Fixed Math

This library implements analytic/trigonometric functions for fixed point numbers.

Implemented functions:

sqrt from trait Sqrt
- Sqrt is not implemented for fixed numbers with less than 2 integer bits, but there are functions that work on those types: sqrt_i1, ...
sin_cos, sin, cos, tan from trait SinCos
- SinCos is not implemented for fixed numbers with less than 8 (TODO 7) integer bits because the there are table values that would overflow on those types.
- All calculations are made in degrees
- except that there is a sin_cos_rad function which is very imprecise; check source code for why, feel free to fix it (its not a priority for me)

Optional Features

std : std feature of fixed, there is no proper no-std support yet...

Examples

There are traits and standalone functions, see examples on how to use them.

Errors

Check the examples to see about how much error this implementation produces.

Usually sqrt has an error of around 1-2 Delta.
(Delta = the distance to the next representable number)

sin_cos may produce bigger errors, around 1-2 decimal places.

Benchmarks

You can check or run the benchmarks in benches.

Here are some conclusions I've got to:

SinCos

2022-09-28

Calculation time for sin_cos varies with the fixed number's byte size.

I10F6: ~ 8ns
I16F16: ~ 9ns
I32F32: ~ 18ns
I32F96: ~ 210ns

Notes:

there are many different int bit / frac bit combinations; I did not test them
(int bits must be >= 10 (but maybe I can do something to relax that further))
these are all calculations in degrees
code was compiled with native cpu features
go for FixedI32 instead of FixedI16 unless you are limited by memory much
I did a benchmark in the same style on cordic's sin_cos on FixedI64
- keep in mind that cordic works with radians, I used the same angle values
- so they can take sin_cos of a lot bigger angle on the same number representation size
- this crate was about 1.5-2 times faster on same angle sizes

2023-07-30

System info:

-` .o+` -------- `ooo/ OS: Arch Linux x86_64 `+oooo: Host: X570 AORUS ELITE -CF `+oooooo: Kernel: 6.4.7-arch1-1 -+oooooo+: `/:-:++oooo+: `/++++/+++++++: Shell: fish 3.6.1 `/++++++++++++++: Resolution: 3840x2160 `/+++ooooooooooooo/` DE: Hyprland ./ooosssso++osssssso+` .oossssso-````/ossssss+` -osssssso. :ssssssso. Terminal: WezTerm :osssssss/ osssso+++. CPU: AMD Ryzen 7 5800X (16) @ 3.800GHz /ossssssss/ +ssssooo/- GPU: AMD ATI Radeon RX 7900 XT/7900 XTX `/ossssso+/:- -:/+osssso+- Memory: 32014MiB `+sso+:-` `.-/+oso: `++:. `-/+/ .` `/

Performance is different now and without native cpu features:

I10F6: ~ 430ps
I16F16: ~ 15ns
I32F32: ~ 25ns
I32F96: ~ 255ns

With native cpu features : RUSTFLAGS="-C target-cpu=native" cargo bench:

I10F6: ~ 420ps
I16F16: ~ 8ns
I32F32: ~ 22ns
I32F96: ~ 222ns

Notes:

performance regressed at I32F32 and I32F96
performance improved a lot at I10F6, so we might consider using 16bit fixed point values where we do not need much precision
cordic benchmark not checked...

License

All code in this repository is dual-licensed under either:

MIT License (LICENSE-MIT or http://opensource.org/licenses/MIT)
Apache License, Version 2.0 (LICENSE-APACHE or http://www.apache.org/licenses/LICENSE-2.0)

at your option.

Contributing

Unless you explicitly state otherwise, any contribution intentionally submitted for inclusion in the work by you, as defined in the Apache-2.0 license, shall be dual licensed as above, without any additional terms or conditions.

Attribution

We use code modified from cordic, licensed as BSD-3-Clause:

LICENSE_CORDIC.