Added the JUCE DSP module

modules/juce_dsp/maths/juce_SpecialFunctions.cpp

@@ -0,0 +1,135 @@
+/*
+  ==============================================================================
+
+   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.
+
+  ==============================================================================
+*/
+
+
+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::ellipicIntegralK (double k, double& K, double& Kp) noexcept
+{
+    constexpr int M = 4;
+
+    K = double_Pi * 0.5;
+    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 = double_Pi * 0.5;
+    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;
+    }
+
+    std::complex<double> last = std::cos (0.5 * u * double_Pi);
+
+    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;
+    }
+
+    std::complex<double> last = std::sin (0.5 * u * double_Pi);
+
+    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 / double_Pi * std::asin (last);
+}