1 | /* $NetBSD: casinl.c,v 1.1 2014/10/10 00:48:18 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 | |
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35 | #ifdef __weak_alias |
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36 | __weak_alias(casinl, _casinl) |
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37 | #endif |
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38 | |
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39 | long double complex |
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40 | casinl(long double complex z) |
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41 | { |
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42 | long double complex w; |
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43 | long double complex ca, ct, zz, z2; |
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44 | long double x, y; |
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45 | |
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46 | x = creall(z); |
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47 | y = cimagl(z); |
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48 | |
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49 | #if 0 /* MD: test is incorrect, casin(>1) is defined */ |
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50 | if (y == 0.0L) { |
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51 | if (fabsl(x) > 1.0L) { |
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52 | w = M_PI_2L + 0.0L * I; |
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53 | #if 0 |
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54 | mtherr ("casinl", DOMAIN); |
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55 | #endif |
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56 | } else { |
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57 | w = asinl(x) + 0.0L * I; |
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58 | } |
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59 | return w; |
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60 | } |
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61 | #endif |
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62 | |
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63 | /* Power series expansion */ |
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64 | /* |
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65 | b = cabsl(z); |
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66 | if( b < 0.125L ) |
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67 | { |
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68 | z2.r = (x - y) * (x + y); |
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69 | z2.i = 2.0L * x * y; |
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70 | |
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71 | cn = 1.0L; |
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72 | n = 1.0L; |
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73 | ca.r = x; |
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74 | ca.i = y; |
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75 | sum.r = x; |
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76 | sum.i = y; |
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77 | do |
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78 | { |
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79 | ct.r = z2.r * ca.r - z2.i * ca.i; |
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80 | ct.i = z2.r * ca.i + z2.i * ca.r; |
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81 | ca.r = ct.r; |
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82 | ca.i = ct.i; |
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83 | |
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84 | cn *= n; |
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85 | n += 1.0; |
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86 | cn /= n; |
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87 | n += 1.0; |
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88 | b = cn/n; |
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89 | |
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90 | ct.r *= b; |
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91 | ct.i *= b; |
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92 | sum.r += ct.r; |
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93 | sum.i += ct.i; |
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94 | b = fabsl(ct.r) + fabsl(ct.i); |
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95 | } |
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96 | while( b > MACHEPL ); |
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97 | w->r = sum.r; |
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98 | w->i = sum.i; |
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99 | return; |
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100 | } |
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101 | */ |
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102 | |
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103 | |
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104 | ca = x + y * I; |
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105 | ct = ca * I; |
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106 | /* sqrtl( 1 - z*z) */ |
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107 | /* cmull( &ca, &ca, &zz ) */ |
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108 | /*x * x - y * y */ |
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109 | zz = (x - y) * (x + y) + (2.0L * x * y) * I; |
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110 | |
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111 | zz = 1.0L - creall(zz) - cimagl(zz) * I; |
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112 | z2 = csqrtl(zz); |
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113 | |
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114 | zz = ct + z2; |
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115 | zz = clogl(zz); |
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116 | /* multiply by 1/i = -i */ |
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117 | w = zz * (-1.0L * I); |
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118 | return w; |
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119 | } |
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120 | |
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