layout, in grit it’s ‘-mLs’ and for gfx2gba you’d use ‘-mm 32’ … I think. In any case, after a conversion you’d have a palette, a tileset and a tilemap.


Fig 9.3a: brin_demo palette.
const unsigned short brinMap[2048]=
{
    // Map row 0
    0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x3001,0x3002,
    0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,
    0x3001,0x3002,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,
    0x3001,0x3002,0x0000,0x0000,0x3001,0x3002,0x0000,0x0000,

    // Map row 1
    0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x3003,0x3004,
    0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,
    0x3003,0x3004,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,
    0x3003,0x3004,0x0000,0x0000,0x3003,0x3004,0x0000,0x0000,

    // Map row 2
    0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,0x0000,
    0x3001,0x3002,0x3005,0x3006,0x3007,0x3008,
    // ... etc

Fig 9.3b: brin_demo tileset.

In fig 9.3 you can see the full palette, the tileset and part of the map. Note that the tileset of fig 9.3b is not the same as that of fig 9.1b because the former uses 8×8 tiles while the latter used 16×16 tiles. Note also that the screen entries you see here are either 0 (i.e., the empty tile) or of the form 0x3xxx. The high nybble indicates the palette bank, in this case three. If you’d look to the palette (fig 9.3a) you’d see that this gives bluish colors.

Now on to using these data. Remember the essential steps here:

  • Load the graphics: tiles into charblocks and colors in the background palette.
  • Load a map into one or more screenblocks.
  • Switch to the right mode in REG_DISPCNT and activate a background.
  • Initialize that background’s control register to use the right CBB, SBB and bitdepth.

If you do it correctly, you should have something showing on screen. If not, go to the tile/map/memory viewers of your emulator; they’ll usually give you a good idea where the problem is. A common one is having a mismatch between the CBB and SBB in REG_BGxCNT and where you put the data, which most likely would leave you with an empty map or empty tileset.

The full code of brin_demo is given below. The three calls to memcpy() load up the palette, tileset and tilemap. For some reason, probably related to where the NES and 8-bit Game Boy put screenblocks in video memory, it’s become conventional to place the maps in the last screenblocks on GBA as well. In this case, that’s 30 rather than 31 because we need two blocks for a 64×32t map. For the scrolling part, I’m using two variables to store and update the positions because the scrolling registers are write-only. I’m starting at (192, 64) here because that’s what I used for the scrolling picture of fig 9.2 earlier.

#include <string.h>

#include "toolbox.h"
#include "input.h"
#include "brin.h"

int main()
{
    // Load palette
    memcpy(pal_bg_mem, brinPal, brinPalLen);
    // Load tiles into CBB 0
    memcpy(&tile_mem[0][0], brinTiles, brinTilesLen);
    // Load map into SBB 30
    memcpy(&se_mem[30][0], brinMap, brinMapLen);

    // set up BG0 for a 4bpp 64x32t map, using
    //   using charblock 0 and screenblock 31
    REG_BG0CNT= BG_CBB(0) | BG_SBB(30) | BG_4BPP | BG_REG_64x32;
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    // Scroll around some
    int x= 192, y= 64;
    while(1)
    {
        vid_vsync();
        key_poll();

        x += key_tri_horz();
        y += key_tri_vert();

        REG_BG0HOFS= x;
        REG_BG0VOFS= y;
    }

    return 0;
}

Fig 9.4a: brin_demo at dx=(192, 64).

Fig 9.4b: brin_demo at dx=(0, 0).

Interlude: Fast-copying of non sbb-prepared maps

This is not exactly required knowledge, but should make for an interesting read. In this demo I use a multi-sbb map that was already prepared for that. The converter made sure that the left block of the map came before the right block. If this weren’t the case then you couldn’t load the whole map in one go because the second row of the left block would use the first row of the right block and so on (see fig 9.5).


Fig 9.5 brin_demo without blocking out into SBB's first.

There are few simple and slow ways and one simple and fast way of copying a non sbb-prepared map to a multiple screenblocks. The slow way would be to perform a double loop to go row by row of each screenblock. The fast way is through struct-copies and pointer arithmetic, like this:

typedef struct { u32 data[8]; } BLOCK;

int iy;
BLOCK *src= (BLOCK*)brinMap;
BLOCK *dst0= (BLOCK*)se_mem[30];
BLOCK *dst1= (BLOCK*)se_mem[31];

for(iy=0; iy<32; iy++)
{
    // Copy row iy of the left half
   *dst0++= *src++;     *dst0++= *src++;

     // Copy row iy of the right half
   *dst1++= *src++;     *dst1++= *src++;
}

A BLOCK struct-copy takes care of half a row, so two takes care of a whole screenblock row (yes, you could define BLOCK as a 16-word struct, but that wouldn’t work out anymore. Trust me). At that point, the src pointer has arrived at the right half of the map, so we copy the next row into the right-hand side destination, dst1. When done with that, src points to the second row of the left side. Now do this for all 32 lines. Huzzah for struct-copies, and pointers!

A screenblock demo

The second demo, sbb_reg, uses a 64×64t background to indicate how multiple screenblocks are used for bigger maps in more detail. While the brin_demo used a multi-sbb map as well, it wasn’t easy to see what’s what because the map was irregular; this demo uses a very simple tileset so you can clearly see the screenblock boundaries. It’ll also show how you can use the REG_BG_OFS registers for scrolling rather than REG_BGxHOFS and REG_BGxVOFS.

#include "toolbox.h"
#include "input.h"

#define CBB_0  0
#define SBB_0 28

#define CROSS_TX 15
#define CROSS_TY 10

BG_POINT bg0_pt= { 0, 0 };
SCR_ENTRY *bg0_map= se_mem[SBB_0];


uint se_index(uint tx, uint ty, uint pitch)
{
    uint sbb= ((tx>>5)+(ty>>5)*(pitch>>5));
    return sbb*1024 + ((tx&31)+(ty&31)*32);
}

void init_map()
{
    int ii, jj;

    // initialize a background
    REG_BG0CNT= BG_CBB(CBB_0) | BG_SBB(SBB_0) | BG_REG_64x64;
    REG_BG0HOFS= 0;
    REG_BG0VOFS= 0;

    // (1) create the tiles: basic tile and a cross
    const TILE tiles[2]=
    {
        {{0x11111111, 0x01111111, 0x01111111, 0x01111111,
          0x01111111, 0x01111111, 0x01111111, 0x00000001}},
        {{0x00000000, 0x00100100, 0x01100110, 0x00011000,
          0x00011000, 0x01100110, 0x00100100, 0x00000000}},
    };
    tile_mem[CBB_0][0]= tiles[0];
    tile_mem[CBB_0][1]= tiles[1];

    // (2) create a palette
    pal_bg_bank[0][1]= RGB15(31,  0,  0);
    pal_bg_bank[1][1]= RGB15( 0, 31,  0);
    pal_bg_bank[2][1]= RGB15( 0,  0, 31);
    pal_bg_bank[3][1]= RGB15(16, 16, 16);

    // (3) Create a map: four contingent blocks of 
    //   0x0000, 0x1000, 0x2000, 0x3000.
    SCR_ENTRY *pse= bg0_map;
    for(ii=0; ii<4; ii++)
        for(jj=0; jj<32*32; jj++)
            *pse++= SE_PALBANK(ii) | 0;
}

int main()
{
    init_map();
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0 | DCNT_OBJ;

    u32 tx, ty, se_curr, se_prev= CROSS_TY*32+CROSS_TX;

    bg0_map[se_prev]++; // initial position of cross
    while(1)
    {
        vid_vsync();

        key_poll();

        // (4) Moving around
        bg0_pt.x += key_tri_horz();
        bg0_pt.y += key_tri_vert();

        // (5) Testing se_index 
        // If all goes well the cross should be around the center of
        // the screen at all times.
        tx= ((bg0_pt.x>>3)+CROSS_TX) & 0x3F;
        ty= ((bg0_pt.y>>3)+CROSS_TY) & 0x3F;

        se_curr= se_index(tx, ty, 64);
        if(se_curr != se_prev)
        {
            bg0_map[se_prev]--;
            bg0_map[se_curr]++;
            se_prev= se_curr;
        }

        REG_BG_OFS[0]= bg0_pt;  // write new position
    }
    return 0;
}
sbb_reg
Fig 9.6: sbb_reg. Compare table 9.5, 64×64t background. Note the little cross in the top left corner.

The init_map() contains all of the initialization steps: setting up the registers, tiles, palettes and maps. Unlike the previous demo, the tiles, palette and the map are all created manually because it’s just easier in this case. At point (1), I define two tiles. The first one looks a little like a pane and the second one is a rudimentary cross. You can see them clearly in the screenshot (fig 9.4). The pane-like tile is loaded into tile 0, and is therefore the ‘default’ tile for the map.

The palette is set at point (2). The colors are the same as in table 9.5: red, green, blue and grey. Take note of which palette entries I’m using: the colors are in different palette banks so that I can use palette swapping when I fill the map. Speaking of which …

Loading the map itself (point (3)) happens through a double loop. The outer loop sets the palette-bank for the screen entries. The inner loop fills 1024 SEs with palette-swapped tile-0’s. Now, if big maps used a flat layout, the result would be a big map in four colored bands. However, what actually happens is that you see blocks, not bands, proving that indeed regular maps are split into screenblocks just like table 9.5 said. Yes, it’s annoying, but that’s just the way it is.

That was creating the map, now we turn to the main loop in main(). The keys (point (4)) let you scroll around the map. The RIGHT button is tied to a positive change in x, but the map itself actually scrolls to the left! When I say it like that it may seem counter-intuitive, but if you look at the demo you see that it actually makes sense. Think of it from a hypothetical player sprite point of view. As the sprite moves through the world, you need to update the background to keep the sprite from going off-screen. To do that, the background’s movement should be the opposite of the sprite’s movement. For example, if the sprite moves to the right, you have to move the background to the left to compensate.

Finally, there’s one more thing to discuss: the cross that appears centered on the map. To do this as you scroll along, I keep track of the screen-entry at the center of the screen via a number of variables and the se_index() function. Variables tx and ty are the tile coordinates of the center of the screen, found by shifting and masking the background pixel coordinates. Feeding these to se_index() gives me the screen-entry offset from the screen base block. If this is different than the previous offset, I repaint the former offset as a pane, and update the new offset to the cross. That way, the cross seems to move over the map; much like a sprite would. This was actually designed as a test for se_index(); if the function was flawed, the cross would just disappear at some point. But it doesn’t. Yay me ^_^

The charblock demo

The third demo, cbb_demo, covers some of the details of charblocks and the differences in 4bpp and 8bpp tiles. The backgrounds in question are BG 0 and BG 1. Both will be 32×32t backgrounds, but BG 0 will use 4bpp tiles and CBB 0 and BG 2 uses 8bpp tiles and CBB 2. The exact locations and contents of the screenblocks are not important; what is important is to load the tiles to the starts of all 6 charblocks and see what happens.

#include <toolbox.h>
#include "cbb_ids.h"

#define CBB_4 0
#define SBB_4 2

#define CBB_8 2
#define SBB_8 4

void load_tiles()
{
    int ii;
    TILE *tl= (TILE*)ids4Tiles;
    TILE8 *tl8= (TILE8*)ids8Tiles;

    // Loading tiles. don't get freaked out on how it looks
    // 4-bit tiles to blocks 0 and 1
    tile_mem[0][1]= tl[1];      tile_mem[0][2]= tl[2];
    tile_mem[1][0]= tl[3];      tile_mem[1][1]= tl[4];
    // and the 8-bit tiles to blocks 2 though 5
    tile8_mem[2][1]= tl8[1];    tile8_mem[2][2]= tl8[2];
    tile8_mem[3][0]= tl8[3];    tile8_mem[3][1]= tl8[4];
    tile8_mem[4][0]= tl8[5];    tile8_mem[4][1]= tl8[6];
    tile8_mem[5][0]= tl8[7];    tile8_mem[5][1]= tl8[8];

    // And let's not forget the palette (yes, obj pal too)
    u16 *src= (u16*)ids4Pal;
    for(ii=0; ii<16; ii++)
        pal_bg_mem[ii]= pal_obj_mem[ii]= *src++;
}

void init_maps()
{
    // se4 and se8 map coords: (0,2) and (0,8)
    SB_ENTRY *se4= &se_mem[SBB_4][2*32], *se8= &se_mem[SBB_8][8*32];
    // show first tiles of char-blocks available to bg0
    // tiles 1, 2 of char-block CBB_4
    se4[0x01]= 0x0001;      se4[0x02]= 0x0002;

    // tiles 0, 1 of char-block CBB_4+1
    se4[0x20]= 0x0200;      se4[0x21]= 0x0201;

    // show first tiles of char-blocks available to bg1
    // tiles 1, 2 of char-block CBB_8 (== 2)
    se8[0x01]= 0x0001;      se8[0x02]= 0x0002;

    // tiles 1, 2 of char-block CBB_8+1
    se8[0x20]= 0x0100;      se8[0x21]= 0x0101;

    // tiles 1, 2 of char-block CBB_8+2 (== CBB_OBJ_LO)
    se8[0x40]= 0x0200;      se8[0x41]= 0x0201;

    // tiles 1, 2 of char-block CBB_8+3 (== CBB_OBJ_HI)
    se8[0x60]= 0x0300;      se8[0x61]= 0x0301;
}

int main()
{
    load_tiles();
    init_maps();

    // init backgrounds
    REG_BG0CNT= BG_CBB(CBB_4) | BG_SBB(SBB_4) | BG_4BPP;
    REG_BG1CNT= BG_CBB(CBB_8) | BG_SBB(SBB_8) |  BG_8BPP;
    // enable backgrounds
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0 | DCNT_BG1 | DCNT_OBJ;

    while(1);

    return 0;
}

The tilesets can be found in cbb_ids.c. Each tile contains two numbers: one for the charblock I’m putting it and one for the tile-index in that block. For example, the tile that I want in charblock 0 at tile 1 shows ‘01’, CBB 1 tile 0 shows ‘10’, CBB 1, tile 1 has ‘11’, etc. I have twelve tiles in total, 4 s-tiles to be used for BG 0 and 8 d-tiles for BG 1.

Now, I have six pairs of tiles and I intend to place them in the first tiles of each of the 6 charblock (except for CBBs 0 and 2, where tile 0 would be used as default tiles for the background, which I want to keep empty). Yes six, I’m loading into the sprite charblocks as well. I could do this by hand, calculating all the addresses manually (0600:0020 for CBB 0, tile 1, etc) and hope I don’t make a mistake and can remember what I’m doing when revisiting the demo later, or I can just use my tile_mem and tile8_mem memory map matrices and get the addresses quickly and without any hassle. Even better, C allows struct assignments so I can load the individual tiles with a simple assignment! That is exactly what I’m doing in load_tiles(). The source tiles are cast to TILE and TILE8 arrays for 4bpp and 8bpp tiles respectively. After that, loading the tiles is very simple indeed.

The maps themselves are created in init_maps(). The only thing I’m interested in for this demo is to show how and which charblocks are used, so the particulars of the map aren’t that important. The only thing I want them to do is to be able to show the tiles that I loaded in load_tiles(). The two pointers I create here, se4 and se8, point to screen-entries in the screenblocks used for BG 0 and BG 1, respectively. BG 0’s map, containing s-tiles, uses 1 and 512 offsets; BG 1’s entries, 8bpp tiles, carries 1 and 256 offsets. If what I said before about tile-index for different bitdepths is true, then you should see the contents of all the loaded tiles. And looking at the result of the demo (fig 9.7), it looks as if I did my math correctly: background tile-indices follow the bg’s assigned bitdepth, in contrast to sprites which always counts in 32 byte offsets.

There is, however, one point of concern: on hardware, you won’t see the tiles that are actually in object VRAM (blocks 4 and 5). While you might expect to be able to use the sprite blocks for backgrounds due to the addresses, the actual wiring in the GBA seems to forbid it. This is why you should test on hardware is important: emulators aren’t always perfect. But if hardware testing is not available to you, test on multiple emulators; if you see different behaviour, be wary of the code that produced it.

cbb_demo on VBA
Fig 9.7a: cbb_demo on obsolete emulators (such as VBA and Boycott Adv).
cbb_demo on hardware
Fig 9.7b: cbb_demo on hardware. Spot the differences!

Bonus demo: the ‘text’ in text bg and introducing libtonc

Woo, bonus demo! This example will serve a number of purposes. The first is to introduce libtonc, a library of code to make life on the GBA a bit easier. In past demos, I’ve been using toolbox.h/c to store useful macros and functions. This is alright for very small projects, but as code gets added, it becomes very hard to maintain everything. It’s better to store common functionality in libraries that can be shared among projects.

The second reason is to show how you can output text, which is obviously an important ability to have. Tonclib has an extensive list of options for text rendering – too much to explain here – but its interface is pretty easy. For details, visit the Tonc Text Engine chapter.

Anyway, here’s the example.

#include <stdio.h>
#include <tonc.h>

int main()
{
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    // Init BG 0 for text on screen entries.
    tte_init_se_default(0, BG_CBB(0)|BG_SBB(31));

    tte_write("#{P:72,64}");        // Goto (72, 64).
    tte_write("Hello World!");      // Print "Hello world!"

    while(1);

    return 0;
}

Fig 9.8a: hello demo.

Fig 9.8b: tileset of the hello demo.

Yes, it is indeed a “hello world” demo, the starting point of nearly every introductory C/C++ tutorial. However, those are usually for meant for PC platforms, which have native console functionality like printf() or cout. These do not exist for the GBA. (Or “didn’t”, I should say; there are ways to make use of them nowadays. See tte:conio for details.)

Tonc’s support for text goes through tte_ functions. In this case, tte_init_se_default() sets up background 0 for tile-mapped text. It also loads the default 8×8 font into charblock 0 (see fig 9.8b). After that, you can write to text with tte_write. The sequence #{P:x,y} is the formatting command that TTE uses to position the cursor. There are a number of these, some of which you’ll also see in later chapters.

From this point on, I’ll make liberal use of libtonc’s text capabilities in examples for displaying values and the like. This will mostly happen without explanation, because that won’t be part of the demo. Again, to see the internals, go to the TTE chapter.

Creating and using code libraries

Using the functions themselves is pretty simple, but they are spread out over multiple files and reference even more. This makes it a hassle to find which files you need to add to the list of sources to compile a project. You could add everything, of course, but that’s not a pleasant prospect either. The best solution is to pre-compile the utility code into a library.

Libraries are essentially clusters of object files. Instead of linking the objects into an executable directly, you archive them with arm-none-eabi-ar. The command is similar to the link step as well. Here is how you can create the library libfoo.a from objects foo.o, bar.o and baz.o.

# archive rule
libfoo : foo.o bar.o baz.o
    arm-none-eabi-ar -crs libfoo.a foo.o bar.o baz.o
# shorthand rule: $(AR) rcs $@ $^

The three flags stand for create archive, replace member and create symbol table, respectively. For more on these and other archiving flags, I will refer you to the manual, which is part of the binutils toolset. The flags are followed by the library name, which is followed by all the objects (the ‘members’ you want to archive).

To use the library, you have to link it to the executable. There are two linker flags of interest here: -L and -l. Upper- and lowercase ‘L’. The former, -L adds a library path. The lowercase version, -l, adds the actual library, but there is a twist here: only need the root-name of the library. For example, to link the library libfoo.a, use -lfoo. The prefix lib and extension .a are assumed by the linker.

# using libfoo (assume it's in ../lib)
$(PROJ).elf : $(OBJS)
    $(LD) $^ $(LDFLAGS) -L../lib -lfoo -o $@

Of course, these archives can get pretty big if you dump a lot of stuff in there. You might wonder if all of it is linked when you add a library to your project. The answer is no, it is not. The linker is smart enough to use only the files which functions you’re actually referencing. In the case of this demo, for example, I’m using various text functions, but none of the affine functions or tables, so those are excluded. Note that the exclusion goes by file, not by function. If you only have one file in the library (or #included everything, which amounts to the same thing), everything will be linked.

I intend to use libtonc in a number of later demos. In particular, the memory map, text and copy routines will be present often. Don’t worry about what they do for the demo; just focus on the core content itself. Documentation of libtonc can be found in the libtonc folder (tonc/code/libtonc) and at Tonclib’s website.

Better copy and fill routines: memcpy16/32 and memset16/32

Now that I am using libtonc as a library for its text routines, I might as well use it for its copy and fill routines as well. Their names are memcpy16() and memcpy32() for copies and memset16() and memset32() for fill routines. The 16 and 32 denote their preferred datatypes: halfwords and words, respectively. Their arguments are similar to the conventional memcpy() and memset(), with the exception that the size is the number of items to be copied, rather than in bytes.

void memset16(void *dest, u16 hw, uint hwcount);
void memcpy16(void *dest, const void *src, uint hwcount);

void memset32(void *dest, u32 wd, uint wcount) IWRAM_CODE;
void memcpy32(void *dest, const void *src, uint wcount) IWRAM_CODE;

These routines are optimized assembly so they are fast. They are also safer than the dma routines, and the BIOS routine CpuFastSet(). Basically, I highly recommend them, and I will use them wherever I can.

Linker options: object files before libraries

In most cases, you can change the order of the options and files freely, but in the linker’s case it is important the object files of the projects are mentioned before the linked libraries. If not, the link will fail. Whether this is standard behaviour or if it is an oversight in the linker’s workings I cannot say, but be aware of potential problems here.

In conclusion

Tilemaps are essential for most types of GBA games. They are trickier to get to grips with than the bitmap modes or sprites because there are more steps to get exactly right. And, of course, you need to be sure the editor that gave you the map actually supplied the data you were expecting. Fool around with the demos a little: run them, change the code and see what happens. For example, you could try to add scrolling code to the brin_demo so you can see the whole map. Change screen blocks, change charblock, change the bitdepth, mess up intentionally so you can see what can go wrong, so you’ll be prepared for it when you try your own maps. Once you’re confident enough, only then start making your own. I know it’s the boring way, but you will benefit from it in the long run.

10. The Affine Transformation Matrix (a.k.a. P)

About this page

As you probably know, the GBA is capable of applying geometric transformations like rotating and/or scaling to sprites and backgrounds. To set them apart from the regular items, the transformable ones are generally referred to as Rot/Scale sprites and backgrounds. The transformations are described by four parameters, pa, pb, pc and pd. The locations and exact names differ for sprites and backgrounds but that doesn’t matter for now.

There are two ways of interpreting these numbers. The first is to think of each of them as individual offsets to the sprite and background data. This is how the reference documents like GBATEK and CowBite Spec describe them. The other way is to see them as the elements of a 2x2 matrix which I will refer to as P. This is how pretty much all tutorials describe them. These tutorials also give the following matrix for rotation and scaling:

( 10.1 ) 𝗣 = [ pa pb pc pd ] = [ sxcos(α) sysin(α) -sxsin(α) sycos(α) ]

Now, this is indeed a rotation and scale matrix. Unfortunately, it’s also the wrong one! Or at least, it probably does not do what you’d expect. For example, consider the case with a scaling of sx = 1.5, sy = 1.0 and a rotation of α= 45. You’d probably expect something like fig 10.2a, but what you’d actually get is fig 10.2b. The sprite has rotated, but in the wrong direction, it has shrunk rather than expanded and there’s an extra shear as well. Of course, you can always say that you meant for this to happen, but that’s probably not quite true.

Fig 10.2a: when you say ‘rotate and scale’, you probably expect this…

 

Fig 10.2b: but with P from eq 10.1, this is what you get.

Unfortunately, there is a lot of incorrect or misleading information on the transformation matrix around; the matrix of eq 10.1 is just one aspect of it. This actually starts with the moniker “Rot/Scale”, which does not fit with what actually occurs, continues with the fact that the terms used are never properly defined and that most people often just copy-paste from others without even considering checking whether the information is correct or not. The irony is that the principle reference document, GBATEK, gives the correct descriptions of each of the elements, but somehow it got lost in the translation to matrix form in the tutorials.

In this chapter, I’ll provide the correct interpretation of the P-matrix; how the GBA uses it and how to construct one yourself. To do this, though, I’m going into full math-mode. If you don’t know your way around vector and matrix calculations you may have some difficulties understanding the finer points of the text. There is an appendix on linear algebra for some pointers on this subject.

This is going to be a purely theoretical page: you will find nothing that relates directly to sprites or backgrounds here; that’s what the next two sections are for. Once again, we will be assisted by the lovely metroid (keep in cold storage for safe use). Please mind the direction of the y-axis and the angles, and do not leave without reading the finishing up paragraph. This contains several key implementation details that will be ignored in the text preceding it, because they will only get in the way at that point.

Be wary of documents covering affine parameters

It’s true. Pretty much every document I’ve seen that deals with this subject is problematic in some way. A lot of them give the wrong rotate-scale matrix (namely, the one in eq 10.1), or misname and/or misrepresent the matrix and its elements.

Texture mapping and affine transformations.

General 2D texture mapping

What the GBA does to get sprites and tiled backgrounds on screen is very much like texture mapping. So forget about the GBA right now and look at how texture mapping is done. In fig 10.4a, we see a metroid texture. For convenience I am using the standard Cartesian 2D coordinate system (y-axis points up) and have normalised the texture, which means that the right and top side of the texture correspond precisely with the unit-vectors ex and ey (which are of length 1). The texture mapping brings p (in texture space) to a point q (in screen space). The actual mapping is done by a 2×2 matrix A:

𝗾 = 𝗔 · 𝗽

So how do you find A? Well, that’s actually not that hard. The matrix is formed by lining up the transformed base vectors, which are u and v (this works in any number of dimensions, btw), so that gives us:

𝗔 = [ ux vx uy vy ]

Fig 10.4a: a texture.

A

Fig 10.4b: a texture mapped

A forward texture mapping via affine matrix A.

Affine transformations

The transformations you can do with a 2D matrix are called affine transformations. The technical definition of an affine transformation is one that preserves parallel lines, which basically means that you can write them as matrix transformations, or that a rectangle will become a parallelogram under an affine transformation (see fig 10.4b).

Affine transformations include rotation and scaling, but also shearing. This is why I object to the name “Rot/Scale”: that term only refers to a special case, not the general transformation. It is akin to calling colors shades of red: yes, reds are colors too, but not all colors are reds, and to call them that would give a distorted view of the subject.

As I said, there are three basic 2d transformations, though you can always describe one of these in terms of the other two. The transformations are: rotation (R), scaling (S) and shear (H). Table 10.1 shows what each of the transformations does to the regular metroid sprite. The black axes are the normal base vectors (note that y points down!), the blue axes are the transformed base vectors and the cyan variables are the arguments of the transformation. Also given are the matrix and inverse matrix of each transformation. Why? You’ll see.

( 10.2 ) 𝗔 = [ a b c d ] 𝗔 -1 1 ad-bc [ d -b -c a ]

Table 10.1: transformation matrices and their inverses.

Identity Rotation Scaling Shear
Normal metroid Rotated metroid Scaled metroid Sheared metroid
𝗜 = [ 1 0 0 1 ] 𝗥 ( θ ) = [ cos(θ) -sin(θ) sin(θ) cos(θ) ] 𝗦 ( sx , sy ) = [ sx 0 0 sy ] 𝗛 ( hx , hy ) = [ 1 hx hy 1 ]
𝗜-1 = 𝗜 𝗥-1(θ) = 𝗥() 𝗦-1 ( sx , sy ) = 𝗦 ( 1sx , 1sy ) 𝗛-1 ( hx , hy ) = 𝗛 ( -hx , -hy ) 1 - hx hy

We can now use these definitions to find the correct matrix for enlargements by sx and sy, followed by a counter-clockwise rotation by α (=−θ), by matrix multiplication.

( 10.3 ) 𝗔 = 𝗥() · 𝗦(sx,sy) = [ sxcos(α) sysin(α) -sxsin(α) sycos(α) ]

… ermm, wait a sec … I’m having this strange sense of déja-vu here …

Clockwise vs counterclockwise

It’s a minor issue, but I have to mention it. If the definition of R uses a clockwise rotation, why am I suddenly using a counter-clockwise one? Well, traditionally R is given as that particular matrix, in which the angle runs from the x-axis towards the y-axis. Because y is downward, this comes down to clockwise. However, the affine routines in BIOS use a counter-clockwise rotation, and I thought it’d be a good idea to use that as a guideline for my functions.

Nomenclature: Affine vs Rot/Scale

The matrix P is not a rotation matrix, not a scaling matrix, but a general affine transformation matrix. Rotation and scaling may be what the matrix is mostly used for, but that does not mean they’re the only things possible, as the term ‘Rot/Scale’ would imply.

To set them apart from regular backgrounds and sprites, I suppose ‘Rotation’ or ‘Rot/Scale’ are suitable enough, just not entirely accurate. However, calling the P-matrix by those names is simply wrong.

“Many of the truths we cling to depend greatly upon our own point of view.”

Fig 10.5: Mapping process as seen by humans. u and v are the columns of A (in screen space).

As you must have noticed, eq 10.3 is identical to eq 10.1, which I said was incorrect. So what gives? Well, if you enter this matrix into the pa-pd elements you do indeed get something different than what you’d expect. Only now I’ve proven what you were supposed to expect in the first place (namely a scaling by sx and sy, followed by a counter-clockwise rotation by α). The real question is of course, why doesn’t this work? To answer this I will present two different approaches to the 2D mapping process.

Human point of view

“Hello, I am Cearn’s brain. I grok geometry and can do matrix- transformations in my head. Well, his head actually. When it comes to texture mapping I see the original map (in texture space) and then visualize the transformation. I look at the original map and look at where the map’s pixels end up on screen. The transformation matrix for this is A, which ties texel p to screen pixel q via q= A · p. The columns of A are simply the transformed unit matrices. Easy as π.”

Computer point of view

Fig 10.6: Mapping process as seen by computers. u and v (in texture space) are the columns of B and are mapped to the principle axes in screen space.

“Hello, I am Cearn’s GBA. I’m a lean, mean gaming machine that fits in your pocket, and I can push pixels like no one else. Except perhaps my owner’s GeForce 4 Ti4200, the bloody show-off. Anyway, one of the things I do is texture mapping. And not just ordinary texture-mapping, I can do cool stuff like rotation and scaling as well. What I do is fill pixels, all I need to know is for you to tell me where I should get the pixel’s color from. In other words, to fill screen pixel q, I need a matrix B that gives me the proper texel p via p = B · q. I’ll happily use any matrix you give me; I have complete confidence in your ability to supply me with the matrix for the transformation you require.”

Resolution

I hope you spotted the crucial difference between the two points of view. A maps from texture space to screen space, while B does the exact opposite (i.e., 𝗕=𝗔-1). I think you know which one you should give the GBA by now. That’s right: P = B, not A. This one bit of information is the crucial piece of the affine matrix puzzle.

So now you can figure out P’s elements in two ways. You can stick to the human POV and invert the matrix at the end. That’s why I gave you the inverses of the affine transformations as well. You could also try to see things in the GBA’s way and get the right matrix directly. Tonc’s main affine functions (tonc_video.h, tonc_obj_affine.c and tonc_bg_affine.c) do things the GBA way, setting P directly; but inverted functions are also available using an “_inv” affix. Mind you, these are a little slower. Except for when scaling is involved; then it’s a lot slower.

In case you’re curious, the proper matrix for scale by (sx, sy) and counter-clockwise rotation by α is:

𝗔 = 𝗥() · 𝗦(sx,sy) 𝗣 = 𝗔-1 = ( 𝗥() · 𝗦(sx,sy) )-1 = 𝗦-1(sx,sy) · 𝗥-1()

Using the inverse matrices given earlier, we find

( 10.4 ) 𝗣 = [ pa pb pc pd ] = [ cos(α) sx -sin(α) sx sin(α) sy cos(α) sy ]
Just to make it perfectly clear:

The affine matrix P maps from screen space to texture space, not the other way around!

In other words:

 pa: texture x-increment / pixel

 pb: texture x-increment / scanline

 pc: texture y-increment / pixel

 pd: texture y-increment / scanline

Finishing up

Knowing what the P-matrix is used for is one thing, knowing how to use them properly is another. There are three additional points you need to remember when you’re going to deal with affine objects/backgrounds and the affine matrices.

  1. Datatypes
  2. Luts
  3. Initialisation

Data types of affine elements

Affine transformations are part of mathematics and, generally speaking, math numbers will be real numbers. That is to say, floating point numbers. However, if you were to use floating points for the P elements, you’d be in for two rude surprises.

The first one is that the matrix elements are not floats, but integers. The reason behind this is that the GBA has no floating point unit! All floating-point operations have to be done in software and without an FPU, that’s going to be pretty slow. Much slower than integer math, at any rate. Now, when you think about this, it does create some problems with precision and all that. For example, the (co)sine and functions have a range between −1 and 1, a range which isn’t exactly large when it comes to integers. However, the range would be much greater if one didn’t count in units of 1, but in fractions, say in units of 1/256. The [−1, +1] range then becomes [−256, +256],

This strategy of representing real numbers with scaled integers is known as fixed point arithmetic, which you can read more about in this appendix and on wikipedia. The GBA makes use of fixed point for its affine parameters, but you can use it for other things as well. The P-matrix elements are 8.8 fixed point numbers, meaning a halfword with 8 integer bits and 8 fractional bits. To set a matrix to identity (1s on the diagonals, 0s elsewhere), you wouldn’t use this:

    // Floating point == Bad!!
    pa= pd= 1.0;
    pb= pc= 0.0;

but this:

    // .8 Fixed-point == Good
    pa= pd= 1<<8;
    pb= pc= 0;

In a fixed point system with Q fractional bits, ‘1’ (‘one’) is represented by 2Q or 1<<Q, because simply that’s how fractions work.

Now, fixed point numbers are still just integers, but there are different types of integers, and it is important to use the right ones. 8.8f are 16bit variables, so the logical choice there is short. However, this should be a signed short: s16, not u16. Sometimes is doesn’t matter, but if you want to do any arithmetic with them they’d better be signed. Remember that internally the CPU works in words, which are 32bit, and the 16bit variable will be converted to that. You really want, say, a 16bit “−1” (0xFFFF) to turn into a 32bit “−1” (0xFFFFFFFF), and not “65535” (0x0000FFFF), which is what happens if you use unsigned shorts. Also, when doing fixed point math, it is recommended to use signed ints (the 32bit kind) for them, anything else will slow you down and you might get overflow problems as well.

Use 32-bit signed ints for affine temporaries

Of course you should use 32bit variables for everything anyway (unless you actually want your code to bloat and slow down). If you use 16bit variables (short or s16), not only will your code be slower because of all the extra instructions that are added to keep the variables 16bit, but overflow problems can occur much sooner.

Only in the final step to hardware should you go to 8.8 format. Before that, use the larger types for both speed and accuracy.

LUTs

So fixed point math is used because floating point math is just to slow for efficient use. That’s all fine and good for your own math, but what about mathematical functions like sin() and cos()? Those are still floating point internally (even worse, doubles!), so those are going to be ridiculously slow.

Rather than using the functions directly, we’ll use a time-honored tradition to weasel our way out of using costly math functions: we’re going to build a look-up table (LUT) containing the sine and cosine values. There are a number of ways to do this. If you want an easy strategy, you can just declare two arrays of 360 8.8f numbers and fill them at initialization of your program. However, this is a poor way of doing things, for reasons explained in the section on LUTs in the appendix.

Tonclib has a single sine lut which can be used for both sine and cosine values. The lut is called sin_lut, a const short array of 512 4.12f entries (12 fractional bits), created by my excellut lut creator. In tonc_math.h you can find two inline functions that retrieve sine and cosine values:

//! Look-up a sine and cosine values
/*! \param theta Angle in [0,FFFFh] range
*   \return .12f sine value
*/

INLINE s32 lu_sin(uint theta)
{   return sin_lut[(theta>>7)&0x1FF];           }

INLINE s32 lu_cos(uint theta)
{   return sin_lut[((theta>>7)+128)&0x1FF];     }

Now, note the angle range: 0-10000h. Remember you don’t have to use 360 degrees for a circle; in fact, on computers it’s better to divide the circle in a power of two instead. In this case, the angle is in 2^16^ parts for compatibility with BIOS functions, which is brought down to a 512 range inside the look-up functions.

Initialization

When flagging a background or object as affine, you must enter at least some values into pa-pd. Remember that these are zeroed out by default. A zero-offset means it’ll use the first pixel for the whole thing. If you get a single-colored background or sprite, this is probably why. To avoid this, set P to the identity matrix or any other non-zero matrix.

Tonc’s affine functions

Tonclib contains a number of functions for manipulating the affine parameters of objects and backgrounds, as used by the OBJ_AFFINE and BG_AFFINE structs. Because the affine matrix is stored differently in both structs you can’t set them with the same function, but the functionality is the same. In table 10.2 you can find the basic formats and descriptions; just replace foo with obj_aff or bg_aff and FOO with OBJ or BG for objects and backgrounds, respectively. The functions themselves can be found in tonc_obj_affine.c for objects, tonc_bg_affine.c for backgrounds, and inlines for both in tonc_video.h … somewhere.

Function Description
void foo_copy(FOO_AFFINE *dst, const FOO_AFFINE *src, uint count); Copy affine parameters
void foo_identity(FOO_AFFINE *oaff); P=I
void foo_postmul(FOO_AFFINE *dst, const FOO_AFFINE *src); Post-multiply: D=D·S
void foo_premul(FOO_AFFINE *dst, const FOO_AFFINE *src); Pre-multiply: D=S·D
void foo_rotate(FOO_AFFINE *aff, u16 alpha); Rotate counter-clockwise by α·π/8000h.
void foo_rotscale(FOO_AFFINE *aff, FIXED sx, FIXED sy, u16 alpha); Scale by 1sx and 1sy, then rotate counter-clockwise by α·π/8000h.
void foo_rotscale2(FOO_AFFINE *aff, const AFF_SRC *as); As foo_rotscale(), but input stored in an AFF_SRC struct.
void foo_scale(FOO_AFFINE *aff, FIXED sx, FIXED sy); Scale by 1sx and 1sy
void foo_set(FOO_AFFINE *aff, FIXED pa, FIXED pb, FIXED pc, FIXED pd); Set P's elements
void foo_shearx(FOO_AFFINE *aff, FIXED hx); Shear top-side right by hx
void foo_sheary(FOO_AFFINE *aff, FIXED hy); Shear left-side down by hy
**Table 10.2**: affine functions

Sample rot/scale function

My code for a object version of the scale-then-rotate function (à la eq 10.4) is given below. Note that it is from the computer’s point of view, so that sx and sy scale down. Also, the alpha alpha uses 10000h/circle (i.e., the unit of α is π/8000h = 0.096 mrad, or 180/8000h = 0.0055°) and the sine lut is in .12f format, which is why the shifts by 12 are required. The background version is identical, except in name and type. If this were C++, templates would have been mighty useful here.

void obj_aff_rotscale(OBJ_AFFINE *oaff, int sx, int sy, u16 alpha)
{
    int ss= lu_sin(alpha), cc= lu_cos(alpha);

    oaff->pa= cc*sx>>12;    oaff->pb=-ss*sx>>12;
    oaff->pc= ss*sy>>12;    oaff->pd= cc*sy>>12;
}

With the information in this chapter, you know most of what you need to know about affine matrices, starting with why they should be referred to affine matrices, rather than merely rotation or rot/scale or the other names you might see elsewhere. You should now know what the thing actually does, and how you can set up a matrix for the effects you want. You should also know a little bit about fixed point numbers and luts (for more, look in the appendices) and why they’re Good Things; if it hadn’t been clear before, you should be aware that the choice of the data types you use actually matters, and you should not just use the first thing that comes along.

What has not been discussed here is how you actually set-up objects and backgrounds to use affine transformation, which is what the next two chapters are for. For more on affine transformations, try searching for ‘linear algebra’

11. Affine sprites

Affine sprite introduction

Essentially, affine sprites are still sprites. The difference with regular sprites is that you can perform an affine transformation (hence the name) on them before the rendering stage by setting the right bits in the object attributes and filling in the P matrix. You can read about affine transformations and the P matrix here. It is required reading for this section, as are the sprite and background overview and the regular sprite page.

You may wonder whether this is really worth a separate section. The short answer is yes. A longer answer is yes, because using affine sprites involves a lot more math than regular sprites and I didn’t want to freak out the, erm, ‘mathematically challenged’. The section on regular sprites can stand on its own and you can use it in blissful ignorance of the nasty math that it required for affine sprites.

In this chapter we’ll see how to set-up object to use affine transformations. This in itself is rather easy. Also discussed are a number of potential graphical problems you might run into sooner or later –one of them almost immediately, actually– and how to correct the sprite’s position to make it seem like the transformation’s origin is at an arbitrary point. And, as usual, there will be demo-code illustrating the various topics raised in this chapter.

Affine sprite initialization

To turn a regular sprite into an affine sprite you need to do two things. First, set OBJ_ATTR.attr0{8} to indicate this is a affine sprite. Second, put a number between 0 and 31 into OBJ_ATTR.attr1{8-C}. This number indicates which of the 32 Object Affine Matrices (OBJ_AFFINE structures) should be used. In case you’ve forgotten, the OBJ_AFFINE looks like this:

typedef struct OBJ_AFFINE
{
    u16 fill0[3];
    s16 pa;
    u16 fill1[3];
    s16 pb;
    u16 fill2[3];
    s16 pc;
    u16 fill3[3];
    s16 pd;
} ALIGN4 OBJ_AFFINE;

The signed 16-bit members pa, pb, pc and pd are 8.8 fixed point numbers that form the actual matrix, which I will refer to as P, in correspondence with the elements’ names. For more information about this matrix, go to the affine matrix section. Do so now if you haven’t already, because I’m not going to repeat it here. If all you are after is a simple scale-then-rotate matrix, try this: for a zoom by sx and sy followed by a counter-clockwise rotation by α, the correct matrix is this:

P = [ p a p b p c p d ] = [ cos ( α ) / s x sin ( α ) / s x sin ( α ) / s y cos ( α ) / s y ]

Note that the origin of the transformation is center of the sprite, not the top-left corner. This is worth remembering if you want to align your sprite with other objects, which we’ll do later.

Essential affine sprite steps

  • Set-up an object as usual: load graphics and palette, set REG_DISPCNT, set-up an OAM entry.
  • Set bit 8 of attribute 0 to enable affinity for that object, and choose an object affine matrix to use (attribute 1, bits 8-12).
  • Set that obj affine matrix to something other than all zeroes, for example the identity matrix.

Graphical artifacts

The clipping and discretization artifacts

The procedure that the GBA uses for drawing sprites is as follows: the sprite forms a rectangle on the screen defined by its size. To paint the screen pixels in that area (q) uses texture-pixel p, which is calculated via:

(11.1) p p 0 = P ( q q 0 )

where p0 and q0 are the centers of the sprite in texture and screen space, respectively. The code below is essentially what the hardware does; it scans the screen-rectangle between plus and minus the half-width and half-height (half-sizes because the center is the reference point), calculates the texture-pixel and plots that color.

// pseudocode for affine objects
hwidth= width/2;   // half-width of object screen canvas
hheight= hheight/2;   // half-height of object screen canvas
for(iy=-hheight; iy<hheight; iy++)
{
    for(ix=-hwidth; ix<hwidth; ix++)
    {
        px= (pa*ix + pb*iy)>>8;    // get x texture coordinate
        py= (pc*ix + pd*iy)>>8;    // get y texture coordinate
        color= GetPixel(px0+px, py0+py);   // get color from (px,py)
        SetPixel(qx0+ix, qy0+iy, color);     // set color to (qx, qy)
    }
}

This has two main consequences, the clipping artifact and a discretization artifact.

defanged metroid
Fig 11.1: a partially defanged metroid, since the parts outside the blue square are clipped off.

The clipping artifact is caused by scanning only over the rectangle on-screen. But almost all transformations will cause the texture pixels to exceed that rectangle, and the pixels outside the rectangle will not be rendered. Fig 11.1 shows the screen rect (grey, blue border) and a rotated object (inside the red border). The parts that extend the blue borderlines will not be cut off.

As this is an obvious flaw, there is of course a way around it: set the sprite’s affine mode to double-sized affine (ATTR0_AFF_DBL, OBJ_ATTR.attr0{8,9}). This will double the screen range of valid q coordinates, so you’d have + and − the width and height to play with instead of the half-sizes. This double (well quadruple, really) area means that you can safely rotate a sprite as the maximum distance from the center is ½√2 ≈ 0.707. Of course, you can still get the clipping artifact if you scale up beyond the doubled ranges. Also, note that the sprites’ origin is shifted to the center of this rectangle, so that q0 is now one full sprite-size away from the top-left corner.

The double-size flag also has a second use. Or perhaps I should say misuse. If you set it for a regular sprite, it will be hidden. This is an alternative way to hide unused sprites.

The second artifact, if you can call it that, is a discretization artifact. This is a more subtle point than the clipping artifact and you might not even ever notice it. The problem here is that the transformation doesn’t actually take place at the center of the object, but at the center pixel, rounded up. As an example, look at fig 11.2. Here we have a number-line from 0 to 8; and in between them 8 pixels from 0 to 7. The number at the center is 4, of course. The central pixel is 4 as well, however its location is actually halfway between numbers 4 and 5. This creates an unbalance between the number of pixels on the left and on the right.

The center pixel is the reference point of the transformation algorithm, which has indices (ix, iy) = (0, 0). Fill that into the equations and you’ll see that this is invariant under the transformation, even though mathematically it should not be. This has consequences for the offsets, which are calculated from the pixel, not the position. In fig 11.2, there are 4 pixels on the left, but only 3 on the right. A mirroring operation that would center on pixel 4 would effectively move the sprite one pixel to the right.

Fig 11.3 shows how this affects rotations. It displays lines every grey gridlines every 8 pixels and a 16×16 sprite of a box. Note that at the start the right and left sides do not lie on the gridlines, because the sprite’s width and height is 16, not 17. The other figures are rotations in increments of 90°, which gives nice round numbers in the matrix. When rotating, the center pixel (the red dot in the middle) stays in the same position, and the rest rotate around it, and this process will carry the edges out of the designated 16×16 box of the sprite (the dashed lines).

Numbers vs pixels
Fig 11.2: pixels are between, not on, coordinates.
Rotations
Fig 11.3: Rotations in 90° increments.

The offsets measure distance from the center pixel, not center position.

The offsets that are calculated from the affine matrix use the distances from the center pixel (w/2, h/2), not the center point. As such, there is a half a pixel deviation from the mathematical transformation, which may result in a ±pixel offset for the sprite as a whole and lost texture edges.

The wrapping artifact

Apart from the clipping artifact, there seems to be another; one that I have actually never seen mentioned anywhere. It’s what I call the wrapping artifact. As you know, the position for sprites is given in a 9-bit x-value and an 8-bit y-value, which values wrap around the screen. For x, you can just interpret this as having the [-256, 255] range. For y values, you can’t really do that because the top value for a signed 8-bit integer is 127, which would mean that you’d never be able to put a sprite at the bottom 32 lines. But since the values wrap around, it all works out in the end anyway. With one exception.

There’s never any trouble with regular sprites, and hardly any for affine sprites; the one exception is when you have a 64×64 or 32×64 affine sprite with the double size flag switched on. Such a sprite has a bounding box of 128×128. Now there are three different ways of interpreting the meaning of y > 128:

  1. Full-wrap: the top of the sprite would show at the bottom of the screen, and vice versa.
  2. Positive precedence: consider the [128, 159] range as indicative of the bottom of the screen, and forget the wrap.
  3. Negative precedence: if y value would make the sprite appear partially at the top, consider it to be negative, again neglecting the wrap.

As it happens, the GBA uses the third interpretation. In other words, it uses

// pseudo code
if(oam.y + bbox_height > 256)
    oam.y -= 256;

Note, by the way, that some older emulators (VBA and BoycottAdvance) both use interpretation #2, which may seem more logical, but is incorrect. As you can tell, it can only happen with a 32×64 or 64×64, double-sized sprite, and even then you’ll only notice it under very specific conditions, namely if the transformed sprite has visible pixels inside the top 32 lines of the bounding box. In the case that you have this problem, as far as I can tell the only way to get the sprite showing at the bottom of the screen is if you reduce the height to 32 for the time being.

A very (af)fine demo

I have a really interesting demo for you this time called obj_aff. It features a normal (boxed) metroid, which can be scaled, rotated and scaled. Because these transformations are applied to the current state of the matrix, you can end up with every kind of affine matrix possible by concatenating the different matrices. The controls are as follows:

L,RRotates the sprite CCW and CW, respectively.
D-padShears the sprite.
D-pad+SelMoves sprite around.
A,BExpands horizontally or vertically, respectively.
A,B+SelShrinks horizontally or vertically, respectively. (I ran out of buttons, so had to do it like this).
StartToggles double-size flag. Note that a) the corners of a rotated sprite are no longer clipped and b) the position shifts by 1/2 sprite size.
Start+SelResets P to normal.
SelectControl button (see A, B and Start).

The interesting point of seeing the transformations back to back is that you can actually see the difference between, for example, a scaling followed by a rotation (A=S·R), and a rotate-then-scale (A=R·S). Fig 11.4 and fig 11.5 show this difference for a 45° rotation and a 2× vertical scale. Also, note that the corners are cut off here: the clipping artifact at work – even though I’ve already set the double-size flag here.

R*S affine object.
Fig 11.4: obj_aff, via S(1,2), then R(45°)
S*R affine object.
Fig 11.5: obj_aff, via R(45°), then S(1,2)

The full source code for the obj_aff demo is given below. It’s quite long, mostly because of the amount of code necessary for managing the different affine states that can be applied. The functions that actually deal with affine sprites are init_metr(), get_aff_new() and part of the game loop in objaff_test(); the rest is essentially fluff required to making the whole thing work.

