mirror of
https://github.com/juce-framework/JUCE.git
synced 2026-01-09 23:34:20 +00:00
270 lines
11 KiB
C++
270 lines
11 KiB
C++
/*
|
|
==============================================================================
|
|
|
|
This file is part of the JUCE framework.
|
|
Copyright (c) Raw Material Software Limited
|
|
|
|
JUCE is an open source framework subject to commercial or open source
|
|
licensing.
|
|
|
|
By downloading, installing, or using the JUCE framework, or combining the
|
|
JUCE framework with any other source code, object code, content or any other
|
|
copyrightable work, you agree to the terms of the JUCE End User Licence
|
|
Agreement, and all incorporated terms including the JUCE Privacy Policy and
|
|
the JUCE Website Terms of Service, as applicable, which will bind you. If you
|
|
do not agree to the terms of these agreements, we will not license the JUCE
|
|
framework to you, and you must discontinue the installation or download
|
|
process and cease use of the JUCE framework.
|
|
|
|
JUCE End User Licence Agreement: https://juce.com/legal/juce-8-licence/
|
|
JUCE Privacy Policy: https://juce.com/juce-privacy-policy
|
|
JUCE Website Terms of Service: https://juce.com/juce-website-terms-of-service/
|
|
|
|
Or:
|
|
|
|
You may also use this code under the terms of the AGPLv3:
|
|
https://www.gnu.org/licenses/agpl-3.0.en.html
|
|
|
|
THE JUCE FRAMEWORK IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL
|
|
WARRANTIES, WHETHER EXPRESSED OR IMPLIED, INCLUDING WARRANTY OF
|
|
MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE, ARE DISCLAIMED.
|
|
|
|
==============================================================================
|
|
*/
|
|
|
|
namespace juce::dsp
|
|
{
|
|
|
|
/**
|
|
This class contains various fast mathematical function approximations.
|
|
|
|
@tags{DSP}
|
|
*/
|
|
struct FastMathApproximations
|
|
{
|
|
/** Provides a fast approximation of the function cosh(x) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -5 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType cosh (FloatType x) noexcept
|
|
{
|
|
auto x2 = x * x;
|
|
auto numerator = -(39251520 + x2 * (18471600 + x2 * (1075032 + 14615 * x2)));
|
|
auto denominator = -39251520 + x2 * (1154160 + x2 * (-16632 + 127 * x2));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function cosh(x) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -5 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void cosh (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::cosh (values[i]);
|
|
}
|
|
|
|
/** Provides a fast approximation of the function sinh(x) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -5 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType sinh (FloatType x) noexcept
|
|
{
|
|
auto x2 = x * x;
|
|
auto numerator = -x * (11511339840 + x2 * (1640635920 + x2 * (52785432 + x2 * 479249)));
|
|
auto denominator = -11511339840 + x2 * (277920720 + x2 * (-3177720 + x2 * 18361));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function sinh(x) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -5 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void sinh (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::sinh (values[i]);
|
|
}
|
|
|
|
/** Provides a fast approximation of the function tanh(x) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -5 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType tanh (FloatType x) noexcept
|
|
{
|
|
auto x2 = x * x;
|
|
auto numerator = x * (135135 + x2 * (17325 + x2 * (378 + x2)));
|
|
auto denominator = 135135 + x2 * (62370 + x2 * (3150 + 28 * x2));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function tanh(x) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -5 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void tanh (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::tanh (values[i]);
|
|
}
|
|
|
|
//==============================================================================
|
|
/** Provides a fast approximation of the function cos(x) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -pi and +pi for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType cos (FloatType x) noexcept
|
|
{
|
|
auto x2 = x * x;
|
|
auto numerator = -(-39251520 + x2 * (18471600 + x2 * (-1075032 + 14615 * x2)));
|
|
auto denominator = 39251520 + x2 * (1154160 + x2 * (16632 + x2 * 127));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function cos(x) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -pi and +pi for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void cos (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::cos (values[i]);
|
|
}
|
|
|
|
/** Provides a fast approximation of the function sin(x) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -pi and +pi for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType sin (FloatType x) noexcept
|
|
{
|
|
auto x2 = x * x;
|
|
auto numerator = -x * (-11511339840 + x2 * (1640635920 + x2 * (-52785432 + x2 * 479249)));
|
|
auto denominator = 11511339840 + x2 * (277920720 + x2 * (3177720 + x2 * 18361));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function sin(x) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -pi and +pi for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void sin (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::sin (values[i]);
|
|
}
|
|
|
|
/** Provides a fast approximation of the function tan(x) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -pi/2 and +pi/2 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType tan (FloatType x) noexcept
|
|
{
|
|
auto x2 = x * x;
|
|
auto numerator = x * (-135135 + x2 * (17325 + x2 * (-378 + x2)));
|
|
auto denominator = -135135 + x2 * (62370 + x2 * (-3150 + 28 * x2));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function tan(x) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -pi/2 and +pi/2 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void tan (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::tan (values[i]);
|
|
}
|
|
|
|
//==============================================================================
|
|
/** Provides a fast approximation of the function exp(x) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -6 and +4 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType exp (FloatType x) noexcept
|
|
{
|
|
auto numerator = 1680 + x * (840 + x * (180 + x * (20 + x)));
|
|
auto denominator = 1680 + x *(-840 + x * (180 + x * (-20 + x)));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function exp(x) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -6 and +4 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void exp (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::exp (values[i]);
|
|
}
|
|
|
|
/** Provides a fast approximation of the function log(x+1) using a Pade approximant
|
|
continued fraction, calculated sample by sample.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -0.8 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static FloatType logNPlusOne (FloatType x) noexcept
|
|
{
|
|
auto numerator = x * (7560 + x * (15120 + x * (9870 + x * (2310 + x * 137))));
|
|
auto denominator = 7560 + x * (18900 + x * (16800 + x * (6300 + x * (900 + 30 * x))));
|
|
return numerator / denominator;
|
|
}
|
|
|
|
/** Provides a fast approximation of the function log(x+1) using a Pade approximant
|
|
continued fraction, calculated on a whole buffer.
|
|
|
|
Note: This is an approximation which works on a limited range. You are
|
|
advised to use input values only between -0.8 and +5 for limiting the error.
|
|
*/
|
|
template <typename FloatType>
|
|
static void logNPlusOne (FloatType* values, size_t numValues) noexcept
|
|
{
|
|
for (size_t i = 0; i < numValues; ++i)
|
|
values[i] = FastMathApproximations::logNPlusOne (values[i]);
|
|
}
|
|
};
|
|
|
|
} // namespace juce::dsp
|