git subrepo clone --branch=sono6good https://github.com/essej/JUCE.git deps/juce
subrepo: subdir: "deps/juce" merged: "b13f9084e" upstream: origin: "https://github.com/essej/JUCE.git" branch: "sono6good" commit: "b13f9084e" git-subrepo: version: "0.4.3" origin: "https://github.com/ingydotnet/git-subrepo.git" commit: "2f68596"
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essej
264
deps/juce/modules/juce_dsp/maths/juce_FastMathApproximations.h
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deps/juce/modules/juce_dsp/maths/juce_FastMathApproximations.h
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/*
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==============================================================================
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This file is part of the JUCE library.
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Copyright (c) 2020 - Raw Material Software Limited
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JUCE is an open source library subject to commercial or open-source
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licensing.
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By using JUCE, you agree to the terms of both the JUCE 6 End-User License
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Agreement and JUCE Privacy Policy (both effective as of the 16th June 2020).
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End User License Agreement: www.juce.com/juce-6-licence
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Privacy Policy: www.juce.com/juce-privacy-policy
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Or: You may also use this code under the terms of the GPL v3 (see
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www.gnu.org/licenses).
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JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
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EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
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DISCLAIMED.
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==============================================================================
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*/
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namespace juce
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{
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namespace dsp
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{
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/**
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This class contains various fast mathematical function approximations.
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@tags{DSP}
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*/
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struct FastMathApproximations
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{
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/** Provides a fast approximation of the function cosh(x) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -5 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static FloatType cosh (FloatType x) noexcept
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{
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auto x2 = x * x;
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auto numerator = -(39251520 + x2 * (18471600 + x2 * (1075032 + 14615 * x2)));
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auto denominator = -39251520 + x2 * (1154160 + x2 * (-16632 + 127 * x2));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function cosh(x) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -5 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static void cosh (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::cosh (values[i]);
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}
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/** Provides a fast approximation of the function sinh(x) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -5 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static FloatType sinh (FloatType x) noexcept
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{
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auto x2 = x * x;
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auto numerator = -x * (11511339840 + x2 * (1640635920 + x2 * (52785432 + x2 * 479249)));
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auto denominator = -11511339840 + x2 * (277920720 + x2 * (-3177720 + x2 * 18361));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function sinh(x) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -5 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static void sinh (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::sinh (values[i]);
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}
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/** Provides a fast approximation of the function tanh(x) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -5 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static FloatType tanh (FloatType x) noexcept
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{
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auto x2 = x * x;
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auto numerator = x * (135135 + x2 * (17325 + x2 * (378 + x2)));
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auto denominator = 135135 + x2 * (62370 + x2 * (3150 + 28 * x2));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function tanh(x) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -5 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static void tanh (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::tanh (values[i]);
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}
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//==============================================================================
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/** Provides a fast approximation of the function cos(x) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -pi and +pi for limiting the error.
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*/
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template <typename FloatType>
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static FloatType cos (FloatType x) noexcept
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{
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auto x2 = x * x;
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auto numerator = -(-39251520 + x2 * (18471600 + x2 * (-1075032 + 14615 * x2)));
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auto denominator = 39251520 + x2 * (1154160 + x2 * (16632 + x2 * 127));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function cos(x) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -pi and +pi for limiting the error.
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*/
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template <typename FloatType>
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static void cos (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::cos (values[i]);
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}
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/** Provides a fast approximation of the function sin(x) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -pi and +pi for limiting the error.
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*/
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template <typename FloatType>
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static FloatType sin (FloatType x) noexcept
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{
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auto x2 = x * x;
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auto numerator = -x * (-11511339840 + x2 * (1640635920 + x2 * (-52785432 + x2 * 479249)));
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auto denominator = 11511339840 + x2 * (277920720 + x2 * (3177720 + x2 * 18361));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function sin(x) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -pi and +pi for limiting the error.
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*/
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template <typename FloatType>
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static void sin (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::sin (values[i]);
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}
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/** Provides a fast approximation of the function tan(x) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -pi/2 and +pi/2 for limiting the error.
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*/
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template <typename FloatType>
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static FloatType tan (FloatType x) noexcept
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{
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auto x2 = x * x;
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auto numerator = x * (-135135 + x2 * (17325 + x2 * (-378 + x2)));
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auto denominator = -135135 + x2 * (62370 + x2 * (-3150 + 28 * x2));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function tan(x) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -pi/2 and +pi/2 for limiting the error.
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*/
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template <typename FloatType>
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static void tan (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::tan (values[i]);
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}
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//==============================================================================
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/** Provides a fast approximation of the function exp(x) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -6 and +4 for limiting the error.
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*/
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template <typename FloatType>
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static FloatType exp (FloatType x) noexcept
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{
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auto numerator = 1680 + x * (840 + x * (180 + x * (20 + x)));
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auto denominator = 1680 + x *(-840 + x * (180 + x * (-20 + x)));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function exp(x) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -6 and +4 for limiting the error.
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*/
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template <typename FloatType>
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static void exp (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::exp (values[i]);
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}
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/** Provides a fast approximation of the function log(x+1) using a Pade approximant
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continued fraction, calculated sample by sample.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -0.8 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static FloatType logNPlusOne (FloatType x) noexcept
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{
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auto numerator = x * (7560 + x * (15120 + x * (9870 + x * (2310 + x * 137))));
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auto denominator = 7560 + x * (18900 + x * (16800 + x * (6300 + x * (900 + 30 * x))));
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return numerator / denominator;
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}
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/** Provides a fast approximation of the function log(x+1) using a Pade approximant
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continued fraction, calculated on a whole buffer.
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Note: This is an approximation which works on a limited range. You are
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advised to use input values only between -0.8 and +5 for limiting the error.
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*/
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template <typename FloatType>
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static void logNPlusOne (FloatType* values, size_t numValues) noexcept
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{
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for (size_t i = 0; i < numValues; ++i)
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values[i] = FastMathApproximations::logNPlusOne (values[i]);
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}
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};
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} // namespace dsp
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} // namespace juce
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