// obj_aff.c

#include <tonc.h>
#include <stdio.h>

#include "metr.h"

OBJ_ATTR obj_buffer[128];
OBJ_AFFINE *obj_aff_buffer= (OBJ_AFFINE*)obj_buffer;


// affine transformation constants and variables
enum eAffState
{
    AFF_NULL=0, AFF_ROTATE, AFF_SCALE_X, AFF_SCALE_Y, 
    AFF_SHEAR_X, AFF_SHEAR_Y, AFF_COUNT
};

// 'speeds' of transformations
const int aff_diffs[AFF_COUNT]= { 0, 128, 4, 4, 4, 4 };
// keys for transformation direction
const int aff_keys[AFF_COUNT]=
{ 0, KEY_L, KEY_SELECT, KEY_SELECT, KEY_RIGHT, KEY_UP };
int aff_state= AFF_NULL, aff_value= 0;


void init_metr()
{
    // Places the tiles of a 4bpp metroid sprite into LOW obj VRAM
    memcpy32(tile_mem[4], metr_boxTiles, metr_boxTilesLen/4);
    memcpy32(pal_obj_mem, metrPal, metrPalLen/4);

    // Set up main metroid
    obj_set_attr(obj_buffer, 
        ATTR0_SQUARE | ATTR0_AFF,          // Square affine sprite
        ATTR1_SIZE_64 | ATTR1_AFF_ID(0),   // 64x64, using obj_aff[0]
        0 | 0);                            // palbank 0, tile 0
    obj_set_pos(obj_buffer, 96, 32);
    obj_aff_identity(&obj_aff_buffer[0]);

    // Set up shadow metroid
    obj_set_attr(&obj_buffer[1], 
        ATTR0_SQUARE | ATTR0_AFF,           // Square affine sprite
        ATTR1_SIZE_64 | ATTR1_AFF_ID(31),   // 64x64, using obj_aff[0]
        ATTR2_PALBANK(1) | 0);              // palbank 1, tile 0
    obj_set_pos(&obj_buffer[1], 96, 32);
    obj_aff_identity(&obj_aff_buffer[31]);

    oam_update_all();
}

int get_aff_state()
{
    if(key_is_down(KEY_L | KEY_R))
        return AFF_ROTATE;
    if(key_is_down(KEY_A))
        return AFF_SCALE_X;
    if(key_is_down(KEY_B))
        return AFF_SCALE_Y;
    if(key_is_down(KEY_LEFT | KEY_RIGHT))
        return AFF_SHEAR_X;
    if(key_is_down(KEY_UP | KEY_DOWN))
        return AFF_SHEAR_Y;
    return AFF_NULL;
}

void get_aff_new(OBJ_AFFINE *oa)
{
    int diff= aff_diffs[aff_state];
    aff_value += (key_is_down(aff_keys[aff_state]) ? diff : -diff);

    switch(aff_state)
    {
    case AFF_ROTATE:    // L rotates left, R rotates right
        aff_value &= SIN_MASK;
        obj_aff_rotate(oa, aff_value);
        break;
    case AFF_SCALE_X:   // A scales x, +SELECT scales down
        obj_aff_scale_inv(oa, (1<<8)-aff_value, 1<<8);
        break;
    case AFF_SCALE_Y:   // B scales y, +SELECT scales down
        obj_aff_scale_inv(oa, 1<<8, (1<<8)-aff_value);
        break;
    case AFF_SHEAR_X:   // shear left and right
        obj_aff_shearx(oa, aff_value);
        break;
    case AFF_SHEAR_Y:   // shear up and down
        obj_aff_sheary(oa, aff_value);
        break;
    default:            // shouldn't happen
        obj_aff_identity(oa);
    }
}

void objaff_test()
{
    OBJ_ATTR *metr= &obj_buffer[0], *shadow= &obj_buffer[1];
    OBJ_AFFINE *oaff_curr= &obj_aff_buffer[0]; 
    OBJ_AFFINE *oaff_base= &obj_aff_buffer[1]; 
    OBJ_AFFINE *oaff_new=  &obj_aff_buffer[2];

    int x=96, y=32;
    int new_state;

    // oaff_curr = oaff_base * oaff_new
    // oaff_base changes when the aff-state changes
    // oaff_new is updated when it doesn't
    obj_aff_identity(oaff_curr);
    obj_aff_identity(oaff_base);
    obj_aff_identity(oaff_new);

    while(1)
    {
        key_poll();

        // move sprite around
        if( key_is_down(KEY_SELECT) && key_is_down(KEY_DIR) )
        {
            // move
            x += 2*key_tri_horz();
            y += 2*key_tri_vert();

            obj_set_pos(metr, x, y);
            obj_set_pos(shadow, x, y);
            new_state= AFF_NULL;
        }
        else    // or do an affine transformation
            new_state= get_aff_state();

        if(new_state != AFF_NULL)   // no change
        {
            if(new_state == aff_state)  // increase current transformation
            {
                get_aff_new(oaff_new);
                obj_aff_copy(oaff_curr, obj_aff_base, 1);
                obj_aff_postmul(oaff_curr, oaff_new);
            }
            else        // switch to different transformation type
            {
                obj_aff_copy(oaff_base, oaff_curr, 1);
                obj_aff_identity(oaff_new);
                aff_value= 0;
            }
            aff_state= new_state;
        }

        // START: toggles double-size flag
        // START+SELECT: resets obj_aff to identity
        if(key_hit(KEY_START))
        {
            if(key_is_down(KEY_SELECT))
            {
                obj_aff_identity(oaff_curr);
                obj_aff_identity(oaff_base);
                obj_aff_identity(oaff_new);
                aff_value= 0;
            }
            else
            {
                metr->attr0 ^= ATTR0_DBL_BIT;
                shadow->attr0 ^= ATTR0_DBL_BIT;
            }
        }

        vid_vsync();

        // we only have one OBJ_ATTR, so update that
        obj_copy(obj_mem, obj_buffer, 2);

        // we have 3 OBJ_AFFINEs, update these separately
        obj_aff_copy(obj_aff_mem, obj_aff_buffer, 3);

        // Display the current matrix
        tte_printf("#{es;P:8,136}P =  "
            "#{y:-7;Ps}| %04X\t%04X#{Pr;x:72}|"
            "#{Pr;y:12}| %04X\t%04X#{Pr;p:72,12}|", 
            (u16)oaff_curr->pa, (u16)oaff_curr->pb, 
            (u16)oaff_curr->pc, (u16)oaff_curr->pd);
    }
}

int main()
{
    REG_DISPCNT= DCNT_BG0 | DCNT_OBJ | DCNT_OBJ_1D;
    oam_init(obj_buffer, 128);
    init_metr();

    tte_init_chr4_b4_default(0, BG_CBB(2)|BG_SBB(28));
    tte_init_con();
    tte_set_margins(8, 128, 232, 160);

    objaff_test();

    return 0;
}

Making the metroid an affine sprite is all done inside init_metr(). As you’ve seen how bits are set a number of times by now, it should be understandable. That said, do note that I am filling the first OBJ_AFFINE (the one that the sprite uses) to the identity matrix I. If you keep this fully zeroed-out, you’ll just end up with a 64×64-pixel rectangle of uniform color. Remember that P contains pixel offsets; if they’re all zero, there is no offset and the origin’s color is used for the whole thing. In essence, the sprite is scaled up to infinity.

To be frank though, calling obj_aff_identity() isn’t necessary after a call to oam_init(), as that initializes the matrices as well. Still, you need to be aware of potential problems.

That’s the set-up, now for how the demo does what it does. At any given time, you will have some transformation matrix, P. By pressing a button (or not), a small transformation of the current state will be performed, via matrix multiplication.

  P new = P old D 1

where D is either a small rotation (R), scaling (S) or shear (H). Or a no-op (I). However, there is a little hitch here. This would work nice in theory, but in practice, it won’t work well because the fixed point matrix multiplications will result in unacceptable round-off errors very very quickly. Fortunately, all these transformations have the convenient property that

  D ( a ) D ( b ) = D ( c )

That is to say, multiple small transformations work as one big one. All you have to do is keep track of the current chosen transformation (the variable aff_state, in get_aff_state()), modify the state variable (aff_value), then calculate full transformation matrix (get_aff_new()) and apply that (with obj_aff_postmul()). When a different transformation type is chosen, the current matrix is saved, the state value is reset and the whole thing continues with that state until yet another is picked. The majority of the code is for keeping track of these changes; it’s not pretty, but it gets the job done.

Off-center reference points and object combos

Rotation around off-center point
Fig 11.6: rotation of object around an off-center point.

As mentioned earlier, affine sprites always use their centers as affine origins, but there are times when one might want to use something else to rotate around – to use another point as the reference point. Now, you can’t actually do this, but you can make it look as if you can. To do this, I need to explain a few things about what I like to call anchoring. The anchor is the position that is supposed to remain ‘fixed’; the spot where the texture (in this case the object) is anchored to the screen.

For anchoring, you actually need one set of coordinates for each coordinate-space you’re using. In this case, that’s two: the texture space and the screen space. Let’s call these points p0 and q0, respectively. Where these actually point from is largely immaterial, but for convenience’ sake let’s use the screen and texture origins for this. These points are only the start. In total, there are seven vectors that we need to take into account for the full procedure, and they are all depicted in fig 11.6. Their meanings are explained in the table below.

point description
p0, q0 Anchors in texture and screen space.
cp, cq Object centers in texture and screen space. With the object sizes, s=(w,h), we have cps and cq=ms, where m is ½ or 1, depending on the double-size flag.
rp, rq Distances between object centers and anchors. By definition, rp = P·rq
x Desired object coordinates.

Yes, it is a whole lot of vectors, but funnily enough, most are already known. The center points (cp and cq) can be derived from the objects size and double-size status, the anchors are known in advance because those are the input values, and rp and rq fit the general equation for the affine transformation, eq 11.2, so this links the two spaces. All that’s left now is to write down and solve the set of equations.

(11.2) x + c q + r q = q 0 c p + r p = p 0 r p = P   r q

Three equations with three unknowns, means it is solvable. I won’t post the entire derivation because that’s not all that difficult; what you see in eq 11.3 is the end result in the most usable form.

(11.3) x = q 0 m s P 1 ( p 0 1 2 s )

The right-hand side here has three separate vectors, two of which are part of the input, a scaling flag for the double-size mode, and the inverted affine matrix. Yes, I did say inverted. This is here because the translations to position the object correctly mostly take place in screen-space. The whole term using it is merely rq, the transformed difference between anchor and center in texture space, which you need for the final correction.

Now, this matrix inversion means two things. First, that you will likely have to set up two matrices: the affine matrix itself, and its inverse. For general matrices, this might take a while, especially when considering that if you want scaling, you will have to do a division somewhere. Secondly, because you only have 16 bits for the matrix elements, the inverse won’t be the exact inverse, meaning that aligning the objects exactly will be difficult, if not actually impossible. This is pretty much guaranteed by the hardware itself and I’ll return to this point later on. For now, let’s look at a function implementing eq 11.3 in the case of a 2-way scaling followed by a rotation.

// === in tonc_types.h ===

// This is the same struct that's used in BgAffineSet, 
// where it is called BGAffineSource, even though its uses go 
// beyond just backgrounds.
typedef struct tagAFF_SRC_EX
{
    s32 tex_x, tex_y;   // vector p0: anchor in texture space (.8f)
    s16 scr_x, src_y;   // vector q0: anchor in screen space (.0f)
    s16 sx, sy;         // scales (Q.8)
    u16 alpha;          // CCW angle ( integer in [0,0xFFFF] )
} AFF_SRC_EX;

// === in tonc_core.c === 
// Usage: oam_sizes[shape][size] is (w,h)
const u8 oam_sizes[3][4][2]=
{
    { { 8, 8}, {16,16}, {32,32}, {64,64} }, 
    { {16, 8}, {32, 8}, {32,16}, {64,32} },
    { { 8,16}, { 8,32}, {16,32}, {32,64} },
};

// === in tonc_obj_affine.c ===
void obj_rotscale_ex(OBJ_ATTR *obj, OBJ_AFFINE *oa, AFF_SRC_EX *asx)
{
    int sx= asx->sx, sy= asx->sy;
    int sina= lu_sin(asx->alpha)>>4, cosa= lu_cos(asx->alpha)>>4;

    // (1) calculate P
    oa->pa= sx*cosa>>8;     oa->pb= -sx*sina>>8;
    oa->pc= sy*sina>>8;     oa->pd=  sy*cosa>>8;

    // (2) set-up and calculate A= P^-1
    // sx = 1/sx, sy = 1/sy (.12f)
    sx= Div(1<<20, sx);
    if(sx != sy)
        sy= Div(1<<20, sy);
    else
        sy= sx;
    FIXED aa, ab, ac, ad;   // .8f
    aa=  sx*cosa>>12;   ab= sy*sina>>12;
    ac= -sx*sina>>12;   ad= sy*cosa>>12;

    // (3) get object size
    sx= oam_sizes[obj->attr0>>14][obj->attr1>>14][0];
    sy= oam_sizes[obj->attr0>>14][obj->attr1>>14][1];

    // (4) calculate dx =  q0 - ms - A*(p0-s/2)
    int dx= asx->src_x, dy= asx->src_y;   // .0f
    if(obj->attr0&ATTR0_DBL_BIT)
    {   dx -= sx;       dy -=sy;        }
    else
    {   dx -= sx>>1;    dy -= sy>>1;    }

    sx= asx->tex_x - (sx<<7);      // .8f
    sy= asx->tex_y - (sy<<7);      // .8f
    dx -= (aa*sx + ab*sy)>>16;      // .0 - (.8f*.8f/.16f)
    dy -= (ac*sx + ad*sy)>>16;      // .0 - (.8f*.8f/.16f)

    // (5) update OBJ_ATTR
    obj_set_pos(obj, dx, dy);
}

The AFF_SRC_EX struct and oam_sizes arrays are supporting entities of the function that does the positioning, which is obj_rotscale_ex(). This creates the affine matrix (pa-pd), and carries out all the necessary steps for eq 11.3, namely create the inverse matrix A (aa-ad), calculate all the offsets and correcting for the sizes, and finally updating the OBJ_ATTR. Note that the fixed point accuracy varies a lot, so it is important to comment often on this

As I said, this is not a particularly fast function; it takes roughly a scanline worth of cycles. If you need more speed, I also have a Thumb assembly version which is about 40% faster.

Affine object combo demo


Fig 11.7: object for oacombo.

The demo for this section, oacombo, will display three versions of essentially the same object, namely the circle of fig 11.7. The difference between them is in how they are constructed

  1. 1 32×32p object, full circle.
  2. 2 32×16p objects, two semi-circles.
  3. 4 16×16p objects, four quarter-circles.

The point of this demo will be to rotate them and position the components of the combined sprites (object combos) as if they were a single sprite. This requires off-center anchors and therefore ties in nicely with the subject of this section. To manage the combos, I make use of the following struct.

typedef struct OACOMBO
{
    OBJ_ATTR *sub_obj; // obj pointer for sub-objects
    POINT *sub_pos;     // Local sub-object coords (.8f)
    int sub_count;      // Number of sub-objects
    POINT pos;          // Global position (.8f)
    POINT anchor;       // Local anchor (.8f)
    s16 sx, sy;         // scales (.8f)
    u16 alpha;          // CCW angle
} OACOMBO;

Each combo is composed of sub_count objects; sub_oe is a pointer to the array storing these objects, and sub_pos is a pointer to the list of (top-left) coordinates of these objects, relative to the top-left of the full sprite. This global position is in pos. The anchor (in anchor) is also relative to this position. The global screen-anchor would be at pos+anchor, and the texture-anchor of sub-object ii at anchor-sub_pos[ii].

The rotation will take place around the center of the circle, so that’s an anchor of (16,16). Or, rather (16,16)*256 because they’re .8 fixed point numbers, but that’s not important right now. For the full circle, this will be the center of the object, but it’ll still need to be corrected for the double-size flag. For the other combos, the anchor will not be at the center of their sub-objects.

Because the sub-objects share the same P matrix, it’d be a waste to recalculate it the whole time, so I’m using a modified version of it especially tailored to OACOMBO structs called oac_rotscale(). The code is basically the same though. The oacs[] array forms the three combos, which are initialized at definition because that makes things so much easier. The full circle is at (16,20), the semis at (80,20) and the one composed of quarter circles is at (48,60). The obj_data[] array contains the data for our seven objects, and is copied to obj_buffer in the initialization function. While it is generally true that magic numbers (such as using hex for OAM attributes) are evil, it is also true that they really aren’t central to this story and to spend a lot of space on initializing all of them in the ‘proper’ fashion may actually do more harm than good … this time. I am still using #defines for the anchor and a reference point though, because they appear multiple times in the rest of the code.

// oacombo.c

#include <stdio.h>
#include <tonc.h>


#include "oac_gfx.h"

#define AX   (16<<8)     // X-anchor
#define AY   (16<<8)     // Y-anchor
#define X0    120        // base X
#define Y0    36         // base Y

// === GLOBALS ========================================================

OBJ_ATTR obj_buffer[128];
OBJ_AFFINE *obj_aff_buffer= (OBJ_AFFINE*)obj_buffer;

// Obj templates
const OBJ_ATTR obj_data[7]=
{
    // obj[0]  , oaff[0]: 1 full 32x32p double-affine circle
    { 0x0300, 0x8200, 0x0000, 0x0000 }, 
    // obj[1-2], oaff[1]: 2 32x16p double-affine semi-circles 
    { 0x4300, 0x8200, 0x0000, 0x0000 }, 
    { 0x4300, 0x8200, 0x0008, 0x0000 }, 
    // obj[3-7], oaff[1]: 4 16x16p double-affine quarter-circles
    { 0x0300, 0x4400, 0x0010, 0x0000 }, 
    { 0x0300, 0x4400, 0x0014, 0x0000 }, 
    { 0x0300, 0x4400, 0x0018, 0x0000 }, 
    { 0x0300, 0x4400, 0x001C, 0x0000 }, 
};

POINT sub_pos[7]=
{
    {0,0},
    {0,0},{0,AY}, 
    {0,0},{AX,0}, {0,AY},{AX,AY}, 
};

OACOMBO oacs[3]=
{
    // full 32x32p double-affine circle
    { &obj_buffer[0], &sub_pos[0], 1, 
        {(X0-48)<<8, Y0<<8}, {AX, AY}, 256, 256, 0 },
    // 2 32x16p double-affine semi-circles
    { &obj_buffer[1], &sub_pos[1], 2, 
        {(X0+16)<<8, Y0<<8}, {AX, AY}, 256, 256, 0 },
    // 4 16x16p double-affine quarter-circles
    { &obj_buffer[3], &sub_pos[3], 4, 
        {(X0-16)<<8, (Y0+40)<<8}, {AX, AY}, 256, 256, 0 },
};

void oac_rotscale(OACOMBO *oac)
{
    int alpha= oac->alpha;
    int sx= oac->sx, sy= oac->sy;
    int sina= lu_sin(alpha)>>4, cosa= lu_cos(alpha)>>4;

    // --- create P ---
    OBJ_AFFINE *oaff= 
        &obj_aff_buffer[BF_GET(oac->sub_obj->attr1, ATTR1_AFF_ID)];
    oaff->pa=  cosa*sx>>8;    oaff->pb= -sina*sx>>8;
    oaff->pc=  sina*sy>>8;    oaff->pd=  cosa*sy>>8;

    // --- create A ---
    // sx = 1/sx, sy = 1/sy (.12f)
    sx= Div(1<<20, sx);
    if(sx != sy)
        sy= Div(1<<20, sy);
    else
        sy= sx;
    FIXED aa, ab, ac, ad;
    aa=  sx*cosa>>12;   ab= sy*sina>>12;    // .8f
    ac= -sx*sina>>12;   ad= sy*cosa>>12;    // .8f

    int ii;
    OBJ_ATTR *obj= oac->sub_obj;
    POINT *pt= oac->sub_pos;
    // --- place each sub-object ---
    for(ii=0; ii<oac->sub_count; ii++)
    {
        int dx, dy;     // all .8f
        sx= oam_sizes[obj->attr0>>14][obj->attr1>>14][0]<<7;
        sy= oam_sizes[obj->attr0>>14][obj->attr1>>14][1]<<7;

        dx= oac->pos.x+oac->anchor.x - sx;  // .8f
        dy= oac->pos.y+oac->anchor.y - sy;  // .8f

        if(obj->attr0&ATTR0_DBL_BIT)
        {   dx -= sx;   dy -= sy;   }

        sx= oac->anchor.x - pt->x - sx;
        sy= oac->anchor.y - pt->y - sy;

        dx -= (aa*sx + ab*sy)>>8;       // .8f
        dy -= (ac*sx + ad*sy)>>8;       // .8f      
        BF_SET(obj->attr0, dy>>8, ATTR0_Y);
        BF_SET(obj->attr1, dx>>8, ATTR1_X);

        obj++;   pt++;
    }
}

void init_main()
{
    memcpy32(pal_obj_mem, oac_gfxPal, oac_gfxPalLen/4);
    memcpy32(tile_mem[4], oac_gfxTiles, oac_gfxTilesLen/4);

    // init objs and obj combos
    oam_init();
    memcpy32(obj_buffer, obj_data, sizeof(obj_data)/4);

    REG_DISPCNT= DCNT_BG0 | DCNT_OBJ | DCNT_OBJ_1D;

    tte_init_chr4_b4_default(0, BG_CBB(2)|BG_SBB(28));
    tte_init_con();

    // Some labels
    tte_printf("#{P:%d,%d}1 full #{P:%d,%d}2 semi #{P:%d,%d}4 quarts", 
        X0-48, Y0-16, X0+20, Y0-16, X0-20, Y0+74);
}

int main()
{
    init_main();

    int ii, alpha=0;
    while(1)
    {
        vid_vsync();
        key_poll();
        alpha -= 128*key_tri_shoulder();

        for(ii=0; ii<3; ii++)
        {
            oacs[ii].alpha= alpha;
            oac_rotscale(&oacs[ii]);
        }
        oam_copy(oam_mem, obj_buffer, 128);
    }
    return 0;
}

Fig 11.8: oacombo in action. Note the gaps.

Fig 11.8 on the right shows a screenshot of the demo. There are three main things to point out here. First, all three objects are indeed roughly the same shape, meaning that the function(s) work. But this was never really much in doubt anyway, since it just follows the math. The second point is that there appear to be gaps in the semi- and quarter-circle combos. If you play with the demo yourself for a while, you’ll see these gaps appear and disappear seemingly at random. Meanwhile, the full-circle object looks fine throughout. Well mostly anyway.

The cause of this is related to the third point. Compare the pixel clusters of all three circles, in particular the smaller circles within each of them. Note that even though they use the exact same P matrix, their formations are different! The reason for this is that while we may have positioned the sub-objects to make them form a bigger object, the pixel-mapping for each of them still starts at their centers. This means that the cumulative offsets that determine which source pixel is used for a given screen pixel will be different and hence you’ll get a different picture, which is especially visible at the seams.

If this is a little hard to visualize, try this: open a bitmap editor and draw a single-width diagonal line. Now duplicate this with a (1, 1) pixel offset. Instead of a single thick line, you’ll have two thin ones with a slit in between. The same thing happens here.

The point is that getting affine objects to align perfectly at the seams will be pretty much impossible. Alright, I suppose in some simple cases you might get away with it, and you could spend time writing code that corrects the textures to align properly, but generally speaking you should expect a hardware-caused uncertainty of about a pixel. This will be a noticeable effect at the off-center reference point, which will tend to wobble a bit, or at the seams of affine object combos, where you’ll see gaps. A simple solution to the former would be to rearrange the object’s tiles so that the ref-point is not off-center (sounds cheap I know, but works beautifully), or to have transparent pixels there – you can’t notice something wobbling if it’s invisible, after all. This would also work for the combo, which might also benefit from having the objects overlap slightly, although I haven’t tried that yet. It may be possible to gain some accuracy by adding rounding terms to the calculations, but I have a hunch that it won’t do that much. Feel free to try though.

Don’t let all this talk of the pitfalls of affine objects get to you too much, I’m just pointing out that it might not be quite as simple as you might have hoped. So they come with a few strings, they’re still pretty cool effects. When designing a game that uses them, take the issues raised in this chapter to heart and make sure your math is in order, it might save you a lot of work later on.

12. Affine backgrounds

Introduction

This section covers affine backgrounds: the ones on which you can perform an affine transformation via the P matrix. And that’s all it does. If you haven’t read – and understood! – the sprite/bg overview and the sections on regular backgrounds and the affine transformation matrix, do so before continuing.

If you know how to build a regular background and have understood the concepts behind the affine matrix, you should have little problems here. The theory behind an affine backgrounds are the same as for regular ones, the practice can be different at a number of very crucial points. For example, you use different registers for positioning and both the map-layout and their format are different.

Of the four backgrounds the GBA has, only the last two can be used as affine backgrounds, and only in specific video modes (see table 12.1). The sizes are also different for affine backgrounds. You can find a list of sizes in table 12.2.

Table 12.1: video modes and background type
mode 0 1 2
bg0 reg reg -
bg1 reg reg -
bg2 reg aff aff
bg3 reg - aff
Table 12.2: affine bg sizes
Sz define (tiles) (pixels)
00 BG_AFF_16x16 16x16 128x128
01 BG_AFF_32x32 32x32 256x256
10 BG_AFF_64x64 64x64 512x512
11 BG_AFF_128x128 128x128 1024x1024

Affine background registers

Like their regular counterparts, the primary control for affine backgrounds is REG_BGxCNT. If you’ve forgotten what it does, you can read a description here. The differences with regular backgrounds are the sizes, and that BG_WRAP actually does something now. The other important registers are the displacement vector dx (REG_BGxX and REG_BGxY), and the affine matrix P (REG_BGxPA-REG_BGxPD). You can find their addresses in table 12.3.

Table 12.3: Affine background register addresses. Note that x is 2 or 3 only!
Register length address
REG_BGxCNT 2 0400:0008h + 2·x
REG_BGxPA-PD 2 0400:0020h + 10h·(x-2)
REG_BGxX 4 0400:0028h + 10h·(x-2)
REG_BGxY 4 0400:002ch + 10h·(x-2)

There are a couple of things to take note of when it comes to displacement and transformation of affine backgrounds. First, the displacement dx uses different registers than regular backgrounds: REG_BGxX and REG_BGxY instead of REG_BGxHOFS and REG_BGxVOFS. A second point here is that they are 24.8 fixed numbers rather than pixel offsets. (Actually, they are 20.8 fixed numbers but that’s not important right now.)

I usually use the affine parameters via BG_AFFINE struct instead of REG_BGxPA, etc. The memory map in tonc_memmap.h contains a REG_BG_AFFINE for this purpose. Setting the registers this way is advantageous at times because you’ll usually have a BG_AFFINE struct set up already, which you can then copy to the registers with a single assignment. An example of this is given below.

The elements of the affine transformation matrix P works exactly like they do for affine sprites: 8.8 fixed point numbers that describe the transformation from screen to texture space. However for affine backgrounds they are stored consecutively (2 byte offset), whereas those of sprites are at an 8 byte offset. You can use the bg_aff_foo functions from tonc_bg_affine.c to set them to the transformation you want.

typedef struct tagBG_AFFINE
{
    s16 pa, pb;
    s16 pc, pd;
    s32 dx, dy
} ALIGN4 BG_AFFINE;

//! BG affine params array
#define REG_BG_AFFINE   ((BG_AFFINE*)(REG_BASE+0x0000))
// Default BG_AFFINE data (tonc_core.c)
const BG_AFFINE bg_aff_default= { 256, 0, 0, 256, 0, 0 };

// Initialize affine registers for bg 2
REG_BG_AFFINE[2] = bg_aff_default;

Regular vs affine tilemap scrolling

Affine tilemaps use different scrolling registers! Instead of REG_BGxHOFS and REG_BGxVOFS, they use REG_BGxX and REG_BGxY. Also, these are 32bit fixed point numbers, not halfwords.

Positioning and transforming affine backgrounds

Now that we know what the displacement and transformation registers are, now let’s look at what they do. This is actually a lot trickier subject that you might think, so pay attention. Warning: this is gonna get mathematical again.

The displacement vector dx works the same as for regular backgrounds: dx contains the background-coordinates that are mapped to the screen origin. (And not the other way around!) However, this time dx is in fixed number notation. Likewise, the affine transformation matrix P works the same as for affine sprites: P describes the transformation from screen space to texture space. To put it mathematically, if we define

(12.1a) T(dx)p := p + dx
T−1(dx) = T(−dx)
(12.1b) P = A−1

then

(12.2a) T(dx)q = p
(12.2b) P · q = p

where

p is a point in texture space,
q is a point in screen space,
dx is the displacement vector (REG_BGxX and REG_BGxY).
A is the transformation from texture to screen space,
P is the transformation screen from to texture space, (REG_BGxPA-REG_BGxPD).

The problem with eq 12.2 is that these only describe what happens if you use either a displacement or a transformation. So what happens if you want to use both? This is an important question because the order of transformation matters (like we have seen in the affine sprite demo), and this is true for the order of transformation and displacement as well. As it happens, translation goes first:

(12.3)
q = A · T(−dx) p
T(dx) P · q = p
dx + P · q = p

Another way to say this is that the transformation always uses the top left of the screen as its origin and the displacement tells which background pixels is put there. Of course, this arrangement doesn’t help very much if you want to, say, rotate around some other point on the screen. To do that you’ll have to pull a few tricks. To cover them all in one swoop, we’ll combine eq 12.3 and the general coordinate transformation equation:

(12.4)
dx + P · q = p
P · (q − q0) = p − p0
dx + P · q0 = p0
dx = p0P · q0

So what the hell does that mean? It means that if you use this dx for your displacement vector, you perform your transformation around texture point p0, which then ends up at screen point q0; the P·q0 term is the correction in texture-space you have to perform to have the rotation point at q0 instead of (0,0). So what the hell does that mean? It means that before you try to use this stuff you should think about which effect you are actually trying to pull off and that you have two coordinate systems to work with, not one. When you do, the meaning of eq 12.4 will become apparent. In any case, the function I use for this is bg_rotscale_ex(), which basically looks like this:

typedef struct tagAFF_SRC_EX
{
    s32 tex_x, tex_y;   // vector p0: origin in texture space (24.8f)
    s16 scr_x, scr_y;   // vector q0: origin in screen space (16.0f)
    s16 sx, sy;         // scales (8.8f)
    u16 alpha;          // CCW angle ( integer in [0,0xFFFF] )
} ALIGN4 AFF_SRC_EX;

void bg_rotscale_ex(BG_AFFINE *bgaff, const AFF_SRC_EX *asx)
{
    int sx= asx->sx, sy= asx->sy;
    int sina= lu_sin(asx->alpha), cosa= lu_cos(asx->alpha);

    FIXED pa, pb, pc, pd;
    pa=  sx*cosa>>12;   pb=-sx*sina>>12;    // .8f
    pc=  sy*sina>>12;   pd= sy*cosa>>12;    // .8f

    bgaff->pa= pa;  bgaff->pb= pb;
    bgaff->pc= pc;  bgaff->pd= pd;

    bgaff->dx= asx->tex_x - (pa*asx->scr_x + pb*asx->scr_y);
    bgaff->dy= asx->tex_y - (pc*asx->scr_x + pd*asx->scr_y);
}

This is very similar to the obj_rotscale_ex() function covered in the off-center object transformation section. The math is identical, but the terms have been reshuffled a bit. The background version is actually simpler because the affine offset correction can be done in texture space instead of screen space, which means no messing about with P’s inverse matrix. Or with sprite-size corrections, thank IPU. For the record, yes you can apply the function directly to REG_BG_AFFINE.

Internal reference point registers

There’s one more important thing left to mention about the displacement and transformation registers. Quoting directly from GBATEK (except the bracketed parts):

The above reference points [the displacement registers] are automatically copied to internal registers during each vblank, specifying the origin for the first scanline. The internal registers are then incremented by dmx [REG_BGxPB] and dmy [REG_BGxPD] after each scanline. Caution: Writing to a reference point register by software outside of the Vblank period does immediately copy the new value to the corresponding internal register, that means: in the current frame, the new value specifies the origin of the current scanline (instead of the topmost scanline).

Normally this won’t matter to you, but if you try to write to REG_BGxY during an HBlank things, might not go as expected. As I learned the hard way when I tried to get my Mode 7 stuff working. This only affects affine backgrounds, though; regular ones use other registers.

Mapping format

Both the map layout and screen entries for affine backgrounds are very different from those of regular backgrounds. Ironically, they are also a lot simpler. While regular backgrounds divide the full map into quadrants (each using one full screenblock), the affine backgrounds use a flat map, meaning that the normal equation for getting a screenentry-number n works, making things a whole lot easier.

(12.5) n = tx + ty·tw

The screen entries themselves are also different from those of regular backgrounds as well. In affine maps, they are 1 byte long and only contain the index of the tile to use. Additionally, you can only use 256 color tiles. This gives you access to all the tiles in the base charblock, but not the one(s) after it.

And that’s about it, really. No, wait there’s one more issue: you have to be careful when filling or changing the map because VRAM can only be accessed 16 or 32 bits at a time. So if you have your map stored in an array of bytes, you’ll have to cast it to u16 or u32 first. Or use DMA. OK, now I’m done.

Regular vs affine tilemap mapping differences

There are two important differences between regular and affine map formats. First, affine screen entries are merely one-byte tile indices. Secondly, the maps use a linear layout, rather than the division into 32x32t maps that bigger regular maps use.

sbb_aff demo

sbb_aff demo Fig 12.1: sbb_aff demo.

sbb_aff is to affine backgrounds what sbb_reg was to regular ones, with a number of extras. The demo uses a 64x64 tile affine background, shown in fig 12.1. This is divided into 16 parts of 256 bytes, each of which is filled with tiles of one color and the number of that part on it. Now, if the map-layout for affine backgrounds was the same as regular ones, each part would form a 16x16t square. If it is a flat memory layout, each part would be a 64x16t strip. As you can see in fig 12.1, it is the latter. You can also see that, unlike regular backgrounds, this map doesn’t wrap around automatically at the edges.

The most interesting thing about the demo are the little black and white crosshairs. The white crosshairs indicates the rotation point (the anchor). As I said earlier, you cannot simply pick a map-point p0 and say that that is ‘the’ rotation point. Well you could, but it wouldn’t give the desired effect. Simply using a map-point will give you a rotating map around that point, but on screen it’ll always be in the top-left corner. To move the map anchor to a specific location on the screen, you need an anchor there as well. This is q0. Fill both into eq 12.4 to find the displacement vector you need: dx = p0P·q0. This dx is going to be quite different from both p0 and q0. Its path is indicated by the black crosshairs.

The demo lets you control both p0 and q0. And rotation and scaling, of course. The full list of controls is.

D-pad move map rotation point, p0
D-pad + A move screen rotation point, q0
L,R rotate the background.
B(+Se) scale up and down.
St Toggle wrapping flag.
St+Se Reset anchors and P
#include <stdio.h>
#include <tonc.h>
#include "nums.h"

#define MAP_AFF_SIZE 0x0100

// --------------------------------------------------------------------
// GLOBALS
// --------------------------------------------------------------------

OBJ_ATTR *obj_cross= &oam_mem[0];
OBJ_ATTR *obj_disp= &oam_mem[1];

BG_AFFINE bgaff;

// --------------------------------------------------------------------
// FUNCTIONS
// --------------------------------------------------------------------

void win_textbox(int bgnr, int left, int top, int right, int bottom, int bldy)
{
    REG_WIN0H= left<<8 | right;
    REG_WIN0V=  top<<8 | bottom;
    REG_WIN0CNT= WIN_ALL | WIN_BLD;
    REG_WINOUTCNT= WIN_ALL;

    REG_BLDCNT= (BLD_ALL&~BIT(bgnr)) | BLD_BLACK;
    REG_BLDY= bldy;

    REG_DISPCNT |= DCNT_WIN0;

    tte_set_margins(left, top, right, bottom);
}

void init_cross()
{
    TILE cross=
    {{
        0x00011100, 0x00100010, 0x01022201, 0x01021201,
        0x01022201, 0x00100010, 0x00011100, 0x00000000,
    }};
    tile_mem[4][1]= cross;

    pal_obj_mem[0x01]= pal_obj_mem[0x12]= CLR_WHITE;
    pal_obj_mem[0x02]= pal_obj_mem[0x11]= CLR_BLACK;

    obj_cross->attr2= 0x0001;
    obj_disp->attr2= 0x1001;
}

void init_map()
{
    int ii;

    memcpy32(&tile8_mem[0][1], nums8Tiles, nums8TilesLen/4);
    memcpy32(pal_bg_mem, numsPal, numsPalLen/4);

    REG_BG2CNT= BG_CBB(0) | BG_SBB(8) | BG_AFF_64x64;
    bgaff= bg_aff_default;

    // fill per 256 screen entries (=32x4 bands)
    u32 *pse= (u32*)se_mem[8];
    u32 ses= 0x01010101;
    for(ii=0; ii<16; ii++)
    {
        memset32(pse, ses, MAP_AFF_SIZE/4);
        pse += MAP_AFF_SIZE/4;
        ses += 0x01010101;
    }
}

void sbb_aff()
{
    AFF_SRC_EX asx=
    {
        32<<8, 64<<8,           // Map coords.
        120, 80,                // Screen coords.
        0x0100, 0x0100, 0       // Scales and angle.
    };

    const int DX=256;
    FIXED ss= 0x0100;

    while(1)
    {
        vid_vsync();
        key_poll();

        // dir + A : move map in screen coords
        if(key_is_down(KEY_A))
        {
            asx.scr_x += key_tri_horz();
            asx.scr_y += key_tri_vert();
        }
        else    // dir : move map in map coords
        {
            asx.tex_x -= DX*key_tri_horz();
            asx.tex_y -= DX*key_tri_vert();
        }
        // rotate
        asx.alpha -= 128*key_tri_shoulder();


        // B: scale up ; B+Se : scale down
        if(key_is_down(KEY_B))
            ss += (key_is_down(KEY_SELECT) ? -1 : 1);

        // St+Se : reset
        // St : toggle wrapping flag.
        if(key_hit(KEY_START))
        {
            if(key_is_down(KEY_SELECT))
            {
                asx.tex_x= asx.tex_y= 0;
                asx.scr_x= asx.scr_y= 0;
                asx.alpha= 0;
                ss= 1<<8;
            }
            else
                REG_BG2CNT ^= BG_WRAP;
        }

        asx.sx= asx.sy= (1<<16)/ss;

        bg_rotscale_ex(&bgaff, &asx);
        REG_BG_AFFINE[2]= bgaff;

        // the cross indicates the rotation point
        // (== p in map-space; q in screen-space)
        obj_set_pos(obj_cross, asx.scr_x-3, (asx.scr_y-3));
        obj_set_pos(obj_disp, (bgaff.dx>>8)-3, (bgaff.dy>>8)-3);

        tte_printf("#{es;P}p0\t: (%d, %d)\nq0\t: (%d, %d)\ndx\t: (%d, %d)",
            asx.tex_x>>8, asx.tex_y>>8, asx.scr_x, asx.scr_y,
            bgaff.dx>>8, bgaff.dy>>8);
    }
}

int main()
{
    init_map();
    init_cross();

    REG_DISPCNT= DCNT_MODE1 | DCNT_BG0 | DCNT_BG2 | DCNT_OBJ;

    tte_init_chr4_b4_default(0, BG_CBB(2)|BG_SBB(28));
    tte_init_con();
    win_textbox(0, 8, 120, 232, 156, 8);

    sbb_aff();

    return 0;
}

13. Graphic Effects

So you know how to put sprites and backgrounds on screen, do ya? Now, how about some extra effects to liven up the place? When discussing sprites and backgrounds, we left some flags untouched, namely the mosaic and blending flags. There will be covered here. We’ll also be looking into windowing, with which you can create regions to mask out backgrounds or sprites.

Mosaic

The best description of mosaic is that it makes sprites or tiles look blocky. A mosaic works in two dimensions with parameters wm and hm. These numbers divide your sprite or background into blocks of wm × hm pixels. The top-left pixel of each block is used to fill the rest of that block, which makes it blocky. Fig 13.1 shows a 1x4 mosaic for a metroid sprite. The blue lines indicate the vertical block-boundaries. The first line of each block is copied to the rest of the block, just like I said. Other examples of the mosaic effect are Zelda:LTTP when you hit an electric baddie, or Metroid Fusion when an X changes shape.

a 1x4 mosaiced metroid Fig 13.1: a 1×4 mosaiced metroid.

Using mosaic: sprite/bg flags and REG_MOSAIC

To use mosaic you must do two things. First, you need to enable mosaic. For individual sprites, set OBJ_ATTR.attr0{C}. For backgrounds, set REG_BGxCNT{7}. The set the mosaic levels through REG_MOSAIC, which looks like this:

REG_MOSAIC @ 0400:004Ch
F E D C B A 9 8 7 6 5 4 3 2 1 0
Ov Oh Bv Bh

bits name define description
0-3 Bh MOS_BH# Horizontal BG stretch.
4-7 Bv MOS_BV# Vertical BG stretch.
8-B Oh MOS_OH# Horizontal object stretch.
C-F Ov MOS_OV# Vertical object stretch.

The stretch is across how many pixels the base-pixel is stretched. This corresponds to *wm*−1 or *hm*−1. With a nybble for each effect, you have stretches between 0 and 15, giving mosaic widths and heights between 1 and 16.

Enabling mosaic

For backgrounds, set bit 7 of REG_BGxCNT. For sprites, set bit 12 in attribute 0. Then set the mosaic levels in REG_MOSAIC.

A small mosaic demo

There is a demo called mos_demo that illustrates the use of mosaic for both objects and backgrounds.

// mos_demo.c
//   bg 0, cbb  0, sbb 31, pb 0: text
//   bg 1, cbb  1, sbb 30, pb 1: bg metroid
//   oam 0: tile 0-63: obj metroid

#include <stdio.h>
#include <tonc.h>
#include "metr.h"

void test_mosaic()
{
    tte_printf("#{P:48,8}obj#{P:168,8}bg");
    tte_set_margins(4, 130, 128, 156);

    POINT pt_obj={0,0}, pt_bg={0,0};
    POINT *ppt= &pt_obj;
    while(1)
    {
        vid_vsync();

        // control the mosaic
        key_poll();

        // switch between bg or obj mosaic
        ppt= key_is_down(KEY_A) ? &pt_bg : &pt_obj;
        ppt->x += key_tri_horz();       // inc/dec h-mosaic
        ppt->y -= key_tri_vert();       // inc/dec v-mosaic

        ppt->x= clamp(ppt->x, 0, 0x80);
        ppt->y= clamp(ppt->y, 0, 0x80);

        REG_MOSAIC= MOS_BUILD(pt_bg.x>>3, pt_bg.y>>3, pt_obj.x>>3, pt_obj.y>>3);

        tte_printf("#{es;P}obj h,v: %2d,%2d\n bg h,v: %2d,%2d",
            pt_obj.x>>3, pt_obj.y>>3, pt_bg.x>>3, pt_bg.y>>3);
    }
}

void load_metr()
{
    int ix, iy;

    memcpy32(&tile_mem[1][0], metrTiles, metrTilesLen/4);
    memcpy32(&tile_mem[4][0], metrTiles, metrTilesLen/4);
    memcpy32(pal_obj_mem, metrPal, metrPalLen/4);

    // create object: oe0
    OBJ_ATTR *metr= &oam_mem[0];
    obj_set_attr(metr, ATTR0_SQUARE | ATTR0_MOSAIC, ATTR1_SIZE_64, 0);
    obj_set_pos(metr, 32, 24);              // left-center

    // create bg map: bg1, cbb1, sbb 31

    for(ix=1; ix<16; ix++)
        pal_bg_mem[ix+16]= pal_obj_mem[ix] ^ CLR_WHITE;

    SCR_ENTRY *pse= &se_mem[30][3*32+18];    // right-center
    for(iy=0; iy<8; iy++)
        for(ix=0; ix<8; ix++)
            pse[iy*32+ix]= (iy*8+ix) | SE_PALBANK(1);

    REG_BG1CNT= BG_CBB(1) | BG_SBB(30) | BG_MOSAIC;
}

int main()
{
    // setup sprite
    oam_init(oam_mem, 128);
    load_metr();
    REG_DISPCNT= DCNT_BG0 | DCNT_BG1 | DCNT_OBJ | DCNT_OBJ_1D;

    // set-up text: bg0, cbb0, sbb31
    tte_init_chr4_b4_default(0, BG_CBB(2)|BG_SBB(31));
    tte_init_con();

    test_mosaic();
    return 0;
}
Fig 13.2: mos_demo.

I use two metroids in this demo. The sprite metroid is on the left, and the background metroid with inverted colors is on the right. I’ve shown how to set-up sprites and backgrounds before, so you should be able to follow the steps here because it’s nothing new. Well, except setting the mosaic flags in OBJ_ATTR.attr0 and REG_BG0CNT, which I’ve put in bold here.

The mosaic effect is regulated inside the test_mosaic(). I use two 2d points to keep track of the current level of mosaic. The D-pad is used to increase or decrease the mosaic levels; just the D-pad sets the object’s mosaic and holding down A sets that of the background.

On a code design note, I could have used two if-blocks here, one for objects and one for the background, but I can also switch the mosaic context via a pointer, which saves me some code. Hurray for pointers. Also, the coordinates are in .3 fixed point format, which is how I slow down the changes in the mosaic levels. Again, I could have used timer variables and more checks to see if they had reached their thresholds, but fixed-point timers are much easier and in my view cleaner too.

You should really see the demo on hardware, by the way. Somehow both VBA and no$gba are both flawed when it comes to mosaic. After VBA 1.7.2, it has a problem with horizontal sprite mosaic. I do believe I’ve seen inconsistencies between hardware and scrolling mosaiced backgrounds, but can’t remember where I saw it. As for no$gba, vertical mosaic appears to be disabled for both sprites and backgrounds.

Emulators and mosaic

VBA and no$gba, the most popular GBA emulators both have problems with mosaic. Watch your step.

Blending

If you’re not completely new to gaming or graphics, you may have heard of alpha blending. It allows you to combine the color values two overlapping layers, thus creating transparency (also known as semi-transparency, because something that’s completely transparent is invisible). Some bitmap types also come with an alpha channel, which indicates either the transparency or opacity of the pixel in question.

The basic idea behind blending is this. You have two layers, A and B, that overlap each other. Consider A to be on top of B. The color-value of the a pixel in this region is defined as

(13.1) C = wA·A + wB·B,

where wA and wB are the weights of the layers. The weights are generally normalised (between 0 and 1), with 0 being fully transparent and 1 being fully visible. It is also convenient to think of color-components in this way. Here’s a few things you can do with them:

wA wB effect
1 0 layer A fully visible (hides B; standard)
0 1 layer B fully visible (or A is invisible)
α 1−α Alpha blending. α is opacity in this case.

Note that in these examples the sum of the weights is 1, so that the final color C is between 0 (black) and 1 (white) as well. As we’ll see, there are instances where you can drop out of these ranges; if this happens the values will be clipped to the standard range.

GBA Blending

Backgrounds are always enabled for blending. To enable sprite-blending, set OBJ_ATTR.attr0{a}. There are three registers that control blending, which unfortunately go by many different names. The ones I use are REG_BLDCNT, REG_BLDALPHA and REG_BLDY. Other names are REG_BLDMOD, REG_COLEV and REG_COLEY, and sometimes the ‘E’ in the last two is removed. Be warned. Anyway, the first says how and on which layers the blend should be performed, the last two contain the weights. Oh, since the GBA doesn’t do floating point, the weights are fixed-point numbers in 1.4 format. Still limited by 0 and 1, of course, so there are 17 blend levels.

REG_BLDCNT (REG_BLDMOD) @ 0400:0050h
F E D C B A 9 8 7 6 5 4 3 2 1 0
- bBD bOBJ bBG3 bBG2 bBG1 bBG0 BM aBD aObj aBG3 aBG2 aBG1 aBG0

bits name define description
0-5 aBG0-aBD BLD_TOP# The A (top) layers. BD, by the way, is the back drop, a solid plane of color 0. Set the bits to make that layer use the A-weights. Note that these layers must actually be in front of the B-layers, or the blend will fail.
6-7 BM BLD_OFF, BLD_STD, BLD_WHITE, BLD_BLACK, BLD_MODE# Blending mode.
  • 00: blending is off.
  • 01: normal blend using the weights from REG_ALPHA.
  • 10: blend A with white (fade to white) using the weight from REG_BLDY
  • 11: blend A with black (fade to black) using the weight from REG_BLDY
8-D bBG0-bBD BLD_BOT# The B (bottom) layers. Use the B-weights. Note that these layers must actually lie behind the A-layers, or the blend will not work.

The REG_BLDALPHA and REG_BLDY registers hold the blending weights in the form of eva, evb and ey, all in 1.4 fixed-point format. And no, I do not know why they are called that; they just are.

REG_BLDALPHA (REG_COLEV) @ 0400:0052h
F E D C B A 9 8 7 6 5 4 3 2 1 0
- evb - eva
bits name define description
0-4 eva BLD_EVA# Top blend weight. Only used for normal blending
8-C evb BLD_EVB# Bottom blend weight. Only used for normal blending

REG_BLDY (REG_COLEY) @ 0400:0054h
F E D C B A 9 8 7 6 5 4 3 2 1 0
- ey
bits name define description
0-4 ey BLDY# Top blend fade. Used for white and black fades.

Blending caveats

Blending is a nice feature to have, but keep these points in mind.

  • The A layers must be in front of the B layers. Only then will the blend actually occur. So watch your priorities.
  • In the alpha-blend mode (mode 1) the blend will only take place on the overlapping, non-transparent pixels of layer A and layer B. Non-overlapping pixels will still have their normal colors.
  • Sprites are affected differently than backgrounds. In particular, the blend mode specified by REG_BLDCNT{6,7} is applied only to the non-overlapping sections (so that effectively only fading works). For the overlapping pixels, the standard blend is always in effect, regardless of the current blend-mode.
  • If you are using windows, you need to set the bits 5 and/or 13 in REG_WININ or REG_WINOUT for the blending to work.

The obligatory demo

// bld_demo.c

//   bg 0, cbb  0, sbb 31, pb 15: text
//   bg 1, cbb  2, sbb 30, pb 1: metroid
//   bg 2, cbb  2, sbb 29, pb 0: fence
//   oam 0: tile 0-63: obj metroid

#include <stdio.h>
#include <tonc.h>
#include "../gfx/metr.h"

void test_blend()
{
    tte_printf("#{P:48,8}obj#{P:168,8}bg");
    tte_set_margins(16, SCR_H-4-4*12, SCR_W-4, SCR_H-4);

    u32 mode=0;
    // eva, evb and ey are .4 fixeds
    // eva is full, evb and ey are empty
    u32 eva=0x80, evb= 0, ey=0;

    REG_BLDCNT= BLD_BUILD(
        BLD_OBJ | BLD_BG0,  // Top layers
        BLD_BG1,            // Bottom layers
        mode);              // Mode

    while(1)
    {
        vid_vsync();
        key_poll();

        // Interactive blend weights
        eva += key_tri_horz();
        evb -= key_tri_vert();
        ey  += key_tri_fire();

        mode += bit_tribool(key_hit(-1), KI_R, KI_L);

        // Clamp to allowable ranges
        eva = clamp(eva, 0, 0x81);
        evb = clamp(evb, 0, 0x81);
        ey  = clamp(ey, 0, 0x81);
        mode= clamp(mode, 0, 4);

        tte_printf("#{es;P}mode :\t%2d\neva :\t%2d\nevb :\t%2d\ney :\t%2d",
            mode, eva/8, evb/8, ey/8);

        // Update blend mode
        BFN_SET(REG_BLDCNT, mode, BLD_MODE);

        // Update blend weights
        REG_BLDALPHA= BLDA_BUILD(eva/8, evb/8);
        REG_BLDY= BLDY_BUILD(ey/8);
    }
}

void load_metr()
{
    // copy sprite and bg tiles, and the sprite palette
    memcpy32(&tile_mem[2][0], metrTiles, metrTilesLen/4);
    memcpy32(&tile_mem[4][0], metrTiles, metrTilesLen/4);
    memcpy32(pal_obj_mem, metrPal, metrPalLen/4);

    // set the metroid sprite
    OBJ_ATTR *metr= &oam_mem[0]; // use the first sprite
    obj_set_attr(metr, ATTR0_SQUARE | ATTR0_BLEND, ATTR1_SIZE_64, 0);
    obj_set_pos(metr, 32, 24);       // mid-center

    // create the metroid bg
    // using inverted palette for bg-metroid
    int ix, iy;
    for(ix=0; ix<16; ix++)
        pal_bg_mem[ix+16]= pal_obj_mem[ix] ^ CLR_WHITE;

    SCR_ENTRY *pse= &se_mem[30][3*32+18]; // right-center
    for(iy=0; iy<8; iy++)
        for(ix=0; ix<8; ix++)
            pse[iy*32+ix]= iy*8+ix + SE_PALBANK(1);

    REG_BG0CNT= BG_CBB(0) | BG_SBB(30);
}

// set-up the fence background
void load_fence()
{

    // tile 0 / ' ' will be a fence tile
    const TILE fence=
    {{
        0x00012000, 0x00012000, 0x00022200, 0x22220222,
        0x11122211, 0x00112000, 0x00012000, 0x00012000,
    }};
    tile_mem[2][64]= fence;
    se_fill(se_mem[29], 64);

    pal_bg_mem[0]= RGB15(16, 10, 20);
    pal_bg_mem[1]= RGB15( 0,  0, 31);
    pal_bg_mem[2]= RGB15(16, 16, 16);

    REG_BG2CNT= BG_CBB(2) | BG_SBB(29);
}

int main()
{
    oam_init(oam_mem, 128);
    load_metr();
    load_fence();

    tte_init_chr4_b4_default(0, BG_CBB(0)|BG_SBB(31));
    tte_init_con();

    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0 | DCNT_BG1 | DCNT_BG2 |
        DCNT_OBJ | DCNT_OBJ_1D;

    test_blend();

    return 0;
}
bld_demo Fig 13.3: blend demo; mode=2, eva=0, evb=0, ey=10.

