Remove most instances of float usage

[dxxb]

This PR is not intended for merging as-is. It could be but at a minimum the game needs to be tested and constants / computation may need to be re-tuned. With a bit more effort the last instances of float could be removed (and fixed point trigonometric function used).

Aside from freed up RAM and flash, the speed gain is likely large.

Before:

Program:   28562 bytes (87.2% Full)
(.text + .data + .bootloader)

Data:       1929 bytes (75.4% Full)
(.data + .bss + .noinit)

After (with logo enabled):

Program:   25092 bytes (76.6% Full)
(.text + .data + .bootloader)

Data:       1715 bytes (67.0% Full)
(.data + .bss + .noinit)

[mschwartz]

I tried this early on.

The rounding errors were only part of the problem. 16 bit ints simply do no hold a large enough number. If the joystick Left is held long enough, camera x wraps and enemies and bullets think they’re very far away from the camera. It’s a worse effect in z because all you have to do is survive long enough.

[mschwartz]

Also, as fixed point gets more resolution, the less integer portion and the more costly it is to shift out the fraction.

Moving to longs migh only be a bit better performance, but perhaps the gains in program and RAM minimal, if at all.

[dxxb]

Also, as fixed point gets more resolution, the less integer portion and the more costly it is to shift out the fraction.

Q8.8 are used so in most cases there is no shift involved. Anyway, regardless of the size of the integer portion, 16bit fixed point beats floats on the AVR.

16 bit ints simply do no hold a large enough number.

The game seems mostly fine to me. If something wasn't right I'd try looking for a workaround without sacrificing integer math. One could even say that a glitch once in a while is not that bad compared with what memory/speed gains can allow you to do. About wraparound, if I recall correctly objects in the game world and the camera can never be very far from each other (256 units?). My guess is that we could take advantage of this to prevent glitches caused by wraparound.