IntegerSignal

Header-only C++ library for fast, deterministic, integer-only signal processing and math utilities for microcontrollers. No floating point required.

• Core embedded utilities for constrained targets: lightweight integer math, traits, bit/byte helpers, conversions, mixing, integer square root
• Fixed-point Fraction [-1; 1] and Scale [1/N; N] primitives as first-class DSP features
• Composable Filters and Curves (EMA/DEMA/LowPass, Power/SquareRoot/Clamp...)
• Color models (RGB8 / RGB10 / Fraction 15:15:15) with HSV conversion and interpolation helpers
• Trigonometry: integer sine, cosine, and tangent using lookup tables (8-bit and 16-bit fractional angles) and non–lookup-table variants for minimal footprint

Why IntegerSignal?

• Up to ~10× faster on MCUs without floating point
• Efficient bitwise/branchless code paths due to template specialization
• No external dependencies
• Requires only C++11 or later

Key features

1. Fixed-point Fraction scalars (0..1 and −1..1)

• Unsigned: UQ0.7, UQ0.15, UQ0.31
• Signed: Q0.6, Q0.14, Q0.30
• Typed constants for 1.0 and −1.0
• Operations: multiply by a fractional scalar, interpolate with a fractional scalar, compute scalars from numerator/denominator with clamping

2. Fixed-point Scale factors (unbounded above 1.0)

• Widths: 8-bit, 16-bit, 32-bit with power-of-two units
• Operations: multiply by a scale factor, compute scale factors from numerator/denominator

Additional modules

• Filters: EMA, DEMA, LowPass, and helpers (composable, template-based)
• Curves: Power, Root (square root), Limit/Clamp, ScaleDown, Signed, Strength
• Color models: RGB8 (8 bits per channel), RGB10 (10 bits per channel), Fraction 15:15:15 for high-precision intermediate math; HSV conversion; integer-precise interpolation
• Trigonometry: integer implementations of sine, cosine, and tangent for fractional angles; headers with and without lookup tables to trade accuracy, speed, and size

Quick start

Top-level includes (only headers directly in src/):

#include <IntegerSignal.h>        // Umbrella header: Base, FixedPoint, Filters, Curves, Colors
#include <IntegerTrigonometry.h>  // Trigonometry without lookup tables (minimal footprint)
#include <IntegerTrigonometry8.h> // Trigonometry with 8-bit fractional-angle lookup tables (fast, small tables)
#include <IntegerTrigonometry16.h>// Trigonometry with 16-bit fractional-angle lookup tables (higher precision)

Fractions and scales (minimal usage)

#include <IntegerSignal.h>
using namespace IntegerSignal;

// Fraction (unsigned 0..1): compute 3/4 and apply
auto s = FixedPoint::ScalarFraction::GetScalarU16(3, 4);
uint16_t scaled = FixedPoint::ScalarFraction::Fraction<uint16_t>(s, 400); // -> 300

// Interpolate between 100 and 500 at 3/4
uint16_t y = FixedPoint::ScalarFraction::Interpolate<uint16_t>(s, 100, 500); // -> 400

// Scale factor (> 1.0 and down to 1/unit): map 0..1023 to 0..255
auto k = FixedPoint::FactorScale::GetFactor16(255, 1023);
uint16_t pwm = FixedPoint::FactorScale::Scale<uint16_t>(k, /*adc*/ 512); // ≈ 128

Notes

• Unsigned fractions clamp to [0,1]; signed fractions clamp to [-1,1].
• Scale factors use multiply-and-shift with power-of-two units (no divisions in steady state).

Examples

• Benchmark and feature demos are provided in Examples/Benchmark and Examples/Testing (Arduino IDE: File → Examples → IntegerSignal).

Performance notes

• Integer square root may use ARM CLZ acceleration where available
• Fraction/Scale helpers avoid intermediate overflows via widened math and power-of-two units

Directory structure

• src/FixedPoint/ — Fraction scalars and Scale factors (plus Q-format helpers)
• src/Base/ — core embedded utilities (traits, operations, mix/interpolate, convert, bit/byte helpers, integer square root)
• src/Filter/ — EMA, DEMA, LowPass, and helpers
• src/Curve/ — Power, Root, Limit/Clamp, ScaleDown, etc.
• src/Color/ — RGB8, RGB10, Fraction16, HSV
• src/Trigonometry/ — integer trigonometry helpers
• Examples/ — Arduino sketches

Compatibility

• C++11 or later
• MCUs: 8‑bit AVR, ARM Cortex‑M, and desktop builds for testing
• Arduino-compatible (library.properties provided)