As always, there’s a demo that goes with all this stuff. bld_demo features 2 metroids (the left one is a sprite, the right one (palette inverted) is on background 0) on a fence-like background (bg 1 to be precise) and lets you modify the mode, and the 3 weights independently. The mode, by the way, is given in the top left corner. The controls are:

left, right changes eva. Note that eva is at maximum initially.
down,up changes evb.
B,A Changes ey
L,R Changes mode.

The function of interest is test_blend(). This is where the key handling takes place and where the blend settings are altered. Similar to mos_demo, .3 fixeds are used for the blend weight variables to slow the rate of change to more comfortable levels. To set the blend registers themselves I’m using BUILD() macros and BF_SET(), which work well enough for these purposes. It would be trivially easy to write wrapper functions here of course. Most of the code is pretty standard; just play around with the blend modes and weights and see what happens.

Do take note of how, like I said earlier, the sprite metroid is affected differently than the bg-metroid. The background-background blend behaves exactly as the mode says it should; the sprite, on the other hand, always has a blend if they overlap with the fence’s pixels, and the rest obeys the mode, which is what I told you in the caveats.

Windowing

Windowing allows you to divide the screen into rectangular areas known as, well, windows. There are two basic windows: win0 and win1. There’s also a third type of window, the object window. This creates a window out of the visible pixels of the sprites. You can enable the windows by setting REG_DISPCNT{d,e,f}, respectively.

A rectangular window is defined by its left, right, top and bottom sides. Unless you’re one of those people, who think it’s funny to say that a rectangle has only two sides: an inside and an outside. In fact, this is truer than you think. The union of win0 and win1 is the inside window. There’s also the outside window, which is everything else. In other words:

winIn = win0 | win1
winOut = ~(winIn)
Showing win0, win1, and win_out windows Fig 13.4a: showing win0, win1, and win_out windows.
diagram. Fig 13.4b: win0 in red, win1 in green, winIn is win0 | win1 (blue edge), winOut in grey.

Window boundaries

Both win0 and win1 have 2 registers that define their boundaries. In order these are REG_WIN0H (0400:0040h), REG_WIN1H (0400:0042h), REG_WIN0V (0400:0044h) and REG_WIN1V (0400:0046h), which have the following layout:

REG_WINxH and REG_WINxV @ 0400:0040-0400:0047h
reg F E D C B A 9 8 7 6 5 4 3 2 1 0
REG_WINxH left right
REG_WINxV top bottom

bits name description
0-7 right Right side of window (exclusive)
8-F left Left side of window (inclusive)
-
0-7 bottom Bottom side of window (exclusive)
8-F top Top side of window (inclusive)

So you have one byte for each value. That’s bytes as in unsigned chars. The contents of a window are drawn from starting at the top-left up to, but not including, the bottom-right. What you have to realize is that this is also true when, say, the right value is lower than the left value. In such a case, there’s a wrap-around and everything on that line is inside the window, except the pixels between R and L. If both R < L and B < T then you get a window in the shape of a cross.

Window content

The possible content for the windows are backgrounds 0-3 and objects. No suprise there, right? In total, we have regions: win0, win1, winOut and winObj. REG_WININ (0400:0048h) controls win0 and win1, REG_WINOUT (0400:004ah) takes care of winOut and winObj. There’s one bit for each content-type, plus one for blending, which you will need if you intend to use blending on the contents of that particular window.

register F E D C B A 9 8 7 6 5 4 3 2 1 0
bits - Bld Obj BG3 BG2 BG1 BG0 - Bld Obj BG3 BG2 BG1 BG0
REG_WININ - win1 - win0
REG_WINOUT - winObj - winOut

bits name define description
0-5 BGx, Obj, Bld WIN_BGx, WIN_OBJ, WIN_BLD, WIN_LAYER# Windowing flags. To be used with all bytes in REG_WININ and REG_WINOUT.

There is little in the way of macros or bit-defines here because they’re not really necessary. Do have these in tonc_memdef.h though:

#define WIN_BUILD(low, high)    \
    ( ((high)<<8) | (low) )

#define WININ_BUILD(win0, win1)     WIN_BUILD(win0, win1)

#define WINOUT_BUILD(out, obj)      WIN_BUILD(out, obj)

There are still a few things you should know about windows. First of all, when you turn on windowing in REG_DISPCNT, nothing will show up. There are two reasons for this. Firstly, the boundary registers are all 0, so the whole screen is basically winOut. Secondly, and this is really important: a background or object will only show up in the windows in which it is enabled! This means that unless at least some bits have been set in REG_WININ or REG_WINOUT nothing will show. This presents you with an effective way of hiding stuff, as we’ll see in the demo. There is a third thing that you must remember, namely that win0 takes precedence over win1, which in turn takes precedence over winOut. I’m not sure how winObj fits into this yet.

Windowing necessities

To make windowing work for you, you need to do the following things:

  • Enable windows in REG_DISPCNT
  • Indicate in which window you want things to show up by setting the appropriate bits in REG_WININ and REG_WINOUT. You must set at least some bits here if you have windowing enabled, or nothing will show up at all!
  • Set the desired window sizes in REG_WINxH/V. If you don’t, everything will be considered in the Out-window.

Caveats

There’s something really weird going on when either the top or bottom is outside of the screen. Multiple somethings in fact, see the demo on hardware! for details.

  • If the top is in the [-29, 0⟩ range (i.e., [227, 255]), the window will not be rendered at all. Likewise, if the bottom is inside this range, the window covers the height of the screen. I cannot say exactly what the cause is, but since the VCount also stops at 227, that might have something to do with it.
  • Also, if you move the bottom from, 161 to 160, the window will also cover the whole length, but only for a frame or so.
  • The points mentioned above assume T<B. If the top is bigger, then the effect is reversed.

Windowing weirdness not on emulators

This behaviour does not appear on the emulators I’ve tested on.

VBA clips the windows, like common sense would lead you to believe. (Of course, common sense also tells you that the Sun orbits the Earth or that the stars are pinpricks on a large black canvas. Common sense is hardly common).

MappyVM and BoycottAdvance simply remove the window if any of the boundaries goes off the screen.

Demo: there’s a rocket in my pocket

In case you hadn’t noticed yet, I like the Metroid series. I really like the Metroid series. If you have ever played Super Metroid chances are that you’ve used the X-ray scope, which let’s you see through the layers and find items and secret passages with much more ease. Guess how that was done? Yup, windowing. The windowing demo win_demo essentially does the same thing. There’s a rocket-item hidden behind the background layers and you have an X-ray rectangle which you can move around the screen so you can find it.

The controls are simple: use the D-pad to move the window around; START repositions the rocket. I’ve also added finer movement (A + D-pad) so you can see the strange behaviour the windows seem to exhibit at certain positions.

dir Moves the rectangle.
A + dir Move rectangle by tapping for finer control.
start Randomly change the position of the rocket.

What follows below is the majority of the demo’s code. I have removed the functions that set up the backgrounds and sprite because there’s nothing in them that you haven’t seen before already. The earlier fig 13.4a is a screenshot of the demo in action.

// win_demo.c

//   bg 0, cbb  0, sbb  2, pb 0: numbered forground
//   bg 1, cbb  0, sbb  3, pb 0: fenced background
//   oam 0: tile 0-3: rocket

//   win 0: objects
//   win 1: bg 0
//   win out : bg 1

#include <tonc.h>
#include "nums.h"
#include "rocket.h"

typedef struct tagRECT_U8 { u8 ll, tt, rr, bb; } ALIGN4 RECT_U8;

// window rectangle regs are write only, so buffers are necessary
// Objects in win0, BG 0 in win1
RECT_U8 win[2]=
{
    { 36, 20,  76,  60 },   // win0: 40x40 rect
    { 12, 12 ,228, 148 }    // win1: screen minus 12 margin.
};

// gfx loaders omitted for clarity
void init_front_map();  // numbers tiles
void init_back_map();   // fence
void init_rocket();     // rocket

void win_copy()
{
    REG_WIN0H= win[0].ll<<8 | win[0].rr;
    REG_WIN1H= win[1].ll<<8 | win[1].rr;
    REG_WIN0V= win[0].tt<<8 | win[0].bb;
    REG_WIN1V= win[1].tt<<8 | win[1].bb;
}

void test_win()
{
    win_copy();
    while(1)
    {
        key_poll();
        vid_vsync();

        // key_hit() or key_is_down() 'switch'
        // A depressed: move on direction press (std movement)
        // A pressed  : moves on direction hit (fine movement)
        int keys= key_curr_state();
        if(key_is_down(KEY_A))
            keys &= ~key_prev_state();

        if(keys & KEY_RIGHT)
        {   win[0].ll++;        win[0].rr++;    }
        else if(keys & KEY_LEFT )
        {   win[0].ll--;        win[0].rr--;    }
        if(keys & KEY_DOWN)
        {   win[0].tt++;        win[0].bb++;    }
        else if(keys & KEY_UP )
        {   win[0].tt--;        win[0].bb--;    }

        // (1) randomize rocket position
        if(key_hit(KEY_START))
            obj_set_pos(&oam_mem[0],
                qran_range(0, 232), qran_range(0, 152));

        win_copy();
    }
}

int main()
{
    // obvious inits
    oam_init();
    init_front_map();
    init_back_map();
    init_rocket();

    // (2) windowing inits
    REG_DISPCNT= DCNT_BG0 | DCNT_BG1 | DCNT_OBJ | DCNT_OBJ_1D |
        DCNT_WIN0 |     // Enable win 0
        DCNT_WIN1;      // Enable win 1

    REG_WININ= WININ_BUILD(WIN_OBJ, (WIN_BG0);
    REG_WINOUT= WINOUT_BUILD(WIN_BG1, 0);

    win_copy();     // Initialize window rects

    test_win();

    return 0;
}

Initializing the windows is done at point 2: both win0 and win1 in REG_DISPCNT, objects in win 0, bg 0 in win 1 and bg1 in winOut. The windows’ sizes are set using win_copy() in each frame. I am using two rectangle variables to keep track of where the windows are, because the window-rectangle registers themselves are write only. See fig 13.4 again for the result.

Usually, objects are shown in front of backgrounds. However, because objects are now only set to appear inside win 0, they are effectively hidden everywhere else: you will only see the rocket or parts of it if the rocket and win 0’s rectangle overlap. Furthermore, you will notice that because only objects are set for win 0, the window itself is completely black.

The rest of the demo is rather uneventful. I could explain that the way mask the variable keys with the previous keystate when A is held down lets me switch between the key_hit() and key_is_down() functions, giving me the functionality I require to switch between direct and fine motion for the X-ray window, but it’s not all that interesting and quite besides the point of the demo. What’s also beside the point of the demo, but is interesting to mention, is the randomization of the rocket’s position.

Random numbers

Random numbers on a computer is a somewhat quaint notion. The whole point of a computer is to have a reliable calculator, and random numbers are pretty much the antithesis of that. Computer generated random numbers are also called pseudo-random, because they aren’t intrinsically random, just deterministically generated to seem that way. There are statistical tests to see if a given routine is sufficiently random. However, this isn’t nuclear physics we’re talking about, this is game programming. We mostly need something that can, say, make an enemy zig or zag without any discernable pattern; that it can kill a Monte Carlo simulation is totally irrelevant.

One class of generators are linear congruential generators, which follow the pattern Ni+1 = (a·Ni + c)%m, with Ni∈[0, m⟩. With properly picked parameters a, c and m, the routine can be quite adequate. If you ever encounter a rand() function in any kind of standard library, chances are it’s one of these. Not only are these easy to implement, they are likely to be fast as well.

The following routine qran() is taken from my numerical methods book, Numerical Recipes, pp 275, where it is labelled a quick and dirty generator, but an adequate one. Consisting of one addition and one multiply (m=232, so done automatically), it is very fast. The actual number returned are the top 15 bits from N, because the upper bits are apparently more random than the lower, and also because 15 gives a [0,32767] range, which is something of an unofficial standard, AFAIK. Note that there is a second function, sqran() used to seed the generator. Since the process itself is still deterministic, you need a seed to ensure that you don’t get the same sequence every time. Unless, that is, you actually want that to happen. This isn’t such a strange idea if you think about it: you could use it to generate maps, for example. Instead of storing the whole map so that it looks the same every time you load it, you just store the seed and you’re done. This is how the planetary terrains in Star Control 2 are made; I very much doubt it would have been possible to store bitmaps of all the 1000+ planets it had. This is why sqran() also returns the current N, so you can reset it later if necessary.

// from tonc_core.h/.c
// A Quick (and dirty) random number generator and its seeder

int __qran_seed= 42;     // Seed / rnd holder

// Seed routine
int sqran(int seed)
{
    int old= __qran_seed;
    __qran_seed= seed;
    return old;
}

//! Quick (and very dirty) pseudo-random number generator
/*! \return random in range [0,8000h>
*/
INLINE int qran()
{
    __qran_seed= 1664525*__qran_seed+1013904223;
    return (__qran_seed>>16) & 0x7FFF;
}

I’ll say again, this is not a very advanced random generator, but it’ll be enough for what I need. If you want a better (but slower) one, try the Mersenne Twister. You can find a nice implementation on it on PERN’s new sprite page.

Ranged random numbers

Getting a random number is one thing; getting a random number in a particular range is another. It seems simple enough, of course: for a number between, say, 0 and 240 you’d use modulo 240. However, as the GBA doesn’t have a hardware divide, it’ll cost quite a number of cycles. Fortunately, there is a simple way out of it.

I said that qran(), like stdlib’s rand() has a range between 0 and 0x8000. You can also see this as a range between 0 and 1, if you interpret them as .15 fixed point numbers. By multiplying with 240, you’ll have the desired ranged random number, and it only costs a multiplication and a shift. This technique works for every random number generator, as long as you pay attention to its maximum range and integer overflow (which you should pay attention to anyway). Tonclib’s version of this is called qran_range().

//! Ranged random number
/*! \return random in range [\a min, \a max>
*   \note (max-min) must be lower than 8000h
*/
INLINE int qran_range(int min, int max)
{    return (qran()*(max-min)>>15)+min;     }

In the demo, I’m using qran_range() twice to keep the sprite position inside the screen at all times. While the position itself could be predicted beforehand with some investigation, I don’t think it’ll be that easy. And if you really put that kind of effort in it, I’d say you would deserve something for your troubles. If you reload the demo a few times, you will notice that the sequence of positions is always the same. This is why they’re called pseudo-random. To get a different sequence, the seed value should be different. I haven’t even seeded it once here because it’s not really important for this, but the usual trick to seed it with something involving time: for example, the number of frames or cycles before one actually starts a game, counted from the various intro screens that may precede it. Even a small difference in the seed can produce wildly varying sequences.

Conclusions

Technically speaking you probably won’t really need mosaic, blending or windowing in games, but they’re great for subtle effects, like a ‘shock-hit’ or spotlights. They’re also of great use for various types of scene transitions; a fade to black can be easily implemented using the blend registers. Also fun are various HBlank effects using windows, changing the rectangles every HBlank to give beams, side-way wipes or circlular windows. However, to be able to do that you need to know how to work with interrupts. Or a special case of DMA known as HDMA, which just happens to be up next.

14. Direct Memory Access

DMA … que?

Direct Memory Access (DMA) is fast way of copying data from one place to another. Or, rather, a way of transferring data fast; as it can be used for copying data, but also filling memory. When you activate DMA the so-called DMA controller takes over the hardware (the CPU is actually halted), does the desired transfer and hands control back to the CPU before you even knew it was missing.

There are four DMA channels. Channel 0 has the highest priority; it is used for time-critical operations and can only be used with internal RAM. Channels 1 and 2 are used to transfer sound data to the right sound buffers for playback. The lowest priority channel, channel 3, is for general-purpose copies. One of the primary uses for this channel is loading in new bitmap or tile data.

DMA registers

Every kind of transfer routine needs 3 things: a source, a destination and the amount of data to copy. The whence, whither and how much. For DMA, the source address is put into REG_DMAxSAD and destination address into REG_DMAxDAD. A third register, REG_DMAxCNT, not only indicates the amount to transfer, but also controls other features possible for DMA, like when it should start the transfer, chunk-size, and how the source and destination addresses should be updated after each individual chunk of data. All the DMA registers are 32bits in length, though they can be divided into two 16bit registers if so desired. Those of channel 0 start at0400:00B0h; subsequent channels start at an offset of 12 (see table 14.1).

Table 14.1: DMA register addresses
regfunctionaddress
REG_DMAxSADsource 0400:00B0h + 0Ch·x
REG_DMAxDADdestination 0400:00B4h + 0Ch·x
REG_DMAxCNTcontrol 0400:00B8h + 0Ch·x

DMA controls

The use of the source and destination registers should be obvious. The control register needs some explaining. Although the REG_DMAxCNT registers themselves are 32bits, they are often split into two separate registers: one for the count, and one for the actual control bits.

REG_DMAxCNT @ 0400:00B8+12x
1F1E1D 1C1B1A1918 17 16 1514 13 12 11 10 F E D C B A 9 8 7 6 5 4 3 2 1 0
En I TM - CS R SA DA - N

bitsnamedefinedescription
00-0FN Number of transfers.
15-16DA DMA_DST_INC, DMA_DST_DEC, DMA_DST_FIXED, DMA_DST_RELOAD Destination adjustment.
  • 00: increment after each transfer (default)
  • 01: decrement after each transfer
  • 10: none; address is fixed
  • 11: increment the destination during the transfer, and reset it so that repeat DMA will always start at the same destination.
17-18SA DMA_SRC_INC, DMA_SRC_DEC, DMA_SRC_FIXED, Source Adjustment. Works just like the two bits for the destination. Note that there is no DMA_SRC_RESET; code 3 for source is forbidden.
19 R DMA_REPEAT Repeats the copy at each VBlank or HBlank if the DMA timing has been set to those modes.
1A CS DMA_16, DMA_32 Chunk Size. Sets DMA to copy by halfword (if clear) or word (if set).
1C-1DTM DMA_NOW, DMA_AT_VBLANK, DMA_AT_HBLANK, DMA_AT_REFRESH Timing Mode. Specifies when the transfer should start.
  • 00: start immediately.
  • 01: start at VBlank.
  • 10: start at HBlank.
  • 11: Never used it so far, but here's how I gather it works. For DMA1 and DMA2 it'll refill the FIFO when it has been emptied. Count and size are forced to 1 and 32bit, respectively. For DMA3 it will start the copy at the start of each rendering line, but with a 2 scanline delay.
1E I DMA_IRQ Interrupt request. Raise an interrupt when finished.
1F En DMA_ENABLE Enable the DMA transfer for this channel.

Source and destination addresses

The registers for source and destination addresses work just as you’d expect: just put in the proper addresses. Oh, I should tell you that the sizes for the source and destination addresses are 28 and 27 bits wide, respectively, and not the full 32. This is nothing to worry about though, you can’t access addresses above 1000:0000h anyway. For destination addresses, you can’t use the section above 0800:0000h. But then, being able to copy to ROM would be kind of strange, wouldn’t it?

DMA flags

The REG_DMAxCNT registers can be split in two parts: one with actual flags, and one for the number of copies to do. Either way will work but you must be careful how the flags are defined: using 32-bit #defines for 16-bit registers or vice versa is not a good idea.

There are options to control what will be the next source and destination addresses when one chunk has been transferred. By default, both will increment so that it works as a copier. But you could also keep the source constant so that it’d work more as a memory fill.

What goes into the lower half of REG_DMAxCNT is the number of transfers. This is the number of chunks, not bytes! Best be careful when using sizeof() or something similar here, missing a factor 2 or 4 is very easy. A chunk can be either 16 or 32 bit, depending on bit 26.

More on DMA timing

What the immediate DMA does is easy to imagine, it works as soon as you enable the DMA. Well actually it takes 2 cycles before it’ll set in, but it’s close enough. The other timing settings aren’t that more difficult conceptually, but there is one point of confusion.

Consider the following situation: you want to do something cool to your otherwise standard backgrounds; specifically, you want to do something that requires the background registers to be updated every scanline. I just said that you can copy data at every HBlank (via the DMA_AT_HBLANK timing flag), which seems perfect for the job. If you think about it for a minute, however, you may ask yourself the following question:

When you set the timing to, say, DMA_AT_HBLANK, does it do all the N copies at the next HBlank, or one copy at each HBlank until the list is done?

There is a crucial difference between the two. The first option seems pointless because all copied would be done at once; if your destination is fixed (like they are for background registers), all copies except the last would be lost. In the case of the second one, how would you do more than one copy per HBlank? Clearly, something’s amiss here. There is, on two counts.

For the record, I’m not 100% sure about what I’m going to say here, but I think it’s pretty close to what’s actually going on. The main thing to realize is that as long as the channel is not enabled (REG_DMAxCNT{1f} is cleared), that channel won’t do squat; only after REG_DMAxCNT{1f} has been set will the DMA process be initiated. At the appropriate time (determined by the timing bits), DMA will do all N copies and then shut itself off again.

Unless, that is, the repeat-bit (REG_DMAxCNT{19}) is set. In that case, it will keep doing the copies at the right time until you disable the channel yourself.

Some DMA routines

While it’s not that much trouble to set the three registers manually, it is preferable to hide the direct interaction in subroutines. Now, in older code, you might come across something like this:

// Don't do this. Please.
void dma_copy(int ch, void* src, void* dest, uint count, u32 mode)
{
    switch(ch)
    {
    case 0:
        // set DMA 0
    case 1:
        // set DMA 1
... // etc
    }
}

This will work, but it’s not a nice way of doing things. If your switch-cases differ by a single number, you can usually replace it by a simpe lookup. There are a number of ways of fixing this, but the easiest is by mapping a struct array over the DMA registers, similar to what I did for tile memory. After that, you can just select the channel with the channel variable and simply fill in the addresses and flags.

typedef struct DMA_REC
{
    const void *src;
    void *dst;
    u32 cnt;
} DMA_REC;

#define REG_DMA ((volatile DMA_REC*)0x040000B0)

The following are my three of my DMA routines. First the DMA_TRANSER() macro, which is the overall macro that can be used for anything. Then two routines for general memory copies and fills using 32bit transfers with DMA 3.

// in tonc_core.h

//! General DMA transfer macro
#define DMA_TRANSFER(_dst, _src, count, ch, mode)   \
do {                                            \
    REG_DMA[ch].cnt= 0;                         \
    REG_DMA[ch].src= (const void*)(_src);       \
    REG_DMA[ch].dst= (void*)(_dst);             \
    REG_DMA[ch].cnt= (count) | (mode);          \
} while(0)

//! General DMA copier
INLINE void dma_cpy(void *dst, const void *src, uint count, int ch, u32 mode)
{
    REG_DMA[3].cnt = 0; // shut off any previous transfer
    REG_DMA[3].src = src;
    REG_DMA[3].dst = dst;
    REG_DMA[3].cnt = count;
}

//! General DMA full routine
INLINE void dma_fill(void *dst, volatile u32 src, uint count, int ch, u32 mode)
{
    REG_DMA[3].cnt = 0; // shut off any previous transfer
    REG_DMA[3].src = (const void*)&src;
    REG_DMA[3].dst = dst;
    REG_DMA[3].cnt = count | DMA_SRC_FIXED;
}

//! Word copy using DMA 3
INLINE void dma3_cpy(void *dst, const void *src, u32 size)
{   dma_cpy(dst, src, size/4, 3, DMA_CPY32);  }

//! Word fill using DMA 3
INLINE void dma3_fill(void *dst, const void *src, u32 size)
{   dma_fill(dst, src, size/4, 3, DMA_CPY32);  }

In all cases, I disable any previously operating transfers first. This may seem redundant if DMA stops the CPU, but remember that DMA transfers can be timed as well – you wouldn’t want it to start in the middle of setting the registers. After that, it’s simply a matter of filling the registers. Now, it so happens that there is a 2-cycle delay before any transfer really begins. This means that you could lose a transfer if you ask for transfers in immediate succession. I’m not sure if this is very likely though: memory wait-states themselves already take that much time so you should be safe.

Other notes on these routines: the DMA_TRANSFER() macro’s code sits between a do {} while(0); loop. The problem with macros is that when expanded multiple statements might break nesting-blocks. For example, calling it in the body of an if without braces around it would have the first line as the body, but the rest fall outside it. This kind of loop is one of the ways of preventing that. Another problem with macros is that if the arguments’ names may hide other parts of the macro’s code. Like the src and dst members of the DMA_REC struct; which is why they’re underscored. The fill routines also have something remarkable going on, which you can read about in the next subsection. Lastly, the dma3 inlines use word-transfers and take the byte-size as their last arguments, making them very similar to the standard memcpy() and memset().

I used to have the following macro for my transfers. It uses one of the more exotic capabilities of the preprocessor: the merging-operator ‘##’, which allows you to create symbol names at compile-time. It’s scary, totally unsafe and generally unruly, but it does work. The other macro I gave is better, but I still like this thing too.

#define DMA_TRANSFER(_dst, _src, _count, _ch, _mode)  \
    REG_DMA##_ch##SAD = (u32)(_src),                  \
    REG_DMA##_ch##DAD = (u32)(_dst),                  \
    REG_DMA##_ch##CNT = (_count) | (_mode)            \

As long as you are using a literal number for _ch it’ll form the correct register names. And yes, those comma operators between the statements actually work. They keep the statements separate, and also guard against wrongful nesting just like the do{} while(0) construct does.

On DMA fills

DMA can be used to fill memory, but there are two problems that you need to be aware of before you try it. The first can be caught by simply paying attention. DMA fills don’t work quite in the same way as memset() does. What you put into REG_DMAxSAD isn’t the value you want to fill with, but its address!

“Very well, I’ll put the value in a variable and use its address.” Yes, and that brings us to our second problem, a bug which is almost impossible to find. If you try this, you’ll find that it doesn’t work. Well it fills with something, but usually not what you wanted to fill with. The full explanation is somewhat technical, but basically because you’re probably only using the variable’s address and not its value, the optimizer doesn’t ever initialize it. There is a simple solution, one that we’ve seen before, make it volatile. Or you can use a (inline) function like dma_fill(), which has its source argument set as volatile so you can just insert a number just as you’d expect. Note that if you remove the volatile keyword there, it’ll fail again.

In short: DMA fills need addresses, not direct values. Globals will always work, but if you use local variables or arguments you’ll need to make them volatile. Note that the same thing holds true for the BIOS call CpuFastSet().

DMA; don’t wear it out

DMA is fast, there’s no question about that. It can be up to ten times as fast as array copies. However, think twice about using it for every copy. While it is fast, it doesn’t quite blow every other transfer routine out of the water. CpuFastSet() comes within 10% of it for copies and is actually 10% faster for fills. The speed gain isn’t that big a deal. Another problem is that it stops the CPU, which can screw up interrupts, causing seemingly random bugs. It does have its specific uses, usually in conjunction with timers or interrupts, but for general copies, you might consider other things as well. CpuFastSet() is a good routine, but libtonc also comes with memcpy16()/32() and memset16()/32() routines that are safer than that, and less restrictions. They are assembly routines, though, so you’ll need to know how to assemble or use libraries.

DMA demo : circular windows

dma_demo short

Fig 14.1: palette for dma_demo.

The demo for this chapter may seem a little complicated, but the effect is worth it. The basic use of DMA transfers is so easy that it’s hardly worth having a demo of. Use of triggered DMA is another matter. In this case, we’ll look at HBlank-triggered DMA, or HDMA for short. We’ll use it to update the window sized inside the HBlank to give a circular window effect.

This is easier said than done, of course. The first step in the design is how to use HDMA for this in the first place. Because we need to copy to REG_WIN0H each HBlank, we need to keep the destination fixed. Technically, it needs to be reset to the original destination, but with only one halfword to copy this means the same thing. For the source, we’ll keep track of the data that needs to be copied there in an array with one entry for each scanline, and we’ll progress through the array one scanline at a time (i.e, incrementing source). And of course, the transfer has to occur at each scanline, so we set it to repeat. so basically we need this:

#define DMA_HDMA    (DMA_ENABLE | DMA_REPEAT | DMA_AT_HBLANK | DMA_DST_RELOAD)

As for the circle, we need a routine that can calculate the left and right edges of a circle. There are a couple of algorithms around that can draw circles, for example Bresenham’s version. We’ll use a modified version of it because we only need to store the left and right points instead of drawing a pixel there. Why left-right and not top-bottom? Because the array is scanline-based, so that indicates the y-values already.

It doesn’t really matter what you use actually, as long as you can find the edges. Once you have, all you need to do is setup the DMA in the VBlank and you’re done.

The end result will show something like fig 14.1. It’s the Brinstar background (again) inside the window, and a striped bg outside. The text indicates the position and radius of the window, which can be moved with the D-pad and scaled by A and B.


#include 
#include 

#include "brin.h"

// From tonc_math.h
//#define IN_RANGE(x, min, max) ( (x) >= (min) && (x) < (max) )


// The source array
u16 g_winh[SCREEN_HEIGHT+1];

//! Create an array of horizontal offsets for a circular window.
/*! The offsets are to be copied to REG_WINxH each HBlank, either 
*     by HDMA or HBlank isr. Offsets provided by modified 
*     Bresenham's circle routine (of course); the clipping code is not
*     optional.
*   \param winh Pointer to array to receive the offsets.
*   \param x0   X-coord of circle origin.
*   \param y0   Y-coord of circle origin.
*   \param rr   Circle radius.
*/
void win_circle(u16 winh[], int x0, int y0, int rr)
{
    int x=0, y= rr, d= 1-rr;
    u32 tmp;

    // clear the whole array first.
    memset16(winh, 0, SCREEN_HEIGHT+1);

    while(y >= x)
    {
        // Side octs
        tmp  = clamp(x0+y, 0, SCREEN_WIDTH);
        tmp += clamp(x0-y, 0, SCREEN_WIDTH)<<8;
        
        if(IN_RANGE(y0-x, 0, SCREEN_HEIGHT))       // o4, o7
            winh[y0-x]= tmp;
        if(IN_RANGE(y0+x, 0, SCREEN_HEIGHT))       // o0, o3
            winh[y0+x]= tmp;

        // Change in y: top/bottom octs
        if(d >= 0)      
        {
            tmp  = clamp(x0+x, 0, SCREEN_WIDTH);
            tmp += clamp(x0-x, 0, SCREEN_WIDTH)<<8;
            
            if(IN_RANGE(y0-y, 0, SCREEN_HEIGHT))   // o5, o6
                winh[y0-y]= tmp;
            if(IN_RANGE(y0+y, 0, SCREEN_HEIGHT))   // o1, o2
                winh[y0+y]= tmp;

            d -= 2*(--y);
        }
        d += 2*(x++)+3;
    }
    winh[SCREEN_HEIGHT]= winh[0];
}

void init_main()
{
    // Init BG 2 (basic bg)
    dma3_cpy(pal_bg_mem, brinPal, brinPalLen);
    dma3_cpy(tile_mem[0], brinTiles, brinTilesLen);
    dma3_cpy(se_mem[30], brinMap, brinMapLen);

    REG_BG2CNT= BG_CBB(0)|BG_SBB(30);

    // Init BG 1 (mask)
    const TILE tile= 
    {{
        0xF2F3F2F3, 0x3F2F3F2F, 0xF3F2F3F2, 0x2F3F2F3F, 
        0xF2F3F2F3, 0x3F2F3F2F, 0xF3F2F3F2, 0x2F3F2F3F
    }};
    tile_mem[0][32]= tile;
    pal_bg_bank[4][ 2]= RGB15(12,12,12);
    pal_bg_bank[4][ 3]= RGB15( 8, 8, 8);
    pal_bg_bank[4][15]= RGB15( 0, 0, 0);
    se_fill(se_mem[29], 0x4020);

    REG_BG1CNT= BG_CBB(0)|BG_SBB(29);

    tte_init_chr4_b4_default(0, BG_CBB(2)|BG_SBB(28));
    tte_init_con();
    tte_set_margins(8, 8, 232, 40);

    // Init window
    REG_WIN0H= SCREEN_WIDTH;
    REG_WIN0V= SCREEN_HEIGHT;

    // Enable stuff
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0 | DCNT_BG1 | DCNT_BG2 | DCNT_WIN0;
    REG_WININ= WIN_BUILD(WIN_BG0|WIN_BG2, 0);
    REG_WINOUT= WIN_BUILD(WIN_BG0|WIN_BG1, 0);
}

int main()
{
    int rr=40, x0=128, y0=120;

    init_main();

    while(1)
    {
        vid_vsync();
        key_poll();

        rr += key_tri_shoulder();   // size with B/A
        x0 += key_tri_horz();       // move left/right
        y0 += key_tri_vert();       // move up/down

        if(rr<0)
            rr= 0;

        // Fill circle array
        win_circle(g_winh, x0, y0, rr);
    
        // Init win-circle HDMA
        DMA_TRANSFER(®_WIN0H, &g_winh[1], 1, 3, DMA_HDMA);

        tte_printf("#{es;P}(%d,%d) | %d", x0, y0, rr);
    }
    
    return 0;
} 

The initialization function is mostly just fluff. Mostly, because there is one thing of interest: the calls to dma_cpy to copy the Brinstar palette, tiles and map. Aside from that, nothing to see here.

The main function itself is also pretty standard. Of interest here are the call to win_circle(), which sets up the source-array, and to DMA_TRANSFER() to initialize the HDMA. Note that I’m actually making it start at g_winh[1] instead of just g_winh[0]. The reason for this is that the HBlank occurs after a given scanline, not before it, so we’ll lag one otherwise. The g_winh array is actually 160+1 long, and both entry 0 and 160 describe the data for scanline 0. What’s also important, but not exactly visible here, is that HDMA only occurs on the visible HBlanks, not the ones in the VBlank. This saves up a whole lot of trouble determining how many scanlines to correct for when setting it up.

And then there’s win_circle(). If you’re aware of how the Bresenham circle algorithm work, you know it calculates an offset for one octant and then uses it for the 7 others via symmetry rules. This happens here as well. What doesn’t happen in the original probably is all the clipping (the clamp()s and IN_RANGE()s). However, these steps are absolutely vital here. Going out of bounds horizontally would mean wrong windowing offsets which would make the window turn in on itself. Going out of bounds vertically means going OOB on g_winh for all kind of horrible. Trust me, they are necessary.

Also, notice that I wipe the whole array clean first; this can be done inside the loop, but sometimes it’s just faster to fill the whole thing first and then only update the parts you need. Lastly, as mentioned before, the first scanline’s data is copied to the final entry of the array to account for the way HBlanks happen.

And here ends the chapter on DMA. The use of HDMA in this manner is great for all kinds of effects, not just circular windows. All you need is an array containing scanline-data and a function that sets it up beforehand. Be careful you don’t get your channels mixed up, though.

DMA is the fastest method of copying, but as you block interrupts using memcpy32() is probably safer. The speed difference is only 10% anyway. DMA is also used for sound FIFO, in conjunction with timers. I can’t really show you how to use it for sound, but I can tell you how timers work, and will do so in the next chapter.

15. Timers

Timing is everything

Think of every time you’ve heard a joke ruined because the punch line came too late or too early; think of all the failed jumps in Super Mario Bros (or any other platform game); all the occasions that you skidded at the start of a Mario Kart race for revving too soon; that your invincibility wore off just before you got a red shell up your a[censored]s; that you didn’t quite dodge that hail of bullets in old-skool shooters because of a sudden slow-down. Think of all this and situations like them and you’ll agree that in games, as in life, Timing Is Everything.

Ironically, timers are of less importance. Throughout video-game history programmers have built their games around one timing mechanism: the vertical refresh rate of the screen. In other words, the VBlank. This is a machine-oriented timer (you count frames) rather than a human-oriented one (where you’d count seconds). For consoles, this works very well as the hardware is always the same. (Except, of course, that some countries use NTSC televisions (@ 60 Hz) and others use PAL TVs (@ 50 Hz). Everyone living in the latter category and has access to both kinds knows the difference and curses the fact that it’s the NTSC countries that most games stem from.) While the VBlank timer is pervasive, it is not the only one. The GBA has four clock timers at your disposal. This section covers these timers.

GBA Timers

All conceivable timers work in pretty much the same way. You have something that oscillates with a certain fixed frequency (like a CPU clock or the swing of a pendulum). After every full period, a counter is incremented and you have yourself a timer. Easy, innit?

The basic frequency of the GBA timers is the CPU frequency, which is 224 ≈ 16.78 Mhz. In other words, one clock cycle of the CPU takes 2−24 ≈ 59.6 ns. Since this is a very lousy timescale for us humans, the GBA allows for 4 different frequencies (or, rather periods): 1, 64, 256 and 1024 cycles. Some details of these frequencies are shown in table 15.1. By clever use of the timer registers, you can actually create timers of any frequency, but more on that later. It should be noted that the screen refreshes every 280,896 cycles, exactly.

Table 15.1: Timer frequencies
#cyclesfrequencyperiod
1 16.78 MHz59.59 ns
64 262.21 kHz3.815 μs
256 65.536 kHz15.26 μs
1024 16.384 kHz61.04 μs

Timer registers

The GBA has four timers, timers 0 to 3. Each of these has two registers: a data register (REG_TMxD) and a control register (REG_TMxCNT). The addresses can be found in table 15.2.

Table 15.2: Timer register addresses
regfunctionaddress
REG_TMxDdata 0400:0100h + 04h·x
REG_TMxCNTcontrol 0400:0102h + 04h·x

REG_TMxCNT

REG_TMxCNT @ 0400:0102 + 4x
F E D C B A 9 8 7 6 5 4 3 2 1 0
- En I - CM Fr
bitsnamedefinedescription
0-1Fr TM_FREQ_y Timer frequency. 0-3 for 1, 64, 256, or 1024 cycles, respectively. y in the define is the number of cycles.
2 CM TM_CASCADE Cascade mode. When the counter of the preceding (x−1) timer overflows (REG_TM(x-1)D= 0xffff), this one will be incremented too. A timer that has this bit set does not count on its own, though you still have to enable it. Obviously, this won't work for timer 0. If you plan on using it make sure you understand exactly what I just said; this place is a death-trap for the unwary.
6 I TM_IRQ Raise an interrupt on overflow.
7 En TM_ENABLE Enable the timer.

REG_TMxD

The data register REG_TMxD is a 16-bit number that works a little bit differently than you might expect at first, but in the end it makes sense. The number that you read from the register is the current timer-count. So far, so good. However, the number that you write to REG_TMxD is the initial value that the counter begins at when the timer is either enabled (via TM_ENABLE) or overflows. This has number of ‘interesting’ consequences. To make things a little easier, define variables n of the initial value (the write-number) and c for the current count (the read number).

First of all, when you set an n (of, say, c000h) like this:

    REG_TM2D= 0xc000;

you will not have set the current timer-count c to n (=c000h). In fact, if the timer is disabled, then c= 0. However, as soon as you do enable the counter, then c = n and proceeds from there. And when the timer overflows, it will reset to this value as well. By the way, because n is only the starting value it is important to set n first, and enable the timer afterwards.

Secondly, ask yourself this: what happens when you disable the timer again? Well, the counter retains its current value. However, when you enable it afterwards, c will reset to n again. This is a bit of a drag if you want to disable the timer for a while (during a game-pause for instance) and then pick up where it left of. Well, yeah, but there is a way to make it happen. How? By turning it into a cascade timer via TM_CASCADE! Having that bit set in the REG_TMxCNT will cause the timer to be increased only when the preceding one overflows. If you prevent that from ever happening (if it’s disabled for instance) then you will have effectively disabled your timer.

Lastly, given a certain n, then the timer will overflow after T= 10000hn increments. Or, thanks to the wonders of two’s complement, just T= −n. Combined with a cascade timer (or interrupts) you can build timers of any frequency, which is what you want from a timer.

Writing to REG_TMxD is weird

Writing into REG_TMxD may not do what you think it does. It does not set the timer value. Rather, it sets the initial value for the next timer run.

Timer demo : like clockwork

In today’s demo, I’m going to show how to make a simple digital clock with the timers. To do this, we’ll need a 1 Hz timer. As that’s not available directly, I’m going to set up a cascading timer system with timers 2 and 3. Timer 3 will be set to cascade mode, which is updated when timer 2 overflows. It is possible to set the overflow to happen at a frequency of exactly one Hertz. The clock frequency is 224, or 1024*0x4000. By setting timer 2 to TM_FREQ_1024 and to start at −0x4000, the cascading timer 3 will effectively be a 1 Hz counter.

Clock demo

Fig 15.1: tmr_demo.

Whenever timer 3 is updated, the demo turns the number of seconds into hours, minutes and seconds and prints that on screen (see fig 15.1). Yes, I am using divisions and moduli here because it is the simplest procedure and I can spare the cycles in this particular demo.

The demo can be (un)paused with Select and Start. Start disables timer 2, and thus timer 3 too. Select turns timer 2 into a cascade timer as well, and since timer 1 is disabled, doing this also stops timer 2 (and 3). The difference is what happens when you unpause. By disabling a timer, it will start again at the initial value; but stopping it with a cascade actually keeps the timer active and it will simply resume counting once the cascade is removed. The difference is a subtle one, but the latter is more appropriate.

// Using a the "Berk" font from headspins font collection.

#include <stdio.h>
#include <tonc.h>
#include "berk.h"

void tmr_test()
{
    // Overflow every ~1 second:
    // 0x4000 ticks @ FREQ_1024

    REG_TM2D= -0x4000;          // 0x4000 ticks till overflow
    REG_TM2CNT= TM_FREQ_1024;   // we're using the 1024 cycle timer

    // cascade into tm3
    REG_TM3CNT= TM_ENABLE | TM_CASCADE;

    u32 sec= -1;

    while(1)
    {
        vid_vsync();
        key_poll();

        if(REG_TM3D != sec)
        {
            sec= REG_TM3D;
            tte_printf("#{es;P:24,60}%02d:%02d:%02d", 
                sec/3600, (sec%3600)/60, sec%60);
        }

        if(key_hit(KEY_START))  // pause by disabling timer
            REG_TM2CNT ^= TM_ENABLE;

        if(key_hit(KEY_SELECT)) // pause by enabling cascade
            REG_TM2CNT ^= TM_CASCADE;
    }
}

int main()
{
    // set-up berk font
    tte_init_se(0, BG_CBB(0)|BG_SBB(31), 1, 0, 0, &berkFont, se_drawg);
    tte_init_con();
    memcpy16(pal_bg_mem, berkPal, berkPalLen/4);

    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    tmr_test();

    return 0;
}

This was a rather simple use of timers. Of course, I could have just as easily used the VBlank to keep track of the seconds, which is how it’s usually done anyway. The hardware timers are usually reserved for timed DMA’s, which are used in sound mixers, not for game timers. There is one other use that comes to mind, though, namely profiling: examining how fast your functions are. One of the text system demos uses that to check the speeds of a few copying routines.

16. Interrupts

Introduction

Under certain conditions, you can make the CPU drop whatever it’s doing, go run another function instead, and continue with the original process afterwards. This process is known as an interrupt (two ‘r’s, please). The function that handles the interrupt is an interrupt service routine, or just interrupt; triggering one is called raising an interrupt.

Interrupts are often attached to certain hardware events: pressing a key on a PC keyboard, for example, raises one. Another PC example is the VBlank (yes, PCs have them too). The GBA has similar interrupts and others for the HBlank, DMA and more. This last one in particular can be used for a great deal of nifty effects. I’ll give a full list of interrupts shortly.

Interrupts halt the current process, quickly do ‘something’, and pass control back again. Stress the word “quickly”: interrupts are supposed to be short routines.

Interrupts registers

There are three registers specifically for interrupts: REG_IE (0400:0200h), REG_IF (0400:0202h) and REG_IME (0400:0208h). REG_IME is the master interrupt control; unless this is set to ‘1’, interrupts will be ignored completely. To enable a specific interrupt you need to set the appropriate bit in REG_IE. When an interrupt occurs, the corresponding bit in REG_IF will be set. To acknowledge that you’ve handled an interrupt, the bit needs to be cleared again, but the way to do that is a little counter-intuitive to say the least. To acknowledge the interrupt, you actually have to set the bit again. That’s right, you have to write 1 to that bit (which is already 1) in order to clear it.

Apart from setting the bits in REG_IE, you also need to set a bit in other registers that deal with the subject. For example, the HBlank interrupt also requires a bit in REG_DISPSTAT. I think (but please correct me if I’m wrong) that you need both a sender and receiver of interrupts; REG_IE controls the receiver and registers like REG_DISPSTAT control the sender. With that in mind, let’s check out the bit layout for REG_IE and REG_IF.

REG_IE @ 0400:0200 and REG_IF @ 0400:0202
F EDCB A 9 876 5 4 3210
- C K Dma Com Tm Vct Hbl Vbl

bitsnamedefinedescription
0 Vbl IRQ_VBLANK VBlank interrupt. Also requires REG_DISPSTAT{3}
1 Hbl IRQ_HBLANK HBlank interrupt. Also requires REG_DISPSTAT{4} Occurs after the HDraw, so that things done here take effect in the next line.
2 Vct IRQ_VCOUNT VCount interrupt. Also requires REG_DISPSTAT{5}. The high byte of REG_DISPSTAT gives the VCount at which to raise the interrupt. Occurs at the beginning of a scanline.
3-6Tm IRQ_TIMERx Timer interrupt, 1 bit per timer. Also requires REG_TMxCNT{6}. The interrupt will be raised when the timer overflows.
7 Com IRQ_COM Serial communication interrupt. Apparently, also requires REG_SCCNT{E}. To be raised when the transfer is complete. Or so I'm told, I really don't know squat about serial communication.
8-BDma IRQ_DMAx DMA interrupt, 1 bit per channel. Also requires REG_DMAxCNT{1E}. Interrupt will be raised when the full transfer is complete.
C K IRQ_KEYPAD Keypad interrupt. Also requires REG_KEYCNT{E}. Raised when any or all or the keys specified in REG_KEYCNT are down.
D C IRQ_GAMEPAK Cartridge interrupt. Raised when the cart is removed from the GBA.

Interrupt Service Routines

You use the interrupt registers described above to indicate which interrupts you want to use. The next step is writing an interrupt service routine. This is just a typeless function (void func(void)); a C-function like many others. Here’s an example of an HBlank interrupt.

void hbl_pal_invert()
{
    pal_bg_mem[0] ^= 0x7FFF;
    REG_IF = IRQ_HBLANK;
}

The first line inverts the color of the first entry of the palette memory. The second line resets the HBlank bit of REG_IF indicating the interrupt has been dealt with. Since this is an HBlank interrupt, the end-result is that that the color changes every scanline. This shouldn’t be too hard to imagine.

If you simply add this function to an existing program, nothing would change. How come? Well, though you have an isr now, you still need to tell the GBA where to find it. For that, we will need to take a closer look at the interrupt process as a whole.

On acknowledging interrupts correctly

To acknowledge that an interrupt has been dealt with, you have to set the bit of that interrupt in REG_IF, and only that bit. That means that ‘REG_IF = IRQ_x’ is usually the correct course of action, and not ‘REG_IF |= IRQ_x’. The |= version acknowledges all interrupts that have been raised, even if you haven’t dealt with them yet.

Usually, these two result in the same thing, but if multiple interrupts come in at the same time things will go bad. Just pay attention to what you’re doing.

The interrupt process

The complete interrupt process is kind of tricky and part of it is completely beyond your control. What follows now is a list of things that you, the programmer, need to know. For the full story, see GBATEK : irq control.

  1. Interrupt occurs. Some black magic deep within the deepest dungeons of BIOS happens and the CPU is switched to IRQ mode and ARM state. A number of registers (r0-r3, r12, lr) are pushed onto the stack.
  2. BIOS loads the address located at 0300:7FFC and branches to that address.
  3. The code pointed to by 0300:7FFC is run. Since we’re in ARM-state now, this must to be ARM code!
  4. After the isr is done, acknowledge that the interrupt has been dealt with by writing to REG_IF, then return from the isr by issuing a bx lr instruction.
  5. The previously saved registers are popped from stack and program state is restored to normal.

Steps 1, 2 and 5 are done by BIOS; 3 and 4 are yours. Now, in principle all you need to do is place the address of your isr into address 0300:7FFC. To make our job a little easier, we will first create ourselves a function pointer type.

typedef void (*fnptr)(void);
#define REG_ISR_MAIN *(fnptr*)(0x03007FFC)

// Be careful when using it like this, see notes below
void foo()
{
    REG_ISR_MAIN= hbl_pal_invert;  // tell the GBA where my isr is
    REG_DISPSTAT |= VID_HBL_IRQ;  // Tell the display to fire HBlank interrupts
    REG_IE |= IRQ_HBLANK;          // Tell the GBA to catch HBlank interrupts
    REG_IME= 1;                   // Tell the GBA to enable interrupts;
}

Now, this will probably work, but as usual there’s more to the story.

  • First, the code that REG_ISR_MAIN jumps to must be ARM code! If you compile with the -mthumb flag, the whole thing comes to a screeching halt.
  • What happens when you’re interrupted inside an interrupt? Well, that’s not quite possible actually; not unless you do some fancy stuff we’ll get to later. You see, REG_IME is not the only thing that allows interrupts, there’s a bit for irqs in the program status register (PSR) as well. When an interrupt is raised, the CPU disables interrupts there until the whole thing is over and done with.
  • hbl_pal_invert() doesn’t check whether it has been activated by an HBlank interrupt. Now, in this case it doesn’t really matter because it’s the only one enabled, but when you use different types of interrupts, sorting them out is essential. That’s why we’ll create an interrupt switchboard in the next section.
  • Lastly, when you use BIOS calls that require interrupts, you also need to acknowledge them in REG_IFBIOS (== 0300:7FF8). The use is the same as REG_IF.

On section mirroring

GBA’s memory sections are mirrored ever so many bytes. For example IWRAM (0300:0000) is mirrored every 8000h bytes, so that 0300:7FFC is also 03FF:FFFC, or 0400:0000−4. While this is faster, I’m not quite sure if this should be taken advantage of. no$gba v2.2b marks it as an error, even though this was apparently a small oversight and fixed in v2.2c. Nevertheless, consider yourself warned.

