Crate fixed_math_taylor 

Fixed-Math-Taylor

A high-performance fixed-point trigonometry library optimized for embedded systems and microcontrollers without a floating-point unit (FPU).

Overview

Fixed-Math-Taylor eliminates the overhead of software floating-point emulation on resource-constrained devices by implementing trigonometric functions using only integer arithmetic and bit shifts. Designed specifically for the RP2040 and similar microcontrollers, it provides multiple calculation engines with different precision/speed trade-offs.

Features & Calculation Engines

The library provides three distinct calculation engines, selectable via Cargo features:

• lut (default): Lookup table with linear interpolation. Ultra-fast, highest precision (~0.1% error), 640 bytes Flash. Ideal for control loops, motor control, and audio applications.
• taylor: Taylor series expansion (order 5). Pure algorithmic computation with high precision. Smaller memory footprint, better for algorithms-only use cases.
• fast-sin: Bhaskara I approximation. Medium precision with exceptional speed. Optimal for animations and graphics.

Number Format: Q15 Fixed-Point

All functions return results in Q15 format (16-bit signed integer):

• 32767 represents +1.0
• 0 represents 0.0
• -32768 represents approximately -1.0

To convert to a human-readable float:

let fixed_value: i16 = /* ... */;
let float_value: f32 = (fixed_value as f32) / 32767.0;

Angle Representation

Angles are represented as u16 values (0..=65535):

• 0 = 0 radians
• 16384 ≈ π/2
• 32768 ≈ π
• 65535 ≈ 2π

Quick Start

Add to your Cargo.toml:

[dependencies]
fixed-math-taylor = { version = "0.3", features = ["lut"] }

Basic usage:

use fixed_math_taylor::{sin_fixed, cos_fixed, Angle, Fixed};

let angle: Angle = 16384; // π/2
let sine_value: Fixed = sin_fixed(angle);
let cosine_value: Fixed = cos_fixed(angle);

// Convert to float for display
println!("sin(π/2) ≈ {}", (sine_value as f32) / 32767.0);

Performance Characteristics

Engine	Speed	Precision	Flash Cost	Best For
LUT	Fastest	~0.1% err	640 bytes	Control loops, motor ctrl
Taylor	Fast	High	~500 bytes	Pure algorithms
Fast-Sin	Fastest	Medium	~300 bytes	Graphics, animations

no_std Environment

This crate is #![no_std] compatible and suitable for embedded environments with no standard library. No dynamic allocations are performed.

Dependencies

Zero external dependencies. Pure Rust with platform-independent implementation.

Functions

from_fixed

Converts a Q15 fixed-point value to a float.

radians_to_angle

Converts an angle in radians to the Angle representation used by this library.

to_fixed

Converts a float value to Q15 fixed-point format.

Type Aliases

Angle

An angle in the range [0, 65535], representing a full rotation [0, 2π).

Fixed

A fixed-point number in Q15 format, suitable for storing results from trigonometric functions.