FastMath< F > Class Template Reference

Fast approximations for trigonometric and hyperbolic functions. More...

#include <gin_fastmath.h>

Static Public Member Functions
static F	fastSin (F x)
	Fast sine wave approximation.
static F	fastTanh (const F x)
	Fast hyperbolic tangent approximation.

Detailed Description

template<class F>
class FastMath< F >

Fast approximations for trigonometric and hyperbolic functions.

FastMath provides optimized approximations of trigonometric and hyperbolic functions that trade accuracy for speed. These are useful in DSP applications where perceptual accuracy is more important than mathematical precision, such as waveshaping, modulation, and real-time synthesis.

Key Features:

• Fast sine approximation (valid range: -π to π)
• Fast hyperbolic tangent approximation
• Template class supports float or double
• Inline functions for maximum performance
• Suitable for audio-rate processing

Accuracy vs Speed: These approximations are significantly faster than std:: equivalents but introduce small errors. For most audio applications, the errors are inaudible and the speed benefit is worthwhile.

Usage:

// Fast sine for LFO or modulation
float phase = 0.5f; // 0 to 1
float x = (phase * 2.0f - 1.0f) * M_PI; // Convert to -π to π
float sineValue = FastMath<float>::fastSin(x);
 
// Fast tanh for waveshaping/saturation
float input = audioSample * 3.0f;
float shaped = FastMath<float>::fastTanh(input);

Credits: Based on algorithms by Mike Jarmy (MIT License)

See also

math namespace

Member Function Documentation

fastSin()

template<class F >

static F FastMath< F >::fastSin ( F  x )

static

Fast sine wave approximation.

Computes an approximation of sin(x) using a polynomial approximation. Provides good accuracy with significantly better performance than std::sin.

Valid Range: -π to π

• Values outside this range will produce incorrect results
• For normalized phase (0 to 1), convert to radians first

Algorithm: Based on parabolic approximation with extra precision term.

Parameters

x	Angle in radians (must be in range [-π, π])

Returns

Approximation of sin(x) in range [-1.0, 1.0]

See also

https://web.archive.org/web/20100613230051/http://www.devmaster.net/forums/showthread.php?t=5784

https://www.desmos.com/calculator/f0eryaepsl

fastTanh()

template<class F >

static F FastMath< F >::fastTanh ( const F  x )

static

Fast hyperbolic tangent approximation.

Computes an approximation of tanh(x) using a rational polynomial. Particularly useful for waveshaping and soft-clipping in audio applications.

Characteristics:

• Smooth S-curve from -1 to 1
• Asymptotically approaches ±1 for large |x|
• Good for soft saturation and distortion
• Much faster than std::tanh
• Valid for all input ranges

Algorithm: Rational polynomial approximation optimized for audio.

Parameters

x	Input value (any real number)

Returns

Approximation of tanh(x) in range [-1.0, 1.0]

See also

https://www.kvraudio.com/forum/viewtopic.php?p=5447225#p5447225

https://www.desmos.com/calculator/bjc7zsl4ek

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The documentation for this class was generated from the following file:

• gin_fastmath.h