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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
{
/**
Contains miscellaneous filter design and windowing functions.
@tags{DSP}
*/
struct SpecialFunctions
{
/** Computes the modified Bessel function of the first kind I0 for a
given double value x. Modified Bessel functions are useful to solve
various mathematical problems involving differential equations.
*/
static double besselI0 (double x) noexcept;
/** Computes the complete elliptic integral of the first kind K for a
given double value k, and the associated complete elliptic integral
of the first kind Kp for the complementary modulus of k.
*/
static void ellipticIntegralK (double k, double& K, double& Kp) noexcept;
/** Computes the Jacobian elliptic function cd for the elliptic
modulus k and the quarter-period units u.
*/
static Complex<double> cde (Complex<double> u, double k) noexcept;
/** Computes the Jacobian elliptic function sn for the elliptic
modulus k and the quarter-period units u.
*/
static Complex<double> sne (Complex<double> u, double k) noexcept;
/** Computes the inverse of the Jacobian elliptic function sn
for the elliptic modulus k and the quarter-period units u.
*/
static Complex<double> asne (Complex<double> w, double k) noexcept;
};
} // namespace dsp
} // namespace juce
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