Creating an interrupt switchboard

The hbl_pal_invert() function is an example of a single interrupt, but you may have to deal with multiple interrupts. You may also want to be able to use different isr’s depending on circumstances, in which case stuffing it all into one function may not be the best way to go. Instead, we’ll create an interrupt switchboard.

An interrupt switchboard works a little like a telephone switchboard: you have a call (i.e., an interrupt, in REG_IF) coming in, the operator checks if it is an active number (compares it with REG_IE) and if so, connects the call to the right receiver (your isr).

This particular switchboard will come with a number of additional features as well. It will acknowledge the call in both REG_IF and REG_IFBIOS), even when there’s no actual ISR attached to that interrupt. It will also allow nested interrupts, although this requires a little extra work in the ISR itself.

Design and interface considerations

The actual switchboard is only one part of the whole; I also need a couple of structs, variables and functions. The basic items I require are these.

  • __isr_table[]. An interrupt table. This is a table of function pointers to the different isr’s. Because the interrupts should be prioritized, the table should also indicate which interrupt the pointers belong to. For this, we’ll use an IRQ_REC struct.
  • irq_init() / irq_set_master(). Set master isr. irq_init() initializes the interrupt table and interrupts themselves as well.
  • irq_enable() / irq_disable(). Functions to enable and disable interrupts. These will take care of both REG_IE and whatever register the sender bit is on. I’m keeping these bits in an internal table called __irq_senders[] and to be able to use these, the input parameter of these functions need to be the index of the interrupt, not the interrupt flag itself. Which is why I have II_foo counterparts for the IRQ_foo flags.
  • irq_set() / irq_add() / irq_delete(). Function to add/delete interrupt service routines. The first allows full prioritization of isr’s; irq_add() will replace the current irs for a given interrupt, or add one at the end of the list; irq_delete() will delete one and correct the list for the empty space.

All of these functions do something like this: disable interrupts (REG_IME=0), do their stuff and then re-enable interrupts. It’s a good idea to do this because being interrupted while mucking about with interrupts is not pretty. The functions concerned with service routines will also take a function pointer (the fnptr type), and also return a function pointer indicating the previous isr. This may be useful if you want to try to chain them.

Below you can see the structs, tables, and the implementation of irq_enable() and irq_add(). In both functions, the __irq_senders[] array is used to determine which bit to set in which register to make sure things send interrupt requests. The irq_add() function goes on to finding either the requested interrupt in the current table to replace, or an empty slot to fill. The other routines are similar. If you need to see more, look in tonc_irq.h/.c in libtonc.

//! Interrups Indices
typedef enum eIrqIndex
{
    II_VBLANK=0, II_HBLANK, II_VCOUNT, II_TIMER0,
    II_TIMER1,   II_TIMER2, II_TIMER3, II_SERIAL,
    II_DMA0,     II_DMA1,   II_DMA2,   II_DMA3,
    II_KEYPAD,   II_GAMEPAK,II_MAX
} eIrqIndex;

//! Struct for prioritized irq table
typedef struct IRQ_REC  
{
    u32 flag;   //!< Flag for interrupt in REG_IF, etc
    fnptr isr;  //!< Pointer to interrupt routine
} IRQ_REC;

// === PROTOTYPES =====================================================

IWRAM_CODE void isr_master_nest();

void irq_init(fnptr isr);
fnptr irq_set_master(fnptr isr);

fnptr irq_add(enum eIrqIndex irq_id, fnptr isr);
fnptr irq_delete(enum eIrqIndex irq_id);

fnptr irq_set(enum eIrqIndex irq_id, fnptr isr, int prio);
void irq_enable(enum eIrqIndex irq_id);
void irq_disable(enum eIrqIndex irq_id);
// IRQ Sender information
typedef struct IRQ_SENDER
{
    u16 reg_ofs;    //!< sender reg - REG_BASE
    u16 flag;       //!< irq-bit in sender reg
} ALIGN4 IRQ_SENDER;

// === GLOBALS ========================================================

// One extra entry for guaranteed zero
IRQ_REC __isr_table[II_MAX+1];

static const IRQ_SENDER __irq_senders[] =
{
    { 0x0004, 0x0008 },     // REG_DISPSTAT,    DSTAT_VBL_IRQ
    { 0x0004, 0x0010 },     // REG_DISPSTAT,    DSTAT_VHB_IRQ
    { 0x0004, 0x0020 },     // REG_DISPSTAT,    DSTAT_VCT_IRQ
    { 0x0102, 0x0040 },     // REG_TM0CNT,      TM_IRQ
    { 0x0106, 0x0040 },     // REG_TM1CNT,      TM_IRQ
    { 0x010A, 0x0040 },     // REG_TM2CNT,      TM_IRQ
    { 0x010E, 0x0040 },     // REG_TM3CNT,      TM_IRQ
    { 0x0128, 0x4000 },     // REG_SCCNT_L      BIT(14) // not sure
    { 0x00BA, 0x4000 },     // REG_DMA0CNT_H,   DMA_IRQ>>16
    { 0x00C6, 0x4000 },     // REG_DMA1CNT_H,   DMA_IRQ>>16
    { 0x00D2, 0x4000 },     // REG_DMA2CNT_H,   DMA_IRQ>>16
    { 0x00DE, 0x4000 },     // REG_DMA3CNT_H,   DMA_IRQ>>16
    { 0x0132, 0x4000 },     // REG_KEYCNT,      KCNT_IRQ
    { 0x0000, 0x0000 },     // cart: none
};


// === FUNCTIONS ======================================================

//! Enable irq bits in REG_IE and sender bits elsewhere
void irq_enable(enum eIrqIndex irq_id)
{
    u16 ime= REG_IME;
    REG_IME= 0;

    const IRQ_SENDER *sender= &__irq_senders[irq_id];
    *(u16*)(REG_BASE+sender->reg_ofs) |= sender->flag;

    REG_IE |= BIT(irq_id);
    REG_IME= ime;
}

//! Add a specific isr
fnptr irq_add(enum eIrqIndex irq_id, fnptr isr)
{
    u16 ime= REG_IME;
    REG_IME= 0;

    int ii;
    u16 irq_flag= BIT(irq_id);
    fnptr old_isr;
    IRQ_REC *pir= __isr_table;

    // Enable irq
    const IRQ_SENDER *sender= &__irq_senders[irq_id];
    *(u16*)(REG_BASE+sender->reg_ofs) |= sender->flag;
    REG_IE |= irq_flag;

    // Search for previous occurance, or empty slot
    for(ii=0; pir[ii].flag; ii++)
        if(pir[ii].flag == irq_flag)
            break;
    
    old_isr= pir[ii].isr;
    pir[ii].isr= isr;
    pir[ii].flag= irq_flag;

    REG_IME= ime;
    return old_isr;
}

The master interrupt service routine

The main task of the master ISR is to seek out the raised interrupt in ___isr_table, and acknowledge it in both REG_IF and REG_IFBIOS. If there is an irq-specific service routine, it should call it; otherwise, it should just exit to BIOS again. In C, it would look something like this.

// This is mostly what libtonc's isr_master does, but
// you really need asm for the full functionality
IWRAM_CODE void isr_master_c()
{
    u32 ie= REG_IE;
    u32 ieif= ie & REG_IF;
    IRQ_REC *pir;

    // (1) Acknowledge IRQ for hardware and BIOS.
    REG_IF      = ieif;
    REG_IFBIOS |= ieif;

    // (2) Find raised irq 
    for(pir= __isr_table; pir->flag!=0; pir++)
        if(pir->flag & ieif)
            break;

    // (3) Just return if irq not found in list or has no isr.
    if(pir->flag == 0 || pir->isr == NULL)
        return;

    // --- If we're here have an interrupt routine ---
    // (4a) Disable IME and clear the current IRQ in IE
    u32 ime= REG_IME;
    REG_IME= 0;
    REG_IE &= ~ieif;

    // (5a) CPU back to system mode 
    //> *(--sp_irq)= lr_irq;
    //> *(--sp_irq)= spsr
    //> cpsr &= ~(CPU_MODE_MASK | CPU_IRQ_OFF);
    //> cpsr |= CPU_MODE_SYS;
    //> *(--sp_sys) = lr_sys;

    pir->isr();             // (6) Run the ISR

    REG_IME= 0;             // Clear IME again (safety)

    // (5b) Back to irq mode
    //> lr_sys = *sp_sys++;
    //> cpsr &= ~(CPU_MODE_MASK | CPU_IRQ_OFF);
    //> cpsr |= CPU_MODE_IRQ | CPU_IRQ_OFF;
    //> spsr = *sp_irq++
    //> lr_irq = *sp_irq++;

    // (4b) Restore original ie and ime 
    REG_IE= ie;
    REG_IME= ime;
}

Most of these points have been discussed already, so I won’t repeat them again. Do note the difference is acknowledging REG_IF and REG_IFBIOS: the former uses a simple assignment and the latter an |=. Steps 4, 5 and 6 only execute if the current IRQ has its own service routine. Steps 4a and 5a work as initialization steps to ensure that the ISR (step 6) can work in CPU mode and that it can’t be interrupted unless it asks for it. Steps 4b and 5b unwind 4a and 5a.

This routine would work fine in C, were it not for items 5a and 5b. These are the code to set/restore the CPU mode to system/irq mode, but the instructions necesasry for that aren’t available in C. Another problem is that the link registers (these are used to hold the return addresses of functions) have to be saved somehow, and these definitely aren’t available in C.

Note: I said registers, plural! Each CPU mode has its own stack and link register, and even though the names are the same (lr and sp), they really aren’t identical. Usually a C routine will save lr on its own, but since you need it twice now it’s very unsafe to leave this up to the compiler. Aside from that, you need to save the saved program status register spsr, which indicates the program status when the interrupt occurred. This is another thing that C can’t really do. As such, assembly is required for the master ISR.

So, assembly it is then. The function below is the assembly equivalent of irs_master_c(). It is almost a line by line translation, although I am making use of a few features of the instruction set the compiler wont’t or can’t. I don’t expect you to really understand everything written here, but with some imagination you should be able to follow most of it. Teaching assembly is way beyond the scope of this chapter, but worth the effort in my view. Tonc’s assembly chapter should give you the necessary information to understand most of it and shows where to go to learn more.

    .file   "tonc_isr_master.s"
    .extern __isr_table;

/*! \fn IWRAM_CODE void isr_master()
    \brief  Default irq dispatcher (no automatic nesting)
*/
    .section .iwram, "ax", %progbits
    .arm
    .align
    .global isr_master

    @ --- Register list ---
    @ r0 : &REG_IE
    @ r1 : __isr_table / isr
    @ r2 : IF & IE
    @ r3 : tmp
    @ ip : (IF<<16 | IE)

isr_master:
    @ Read IF/IE 
    mov     r0, #0x04000000
    ldr     ip, [r0, #0x200]!
    and     r2, ip, ip, lsr #16     @ irq= IE & IF

    @ (1) Acknowledge irq in IF and for BIOS
    strh    r2, [r0, #2]
    ldr     r3, [r0, #-0x208]
    orr     r3, r3, r2
    str     r3, [r0, #-0x208]

    @ (2) Search for irq.
    ldr     r1, =__isr_table
.Lirq_search:
        ldr     r3, [r1], #8 
        tst     r3, r2
        bne     .Lpost_search       @ Found one, break off search
        cmp     r3, #0
        bne     .Lirq_search        @ Not here; try next irq

    @ (3) Search over : return if no isr, otherwise continue.
.Lpost_search:
    ldrne   r1, [r1, #-4]           @ isr= __isr_table[ii-1].isr
    cmpne   r1, #0
    bxeq    lr                      @ If no isr: quit

    @ --- If we're here, we have an isr ---

    @ (4a) Disable IME and clear the current IRQ in IE
    ldr     r3, [r0, #8]            @ Read IME 
    strb    r0, [r0, #8]            @ Clear IME
    bic     r2, ip, r2
    strh    r2, [r0]                @ Clear current irq in IE
    
    mrs     r2, spsr
    stmfd   sp!, {r2-r3, ip, lr}    @ sprs, IME, (IE,IF), lr_irq

    @ (5a) Set mode to sys
    mrs     r3, cpsr
    bic     r3, r3, #0xDF
    orr     r3, r3, #0x1F
    msr     cpsr, r3

    @ (6) Call isr
    stmfd   sp!, {r0,lr}            @ &REG_IE, lr_sys
    mov     lr, pc
    bx      r1
    ldmfd   sp!, {r0,lr}            @ &REG_IE, lr_sys

    @ --- Unwind ---
    strb    r0, [r0, #8]            @ Clear IME again (safety)
    @ (5b) Reset mode to irq
    mrs     r3, cpsr
    bic     r3, r3, #0xDF
    orr     r3, r3, #0x92
    msr     cpsr, r3

    @ (4b) Restore original spsr, IME, IE, lr_irq
    ldmfd   sp!, {r2-r3, ip, lr}    @ sprs, IME, (IE,IF), lr_irq
    msr     spsr, r2
    strh    ip, [r0]
    str     r3, [r0, #8]
    
    bx      lr

Nested irqs are nasty

Making a nested interrupt routine work is not a pleasant exercise when you only partially know what you’re doing. For example, that different CPU modes used different stacks took me a while to figure out, and it took me quite a while to realize that the reason my nested isrs didn’t work was because there are different link registers too.

The isr_master_nest is largely based on libgba’s interrupt dispatcher, but also borrows information from GBATEK and A. Bilyk and DekuTree’s analysis of the whole thing as described in forum:4063. Also invaluable was the home-use debugger version of no$gba, hurray for breakpoints.

If you want to develop your own interrupt routine, these sources will help you immensely and will keep the loss of sanity down to somewhat acceptable levels.

Deprecation notice

I used to have a different master service routine that took care of nesting and prioritizing interrupts automatically. Because it was deemed too complicated, it has been replaced with this one.

Nested interrupts are still possible, but you have to indicate interruptability inside the isr yourself now.

Nested interrupt demo

Today’s demo shows a little bit of everything described above:

  • It’ll display a color gradient on the screen through the use of an HBlank interrupt.
  • It will allow you to toggle between two different master isrs: The switchboard isr_master which routes the program flow to an HBlank isr, and an isr in C that handles the HBlank interrupt directly. For the latter to work, we’ll need to use ARM-compiled code, of course, and I’ll also show you how in a minute.
  • Finally, having a nested isr switchboard doesn’t mean much unless you can actually see nested interrupts in action. In this case, we’ll use two interrupts: VCount and HBlank. The HBlank isr creates a vertical color gradient. The VCount isr will reset the color and tie up the CPU for several scanlines. If interrupts don’t nest, you’ll see the gradient stop for a while; if they do nest, it’ll continue as normal.
  • And just for the hell of it, you can toggle the HBlank and VCount irqs on and off.

The controls are as follows:

A Toggles between asm switchboard and C direct isr.
B Toggles HBlank and VCount priorities.
L,R Toggles VCount and HBlank irqs on and off.
#include <stdio.h>
#include <tonc.h>

IWRAM_CODE void isr_master();
IWRAM_CODE void hbl_grad_direct();

void vct_wait();
void vct_wait_nest();


CSTR strings[]= 
{
    "asm/nested",   "c/direct", 
    "HBlank",       "VCount"
};

// Function pointers to master isrs.
const fnptr master_isrs[2]= 
{
    (fnptr)isr_master,
    (fnptr)hbl_grad_direct 
};

// VCount interrupt routines.
const fnptr vct_isrs[2]= 
{
    vct_wait, 
    vct_wait_nest
};


// (1) Uses tonc_isr_master.s' isr_master() as a switchboard
void hbl_grad_routed()
{
    u32 clr= REG_VCOUNT/8;
    pal_bg_mem[0]= RGB15(clr, 0, 31-clr);
}

// (2a) VCT is triggered at line 80; this waits 40 scanlines
void vct_wait()
{
    pal_bg_mem[0]= CLR_RED;
    while(REG_VCOUNT<120);
}

// (2b) As vct_wait(), but interruptable by HBlank
void vct_wait_nest()
{
    pal_bg_mem[0]= CLR_RED;
    REG_IE= IRQ_HBLANK;     // Allow nested hblanks
    REG_IME= 1;
    while(REG_VCOUNT<120);
}


int main()
{
    u32 bDirect=0, bVctPrio= 0;

    tte_init_chr4_b4_default(0, BG_CBB(2)|BG_SBB(28));
    tte_set_drawg((fnDrawg)chr4_drawg_b4cts_fast);
    tte_init_con();
    tte_set_margins(8, 8, 128, 64);

    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    // (3) Initialize irqs; add HBL and VCT isrs 
    // and set VCT to trigger at 80
    irq_init(master_isrs[0]);
    irq_add(II_HBLANK, hbl_grad_routed);
    BFN_SET(REG_DISPSTAT, 80, DSTAT_VCT);
    irq_add(II_VCOUNT, vct_wait);
    irq_add(II_VBLANK, NULL);

    while(1)
    {
        //vid_vsync();
        VBlankIntrWait();
        key_poll();

        // Toggle HBlank irq
        if(key_hit(KEY_R))
            REG_IE ^= IRQ_HBLANK;

        // Toggle Vcount irq
        if(key_hit(KEY_L))
            REG_IE ^= IRQ_VCOUNT;

        // (4) Toggle between 
        // asm switchblock + hbl_gradient (red, descending)
        // or purely hbl_isr_in_c (green, ascending)
        if(key_hit(KEY_A))
        {
            bDirect ^= 1;
            irq_set_master(master_isrs[bDirect]);
        }

        // (5) Switch priorities of HBlank and VCount
        if(key_hit(KEY_B))
        {
            //irq_set(II_VCOUNT, vct_wait, bVctPrio);
            bVctPrio ^= 1;
            irq_add(II_VCOUNT, vct_isrs[bVctPrio]);
        }

        tte_printf("#{es;P}IRS#{X:32}: %s\nPrio#{X:32}: %s\nIE#{X:32}: %04X", 
            strings[bDirect], strings[2+bVctPrio], REG_IE);
    }

    return 0;
}

The code listing above contains the main demo code, the HBlank, and VCount isrs that will be routed and some sundry items for convenience. The C master isr called hbl_grad_direct() is in another file, which will be discussed later.

First, the contents of the interrupt service routines (points 1 and 2). Both routines are pretty simple: the HBlank routine (hbl_grad_routed()) uses the value of the scanline counter to set a color for the backdrop. At the top, REG_VCOUNT is 0, so the color will be blue; at the bottom, it’ll be 160/8=20, so it’s somewhere between blue and red: purple. Now, you may notice that the first scanline is actually red and not blue: this is because a) the HBlank interrupt occurs after the scanline (which has caused trouble before in the DMA demo) and b) because HBlanks happen during the VBlank as well, so that the color for line 0 is set at REG_VCOUNT=227, which will give a bright red color.

The VCount routines activate at scanline 80. They set the color to red and then waits until scanline 120. The difference between the two is that vct_wait() just waits, but vct_wait_nest() enables the HBlank interrupt. Remember that isr_master disables interrupts before calling an service routine, so the latter Vcount routine should be interrupted by hbl_grad_routed(), but the former would not. As you can see from fig 16.1a and fig 16.1b, this is exactly what happens.

Point 3 is where the interrupts are set up in the first place. The call to irq_init() clears the isr table and sets up the master isr. Its argument can be NULL, in which case the tonc’s default master isr is used. The calls to irq_add() initialize the HBlank and VCount interrupts and their service routines. If you don’t supply a service routine, the switchboard will just acknowledge the interrupt and return. There are times when this is useful, as we’ll see in the next chapter. irq_add() already takes care of both REG_IE and the IRQ bits in REG_DISPSTAT; what it doesn’t do yet is set the VCount at which the interrupt should be triggered, so this is done separately. The order of irq_add() doesn’t really matter, but lower orders are searched first so it makes sense to put more frequent interrupts first.

You can switch between master service routines with irq_set_master(), as is done at point 4. Point 5 chooses between the nested and non-nested VCount routine.

Gradient hbl>vct
Fig 16.1a: Gradient; nested vct_wait_nested.
Gradient vct>hbl
Fig 16.1b: Gradient; non-nested vct_wait.
Gradient hbl in C
Fig 16.1c: Gradient; HBlank in master ISR in C.

This explains most of what the demo can show. For Real Life use, irq_init() and irq_add() are pretty much all you need, but the demo shows some other interesting things as well. Also interesting is that the result is actually a little different for VBA, no$gba and hardware, which brings up another point: interrupts are time-critical routines, and emulating timing is rather tricky. If something works on an emulator but not hardware, interrupts are a good place to start looking.

This almost concludes demo section, except for one thing: the direct HBlank isr in C. But to do that, we need it in ARM code and to make it efficient, it should be in IWRAM as well. And here’s how we do that.

Using ARM + IWRAM code

The master interrupt routines have to be ARM code. As we’ve always compiled to Thumb code, this would be something new. The reason that we’ve always compiled to Thumb code is that the 16bit buses of the normal code sections make ARM-code slow there. However, what we could do is put the ARM code in IWRAM, which has a 32bit bus (and no waitstates) so that it’s actually beneficial to use ARM code there.

Compiling as ARM code is actually quite simple: use -marm instead of -mthumb. The IWRAM part is what causes the most problems. There are GCC extensions that let you specify which section a function should be in. Tonclib has the following macros for them:

#define EWRAM_DATA __attribute__((section(".ewram")))
#define IWRAM_DATA __attribute__((section(".iwram")))
#define  EWRAM_BSS __attribute__((section(".sbss")))

#define EWRAM_CODE __attribute__((section(".ewram"), long_call))
#define IWRAM_CODE __attribute__((section(".iwram"), long_call))


// --- Examples of use: ---
// Declarations
extern EWRAM_DATA u8 data[];
IWRAM_CODE void foo();


// Definitions
EWRAM_DATA u8 data[8]= { ... };

IWRAM_CODE void foo()
{
    ....
}

The EWRAM/IWRAM things should be self-explanatory. The DATA_IN_x things allow global data to be put in those sections. Note that the default section for data is IWRAM anyway, so that may be a little redundant. EWRAM_BSS concerns uninitialized globals. The difference with initialized globals is that they don’t have to take up space in ROM: all you need to know is how much space you need to reserve in RAM for the array.

The function variants also need the long_call attribute. Code branches have a limited range and section branches are usually too far to happen by normal means and this is what makes it work. You can compare them with ‘far’ and ‘near’ that used to be present in PC programming.

It should be noted that these extensions can be somewhat fickle. For one thing, the placement of the attributes in the declarations and definitions seems to matter. I think the examples given work, but if they don’t try to move them around a bit and see if that helps. A bigger problem is that the long_call attribute doesn’t always want to work. Previous experience has led me to believe that the long_call is ignored unless the definition of the function is in another file. If it’s in the same file as the calling function, you’ll get a ‘relocation error’, which basically means that the jump is too far. The upshot of this is that you have to separate your code depending on section as far as functions are concerned. Which works out nicely, as you’ll want to separate ARM code anyway.

So, for ARM/IWRAM code, you need to have a separate file with the routines, use the IWRAM_CODE macro to indicate the section, and use -marm in compilation. It is also a good idea to add -mlong-calls too, in case you ever want to call ROM functions from IWRAM. This option makes every call a long call. Some toolchains (including DKP) have set up their linkscripts so that files with the extension .iwram.c automatically go into IWRAM, so that IWRAM_CODE is only needed for the declaration.

In this case, that’d be the file called isr.iwram.c. This contains a simple master isr in C, and only takes care of the HBlank and acknowledging the interrupts.

#include <tonc.h>

IWRAM_CODE void hbl_grad_direct();

// an interrupt routine purely in C
// (make SURE you compile in ARM mode!!)
void hbl_grad_direct()
{
    u32 irqs= REG_IF & REG_IE;

    REG_IFBIOS |= irqs;
    if(irqs & IRQ_HBLANK)
    {
        u32 clr= REG_VCOUNT/8;
        pal_bg_mem[0]= RGB15(0, clr, 0);
    }

    REG_IF= irqs;
}

Flags for ARM+IWRAM compilation

Replace the ‘-mthumb’ in your compilation flags by ‘-marm -mlong-calls’. For example:

CBASE   := $(INCDIR) -O2 -Wall

# ROM flags
RCFLAGS := $(CBASE) -mthumb-interwork -mthumb
# IWRAM flags
ICFLAGS := $(CBASE) -mthumb-interwork -marm -mlong-calls

For more details, look at the makefile for this project.

17. BIOS Calls


Introduction

Apart from hardware interrupts, like HBlank and cartridge interrupts, there are also things called software interrupts, also known as BIOS calls. The software interrupts work very much like ordinary functions: you set-up input, call the routine, and get some output back. The difference lies in how you reach the code; for normal functions you just, well, jump to the routine you want. Software interrupts use the swi instruction, which diverts the program flow to somewhere in BIOS, carries out the requested algorithm and then restores the normal flow of your program. This is similar to what hardware interrupts do, only now you raise the interrupt programmatically. Hence: software interrupt.

The GBA BIOS has 42 software interrupts, with basic routines for copying, math (division, square root), affine transformations for sprites and backgrounds, decompression among others. There are also some very special functions like the IntrWait routines, which can stop the CPU until a hardware interrupt occurs. The VBlank variant is highly recommended, which is what makes this chapter important.

Using software interrupts isn’t too hard if it weren’t for one thing: the swi instruction itself. This again requires some assembly. However, not much assembly, and it’s easy to write C wrappers for them, which we’ll also cover here.

The BIOS functions

Calling the BIOS functions can be done via the ‘swi n’ instruction, where n is the BIOS call you want to use. Mind you, the exact numbers you need to use depends on whether your code is in ARM or Thumb state. In Thumb the argument is simply the n itself, but in ARM you need to use n<<16. Just like normal functions, the BIOS calls can have input and output. The first four registers (r0-r3) are used for this purpose; though the exact purpose and the number of registers differ for each call.

Here’s a list containing the names of each BIOS call. I am not going to say what each of them does since other sites have done that already and it seems pointless to copy their stuff verbatim. For full descriptions go to GBATEK, for example. I will give a description of a few of them so you can get a taste of how they work.

Full list

id Name id Name
0x00 SoftReset 0x08 Sqrt
0x01 RegisterRamReset0x09 ArcTan
0x02 Halt 0x0A ArcTan2
0x03 Stop 0x0B CPUSet
0x04 IntrWait 0x0C CPUFastSet
0x05 VBlankIntrWait 0x0D BiosChecksum
0x06 Div 0x0E BgAffineSet
0x07 DivArm 0x0F ObjAffineSet
 
0x10 BitUnPack 0x18 Diff16bitUnFilter
0x11 LZ77UnCompWRAM 0x19 SoundBiasChange
0x12 LZ77UnCompVRAM 0x1A SoundDriverInit
0x13 HuffUnComp 0x1B SoundDriverMode
0x14 RLUnCompWRAM 0x1C SoundDriverMain
0x15 RLUnCompVRAM 0x1D SoundDriverVSync
0x16 Diff8bitUnFilterWRAM 0x1E SoundChannelClear
0x17 Diff8bitUnFilterVRAM 0x1F MIDIKey2Freq
 
0x20 MusicPlayerOpen 0x28 SoundDriverVSyncOff
0x21 MusicPlayerStart 0x29 SoundDriverVSyncOn
0x22 MusicPlayerStop 0x2A GetJumpList
0x23 MusicPlayerContinue
0x24 MusicPlayerFadeOut
0x25 MultiBoot
0x26 HardReset
0x27 CustomHalt

Div, Sqrt, Arctan2 and ObjAffineSet descriptions

0x06: Div
Input:

r0: numerator

r1: denominator

Output:

r0: numerator / denominator

r1: numerator % denominator

r3: abs(numerator / denominator)

Note: do NOT divide by zero!
0x08: Sqrt
Input:

r0: num, a unsigned 32-bit integer

Output:

r1: sqrt(num)


0x0a: ArcTan2
Input:

r0: x, a signed 16bit number (s16)

r1: y, a signed 16bit number (s16)

Output:

r0: x≥0 : θ= arctan(y/x) ∨ x<0 : θ= sign(y)*(π − arctan(|y/x|).

This does the full inverse of y = x*tan(θ). The problem with the tangent is that the domain is a semi-circle, as is the range of arc tangent. To get the full circle range, both x and y values are required for not only their quotient, but their signs as well. The mathematical range of θ is [−π, π⟩, which corresponds to [−0x8000, 0x8000⟩ (or [0, 2π⟩ and [0, 0xFFFF] if you like)
0x0f: ObjAffineSet
Input:

r0: source address

r1: destination address

r2: number of calculations

r3: Offset of P matrix elements (2 for bgs, 8 for objects)

The source address points to an array of AFF_SRC structs (also known as ObjAffineSource, which is a bit misleading since you can use them for backgrounds as well). The AFF_SRC struct consist of two scales sx , sy and an angle α, which again uses the range [0, 0xFFFF] for 2π. The resulting P:

(17.1)     P = [ s x cos α s x sin α s y sin α s y cos α ]

By now you should know what this does: it scales horizontally by 1/sx, vertically by 1/sy followed by a counter-clockwise rotation by α. ObjAffineSet() does almost exactly what obj_aff_rotscale() and bg_aff_rotscale() do, except that ObjAffineSet() can also set multiple matrices at once.

The source data is kept in ObjAffineSource (i.e., AFF_SRC) structs. Now, as the routine sets affine matrices, you might think that the destinations are either OBJ_AFFINE or ObjAffineDest structs. However, you’d be wrong. Well, partially anyway. The problem is that the destination always points to a pa-element, which is not necessarily the first element in struct. You will make the mistake of simply supplying an OBJ_AFFINE pointer when you try to use it to fill those. Don’t say I didn’t warn you.

Two other things need to be said here as well. First, once again we have a bit of a misnomer: ObjAffineSet doesn’t really have much to do with objects per se, but can be used in that capacity by setting r3 to 8 instead of 2. The second is that the routine can also be used to set up multiple arrays via r2. However, be careful when you do this with devkitPro 19. ObjAffineSet() expects its source structs to be word-aligned, which they won’t be unless you add the alignment attributes yourself.

// Source struct. Note the alignment!
typedef struct AFF_SRC
{
    s16 sx, sy;
    u16 alpha;
} ALIGN4 AFF_SRC, ObjAffineSource;

// Dst struct for background matrices
typedef struct Aff_DST
{
    s16 pa, pb;
    s16 pc, pd;
} ALIGN4 AFF_DST, ObjAffineDest;

// Dst struct for objects. Note that r1 should be
// the address of pa, not the start of the struct
typedef struct OBJ_AFFINE
{
    u16 fill0[3];    s16 pa;
    u16 fill1[3];    s16 pb;
    u16 fill2[3];    s16 pc;
    u16 fill3[3];    s16 pd;
} ALIGN4 OBJ_AFFINE;

Using BIOS calls

Assembly for BIOS calls

You might think this whole discussion was rather pointless since you can’t access the registers and the swi instruction unless you use assembly, which will be pretty tough, right? Well, no, yes and no. The necessary assembly steps for BIOS calls are actually rather simple, and are given below.

@ In tonc_bios.s

@ at top of your file
    .text           @ aka .section .text
    .code 16        @ aka .thumb

@ for each swi (like division, for example)
    .align 2        @ aka .balign 4
    .global Div
    .thumb_func
Div:
    swi     0x06
    bx      lr

This is assembly code for the GNU assembler (GAS); for Goldroad or ARM STD the syntax is likely to be slightly different. The first thing you need to do is give some directives, which tells some details about the following code. In this case, we use the ‘.text’ to put the code in the text section (ROM or EWRAM for multiboot). We also say that the code is Thumb code by using ‘.code 16’ or ‘.thumb’. If you place these at the top of the file, they’ll hold for the rest of the thing. For each BIOS call, you’ll need the following 6 items.

  • Word-alignment. Or at least halfword alignment, but words are probably preferable. There are two directives for this, .align n and .balign m. The former aligns to 2 n so requires ‘.align 2’; the latter aligns to m so you can just use ‘balign m’. Note that both will only work on the next piece of code or data and no further, which is why it’s best to add it for each function.
  • Scope. The .global name directive makes a symbol out of name, which will then be visible for other files in the project as well. A bit like extern or, rather, an anti-static.
  • Thumb indicator It would seem that .code 16 alone isn’t enough, you also need .thumb_func. In fact, if I read the manual correctly this one also implies .code 16, which would make that directive redundant.
  • Label. ‘name:’ marks where the symbol name starts. Obviously, to use a function it must actually exist.
  • BIOS call To actually activate the BIOS call, use ‘swi n’, with n the BIOS call you want.
  • Return And we’re practically done already, all we have to do now is return to the caller with ‘bx lr’.

See? It’s really not that complicated. Sometimes you might want a little more functionality than this, but for the most part you only need two measly instructions.

The Arm Architecture Procedure Call Standard

That’s all fine and good, but that still leaves the questions of a) how do I combine this with C code and b) where’d all the input and output go? The answer to the first is simple: just add a function declaration like usual:

// In tonc_bios.h

int Div(int num, int denom);

Mkay, but that still doesn’t explain where my input and output went. Well actually … it does.

“I am not sure how clouds get formed. But the clouds know how to do it, and that is the important thing”

Found that quote long ago in one of those Kids on Science lists, and I’m always reminded of it when programming. The thing about computers is that they don’t think in terms of input, output, text, pictures etc. Actually, they don’t think at all, but that’s another story. All a computer sees is data; not even code and data, just data since code is data too. Of course, you may not see it that way because you’re used to C or VB or whatever, but when all is said and done, it’s all just ones and zeros. If the ones and zeros come to the CPU via the program counter (PC register, r15) it’s code, otherwise it’s data.

So how does that explain the input/output? Well, it doesn’t do it directly, but it points to how you should be looking at the situation. Consider you’re the compiler and you have to convert some bloke’s C code into machine code (or assembly, which is almost the same thing) that a CPU can actually use. You come across the line “q= Div(x,y);”. What does Div() do? Well, if there’s no symbol in the C-file for that name (and there isn’t, as it’s in tonc_bios.s), you wouldn’t know. Technically, you don’t even know what it is. But Div knows, and that’s the important thing. At least, that’s almost how it works. The compiler should still need to know what sort of critter Div is to avoid confusion: A variable? A macro? A function? That’s what the declarations are for. And the declaration above says that Div is a function that expects two signed integers and returns one too. As far as the compiler’s concerned, it ends there.

Of course, that still doesn’t explain how the compiler knows what do to. Well, it simply follows the ARM Architecture Procedure Call Standard, AAPCS for short. This states how functions should pass arguments to each other. This PDF document can be found here and if you’re contemplating assembly is a very worthwhile download.

For now, here’s what you need to know. The first four arguments are placed in the first four registers r0-r3, every one after that is placed on the stack. The output value is placed in r0. As long as you take the argument list of the BIOS call as the list in the declaration, it should work fine. Note that the declaration also takes care of any casting that needs to be done. It is important that you realize just what the declaration means here: it determines how the function is called, not the actual definition assembly function. Or even C function. Things can go very wrong if you mess up the declaration.

Another thing the AAPCS tells you is that register r0-r3 (and r12) are so-called scratch registers. This means that the caller expects the called function to mess these up. After the function returns their contents are to be considered undefined – unless you’re the one writing both asm functions, in which case there may be certain … allowances. Having these as scratch registers means that a function can use them without needing to push and pop the originals on and off the stack, thus saving time. This does not hold for the other registers, though: r4-r11, r13, r14 must be returned in the way the calling function got them. The last one, r15, is exempt from this, as you shouldn’t screw around with the program counter.

Inline assembly

Actually, you don’t even need a full assembly file for BIOS calls: you could use inline assembly. With inline assembly, you can mix C code and assembly code. Since the functions are usually rather simple, you could use something like

// In a C file
int Div(int num, int denom)
{   asm("swi 0x06");   }

This does exactly the same thing as the assembly version of Div. However, you need to be careful with inline assembly because you can’t see the code around it and might accidentally clobber some registers that you shouldn’t be messing with, thus ruining the rest of the code. For the full rules on inline assembly, see the GCC manual. You can also find a short faq on inline assembly use at devrs.com. The ‘proper’ syntax of inline assembly isn’t the friendliest in the world, mind you, and there are other problems as well. Consider the C function given above. Since it doesn’t really do anything itself, the optimiser may be tempted to throw it away. This will happen with -O3 unless you take appropriate precautions. Also, the compiler will complain that the function doesn’t return anything, even though it should. It has a point, of course, considering that part is taken care of inside the assembly block. There are probably a few other problems that I’m not aware of at present; in the end it’s easier to use the full-assembly versions so you know what’s happening.

The swi_call macro

On the other hand, there are also BIOS calls that use no arguments, which can be run via a mere macro. The swi_call(x) macro will run the BIOS call x, and can be found in swi.h, and in Wintermute’s libgba, which is where I got it from. It’s a little more refined than the Div function given above. First, it uses the volatile keyword, which should keep your optimizer from deleting the function (just like we did for all the registers). Secondly, it uses a clobber list (after the triple colons). This will tell the compiler which registers are used by the inline assembly. Thirdly, it will take care of the Thumb/ARM switch automatically. If you use the -mthumb compiler option, the compiler will define __thumb__ for us, which we will now use to get the right swi-number. Clever, eh?

#ifndef(__thumb__)
#define swi_call(x)   asm volatile("swi\t"#x ::: "r0", "r1", "r2", "r3")
#else
#define swi_call(x)   asm volatile("swi\t"#x"<<16" ::: "r0", "r1", "r2", "r3")
#endif

By the way, if you want more information about assembly, you can find a number of tutorials on ARM assembly at gbadev.org. Another nice way to learn is by using the -S compiler flag, which will give you a compiler-generated assembly file of your code. This will show you exactly what the compiler does to your code, including optimisation steps and use of the AAPCS. Really, you should see this at least once.

It may also help to use -fverbose-asm, which will write out the original variable names and operations in comments. Usually in the right place too. Also handy is the ASM_CMT() macro shown below. This will give you some hints as to where specific blocks of code are. But again, not all the time.

#define ASM_CMT(str) asm volatile("@ " str)

//In code. Outputs "@ Hi, I'm here!" in the generated asm
ASM_CMT("Hi, I'm here!");

Demo graphs

math graphs

Fig 17.1: div, sqrt, arctan2, sin and cos graphs, courtesy of BIOS.

To illustrate the use of BIOS calls I am using Div, Sqrt, ArcTan and ObjAffineSet to create graphs if a hyperbole, square root, sine and cosine. I’ve scaled them in such a way so that they fit nicely on the 240x160 screen. The definitions are

division y= 2560/x
square root y= 160*sqrt(x/240)
arctan y= 80 + 64*(2/π)*(arctan(x-120)/16))
sine y= 1*sy*sin(2π·x/240) ; sy= 80
cosine y= 80*sx*cos(2π·x/240) ; sx= 1

and these functions have been plotted in fig 1. If you’re wondering how I got the sine and cosine values, as there are no calls for those, take a look at eq 1 again. The P matrix has them. I’ve used pa for the cosine and pc for the sine. Note that the graphs appear instantly; there is no sense of loading time while the graphs are plotted. An earlier version of the mode 7 demo (or PERNs mode 7 demo) used calls to the actual division, sine and cosine functions to build up the LUTs. Even with the symmetry rules of trigonometry, sin() and cos() are still noticeably slower than the BIOS equivalent.

#include <stdio.h>
#include <tonc.h>

// === swi calls ======================================================

// Their assembly equivalents can be found in tonc_bios.s

void VBlankIntrWait()
{   swi_call(0x05); }

int Div(int num, int denom)
{   swi_call(0x06); }

u32 Sqrt(u32 num)
{   swi_call(0x08); }

s16 ArcTan2(s16 x, s16 y)
{   swi_call(0x0a); }

void ObjAffineSet(const AFF_SRC *src, void *dst, int num, int offset)
{   swi_call(0x0f); }


// === swi demos ======================================================

// NOTE!
// To be consistent with general mathematical graphs, the 
// y-axis has to be reversed and the origin moved to the 
// either the bottom or mid of the screen via
// "iy = H - y"
// or
// "iy = H/2 - y"
//
// functions have been scaled to fit the graphs on the 240x160 screen

// y= 2560/x
void div_demo()
{
    int ix, y;

    for(ix=1; ix<SCREEN_WIDTH; ix++)
    {
        y= Div(0x0a000000, ix)>>16;
        if(y <= SCREEN_HEIGHT)
            m3_plot(ix, SCREEN_HEIGHT - y, CLR_RED);
    }
    tte_printf("#{P:168,132;ci:%d}div", CLR_RED);
}

// y= 160*sqrt(x/240)
void sqrt_demo()
{
    int ix, y;
    for(ix=0; ix<SCREEN_WIDTH; ix++)
    {
        y= Sqrt(Div(320*ix, 3));
        m3_plot(ix, SCREEN_HEIGHT - y, CLR_LIME);
    }
    tte_printf("#{P:160,8;ci:%d}sqrt", CLR_LIME);
}

// y = 80 + tan((x-120)/16) * (64)*2/pi
void arctan2_demo()
{
    int ix, y;
    int ww= SCREEN_WIDTH/2, hh= SCREEN_HEIGHT/2;
    for(ix=0; ix < SCREEN_WIDTH; ix++)
    {
        y= ArcTan2(0x10, ix-ww);
        m3_plot(ix, hh - y/256, CLR_MAG);
    }
    tte_printf("#{P:144,40;ci:%d}atan", CLR_MAG);
}

// wX= 1, wY= 80
// cc= 80*sx*cos(2*pi*alpha/240)
// ss=  1*sy*sin(2*pi*alpha/240)
void aff_demo()
{
    int ix, ss, cc;
    ObjAffineSource af_src= {0x0100, 0x5000, 0};    // sx=1, sy=80, alpha=0
    ObjAffineDest af_dest= {0x0100, 0, 0, 0x0100};  // =I (redundant)

    for(ix=0; ix<SCREEN_WIDTH; ix++)
    {
        ObjAffineSet(&af_src, &af_dest, 1, BG_AFF_OFS);
        cc= 80*af_dest.pa>>8; 
        ss= af_dest.pc>>8;
        m3_plot(ix, 80 - cc, CLR_YELLOW);
        m3_plot(ix, 80 - ss, CLR_CYAN);
        // 0x010000/0xf0 = 0x0111.111...
        af_src.alpha += 0x0111;
    }

    tte_printf("#{P:48,38;ci:%d}cos", CLR_YELLOW);
    tte_printf("#{P:72,20;ci:%d}sin", CLR_CYAN);
}

// === main ===========================================================

int main()
{
    REG_DISPCNT= DCNT_MODE3 | DCNT_BG2;

    tte_init_bmp_default(3);
    tte_init_con();

    div_demo();
    sqrt_demo();
    aff_demo();

    arctan2_demo();
    
    while(1);
    
    return 0;
}

Vsyncing part II, VBlankIntrWait

Until now, all demos used the function vid_vsync to synchronize the action to the VBlank (see the graphics introduction). What this did was to check REG_VCOUNT and stay in a while loop until the next VBlank came along. While it works, it’s really a pretty poor way of doing things for two reasons. First, because of the potential problem when you are in a VBlank already, but that one had been covered. The second reason is more important: while you’re in the while loop, you’re wasting an awful lot of CPU cycles, all of which slurp battery power.

swi_vsync

Fig 17.2: swi_vsync demo.

There are a number of BIOS calls that can put the CPU into a low power mode, thus sparing the batteries. The main BIOS call for this is Halt (#2), but what we’re currently interested in is VBlankIntrWait (#5). This will set things up to wait until the next VBlank interrupt. To use it, you have to have interrupts switched on, of course, in particular the VBlank interrupt. As usual, the VBlank isr will have to acknowledge the interrupt by writing to REG_IF. But it also has to write to its BIOS equivalent, REG_IFBIOS. This little bit of information is a little hard to find elsewhere (in part because few tutorials cover BIOS calls); for more info, see GBATEK, BIOS Halt Functions. Fortunately for us, the switchboard presented in the interrupts section has this built in.

To show you how to set it up, see the swi_vsync demo. The most important code is given below; a screen shot can be found in fig 2. What it does is give a rotating metroid sprite with an angular velocity of π rad/s (this corresponds to Δθ = 0x10000/4/60= 0x0111). The basic steps for interrupt handling should be familiar, except the fact that there’s no real VBlank isr because the switchboard already takes care of acknowledging the interrupt. After that it’s pretty simple: we use ObjAffineSet() to calculate the required affine matrix and VBlankIntrWait puts the CPU on Halt until the next VBlank interrupt.

// inside main, after basic initialisations

AFF_SRC as= { 0x0100, 0x0100, 0 };
OBJ_AFFINE oaff;

// enable isr switchboard and VBlank interrupt
irq_init(NULL);
irq_add(II_VBLANK, NULL);

while(1)
{
    VBlankIntrWait();

    // Full circle = 10000h
    // 10000h/4/60= 111h -> 1/4 rev/s = 1 passing corner/s
    as.alpha += 0x0111;
    ObjAffineSet(&as, &oaff.pa, 1, 8);

    obj_aff_copy(obj_aff_mem, &oaff, 1);
}

Prefer VBlankIntrWait() over vid_vsync()

Waiting for the VBlank via vid_vsync() (or its functional equivalent) is not a good idea: it wastes too much battery power. The recommended procedure is using VBlankIntrWait() to halt the processor, to be woken again on the VBlank interrupt.

Acknowledging IntrWait routines

VBlankIntrWait() is only one of the BIOS’s IntrWait() routines that can stop the CPU until an interrupt has been raised. However, it doesn’t look at REG_IF but at REG_IFBIOS (0300:7FF8) for the acknowledgement of the interrupt. If your game locks up after trying VBlankIntrWait(), this may be why. Note that you may find the address under other names, as there isn’t really an official one for it.

Final thoughts

Now that you know how to use them, I should warn you that you shouldn’t go overboard with them. It appears that the BIOS routines have been designed for space, not speed, so they aren’t the fastest in the world. Not only that, there’s an overhead of at least 60 cycles for each one (mind you, normal functions seem to have a 30 cycle overhead). If speed is what you’re after then the BIOS calls may not be the best thing; you can probably find faster routines on the web … somewhere. This doesn’t mean that the BIOS routines can’t be useful, of course, but if you have alternative methods, use those instead. Just remember that that’s an optimisation step, which you shouldn’t do prematurely.

18. Beep! GBA sound introduction

Introduction to GBA sound

Apart from graphics and interaction, there is one other sense important to games: audio. While graphics may set the scene, sound sets the mood, which can be even more important that the graphics. Try playing Resident Evil with, say, “Weird Al” Yankovic playing: it simply doesn’t work, the atmosphere is lost.

The GBA has six sound channels. The first four are roughly the same as the original Game Boy had: two square wave generators (channels 1 and 2), a sample player (channel 3) and a noise generator (channel 4). Those are also referred to as the DMG channels after the Game Boy’s code name “Dot Matrix Game.” New are two Direct Sound channels A and B (not to be confused with Microsoft’s DirectSound, the DirectX component). These are 8-bit digital pulse code modulation (PCM) channels.

I should point out that I really know very little about sound programming, mostly because I’m not able to actually put together a piece of music (it’s kinda hard to do that when you already have music playing). If you want to really learn about sound programming, you should look at Belogic.com, where almost everybody got their information from, and deku.gbadev.org, which shows you how to build a sound mixer. Both of these sites are excellent.

I may not know much about sound creation/programming, but at its core sound is a wave in matter; waves are mathematical critters, and I do know a thing or two about math, and that’s kind of what I’ll do here for the square wave generators.

Sound and Waves

Consider if you will, a massive sea of particles, all connected to their neighbours with little springs. Now give one of them a little push. In the direction of the push, the spring compresses and relaxes, pushing the original particle back to its normal position and passing on the push to the neighbour; this compresses the next spring and relays the push to its neighbour, and so on and so on.

This is a prime example of wave behaviour. Giving a precise definition of a wave that covers all cases is tricky, but in essence, a wave is a transferred disturbance. There are many kinds of waves; two major classes are longitudinal waves, which oscillate in the direction of travel, and transverse waves, which are perpendicular to it. Some waves are periodic (repeating patterns over time or space), some aren’t. Some travel, some don’t.

Waves

The canonical wave is the harmonic wave. This is any function ψ(x) that’s a solution to eq 18.1. The name of the variable doesn’t really matter, but usually it’s either spatial (x, y, z) or temporal (t), or all of these at the same time. The general solution can be found in eq 18.2. Or perhaps I should say solutions, as there are many ways of writing them down. They’re all equivalent though, and you can go from one to the other with some trickery that does not concern us at this moment.

(18.1) d 2 d x 2 ψ ( x ) + k 2 ψ ( x ) = 0

General solution(s):

(18.2) ψ ( x ) = A c o s ( k x ) + B s i n ( k x ) = C e i k x + D e i k x = E s i n ( k x + φ 0 )
it's a sine wave

Fig 18.1: a harmonic wave

A full wave can be described by three things. First, there’s the amplitude A, which gives half-distance between the minimum and maximum. Second, the wavelength λ, which is the length after which the wave repeats itself (this is tied to wave-number k= 2π/λ). Then there’s phase constant φ0, which defines the stating point. If the wave is in time, instead of a wavelength you have period T, frequency f=1/T (and angular frequency ω= 2πf= 2π/T). You can see what each of these parameters is in fig 18.1.

One of the interesting things about the wave equation is that it is a linear operation on ψ. What that means is that any combination of solutions is also a solution; this is the superposition principle. For example, if you have two waves ψ1 and ψ2, then Ψ = aψ1 + bψ2 is also a wave. This may sound like a trivial thing but I assure you it’s not. The fact that non-linear equations (and they exist too) tend to make scientists cringe a little should tell you something about the value of linear equations.

Sound waves

Sound is also a wave. In fact, it is a longitudinal pressure wave in matter and pretty much works as the system of particles on springs mentioned earlier with whole sets of molecules moving back and forth. In principle, it has both spatial and temporal structure, and things can get hideously complex if you want to deal with everything. But I’ll keep it easy and only consider two parts: amplitude A and period and frequency T and f. As you probably know, the tone of a sound is related to the frequency. Human hearing has a range between 20 Hz and 20 kHz, and the higher the frequency (that is, the more compressed the wave), the higher the tone. Most sounds are actually a conglomeration of different waves, with different amplitudes and frequencies – the superposition principle at work. The funny thing about this is that if you added all those components up to one single function and plot it, it wouldn’t look like a sine wave at all anymore. What’s even funnier is that you can also reverse the process and take a function –any function– and break it up into a superposition of sine and cosine waves, and so see what kind of frequencies your sound has. This is called Fourier Transformation, and we’ll get to that in a minute.

Musical scale

While the full range between 20 Hz and 20 kHz is audible, only a discrete set of frequencies are used for music, which brings us to the notion of the musical scale. Central to these are octaves, representing a frequency doubling. Each octave is divided into a number of different notes; 12 in Western systems, ranging from A to G, although octave numbering starts at C for some reason. Octave 0 starts at the central C, which has a frequency of about 262 Hz (see also table 18.1. And yes, I know there are only 7 letters between A and G, the other notes are flats and sharps that lie between these notes. The ‘12’ refers to the number of half-notes in an octave. The musical scale is logarithmic; each half-note being 21/12 apart. Well, almost anyway: for some reason, some notes don’t quite fit in exactly.

