Fixed Math

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

Implemented functions:

• sqrt from trait FixedSqrt
  • FixedSqrt 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 FixedSinCos
  • FixedSinCos is not implemented for fixed numbers with less than 7 integer bits, but there are functions that work on some of those types: sin_cos_i7, ...
  • 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)

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

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.

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

• LICENSE_CORDIC.

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.