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juce_SpecialFunctions.cpp
1/*
2 ==============================================================================
3
4 This file is part of the JUCE library.
5 Copyright (c) 2022 - Raw Material Software Limited
6
7 JUCE is an open source library subject to commercial or open-source
8 licensing.
9
10 By using JUCE, you agree to the terms of both the JUCE 7 End-User License
11 Agreement and JUCE Privacy Policy.
12
13 End User License Agreement: www.juce.com/juce-7-licence
14 Privacy Policy: www.juce.com/juce-privacy-policy
15
16 Or: You may also use this code under the terms of the GPL v3 (see
17 www.gnu.org/licenses).
18
19 JUCE IS PROVIDED "AS IS" WITHOUT ANY WARRANTY, AND ALL WARRANTIES, WHETHER
20 EXPRESSED OR IMPLIED, INCLUDING MERCHANTABILITY AND FITNESS FOR PURPOSE, ARE
21 DISCLAIMED.
22
23 ==============================================================================
24*/
25
26 namespace juce::dsp
27{
28
29 double SpecialFunctions::besselI0 (double x) noexcept
30{
31 auto ax = std::abs (x);
32
33 if (ax < 3.75)
34 {
35 auto y = x / 3.75;
36 y *= y;
37
38 return 1.0 + y * (3.5156229 + y * (3.0899424 + y * (1.2067492
39 + y * (0.2659732 + y * (0.360768e-1 + y * 0.45813e-2)))));
40 }
41
42 auto y = 3.75 / ax;
43
44 return (std::exp (ax) / std::sqrt (ax))
45 * (0.39894228 + y * (0.1328592e-1 + y * (0.225319e-2 + y * (-0.157565e-2 + y * (0.916281e-2
46 + y * (-0.2057706e-1 + y * (0.2635537e-1 + y * (-0.1647633e-1 + y * 0.392377e-2))))))));
47}
48
49 void SpecialFunctions::ellipticIntegralK (double k, double& K, double& Kp) noexcept
50{
51 constexpr int M = 4;
52
53 K = MathConstants<double>::halfPi;
54 auto lastK = k;
55
56 for (int i = 0; i < M; ++i)
57 {
58 lastK = std::pow (lastK / (1 + std::sqrt (1 - std::pow (lastK, 2.0))), 2.0);
59 K *= 1 + lastK;
60 }
61
62 Kp = MathConstants<double>::halfPi;
63 auto last = std::sqrt (1 - k * k);
64
65 for (int i = 0; i < M; ++i)
66 {
67 last = std::pow (last / (1.0 + std::sqrt (1.0 - std::pow (last, 2.0))), 2.0);
68 Kp *= 1 + last;
69 }
70}
71
72Complex<double> SpecialFunctions::cde (Complex<double> u, double k) noexcept
73{
74 constexpr int M = 4;
75
76 double ke[M + 1];
77 double* kei = ke;
78 *kei = k;
79
80 for (int i = 0; i < M; ++i)
81 {
82 auto next = std::pow (*kei / (1.0 + std::sqrt (1.0 - std::pow (*kei, 2.0))), 2.0);
83 *++kei = next;
84 }
85
86 // NB: the spurious cast to double here is a workaround for a very odd link-time failure
87 std::complex<double> last = std::cos (u * (double) MathConstants<double>::halfPi);
88
89 for (int i = M - 1; i >= 0; --i)
90 last = (1.0 + ke[i + 1]) / (1.0 / last + ke[i + 1] * last);
91
92 return last;
93}
94
95Complex<double> SpecialFunctions::sne (Complex<double> u, double k) noexcept
96{
97 constexpr int M = 4;
98
99 double ke[M + 1];
100 double* kei = ke;
101 *kei = k;
102
103 for (int i = 0; i < M; ++i)
104 {
105 auto next = std::pow (*kei / (1 + std::sqrt (1 - std::pow (*kei, 2.0))), 2.0);
106 *++kei = next;
107 }
108
109 // NB: the spurious cast to double here is a workaround for a very odd link-time failure
110 std::complex<double> last = std::sin (u * (double) MathConstants<double>::halfPi);
111
112 for (int i = M - 1; i >= 0; --i)
113 last = (1.0 + ke[i + 1]) / (1.0 / last + ke[i + 1] * last);
114
115 return last;
116}
117
118Complex<double> SpecialFunctions::asne (Complex<double> w, double k) noexcept
119{
120 constexpr int M = 4;
121
122 double ke[M + 1];
123 double* kei = ke;
124 *kei = k;
125
126 for (int i = 0; i < M; ++i)
127 {
128 auto next = std::pow (*kei / (1.0 + std::sqrt (1.0 - std::pow (*kei, 2.0))), 2.0);
129 *++kei = next;
130 }
131
132 std::complex<double> last = w;
133
134 for (int i = 1; i <= M; ++i)
135 last = 2.0 * last / ((1.0 + ke[i]) * (1.0 + std::sqrt (1.0 - std::pow (ke[i - 1] * last, 2.0))));
136
137 return 2.0 / MathConstants<double>::pi * std::asin (last);
138}
139
140} // namespace juce::dsp
juce::MathConstants
Definition juce_MathsFunctions.h:139
juce::dsp::SpecialFunctions::sne
static Complex< double > sne(Complex< double > u, double k) noexcept
Definition juce_SpecialFunctions.cpp:95
juce::dsp::SpecialFunctions::besselI0
static double besselI0(double x) noexcept
Definition juce_SpecialFunctions.cpp:29
juce::dsp::SpecialFunctions::cde
static Complex< double > cde(Complex< double > u, double k) noexcept
Definition juce_SpecialFunctions.cpp:72
juce::dsp::SpecialFunctions::asne
static Complex< double > asne(Complex< double > w, double k) noexcept
Definition juce_SpecialFunctions.cpp:118
juce::dsp::SpecialFunctions::ellipticIntegralK
static void ellipticIntegralK(double k, double &K, double &Kp) noexcept
Definition juce_SpecialFunctions.cpp:49