1 | /* $NetBSD: cephes_subrl.c,v 1.2 2014/10/10 14:06:40 christos Exp $ */ |
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2 | |
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3 | /*- |
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4 | * Copyright (c) 2007 The NetBSD Foundation, Inc. |
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5 | * All rights reserved. |
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6 | * |
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7 | * This code is derived from software written by Stephen L. Moshier. |
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8 | * It is redistributed by the NetBSD Foundation by permission of the author. |
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9 | * |
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10 | * Redistribution and use in source and binary forms, with or without |
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11 | * modification, are permitted provided that the following conditions |
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12 | * are met: |
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13 | * 1. Redistributions of source code must retain the above copyright |
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14 | * notice, this list of conditions and the following disclaimer. |
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15 | * 2. Redistributions in binary form must reproduce the above copyright |
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16 | * notice, this list of conditions and the following disclaimer in the |
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17 | * documentation and/or other materials provided with the distribution. |
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18 | * |
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19 | * THIS SOFTWARE IS PROVIDED BY THE NETBSD FOUNDATION, INC. AND CONTRIBUTORS |
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20 | * ``AS IS'' AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED |
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21 | * TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR |
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22 | * PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE FOUNDATION OR CONTRIBUTORS |
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23 | * BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR |
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24 | * CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF |
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25 | * SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS |
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26 | * INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN |
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27 | * CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) |
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28 | * ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
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29 | * POSSIBILITY OF SUCH DAMAGE. |
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30 | */ |
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31 | |
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32 | #include <complex.h> |
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33 | #include <math.h> |
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34 | #include "cephes_subrl.h" |
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35 | |
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36 | /* calculate cosh and sinh */ |
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37 | |
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38 | void |
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39 | _cchshl(long double x, long double *c, long double *s) |
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40 | { |
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41 | long double e, ei; |
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42 | |
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43 | if (fabsl(x) <= 0.5L) { |
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44 | *c = coshl(x); |
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45 | *s = sinhl(x); |
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46 | } else { |
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47 | e = expl(x); |
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48 | ei = 0.5L / e; |
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49 | e = 0.5L * e; |
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50 | *s = e - ei; |
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51 | *c = e + ei; |
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52 | } |
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53 | } |
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54 | |
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55 | /* Program to subtract nearest integer multiple of PI */ |
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56 | |
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57 | /* extended precision value of PI: */ |
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58 | static const long double DP1 = 3.14159265358979323829596852490908531763125L; |
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59 | static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; |
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60 | #ifndef __vax__ |
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61 | static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; |
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62 | #define MACHEPL 1.1e-38L |
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63 | #else |
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64 | static const long double DP3 = 0L; |
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65 | #define MACHEPL 1.1e-19L |
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66 | #endif |
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67 | |
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68 | long double |
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69 | _redupil(long double x) |
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70 | { |
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71 | long double t; |
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72 | long long i; |
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73 | |
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74 | t = x / M_PIL; |
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75 | if (t >= 0.0L) |
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76 | t += 0.5L; |
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77 | else |
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78 | t -= 0.5L; |
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79 | |
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80 | i = t; /* the multiple */ |
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81 | t = i; |
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82 | t = ((x - t * DP1) - t * DP2) - t * DP3; |
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83 | return t; |
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84 | } |
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85 | |
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86 | /* Taylor series expansion for cosh(2y) - cos(2x) */ |
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87 | |
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88 | long double |
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89 | _ctansl(long double complex z) |
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90 | { |
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91 | long double f, x, x2, y, y2, rn, t; |
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92 | long double d; |
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93 | |
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94 | x = fabsl(2.0L * creall(z)); |
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95 | y = fabsl(2.0L * cimagl(z)); |
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96 | |
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97 | x = _redupil(x); |
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98 | |
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99 | x = x * x; |
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100 | y = y * y; |
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101 | x2 = 1.0; |
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102 | y2 = 1.0; |
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103 | f = 1.0; |
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104 | rn = 0.0; |
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105 | d = 0.0; |
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106 | do { |
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107 | rn += 1.0L; |
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108 | f *= rn; |
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109 | rn += 1.0L; |
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110 | f *= rn; |
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111 | x2 *= x; |
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112 | y2 *= y; |
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113 | t = y2 + x2; |
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114 | t /= f; |
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115 | d += t; |
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116 | |
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117 | rn += 1.0L; |
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118 | f *= rn; |
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119 | rn += 1.0L; |
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120 | f *= rn; |
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121 | x2 *= x; |
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122 | y2 *= y; |
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123 | t = y2 - x2; |
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124 | t /= f; |
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125 | d += t; |
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126 | } while (fabsl(t/d) > MACHEPL); |
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127 | return d; |
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128 | } |
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