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/*
==============================================================================
This file is part of the JUCE library.
Copyright (c) 2017 - ROLI Ltd.
JUCE is an open source library subject to commercial or open-source
licensing.
By using JUCE, you agree to the terms of both the JUCE 5 End-User License
Agreement and JUCE 5 Privacy Policy (both updated and effective as of the
27th April 2017).
End User License Agreement: www.juce.com/juce-5-licence
Privacy Policy: www.juce.com/juce-5-privacy-policy
Or: You may also use this code under the terms of the GPL v3 (see
www.gnu.org/licenses).
JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
DISCLAIMED.
==============================================================================
*/
namespace juce
{
namespace 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 dsp
} // namespace juce
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