1 | |
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2 | /* @(#)z_asine.c 1.0 98/08/13 */ |
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3 | /****************************************************************** |
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4 | * The following routines are coded directly from the algorithms |
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5 | * and coefficients given in "Software Manual for the Elementary |
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6 | * Functions" by William J. Cody, Jr. and William Waite, Prentice |
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7 | * Hall, 1980. |
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8 | ******************************************************************/ |
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9 | |
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10 | /* |
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11 | FUNCTION |
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12 | <<asin>>, <<asinf>>, <<acos>>, <<acosf>>, <<asine>>, <<asinef>>---arc sine or cosine |
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13 | |
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14 | INDEX |
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15 | asin |
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16 | INDEX |
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17 | asinf |
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18 | INDEX |
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19 | acos |
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20 | INDEX |
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21 | acosf |
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22 | INDEX |
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23 | asine |
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24 | INDEX |
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25 | asinef |
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26 | |
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27 | SYNOPSIS |
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28 | #include <math.h> |
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29 | double asine(double <[x]>); |
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30 | float asinef(float <[x]>); |
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31 | double asin(double <[x]>); |
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32 | float asinf(float <[x]>); |
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33 | double acos(double <[x]>); |
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34 | float acosf(float <[x]>); |
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35 | |
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36 | DESCRIPTION |
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37 | |
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38 | <<asin>> computes the inverse sine or cosine of the argument <[x]>. |
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39 | Arguments to <<asin>> and <<acos>> must be in the range @minus{}1 to 1. |
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40 | |
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41 | <<asinf>> and <<acosf>> are identical to <<asin>> and <<acos>>, other |
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42 | than taking and returning floats. |
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43 | |
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44 | RETURNS |
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45 | @ifnottex |
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46 | <<asin>> and <<acos>> return values in radians, in the range of -pi/2 to pi/2. |
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47 | @end ifnottex |
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48 | @tex |
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49 | <<asin>> and <<acos>> return values in radians, in the range of $-\pi/2$ to $\pi/2$. |
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50 | @end tex |
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51 | |
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52 | If <[x]> is not in the range @minus{}1 to 1, <<asin>> and <<asinf>> |
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53 | return NaN (not a number), set the global variable <<errno>> to |
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54 | <<EDOM>>, and issue a <<DOMAIN error>> message. |
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55 | |
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56 | */ |
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57 | |
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58 | /****************************************************************** |
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59 | * Arcsine |
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60 | * |
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61 | * Input: |
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62 | * x - floating point value |
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63 | * acosine - indicates acos calculation |
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64 | * |
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65 | * Output: |
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66 | * Arcsine of x. |
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67 | * |
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68 | * Description: |
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69 | * This routine calculates arcsine / arccosine. |
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70 | * |
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71 | *****************************************************************/ |
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72 | |
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73 | #include "fdlibm.h" |
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74 | #include "zmath.h" |
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75 | |
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76 | #ifndef _DOUBLE_IS_32BITS |
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77 | |
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78 | static const double p[] = { -0.27368494524164255994e+2, |
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79 | 0.57208227877891731407e+2, |
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80 | -0.39688862997404877339e+2, |
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81 | 0.10152522233806463645e+2, |
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82 | -0.69674573447350646411 }; |
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83 | static const double q[] = { -0.16421096714498560795e+3, |
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84 | 0.41714430248260412556e+3, |
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85 | -0.38186303361750149284e+3, |
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86 | 0.15095270841030604719e+3, |
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87 | -0.23823859153670238830e+2 }; |
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88 | static const double a[] = { 0.0, 0.78539816339744830962 }; |
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89 | static const double b[] = { 1.57079632679489661923, 0.78539816339744830962 }; |
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90 | |
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91 | double |
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92 | asine (double x, |
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93 | int acosine) |
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94 | { |
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95 | int flag, i; |
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96 | int branch = 0; |
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97 | double g, res, R, P, Q, y; |
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98 | |
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99 | /* Check for special values. */ |
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100 | i = numtest (x); |
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101 | if (i == NAN || i == INF) |
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102 | { |
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103 | errno = EDOM; |
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104 | if (i == NAN) |
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105 | return (x); |
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106 | else |
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107 | return (z_infinity.d); |
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108 | } |
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109 | |
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110 | y = fabs (x); |
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111 | flag = acosine; |
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112 | |
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113 | if (y > 0.5) |
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114 | { |
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115 | i = 1 - flag; |
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116 | |
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117 | /* Check for range error. */ |
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118 | if (y > 1.0) |
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119 | { |
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120 | errno = ERANGE; |
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121 | return (z_notanum.d); |
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122 | } |
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123 | |
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124 | g = (1 - y) / 2.0; |
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125 | y = -2 * sqrt (g); |
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126 | branch = 1; |
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127 | } |
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128 | else |
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129 | { |
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130 | i = flag; |
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131 | if (y < z_rooteps) |
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132 | res = y; |
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133 | else |
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134 | g = y * y; |
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135 | } |
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136 | |
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137 | if (y >= z_rooteps || branch == 1) |
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138 | { |
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139 | /* Calculate the Taylor series. */ |
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140 | P = ((((p[4] * g + p[3]) * g + p[2]) * g + p[1]) * g + p[0]) * g; |
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141 | Q = ((((g + q[4]) * g + q[3]) * g + q[2]) * g + q[1]) * g + q[0]; |
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142 | R = P / Q; |
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143 | |
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144 | res = y + y * R; |
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145 | } |
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146 | |
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147 | /* Calculate asine or acose. */ |
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148 | if (flag == 0) |
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149 | { |
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150 | res = (a[i] + res) + a[i]; |
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151 | if (x < 0.0) |
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152 | res = -res; |
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153 | } |
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154 | else |
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155 | { |
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156 | if (x < 0.0) |
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157 | res = (b[i] + res) + b[i]; |
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158 | else |
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159 | res = (a[i] - res) + a[i]; |
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160 | } |
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161 | |
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162 | return (res); |
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163 | } |
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164 | |
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165 | #endif /* _DOUBLE_IS_32BITS */ |
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