Table 18.1: notes & frequencies of octave 0
half-note 0 1 2 3 4 5 6 7 8 9 10 11 (12)
name C C# D D# E F F# G G# A A# B (C)
freq (Hz) 261.7 277.2 293.7 311.2 329.7 349.3 370.0 392.0 415.3 440.0 466.2 493.9 (523.3)

Fourier transforms and the square wave

Fourier transformations are a way of going describing a function in the time domain as a distribution of frequencies called a spectrum. They’re also one of the many ways that professors can scare the bejebus out of young, natural-science students. Don’t worry, I’m sure you’ll get through this section unscathed >:). For well- to reasonably-behaved functions, you can rewrite them as series of very well-behaved functions such as polynomials, exponentials and also waves. For example, as a Fourier series, a function may look like eq 18.3.

(18.3) f ( x ) = 1 2 A 0 + n > 0 A m cos ( m ω t ) + n > 0 B m sin ( m ω t )

Of course, the whole thing relies on being able to find the coefficients Am and Bm. While it is fairly straightforward to derive the equations for them, I’ll leave that as an exercise for the reader and just present the results in the form of eq 18.4. I should mention that there are actually a few ways of defining Fourier transforms. For example, there are versions that don’t integrate over [0,T], but over [−½T, ½T]; or use the complex exponential instead of sines and cosines, but in the end they’re all doing the same thing.

(18.4) A m = 2 T 0 T f ( t ) cos ( m ω t ) d t B m = 2 T 0 T f ( t ) sin ( m ω t ) d t
sharp transitions between flat crest and flat trough

Fig 18.2: a square wave

As an example, let’s take a look at the square wave shown in fig 18.2. A square wave is on (1) for a certain time (parameter h), then off (0) for the rest of the cycle. It’s still a periodic wave, so it doesn’t really matter where we place the thing along the t-axis. I centered it on the peak for convenience: doing so makes it a symmetrical wave which has the nice properly of removing all the anti-symmetrical sine waves. A0=h/T because it’s the average of the function and the rest of the Am’s follow from eq 18.4.

(18.5) A m = 2 π sin ( π m h / T ) m = 2 T h sin ( π h / T m ) π h / T m

Am is a sinc function: sin(x)/x. For high m it approaches zero (as it should, since higher terms should be relatively less important), but also interesting is that of the higher terms some will also vanish because of the sine. This will happen whenever m is a multiple of T/h.

GBA sound

Sound registers

For graphics, you only had to deal with two registers (REG_DISPCNT and REG_BGxCNT) to get a result; for sound, you have to cover a lot of registers before you get anything. The DMG channels each have 2 or 3 registers – some with similar functionality, some not. Apart from that, there are four overall control registers.

The register nomenclature seems particularly vexed when it comes to sound. There are basically two sets of names that you can find: one consisting of REG_SOUNDxCNT followed by _L, _H and _X in a rather haphazard manner; the other one uses a REG_SGxy and REG_SGCNTy structure (x=1, 2, 3 or 4 and y=0 or 1). I think the former is the newer version, which is funny because the older is more consistent. Oh well. In any case, I find neither of them very descriptive and keep forgetting which of the L/H/X or 0/1 versions does what, so I use a third set of names based on the ones found in tepples’ pin8gba.h, which IMHO makes more sense than the other two.

Table 18.2: Sound register nomenclature.
offset function old new tonc
60h channel 1 (sqr) sweep REG_SG10 SOUND1CNT_L REG_SND1SWEEP
62h channel 1 (sqr) len, duty, env SOUND1CNT_H REG_SND1CNT
64h channel 1 (sqr) freq, on REG_SG11 SOUND1CNT_X REG_SND1FREQ
68h channel 2 (sqr) len, duty, env REG_SG20 SOUND2CNT_L REG_SND2CNT
6Ch channel 2 (sqr) freq, on REG_SG21 SOUND2CNT_H REG_SND2FREQ
70h channel 3 (wave) mode REG_SG30 SOUND3CNT_L REG_SND3SEL
72h channel 3 (wave) len, vol SOUND3CNT_H REG_SND3CNT
74h channel 3 (wave) freq, on REG_SG31 SOUND3CNT_X REG_SND3FREQ
78h channel 4 (noise) len, vol, env REG_SG40 SOUND4CNT_L REG_SND4CNT
7Ch channel 4 (noise) freq, on REG_SG41 SOUND4CNT_H REG_SND4FREQ
80h DMG master control REG_SGCNT0 SOUNDCNT_L REG_SNDDMGCNT
82h DSound master control SOUNDCNT_H REG_SNDDSCNT
84h sound status REG_SGCNT1 SOUNDCNT_X REG_SNDSTAT
88h bias control REG_SGBIAS SOUNDBIAS REG_SNDBIAS

“Oh great. This is going to be one of ‘tegel’ things isn’t it? Where you think you’ve got something nice but different going, then later you revert to the standard terminology to conform with the rest of the world. Right?”

No, I’ll stick to these names. Probably. Hopefully. … To be honest, I really don’t know :P. This is not really a big deal, though: you can easily switch between names with a few defines or search & replaces. Anyway, REG_SNDxFREQ contains frequency information and REG_SNDxCNT things like volume and envelope settings; in some cases, the bit layouts are even exactly the same. Apart from the sweep function of channel 1, it is exactly the same as channel 2.

Master sound registers

REG_SNDDMGCNT, REG_SNDDSCNT and REG_SNDSTAT are the master sound controls; you have to set at least some bits on each of these to get anything to work.

REG_SNDDMGCNT (SOUNDCNT_L / SGCNT0_L ) @ 0400:0080h
FEDCBA98 76 5 432 1 0
R4 R3 R2 R1 L4 L3 L2 L1 - RV - LV
bitsnamedefinedescription
0-2LV   Left volume
4-6RV   Right volume
8-BL1-L4 SDMG_LSQR1, SDMG_LSQR2, SDMG_LWAVE, SDMG_LNOISE Channels 1-4 on left
C-FR1-R4 SDMG_RSQR1, SDMG_RSQR2, SDMG_RWAVE, SDMG_RNOISE Channels 1-4 on right

REG_SNDDMGCNT controls the main volume of the DMG channels and which ones are enabled. These controls are separate for the left and right speakers. Below are two macros that make manipulating the register easier. Note that they don’t actually set the register, just combine the flags.

#define SDMG_SQR1    0x01
#define SDMG_SQR2    0x02
#define SDMG_WAVE    0x04
#define SDMG_NOISE   0x08

#define SDMG_BUILD(_lmode, _rmode, _lvol, _rvol)    \
    ( ((_lvol)&7) | (((_rvol)&7)<<4) | ((_lmode)<<8) | ((_rmode)<<12) )

#define SDMG_BUILD_LR(_mode, _vol) SDMG_BUILD(_mode, _mode, _vol, _vol)
REG_SNDDSCNT (SOUNDCNT_H / SGCNT0_H) @ 0400:0082h
FEDCBA98 7 6 5 432 1 0
BF BT BL BR AF AT AL AR - BV AV DMGV
bitsnamedefinedescription
0-1DMGV SDS_DMG25, SDS_DMG50, SDS_DMG100 DMG Volume ratio.
  • 00: 25%
  • 01: 50%
  • 10: 100%
  • 11: forbidden
2 AV SDS_A50, SDS_A100 DSound A volume ratio. 50% if clear; 100% of set
3 BV SDS_B50, SDS_B100 DSound B volume ratio. 50% if clear; 100% of set
8-9AR, AL SDS_AR, SDS_AL DSound A enable Enable DS A on right and left speakers
A AT SDS_ATMR0, SDS_ATMR1 Dsound A timer. Use timer 0 (if clear) or 1 (if set) for DS A
B AF SDS_ARESET FIFO reset for Dsound A. When using DMA for Direct sound, this will cause DMA to reset the FIFO buffer after it's used.
C-F BR, BL, BT, BF SDS_BR, SDS_BL, SDS_BTMR0, SDS_BTMR1, SDS_BRESET As bits 8-B, but for DSound B

Don’t know too much about REG_SNDDSCNT, apart from that it governs PCM sound, but also has some DMG sound bits for some reason. REG_SNDSTAT shows the status of the DMG channels and enables all sound. If you want to have any sound at all, you need to set bit 7 there.

REG_SNDSTAT (SOUNDCNT_X / SGCNT1) @ 0400:0084h
F E D C B A 9 8 76 5 4 3210
- MSE - 4A 3A 2A 1A
bitsnamedefinedescription
0-31A-4A SSTAT_SQR1, SSTAT_SQR2, SSTAT_WAVE, SSTAT_NOISE Active channels. Indicates which DMG channels are currently playing. They do not enable the channels; that's what REG_SNDDMGCNT is for.
7 MSE SSTAT_DISABLE, SSTAT_ENABLE Master Sound Enable. Must be set if any sound is to be heard at all. Set this before you do anything else: the other registers can't be accessed otherwise, see GBATEK for details.

Sound register access

Emulators may allow access to sound registers even if sound is disabled (REG_SNDSTAT{7} is clear), but hardware doesn’t. Always enable sound before use.

GBA Square wave generators

The GBA has two square sound generators, channels 1 and 2. The only difference between them is channel 1’s frequency sweep, which can make the frequency rise or drop exponentially as it’s played. That’s all done with REG_SND1SWEEP. REG_SNDxCNT controls the wave’s length, envelope and duty cycle. Length should be obvious. The envelope is basically the amplitude as function of time: you can make it fade in (attack), remain at the same level (sustain) and fade out again (decay). The envelope has 16 volume levels and you can control the starting volume, direction of the envelope and the time till the next change. Volumes are linear: 12 produces twice the amplitude of 6. The duty refers to the ratio of the ‘on’ time and the period, in other words D = h/T.

Of course, you can control the frequency as well, namely with REG_SNDxFREQ. However, it isn’t the frequency that you enter in this field. It’s not exactly the period either; it’s something I’ll refer to as the rate R. The three quantities are related, but different in subtle ways and chaos ensues when they’re confused – and they often are in documentation, so be careful. The relation between frequency f and rate R is described by eq 18.6; if the rate goes up, so does the frequency. Since R ∈ [0, 2047], the range of frequencies is [64 Hz, 131 kHz]. While this spans ten octaves, the highest ones aren’t of much use because the frequency steps become too large (the denominator in eq eq 18.6 approaches 0).

(18.6a) f ( R ) = 2 17 2048 R
(18.6b) R ( f ) = 2048 2 17 f

Square sound registers

Both square-wave generators have registers REG_SNDxCNT for envelope/length/duty control and REG_SNDxFREQ for frequency control. Sound 1 also has sweep control in the form of REG_SND1SWEEP. Look in table 18.2 for the traditional names; note that in traditional nomenclature the suffixes for control and frequency are different for channels 1 and 2, even though they have exactly the same function.

REG_SND1CNT (SOUND1CNT_H / SG10_H) @ 0400:0062h
and
REG_SND2CNT (SOUND2CNT_L / SG20_L) @ 0400:0068h
F E D CBA 9 87 65 4 3 2 1 0
EIV ED EST D L
bitsnamedefinedescription
0-5L SSQR_LEN# Sound Length. This is a write-only field and only works if the channel is timed (REG_SNDxFREQ{E}). The length itself is actually (64−L)/256 seconds for a [3.9, 250] ms range.
6-7D SSQR_DUTY1_8, SSQR_DUTY1_4, SSQR_DUTY1_2, SSQR_DUTY3_4, SSQR_DUTY# Wave duty cycle. Ratio between on and of times of the square wave. Looking back at eq 18.2, this comes down to D=h/T. The available cycles are 12.5%, 25%, 50%, and 75% (one eighth, quarter, half and three quarters).
8-AEST SSQR_TIME# Envelope step-time. Time between envelope changes: Δt = EST/64 s.
B ED SSQR_DEC, SSQR_INC Envelope direction. Indicates if the envelope decreases (default) or increases with each step.
C-FEIV SSQR_IVOL# Envelope initial value. Can be considered a volume setting of sorts: 0 is silent and 15 is full volume. Combined with the direction, you can have fade-in and fade-outs; to have a sustaining sound, set initial volume to 15 and an increasing direction. To vary the real volume, remember REG_SNDDMGCNT.
Fourier transform of square wave
Fig 18.3: Square wave spectrum. (integer m only)
  A m = 2 π s i n ( π D m ) m

Some more on the duty cycle. Remember we’ve done a Fourier analysis of the square wave so we could determine the frequencies in it. Apart from the base frequency, there are also overtones of frequencies m·f. The spectrum (see fig 18.3) gives the amplitudes of all these frequencies. Note that even though the figure has lines, only integral values of m are allowed. The base frequency at m=1 has the highest significance and the rest falls off with 1/m. The interesting part is when the sine comes into play: whenever m·D is an integer, that component vanishes! With a fractional duty number –like the ones we have– this happens every time m is equal to the denominator. For the 50% duty, every second overtone disappears, leaving a fairly smooth tone; for 12.5%, only every eighth vanishes and the result is indeed a noisier sound. Note that for both ¼ and ¾ duties every fourth vanishes so that they should be indistinguishable. I was a little surprised about this result, but sure enough, when I checked they really did sound the same to me.

REG_SND1FREQ (SOUND1CNT_X / SG11) @ 0400:0062h
and
REG_SND2FREQ (SOUND2CNT_H / SG21) @ 0400:006Ch
FED C B A 9 8 7 6 5 4 3 2 1 0
Re T - R
bitsnamedefinedescription
0-AR SFREQ_RATE# Sound rate. Well, initial rate. That's rate, not frequency. Nor period. The relation between rate and frequency is f = 217/(2048-R). Write-only field.
E T SFREQ_HOLD, SFREQ_TIMED Timed flag. If set, the sound plays for as long as the length field (REG_SNDxCNT{0-5}) indicates. If clear, the sound plays forever. Note that even if a decaying envelope has reached 0, the sound itself would still be considered on, even if it's silent.
F Re SFREQ_RESET Sound reset. Resets the sound to the initial volume (and sweep) settings. Remember that the rate field is in this register as well and due to its write-only nature a simple ‘|= SFREQ_RESET’ will not suffice (even though it might on emulators).

REG_SND1SWEEP (SOUND1CNT_L / SG10_L) @ 0400:0060h
F E D C B A 9 8 76 5 432 1 0
- T M N
bitsnamedefinedescription
0-2N SSW_SHIFT# Sweep number. Not the number of sweeps; see the discussion below.
3 M SSW_INC, SSW_DEC Sweep mode. The sweep can take the rate either up (default) or down (if set).
4-6T SSW_TIME# Sweep step-time. The time between sweeps is measured in 128 Hz (not kHz!): Δt = T/128 ms ≈ 7.8T ms; if T=0, the sweep is disabled.

I’m reasonably confident that the exact workings of shifts are explained without due care in most documents, so here are a few more things about it. Sure enough, the sweep does make the pitch go up or down which is controlled by bit 3, and the step-time does change the pitch after that time, but exactly what the sweep-shift does is ambiguous at best. The information is in there, but only if you know what to look for. The usual formula given is something like:

T = T ± T 2 n

That’s what belogic gives and if you know what the terms are you’ll be fine. Contrary to what you may read, the sweep does not apply to the frequency (f). It does not apply to the period (T, see above). It applies to the rate (R). If you look in emulators, you can actually see the rate-value change.

Second, the n in the exponent is not the current sweep index that runs up to the number of sweep shifts. It is in fact simply the sweep shift number, and the sweeps continue until the rate reaches 0 or the maximum of 2047.

The formulas you may see do say that, but it’s easy to misread them. I did. Eq 18.7 holds a number of correct relations. R is the rate, n is the sweep shift (18.7c explains why it’s called a shift (singular, not plural)), and j is the current sweep index. You can view them in a number of ways, but they all boil down to exponential functions, that’s what ‘dy*(x) = a·y(x)dx*’ means, after all. For example, if n=1, then you get 1½j and ½j behaviour for increasing and decreasing sweeps, respectively; with n=2 it’s 1¼j and ¾j, etc. The higher the shift, the slower the sweep.

(18.7a) Δ R = 2 n R
(18.7b) R j = R j 1 ± R j 1 2 n = R j 1 ( 1 ± 2 n ) = R 0 ( 1 ± 2 n ) j
(18.7c) R += R >> n;

Playing notes

Even though the rates are equal, some may be considered more equal than others. I’ve already given a table with the frequencies for the standard notes (table 18.1) of octave 0. You can of course convert those to rates via eq 18.6b and use them as such. However, it might pay to figure out how to play the notes of all octaves.

To do this, we’ll use some facts I mentioned in section 18.2.3. about the make-up of the musical scale. While I could make use of the logarithmic relation between successive notes (Δf=21/12·f), I’ll restrict myself to the fact that notes between octaves differ by a factor of two. We’ll also need the rate-frequency relation (obviously). That’s the basic information you need, I’ll explain more once we get through all the math. Yes, it’s more math, but it’ll be the last of this page, I promise.

The equations we’ll start with are the general frequency equation and the rate-frequency relation. In these we have rate R, frequency f and octave c. We also have a base octave C and frequency F in that base octave.

  f ( F , c ) = F 2 c C R ( F , c ) = 2 11 2 17 f ( F , c )

And now for the magic. And you are expected to understand this.

(18.8) R ( F , c ) = 2 11 2 17 f ( F , c ) = 2 11 2 17 F 2 c C = 2 11 2 17 + C c F = 2 11 1 F 2 17 + C + m ( c + m ) = 2 11 2 17 + C + m F 2 ( c + m )

Right, and now for why this thing’s useful. Remember that the GBA has no hardware division or floating-point support, so we’re left with integers and (if possible) shifts. That’s why the last term in the last step of eq 18.8 was separated. The term with F gives a rate offset for the base octave, which we need to divide (read: shift) by the octave offset term for the different octaves. Remember that integer division truncates, so we need a big numerator for the most accuracy. This can be done with a large C and by adding an extra term m. Basically, this makes it an mf fixed point division. The workable octave range is −2 to 5, so we take C=5. The value for m is almost arbitrary, but needs to be higher than two because of the minimum octave is −2, and a shift can never be negative. m=4 will suffice.

Note that there is still a division in there. Fortunately, there are only twelve values available for F, so might just as well store the whole term in a look-up table. The final result is listing 18.1 below.

// Listing 18.1: a sound-rate macro and friends

typedef enum 
{
    NOTE_C=0, NOTE_CIS, NOTE_D,   NOTE_DIS, 
    NOTE_E,   NOTE_F,   NOTE_FIS, NOTE_G, 
    NOTE_GIS, NOTE_A,   NOTE_BES, NOTE_B
} eSndNoteId;

// Rates for equal temperament notes in octave +5
const u32 __snd_rates[12]=
{
    8013, 7566, 7144, 6742, // C , C#, D , D#
    6362, 6005, 5666, 5346, // E , F , F#, G
    5048, 4766, 4499, 4246  // G#, A , A#, B
};

#define SND_RATE(note, oct) ( 2048-(__snd_rates[note]>>(4+(oct))) )

// sample use: note A, octave 0
    REG_SND1FREQ= SFREQ_RESET | SND_RATE(NOTE_A, 0);

Here you have a couple of constants for the note-indices, the LUT with rate-offsets __snd_rates and a simple macro that gives you what you want. While __snd_rates is constant here, you may consider a non-const version to allow tuning. Not that a square wave is anything worth tuning, but I’m just saying … y’know.

One possible annoyance is that you have to splice the note into a note and octave part and to do that dynamically you’d need division and modulo by 12. Or do you? If you knew a few things about division by a constant is multiplication by its reciprocal, you’d know what to do. (Hint: c=(N*43>>9)−2, with N the total note index between 0 and 95 (octave −2 to +5).)

Demo time

I think I’ve done about enough theory for today, don’t you dear reader?

“ @_@ ”

I’ll take that as a yes. The demo in question demonstrates the use of the various macros of this chapter, most notably SND_RATE. It also shows how you can play a little song – and I use the term lightly – with the square wave generator. I hope you can recognize which one.

#include <stdio.h>
#include <tonc.h>

u8 txt_scrolly= 8;

const char *names[]=
{   "C ", "C#", "D ", "D#", "E ", "F ", "F#", "G ", "G#", "A ", "A#", "B "  };

// === FUNCTIONS ======================================================

// Show the octave the next note will be in
void note_prep(int octave)
{
    char str[32];
    siprintf(str, "[  %+2d]", octave);
    se_puts(8, txt_scrolly, str, 0x1000);
}


// Play a note and show which one was played
void note_play(int note, int octave)
{
    char str[32];

    // Clear next top and current rows
    SBB_CLEAR_ROW(31, (txt_scrolly/8-2)&31);
    SBB_CLEAR_ROW(31, txt_scrolly/8);   

    // Display note and scroll
    siprintf(str, "%02s%+2d", names[note], octave);
    se_puts(16, txt_scrolly, str, 0);

    txt_scrolly -= 8;
    REG_BG0VOFS= txt_scrolly-8;

    // Play the actual note
    REG_SND1FREQ = SFREQ_RESET | SND_RATE(note, octave);
}


// Play a little ditty
void sos()
{
    const u8 lens[6]= { 1,1,4, 1,1,4 };
    const u8 notes[6]= { 0x02, 0x05, 0x12,  0x02, 0x05, 0x12 };
    int ii;
    for(ii=0; ii<6; ii++)
    {
        note_play(notes[ii]&15, notes[ii]>>4);
        VBlankIntrDelay(8*lens[ii]);
    }
}

int main()
{
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    irq_init(NULL);
    irq_add(II_VBLANK, NULL);

    txt_init_std();
    txt_init_se(0, BG_CBB(0) | BG_SBB(31), 0, CLR_ORANGE, 0);
    pal_bg_mem[0x11]= CLR_GREEN;

    int octave= 0;

    // turn sound on
    REG_SNDSTAT= SSTAT_ENABLE;
    // snd1 on left/right ; both full volume
    REG_SNDDMGCNT = SDMG_BUILD_LR(SDMG_SQR1, 7);
    // DMG ratio to 100%
    REG_SNDDSCNT= SDS_DMG100;

    // no sweep
    REG_SND1SWEEP= SSW_OFF;
    // envelope: vol=12, decay, max step time (7) ; 50% duty
    REG_SND1CNT= SSQR_ENV_BUILD(12, 0, 7) | SSQR_DUTY1_2;
    REG_SND1FREQ= 0;

    sos();

    while(1)
    {
        VBlankIntrWait();
        key_poll();

        // Change octave:
        octave += bit_tribool(key_hit(-1), KI_R, KI_L);
        octave= wrap(octave, -2, 6);
        note_prep(octave);

        // Play note
        if(key_hit(KEY_DIR|KEY_A))
        {
            if(key_hit(KEY_UP))
                note_play(NOTE_D, octave+1);
            if(key_hit(KEY_LEFT))
                note_play(NOTE_B, octave);
            if(key_hit(KEY_RIGHT))
                note_play(NOTE_A, octave);
            if(key_hit(KEY_DOWN))
                note_play(NOTE_F, octave);
            if(key_hit(KEY_A))
                note_play(NOTE_D, octave);
        }

        // Play ditty
        if(key_hit(KEY_B))
            sos();      
    }
    return 0;
}

The bolded code in main() initializes the sound register; nothing fancy, but it has to be done before you hear anything at all. It is important to start with REG_SNDSTAT bit 7 (SSTAT_ENABLE), i.e., the master sound enable. Without it, you cannot even access the other registers. Setting volume to something non-zero is a good idea too, of course. Then we turn off the sweep function and set sound 1 to use a fading envelope with a 50% duty. And that’s where the fun starts.

I’ll explain what sos() in a little while, first something about the controls of the demo. You can play notes with the D-pad and A (hmm, there’s something familiar about that arrangement). The octave c you’re working in can be changed with L and R; the background color changes with it. B plays sos() again.

A / D-pad Play a note
↑ : D (next octave)
← : B
→ : A
↓ : F
A : D
L / R Decrease / Increase current octave ([-2, 5], wraps around)
B Play a little tune.

The D-pad and A select a note to play, which is handled by note_play(). The bolded line there plays the actual note, the rest is extra stuff that writes the note just played to the screen and scrolls along so you can see the history of what’s been played. The code for this is kinda ugly, but is not exactly central to the story so that’s fine.

Playing a little ditty

So what is sos() all about then? Let’s take another look.

void sos()
{
    const u8 lens[6]= { 1,1,4, 1,1,4 };
    const u8 notes[6]= { 0x02, 0x05, 0x12,  0x02, 0x05, 0x12 };
    int ii;
    for(ii=0; ii<6; ii++)
    {
        note_play(notes[ii]&15, notes[ii]>>4);
        VBlankIntrDelay(8*lens[ii]);
    }
}

There are two arrays here, notes and lens, and a loop over all elements. We take a byte from notes and use the nybbles for octave and note information, play the note, then wait a while –the length is indicated by the lens array– before the next note is played. Basically, we’re playing music. Hey, if the likes of Schnappi and Crazy Frog can make it into the top 10, I think I’m allowed to call this music too, alright? Alright.

The point I’m trying to make is that it’s very well possible to play a tune with just the tone generators. Technically you don’t need digitized music and all that stuff to play something. Of course, it’ll sound better if you do, but if you just need a little jingle the tone generators may be all you need. Twelve years of Game Boy games using only tone generators prove this. Just define some notes (the nybble format for octaves and notes will do) and some lengths and you have the basics already. You could even use more than one channel for different effects.

If you understood that, then get this: the note+length+channel idea is pretty much what tracked music (mod, it, xm, etc) does, only they use a more sophisticated wave than a square wave. But the principle is the same. Getting it to work takes a little more effort, but that’s what Deku’s sound mix tutorial is for.

19. Text systems

Deprecation notice

This chapter has been superceded by TTE. Information from this chapter can still be useful, but for serious work, TTE should be preferred.

Introduction

#include <stdio.h>

int main()
{
    printf("Hello World");
    return 0;
}

Aaah, yes, “Hello world”: the canonical first example for every C course and system. Except for consoles. While printing text on a PC is the easiest thing in the world, it is actually a little tricky on a console. It’s not that there’s no printf() function, but rather that there is nowhere for it to write to or even a font to write with (and that’s hardly the full list of things to consider). Nope, if you want to be able to display text, you’ll have to build the whole thing from scratch yourself. And you do want to be able to write text to the screen,

So, what do we need for a text system? Well, that’s actually not a simple question. Obviously, you need a font. Just a bitmap with the various characters here, no need to depress ourselves with vector-based fonts on a GBA. Second, you need a way of taking specific characters and show them on the screen.

But wait a minute, which video mode are we using? There’s tilemaps, bitmap modes and sprites to choose from, all of which need to be dealt with in entirely different ways. Are we settling for one of them, or create something usable for all? Also, what is the font we’re using, and what are the character sizes? Fixed width or variable width? Variable width and sizes aren’t much of a problem for the bitmap modes, but it’s a bitch to splice them for tiles. Also, just for tiles, do we keep the full font in VRAM? If so, that’s a lot of tiles, especially considering you’ll hardly be using all of them at the same time. It would be more VRAM efficient to only copy in the glyphs that you’re using at that time. This will take some management, though.

Just with these items, you’d have enough options for over 20 different text system implementations, all incompatible in very subtle ways. At the very least you’ll need putc() and puts() for each. And then perhaps a printf()-like function too; for each text-type, mind you, because glyph placement goes on the inside. Maybe a screen clear too; or how about scrolling functionality. Well, you get the idea.

I suppose it’s possible to create a big, complicated system, tailoring to every need anyone could possibly have. But I’m not going to. Firstly, because it’s a bit waste of time: the chances you’ll need the ability to run, say, bitmap and tilemap modes concurrently are virtually –if not actually– nil. Most of the time, you’ll use a single video mode and stick to that. Spending time (and space) for allow every variation imaginable, when hardly any will ever be used is probably not worth the trouble. Besides, writing tons of code that is almost identical except for some small detail in the heart of the routine is just plain bleh.

The point of this chapter is to show how to build and use a set of simple, lightweight text writers. Don’t expect the mother of all text systems, I’m mainly interested in getting the essential thing done, namely getting the characters of a string on the screen. This is a core text system, with the following features:

  • Bitmap (mode 3, 4, 5), regular tilemap (mode 0, 1) and sprite support.
  • There will be a xxx_puts() for showing the string, and a xxx_clrs() to wipe it. Their arguments will a string, the position to plot to, and some color information. If you want scrolling and/or format specifiers, I’ll leave that up to you.
  • The font is a fixed width, monochrome font with one 8x8 tile per character. The glyphs can be smaller than 8x8, and I’ll even leave in hooks that allow variable widths, but things just get horrible if I’d allowed for multi-tile fonts.
  • A variable character map. This is a great feature if you plan on using only a small set of characters, or non-ascii glyph orders.

This arrangement allows for the most basic cases and allows for some variations in set-up, but very little on the side. However, those extras would probably be very game specific anyway, and might be ill suited for a general text system. If you want extras, it shouldn’t be too hard to write them yourself.

No printf(). O rly?

I said that there is no printf() on the GBA, but this isn’t quite true; not anymore, anyway. It is possible to hook your own IO-system to the standard IO-routines, which is done in libgba.

Semi-obsolete

I have another text system here that is much more powerful (as in, really working on every video mode and has a printf too) than what’s described in this page. However, it’s rather large, not completely finished and it would take some time to write the description page and alter the text to fit the demos again. A libtonc version that has the relevant changes can be found at http://www.coranac.com/files/misc/tonclib-1.3b.rar.

Text system internals

Variables

For keeping track of the text-system’s state, we’ll need a couple of variables. The obvious variables are a font and a character map. Because I like to keep things flexible, I’ll also use two pointers for these so that you can use your own font and char-map if you want. You also need to know where it is you want to write to, which is done via a base-destination pointer. As extras, I’ll also have character size variables for variable glyph spacing, and even a pointer to a char-width array, for a possible variable-width font.

I’ll use a struct to store these, partially because it’s easier for me to maintain, but also because the CPU and compiler can deal with them more efficiently. I’ll also leave a few bytes empty for any eventual expansion. Finally, an instance of this struct, and a pointer to it so you can switch between different systems if you ever need to (which is unlikely, but still). Yes, I am wasting a few bytes, but if you max out IWRAM over this, I dare say you have bigger problems to worry about.

// In text.h
typedef struct tagTXT_BASE
{
    u16 *dst0;      // writing buffer starting point
    u32 *font;      // pointer to font used
     u8 *chars;     // character map (chars as in letters, not tiles)
     u8 *cws;       // char widths (for VWF)
     u8  dx,dy;     // letter distances
    u16  flags;     // for later
     u8  extra[12]; // ditto
} TXT_BASE;

extern TXT_BASE __txt_base, *gptxt;

// In text.c
TXT_BASE __txt_base;                Main TXT_BASE instance
TXT_BASE *gptxt= &__txt_base;        and a pointer to it

The font

Default tonc font

Fig 19.1: Default tonc font: mini-ascii, monochrome, 8x8 pixels per glyph.

fig 19.1 shows the font I’ll be using. This particular font is monochrome and each of the glyphs fits into an 8x8 box. The 96 glyphs themselves a subset of the full ASCII that I’ll refer to as mini-ascii. It’s the lower ascii half that contains the majority of the standard ASCII table, but leaves out ASCII 0-31 because they’re escape codes and not really part of the printable characters anyway.

It is possible to use a different font with another glyph order, but the functions I’ll present below rely on one tile per glyph, and in tile layout. I need this arrangement because I intend to use it for all modes, and non single-tile formats would be hell in tile modes.

Another restriction is that the font must be bitpacked to 1bpp. I have a couple of reasons for this. First, there is the size consideration. A 96 glyph, 16bit font (for modes 3/5) would take up 12kB. Pack that to 1bpp and it’s less that one kB! Yes, you’re restricted to monochrome, but for a font, that’s really not much of a problem. Often fonts are monochrome anyway and using 16 bits where you only need one seems a bit of a waste. Secondly, how would you get a 16bpp font to work for 4bpp or 8bpp tiles? Going from a low bpp to a higher one is just a lot easier. Of course, if you don’t like this arrangement, feel free to write your own functions.

As for the font data itself, here is the whole thing.

const unsigned int toncfontTiles[192]=
{
    0x00000000, 0x00000000, 0x18181818, 0x00180018, 0x00003636, 0x00000000, 0x367F3636, 0x0036367F,
    0x3C067C18, 0x00183E60, 0x1B356600, 0x0033566C, 0x6E16361C, 0x00DE733B, 0x000C1818, 0x00000000,
    0x0C0C1830, 0x0030180C, 0x3030180C, 0x000C1830, 0xFF3C6600, 0x0000663C, 0x7E181800, 0x00001818,
    0x00000000, 0x0C181800, 0x7E000000, 0x00000000, 0x00000000, 0x00181800, 0x183060C0, 0x0003060C,
    0x7E76663C, 0x003C666E, 0x181E1C18, 0x00181818, 0x3060663C, 0x007E0C18, 0x3860663C, 0x003C6660,
    0x33363C38, 0x0030307F, 0x603E067E, 0x003C6660, 0x3E060C38, 0x003C6666, 0x3060607E, 0x00181818,
    0x3C66663C, 0x003C6666, 0x7C66663C, 0x001C3060, 0x00181800, 0x00181800, 0x00181800, 0x0C181800,
    0x06186000, 0x00006018, 0x007E0000, 0x0000007E, 0x60180600, 0x00000618, 0x3060663C, 0x00180018,

    0x5A5A663C, 0x003C067A, 0x7E66663C, 0x00666666, 0x3E66663E, 0x003E6666, 0x06060C78, 0x00780C06,
    0x6666361E, 0x001E3666, 0x1E06067E, 0x007E0606, 0x1E06067E, 0x00060606, 0x7606663C, 0x007C6666,
    0x7E666666, 0x00666666, 0x1818183C, 0x003C1818, 0x60606060, 0x003C6660, 0x0F1B3363, 0x0063331B,
    0x06060606, 0x007E0606, 0x6B7F7763, 0x00636363, 0x7B6F6763, 0x00636373, 0x6666663C, 0x003C6666,
    0x3E66663E, 0x00060606, 0x3333331E, 0x007E3B33, 0x3E66663E, 0x00666636, 0x3C0E663C, 0x003C6670,
    0x1818187E, 0x00181818, 0x66666666, 0x003C6666, 0x66666666, 0x00183C3C, 0x6B636363, 0x0063777F,
    0x183C66C3, 0x00C3663C, 0x183C66C3, 0x00181818, 0x0C18307F, 0x007F0306, 0x0C0C0C3C, 0x003C0C0C,
    0x180C0603, 0x00C06030, 0x3030303C, 0x003C3030, 0x00663C18, 0x00000000, 0x00000000, 0x003F0000,

    0x00301818, 0x00000000, 0x603C0000, 0x007C667C, 0x663E0606, 0x003E6666, 0x063C0000, 0x003C0606,
    0x667C6060, 0x007C6666, 0x663C0000, 0x003C067E, 0x0C3E0C38, 0x000C0C0C, 0x667C0000, 0x3C607C66,
    0x663E0606, 0x00666666, 0x18180018, 0x00301818, 0x30300030, 0x1E303030, 0x36660606, 0x0066361E,
    0x18181818, 0x00301818, 0x7F370000, 0x0063636B, 0x663E0000, 0x00666666, 0x663C0000, 0x003C6666,
    0x663E0000, 0x06063E66, 0x667C0000, 0x60607C66, 0x663E0000, 0x00060606, 0x063C0000, 0x003E603C,
    0x0C3E0C0C, 0x00380C0C, 0x66660000, 0x007C6666, 0x66660000, 0x00183C66, 0x63630000, 0x00367F6B,
    0x36630000, 0x0063361C, 0x66660000, 0x0C183C66, 0x307E0000, 0x007E0C18, 0x0C181830, 0x00301818,
    0x18181818, 0x00181818, 0x3018180C, 0x000C1818, 0x003B6E00, 0x00000000, 0x00000000, 0x00000000,
};

Yes, this is the entire font, fitting nicely on one single page. This is what bitpacking can do for you but, like any compression method, it may be a little tricky seeing that it is indeed the font given earlier, so here’s a little explanation of what you got in front of you.

Bitpacking

table 19.1: Big endian vs little endian interpretation of byte-sequence 01h, 02h, 03h, 04h
big u32 0x01020304
big u16 0x0102 0x0304
u8 0x01 0x02 0x03 0x04
little u16 0x0201 0x0403
little u32 0x04030201

Bitpacking isn’t hard to understand. Data is little more a big field of bits. In bitpacking, you simply drop bits at regular intervals and tie the rest back together. Our font is monochrome, meaning we only have one bit of information. Now, even in the smallest C datatype, bytes, this would leave 7 bits unused if you were to use one byte per pixel. However, you could also cram eight pixels into one byte, and thus save a factor 8 in space. For the record, that’s a compression level of 88%, pretty good I’d say. Of course, if you read all the other pages already, you’d have already recognized instances of bitpacking: 4bpp tiles are bitpacked with 2 pixels/byte. So this stuff shouldn’t be completely new.

Bitpacking can save a lot of room, and in principle, it’s easy to do, as it’s just a matter of masking and shifting. There is one major catch, however: endianness. You already seen one incarnation of this in other data-arrays: the word 0x01234567 would actually be stored as the byte-sequence 0x67, 0x45, 0x23, 0x01 on ARM (and intel) systems. This is called little-endian, because the little end (the lower bytes of a multi-byte type) of the word are stored in the lower addresses. There is also big-endian, which stores the most significant bytes first. You can see the differences in table 19.1. Some hex editors or memory viewers (in VBA for example) allow you to switch viewing data as bytes, halfwords or words, so you can see the differences interactively there. Please remember that the data itself does not change because of this, you just look at it in a different way.

For bitpacking, you also have to deal with endianness at the bit level. The font data is packed in a consistent bit-little and byte-little format for three reasons. First, this is how GBA bitpacked stuff works anyway, so you can use the BIOS BitUnpack routine for it. Second, it is a more natural form in terms of counting: lower bits come first. Third, because you can shift down all the time and discard covered bits that way, masking is easier and faster. Now, big-endian would be more natural visually due to the fact we write numbers that way too, so bitmaps are often bit-little as well. Windows BMP files, for example, these have their leftmost pixels in the most significant bits, making them bit-big. However, Windows runs on Intel architecture, which is actually byte little-endian, for maximum confusion. Sigh. Oh well.

In case it’s still a bit hazy, fig 19.2 shows how the ‘F’ is packed from 8x8 pixels into 2 words. All 64 pixels are numbered 0 to 63. These correspond to the bit-numbers. Each eight successive bits form a byte: 0-7 make up byte 0, 8-15 form byte 1, etc. Note how the bits seem to mirror horizontally, because we generally write numbers big-endian. So try to forget about that and think of bits in memory to walk through from 0 to 63. You can also view the bits as words, bits 0-31 for word 0 and 32-63 for word 1.

pixels bits bytes words
pixels
  7 6 5 4 3 2 1 0  
  0 1 1 1 1 1 1 0  
0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0
0 0 0 1 1 1 1 0
0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0
0 0 0 0 0 1 1 0
0 0 0 0 0 0 0 0
 
  0x7E  
0x06
0x06
0x1E
  0x06  
0x06
0x06
0x00
 
  0x1E06067E  
  0x00060606  
fig 19.2: ‘F’, from 8x8 tile to 1bpp bit-little, byte-little words.

Character map

Having the mini-ascii font is nice and all but as strings are full-ascii, this may present a problem. Well, not really, but there are several ways of going about the conversion.

First, you can create a giant switch-block that converts, say, ‘A’ (ascii 65) into glyph-index 33. And do that for all 96 glyphs. It should be obvious that this is a dreadful way of going about things. Well it should, but apparently it’s not because code like that is out there; I only mention it here so you can recognize it for what it is and stay to far, far away from it. Simply put, if you have a switch-block where the only difference between the cases is returning a different offset –and a fixed offset at that– you’re doing something very, very wrong.

A second method which is an enormous improvement in every way is to simply subtract 32. That’s how mini-ascii was defined after all. Quick, short, and to the point.

However, I kinda like the third option: look-up tables. We’ve already seen how useful LUTs can be for mathematics, but you can use them for a lot more than that. In this case, the lut is a charcter map, containing the glyph-index for each ascii character. This has almost all the benefits of the simple subtract (a look-up may be a few cycles slower), but is much more flexible. For example, you can have non-ascii charmaps or alias the cases, things like that. Another ‘interesting’ thing is that you don’t really need the font to be text as such, it can be any kind of mapped image data; with a lut you could easily use the text system for drawing borders, as long as you have a border ‘font’ for it. The lut I’m using is 256 bytes long. This may not be enough for Unicode (sorry Eastern dudes), but it’s enough to suit my purposes.

General design

The first thing to do code-wise is to initialize the members of the text-base. That means attach the font, set the glyph sizes, and initialize the lut. This can be done with txt_init_std().


u8 txt_lut[256];

// Basc initializer for text state
void txt_init_std()
{
    gptxt->dx= gptxt->dy= 8;

    gptxt->dst0= vid_mem;
    gptxt->font= (u32*)toncfontTiles;
    gptxt->chars= txt_lut;
    gptxt->cws= NULL;

    int ii;
    for(ii=0; ii<96; ii++)
        gptxt->chars[ii+32]= ii;
}

Depending on the type of text, you may need more specialized initializers, which we’ll get to when the time comes. As for writing a string, the basic structure can bee seen below. It’s actually quite simple and very general, but unfortunately the fact that xxx_putc() is in the inner loop means that you have to have virtually identical wrappers around each char-plotter for each text method. I also have functions called xxx_clrs() that clear the string from the screen (they don’t wipe the whole screen). They are almost identical to their puts() siblings in form and also rather simple, so I won’t elaborate on them here.

// Pseudo code for xxx_puts
void xxx_puts(int x, int y, const char *str, [[more]])
{
    [[find real writing start]]
    while(c=*str++)     // iterate through string
    {
        switch(c)
        {
        case [[special chars ('\n' etc)]]:
            [[handle special]]
        case [[normal chars]]:
            [[xxx_putc(destination pointer, lut[c])]]
            [[advance destination]]
        }
    }
}

Bitmap text

Bitmap text concerns modes 3, 4 and 5. If you can do mode 3, you pretty much have mode 5 as well, as the two differ only by the pitch and, perhaps, the starting point. Mode 4 is different, not only because it’s 8bpp, but also because this means we have to do 2 pixels at once.

Internal routines

I tend to do bitmap related functions in two parts: there are internal 16bit and 8bit functions that take an address and pitch as their arguments, and then inline interface functions with coordinates that call these. The internal 16bit writer is given in below, with an explanation of the main parts below that.

void bm16_puts(u16 *dst, const char *str, COLOR clr, int pitch)
{
    int c, x=0;

    while((c=*str++) != 0)      // (1) for each char in string
    {
        // (2) real char/control char switch
        if(c == '\n')       // line break
        {
            dst += pitch*gptxt->dy;
            x=0;
        }
        else                // normal character
        {
            int ix, iy;
            u32 row;
            // (3) point to glyph; each row is one byte
            u8 *pch= (u8*)&gptxt->font[2*gptxt->chars[c]];
            for(iy=0; iy<8; iy++)
            {
                row= pch[iy];
                // (4) plot pixels until row-byte is empty
                for(ix=x; row>0; row >>= 1, ix++)
                    if(row&1)
                        dst[iy*pitch+ix]= clr;
            }
            x += gptxt->dx;
        }
    }
}
  1. Traditional way to loop through all characters in a string. c will be the character we have to deal with, unless it’s the delimiter ('\0'), then we’ll stop.
  2. Normal char/control char switch. Control characters like '\n' and '\t' should be taken care of separately. I’m only checking for the newline right now, but others could easily be added.
  3. This is where it gets interesting. What this line does is first use the lut to look up the glyph index in the font, look up the actual glyph in the font (multiply by 2 because there are 2 words/glyph), and then set-up a byte-pointer pch to point to the glyph.
    A couple of things come together here. First, because all glyphs are exactly 8 bytes apart, finding the glyph data is very easy. If you create your own text system with your own fonts, I’d advise using constant offsets, even if it wastes pixels like you would for small characters like ‘I’. Second, because of the 1bpp tiled format, each row is exactly one byte long, and all the glyphs bits are in consecutive bytes, so you don’t have to jump around for each new row. This is a good thing.
  4. The ix loop is even more interesting. First, we read the actual row of pixels into the (word) variable row. To test whether we need to write a pixel, we simply check for a given bit. However, because the packing is little endian, this allows for two shortcuts.
    The first one is that looping through the bits goes from low to high bits, meaning that we can simply shift-right on each iteration and test bit 0. The corollary to this is that the bits we’ve already done are thrown away, and this means that when row is 0, there will be no more pixels, and we’re done for that row. As this short-circuit happens inside the inner of a triple loop, the speed-up can be substantial.

This function only does the bare essentials to get a string on screen. It plots the non-zero pixels only (transparent characters), there is no wrapping at the side and no scrolling. The only non-trivial feature is that it can do line-breaks. When those happen, the cursor returns to the original x-position on screen.

The 8bit function is almost identical to this one, ‘almost’ because of the no-byte-write rule for VRAM. The obvious ones are that the pitch and character spacing need to be halved. I’m also making it requirement that the start of each character needs to be on an even pixel boundary. By doing so, you can have an almost identical inner loop as before; it just does two pixels in it instead of one. Yes, it’s a hack; no, I don’t care.

void bm8_puts(u16 *dst, const char *str, u8 clrid)
{
    int c, x=0, dx= gptxt->dx >> 1;

    while((c=*str++) != 0)
    {
        // <snip char-switch and iy loop>
                for(ix=x; row>0; row >>= 2, ix++)
                {
                    pxs= dst[iy*120+ix];
                    if(row&1)
                        pxs= (pxs&0xFF00) | clrid;
                    if(row&2)
                        pxs= (pxs&0x00FF) | (clrid<<8);

                    dst[iy*120+ix]= pxs;
                }
        // <snip>
    }
}

Interface functions

The interface functions are straightforward. All they have to do is set-up the destination start for the internal routines, and for the 16bit versions, provide a pitch. Mode 3 uses vid_mem as its base, and mode 4 and 5 use vid_page to make sure it works with page flipping. m4_puts() also ensures that the characters start at even pixels, and please remember that this routine uses a color-index, rather than a true color.

// Bitmap text interface. Goes in text.h
INLINE void m3_puts(int x, int y, const char *str, COLOR clr)
{    bm16_puts(&vid_mem[y*240+x], str, clr, 240);     }

INLINE void m4_puts(int x, int y, const char *str, u8 clrid)
{    bm8_puts(&vid_page[(y*240+x)>>1], str, clrid);   }

INLINE void m5_puts(int x, int y, const char *str, COLOR clr)
{    bm16_puts(&vid_page[y*160+x], str, clr, 160);    }

Clearing text

Doing a text clear is almost the same as writing out a string. The only functional difference is that you’re always putting a space (or rather, a solid filled rectangle) instead of the original characters. You still need the full string you tell you how long the line goes on, and how many lines there are.

With that in mind, the bm16_clrs() function below shouldn’t be that hard to understand. The whole point of it is to read the string to find out the length in pixels of each line in the string (nx*gptxt->dx), then fill the rectangle spanned by that length and the height of the characters (gptxt->dy). There’s some bookkeeping to make sure it all goes according to plan, but in the end that’s all it does. The same goes for the clear routines of the other text-types, so I’m not going to show those.

void bm16_clrs(u16 *dst, const char *str, COLOR clr, int pitch)
{
    int c, nx=0, ny;

    while(1)
    {
        c= *str++;
        if(c=='\n' || c=='\0')
        {
            if(nx>0)
            {
                nx *= gptxt->dx;
                ny= gptxt->dy;
                while(ny--)
                {
                    memset16(dst, clr, nx);
                    dst += pitch;
                }
                nx=0;
            }
            else
                dst += gptxt->dy*pitch;
            if(c=='\0')
                return;
        }
        else
            nx++;
    }
}

Tilemap text

In some ways, text for tile-modes is actually easier than for bitmaps, as you can just stuff the font into a charblock and then you don’t need any reference to the font itself anymore. That is, unless you want to have a variable width font, in that case you’ll be in bit-shifting hell. But I’m sticking to a fixed width, single tile font, which keeps things very simple indeed.

Tile initialisation

The first order of business is to be able to unpack the font to either 4 or 8 bit. The easiest way of doing this is to just setup a call to BitUnpack() and be done with it. However, VBA’s implementation of it isn’t (or wasn’t, they may have fixed it by now) quite correct for what I had planned for it, so I’m going to roll my own. Arguments dstv and srcv are the source and destination addresses, respectively; len is the number of source bytes and bpp is the destination bitdepth. base serves two purposes. Primarily, it is a number to be added to all the pixels if bit 31 is set, or to all except zero values if it is clear. This allows a greater range of outcomes than just the 0 and 1 that a source bitdepth of one would supply; and an other cute trick that I’ll get to later.

// Note, the BIOS BitUnpack does exactly the same thing!
void txt_bup_1toX(void *dstv, const void *srcv, u32 len, int bpp, u32 base)
{
    u32 *src= (u32*)srcv;
    u32 *dst= (u32*)dstv;

    len= (len*bpp+3)>>2;    // # dst words
    u32 bBase0= base&(1<<31);    // add to 0 too?
    base &= ~(1<<31);

    u32 swd, ssh=32;    // src data and shift
    u32 dwd, dsh;       // dst data and shift
    while(len--)
    {
        if(ssh >= 32)
        {
            swd= *src++;
            ssh= 0;
        }
        dwd=0;
        for(dsh=0; dsh<32; dsh += bpp)
        {
            u32 wd= swd&1;
            if(wd || bBase0)
                wd += base;
            dwd |= wd<<dsh;
            swd >>= 1;
            ssh++;
        }
        *dst++= dwd;
    }
}

The actual map-text initialization is done by txt_init_se(). Its first two arguments are exactly what you’d expect: the background that the system should use for text and the control-flags that should go there (charblock, screenblock, bitdepth, all that jazz). The third argument, se0, indicates the ‘base’ for palette and tile indexing, similar to the base for unpacking. The format is just like normal screen entries: se0{0-9} indicate the tile offset, and se0{C-F} are for the 16 color palette bank. clrs contains the color for the text, which will go into the palette indicated by the sub-palette and the fifth argument, base, the base for bit-unpacking.

For now, ignore the second color in clrs, and the extra palette write for 4 bpp. In all likelihood, you don’t want to know. I’m going to tell you about them later anyway, though.

void txt_init_se(int bgnr, u16 bgcnt, SB_ENTRY se0, u32 clrs, u32 base)
{
    bg_cnt_mem[bgnr]= bgcnt;
    gptxt->dst0= se_mem[BF_GET(bgcnt, BG_SBB)];

    // prep palette
    int bpp= (bgcnt&BG_8BPP) ? 8 : 4;
    if(bpp == 4)
    {
        COLOR *palbank= &pal_bg_mem[BF_GET(se0, SE_PALBANK)<<4];
        palbank[(base+1)&15]= clrs&0xFFFF;
        palbank[(base>>4)&15]= clrs>>16;
    }
    else
        pal_bg_mem[(base+1)&255]= clrs&0xFFFF;

    // account for tile-size difference
    se0 &= SE_ID_MASK;
    if(bpp == 8)
        se0 *= 2;

    // Bitunpack the tiles
    txt_bup_1toX(&tile_mem[BF_GET(bgcnt, BG_CBB)][se0],
        toncfontTiles, toncfontTilesLen, bpp, base);
}

If you don’t want to deal with all kinds of offsets, you can just leave the third and fifth arguments zero. It’s probably not a good idea to leave the others zero, but for those two it’s not a problem.

