1 | /* $NetBSD: casin.c,v 1.1 2007/08/20 16:01:31 drochner 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 | * imported and modified include for newlib 2010/10/03 |
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32 | * Marco Atzeri <marco_atzeri@yahoo.it> |
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33 | */ |
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34 | |
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35 | /* |
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36 | FUNCTION |
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37 | <<casin>>, <<casinf>>---complex arc sine |
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38 | |
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39 | INDEX |
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40 | casin |
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41 | INDEX |
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42 | casinf |
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43 | |
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44 | SYNOPSIS |
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45 | #include <complex.h> |
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46 | double complex casin(double complex <[z]>); |
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47 | float complex casinf(float complex <[z]>); |
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48 | |
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49 | |
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50 | DESCRIPTION |
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51 | These functions compute the complex arc sine of <[z]>, |
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52 | with branch cuts outside the interval [-1, +1] along the real axis. |
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53 | |
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54 | <<casinf>> is identical to <<casin>>, except that it performs |
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55 | its calculations on <<floats complex>>. |
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56 | |
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57 | RETURNS |
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58 | @ifnottex |
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59 | These functions return the complex arc sine value, in the range |
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60 | of a strip mathematically unbounded along the imaginary axis |
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61 | and in the interval [-pi/2, +pi/2] along the real axis. |
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62 | @end ifnottex |
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63 | @tex |
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64 | These functions return the complex arc sine value, in the range |
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65 | of a strip mathematically unbounded along the imaginary axis |
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66 | and in the interval [$-\pi/2$, $+\pi/2$] along the real axis. |
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67 | @end tex |
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68 | |
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69 | PORTABILITY |
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70 | <<casin>> and <<casinf>> are ISO C99 |
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71 | |
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72 | QUICKREF |
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73 | <<casin>> and <<casinf>> are ISO C99 |
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74 | |
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75 | */ |
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76 | |
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77 | |
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78 | #include <complex.h> |
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79 | #include <math.h> |
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80 | |
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81 | #ifdef __weak_alias |
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82 | __weak_alias(casin, _casin) |
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83 | #endif |
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84 | |
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85 | double complex |
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86 | casin(double complex z) |
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87 | { |
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88 | double complex w; |
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89 | double complex ca, ct, zz, z2; |
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90 | double x, y; |
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91 | |
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92 | x = creal(z); |
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93 | y = cimag(z); |
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94 | |
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95 | #if 0 /* MD: test is incorrect, casin(>1) is defined */ |
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96 | if (y == 0.0) { |
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97 | if (fabs(x) > 1.0) { |
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98 | w = M_PI_2 + 0.0 * I; |
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99 | #if 0 |
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100 | mtherr ("casin", DOMAIN); |
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101 | #endif |
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102 | } else { |
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103 | w = asin(x) + 0.0 * I; |
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104 | } |
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105 | return w; |
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106 | } |
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107 | #endif |
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108 | |
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109 | /* Power series expansion */ |
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110 | /* |
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111 | b = cabs(z); |
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112 | if( b < 0.125 ) |
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113 | { |
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114 | z2.r = (x - y) * (x + y); |
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115 | z2.i = 2.0 * x * y; |
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116 | |
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117 | cn = 1.0; |
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118 | n = 1.0; |
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119 | ca.r = x; |
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120 | ca.i = y; |
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121 | sum.r = x; |
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122 | sum.i = y; |
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123 | do |
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124 | { |
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125 | ct.r = z2.r * ca.r - z2.i * ca.i; |
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126 | ct.i = z2.r * ca.i + z2.i * ca.r; |
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127 | ca.r = ct.r; |
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128 | ca.i = ct.i; |
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129 | |
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130 | cn *= n; |
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131 | n += 1.0; |
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132 | cn /= n; |
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133 | n += 1.0; |
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134 | b = cn/n; |
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135 | |
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136 | ct.r *= b; |
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137 | ct.i *= b; |
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138 | sum.r += ct.r; |
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139 | sum.i += ct.i; |
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140 | b = fabs(ct.r) + fabs(ct.i); |
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141 | } |
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142 | while( b > MACHEP ); |
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143 | w->r = sum.r; |
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144 | w->i = sum.i; |
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145 | return; |
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146 | } |
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147 | */ |
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148 | |
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149 | |
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150 | ca = x + y * I; |
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151 | ct = ca * I; |
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152 | /* sqrt( 1 - z*z) */ |
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153 | /* cmul( &ca, &ca, &zz ) */ |
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154 | /*x * x - y * y */ |
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155 | zz = (x - y) * (x + y) + (2.0 * x * y) * I; |
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156 | |
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157 | zz = 1.0 - creal(zz) - cimag(zz) * I; |
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158 | z2 = csqrt(zz); |
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159 | |
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160 | zz = ct + z2; |
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161 | zz = clog(zz); |
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162 | /* multiply by 1/i = -i */ |
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163 | w = zz * (-1.0 * I); |
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164 | return w; |
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165 | } |
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