145 lines
4.0 KiB
C++
145 lines
4.0 KiB
C++
/*
|
|
==============================================================================
|
|
|
|
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
|
|
{
|
|
|
|
double SpecialFunctions::besselI0 (double x) noexcept
|
|
{
|
|
auto ax = std::abs (x);
|
|
|
|
if (ax < 3.75)
|
|
{
|
|
auto y = x / 3.75;
|
|
y *= y;
|
|
|
|
return 1.0 + y * (3.5156229 + y * (3.0899424 + y * (1.2067492
|
|
+ y * (0.2659732 + y * (0.360768e-1 + y * 0.45813e-2)))));
|
|
}
|
|
|
|
auto y = 3.75 / ax;
|
|
|
|
return (std::exp (ax) / std::sqrt (ax))
|
|
* (0.39894228 + y * (0.1328592e-1 + y * (0.225319e-2 + y * (-0.157565e-2 + y * (0.916281e-2
|
|
+ y * (-0.2057706e-1 + y * (0.2635537e-1 + y * (-0.1647633e-1 + y * 0.392377e-2))))))));
|
|
}
|
|
|
|
void SpecialFunctions::ellipticIntegralK (double k, double& K, double& Kp) noexcept
|
|
{
|
|
constexpr int M = 4;
|
|
|
|
K = MathConstants<double>::halfPi;
|
|
auto lastK = k;
|
|
|
|
for (int i = 0; i < M; ++i)
|
|
{
|
|
lastK = std::pow (lastK / (1 + std::sqrt (1 - std::pow (lastK, 2.0))), 2.0);
|
|
K *= 1 + lastK;
|
|
}
|
|
|
|
Kp = MathConstants<double>::halfPi;
|
|
auto last = std::sqrt (1 - k * k);
|
|
|
|
for (int i = 0; i < M; ++i)
|
|
{
|
|
last = std::pow (last / (1.0 + std::sqrt (1.0 - std::pow (last, 2.0))), 2.0);
|
|
Kp *= 1 + last;
|
|
}
|
|
}
|
|
|
|
Complex<double> SpecialFunctions::cde (Complex<double> u, double k) noexcept
|
|
{
|
|
constexpr int M = 4;
|
|
|
|
double ke[M + 1];
|
|
double* kei = ke;
|
|
*kei = k;
|
|
|
|
for (int i = 0; i < M; ++i)
|
|
{
|
|
auto next = std::pow (*kei / (1.0 + std::sqrt (1.0 - std::pow (*kei, 2.0))), 2.0);
|
|
*++kei = next;
|
|
}
|
|
|
|
// NB: the spurious cast to double here is a workaround for a very odd link-time failure
|
|
std::complex<double> last = std::cos (u * (double) MathConstants<double>::halfPi);
|
|
|
|
for (int i = M - 1; i >= 0; --i)
|
|
last = (1.0 + ke[i + 1]) / (1.0 / last + ke[i + 1] * last);
|
|
|
|
return last;
|
|
}
|
|
|
|
Complex<double> SpecialFunctions::sne (Complex<double> u, double k) noexcept
|
|
{
|
|
constexpr int M = 4;
|
|
|
|
double ke[M + 1];
|
|
double* kei = ke;
|
|
*kei = k;
|
|
|
|
for (int i = 0; i < M; ++i)
|
|
{
|
|
auto next = std::pow (*kei / (1 + std::sqrt (1 - std::pow (*kei, 2.0))), 2.0);
|
|
*++kei = next;
|
|
}
|
|
|
|
// NB: the spurious cast to double here is a workaround for a very odd link-time failure
|
|
std::complex<double> last = std::sin (u * (double) MathConstants<double>::halfPi);
|
|
|
|
for (int i = M - 1; i >= 0; --i)
|
|
last = (1.0 + ke[i + 1]) / (1.0 / last + ke[i + 1] * last);
|
|
|
|
return last;
|
|
}
|
|
|
|
Complex<double> SpecialFunctions::asne (Complex<double> w, double k) noexcept
|
|
{
|
|
constexpr int M = 4;
|
|
|
|
double ke[M + 1];
|
|
double* kei = ke;
|
|
*kei = k;
|
|
|
|
for (int i = 0; i < M; ++i)
|
|
{
|
|
auto next = std::pow (*kei / (1.0 + std::sqrt (1.0 - std::pow (*kei, 2.0))), 2.0);
|
|
*++kei = next;
|
|
}
|
|
|
|
std::complex<double> last = w;
|
|
|
|
for (int i = 1; i <= M; ++i)
|
|
last = 2.0 * last / ((1.0 + ke[i]) * (1.0 + std::sqrt (1.0 - std::pow (ke[i - 1] * last, 2.0))));
|
|
|
|
return 2.0 / MathConstants<double>::pi * std::asin (last);
|
|
}
|
|
|
|
} // namespace dsp
|
|
} // namespace juce
|