Screen entry writer

This is arguably the most simple of the text writers. As there is one glyph per screen entry, all you have to do is write a single halfword to the screenblock in the right position and you have a letter. Repeat this for a whole string.

There are a few things to note about this implementation, though. First, like before, no kind of wrapping or scrolling. If you want that, you’ll have to do all that yourself. Also, the x and y coordinates are still in pixels, not tiles. I’ve done this mainly for consistency with the other writers, nothing more. Oh, in case you hadn’t noticed before, gptxt->dst0 is initialized to point to the start of the background’s screenblock in txt_init_se(). Lastly, se0 is added to make up the actual screen entry; if you had a non-zero se0 in initialization, chances are you’d want to use it here too.

void se_puts(int x, int y, const char *str, SB_ENTRY se0)
{
    int c;
    SB_ENTRY *dst= &gptxt->dst0[(y>>3)*32+(x>>3)];

    x=0;
    while((c=*str++) != 0)
    {
        if(c == '\n')    // line break
        {    dst += (x&~31) + 32;    x=0;    }
        else
            dst[x++] = (gptxt->chars[c]) + se0;
    }
}

Sprite text

Sprite text is similar to tilemap text, only you use OBJ_ATTRs now instead of screen entries. You have to set the position manually (attributes 0 and 1), and attribute 2 is almost the same as the screen entry for regular tilemaps. The initializer txt_init_obj() is similar to txt_init_se(), except that the tilemap details have been replaced by their OAM counterparts. Instead of a screenblock, we point to a base OBJ_ATTR oe0, and attr2 works in much the same way as se0 did. The code is actually simpler because we can always use 4bpp tiles for the objects that we use, without upsetting the others.

// OAM text initializer
void txt_init_obj(OBJ_ATTR *oe0, u16 attr2, u32 clrs, u32 base)
{
    gptxt->dst0= (u16*)oe0;

    COLOR *pbank= &pal_obj_mem[BF_GET(attr2, ATTR2_PALBANK)<<4];
    pbank[(base+1)&15]= clrs&0xFFFF;
    pbank[(base>>4)&15]= clrs>>16;

    txt_bup_1toX(&tile_mem[4][attr2&ATTR2_ID_MASK], toncfontTiles,
        toncfontTilesLen, 4, base);
}

// OAM text writer
void obj_puts(int x, int y, const char *str, u16 attr2)
{
    int c, x0= x;
    OBJ_ATTR *oe= (OBJ_ATTR*)gptxt->dst0;

    while((c=*str++) != 0)
    {
        if(c == '\n')    // line break
        {    y += gptxt->dy; x= x0; }
        else
        {
            if(c != ' ') // Only act on a non-space
            {
                oe->attr0= y & ATTR0_Y_MASK;
                oe->attr1= x & ATTR1_X_MASK;
                oe->attr2= gptxt->chars[c] + attr2;
                oe++;
            }
            x += gptxt->dx;
        }
    }
}

The structure of the writer itself should feel familiar now. The attr2 again acts as a base offset to allow palette swapping and an offset tile start. Note that I’m only entering the position in attributes 0 and 1, and nothing else. I can do this because the rest of the things are already set to what I want, namely, 8x8p sprites with 4bpp tiles and no frills. Yes, this may screw things up for some, but if I did mask out everything properly, it’d screw up other stuff. This is a judgement call, feel free to disagree and change it.

That writer always starts at a fixed OBJ_ATTR, overwriting any previous ones. Because that might be undesirable, I also have a secondary sprite writer, obj_puts2, which takes an OBJ_ATTR as an argument to serve as the new base.

INLINE void obj_puts2(int x, int y, const char *str, u16 attr2, OBJ_ATTR *oe0)
{
    gptxt->dst0= (u16*)oe0;
    obj_puts(x, y, str, attr2);
}

There are some side notes on memory use that I should mention. Remember, there are only 128 OBJATTRs, and at one entry/glyph it may become prohibitively expensive if used extensively. In the same vein, 1024 tiles may seem like a lot, but you can run out quickly if you have a couple of complete animations in there as well. Also, remember that you only have 512 tiles in the bitmap modes: a full ASCII character set in bitmap modes would take up _half the sprite tiles!

If you’re just using it to for a couple of characters you’re not likely to run into trouble, but if you want screens full of text, you might be better of with something else. There are ways to get around these things, of course; quite simple ways, even. But because they’re really game-specific, it’s difficult to give a general solution for it.

Some demos

Bitmap text demo

I suppose I could start with “Hello world”, but as that’s pretty boring I thought I’d start with something more interesting. The txt_bm demo does something similar to bm_modes: namely show something on screen and allow switching between modes 3, 4 and 5 to see what the differences are. Only now, we’re going to use the bitmap puts() versions to write the actual strings indicating the current mode. Because that’s still pretty boring, I’m also going to put a movable cursor on screen and write out its coordinates. Here’s the full code:

#include <stdio.h>
#include <tonc.h>

#define CLR_BD    0x080F

const TILE cursorTile=
{{  0x0, 0x21, 0x211, 0x2111, 0x21111, 0x2100, 0x1100, 0x21000  }};

void base_init()
{
    vid_page= vid_mem;

    // init interrupts
    irq_init(NULL);
    irq_add(II_VBLANK, NULL);

    // init backdrop
    pal_bg_mem[0]= CLR_MAG;
    pal_bg_mem[CLR_BD>>8]= CLR_BD;
    pal_bg_mem[CLR_BD&255]= CLR_BD;
    m3_fill(CLR_BD);

    // init mode 4 pal
    pal_bg_mem[1]= CLR_LIME;
    pal_bg_mem[255]= CLR_WHITE;

    // init cursor
    tile_mem[5][0]= cursorTile;
    pal_obj_mem[1]= CLR_WHITE;
    pal_obj_mem[2]= CLR_GRAY;
}

int main()
{
    base_init();

    txt_init_std();

    // (1) print some string so we know what mode we're at
    m3_puts( 8,  8, "mode 3", CLR_CYAN);
    m4_puts(12, 32, "mode 4", 1);
    m5_puts(16, 40, "mode 5", CLR_YELLOW);

    // init variables
    u32 mode=3, bClear=0;
    OBJ_ATTR cursor= { 80, 120, 512, 0 };

    // init video mode
    REG_DISPCNT= DCNT_BG2 | DCNT_OBJ | 3;

    // init cursor string
    char str[32];
    siprintf(str, "o %3d,%3d", cursor.attr1, cursor.attr0);

    while(1)
    {
        VBlankIntrWait();
        oam_mem[0]= cursor;
        key_poll();

        if(key_hit(KEY_START))
            bClear ^= 1;

        // move cursor
        cursor.attr1 += key_tri_horz();
        cursor.attr0 += key_tri_vert();

        // adjust cursor(-string) only if necessary
        if(key_is_down(KEY_ANY))
        {
            // (2) clear previous coords
            if(bClear)
                bm_clrs(80, 112, str, CLR_BD);

            cursor.attr0 &= ATTR0_Y_MASK;
            cursor.attr1 &= ATTR1_X_MASK;
            // (3) update cursor string
            siprintf(str, "%c %3d,%3d", (bClear ? 'c' : 'o'),
                cursor.attr1, cursor.attr0);
        }

        // switch modes
        if(key_hit(KEY_L) && mode>3)
            mode--;
        else if(key_hit(KEY_R) && mode<5)
            mode++;
        REG_DISPCNT &= ~DCNT_MODE_MASK;
        REG_DISPCNT |= mode;

        // (4) write coords
        bm_puts(80, 112, str, CLR_WHITE);
    }

    return 0;
}

fig 19.3: txt_bm demo.

Controls:

D-padMoves cursor.
StartToggles string clearing.
L, RDecrease or increase mode.

Many things here should be either self explanatory or fairly irrelevant. The interesting things are indicated by numbers, so let’s go through them, shall we?

1. Mode indicators. This is where we write three strings to VRAM, indicating the modes. Note that the interfaces are nearly identical; the only real difference is that the fourth argument for m4_puts() is a palette index, rather than a real color.

2. Clear previous cursor-string. The cursor string keeps track of the cursor as you move across the screen. The first thing you’ll notice is that the string turns into a horrible mess because the bitmap writers only write the non-zero pixels of the font. In other words, it does not clear out the rest of the space allotted for that glyph. Essentially mx_puts() are transparent string writers.

Sure, I could have added a switch that would erase the whole glyph field to the writers. Quite easily, actually, it only takes an extra else clause. However, the current way is actually more practical. For one thing, what if you actually want transparency? You’d have to write another routine just for that. The method I’ve chosen is to have an extra clearing routine (which you’d probably need anyway). To overwrite the whole glyphs, simply call mx_clrs() first; which is what I’m doing here. Well, as long as the bClear variable is set (toggle with Start).

A second reason is that this method is just so much faster. Not only because I wouldn’t be able to use my premature breaking from the ix-loop if I had to erase the whole field and the mere presence of an extra branch adds more cycles (inside a triple loop), but plotting individual characters will always be slower than to do it by whole blocks at a time. mx_clrs() uses memset16(), which is basically CpuFastSet() plus safeties, and will be faster after just a mere half a dozen pixels.

Oh, in case you’re wondering why I’m talking about mx_clrs() when the code mentions bm_clrs(), the latter function is merely a function that uses a switch-block with the current bitmap mode to call the correct mode-specific string clearer.

3. Updating the cursor string. As the writers don’t have format specification fields, how can we write numbers? Simple, use sprintf() to prepare a string first, and then use that one instead. Or rather, use siprintf(). This is an integer-only version of sprintf(), which is better suited to GBA programming since you’re not supposed to use floating point numbers anyway. It should be relatively simple to create functions to wrap around siprintf() and mx_puts(), but I’m not sure it’s worth the effort.

I should perhaps point out that using siprintf and other routines that can turn numbers into strings use division by 10 to do so, and you know what that means. And even if you do not ask it to convert numbers, it calls a dozen or so routines from the standard library, which adds around 25kb to your binary. This isn’t much for ROM, but for multiboot things (256kb max) it may become problematic. With that in mind, I’d like you to take a look at posprintf by Dan Posluns. This is hand-coded assembly using a special algorithm for the decimal conversion. It may not be as rich in options as siprintf(), but it’s both faster and smaller by a very large margin, so definitely worth checking out.

4. Write cursor string. This writes the current cursor string to position (80, 120). Like in the cases of wiping the string, I’m using a bm_puts() function that switches between the current mode writers.

Sprite text; Hello world!

Yes! Hello world! Now, in principle, all you have to do is call txt_init(), txt_init_obj() and then obj_puts() with the right parameters, but again that’s just boring, so I’ll add some interesting things as well. The txt_obj demo shows one of the things best performed with sprites: individual letter animation. The letters of the phrase “hello world!” will fall from the top of the screen, bouncing to a halt on the floor (a green line halfway across the screen).

#include <tonc.h>

// === CONSTANTS & STRUCTS ============================================

#define POS0 (80<<8)
#define GRAV 0x40
#define DAMP 0xD0
#define HWLEN 12

const char hwstr[]= "Hello world!";

typedef struct
{
    u32 state;
    int tt;
    FIXED fy;
    FIXED fvy;
} PATTERN;

// === FUNCTIONS ======================================================

void pat_bounce(PATTERN *pat)
{
    if(pat->tt <= 0)    // timer's run out: play pattern
    {
        pat->fvy += GRAV;
        pat->fy += pat->fvy;

        // touched floor: bounce
        if(pat->fy > POS0)
        {
            // damp if we still have enough speed
            // otherwise kill movement
            if(pat->fvy > DAMP)
            {
                pat->fy= 2*POS0-pat->fy;
                pat->fvy= DAMP-pat->fvy;
            }
            else
            {
                pat->fy= POS0;
                pat->fvy= 0;
            }
        }
    }
    else    // still in waiting period
        pat->tt--;
}

int main()
{
    REG_DISPCNT= DCNT_MODE3 | DCNT_BG2 | DCNT_OBJ;

    irq_init(NULL);
    irq_add(II_VBLANK, NULL);
    memset16(&vid_mem[88*240], CLR_GREEN, 240);

    // (1) init sprite text
    txt_init_std();
    txt_init_obj(&oam_mem[0], 0xF200, CLR_YELLOW, 0xEE);
    // (2) 12 px between letters
    gptxt->dx= 12;

    // (3) init sprite letters
    OBJ_ATTR *oe= oam_mem;
    obj_puts2(120-12*HWLEN/2, 8, hwstr, 0xF200, oe);

    int ii;
    PATTERN pats[HWLEN];

    for(ii=0; ii<HWLEN; ii++)
    {
        // init patterns
        pats[ii].state=0;
        pats[ii].tt= 3*ii+1;
        pats[ii].fy= -12<<8;
        pats[ii].fvy= 0;

        // init sprite position
        oe[ii].attr0 &= ~ATTR0_Y_MASK;
        oe[ii].attr0 |= 160;
    }

    while(1)
    {
        VBlankIntrWait();

        for(ii=0; ii<HWLEN; ii++)
        {
            pat_bounce(&pats[ii]);

            oe[ii].attr0 &= ~ATTR0_Y_MASK;
            oe[ii].attr0 |= (pats[ii].fy>>8)& ATTR0_Y_MASK;
        }
    }

    return 0;
}

fig 19.4: txt_obj demo.

Very little of this code is actually concerned with the string itself, namely the items 1, 2 and 3. There’s a call to txt_init_std() for the basic initialization and a call to the sprite text initializer, txt_init_obj(). The second argument is the base for attribute 2 (if you don’t remember what attribute 2 is, see the chapter on sprites again); 0xF200 means I’m using the sub-palette 15 and start the character tiles at tile-index 512 (because of the bitmap mode). The font color will be yellow, and out at index 255. That’s 240 from the pal-bank, 0x0E=14 from the unpacking and 1 for the actual 1bpp pixels 240+14+1=255. After this call, I’m also setting the horizontal pixel offset to 12 to spread out the letters a little bit. After that, I just call obj_puts2() to set up the first few sprites of OAM so that they show “hello world!” centered at the top of the screen.

I could have stopped there, but the demo is actually just beginning. The thing about using sprites as glyphs is that they can still act as normal sprites; obj_puts() just sets them up to use letters instead of graphics that are more sprite-like.

Bouncy, bouncy, bouncy

The goal here is to let the letters drop from the top of the screen, the bounce up again when it hits a floor, but with a little less speed than before due to friction and what not. Physically, the falling part is done using a constant acceleration, g. Acceleration is the change in velocity, so the velocity is linear; velocity is the change in position, so the height is parabolic. At the bounce, we do an inelastic collision; in other words, one where energy is lost. In principle, this would mean that the difference between the squares of the velocities before and after the collision differ by a constant ( |vout|^2^ - |vin|^2^ = Q ). However, this would require a square root to find the new velocity, and I don’t care for that right now so I’m just going to scrap the squares here. I’m sure there are situations where this is actually quite valid :P. As a further simplification, I’m doing a first-order integration for the position. With this, the basic code for movement becomes very simple

// 1D inelastic reflections
// y, vy, ay: position, velocity, acceleration.
// Q: inelastic collision coefficient.
vy += ay;
 y += vy;
if(y>ymay)  // collision
{
    if((ABS(vy)>Q)
    {
        vy= -(vy-SGN(vy)*Q);  // lower speed, switch direction
        y= 2*ymay-y;          // Mirror y at r: y= r-(y-r)= 2r-y
    }
    else  // too slow: stop at ymay
    {   vy= 0; y= ymay; }
}

This could be replaced by the following, more accurate code, using second-order integration and ‘proper’ recoil, but you hardly notice anything from the improved integration. I actually prefer the look of the simple, linear recoil over the square root though.

// accelerate
 k= vx+GRAV;
// Trapezium integration rule:
//   x[i+1]= x[i] + (v[i]+v[i+1])/2;
 x += (vx+k)/2;
vx= k;
if(x>xmax)  // collision
{
    if(vx*vx > Q2)
    {   vx= -Sqrt(vx*vx-Q2); x= 2*xmax-x; }
    else
    {   vx= 0;               x= xmax;     }
}

Map text : colors and borders

Next up is the first of two map text demos. The official name for what I call a regular background is “text background”, and they’re called that for a reason: in most cases when there is text, it’s done using regular backgrounds. Of course, in most cases everything else is also done with those, so strictly speaking associating them with “text” is a misnomer, but we’ll let that one slide for today. The first demo is about how you can use the text functions for a variety of effects. Apart from simply showing text (boring), you’ll see palette swapping and framing text, and how you can easily use different fonts and borders concurrently. Because of the way I’ve designed my functions, all this takes is a change in a parameter. Cool huh.

The demo will also feature adding shading to a monochrome font, and adding an opaque background for it. Now, the way I’m going about this will probably reserve me a place in the Computer Science Hell, but, well, the coolness of the tricks will probably keep me from burning up there.

#include <tonc.h>
#include "border.h"

// === CONSTANTS & STRUCTS ============================================

#define TID_FRAME0        96
#define TID_FRAME1       105
#define TID_FONT           0
#define TID_FONT2        128
#define TID_FONT3        256
#define TXT_PID_SHADE   0xEE
#define TXT_PID_BG      0x88

// === FUNCTIONS ======================================================

void init()
{
    int ii;
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    irq_init(NULL);
    irq_add(II_VBLANK, NULL);

    txt_init_std();

    // (1a) Basic se text initialization
    txt_init_se(0, BG_CBB(0) | BG_SBB(31), 0x1000, CLR_RED, 0x0E);

    // (1b) again, with a twist
    txt_init_se(0, BG_CBB(0) | BG_SBB(31), 0xF000|TID_FONT2,
        CLR_YELLOW | (CLR_MAG<<16), TXT_PID_SHADE);

    // (1c) and once more, with feeling!
    txt_init_se(0, BG_CBB(0) | BG_SBB(31), 0xE000|TID_FONT3,
        0, TXT_PID_SHADE);
    u32 *pwd= (u32*)&tile_mem[0][TID_FONT3];
    for(ii=0; ii<96*8; ii++)
        *pwd++ |= quad8(TXT_PID_BG);

    // extra border initialisation
    memcpy32(pal_bg_mem, borderPal, borderPalLen/4);
    memcpy32(&tile_mem[0][TID_FRAME0], borderTiles, borderTilesLen/4);

    // (2) overwrite /\ [] `% ^_ to use border tiles
    //  / ^ \
    //  [ # ]
    //  ` _ '
    const u8 bdr_lut[9]= "/^\\[#]`_\'";
    for(ii=0; ii<9; ii++)
        gptxt->chars[bdr_lut[ii]]= TID_FRAME0+ii;

    // (3) set some extra colors
    pal_bg_mem[0x1F]= CLR_RED;
    pal_bg_mem[0x2F]= CLR_GREEN;
    pal_bg_mem[0x3F]= CLR_BLUE;

    pal_bg_mem[0xE8]= pal_bg_mem[0x08]; // bg
    pal_bg_mem[0xEE]= CLR_ORANGE;   // shadow
    pal_bg_mem[0xEF]= pal_bg_mem[0x0F]; // text
}

void txt_se_frame(int l, int t, int r, int b, u16 se0)
{
    int ix, iy;
    u8 *lut= gptxt->chars;
    u16 *pse= (u16*)gptxt->dst0;
    pse += t*32 + l;
    r -= (l+1);
    b -= (t+1);

    // corners
    pse[32*0  + 0] = se0+lut['/'];
    pse[32*0  + r] = se0+lut['\\'];
    pse[32*b  + 0] = se0+lut['`'];
    pse[32*b  + r] = se0+lut['\''];

    // horizontal
    for(ix=1; ix<r; ix++)
    {
        pse[32*0+ix]= se0+lut['^'];
        pse[32*b+ix]= se0+lut['_'];
    }
    // vertical + inside
    pse += 32;
    for(iy=1; iy<b; iy++)
    {
        pse[0]= se0+lut['['];
        pse[r]= se0+lut[']'];
        for(ix=1; ix<r; ix++)
            pse[ix]= se0+lut['#'];
        pse += 32;
    }
}

int main()
{
    init();

    // (4a) red, green, blue text
    se_puts(8, 16, "bank 1:\n  red",   0x1000);
    se_puts(8, 40, "bank 2:\n  green", 0x2000);
    se_puts(8, 72, "bank 3:\n  blue",  0x3000);
    // (4b) yellow text with magenta shadow
    se_puts(8, 96, "bank 15:\n yellow, \nwith mag \nshadow", 0xF000|TID_FONT2);

    // (5a) framed text, v1
    txt_se_frame(10, 2, 29, 9, 0);
    se_puts( 88, 24, "frame 0:", 0);
    se_puts(104, 32, "/^\\[#]`_'", 0);
    se_puts( 88, 40, "bank  0:\n  basic text,\n  transparent bg", 0);

    // (5b) framed text, v2
    txt_se_frame(10, 11, 29, 18, TID_FRAME1-TID_FRAME0);
    se_puts( 88,  96, "frame 1:", 0xE000|TID_FONT3);
    se_puts(104, 104, "/^\\[#]`_'", 9);
    se_puts( 88, 112, "bank 14:\n  shaded text\n  opaque bg", 0xE000|TID_FONT3);

    while(1)
        VBlankIntrWait();
    return 0;
}
txt_se1 demo
fig 19.5a: First map text demo.
txt_se1 tileset
fig 19.5b: accompanying tileset.

Code rundown

fig 19.5 shows what this code produces. All the actual text drawing is done in the main function, and I’ll go by them one by one. The first three things are red, green and blue text (point 4a), done using palette swapping. I’ve loaded up red, green and blue to palette indices 0x1F, 0x2F and 0x3F (point 3), and can switch between them with the last parameter of se_puts(), which you will recall is added to each of the screen entries. The values 0x1000, 0x2000 and 0x3000 indicate that we’ll use palette banks 1, 2 and 3, respectively.

If you look closely, you’ll see that fourth text (point 4b) is yellow with a magenta (no it’s not pink, it’s magenta) shading on the right edge of each letter. At least part of this is done with the se0 parameter, which is now 0xF080. The reason it’s shaded is because of the last part: I’m actually using a slightly different font, one that starts at tile 128. I’ll repeat, the reason I can do all this with the same function is because of that offset parameter of se_puts().

Points (5a) and (5b) are for framing, and the text inside it. The function txt_se_frame() draws my border. It takes a rectangle as its input, and draws a frame on it. Note that the frame includes the top-left, but excludes the bottom-right. Again, I have one extra se0 parameter as an offset. This is how the second border is actually done; I just offset the thing by the difference between border tiles.

The borders themselves are actually drawn pretty much as if they were text. In init() I’ve reassigned nine characters in the character lut to use the tile indices for the primary border tileset (point 2). There is no particular reason I’m doing this, other than the mere fact that I can. Just illustrating the things you can do with a text writer and some clever lut manipulation.

The texts inside the frames are an interesting story as well. As you can see from the text in the first frame, the standard text doesn’t quite work. The problem is that the main tileset I’m using is transparent, but the frame’s background isn’t. Mix the two and they’ll clash. So how to solve that? Well, you create another font, one that does not have 0 as its background color. There are a number of ways to do that, one of them being adding 1<<31 to the bit-unpacking flag. But I’m opting for another method, which I’ll get into later. Note that whatever I’m doing, it does work: the text in the second frame is opaque after all. Note that I’m writing that text using pal-bank 14, and am now using a third tileset for the fonts.

Now, up to this point it’s all been pretty easy. The usage of se_puts() and txt_se_frame() I mean. I hope you understood all of the above, because the rest is going to be pretty interesting. Not quite “oh god, oh god, we’re all gonna die”-interesting, but still a mite hairy for some.

Bit fiddling fun

I’ve indicated that I’m using three different fonts. But if you study the code, you will find no trace of font definitions or copies. That’s because there are none: it’s all based on the same bit-packed font I showed earlier. Also, the mathematically inclined will have noticed that bitpacking a 1bpp font will result in two colors. That’s what 1bpp means, after all. But I have a background color, a foreground color, and shading; that’s three. Furthermore, there doesn’t seem to be any code that does the shading. This all leads to one simple question, namely: what the hell am I doing?

Well … this:

#define TID_FONT           0
#define TID_FONT2        128
#define TID_FONT3        256
#define TXT_PID_SHADE   0xEE
#define TXT_PID_BG      0x88

// (1a) Basic se text initialization
txt_init_se(0, BG_CBB(0) | BG_SBB(31), 0x1000, CLR_RED, 0x0E);

// (1b) again, with a twist
txt_init_se(0, BG_CBB(0) | BG_SBB(31), 0xF000|TID_FONT2,
    CLR_YELLOW | (CLR_MAG<<16), TXT_PID_SHADE);

// (1c) and once more, with feeling!
txt_init_se(0, BG_CBB(0) | BG_SBB(31), 0xE000|TID_FONT3,
    0, TXT_PID_SHADE);
u32 *pwd= (u32*)&tile_mem[0][TID_FONT3];
for(ii=0; ii<96*8; ii++)
    *pwd++ |= quad8(TXT_PID_BG);

These six statements set up the three fonts, complete with shading and opacity. The first one sets up the standard font, in charblock 0, screenblock 31, pal-bank 1 and using 0x0E for the bit-unpacking offset, so that the text color is at 0x1F. We’ve seen the same thing with the object text.

Table 19.2: bit-unpacking with with base 0xEE.
bit val 7 6 5 4 3 2 1 0
0 0 . . . . . . . 0
1 1 . . . . . E F .
2 1 . . . . E F . .
3 1 . . . E F . . .
4 0 . . . 0 . . . .
5 0 . . 0 . . . . .
6 1 E F . . . . . .
7 0 0 . . . . . . .
OR: E F 0 E F F F 0

The second call to txt_se_init() sets up the second font set, the one with shading. se0 indicates the use of pal-bank 15 and to start at 128, but the important stuff happens in the clrs and base parameters. There are now two colors in clrs, yellow and magenta. The lower halfword will be the text color, and the upper halfword the shading color.

The actual shading happens because of the value of base, which is 0xEE, and the way the whole bit-unpacking routine works. The offset is added to each ‘on’-bit in the packed font, giving 0xEF, which is then ORred to the current word with the appropriate shift. Because we’re dealing with a 4bpp font, the result will actually overflow into the next nybble. Now, if the next bit is also on, it’ll OR 0xEF with the overflow value of 0x0E. As 0xF | 0xE is just 0xF, it’s as if the overflow never happened. But, if the next bit was off, the value for that pixel would be 0xE. Lastly, if there was no overflow for a zero source bit, the result is a 0. And now we have the three possible values: 0 (background), 14 (shade) and 15 (text). table 19.2 shows the procedure more graphically. The bits for the source byte are on the left, and the bit-unpacked result for each bit on the grid on the right, in the correct position. These are then ORed together for the end result. For 0x46 that’d be the word 0xEF0EFFF0. One word is one row of 8 pixels in a 4bpp tile, and because lower nybbles are the left-most pixels, the shade will be on the right of the character even though it uses the more significant bits.

The base 0xEE is one of many values for which this trick works. The key thing is that the high nybble must be completely overwritten by the lower nybble+1. Any number with equal and even nybbles will work.

Now, I’ll be the first to admit that this is something of a hack. A lot of things have to come together for it to work. The word-size must be able to fit a whole tile row, both packed and unpacked data must be little-endian in both bit and byte order, and the unpacking routine must actually allow overflow, and probably a few other things that escape me right now. All of these conditions are satisfied on the GBA, but I doubt very much if you can use the trick on other systems. There are other ways of applying shading, of course, better ones at that. It’s just so deliciously nasty that I can’t resist using it.

The final txt_se_init() work pretty much in the same way as the second one: shading through overflow. What it doesn’t do is make the tiles opaque. While it’s possible to do that with BitUnpack, you can’t have that and shading with one call, that simply doesn’t work. But there are other ways. All we really need for the tiles to be opaque is some value other than zero for it for the background pixels. Well, that’s easily done: just offset (add or OR) everything by a number. In this case I can’t add a value because the text value is already at maximum, so I’ll use OR here. The value I’ll OR with is 0x88888888, which doesn’t change the text or shading, but sets the background pixels to use 8, so we’ve got what we wanted.

And that, as they say, is how we do that. Or at least how I do that. If the above seems like mumbo-jumbo to you, no one’s forcing you to do it in the same way. You can always take the easy way out and include multiple fonts into the program rather than construct them from what you have. I’m just showing what can be done with a little creating coding.

Map text : profiling

The last thing I’ll show you is an easy one, but something that might come in handy when it’s time to optimize a few things. In case you haven’t noticed, debugging GBA programs isn’t quite as easy as debugging PC programs. There is the possibility of debugging with Insight and the GDB (the GCC debugger), but even then things are iffy, or so I hear. Well, now that you can print your own text, you can at least do something of that sort. Write out diagnostic messages and the like.

But that’s not what I’m going to show you now. The last demo will show you how to do something that usually comes after debugging: profiling. Profiling tells you how much time is spent doing what, so you can tell what would be the best places to try to optimize. What I’ll show you is a simple way of getting the time spent inside a function. Stuff like that is good to know, especially on a platform like this where you still have to worry about things like speed and efficiency and other silly stuff like that.

The next demo will clock five different ways of copying data, in this case a mode 4 bitmap from EWRAM (my code is set up for multiboot by default, which means everything goes in EWRAM rather than ROM) to VRAM. The methods are:

  • u16 array. Copy in 16-bit (halfword) chunks. Probably the one you’ll see most in other tutorials, but not here. With reason, as we’ll see in a minute.
  • u32 array. Copy in 32-bit (word) chunks.
  • memcpy(). The standard C copy routine, the one I’m using in the earlier demos. Well, nowadays I am.
  • memcpy32(). Home grown assembly, explained in detail here. Basically does what CpuFastSet() does, only without the restriction that the number of words must be a multiple of 8.
  • dma_memcpy(). Copy via 32-bit DMA.
#include <string.h>
#include <stdio.h>
#include <stdlib.h>

#include <tonc.h>

#include "gba_pic.h"

// === CONSTANTS & STRUCTS ============================================

int gtimes[5];

const char *strs[5]=
{   "u16 array", "u32 array", "memcpy", "memcpy32", "DMA32" };

// === FUNCTIONS ======================================================

// copy via u16 array
void test_0(u16 *dst, const u16 *src, u32 len)
{
    u32 ii;
    profile_start();
    for(ii=0; ii<len/2; ii++)
        dst[ii]= src[ii];
    gtimes[0]= profile_stop();
}

// copy via u32 array
void test_1(u32 *dst, const u32 *src, u32 len)
{
    u32 ii;
    profile_start();
    for(ii=0; ii<len/4; ii++)
        dst[ii]= src[ii];
    gtimes[1]= profile_stop();
}

// copy via memcpy
void test_2(void *dst, const void *src, u32 len)
{
    profile_start();
    memcpy(dst, src, len);
    gtimes[2]= profile_stop();
}

// copy via my own memcpy32
void test_3(void *dst, const void *src, u32 len)
{
    profile_start();
    memcpy32(dst, src, len/4);
    gtimes[3]= profile_stop();
}

// copy using DMA
void test_4(void *dst, const void *src, u32 len)
{
    profile_start();
    dma3_cpy(dst, src, len);
    gtimes[4]= profile_stop();
}

int main()
{
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    irq_init(NULL);
    irq_add(II_VBLANK, NULL);

    test_0((u16*)vid_mem, (const u16*)gba_picBitmap, gba_picBitmapLen);
    test_1((u32*)vid_mem, (const u32*)gba_picBitmap, gba_picBitmapLen);
    test_2(vid_mem, gba_picBitmap, gba_picBitmapLen);
    test_3(vid_mem, gba_picBitmap, gba_picBitmapLen);
    test_4(vid_mem, gba_picBitmap, gba_picBitmapLen);

    // clear the screenblock I'm about to use
    memset32(&se_mem[7], 0, SBB_SIZE/4);

    // init map text
    txt_init_std();
    txt_init_se(0, BG_SBB(7), 0, CLR_YELLOW, 0);

    // print results
    int ii;
    char str[32];
    for(ii=0; ii<5; ii++)
    {
        siprintf(str, "%12s %6d", strs[ii], gtimes[ii]);
        se_puts(8, 8+8*ii, str, 0);
    }

    while(1)
        VBlankIntrWait();

    return 0;
}

The code should be self-explanatory. I have five functions for the things I want to profile. I chose separate functions because then I know optimisation will not interfere (it sometimes moves code around). After running these functions, I set-up my text functions and print out the results.

The profiling itself uses two macros, profile_start() and profile_stop(). These can be found in core.h of libtonc. What the macros do is start and stop timers 2 and 3, and then return the time in between the calls. This does mean that the code you’re profiling cannot use those timers.

INLINE void profile_start()
{
    REG_TM2D= 0;    REG_TM3D= 0;
    REG_TM2CNT= 0;  REG_TM3CNT= 0;
    REG_TM3CNT= TM_ENABLE | TM_CASCADE;
    REG_TM2CNT= TM_ENABLE;
}

INLINE u32 profile_stop()
{
   REG_TM2CNT= 0;
   return (REG_TM3D<<16)|REG_TM2D;
}
txt_se2 on vba
fig 19.6a: txt_se2 on VBA.
txt_se2 on no$gba
fig 19.6b: txt_se2 on no$gba.
table 19.3: timing results for hardware, vba and no$gba.
  hardware vba no$gba vba err no$ err
u16 array 614571 499440 614571 -18.73 0.00
u32 array 289825 230383 288098 -20.51 -0.60
memcpy 195156 161119 194519 -17.44 -0.33
memcpy32 86816 79336 85329 -8.62 -1.71
DMA32 76889 250 76888 -99.67 0.00

Fig 19.6 shows the timing results, as run in VisualBoy Advance and no$gba. Note that they are not quite the same. So you do what you should always do when two opinions differ: get a third one. In this case, I’ll use the only one that really matters, namely hardware. You can see a comparison of the three in table 19.3, which will tell you that no$gba is very accurate in its timing, but VBA not so much. I guess you can still use it to get an estimate or relative timings, but true accuracy will not be found there. For that you need hardware or no$gba.

About the numbers themselves. The spread is about a factor 9, which is quite a lot. None of the techniques shown here are particularly hard to understand, and data copying is something that you could spend a lot of time doing, so might as well take advantage of the faster ones from the get go.

Most of the tutorial code and probably a lot of demo code you can find out there uses the u16-array method of copying; presumably because byte-copies are unavailable for certain sections. But as you can see, u16 copies are more than twice as slow as u32 copies! Granted, it is not the slowest method of copying data, but not by much (using u16 loop variables –also a common occurence– would be slower by about 20%; try it and you’ll see). The GBA is a 32-bit machine. It likes 32-bit data, and its instruction sets are better at dealing with 32-bit chunks. Let go of the u16 fetish you may have picked up elsewhere. Use word-sized data if you can, the others only if you have to. That said, do watch your data alignment! u8 or u16 arrays aren’t always word-aligned, which will cause trouble with casting.

GCC and waitstates vs timing results

Giving exact timing results is tricky due to a number of factors. First, on the hardware side there are different memory sections with different wait states that complicate things unless you sit down, read the assembly and add up the cycle-counts of the instructions. This is a horrible job, trust me. The second problem is that GCC hasn’t reached the theoretical optimum for this code yet, so the results tend to vary with new releases. What you see above is a good indication, but your mileage may vary.

There are a number of fast ways of copying large chunks of data. Faster than writing your own simple loop that is. Common ones are the standard memcpy(), which is available for any platform, and two methods that are GBA specific: the CpuFastSet() BIOS call (or my own version memcpy32() and DMA. The first two require word-alignment; DMA merely works better with it. The performance of memcpy() is actually not too shabby, and the fact that it’s available everywhere means that it’s a good place to start. The others are faster, but come at a cost: memcpy32() is hand written assembly; CpuFastSet() requires a word-count divisible by 8, and DMA locks up the CPU, which can interfere with interrupts. You would do well to remember these things when you find you need a little more speed.

Other considerations

These couple of functions barely scratch the surface as far as text systems are concerned. You can have larger fonts, colored fonts, proper shading, variable character widths, and more. Each of these can apply to each of the modes, with extra formatting for text justification and alignment, updating tile-memory in conjunction with map/OAM changes to cut down on VRAM use, etc, etc. To take an in-depth look at all the variations would take an entire site by itself, so I’ll leave it at this. I just hope you’ve picked up on some of the basics that go into text systems. What you do with that knowledge I leave up to you.

20. Mode 7 Part 1

Right, and now for something cool: mode 7. Not just how to implement it on the GBA, but also the math behind it. You need to know your way around tiled backgrounds (especially the transformable ones) interrupts. Read up on those subjects if you don’t. The stuff you’ll find here explains the basics of Mode 7. I also have an advanced page, but I urge you to read this one first, since the math is still rather easy compared to what I’ll use there.

Introduction

Way, way back in 1990, there was the Super NES, the 16bit successor to the Nintendo Entertainment System. Apart from the usual improvements that are inherent to new technology, the SNES was the first console to have special hardware for graphic tricks that allowed linear transformations (like rotation and scaling) on backgrounds and sprites. Mode7 took this one step further: it not only rotated and scaled a background, but added a step for perspective to create a 3D look.

One could hardly call Mode 7 yet another pretty gimmick. For example, it managed to radically change the racing game genre. Older racing games (like Pole Position and Outrun) were limited to simple left and right bends. Mode 7 allowed more interesting tracks, as your vision wasn’t limited to the part of the track right in front of you. F-Zero was the first game to use it and blew everything before it out of the water (the original Fire Field is still one of the most vicious tracks around with its hairpins, mag-beams and mines). Other illustrious games were soon to follow, like Super Mario Kart (mmmm, Rainbow Road. 150cc, full throttle all the way through *gargle*) and Pilotwings.

Since the GBA is essentially a miniature SNES, it stands to reason that you could do Mode7 graphics on it as well. And, you’d be right, although I heard the GBA Mode7 is a little different as the SNES’. On the SNES the video modes really did run up to #7 (see the SNESdev Wiki) The GBA only has modes 0-5. So technically “GBA Mode 7” is a yet another misnomer. However, for everyone who’s not a SNES programmer (which is nearly everyone, me included) the term is synonymous with the graphical effect it was famous for: a perspective view. And you can create a perspective view on the GBA, so in that sense the term’s still true.

I’m not sure about the SNES, but GBA Mode 7 is a very much unlike true 3D APIs like OpenGL and Direct3D. On those systems, you can just give the proper perspective matrix and place it into the pipeline. On the GBA, however, you only have the general 2D transformation matrix P and displacement dx at your disposal and you have to do all the perspective calculations yourself. This basically means that you have to alter the scaling and translation on every scanline using either the HBlank DMA or the HBlank interrupt.

In this tutorial, I will use the 64x64t affine background from the sbb_aff demo (which looks a bit like fig 20.1), do the Mode7 mojo and turn it into something like depicted in fig 20.2. The focus will be on showing, in detail, how the magic works. While the end result is given as a HBlank interrupt function; converting to a HBlank DMA case shouldn’t be to hard.

This is your map.
Fig 20.1: this is your map (well, kinda)
This is your map in mode7.
Fig 20.2: this is your map in mode7.

Getting a sense of perspective

(If you are familiar with the basics of perspective, you can just skim this section.)
If you’ve ever looked at a world map or a 3D game, you know that when mapping from 3D to 2D, something’ has to give. The technical term for this is projection. There are many types of projection, but the one we’re concerned with is perspective, which makes objects look smaller the further off they are.

We start with a 3D space like the one in fig 20.3. In computer graphics, it is customary to have the x-axis pointing to the right and the y-axis pointing up. The z-axis is the determined by the handedness of the space: a right-handed coordinate system has it pointing to the back (out of the screen), which in a left-handed system it’s pointing to the front. I’m using a right-handed system because my mind gets hopelessly confused in a left-handed system when it comes to rotation and calculating normals. Another reason is that this way the screen coordinates correspond to (x, z) values. It is also customary to have the viewer at the origin (for a different viewer position, simply translate the world in the other direction). For a right-handed system, this means that you’re looking down the negative z-axis.

Of course, you can’t see everything: only the objects inside the viewing volume are visible. For a perspective projection this is defined by the viewer position (the origin in our case) and the projection plane, located in front of the viewer at a distance D. Think of it as the screen. The projection plane has a width W and height H. So the viewing volume is actually a viewing pyramid, though in practice it is usually a viewing frustum (a beheaded pyramid), since there is a minimum and maximum to the distance you can perceive as well.

Fig 20.4 shows what the perspective projection actually does. Given is a point (y, z) which is projected to point (yp, −D) on the projection plane. The projected z-coordinate, by definition, is −D. The projected y-coordinate is the intersection of the projection plane and the line passing through the viewer and the original point:

(20.1) y p = y · D z

Basically, you divide by z / D . Since it is so important a factor it has is own variable: the zoom factor λ:

(20.2) λ = z / D = y / y p

As a rule, everything in front the projection plane (λ<1) will be enlarged, and everything behind it (λ>1) is shrunk.

3D coordinate system
Fig 20.3: 3D coordinate system showing the viewing pyramid defined by the origin, and the screen rectangle (W×H) at z= −D
projection step, side view
Fig 20.4: Side view; point (y, z) is projected onto the (z = −D plane. The projected point is yp = y·D/z

Enter Mode 7

Fig 20.3 and fig 20.4 describe the general case for perspective projection in a 3D world with tons of objects and viewer orientations. The case for Mode 7 is considerably less complicated than that:

  • Objects. We only work with two objects: the viewer (at point a = (ax, ay, az) ) and the floor (at y=0, by definition).
  • Viewer orientation. In a full 3D world, the viewer orientation is given by 3 angles: yaw (y-axis), pitch (x-axis) and roll (z-axis). We will limit ourselves to yaw to keep things simple.
  • The horizon issue. Because the view direction is kept parallel to the floor, the horizon should go in the center of the screen. This would leave the top half of the screen empty, which is a bit of a waste. To remedy this we only use the bottom half of the viewing volume, so that the horizon is at the top of the screen. Note that even though the top and bottom view-lines are now the same as when you would look down a bit, the cases are NOT equal as the projection plane is still vertical. It is important that you realize the difference.
Side view of Mode7 perspective Fig 20.5: side view of Mode 7 perspective

Fig 20.5 shows the whole situation. A viewer at y = ay is looking in the negative z-direction. At a distance D in front of the viewer is the projection plane, the bottom half of which is displayed on the GBA screen of height H (=160). And now for the fun part. The GBA doesn’t have any real 3D hardware capabilities, but you can fake it by cleverly manipulating the scaling and translation REG_BGxX-REG_BGxPD for every scanline. You just have to figure out which line of part of the floor goes into which scanline, and at which zoom level. Effectively, you’re building a very simple ray-caster.

The math

Conceptually, there are four steps to Mode 7, depicted in fig 20.6a-d. Green figures indicate the original map; red is the map after the operation. Given a scanline h, here’s what we do:

  1. Pre-translation by a= (ax, az). This places the viewer at the origin, which is where we need it for steps b and c.
  2. Rotation by α. This takes care of the yaw angle. These steps have been the same as for normal transformable backgrounds so you shouldn’t have any difficulty understanding them.
  3. Perspective division. Next, we scale the whole thing by 1/λ. From eq 20.2 we have λ = ay/h. The line z = zh is the line that belongs on scanline h. The new position of this line after scaling is z = −D, since that was the whole point of perspective division.
  4. Post-translation by (−xs). Note the minus sign. After the perspective division, all that remains is moving the fully transformed map back to its proper screen position (the beige area). For obvious reasons the horizontal component should be half the screen width. The vertical move should move the floor-line to the scanline, so the vector is:
(20.3) x s = W / 2 = 120 y s = ( D + h )
Fig 20.6a-d: The 4 steps of mode 7
pre-translate rotate scale post-translate
Fig 20.6a: pre-translate by (ax, az) Fig 20.6b: rotate by α Fig 20.6c: scale by 1/λ Fig 20.6d: post-translate by (xs, ys)

Putting it all together

While the steps described above are indeed the full procedure, there are still a number of loose ends to tie up. First of all, remember that the GBA’s transformation matrix P maps from screen space to background space, which is actually the inverse of what you’re trying to do. So what you should use is:

(20.4) P = S ( λ ) R ( a ) = [ λ cos ( a ) λ sin ( a ) λ sin ( a ) λ cos ( a ) ]

And yes, the minus sign is correct for a counter-clockwise rotation (R is defined as a clockwise rotation). Also remember that the GBA uses the following relation between screen point q and background point p:

(20.5) d x + P q = p

that is, one translation and one transformation. We have to combine the pre- and post-translations to make it work. We’ve seen this before in eq 4 in the affine background page, only with different names. Anyway, what you need is:

(20.6) d x + P q = p P ( q x s ) = p a d x + P x s = a d x = a P x s

So for each scanline you do the calculations for the zoom, put the P matrix of eq 20.4 into REG_BGxPA-REG_BGxPD, and a−P·xs into REG_BGxX and REG_BGxY and presto! Instant Mode 7.

Well, almost. Remember what happens when writing to REG_BGxY inside an HBlank interrupt: the current scanline is perceived as the screen’s origin null-line. In other words, it does the +h part of ys automatically. Renaming the true ys to ys0, what you should use is

(20.7) y s = y s 0 h = D

Now, in theory you have everything you need. In practice, though, there are a number of things that can go wrong. Before I go into that, here’s a nice, (not so) little demo.

Threefold demo

As usual, there is a demo. Actually, I have several Mode 7 demos, but that’s not important right now. The demo is called m7_demo and the controls are:

D-padStrafe.
L, Rturn left and right (i.e., rotate map right and left, respectively)
A, BMove up and down, though I forget which is which.
SelectSwitch between 3 different Mode7 types (A, B, C)
StartResets all values (a= (256, 32, 256), α= 0)

“Switch between 3 different Mode7 types”? That’s what I said, yes. Make sure you move around in all three types. Please. There’s a label in the top-left corner indicating the current type.

blocky
Fig 20.7a: Type A: blocked.
sawtooth
Fig 20.7b: Type B: sawtooth.
smooth
Fig 20.7c: Type C: smooth.

Order, order!

Fiddled with my demo a bit? Good. Noticed the differences between the three types? Even better! For reference, take a look at Figs 20.7a-c, which correspond to the types. They adequately show what’s different.

  • Type A is horribly blocky. Those numbers in the red tiles are supposed to be ‘8’s. Heh, numbers? What numbers!
  • Type B is better. The left-hand side is smooth, but there’s still some trouble on the right-hand side. But at least you can see eights with some imagination.
  • Type C. Now we’re talking! The centerline is clear, which is important since that’s what you’re looking at most of the time. But even on the sides, things are looking pretty decent.

So we have three very different Mode7 results, but I guarantee you it’s all based on the same math. So how come one method looks so crummy, and the other looks great?

The code

Here are the two HBlank ISRs that create the types. Types A and B are nearly identical, except for one thing. Type C is very different from the others. If you have a thing for self-torture, try explaining the differences from the code alone. I spent most of yesterday night figuring out what made Type C work, so I have half a mind of leaving you hanging. Fortunately for you, that half’s asleep right now.

#define M7_D   128

extern VECTOR cam_pos;          // Camera position
extern FIXED g_cosf, g_sinf;    // cos(phi) and sin(phi), .8f
// --- Type A ---
// (offset * zoom) * rotation
// All .8 fixed
void m7_hbl_a()
{
    FIXED lam, xs, ys;

    lam= cam_pos.y*lu_div(REG_VCOUNT)>>16;  // .8*.16/.16 = .8

    // Calculate offsets (.8)
    xs= 120*lam;
    ys= M7_D*lam;

    REG_BG2PA= (g_cosf*lam)>>8;
    REG_BG2PC= (g_sinf*lam)>>8;

    REG_BG2X = cam_pos.x - ( (xs*g_cosf-ys*g_sinf)>>8 );
    REG_BG2Y = cam_pos.z - ( (xs*g_sinf+ys*g_cosf)>>8 );  
}
// --- Type B ---
// (offset * zoom) * rotation
// Mixed fixed point: lam, xs, ys use .12
void m7_hbl_b()
{
    FIXED lam, xs, ys;

    lam= cam_pos.y*lu_div(REG_VCOUNT)>>12;  // .8*.16/.12 = .12

    // Calculate offsets (.12f)
    xs= 120*lam;
    ys= M7_D*lam;

    REG_BG2PA= (g_cosf*lam)>>12;
    REG_BG2PC= (g_sinf*lam)>>12;

    REG_BG2X = cam_pos.x - ( (xs*g_cosf-ys*g_sinf)>>12 );
    REG_BG2Y = cam_pos.z - ( (xs*g_sinf+ys*g_cosf)>>12 );   
}
// --- Type C ---
// offset * (zoom * rotation)
// Mixed fixed point: lam, lcf, lsf use .12
// lxr and lyr have different calculation methods
void m7_hbl_c()
{
    FIXED lam, lcf, lsf, lxr, lyr;

    lam= cam_pos.y*lu_div(REG_VCOUNT)>>12;  // .8*.16 /.12 = 20.12
    lcf= lam*g_cosf>>8;                     // .12*.8 /.8 = .12
    lsf= lam*g_sinf>>8;                     // .12*.8 /.8 = .12
    
    REG_BG2PA= lcf>>4;
    REG_BG2PC= lsf>>4;

    // Offsets
    // Note that the lxr shifts down first! 

    // horizontal offset
    lxr= 120*(lcf>>4);      lyr= (M7_D*lsf)>>4;
    REG_BG2X= cam_pos.x - lxr + lyr;

    // vertical offset
    lxr= 120*(lsf>>4);      lyr= (M7_D*lcf)>>4; 
    REG_BG2Y= cam_pos.z - lxr - lyr;
}

The discussion (technical)

All three versions do the following things: calculate the zoom-factor λ, using eq 2 and a division LUT, calculate the affine matrix using λ and stored versions of cos(φ) and sin(φ), and calculate the affine offsets. Note that only pa and pc are actually calculated; because the scanline offset is effectively zero all the time, pb and pd have no effect and can be ignored. Those are the similarities, but what’s more interesting are the differences:

  1. Fixed point. Type A uses .8 fixed point math throughout, but B and C use a combination of .12 and .8 fixeds.
  2. Calculation order of the affine offset The affine displacement dx is a combination of 3 parts: scale, rotation and offsets. Type A and B use dx = (offset*scale)*rotation, while C uses dx = offset*(scale*rotation). Because type C does the offsets last, it can also use different fixed-points for the offsets.
Table 20.1: division tables and zoom factors. ay=32
h 1/h λ (true) λ(.8)
157 0.01a16d..h 0.342da7h 0.34h
158 0.019ec8..h 0.33d91dh 0.33h
159 0.019c2d..h 0.3385a2h 0.33h
160 0.019999..h 0.333333h 0.33h

These two (well, 2 and a half, really) differences are enough to explain the differences in the results. Please remember that the differences in the code are quite subtle: fixed point numbers are rarely used outside consoles, and results changing due to the order of calculation is probably even rarer. Yet is these two items that make all the difference here.

