[](https://crates.io/crates/const_poly)
Evaluate any multivariable equation or polynomial at compile time with high accuracy and zero runtime overhead.
## Features
- `no_std` compatible – no heap allocations, no panics.
- Full compile-time evaluation of arbitrarily complex equations with high numerical accuracy (benchmarked at 1e-7).
- Fully documented with code examples, user-friendly macros, benchmarking, and a comprehensive suite of tests.
- Define expressions using variety of mathematical functions, all evaluable at compile time:
- `Identity`: the variable itself (no function applied)
- `Pow(u32)`: power function `x^n` where `n` is the exponent
- `Sin`: sine function
- `Cos`: cosine function
- `Tan`: tangent function
- `Exp`: exponential function (e^x)
- `Ln`: natural logarithm
- `Sqrt`: square root function
- `Arctan`: arctangent function
- `Sinh`: hyperbolic sine function
- `Cosh`: hyperbolic cosine function
## Who is this for?
- This library is primarily meant to empower scientific computing and mathematical libraries in rust to perform all numerical approximations entirely at compile time.
- Embedded and no_std environments where heapless, panic-free code is essential.
- Metaprogramming and symbolic math tools that benefit from evaluating complex expressions entirely at compile time.
## Examples
### Simple Sine Polynomial (1 variable, 1 term):
```rust
use const_poly::{const_poly, Polynomial};
use const_poly::VarFunction::Sin;
const POLY_1V_1T: Polynomial<1, 1> = const_poly!({
[2.0, [Sin]] // 2 * sin(x)
});
const VARS: [f64; 1] = [1.2]; // sin(1.2) ≈ 0.932039
const RESULT: f64 = POLY_1V_1T.evaluate(VARS); // ≈ 1.864078
```
### Mixed Trigonometric Polynomial (2 Variables, 2 terms):
```rust
use const_poly::{const_poly, Polynomial};
use const_poly::VarFunction::{Cos, Sin};
const POLY_2V_2T: Polynomial<2, 2> = const_poly!({
[1.0, [Sin, Cos]], // sin(x) * cos(y)
[0.75, [Cos, Sin]] // 0.75 * cos(x) * sin(y)
});
const VARS: [f64; 2] = [0.9, 1.1];
const RESULT: f64 = POLY_2V_2T.evaluate(VARS); // ~ 0.7705881
```
### Powers with Mixed Exponents (3 Variables, 5 terms):
```rust
use const_poly::{const_poly, Polynomial};
use const_poly::VarFunction::Pow;
const POLY_3V_5T: Polynomial<3, 5> = const_poly!({
[1.2, [Pow(2), Pow(-1), Pow(0)]], // 1.2 * x² * y⁻¹ * z⁰
[-0.8, [Pow(3), Pow(1), Pow(-2)]], // -0.8 * x³ * y¹ * z⁻²
[2.5, [Pow(-3), Pow(4), Pow(1)]], // 2.5 * x⁻³ * y⁴ * z¹
[-1.1, [Pow(0), Pow(-2), Pow(3)]], // -1.1 * x⁰ * y⁻² * z³
[0.9, [Pow(1), Pow(2), Pow(-1)]] // 0.9 * x¹ * y² * z⁻¹
});
const VARS: [f64; 3] = [2.0, 3.0, 0.5];
const RESULT: f64 = POLY_3V_5T.evaluate(VARS); //~ -30.159027778
```
### Powers with mixed exponents, trignometric and log functions (4 variables, 4 terms):
```rust
use const_poly::{const_poly, Polynomial};
use const_poly::VarFunction::*;
const POLY_4V_4T: Polynomial<4, 4> = const_poly!({
[3.0, [Identity, Sin, Pow(2), Cos]], // 3.0 * x₀ * sin(x₁) * x₂² * cos(x₃)
[-1.2, [Pow(3), Tan, Exp, Identity]], // -1.2 * x₀³ * tan(x₁) * exp(x₂) * x₃
[0.7, [Ln, Sqrt, Arctan, Sinh]], // 0.7 * ln(x₀) * sqrt(x₁) * atan(x₂) * sinh(x₃)
[1.1, [Cosh, Identity, Pow(1), Sin]] // 1.1 * cosh(x₀) * x₁ * x₂ * sin(x₃)
});
const VARS = [0.5, 1.5, 2.5, 3.5];
const RESULT = POLY_4V_4T.evaluate(VARS); // ~ -112.280027300776
```
## Benchmarks
See [BENCHMARKS.md](./BENCHMARKS.md)
## Contributions Guide
See [CONTRIBUTIONS.md](./CONTRIBUTIONS.md)
## LICENSE
const_poly is licensed under the MIT license.
## Contact
anmolkathail@gmail.com
If you use this library in your project, a shoutout or mention would be awesome!
## TODO
- Add polynomial operations like add/subtract/multiply.
- Add more benchmarking.