Fixed-point mathematical functions which are accurate, fast, safe, and machine independent.
use fixed::types::I16F16;
use fixed_analytics::{sin, cos, sqrt, ln};
let angle = I16F16::from_num(0.5);
let (s, c) = (sin(angle), cos(angle));
let root = sqrt(I16F16::from_num(2.0)).unwrap();
assert!((root.to_num::<f32>() - 1.414).abs() < 0.001);
let log = ln(I16F16::E).unwrap();
assert!((log.to_num::<f32>() - 1.0).abs() < 0.01);Requires Rust 1.88 or later.
[dependencies]
fixed_analytics = "0.5.1"For no_std environments:
[dependencies]
fixed_analytics = { version = "0.5.1", default-features = false }Total functions return T directly and handle all inputs, possibly with saturation.
Fallible functions return Result<T, Error> and fail on domain violations.
| Category | Total Functions | Fallible Functions |
|---|---|---|
| Trigonometric | sin, cos, tan, sin_cos, atan, atan2 |
asin, acos |
| Hyperbolic | sinh, cosh, tanh, sinh_cosh, asinh |
acosh, atanh, acoth, coth |
| Exponential | exp, pow2 |
ln, log2, log10 |
| Algebraic | — | sqrt |
Functions are calculated via CORDIC, Newton-Raphson, and Taylor series techniques.
The following total functions saturate, clamping to the representable range near the following thresholds.
| Function | I16F16 Threshold | I32F32 Threshold | Result |
|---|---|---|---|
exp |
x ≥ 22.2 | x ≥ 44.4 | T::MAX |
exp |
x ≤ -9.2 | x ≤ -16.2 | Zero |
pow2 |
x ≥ 15.0 | x ≥ 31.0 | T::MAX |
pow2 |
x ≤ -13.2 | x ≤ -23.3 | Zero |
sinh |
|x| ≥ 11.1 | |x| ≥ 22.2 | T::MAX or T::MIN |
cosh |
|x| ≥ 11.1 | |x| ≥ 22.2 | T::MAX |
tan |
|x - pole| < 8e-5 | |x - pole| < 5e-10 | T::MAX or T::MIN |
Where for tan, "pole" refers to ±π/2, ±3π/2, ±5π/2, ...
Relative error statistics measured against MPFR reference implementations. The file tools/accuracy-bench/baseline.json contains further measurements.
| Function | I16F16 Mean | I16F16 Median | I16F16 P95 | I32F32 Mean | I32F32 Median | I32F32 P95 |
|---|---|---|---|---|---|---|
| sin | 6.19e-4 | 9.34e-5 | 1.30e-3 | 1.22e-8 | 1.79e-9 | 2.52e-8 |
| cos | 6.82e-4 | 1.02e-4 | 1.46e-3 | 1.30e-8 | 1.91e-9 | 2.83e-8 |
| tan | 2.47e-4 | 9.84e-5 | 6.70e-4 | 6.00e-9 | 1.89e-9 | 1.40e-8 |
| asin | 2.87e-4 | 5.93e-5 | 6.46e-4 | 5.34e-9 | 8.82e-10 | 1.03e-8 |
| acos | 3.61e-5 | 2.18e-5 | 1.14e-4 | 5.37e-10 | 3.19e-10 | 1.71e-9 |
| atan | 2.71e-5 | 2.21e-5 | 6.29e-5 | 3.69e-10 | 2.92e-10 | 8.74e-10 |
| sinh | 1.82e-4 | 1.34e-4 | 5.03e-4 | 1.05e-8 | 2.35e-9 | 9.30e-9 |
| cosh | 1.73e-4 | 1.23e-4 | 5.00e-4 | 1.02e-8 | 2.07e-9 | 9.16e-9 |
| tanh | 2.08e-5 | 1.38e-5 | 5.89e-5 | 1.64e-9 | 1.31e-10 | 1.23e-9 |
| coth | 1.20e-5 | 4.83e-6 | 5.57e-5 | 4.00e-10 | 1.39e-10 | 1.30e-9 |
| asinh | 6.44e-4 | 4.83e-4 | 1.75e-3 | 1.03e-8 | 7.59e-9 | 2.85e-8 |
| acosh | 6.74e-4 | 5.21e-4 | 1.80e-3 | 1.05e-8 | 7.96e-9 | 2.88e-8 |
| atanh | 3.01e-4 | 5.90e-5 | 6.25e-4 | 6.68e-9 | 1.32e-9 | 1.44e-8 |
| acoth | 2.10e-3 | 1.33e-3 | 6.67e-3 | 4.26e-8 | 2.62e-8 | 1.39e-7 |
| exp | 1.14e-2 | 6.67e-5 | 7.87e-2 | 1.91e-7 | 2.24e-9 | 1.30e-6 |
| ln | 1.35e-5 | 8.76e-6 | 2.97e-5 | 4.50e-10 | 3.48e-10 | 9.17e-10 |
| log2 | 1.33e-5 | 8.48e-6 | 2.92e-5 | 3.46e-10 | 2.24e-10 | 7.21e-10 |
| log10 | 1.44e-5 | 9.28e-6 | 3.14e-5 | 4.49e-10 | 3.27e-10 | 9.07e-10 |
| pow2 | 7.28e-4 | 4.74e-5 | 4.71e-3 | 1.15e-8 | 1.06e-9 | 7.38e-8 |
| sqrt | 1.77e-7 | 1.16e-7 | 4.74e-7 | 2.70e-12 | 1.78e-12 | 7.16e-12 |