Let’s start with types A and B, which differ only by the fixed-point of lam. λ is the ration of the camera height and the scanline, which will often be quite small – smaller than 1 at any rate. table 20.1 shows a few of the numbers. Note that using a λ with only 8 fractional bits means that you’ll often have the same number for multiple scanlines, which carries through in the later calculations. This is why type A, which plays by the rules and uses a constant fixed-point like a good little boy, is so blocky at low altitudes. The four extra bits of type B gives much better results. Rules are nice and all, but sometimes they needs to be broken to get results.

Now, you will notice that type B still has a bit of distortion, so why only go to .12 fixeds in type B, why not 16? Well, with 16 you can get into trouble with integer overflow. It’d be alright for calculating xs and ys, but we still have to rotate these values later on as well. OK, so we’ll use 64bit math, then the 32bit overflow wouldn’t matter and we could use even more fixed point bits! After all, more == better, right?

Well, no. Bigger/stronger/more does not always mean better (see the DS vs PSP). The remaining distortion is not a matter of the number of fixed-point bits; not exactly. You could use a 128bit math and .32f division and trig tables for all I care; it wouldn’t matter here, because that’s not were the problem is.

The problem, or at least part of it, is the basic algorithm used in types A and B. If you look back to the theory, you’ll see that the affine matrix is calculated first, then the offsets. In other words, first combine the scale and rotation, then calculate the offset-correction, P·xs. This is how the affine parameters in the GBA work anyway. However, this is actually only the first step. If you follow that procedure, you’d still get the jagged result. The real reason for these jaggies is the order of calculation of lxr.

// Multiply, then shift to .8 (A and B)
    lxr= (120*lcf)>>4;

// Shift to .8 first, then multiply (C)
    lxr= 120*(lcf>>4);

Getting lxr = pa/c·xs requires two parts: multiplication with P elements and the shift down to .8 fixeds. You might expect doing the shift last would be better because it has a higher precision. The funny thing is that it doesn’t! Shifting pa or pc down to 8 fractional bits before the multiplication is what gets rid of the remaining distortions, reversing the order of operations doesn’t.

As for why, I’m not 100% sure, but I can hazard a guess. The affine transformation takes place around the origin of the screen, and to place the origin somewhere else we need to apply a post-translation by xs. The crucial point I think is that xs is a point in screen-space which uses normal integers, not fixed points. However, it only applies to xs because that really represents an on-screen offset; ys is actually not a point on the screen but the focal distance of the camera. On the other hand, it might have something to do with the internal registers for the displacement.

The verdict

Obviously, type C is the one you want. It really bugs the hell out of me that I didn’t think of it myself. And the fact that I did use the scale-rotation multiplication but abandoned it because I screwed up with the multiplication by the projection distance D doesn’t help either (yes, this sentence makes sense). The code of m7_hbl_c shown above works, even though it only uses 32-bit math. As long as you do the scale-rotation multiplication first and shift down to .8 fixeds before you multiply by 120 in the calculation of wxr everything should be fine.

Final Thoughts

This has been one of those occasions that show that programming (especially low-level programming) is as much of a science as an art. Even though the theory for the three mode 7 versions was the same, the slight differences in the order and precision of the calculations in the implementations made for very noticeable differences in the end result. When it comes to mode 7, calculate the affine matrix before the correction offset. But most importantly, the x-offset for the screen should not be done in fixed point.

Secondly, this was only the basic theory behind mode 7 graphics. No sprites, no pitch-angle and no horizon, and tailored to the GBA hardware from the start. In the next chapter, we’ll derive the theory more extensively following standard 3D theory with linear algebra. This chapter will also show how to position sprites in 3D and how to do other things with them like animating for rotation and sorting, and also present variable-pitch and a horizon. If this sounds complicated, well, I supposed that it is. It’s definitely worth a look, though.

21. Mode 7 Part 2

Introduction

Mode 7: part 1 covered the basics of how to get an affine background to look like a 3D plane, and discussed some of the trickier parts of the fixed point arithmetic involved. Getting the basic look of a 3D plane is only the first step.

In this chapter, we’ll look into the general math involved of creating a 3D world and translate it back to a form we can use for mode 7. This includes translations in all directions and looking around (yaw) like before, but also a pitch angle for looking up and down. We’ll also see how to deal with the horizon and use a background for the backdrop above the horizon. I’ll even throw in a bit of fogging to occlude the distant parts of the ground.

I’ll discuss also working with sprites in 3D space. Not just the transformation from 3D space to 2D screen, but also culling, scaling for distance (which is not as simple as one might think), animation and sorting. Note that this part of the chapter is basic 3D sprite theory, and can be applied to 3D games that use sprites in some way.

The theory part of the chapter is going to be very math-heavy, as 3D theory always is. Knowing a little bit about linear algebra certainly wouldn’t hurt. The full story about geometry is beyond the scope of Tonc, but this stuff is quite general; most books on 3D programming will have a chapter on geometric transformations, so you can look at those if you get a little lost here.

This chapter touches on almost all of the topics covered so far. It uses affine objects, backgrounds (both regular and affine), interrupts, color effects and a few more. If your understanding of any of these is lacking, you could be in for a rough time here.

full mode 7 full mode 7
Fig 21.1: m7_ex; with horizon, sprites, variable pitch angle and distance fogging.

What we’re going to try to do is re-create a scene from the SNES Mario Kart (see fig 21.1; apologies to Nintendo for using the graphics, but I don’t have a lot of options here :\). This is just a freeze-frame of the game, not actual game play is involved, but this should present a nice target to aim for. The code is distributed over a number of files: mode7.c for the simple mode 7 functions and mode7.iwram.c for the less simple mode 7 functions and interrupt routines. The code of demo-specific code can be found in m7_ex.c, which does the set-up, interaction and main loop. The basic controls are as follows:

D-pad Looking
A/B Back/forward
L/R Strafing
Select+A/B Float up/down
Start Menu

Movement and looking follows FPS/aircraft motion, or at least as well as could be expected with the number of buttons available. There are several extra options which have been put in a menu. First is motion control which sets difference methods of movement. Option ‘local’ follows the camera axis for flight-controls, ‘level’ gives movement parallel to the ground, like FPSs usually do, and ‘global’ uses world axis for movement. Other options include toggling fog on or off and resetting the demo.

Basic mode 7 theory

Fig 21.2 shows what we’re up against: we have a camera located at acw, which has some orientation with respect to the world coordinate system. What we have to do is find the transformation that links screen point xs to world point xw. There are a number of ways to do this. You already saw one in the first mode 7 chapter, where we I had the GBA hardware in mind from the start. You could extend this to the general mode 7 case (with a non-zero pitch) with some effort. You could also use pure trigonometry, which is a minefield of minus signs and potential sine-cosine mix-ups. Still, it is possible. What I’ll use here, though, is linear algebra. There are several reasons for this choice. Firstly, linear algebra has a very concise notation, so you can write down the final solution in just a few lines (in fact, once you get through the definitions, the solution that covers all cases can be written down in 2 lines). Furthermore, the equations are well structured and uniform in appearance, making debugging easier. Then there’s the fact that inverting the whole thing is very easy. And lastly, it’s what true 3D systems use too, so the theory can be applied outside the mode 7 arena as well. Conversely, if you know basic 3D theory, you’ll feel right at home here.

overview
Fig 21.2: The basic 3D situation. The trick is to relate screen point xs to world point xw, taking the camera position acw and its orientation into account.

Definitions

Before you can do anything, though, you need to know exactly what we’re going to use. The first thing to note is that we have two main coordinate systems: the world system Sw and the camera system Sc. Inside the camera system we have two minor coordinate systems, namely the projection space Sp and screen space Ss. Now, for every transformation between systems Si and Sj the following relation holds:

(21.1) M i j     x j = x i a j i

where

xi the coordinate vector in system Si;
xj the coordinate vector in system Sj;
aji the origin of system Sj, expressed in coordinates of system Si;
Mij the transformation matrix, which is basically the matrix formed by the principle vectors of Sj, in terms of Si.

Once you get over the initial shock of the many indices (meh, in general relativity you have something called the Riemann tensor, which has four indices), you’ll see that this equation makes sense. If you don’t get it right away, think of them as arrays and matrices. An observant reader will also recognise the structure in the screen↔map transformation we had for affine maps: P·q = p − dx. Eq 21.1 is a very general equation, by the way, it holds for every kind of linear coordinate transformation. In fact, systems Si and Sj don’t even have to have the same number of dimensions!

As said, we have 4 systems in total, so we have 4 subscripts for w(orld), c(amera), p(rojection), s(creen). Remember these, for they will appear on a very regular basis. The final forms of the matrices and origins depend very much on the exact definitions of these systems, so make sure you know exactly what each means.

World system

The first of these, the world system Sw, is easy to deal with. This is simply a right-handed Cartesian system with principle axes i, j, and k, which are its x-, y- and z-axes, respectively. In the right-handed system that is used in computer graphics, the x-axis (i) points to the right, the y-axis (j) points up and the z-axis (k) points backward! This means that you’re looking in the negative z direction, which may seem weird at first. If you absolutely must have a forward pointing k, you could use a left-handed system. While this utterly destroys my 3d intuition, if you want it be my guest. Before you do that, though, remember that the map marks the floor of world space and in a right-handed system, the texture coordinates will match up neatly to world coordinates.

The camera frame

word to camera transformation
Fig 21.3: Camera orientation {u, v, w} in world space {i, j, k}, given by angles θ and φ

The transformation to the camera system is probably the major hurdle in the whole thing. At least it would be if it wasn’t for matrices. Rewriting eq 21.1, the transformation between camera and world space is given by

(21.2) C     x c = x w a c w

As you can expect, the origin of camera space is the camera position, acw. The camera matrix C is formed by the principle axes of camera space, which are u, v and w for the local x-, y- and z-axes, respectively. This means that the camera matrix is C = [u v w].

The orientation of the camera with respect to world space is defined by 3 angles: pitch (rotation around the x-axis), yaw (rotation around the y-axis) and roll (around z-axis). The combination of these give C. Traditionally, the rotation direction of these is such that if you look down one of these axes, a positive angle turns the system counter-clockwise. However, I’ll do the exact opposite, because it makes a number of things easier. Additionally, I will only be using two angles: pitch and yaw. For mode 7 it is impossible to incorporate roll into the picture. Why? Look at it this way: if you’re rolled on your side, the ground would be on the right or left of the screen, which would require a vertical perspective division, which is impossible to achieve since we can only change the affine parameters at HBlank. Therefore, only pitch (θ) and yaw (φ) are allowed. I want my positive θ and φ to the view down and right, respectively, meaning I need the following rotation matrices:

(21.3a) R x ( θ ) = [ 1 0 0 0 cos ( θ ) sin ( θ ) 0 sin ( θ ) cos ( θ ) ]
(21.3b) R y ( φ ) = [ cos ( φ ) 0 sin ( φ ) 0 1 0 sin ( φ ) 0 cos ( φ ) ]

But now the next problem arises: do we do pitch first, or yaw? That really depends on what kind of effect you want to have and in relation to what system you do your rotation. There is actually only one order that is possible for the same reason that roll wasn’t allowed: you cannot have a vertical perspective. What this boils down to is that u (the x-axis of the camera frame) must be parallel to the ground plane, i.e., uy must be zero. In order to do that, you must do pitch first, then yaw. This is depicted in fig 21.3. To get a feel for this: stand up, tilt your head down (pitch θ>0), then turn to your right (yaw φ>0). The full camera matrix then becomes:

(21.4) C ( θ , φ ) = R y ( φ )     R x ( θ ) = [ cos ( φ ) sin ( φ ) s i n ( θ ) sin ( φ ) cos ( θ ) 0 cos ( θ ) sin ( θ ) sin ( θ ) cos ( θ ) sin ( θ ) cos ( φ ) cos ( θ ) ]

Aside from being correct, this matrix has two nice properties. Firstly, the column vectors are of unit length. Secondly, the component vectors are perpendicular. This means that C is an orthogonal matrix, which has the very nice feature that C−1 = CT. This makes the world→camera transformation a relatively simple operation.

One last thing here: if you were to rotate the camera system by 180° around i, this would give you a forward pointing w and a downward pointing v, both of which decrease the number of awkward minus signs in later calculations, at the expense of an awkward camera frame. Whether you want to do this is up to you.

Matrix transforms and the system they occur in.

I said that to mimic the rotations of C you to tilt your head first (θ), then rotate your body (φ). You might think that you can get the same effect by doing it the other way: turn first, then look down. However, this is incorrect.

It may feel the same, but in the second case you’d not actually be using the Rx(θ) to invoke the tilt. A matrix isn’t a thing in itself, it ‘lives’ in a space. In this case, both Rx(θ) and Ry(φ) are defined in terms of the world coordinate system, and when applying them the directions follow the world’s axes. The turn-then-tilt order would use Rx(θ) in a local frame, which is a legal operation, but not the one that the math requires.

I know it’s a subtle point, but there really is an important difference. Try visualizing it with a 90° rotation in both orders, maybe that’d help.

The projection plane


Fig 21.4: perspective projection.

To create the illusion of depth we need a perspective view. For this, you need a center of projection (COP) and a projection plane. Naturally, both need to be in camera space. While you’re free to choose these any way you want, you can simplify matters by placing the center of projection at the origin of camera space and the projection plane at a distance D in front of the camera, so that the plane is given by xp = (xpyp, −D). Yes, that’s a negative zp, because we’re looking in the negative z-direction. The projected coordinates are the intersections of the line between COP and xc, and the projection plane. Since the COP is at the origin, the relation between xc and xp is

(21.5) λ   x p = x c

Here λ is a simple scaling factor, the value of which can be determined in a variety of ways, depending of the information available at the point in your derivations. For example, since zp = −D, by definition, we have λ = −zc / D. Later we’ll see another expression. The interesting thing about this expression is that λ is proportional to the distance in camera space, which in turn tells you how much the camera position is to be scaled down, or zoomed. This is useful, since the scaling parameters of the affine matrix scales down as well. Also, the distance D attenuates the scaling, which means that it acts as a focus length. Note that when zc = −D, the scale is one, meaning that the objects at this distance appear in their normal size.

Viewport and viewing volume


Fig 21.5: Viewing frustum in camera space. The green rectangle is the visible part of the projection plane (i.e., the screen).

Before I give the last step of the transformation to the screen, I have to say a few words about the viewport and the viewing volume. As you can imagine, you can only see a certain portion of the world. You see the world through a region called the viewport. This is an area on the projection plane, usually rectangular, that defines the horizontal and vertical boundaries of what you can see. In particular, you have a left side (L), right side (R), top (T) and bottom (B). With the axes defined as they are and the origin is usually centered (see fig 21.5, inset), we have R>0>L and T>0>B. Yup, in this particular case L is negative, and T is positive!

The width and height of the viewport are W = |R−L| and H = |B−T|, respectively. Together with the center of projection, the viewport defines the viewing volume (see fig 21.5). For a rectangular viewport this will be a pyramid.

Most of the time you will want boundaries in depth as well, because things too near will obstruct everything else from view (besides, dividing by 0 is never good), and very distant objects will become so small that they are barely noticeable, and why waste so many calculations on a handful of pixels? These boundaries in depth are called the near (N) and far (F) planes, and will turn the viewing volume in a frustum. The numbers for these distances are a matter of taste. Whatever you use, be aware that the z-values are actually negative. I would prefer to have the values of N and F positive, so that the order or distance is 0>−N>−F.

Another point is the notion of the field of view (FOV). This is the horizontal angle α that you can see, meaning that

(21.6) tan ( ½ α ) = ½ W D

I am told that a commonly used FOV is about 90°, which would require D = ½W. With D = 128 you get close enough to this requirement, with the added benefit that it’s a power of 2, but that, of course, is an implementation detail. However, it seems that D = 256 is more common, so we’ll use that instead.

The screen


Fig 21.6: screen space vs camera space

The last step is the one from the projection plane onto the screen. This step is almost trivial, but the almost can cause you a lot of trouble if you’re not careful. The situation is shown in fig 21.6, where you are looking through the camera. The axes u and v are the up and right axes of the camera system, while the green arrows denote the x- and y-axes of screen space. And if you have paid attention to any of the tutorials, you should know that the screen’s y-axis points down. This is bugfest number 1. Also, the origins of camera and screen space differ. Since the screen corresponds to the viewport, the origin of the screen in camera/projection space is asp = (L, T, −D). Be careful not to reverse the signs here; that would be bugfest number 2. Also remember that since this is in camera space, L is negative and T is positive. Taking both the inverted vertical axis and the origin of screen-space in mind, we have

(21.7) S ( 1 , 1 , 1 ) x s = x p a s p

The scaling matrix reverses the sign of the y-axis. We could have avoided the extra matrix if we had rotated the camera frame by another 180°, in which case v would have pointed down and w would have pointed forward. But I didn’t, so we’ll have to live with it here. Also, since the origin of the screen in camera space, is asp = (L, T, −D), the screen position is xs = (xsys, 0), in other words zs is always zero. If you want to check whether everything is OK, see if the corners of the viewport give the right screen coordinates.

Theory summary

And that’s basically it, phew. Since it took three pages to get here, I’ll repeat the most important things. First, the main equations we need are:

(21.8a) λ C     x p = x w a c w
(21.8b) S ( 1 , 1 , 1 ) x s = ( x p a s p )

where

xw coordinates in world space;
xp coordinates on the projection plane, xp= (xp, yp, −D);
xs coordinates on the screen, xs= (xs, ys, 0);
acw the location of the camera in world space;
asp the location of the screen origin in camera space space, asp = (L, T, −D);
C the camera matrix, as function of pitch θ and yaw φ: C = Ry(φ)· Rx(θ);
λ the scaling factor. Its value can be determined by the boundary conditions.

Remember these equations and terms, for I will refer to them often. The break between eq 21.8a and eq 21.8b is by design: all the real information is in eq 21.8a; eq 21.8b is just a final step that needs to be taken to complete the transformation. In the remainder of the text, I will make frequent use of eq 21.8a and leave out eq 21.8b unless necessary. Other interesting things to know:

  • World system Sw = {i,j,k} and camera system Sc = {u, v, w} are right-handed Cartesian coordinate systems. As expected, the columns of camera matrix C are the principle axes of Sc: C = [u v w];

  • The viewport and viewing frustum are in camera space, meaning that their boundaries are too. This means that

    R > 0 > L (horizontal)
    T > 0 > B (vertical)
    0 > −N > −F (depth)
  • If we use the GBA screen size as a basis (W = 240, H = 160), and D = 256, reasonable values for the viewing frustum boundaries are the following, but you can pick others if you want.

    L = −120 R = −120
    T = 80 B = −80
    N = 24 F = 1024

Horizon and backdrop

Take the essential mode 7 case: a floor in perspective. Due to the perspective division, the distant parts of the floor will approach a single line: the horizon. Since the map really is just a floor, the horizon really will be just that: one horizontal line. The space above that is usually empty, but to make it a little less bland, we will use a backdrop: a panorama view of the distant environment that moves along with the camera’s rotation.

Finding the horizon

Roughly put, the horizon is where z = −∞. If you have lines on the floor, the horizon is where all parallel lines seem to meet: the vanishing line. Naturally, if you only have a floor, then you should only draw it below the horizon and the graphics above it should be part of a skybox. I’m sure you’ve seen this in the original Mario Kart and other mode 7 racers. Since we’re limited to a roll-less camera, the horizon will always be a horizontal line: one scanline ys,h. To find it, all we have to do is take the y-component of eq 21.8a and rearrange the terms to get

(21.9a) λ ( v y   y p , h   w y D ) = a c w , y y p , h = ( w y D a c w , y / λ ) / v y

And if we were to take our horizon at infinity, them λ = −∞, which would reduce eq 21.9 to

(21.9b) y p , h = D   w y / v y = D tan ( θ )

However, you need to think about whether you want to use this simplified equation. At very large λ, the gaps in displayed map points are so large that you’re effectively showing noise, which can be very ugly indeed. A better way would be making use of the far clipping plane at zc = −F. In that case, λ = F/D and we can use eq 21.9 to calculate the horizon, which will be something like

(21.9c) y p , h = D / F     ( F w y     a c w , y ) / v y

As expected, if F = −∞ then eq 21.9c reduces to eq 21.9b. Regardless of whether you chose a finite of infinite zc, the horizon will be at scanline ys,h = T − yp,h.

Using the horizon

The horizon marks the line between the map and ‘far far away’: between the floor and the backdrop. The floor should be an affine background, obviously; for the backdrop, we will use a regular background, although that’s not required. What we need to a way to switch between the two at the horizon scanline. The simplest way is by HBlank interrupt: once the horizon scanline is reached, make the switch between floor and backdrop settings in the BG control registers and perhaps initiate HDMA for the affine parameter transfers if you chose to use DMA for that.

Switching between the backdrop and floor backgrounds is actually trickier than it sounds. You could, for example, have a separate background for each and enable/disable them depending on your needs. The problem is that it seems to take about 3 scanlines before a background is fully set up in hardware (see forum:1303), so you’ll see crap during that time. In other words, this solution is no good.

An other way would be to have one background for both and switch the video-mode from 0 to 1 or 2. This won’t give you 3 lines of garbage, but now another problem arises: chances are very high that the backdrop and floor have very different tiles and map attributes. This is easy to solve though: simply change the screen (and char) base blocks in REG_BGxCNT.

bg-switch
Fig 21.7: Switch video-mode and background parameters at the horizon.
panorama
Fig 21.8: peeling a panoramic view from a cylinder.

Making and placing the backdrop

The space directly above the horizon is for the backdrop. You probably want a nice image of a distant town or tree line over there, not just a boring empty sky. The backdrop offers a panoramic view, which can be considered a map painted on the inside of a cylinder and then peeled off to a normal 2D surface (see fig 21.8). The idea is to put that surface on a background and the scroll around.

Vertically, the bottom of the background should connect to the horizon. Because regular backgrounds use wrap-around coordinates this is actually quite easy: place the ground-level of the backdrop at the bottom of a screen-block and set the vertical offset to −ys,h.

Horizontally, there are several issues to be aware of. The first is the width of the map, which is simply the perimeter P of the cylinder. As we should have a scrolled a full map’s width for a 360° rotation, the correct scroll ratio per unit angle is simply P/2π = R, the radius. In principle, R is arbitrary, but the best result can be had when the field of view formed by the angle of the panorama (αp = W/R), is equal to the camera field-of-view angle αc from eq 21.6. If all is right we should have αp = αc = α.

(21.10) α = 2     arctan ( ½ W D ) α = W R R = ½ W arctan ( ½ W D ) D 1 ( ½ W D ) 2   /   3

That last approximation stems from the first couple of terms of the Taylor series of the arctangent. Interestingly enough, even RD seems somewhat adequate. Anyway, filling in W = 240 and D = 256 gives P = 1720, which isn’t a very convenient map size, is it? Now, it is possible to create a map of any size and update VRAM if we go outside the screenblock’s boundaries (commercial games do it all the time), but doing so would distract for the subject at hand, so you know what? We’re going to bend the rules a bit and just force P = 1024.

“Wait a sec … you can’t do that!” Well, yes I can actually. I’m not supposed to do it, but that’s another issue. The fact of the matter is that, I don’t think there is a single mode 7 game that scrolls the backdrop properly! For example, the Mario Kart’s often use multiple backgrounds with different scrolling speeds in their backdrops, which is absolutely ridiculous, mathematically speaking, because looking around doesn’t change relative lines of sight. But I guess nobody noticed or at least nobody cares. What I’m trying to say is: we’re in good company :P

So, we just define a perimeter value and with it backdrop map-width ourselves. In this case I’m going to use P = 1024, which is a nice round number and for which we can use a 512 px wide tile-map will effectively end up as a panorama with 180° rotational symmetry. Taking into account the circle partitioning of 2π ⇔ 10000h, the scrolling value is simply φ*P/10000h = φ/64. We’ll have to offset this by L as well because I want to map φ = 0 to due north. The final position of the backdrop is given in 21.11.

(21.11) d x = φ / 64 + L d y = y s , h

The floor

Affine parameters for the floor

Eq 21.8 describes the world↔screen transformation but that information uses 3D vectors, while the GBA only has a 2×2 affine matrix P and a 2D displacement vector dx at its disposal. So we have some rewriting to do. Now, I could give you the full derivation, 2d↔3d conversions and all, but something tells me you really don’t want to see that. So instead, I’ll give you the set of equations you need to solve, and hints on how to do that.

(21.12) λ C     x p = x w a c w S ( 1 , 1 , 1 )     x s = ( x p a s p ) P     q = p d x

The first two equations are just eq 21.8 again, I just them list for completeness. The last equation is the relation between screen point q and map point p for an affine map, an equation that should be familiar by now. Now, remember that our map lies on the floor, in other words p = (xwzw). The 2D screen point q is, of course, similar to the 3D screen vector of xs. The only thing that you have to remember is that when writing to REG_BGxY, the left of the current scanline is taken as the origin, so that effectively q = (xs, 0), which in turn means that pb and pd are of no consequence. The values of the other elements of P are simply the x- and z-components of the scaled camera x-axis, λu. If you use these values, you will see that eventually you will end up with an expression that can best be summed up by:

(21.13) d x = a c w + λ C     b

where

d x = ( d x ,   0 ,   d y ) b = ( L ,   T y s , D )

Everything you need for the displacement is neatly packed into this one equation, now we need to disassemble it to construct the algorithm. First, we can use the y-component of dx’ to calculate λ. Once we have that we can use it to calculate the other two elements, i.e., the actual affine offsets. The affine matrix was already given earlier.

Eq 21.14 gives all the relations explicitly, though I hope you’ll forgive me when I prefer the conciseness of eq 21.13 myself.

(21.14) λ = a c w , y   /   ( ( y s T ) v y   + D w y ) p a = λ   u x p c = λ   u z d x = a c w , x   +   λ ( L u x   +   ( T y s ) v x   D w x ) d y = a c w , z   +   λ ( L u z   +   ( T y s ) v z D w z )

Note that if we take the top at 0 and no pitch (T=0 and θ=0) we have exactly the same result as in the first mode 7 chapter, and if we look straight down (θ=90°), the whole thing reduces to a simple scaling/rotation around point (−L, T), which is exactly it should be. Eq 21.14 is the general equation for mode 7; for the implementation, you can often make a number of shortcuts that speed up calculation, but well get to that later.

Distance fogging

In the real world, light coming from far away objects has to travel through the atmosphere, which scatters the photons, attenuating the beam. What you’ll end up seeing is partly the object itself and partly the ambient color, and the further the original object, the smaller its contribution is. Because such effect is most easily visible in fog conditions, I’ll call this effect fogging.

Fogging offers a hint of distance and including it can increase the sense of depth. Also, it can hide objects popping into view as they’re loaded. GBA-wise, it can be implemented by using different alpha-blends at every scanline.

The fundamental equation for this is the following differential equation:

d I = I   k ( ν )   ρ   d z

where I is the intensity; k(ν) is the absorption coefficient of the medium, which depends on the frequency of the light, ν and possibly position; ρ is the density and z is the distance. Solving this would lead to an exponential decay over distance. And I do mean real distance, with squares and roots and everything.

Fortunately, we don’t have to use something that complicated; all we really need is some functional relation that gives 0 at infinity and 1 close up. Interestingly enough, we already have something like that, namely λ as function of the scanline (see 21.14). This is basically a hyperbola, all you have to do then is fiddle with scalers and offsets a bit to get something that looks nice. In my case, λ*6/16 seems to work well enough.

fog off fog on
Fig 21.9: fog off (left) and on (right).

Fig 21.9 shows screenshots with and without the fogging effect as seen from a fairly high altitude. The distance to the floor is relatively small at the bottom of the screen, so those are still very visible. At the horizon, the floor is completely obscured by the orange fog; which is actually a good thing, as the lines near the horizon are usually not much to look at anyway.

By the way, note that I said orange fog. If you’d paid attention in the graphics effects chapter will know that the GBA only has fading modes for white and black. Nevertheless, fades to an arbitrary color are very much possible, but I’ll explain once we get to the implementation. While you ponder over how it can be done, I’ll move on to 3D sprites.

Sprites

Sprites and 3D are a strange combination. By their very nature, sprites are 2D objects – like stickers stuck against the viewport (i.e., the screen). To make them appear part of the 3D world, you have to make them move over the screen in such a way that they appear to move with the world and scale them according to their distance. Once again, the basic of this is eq 21.8, but there is considerably more to it.

Four topics must be covered here. The first is sprite positioning. Eq 21.8 will work at point/pixel level, and a sprite is a simple rectangle. While it’s possible to rewrite the sprite’s pixels to work around that, it kind of defeats the purpose of using sprites in the first place. Instead, we’ll link one point on the object to the world coordinate of the sprite and set the OAM position and matrix to accommodate this. This is basically the theory of anchoring discussed in the affine object chapter.

Next up: sprite culling. Once you have the correct OAM positions you can’t use them as is, you have to make sure the sprite is only active if it is actually visible inside the viewport. If not, it should be disabled.

Then there’s the matter of sprite animation. Consider Toad’s kart in fig 21.10, which has the correct anchored position, but no matter which angle you look at it, it’ll always show the same side. To make it look as if you can actually move around the object, we’ll use different frames of animation to show different sides.

Lastly, sprite sorting. By default, objects will be ordered according to the objects’ numbers: obj 0 over obj 1, over obj 2, etc. Always linking a sprite to the same object means that the order would be wrong if you look at them from the other side, so we need to sort them by distance.

Those are the main issues to deal with. There are a few others, like placing a shadow, and using pre-scaled objects to get around the hardware limitation of 32 affine matrices, but these are fairly easy if the other points are already taken care of. One thing I will discuss as well is what I call object normalization: applying an extra scaling for objects so that they don’t grow too big for their clipping rectangle.

normal view looking down looking down and left
Fig 21.10: anchored sprite. The position is good, but no matter how you turn, Toad always turns away. Maybe it's the hat.

Positioning and anchoring

Positioning sprites consists of two facets. The first is to transform the sprites world position xw to a position on the screen xs. After that, you need to use that point to determine the most appropriate OAM coordinates.

The first part is just another application of eq 21.8 again, only in reverse. Normally, inverting 3D matrix is a particularly un-fun process, but the camera matrix happens to be an orthonormal matrix. An orthonormal matrix is a matrix of which the component vectors are orthogonal (perpendicular to each other) and have a length of 1. The neat thing about an orthonormal matrix is that its inverse is simply its transpose: C−1 = CT. That leads us to the following equations:

(21.15) x p = C T     ( x w a c w ) / λ x s = S ( 1 , 1 , 1 )     ( x p a s p )

The only real unknown here is λ, which we can calculate by using the fact that zp = −D. Now let the distance between camera and sprite be r = xw − acw; using C = [u v w], we find

λ = w r / D x p = u r / λ y p = v r / λ
a sprite, with anchor
Fig 21.11: a 32×32 sprite, with the anchor p0 relative to the top-left.

Finding the screen position of xw is trivial after that. And now the anchoring part. Instead of stickers, think of objects as pieces of pater to be tacked onto a board (i.e., the screen). The tack goes through one spot of the object, and that spot is fixed to the board. That spot is the anchor. For affine objects it’s not quite as simple as that, because we have to specify OAM coordinates rather than anchor coords, so there is some math involved in how to express the OAM coordinates x in terms of the texture anchor p0 and the screen anchor q0. This theory was covered in the affine object chapter, which led to eq 21.16. The other quantities there are size of the objects, s = (wh), and m which is ½ for normal affine objects and 1 for double-size affine objects.

(21.16) x = q 0 m s P 1     ( p 0 ½ s )

Now the task is to link the data we have to this equation. The screen anchor q0 is just xs. The texture anchor p0 is the pixel in texture space you want to keep fixed and is yours to choose. For the kart-sprite, it makes sense to put it near the bottom of the kart, as is depicted in fig 21.11. ‘Vector’ s is given by the size of the object, which in this case is (32, 32) and because I’m choosing to always use double-size objects here, m=1. The P-matrix is just a scaling by λ, unless you want to add other things as well. All that remains then is just to fill it in the numbers.

Sprite culling


Fig 21.12: View-frustum with sprites a, b and c. b and c are visible, a is not.

Culling is the process removing any part of the world that cannot be seen. In this case, it means removing those sprites that do not fall within the viewing volume. This is a very smart thing to do, and it makes even more sense for sprites, because not doing so would seriously screw things up because OAM couldn’t cope with the possible range of xs.

The first thing to do would be a distance check: if the object is too far away, it should not be seen. It’s also a good idea to have a near-plane distance check. Then you have to test it for intersections with the viewport. Each sprite is bounded by a certain rectangle on the projection plane and if this is completely outside the viewport, the object should not be rendered.

Fig 21.12 shows a few examples of this. Objects a and b have already been projected onto the projection plane. Object a is outside the viewport, and should be disabled. Object b is partially visible and should be rendered. Object c is not projected yet, but falls between the near and far plane and should at least be tested (and then found fully visible).

It’s actually easier to do the view volume checks in 3D camera space instead of 2D projection space. The object rectangle can easily be calculated from xc = CT·r, the anchor p0 and the size s. The viewport will have to be scaled by λ, and this gives us the following rests to perform:

Table 21.1: Object rect and culling tests in camera space. Note the signs!
 Object positionVisible if
Depth d = z c = w r N d   & &   d < F
Horizontal l = x c p 0 , x λ L l + w   & &   l < λ R
Vertical t = y c p 0 , y λ T     t + h   & &   t < λ B

If all these conditions are true, then the object should be visible. Now, please note the signs of the tests, particularly in the vertical checks.

Animation

view angle
Fig 21.13: Finding the view-angle ψ.

Rotation animation, to be precise. As we saw in fig 21.10, the sprite will show the same side regardless of where you are looking from. This is only logical, as the sprite is not actually a 3D entity. To make it look a little more 3D, we need to have images of the sprite taken from different camera angles, and then pick the one we need depending on which angle we’re looking from.

First, finding the correct view angle, ψ. Fig 21.13 shows the general situation. The angle you need is the angle between the vector between the camera and the object (red, dashed) and the global looking direction of the object. In the figure, you can see the global direction angles for the camera and object: φc and φo, respectively. Also indicated is the angle between the camera direction and the sprite, α. If you look at these angles closely, you’ll see that φc + α + ψ = φo. In other words:

(21.17) ψ = φ 0 φ c α = φ 0 φ c arctan ( x c / z c )

Whether the minus-sign inside the arctan() is necessary depends on how you define the terms all the terms. Eq 21.17 is the fully correct version, but if the arctan doesn’t appeal to you, you’ll be glad to know that in most cases the α-term can be safely ignored without anyone noticing.

Now that we have our viewing angle, we need to use it somehow. Suppose you have N frames of rotation, which divides the circle into equal parts each 2π/N radians wide. To get the slice that ψ is in, we merely have to divide by the angle of each slice: i = ψ/(2π/N) = N·ψ/(2π). If you have defined your circle in power-of-two divisions (which we have) then this part is ridiculously easy: just use a right-shift. Once you have the frame-index, the rest should be easy. Mostly. There are some intricacies that that can fog things up, but those are implementation-dependent and will be saved for later.

Sprite sorting

Disregarding priority bits for the moment, the order of objects on-screen is determined by the object number: a lower number will be in front of higher numbers. In 2D games, you can often ignore this because sprites will be on the same layer; in 3D games, you really, really can’t. Take fig 21.14, for example. The four thwomps here have a specific object order. In the left picture, the closest thwomp happens to have the lowest object and the visual ordering is correct. When viewed from the other side, however, (middle picture) things are a little different. There are two visual cues for depth: scaling (more distance is smaller) and occlusion (distance objects are obscured by closer objects). In the middle picture, these two conflict because the closest object has the highest number, making the overall picture a little disconcerting. In the picture on the right, everything looks okay again, because steps were taken to ensure the correct object order.

default order non-sorted sorted
Fig 21.14. Non-sorted objects look alright (left) from one angle, but not from the other way (middle). You need to sort them to get the correct order (right).

What needs to be done is sort the objects in OAM according to depth; a kind of Z-buffer for objects. The depth of a sprite is simply zc, and we need to fill OAM with the sprite’s object attributes in order of ascending zc. For good measure, it’s probably a good idea to give hidden objects the maximum depth-value possible or to leave them out of the sorting process entirely.

There are many possible strategies for sorting the objects. My own choice aright now would be to not sort the sprites or objects directly but to create an index table, which indicates the order the sprites’ attributes should go into OAM. The pseudo-code for this is given below. Which algorithm you use to sort the keys doesn’t really matter at this time, as long as it does the job. I’m sure that faster methods can be found, but probably at the expense of more code and I want to keep things relatively simple.

// Pseudo code for sorting sprites for OAM
void spr_sort()
{
    int ids[N];     // Index table
    int keys[N];    // Sort keys

    // Create initial index and sort-key table
    for ii=0; ii<N; ii++)
    {
        ids[ii]= ii;
        keys[ii]= is_visible(sprite[ii]) ? sprite[ii].depth : DEPTH_MAX;
    }

    // Sort keys (i.e., fill ids)
    id_sort(ids, keys);

    // Fill OAM according to
    for(ii=0; ii<N; ii++)
        oam_mem[ii]= sprite[ids[ii]].obj;
}

Renormalization

I wouldn’t be surprised if you’ve never heard of this term before. Normalization means that you scale a quantity to a user-friendly value – usually 1. You have already scaled the sprite by a factor λ, but that’s not enough. In most cases, you have to scale it further, i.e renormalize it. Here’s why.

By definition, the scaling factor λ will be one when zc = −D. Now consider what happens if you look at a closer object, say at zc = −½D. In this case, λ will be ½ and the object will be scaled by a factor of two. In other words, it’ll already fill the double-size canvas. And higher scales are possible too: with the suggested values of D = 256 and N = 24, you could end up with scaling of 10! This will not do.

It is possible to get around this by moving the near-plane further away. However, then you’ll see object disappearing if they’re still quite far off, which will look just as strange as seeing them clipped. A better solution is to give the objects an extra scaling factor. In m7_ex I have scaled the objects by an additional factor of ¼, so that a 32x32 sprite is actually only 8x8 ‘world’-pixels in size. This seems to work out quite nicely.

This renormalization means that you’re actually working with two separate scaling factors: one for the coordinate transformation, and one for visual effects. It is the visual scaling you need to use in positioning and culling the sprites, not the transformation scaling; the latter’s influence stops once you’ve found the screen-position of the anchor.

There’s probably an official term for this process, but I wouldn’t know what it is. I’m familiar with the process of renormalization from physics (a few Dutch professors got the Nobel Prize for this subject a few years back) and it seemed to fit. If you know the official term, I’d like to hear it.

norm 1x norm 2x norm 4x
Fig 21.15. Object renormalization. Left: normal (ew, no!). Middle: ×½ (hmmm, no). Right: ×¼ (yeah, that's it).

And with that, we’ve reached the end of the theory. Now to actually implement all of this.

Implementation

Design considerations.

My aim here is not to merely dish out a couple of functions that can make mode 7 happen, but also provide something that can be easily modified if necessary. The code of the m7_ex demo is spread over 4 files: one for the things specific to the demo itself m7_ex.c; and three for mode 7 specific stuff, mode7.h, mode7.c and mode7.iwram.c. Yes, iwram functions too; some of these things are going to be computation extensive and I want them as fast as possible right off the bat. I’m also borrowing the object sorter from the priority demo.

There are three main areas of interest here: the camera, background stuff and sprites. For each of these we will use a struct and/or array to keep their data so it’s nice and OOPy. There will also be a sort of manager struct for the mode 7 stuff as a whole. And, of course, we need constants for the view volume, focus length and a few other items. A handful of functions will then operate on these items to give up what we need.

Constants

There aren’t too many constants. Most have to do with the viewport, the others with the focus and renormalization.

#define M7_D        256     //!< Focal length
#define M7_D_SHIFT    8     //!< Focal shift
#define M7O_NORM      2     //!< Object renormalization shift (by /4)

// View frustum limits
#define M7_LEFT     (-120)      //!< Viewport left
#define M7_RIGHT     120        //!< Viewport right
#define M7_TOP        80        //!< Viewport top (y-axis up)
#define M7_BOTTOM   (-80)       //!< Viewport bottom (y-axis up!)
#define M7_NEAR       24        //!< Near plane (objects)
#define M7_FAR       512        //!< Far plane (objects)

#define M7_FAR_BG    768        //!< Far plane (floor)

Structs and variables

Mode 7 would be a wonderful place to use classes, but since I’m working in C, not C++, I’m sticking to structs. Apart from the BG_AFFINE struct I presented in the affine background page, you need one struct for the camera and one struct for the mode 7 objects. I’m also using a mode 7 container struct to keep track of all the parts that go into the mode 7 functionality, so that you won’t have loose global variables lying around the place.

You’re free to create your own structs for these, but the ones I will use are given below. If you’ve been paying attention, most of the members should be familiar. Oh, the POINT and VECTOR structs are 2D and 3D vectors, of course.

//! 3D sprite struct
typedef struct M7_SPRITE
{
    VECTOR pos;     //!< World position.
    POINT anchor;   //!< Sprite anchor.
    OBJ_ATTR obj;   //!< Object attributes.
    s16 phi;        //!< Azimuth angle.
    u8 obj_id;      //!< Object index.
    u8 aff_id;      //!< OBJ_AFFINE index.
    TILE *tiles;    //!< Gfx pointer.
    VECTOR pos2;    //!< Position in cam space (subject to change)
} M7_SPRITE;

//! 3D camera struct
typedef struct M7_CAM
{
    VECTOR pos;     //!< World position.
    int theta;      //!< Polar angle.
    int phi;        //!< Azimuth angle.
    VECTOR u;       //!< local x-axis (right)
    VECTOR v;       //!< local y-axis (up)
    VECTOR w;       //!< local z-axis (back)
} M7_CAM;


//! One struct to bind them all
typedef struct M7_LEVEL
{
    M7_CAM *camera;         //!< Camera variables
    BG_AFFINE *bgaff;       //!< Affine parameter array
    M7_SPRITE *sprites;     //!< 3D sprites
    int horizon;            //!< Horizon scanline (sorta)
    u16 bgcnt_sky;          //!< BGxCNT for backdrop
    u16 bgcnt_floor;        //!< BGxCNT for floor
} M7_LEVEL;

There’s not much more I have to say about these structs. The M7_SPRITE has the attributes of its object as a member itself, rather than an index or pointer to any sort of buffer. The reason behind this is essentially “why the hell not”. Because I have to sort the objects anyway, using an extra buffer might not be worthwhile, so I chose this. I’m also keeping track of the position in camera space because I need it on more than one occasion, and a TILE pointer for graphics. The reason for this will become apparent when we implement animation.

The M7_LEVEL holds pointers to the main variables for mode 7 (the camera, affine array and sprites) as well as the horizon scanline needed to switch from backdrop to floor, and two variables containing the data of the bg control register, as this will be different for the backdrop and floor.

Now we need these four variables using these structs. Because these are technically part of the demo itself, I’ve put them in m7_ex.c instead of the main mode 7 code, although that code does require an actual m7_level variable to exist for the HBlank interrupt. SPR_COUNT is the number of sprites, which is definitely demo specific. There are 161 entries in m7_bgaffs rather than just 160 for the same reason as in the DMA demo: HBlank sets up the next line, rather than the current one, and having this is better (and faster) than the alternative with if/else blocks.

M7_CAM m7_cam;
BG_AFFINE m7_bgaffs[SCREEN_HEIGHT+1];
M7_SPRITE m7_sprites[SPR_COUNT];

M7_LEVEL m7_level;

Type and order of struct members

My usual advice is to use ints for your data types, but for structs this may not always be the best thing to do. Local variables may not use up memory, but structs do. And when you have arrays of structs, the extra space that word-sized members cost adds up quickly. So in that case feel free to use non-ints.

Having said that, when it’s time to use those members it can pay to copy its data to a local 32bit variable, rather an using a byte or halfword member for all the calculations.

Also, and this is very important, you won’t be saving any space if you don’t pay attention to the order of the members. An int will still require word-alignment, even when it comes right after a byte member. The compiler may add padding after bytes and halfwords to ensure the next member is correctly aligned. It’d be best if you ordered the members in such a way that there’s as little padding as possible.

Background functions

These are my four main background functions:

  • void m7_prep_horizon(M7_LEVEL *level). Calculates the horizon scanline.
  • IWRAM_CODE void m7_prep_affines(M7_LEVEL *level). Calculates the affine parameters for the floor, based on camera position and orientation..
  • void m7_update_sky(const M7_LEVEL *level). Positions the backdrop.
  • IWRAM_CODE void m7_hbl_floor(). HBlank interrupt routine. Switches to mode 2 when necessary and copies affine parameters and creates fog effect.

m7_prep_horizon() and m7_update_sky() are simple implementations of eq 21.9 and eq 21.17, respectively, so I can be brief with these.

//! Calculate the horizon scanline
void m7_prep_horizon(M7_LEVEL *level)
{
    int horz;
    M7_CAM *cam= level->camera;

    if(cam->v.y != 0)
    {
        horz= M7_FAR_BG*cam->w.y - cam->pos.y;
        horz= M7_TOP - Div(horz*M7_D, M7_FAR_BG*cam->v.y);
    }
    else    // looking straight down (w.y > 0) means horizon at -inf scanline
        horz= cam->w.y > 0 ? INT_MIN : INT_MAX;

    level->horizon= horz;
}

//! Update sky-bg position
void m7_update_sky(const M7_LEVEL *level)
{
    REG_BG2HOFS= (level->camera->phi>>6)+M7_LEFT;
    REG_BG2VOFS= -clamp(level->horizon, 0, 228)-1;
}

The horizon calculation makes use of a clipping far-plane, though this is not strictly necessary. If you want the horizon at infinity, remove the subtraction by the camera’s height and use M7_FAR_BG = 1. Note the check for vy = 0. As vy = cos(θ), this will be true when looking straight up or straight down. The distinction is important because sees the sky (no affine bg) and one sees only floor (no backdrop). Technically these should be ±infinity, but as this is fixed-point, INT_MIN/MAX will have to do.

As for the backdrop placement: I’m taking a lot of shortcuts here. A mathematically correct backdrop would use a background map 1720 pixels wide. It can be done, but mostly it’s just annoying. Instead, I’m using a 512x256p regular background and use P = 1024 in the angle→scroll-offset conversion. This means the map shows up twice in one 360° rotation and that the dx is just φ/64. Yes, the floor and backdrop field-of-view will be slightly out of sync, but you’ll only notice if you know what to look for, so that’s alright.

Strictly speaking, the vertical offset should be bgHeight − horizon, but the bg-height can be ignored due to wrapping. The reason I’m also clamping the horizon to the size of the viewport is because the horizon scanline can become very large – the tan(θ) in it will approach infinity when looking up, remember? If you don’t clamp it you’ll scroll through the whole backdrop map a couple of times when panning up, which just looks awful.

Preparing the affine parameter table

Calculating the affine parameters happens in m7_prep_affines(). You could try to do this in the HBlank isr, but because it requires a division, it would simply take too long. Also, doing it in one spot is more efficient, as you only have to set-up the variables once. This routine carries out the calculations of eq 21.14. It has to do quite a number of calculations for each scanline, including a division, so you can expect it to be rather costly; which is why I’m putting it in IWRAM right from the start.

Now, you don’t have to calculate things for every scanline: just the ones below the horizon. As for implementing eq 21.14 itself: it turns out that it works much better if you take the camera matrix apart again and work with sines and cosines of θ and φ, rather than the nine matrix entries. This next paragraph will explain how, but feel free to skip it and go onto the code.

Remember that the camera matrix is C = Ry(φ)·Rx(θ); and that λ and dx are calculated via eq 21.13: dx′ = acw + λ·C·b. You can break up C can combine it with b to form b′ = Rx(θ)·b. This new vector takes care of the pitch entirely – it’s as if we only had a rotation around the vertical axis, i.e., the case discussed in the previous chapter. With this pre-rotation, the code becomes simpler and faster.

IWRAM_CODE void m7_prep_affines(M7_LEVEL *level)
{
    if(level->horizon >= SCREEN_HEIGHT)
        return;

    int ii, ii0= (level->horizon>=0 ? level->horizon : 0);

    M7_CAM *cam= level->camera;
    FIXED xc= cam->pos.x, yc= cam->pos.y, zc=cam->pos.z;

    BG_AFFINE *bga= &level->bgaff[ii0];

    FIXED yb, zb;           // b' = Rx(theta) *  (L, ys, -D)
    FIXED cf, sf, ct, st;   // sines and cosines
    FIXED lam, lcf, lsf;    // scale and scaled (co)sine(phi)
    cf= cam->u.x;      sf= cam->u.z;
    ct= cam->v.y;      st= cam->w.y;
    for(ii= ii0; ii<SCREEN_HEIGHT; ii++)
    {
        yb= (ii-M7_TOP)*ct + M7_D*st;
        lam= DivSafe( yc<<12,  yb);     // .12f

        lcf= lam*cf>>8;                 // .12f
        lsf= lam*sf>>8;                 // .12f

        bga->pa= lcf>>4;                // .8f
        bga->pc= lsf>>4;                // .8f

        // lambda·Rx·b
        zb= (ii-M7_TOP)*st - M7_D*ct;   // .8f
        bga->dx= xc + (lcf>>4)*M7_LEFT - (lsf*zb>>12);  // .8f
        bga->dy= zc + (lsf>>4)*M7_LEFT + (lcf*zb>>12);  // .8f

        // hack that I need for fog. pb and pd are unused anyway
        bga->pb= lam;
        bga++;
    }
    level->bgaff[SCREEN_HEIGHT]= level->bgaff[0];
}

We begin by getting the scanline to begin calculating at (which may be nothing), and defining lots of temporaries. Not all of the temporaries are necessary, but they make the code more readable. Names aside, the code within the loop is very similar to that of hbl_mode7_c in the first mode 7 demo, except that in calculating λ we use a rotated ys-value, and in calculating the offsets a rotated zs (= −D) value. Annnd, that’s it.

The comments behind the calculations indicate the fixed-point count of the results, which in this case can be either .8f or .12f. Now hear this: it is very important that the scaled (co)sine of φ, lcf and lsf, use 12 bits of precision or more. I’ve tried 8, it’s not pretty – the displacements are all off at close range. Secondly, note the order of multiplications and shifts in the displacements; it is also very important that these stay the way they are. Particularly the one with L: the multiplication by M7_LEFT must happen after the shift, trust me on this.

The last interesting point is the line after the loop, which copies the parameters for scanline 0 to the back of the array to compensate for the HBlank-interrupt obiwan error.

This function is probably as fast as you can make it in C, and it the compiler does its job pretty well so there is little to be gained by going to manual assembly. This does not mean it doesn’t still take quite some time. The division alone costs something like 100 to 400 cycles (the cycle-count for BIOS division is roughly 90 + 13/significant bit). At one division per scanline, this can really add up. The best strategy to deal with this is to not do it if you don’t have to. If you use a fixed pitch angle, you can precalculate all the divisions and just look them up. If you must have a variable pitch, you can also go the trig way. Look back at fig 21.14. If β is the angle between (0, yp, −D) and (0, 0, −D), then tan(β) = yp/D. With a good deal of trigonometry, you could rewrite the formula for λ to

(21.18) λ = a c w , y / D   cos ( β ) / sin ( θ + β )

You can get β via an arctan LUT of 160 entries, one for each scanline (hey, you could even put that into pd!), and then use a 1/sine LUT. You have to be careful to use large enough LUTs, though. Since the arguments of LUTs are integers, β will be truncated, and you will lose a lot of accuracy though this, especially near the horizon. Now, I haven’t actually tried the trig-way yet, but I have done some basic tests in Excel which would suggest that with a 1/sine LUT of 512/circle, you’d get λ-errors well over 10% near the horizon, and errors around 1% everywhere else. With that in mind, I’d suggest 1024/circle at least. Or interpolating between LUT entries, which you can do with libtonc’s lu_lerp16() and lu_lerp32() functions.

