Solving the mystery of ARM7TDMI multiply carry flag

The processor in the Game Boy Advance, the ARM7TDMI, has a weird characteristic where the carry flag is set to a “meaningless value” after a multiplication operation.

What this means is that software cannot and should not rely on the value of the carry flag after multiplication executes. It can be set to anything. Any value. 0, 1, a horse, whatever. This has been a source of memes in the emulator development community for a few years – people would frequently joke about how the implementation of the carry flag may as well be cpu.flags.c = rand() & 1;. And they had a point – the carry flag seemed to defy all patterns; nobody understood why it behaves the way it does. But the one thing we did know, was that the carry flag seemed to be deterministic. That is, under the same set of inputs to a multiply instruction, the flag would be set to the same value. This was big news, because it meant that understanding the carry flag could give us key insight into how this CPU performs multiplication.

And just to get this out of the way, the carry flag’s behavior after multiplication isn’t an important detail to emulate at all. Software doesn’t rely on it. And if software did rely on it, then screw the developers who wrote that software. But the carry flag is a meme, and it’s a really tough puzzle, and that was motivation enough for me to give it a go. Little did I know it’d take 3 years of on and off work.
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Please don’t make me understand any of this.