Aside from going triggy with it, you can probably speed up the division as well in a number of ways. But before you go and optimize this, ask yourself if you really need it first. Premature optimization is the root of all evil, after all.

Speed-ups for affine calculations

Tried three optimizations recently. First, ARM/IWRAM, which brings the thing down to 23k-58k cycles. Then, a little refactoring that presented itself in a discussion with sgeos: the camera vectors can resolve to a smaller set of variables, saving 10-20%. Then, the trig thing, which can bring the whole thing down to 10-20k or even 7k-14k max, depending on whether you get cos(β) and 1/sin(θ+β) via large luts, or smaller luts and linear interpolation. Once you get the math, shifts, and signs in order, it works like a charm.

The mode 7 HBlank interrupt routine

To keep things simple, nearly everything that has to happen during VDraw happens inside one HBlank isr called m7_hbl_floor(). Earlier versions of this demo used a system of VCount/HBlank interrupts, but that turned out to be more trouble than it’s worth. This is also an IWRAM routine because it really needs to be as fast as possible. The interrupt service routine does the following things:

  1. Check vcount for floor-range. If this scanline is not part of the floor, return.
  2. Check vcount for horizon. At reaching the horizon scanline the video mode should change and REG_BG2CNT should be set to the floor’s settings.
  3. Copy affine parameters to REG_BG_AFFINE[2]. Copy the next scanline’s parameters to REG_BG_AFFINE[2], as we’ve already past the current scanline.
  4. Fogging. Fade to orange in this case.
// from tonc_core.h
//! Range check; true if xmin<=x<xmax
#define IN_RANGE(x, min, max)  ( (x) >= (min) && (x) < (max) )
IWRAM_CODE void m7_hbl_floor()
{
    int vc= REG_VCOUNT;
    int horz= m7_level.horizon;

    // (1) Not in floor range: quit
    if(!IN_RANGE(vc, horz, SCREEN_HEIGHT) )
        return;

    // (2) Horizon: switch to mode 1; set-up bg control for floor
    if(vc == horz)
    {
        BF_SET(REG_DISPCNT, DCNT_MODE1, DCNT_MODE);
        REG_BG2CNT= m7_level.bgcnt_floor;
    }

    // (3) Looking at floor: copy affine params
    BG_AFFINE *bga= &m7_level.bgaff[vc+1];
    REG_BG_AFFINE[2] = *bga;

    // (4) A distance fogging with high marks for hack-value
    u32 ey= bga->pb*6>>12;
    if(ey>16)
        ey= 16;

    REG_BLDALPHA= BLDA_BUILD(16-ey, ey);
}

Points (3) and (4) could benefit from a bit more explanation. As mentioned several times now, the isr of any scanline vc should set-up the parameters of next scanline, which is why we’re copying from level.bgaff[vc+1] rather than just [vc]. Scanline zero’s uses the set from vc = 160, which is alright because we’ve copied zero’s data to the last element in the array. As usual, struct copies ftw.

For the fogging I use pb which filled with λ in m7_prep_affines() for this very reason. A scaled λ is not the most accurate model for fogging, but the effect looks well enough. Because the blending registers cap at 16, I need to make sure it doesn’t wrap around at higher values.

This still leaves the question of what I’m actually blending with, as orange isn’t part of the GBA’s fade repertoire. At least, not directly. It is, however, quite possible to blend with the backdrop, which just shows bg-color 0. This color can be anything, including orange.

Sprites and objects

Sprite and object handling has been distributed over the following three functions:

  • void update_sprites(). This is the main sprite handler, which calls other functions to do positioning, sorting and animation.
  • IWRAM_CODE void m7_prep_sprite(M7_LEVEL *level, M7_SPRITE *spr). This calculates the correct position and scale of the sprite.
  • void kart_animate(M7_SPRITE *spr, const M7_CAM *cam). This selects the correct frame for rotating around the karts.

Only m7_prep_sprite() is actually part of the mode 7 functions; the others could very well differ for every mode 7 game you have in mind. The main sprite handler, update_sprites(), is pretty simple: it needs to call m7_prep_sprite() for each sprite and create the sprite’s sorting key, sort all the sprites and copy the sorted attributes to OAM. It also calls kart_animate() for each kart-sprite for their animations; if I had animations for the thwomps or other sprites they’d probably go here as well.

void update_sprites()
{
    int ii;

    M7_SPRITE *spr= m7_level.sprites;
    for(ii=0; ii<SPR_COUNT; ii++)
    {
        m7_prep_sprite(&m7_level, &spr[ii]);

        // Create sort key
        if(BF_GET2(spr[ii].obj.attr0, ATTR0_MODE) != ATTR0_HIDE)
            sort_keys[ii]= spr[ii].pos2.z;
        else
            sort_keys[ii]= INT_MAX;
    }

    // Sort the sprites
    id_sort_shell(sort_keys, sort_ids, SPR_COUNT);

    // Animate karts
    for(ii=0; ii<8; ii++)
        kart_animate(&spr[ii], m7_level.camera);

    // Update real OAM
    for(ii=0; ii<SPR_COUNT; ii++)
        obj_copy(&oam_mem[ii], &spr[sort_ids[ii]].obj, 1);
}

Most of the code has to do with sorting the sprites, which was already described in the theory. The pos2 member of the sprites is set by m7_prep_sprite() to contain the sprite’s position in camera space. The sorting routine id_sort_shell() is the index-table sorter described in the priority section.

If I had wanted to have more advanced animation or sprite things, they’d be put here as well. But I didn’t, so I haven’t.

Sprite positioning and scaling

The function m7_prep_sprite() calculates the correct on-screen position for a sprite, sets up the affine matrix with the proper (renormalized) scales and hides the sprite if it falls outside the view volume.

The first step is convert to the convert the world-position of the sprite to a vector in the camera space, using the first part of eq 21.15: xc = CT·r, with r being the position of the sprite relative to the camera: r = xwacw. This is put into variable vc, but with the signs of y and z switched! This makes subsequent calculations a little easier. This vector is also stored in spr->pos2, which is used in sorting elsewhere.

The second step is checking whether the sprite would actually be visible, using the conditions from table 21.1, with one exception: the checks now use the renormalized rectangle of the sprite. Leaving that part out could create artifacts for some orientations. To calculate the sprite rectangle I’m using the sizes of the object rectangle. It is possible to get a tighter fit if you’d also define a sprite rectangle indicating the visible pixels within the object frame, but that might be going a little too far here.

Note that most of the code from the bounds checks on is done in a do-while(0) loop. This pattern is sort of a poor-man’s try/catch block – I could have used gotos here, but as they’re considered harmful I decided against it. Anyway, an out-of-bounds ‘exception’ here would indicate that the sprite should be hidden, which is done in step (5).

If we’ve passed the bounds-checks, we need to set-up the affine matrix and calculate the object’s position via the anchoring equation of eq 21.16.

//! Setup an object's attr/affine with the right attributes
/*! \param level    Mode 7 level data
*   \param spr      3D sprite to calculate for
*/
IWRAM_CODE void m7_prep_sprite(M7_LEVEL *level, M7_SPRITE *spr)
{
    M7_CAM *cam= level->camera;
    VECTOR vr, vc;      // Difference and inverted-cam vector
    int sx, sy;         // Object size
    RECT rect;          // Object rectangle

    // (1) Convert to camera frame
    vec_sub(&vr, &spr->pos, &cam->pos);
    vc.x=  vec_dot(&vr, &cam->u);
    vc.y= -vec_dot(&vr, &cam->v);
    vc.z= -vec_dot(&vr, &cam->w);
    spr->pos2= vc;

    OBJ_ATTR *obj= &spr->obj;
    sx= obj_get_width(obj);
    sy= obj_get_height(obj);

    // --- Check with viewbox ---
    do
    {
        // (2a) check distance
        if(M7_NEAR*256 > vc.z || vc.z > M7_FAR*256)
            break;

        // (2b) check horizontal
        rect.l= vc.x - spr->anchor.x*(256>>M7O_NORM);
        rect.r= rect.l + sx*(256>>M7O_NORM);
        if(M7_LEFT*vc.z > rect.r*M7_D || rect.l*M7_D > M7_RIGHT*vc.z)
            break;

        // (2c) check vertical
        rect.t= vc.y - spr->anchor.y*(256>>M7O_NORM);
        rect.b= rect.t + sy*(256>>M7O_NORM);
        if(-M7_TOP*vc.z > rect.b*M7_D || rect.t*M7_D > -M7_BOTTOM*vc.z)
            break;

        // (3) Set-up affine matrix
        OBJ_AFFINE *oa= &obj_aff_mem[spr->aff_id];
        oa->pa= oa->pd= vc.z>>(M7_D_SHIFT-M7O_NORM);    // normalized lambda
        oa->pb= oa->pb= 0;

        FIXED scale= DivSafe(M7_D<<16, vc.z);   // (.16 / .8) = .8

        // (4) anchoring
        // Base anchoring equation:
        // x = q0 - s - A(p0 - s/2)
        // In this case A = 1/lam; and q0 = xc/lam
        // -> x = (xc - p0 + s/2)/lam - s + screen/2
        int xscr, yscr;
        xscr  = spr->anchor.x*256 - sx*128;             // .8
        xscr  = (vc.x - (xscr>>M7O_NORM))*scale>>16;    // .0
        xscr += -sx - M7_LEFT;

        yscr  = spr->anchor.y*256 - sy*128;             // .8
        yscr  = (vc.y - (yscr>>M7O_NORM))*scale>>16;    // .0
        yscr += -sy + M7_TOP;
        obj_unhide(obj, ATTR0_AFF_DBL);
        obj_set_pos(obj, xscr, yscr);

        return;
    }
    while(0);

    // (5) If we're here, we have an invisible sprite
    obj_hide(obj);
}

Kart animation

The basic theory for animation around a sprite is simple, namely eq 21.17: the viewing angle ψ is the difference between the global sprite angle φo, and the camera angle φc and the angle to the sprite in camera-space α: ψ = φo−φc−α. The angle translates to an animation frame to use and you’re done.

In theory.

The practice has a number of snares, especially the way SMK does it. First, look at fig 21.16. These 12 frames are the ones that Super Mario Kart uses for Toad. The first complication is that this is only the right side of the rotation; the left side is done via mirroring. That’s easy enough: just change the sign of pa of the view-angle is negative.

The second problem is the number of tiles. 12 frames for half a circle means 24 for the full rotation (well 22 actually, as we don’t need to duplicate the front and back frames). At 4x4=16 tiles each, this gives 384 tiles for Toad alone (and only the rotation animation at that!) Multiply by 8 for the full set of characters and you’re way out of VRAM. This means that you can’t load all the frames into VRAM in one go and use an object’s tile-index for animation: you have to dynamically load frames you need. This is why the sprite struct had a tiles member, pointing to the full sprite sheet in ROM.

The third complication is that the frames aren’t uniformly divided over the circle. If you look closely, the first 8 frames are for angles 0° through 90°, the remaining four for 90°-180°. The reason behind this is that most of the time you’ll see the karts from the back, so it pays to have more frames for those. Now, in the theory we could calculate the animation frame quite nicely, namely N·ψ/216. However, that relied on having N equal slices, which we don’t have anymore. Or do we?

Well no, we don’t have equal slices anymore. But we can make equal slices again, using a sort of mapping. Fig 21.17 shows could the principle works. In the figure there are 12 main partitions (inside circle), with 0, 1, 10 and 11 covering more angular space than 2-9. However, we can also divide the circle into 16 parts (outer circle), and use the same frame for multiple entries. For example, slice-0 of the main sequence is now covered by slice-0 and slice-1 of the new sequence. While it’s possible to use if/else blocks to the mapping, it’s easier on everyone to just use a LUT for it. This actually takes care of two other problems I hadn’t mentioned before, namely that mirroring would require some sort of reversal of the normal sequence, and the fact that the slices actually have to be offset by half a slice so that you don’t have a slice-switch when looking exactly at the front or back, for example. A LUT solves all those problems in one go.

animation frames
Fig 21.16: Toad's frames from different angles.
view LUT
Fig 21.17: Using ψ for 16-element LUT entry, instead of 12 non-equal partitions.
const u8 cKartFrames[32]=
{
     0,  1,  2, 3, 4, 5, 6, 7, 7, 8, 8, 9, 9, 10, 10, 11,
    11, 10, 10, 9, 9, 8, 8, 7, 7, 6, 5, 4, 3,  2,  1,  0,
};

//! Animate kart sprite
void kart_animate(M7_SPRITE *spr, const M7_CAM *cam)
{
    OBJ_ATTR *obj= &spr->obj;

    if(BF_GET2(obj->attr0,ATTR0_MODE) == ATTR0_HIDE)
        return;

    TILE *dst= &tile_mem[4][BF_GET(obj->attr2, ATTR2_ID)];
    s16 psi= spr->phi - cam->phi;

    // Extra arctan angle for correctness
    if(g_state & STATE_OBJ_VIEW_ATAN)
        psi -= ArcTan2(spr->pos2.z>>8, spr->pos2.x>>8);

    memcpy32(dst, &spr->tiles[cKartFrames[(psi>>11)&31]*16], 16*8);

    OBJ_AFFINE *oa= &obj_aff_mem[spr->aff_id];
    if(psi < 0)
        oa->pa= -oa->pa;
}

The snippet above shows the kart’s angle-LUT and animation routine. The LUT has 32 entries, with the first and last 7 using single chunks and the rest being doubled. Also note that the LUT is symmetric, which is required for the mirroring.

The routine itself isn’t exactly pretty, but it gets the job done. It checks whether the sprite is visible first and bugs out if it’s not: no point in doing work if we can’t see its results. The sprite’s in-camera angle, α, requires an arctan. I’ve added a switch in the menu so you can see the results with and without the α-correction, and I think you’ll find that the difference is pretty small. Since I always use the same VRAM for each sprite, finding the destination of the tile-copy is easy; finding the source frame looks a little ugly, but it’s just the ψ→slice conversion and the look-up, really.

Rounding up: the main loop and other fluff

The hard parts of mode 7 have more or less been covered now, with the possible exception of the main loop, which we’ll get to in a moment. There is, of course, initialization of the registers, the sprites and mode 7 variables, loading of VRAM and input, but that’s rather easy and tends to vary from game to game anyway. For those things, please see the actual code.

The main program flow

In the snippet below you can see the main() function and its major branches. init_main() sets up the main mode 7 variables, m7_level through m7_init(), initializes the VBlank and HBlank interrupts and various other things. The main loop is quite short. The function input() does both the movement of the camera and menu.

After that come the actual mode 7 functions. m7_prep_horizon() has to come first, but the order of the rest is pretty arbitrary. I would suggest calling m7_prep_affines() last, though: it’s the most costly function here, but it’d be alright to let it run into VDraw time. Not that that happens here (I’ve clocked the main loop to end around scanline 170-210), but it’d be okay if it did.

int main()
{
    init_main();

    while(1)
    {
        VBlankIntrWait();
        input();

        m7_prep_horizon(&m7_level);
        // Switch to backdrop display.
        if(m7_level.horizon > 0)
        {
            BF_SET(REG_DISPCNT, DCNT_MODE0, DCNT_MODE);
            REG_BG2CNT= m7_level.bgcnt_sky;
            REG_BLDALPHA= 16;
        }
        m7_update_sky(&m7_level);

        update_sprites();
        m7_prep_affines(&m7_level);
    }

    return 0;
}

Movement in 3D

This is the last thing I want to cover: how to move things in 3D. To be precise: how to do different methods of motion in 3D; which I’m sure people might want to know.

3D movement is actually much the same as 2D movement, except with an extra dimension. The reason why people sometimes find it difficult is that they think in terms of angles, when what they should be thinking in is vectors. Vector-based movement (or vector-based anything) usually makes things much easier than with angles and trigonometry. This is also why the theory of this chapter has been using vectors and matrices.

Here I’ll look into three different modes of camera movements: one using the world coordinate system, one using the camera system, and one somewhere in between so that it stays parallel to the ground. But first, let’s take a look at what moving in a certain direction actually means.

Every object in 3D space has its own little coordinate space, the local frame. This is defined as a set of 3 vectors, denoting the directions of the local x, y and z directions. In the case of the camera, I named these u, v and w, respectively. The local matrix is just another way of writing down this set of vectors. Movement is usually defined as steps along these vectors.

As an example of this, consider your head to be the camera and use arrows to indicate the local axes: u would stick out of your right ear, v out of the top of your head and w out the back. A step right would be along the u direction, and one forward along −w. A general movement could be written as x steps right, y steps up, and z steps back. x, y and z are used as multipliers for the direction vectors, and the final displacement in global space is dx = x·u + y·v + z·w.

And where matrices come in. Those three multipliers can be written a vector r = (xyz), which is the distance vector in local space. The three directions formed a matrix C, The definition of dx given above is nothing else than the long way of writing down dx = C·r. The matrix multiplication is just shorthand for “scale the vectors of C by the elements of r and add them all up”. Note that this procedure would work for any object, in any orientation. All you need to do is find the correct local matrix.

In my case, I construct vector r in input(), based on various buttons. At this point it doesn’t really mean anything yet. Each of the movement methods has its own set of directions and hence its own matrix that has to be applied to r; I have functions that can perform them and add the results to the camera position. All of these can be found in table 21.2 and the code below it.

The ‘level’ (that is, level to the ground) is probably the most common for camera systems for ground-based objects, though using the local system might make sense for flying objects. Experiment with them and see what you like.

Table 21.2: Movement methods and their associated transformations to world-space. New position of an object is given by xw += vw.
Method Function Transformation
Global frame m7_translate_global() dx = I · r = r
Local (camera) frame m7_translate_local() dx = C(θ, φ) · r
Level: local but parallel to ground m7_translate_level() dx = Ry(φ) · r
//! Translate by \a dir in global frame
void m7_translate_global(M7_CAM *cam, const VECTOR *dir)
{
    vec_add_eq(&cam->pos, dir);
}

//! Translate by \a dir in local frame
void m7_translate_local(M7_CAM *cam, const VECTOR *dir)
{
    cam->pos.x += (cam->u.x * dir->x + cam->v.x * dir->y + cam->w.x * dir->z) >> 8;
    cam->pos.y += ( 0                + cam->v.y * dir->y + cam->w.y * dir->z) >> 8;
    cam->pos.z += (cam->u.z * dir->x + cam->v.z * dir->y + cam->w.z * dir->z) >> 8;
}

//! Translate by \a dir using local frame for x/y, but global z
void m7_translate_level(M7_CAM *cam, const VECTOR *dir)
{
    cam->pos.x += (cam->u.x * dir->x - cam->u.z * dir->z)>>8;
    cam->pos.y += dir->y;
    cam->pos.z += (cam->u.z * dir->x + cam->u.x * dir->z)>>8;
}

If you’re not really familiar with matrices they may seem bright and scary, but they can be a lifesaver once you get used to them a bit. There is a reason why large 3D systems use them non-stop; doing everything by raw trig is hard, very hard. Matrices allow you to work within whatever coordinate system is most natural to the task at hand, and then transform to whatever system you need in the end. If you have any work related to geometry, learning more about the basics of linear algebra (the rules for vector and matrix use) is well worth the effort.

Side note : centering on a sprite

As an example of how easy matrices can make life, consider the issue of centering the camera on a given sprite and then rotating around it. You have the camera matrix C, the distance you want to view from, Z and presumably the sprite position, xw. What you need to do is: move the camera to the sprite’s position, then take Z steps back. In other words acw = xw+C·(0, 0, Z), which boils down to acw = xw+Zw,

Once you know the camera matrix, positioning it practically writes itself.

Concluding remarks

It’s done, finally! This chapter’s text explained the most important elements of a mode 7 game: calculation of the affine parameters, adding a horizon and backdrop, positioning, sorting and animating 3D sprites and as a bonus how to use create a distance fogging effect. In the preceding text, I’ve used stuff from just about every subject described in the rest of Tonc, and not just the easy parts. If you’re here and understood all or most of the above, congratulations.

But still I’ve omitted a few things that would make it a little better. Getting rid of all those divisions in the λ calculations, for instance. Or getting around the 32 affine object limitation or placing shadows for the sprites on the floor. Nor have I shown how to correctly allow for loopings, instead of clamping the pitch at straight up or down. These things are relatively easy to grasp, conceptually, but implementing them would require a lot more code. If you understood this text, I’m sure you can figure it out on your own.

22. Tonc’s Text Engine

Introduction

The other page on text described how you could get text on backgrounds and objects. It worked, but there were several limitations. For instance, it was limited to 8×8 fonts, didn’t support all video modes and had no formatted text capabilities.

Tonc’s Text Engine (TTE) remedies many of these shortcomings. In this chapter I’ll describe the goals and basic design of the system and some of the implementation details. In particular, I’ll describe how to build writers for use of the different kinds of surfaces. In some cases, I’ll optimize the living hell out of them because it is possible for a glyph renderer to take multiple scanlines for a single character if you don’t pay attention. And yes, this will be done in assembly.

I’ll also show how you can add some basic scripting to change cursor positions, colors and even fonts dynamically. A few years ago, Wintermute changed the standard C library in devkitARM to make the stdio routines accessible for GBA and NDS. I’ll also show how you can make use of this.

And, of course, there will be demos. Oh, will there be demos. There are about 10 of them in fact, so I’m going to do things a little bit differently than before: there will be one project containing a menu with all the examples. Not all examples will be shown here because that’d just be too much.

Lastly, it is expected that by now you have a decent knowledge of GBA programming, so I’m going to keep the amount of GBA-specific exposition to a minimum. When you see functions used that haven’t been covered already, turn to GBATEK, the project’s code or libtonc’s code for details.

Basic design

TTE Goals

The following list has the things I most wanted in TTE:

  • A comprehensive and extensible set of glyph writers, usable for all occasions. Well almost all occasions. The old system worked for regular backgrounds, bitmap modes and objects, I’m now extending that set to affine backgrounds and tile-rendering. If what you need isn’t present in the standard set, you can easily create your own writer and use that one instead. The writer will accept UTF-8 strings, meaning you’re not limited to 256 characters.
  • Fonts: arbitrary widths and heights and variable width characters. Instead of being limited to 8x8@1 glyphs; the standard writers in TTE are able to use fonts of any width and height (within reason: no screen-filling glyphs please) and variable width fonts (again, within reason: VWF for tilemaps makes little sense). In principle, there are possibilities to use arbitrary bitdepths as well, but the standard renderers are limited to 1bpp.
  • A simple writer-interface independent of surface details. For the old system I had m3_puts(), se_puts(), obj_puts() and such. This worked, but it meant you had to use something different for the different modes. In TTE, there are different initializers for the different modes to set up the system, and a single string writer tte_write() that just works.
  • Scripting for text parameters. By that I mean that you can control parameters like position and output color by the strings themselves. The functionality for this is pretty basic, but it works well enough. Note: this is not a full dialog system! That said, it should be possible to build one around it.
  • printf() support. For rather obvious reasons.

Structures and main components

All the relevant information for TTE is kept gathered in three structs: a text context, TTC; a font description, TFont; and a graphic surface description, TSurface.

The TTC struct contains the main parameters for the engine: information about the surface were rendering to, cursor positions, font information, color attributes and a few other things. It also contains two callbacks for drawing and erasing glyphs.

The TFont struct has a pointer to the glyph data, glyph/cell dimensions and a few other things. There are also pointers to width and height tables to allow variable width and height fonts. I’ve hacked a TFont creator into usenti a while back so that I could easily create these things from standard fonts, but you can also make your own from scratch.

The TSurface struct actually has nothing to do with text. Instead, it’s a struct describing the kind of surface we’re rendering on. This can be bitmaps, tiles, tilemaps or whatever. Tonclib has basic pixel, line and rectangle routines for dealing with these surfaces, so I might as well use them.

//# From tonc_tte.h : main TTE types.

typedef struct TFont
{
    const void  *data;      //!< Character data.
    const u8    *widths;    //!< Width table for variable width font.
    const u8    *heights;   //!< Height table for variable height font (mostly unused).
    u16 charOffset;         //!< Character offset
    u16 charCount;          //!< Number of characters in font.
    u8  charW;              //!< Character width (fwf).
    u8  charH;              //!< Character height.(fhf).
    u8  cellW;              //!< Glyph cell width.
    u8  cellH;              //!< Glyph cell height.
    u16 cellSize;           //!< Cell-size (bytes).
    u8  bpp;                //!< Font bitdepth;
    u8  extra;              //!< Padding. Free to use.
} TFont;

//! TTE context struct.
typedef struct TTC
{
    // Members for renderers
    TSurface dst;           //!< Destination surface.
    s16 cursorX;            //!< Cursor X-coord.
    s16 cursorY;            //!< Cursor Y-coord.
    TFont *font;            //!< Current font.
    u8  *charLut;           //!< Character mapping lut, if any.
    u16 cattr[4];           //!< ink, shadow, paper and special color attributes.
    // Higher-up members
    u16 reserved;
    u16 ctrl;               //!< BG control flags.
    u16 marginLeft;
    u16 marginTop;
    u16 marginRight;
    u16 marginBottom;
    s16 savedX;
    s16 savedY;
    // Callbacks and table pointers
    fnDrawg  drawgProc;         //!< Glyph render procedure.
    fnErase  eraseProc;         //!< Text eraser procedure.
    const TFont **fontTable;    //!< Pointer to font table for
    const char  **stringTable;  //!< Pointer to string table for
} TTC;
//# Supporting types

//! Glyph render function format.
typedef void (*fnDrawg)(int);

//! Erase rectangle function format.
typedef void (*fnErase)(int left, int top, int right, int bottom);

typedef struct TSurface
{
    u8  *data;          //!< Surface data pointer.
    u32 pitch;          //!< Scanline pitch in bytes.
    u16 width;          //!< Image width in pixels.
    u16 height;         //!< Image width in pixels.
    u8  bpp;            //!< Bits per pixel.
    u8  type;           //!< Surface type.
    u16 palSize;        //!< Number of colors.
    u16 *palData;       //!< Pointer to palette.
} TSurface;

TFont details


Fig 22.1: Verdana 9 character sheet

Fig 22.1 shows a character sheet that TFont can use. The sheet is a matrix of cells and each cell contains a character. The cellW/H members are the dimensions of these cells; cellSize is the number of bytes per cell.

Each cell has one glyph, but the actual glyphs can be smaller than the cells (white vs magenta parts). This does waste a bit of memory, but it also has several benefits. One of the benefits is that you can use cellSize to quickly find the address of any given glyph. Second, because I want by fonts to be usable for both bitmaps and tiles, my glyph boxes would have to be multiples of 8 anyway. Additionally, this particular font will be 1bpp, meaning that even with the wasted parts I’ll still have a very low memory footprint (3.5kB).

For fixed-width or fixed-height fonts, members charW and charH denote the actual character width and height. For fonts of variable widths, the widths member points to the a byte-array containing the widths of the glyphs and something similar is true for the heights. charOffset is the (ASCII) character the data starts at. Font sheets often start at a space (’ ’), so this tends to be 32. charCount is the number of characters and can be used if you need to copy the whole sheet to VRAM (like in the case of tile-mapping).

Please note that how the data in a TFont is used depends almost entirely on the glyph renderer. Most renderers that come with libtonc expect this format:

  • Bitpacked to 1 bpp, for size reasons. And for rendering speed too, actually, since memory loads are expensive.
  • Tiled-by-glyph. The data for each glyph is contingent with cellSize bytes between each glyph. This is similar to how 1D object work with one important difference:
  • the tiles in each glyph are column-major (tile 1 is under tile 0). This in contrast to objects, which tend to be row-major (tile 1 is to the right of tile 0). I will refer to this format as tile-strips. The reason behind this choice will be given later.

There are exceptions to this, but most renderers presented here will use this format. If you want to make your own renderers, you’re free to use any format for the data you think is appropriate.

TTC details

The text context, TTC, contains the most important data of the system. Starting at the top: the surface, dst. This defines the surface we’re rendering to. The most relevant items there are its memory address, pitch: the number of bytes per scanline. The pitch is a very important parameter for rendering, more important than the width and height in fact. The surface also has palette members, which can be used to access its colors. Much like the TFont members, how this data is used largely depends on the renderer.

The members cursorX/Y are for the current cursor position. The margin rectangle indicates which part of the screen should be used for text. If the cursor exceeds the right margin, it will be moved to the left margin and one line down. The margins are also used for screen-clears and returning to the top of the page.

The cattr table is something special. Its entries are color attributes. Parameters for ink (foreground color), shadow, paper (background color) are put here, along with a ‘special’ field which is very much context-specific. Note that these color attributes do not necessarily represent colors. In modes 3 and 5 they’re colors, but for mode 4 and tile writers they’re color indices. There’s probably a nicer name for this than ‘color attribute’, but sodomy non sapiens.

Rendering glyphs and erasing (parts of) the screen is done through the callbacks drawgProc and eraseProc. The idea is that you initialize the system with the routines appropriate for your text format and TTE uses them to do the actual writing. I should point out that using callbacks for rendering a single glyph can have a significant overhead, especially for the simpler kinds of text like tilemaps.

Main TTE variables and functions.

The state of the TTE system is kept in a TTC variable accessible through tte_get_context(). All changes to the system go through there. In some cases, it is useful to have two sets of state and switch between them when appropriate (like when you have two screens. Y hello thar, NDS). For that you can use tte_set_context) to redirect the pointer.

TTC __tte_main_context;
TTC *gp_tte_context= &__tte_main_context;

//! Get the master text-system.
INLINE TTC *tte_get_context()
{   return gp_tte_context;                          }


//! Set the master context pointer.
void tte_set_context(TTC *tc)
{
    gp_tte_context= tc ? tc : &__tte_main_context;
}

To print characters, you can use tte_putc() and tte_write().

//! Get the glyph index of character \a ch.
INLINE uint tte_get_glyph_id(int ch)
{
    TTC *tc= tte_get_context();
    ch -= tc->font->charOffset;
    return tc->charLut ? tc->charLut[ch] : ch;
}

//! Get the width of glyph \a id.
INLINE uint tte_get_glyph_width(uint gid)
{
    TFont *font= tte_get_context()->font;
    return font->widths ? font->widths[gid] : font->charW;
}

//! Render a character.
int tte_putc(int ch)
{
    TTC *tc= tte_get_context();
    TFont *font= tc->font;

    // (4) translate from character to glyph index
    uint gid= tte_get_glyph_id(ch);

    // (5) get width for cursor update
    int charW= tte_get_glyph_width(gid);

    if(tc->cursorX+charW > tc->marginRight)
        [[ simulate newline ]]

    // (6) Draw and update position
    tc->drawgProc(gid);
    tc->cursorX += charW;

    return charW;
}
//! Render a string.
/*! \param text String to parse and write.
    \return     Number of parsed characters.
*/
int tte_write(const char *text)
{
    int ch;
    uint gid, charW;
    const char *str= text;
    TTC *tc= tte_get_context();

    while( (ch= *str++) != '\0' )
    {
        // (1) Act according to character type
        switch(ch)
        {
        case '\n':  [[ update cursorX/Y for newline ]];     break;
        case '\t':  [[ update cursorX for tab ]];           break;
        default:
            // (2) more special thingies
            if(ch=='#' && str[0]=='{')          // (2a) Command sequence
            {
                str= tte_cmd_default(str+1);
                break;
            }
            else if(ch=='\\' && str[0]=='#')    // (2b) Escaped command
                ch= *str++;
            else if(ch>=0x80)                   // (2c) UTF8 character
                ch= utf8_decode_char(str-1, &str);

            // (3) draw character
            tte_putc(ch);
        }
    }

    return str - text;
}

I’ve omitted the code for a few things here, the idea should be clear. First, read a character. Then, check whether it’s a special character (new line, tab, formatting command) and if so, act accordingly. Because tte_write() supports UTF-8, we also check for that and decode the string for a full UFT-8 character. After that’s all done, we pass the character on to tte_putc(), which translates it to a glyph index, draws the glyph and advances the cursor.

Note: the way described here is a method of doing things; it’s not the method, because that doesn’t actually exist. Several steps done here may be overkill for the kind of text you had in mind. For example, getting from the character to the glyph index is done by the font’s character offset and a potential character look-up table, neither of which is strictly necessary. Likewise, wrapping at the edges may already be done in the string itself with newline characters. On the other hand, you might like more complex wrapping, text alignment, scrolling, and who knows what else. If you want these things, creating your own routine shouldn’t be too difficult.

On nomenclature

Some terms I use in TTE have a very specific meaning. Because the differences between terms can be subtle, it is important to define the term explicitly. Additionally, TTE uses several acronyms and abbreviations that need to be clarified.

  • char(acter) vs glyph index. ‘Character’ refers to the ASCII character; the ‘glyph index’ is the corresponding index in the font. For example, ‘A’ is character 65, but if the font starts at a space (’ ’, ASCII 32) the ‘A’ is glyph index 65−32=33. As a rule, variables named ch are characters and gid means glyph index. The input of the renderers is the glyph index, and not the character.

  • Surface. Surface is the term I’m using to describe whatever I’m manipulating to show text. This is usually VRAM, but can be other things as well, like OBJ_ATTRs for object text.

  • Pitch. The pitch is actually a common term in graphics, but since graphics terms may not be so common, it’s worth repeating. Technically, the pitch is the number of scanlines between rows. I’m extending it a little to mean the characteristic major distance for matrices. Matrices are 2D entities, and they’ll have adjacent elements in one direction and a larger distance for the other. These usually are x and y, respectively, but not always. The minor distance will be referred to as stride.

  • Color vs color attribute. The ‘color’ is the real 5.5.5 BGR color; the ‘color attribute’ is whatever the renderer will use on the surface. This can be a color, but it can also be a palette index or something else entirely. The interpretation is up to the renderer.

  • Render/Text family. This is a conceptual group-name for a specific kind of text. Table 22.1 gives an overview of the families available. This largely corresponds to the TSurface types.

  • Renderer types. Within each family there can be different renderers for different kinds of fonts and effects. For example, when rendering to an 8bpp bitmap (the bmp8 family), you can have different renderers for different font bitdepths (1bpp or 8bpp, for example) or glyph layouts (bitmapped or tiled). They can render some pixels transparently, or apply anti-aliasing. Or any combination of those. The point is there are a lot of options here.

    Because I really don’t like names that span a whole line, I will use abbreviations in the renderer’s name to indicate what it does; see table 22.2 for what they mean. For the most part, the renderers will be for fonts with arbitrary width and height, with a 1bpp tile-stripped glyphs, with they will draw them transparently and re-coloring of pixels. This is indicated by *_b1cts.

Table 22.1: TTE render family indicators and initializers. 4bpp Tiles can be row or column major (crh4r or chr4c).
Family prefix Initializer
Regular tilemap (mode 0/1) se void tte_init_se(int bgnr, u16 bgcnt, SCR_ENTRY se0, u32 colors, u32 bupofs, const TFont *font, fnDrawg proc);
Affine tilemap (mode 1/2) ase void tte_init_ase(int bgnr, u16 bgcnt, u8 ase0, u32 colors, u32 bupofs, const TFont *font, fnDrawg proc);
4bpp Tiles (modes 0/1/obj) chr4(c/r) void tte_init_chr4(c/r)(int bgnr, u16 bgcnt, u32 cattrs, u32 colors, const TFont *font, fnDrawg proc);
8bpp bitmap (mode 4) bmp8 void tte_init_bmp(int vmode, const TFont *font, fnDrawg proc);
16bpp bitmap (mode3/5) bmp16 void tte_init_bmp(int vmode, const TFont *font, fnDrawg proc);
objects obj void tte_init_obj(OBJ_ATTR *dst, u32 attr0, u32 attr1, u32 attr2, u32 colors, u32 bupofs, const TFont *font, fnDrawg proc);

Table 22.2: Render type summary.
Code Description
bx Bitdepth of source font. (b1 = 1 bpp)
wx Specific width (w8 = width 8)
hx Specific height (h8 = height 8)
c Re-coloring. Color attributes are applied to the pixels in some way.
t/o Transparent or opaque paper pixels.
s Glyphs are in tile-strip format.

Lastly, a note on some of the abbreviations I use in the rendering code. A number of terms come up again and again, and I’ve taken to use a shorthand notation for these items. The basic format is fooX where foo is the relevant bitmap/surface and X is a one-letter code for things like width, height, data and others. Yes, the use of single-letter names is frowned upon and I don’t advocate their use in general, but I’ve found that in this particular case, if used judiciously, they have helped me read my own code.

Table 22.3: Abbreviations used in rendering code.
Term Meaning
fooW Width of foo
fooH Height of foo
fooB Bitdepth of foo
fooP Pitch of foo
fooD Primary data-pointer for foo
fooL Secondary data-pointer for foo
fooS Size of foo
fooN Number/count of foo

Tilemapped text

Regular tilemap text

Tilemapped text is the easiest to implement, because you don’t really have to render anything at all. You simply load up all the font’s tiles into a charblock and place screen-entries for the actual text.

The initializer for regular tilemaps is tte_init_se(). It’s identical to txt_init_se() except for the two extra parameters at the end: font and proc. These represent the font to use and the renderer that does the surface manipulation. Every initializer in TTE has those two parameters. It’s safe to pass NULL to them if you’re not sure what to use; in that case, the default option for that family will be used.

If font is NULL, you’ll get the default font. This is either system8Font for fixed-width occasions or verdana9Font (fig 22.1) when variable width is suitable. These can also be referenced via fwf_default and vwf_default, respectively.

Each family also has a default renderer, #defined as foo_drawg_default, where foo is the family prefix. The default renderers are the general routines, suitable for all character widths and heights (fixed or variable fonts). Of course, this does mean that they will be slower than routines written to work with a specific glyph size. This is particularly true for tilemapped text, and for that reasons specific _w8h8 and _w8h16 versions are available there as well.

The initializers tend to be long and boring, so I won’t waste too much space on them here. Basically, they clear out the text context, assign some sensible values to the margins and surface variables, set up the font, the renderer and the eraser. They also fill some of the palette and color attributes.

The code I’ll show in this chapter will mostly be about the renderers themselves. Below you can see the code for the default screen-entry writer, se_drawg_s(), and the one specific for 8×8 fonts, se_drawg_w8h8

//! Character-plot for reg BGs, any sized, vertically tiled font.
void se_drawg_s(uint gid)
{
    int ix, iy;

    // (1) Get main variables.
    TTC *tc= tte_get_context();
    TFont *font= tc->font;
    uint charW= (font->cellW+7)/8, charH= (font->cellH+7)/8;

    uint x0= tc->cursorX, y0= tc->cursorY;
    uint dstP= tc->dst.pitch/2;
    u16 *dstD= (u16*)(tc->data + (y0*dstP+x0)*2);

    // (2) Get the base tile index.
    u32 se= tc->cattr[TTE_SPECIAL] + gid*charW*charH;

    // (3) Loop over all tiles to draw glyph.
    for(ix=0; ix<charW; ix++)
    {
        for(iy=0; iy<charH; iy++)
            dstD[iy*dstP]= se++;
        dstD++;
    }
}

//! Character-plot for reg BGs using an 8x8 font.
void se_drawg_w8h8(uint gid)
{
    TTC *tc= tte_get_context();

    uint x0= tc->cursorX, y0= tc->cursorY;
    uint dstP= tc->dst.pitch/2;
    u16 *dstD= (u16*)(tc->data + (y0*dstP+x0)*2);

    dstD[0]= tc->cattr[TTE_SPECIAL] + gid;
}

Let’s start with the simpler one: se_drawg_w8h8(). An 8×8 glyph on a GBA tilemap simply means write a single screen-entry to the right place. The right place here is derived from the cursor position and the surface data (tc->dst). The ‘special’ color attribute is used as a modifier to the glyph index for things like palette swapping.

Note that the routine just handles plotting the glyph. Transforming from ASCII to glyph index and repositioning the cursor is all done elsewhere.

The more generalized routine, se_drawg_s() is a little more complex. It still starts by getting a pointer to the glyph’s destination, dstD, and pitch (the distance to the next line), dstP. All renderers start with something like this. All renderers also retrieve the character’s width and height – unless the sizes are specified in advance. The names I use for rendering are always the same, so you should be able to tell what means what even when the formulas for initializing them can be a tad icky.

Anyway, after getting the pointer and pitch, the tile-index for the top-left of the glyph is calculated and put this into se. After that, we loop over the different tiles of the glyph in both directions. Note that the order of the loop is column-major, not row-major, because that’s the way the default fonts were ordered.

As it happens, column-major rendering tends to be more efficient for text, because glyphs are usually higher than they are wide. Also, for tilemap text charW and charH tend to be small – often 1 or 2. This means that it is extremely inefficient to use loops; we’ll see how inefficient in the “Profiling the renderers” subsection.. Unrolling them, like se_drawg_w8h8() and se_drawg_w8h16() do, gives a much better performance.

Regular tilemap example

void test_tte_se4()
{
    irq_init(NULL);
    irq_add(II_VBLANK, NULL);
    REG_DISPCNT= DCNT_MODE0 | DCNT_BG0;

    // --- (1) Base TTE init for tilemaps ---
    tte_init_se(
        0,                      // Background number (BG 0)
        BG_CBB(0)|BG_SBB(31),   // BG control (for REG_BGxCNT)
        0,                      // Tile offset (special cattr)
        CLR_YELLOW,             // Ink color
        14,                     // BitUnpack offset (on-pixel = 15)
        NULL,                   // Default font (sys8)
        NULL);                  // Default renderer (se_drawg_s)

    // --- (2) Init some colors ---
    pal_bg_bank[1][15]= CLR_RED;
    pal_bg_bank[2][15]= CLR_GREEN;
    pal_bg_bank[3][15]= CLR_BLUE;
    pal_bg_bank[4][15]= CLR_WHITE;
    pal_bg_bank[5][15]= CLR_MAG;

    pal_bg_bank[4][14]= CLR_GRAY;

    // --- (3) Print some text ---

    // "Hello world in different colors"
    tte_write("\n Hello world! in yellow\n");
    tte_write(" #{cx:0x1000}Hello world! in red\n");
    tte_write(" #{cx:0x2000}Hello world! in green\n");

    // Color use explained
    tte_set_pos(8, 64);
    tte_write("#{cx:0x0000}C#{cx:0x1000}o#{cx:0x2000}l");
    tte_write("#{cx:0x3000}o#{cx:0x4000}r#{cx:0x5000}s");
    tte_write("#{cx:0} provided by \\#{cx:#}.");


    // --- (4) Init for 8x16 font and print something ---
    GRIT_CPY(&tile_mem[0][256], cyber16Glyphs); // Load tiles
    tte_set_font(&cyber16Font);                 // Attach font
    tte_set_special(0x4100);                    // Set special to tile 256, pal 4
    tte_set_drawg(se_drawg_w8h16);              // Attach renderer

    tte_write("#{P:8,80}Also available in 8x16");

    key_wait_till_hit(KEY_ANY);
}

The code above demonstrates a few of the things you can do with TTE for tilemaps. The call to tte_init_se() initializes the system to display text on BG 0, using charblock 0 and screenblock 31 and to use the default font and renderer. Parameter five is the bit-unpack offset; by setting it to 14, all the 1-valued pixels in the font move to 14+1=15, the last index in a palette bank. I’m also setting a few other colors so that the palette will look like fig 22.3b.

In step 3, I print some text with tte_write(). The different colors are done by using #{cx:num} in the string, which sets the special color-attribute to num. More on these kinds of commands in the “Scripting, console IO and other niceties” section.. Since the se-renderers add this value to the glyph index for the final output, it can be used for palette swapping.

Step 4 demonstrates how to load up and use a second font. The cyber16Font is a rendition of the 8×16 font used in ye olde SNES game, Cybernator (see fig 22.2). This font was exported as 4bpp data so I can just copy it into VRAM directly, but I do need to use an offset because I want to keep the old font as well. The charblock now has two sets of glyphs (see fig 22.3c).

Cybernator font: 8×16.
Fig 22.2: Cybernator font: 8×16.
test_tte_se4
Fig 22.3a: test_tte_se4 output.
Palette for <code>test_tte_se4</code>.
Fig 22.3b: Palette.
VRAM Tiles for <code>test_tte_se4</code>.
Fig 22.3c: Tileset.

In principle, all I need to do to use a different font is to select it with tte_set_font(), but since the tiles are at an offset, I also need to adjust the special color attribute. The value of 0x4100 is used here to account for the offset (0x0100) as well as the palette-bank (0x4000). I’m also selecting a different renderer for the occasion, although that’s mostly for show here because the default renderer can handle 8×16 fonts just as well. After that, I just call tte_write() again to print a new string in using the new font.

Affine tilemap text

Text for affine tilemaps works almost the same as for regular tilemaps; you just have to remember the differences between the two kinds of backgrounds, like map size and available bitdepth. The functions’ prototypes are the same, except that se is replaced by ase.

Internally, the only real difference is in what the renderers are to output, namely bytes instead of halfwords. And here we run into that quaint little fact of VRAM again: you can’t write single bytes to VRAM. This means that the renderers will be a little more complicated. But only a little: simply call a byte-plotting routine for the screen-entry placement. Because affine maps are essentially 8bpp bitmap surfaces, I can use the standard plotter for 8bpp bitmap surfaces: _sbmp8_plot(). Aside from this one difference, the ase_ renderers are identical to the se_ counterparts.


//! Character-plot for affine BGs using an 8x8 font.
void ase_drawg_w8h8(uint gid)
{
    TTC *tc= tte_get_context();
    u8 se= tc->cattr[TTE_SPECIAL] + gid;

    _sbmp8_plot(&tc->dst, tc->cursorX/8, tc->cursorY/8, se);
}

//! Character-plot for affine BGs, any sized, vertically oriented font.
void ase_drawg_s(int gid)
{
    TTC *tc= tte_get_context();
    TFont *font= tc->font;
    uint charW= (font->cellW+7)/8, charH= (font->cellH+7)/8;
    uint x0= tc->cursorX/8, y0= tc->cursorY/8;

    u8 se= tc->cattr[TTE_SPECIAL] + gid*charW*charH;

    int ix, iy;
    for(ix=0; ix<charW; ix++)
        for(iy=0; iy<charH; iy++, se++)
            _sbmp8_plot(&tc->dst, ix+x0, iy+y0, se);
}

The demo for affine map text is text_tte_ase(). The idea is simple here: set up the text for a 256×256 pixel map, write some text onto it and rotate the background to illustrate that it is indeed an affine background. The center of rotation is the “o” at the center of the screen. To place it there, I’ve used the #{P:x,y} code; this sets the cursor to the absolute position given by (x, y). The other string is also positioned on the map in this manner.

void test_tte_ase()
{
    irq_init(NULL);
    irq_add(II_VBLANK, NULL);
    REG_DISPCNT= DCNT_MODE1 | DCNT_BG2;

    // Init affine text for 32x32t bg
    tte_init_ase(
        2,                      // BG number
        BG_CBB(0) | BG_SBB(28) | BG_AFF_32x32,  // BG control
        0,                      // Tile offset (special cattr)
        CLR_YELLOW,             // Ink color
        0xFE,                   // BUP offset (on-pixel = 255)
        NULL,                   // Default font (sys8)
        NULL);                  // Default renderer (ase_drawg_s)

    // Write something
    tte_write("#{P:120,80}o");
    tte_write("#{P:72,104}Round, round, #{P:80,112}round we go");

    // Rotate it
    AFF_SRC_EX asx= { 124<<8, 84<<8, 120, 80, 0x100, 0x100, 0 };
    bg_rotscale_ex(&REG_BG_AFFINE[2], &asx);

    while(1)
    {
        VBlankIntrWait();
        key_poll();

        asx.alpha += 0x111;
        bg_rotscale_ex(&REG_BG_AFFINE[2], &asx);

        if(key_hit(KEY_START))
            break;
    }
}
<code>test_tte_ase</code>.
Fig 22.4: test_tte_ase.

Bitmapped text

Bitmap text rendering is a little different from map text and can range in difficulty from easy to insane, depending on your wishes. At its core, though, it’s always the same process: loop over all pixels and draw them on the destination surface. For example, a generic glyph renderer that draws pixels transparently could look something like this.

// Pseudo code for a general glyph printer.
void foo_drawg(uint gid)
{
    TTC *tc= tte_get_context();
    TFont *font= tc->font;

    // Drawing with color keying.
    // Loop over all pixels. If the glyph's pixel is not zero, draw it.
    // Other wise, nevermind.
    for(iy=0; iy<tte_get_glyph_height(gid); iy++)
    {
        for(ix=0; ix<tte_get_glyph_width(gid); ix++)
        {
            u16 color= font_get_pixel(font, gid, ix, iy);
            if(color != 0)
                foo_plot(&tc->dst, tc->cursorX+ix, tc->cursorY+iy, color);
        }
    }
}

Here, foo can mean any rendering family. foo_plot() is a general pixel plotter and font_get_pixel() a pixel retriever. The implementations of those functions depend on the specifics of the font and surface, but the glyph renderer doesn’t need to know about that.

Basic bmp16 to bmp16 glyph printer

This next function is an example of a 16bpp font to 16bpp bitmap printer.

//! Glyph renderer from bmp16 glyph to bmp16 destination.
void bmp16_drawg(uint gid)
{
    // (1a) Basic variables
    TTC *tc= tte_get_context();
    TFont *font= tc->font;

    u16 *srcD= (u16*)(font->data+gid*font->cellSize), *srcL= srcD;
    uint charW= tte_get_glyph_width(gid)
    uint charH= tte_get_glyph_height(gid);

    uint x0= tc->cursorX, y0= tc->cursorY;
    uint srcP= font->cellW, dstP= tc->dst.pitch/2;
    u16 *dstD= (u16*)(tc->dst.data + (y0*dstP + x0)*2);

    // (2) The actual rendering
    uint ix, iy;
    for(iy=0; iy<charH; iy++)
    {
        for(ix=0; ix<charW; ix++)
            if(srcD[ix] != 0)
                dstD[ix]= srcD[ix];

        srcD += srcP;
        dstD += dstP;
    }
}

Blocks 1a and 1b set up the main variables to use in the loop. The most important are the source and destination pointers, srcD and dstD, and their pitches, srcP and dstP. Notice that the source pitch, srcP, is the not the character width, but the cell width, because the fonts are organized on a cell-grid. The code at point 2 selectively copies pixels from the font to the surface.

Intermezzo : considerations for performance

You may wonder why bmp16_drawg() doesn’t follow the pattern in the earlier foo_drawg() more closely. The answer is, of course, performance. And before anyone quotes Knuth on me: not every effort to make your code fast is premature optimization. When you can improve the speed of the code without spending too much effort of a loss of readability, there’s not much reason not to.

In this case, the optimizations I’ve applied here fall into two categories: local variables and pointer arithmetic. These techniques – that every C programmer should know – managed to boost the speed by a factor of 5.

Let’s start with pointers. I’m using pointer to my advantage in two places here. First, instead of using the font-data pointer and destination pointer directly, I create pointers srcD and dstD and d