1 | |
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2 | /* @(#)z_atangent.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 | <<atan>>, <<atanf>>, <<atan2>>, <<atan2f>>, <<atangent>>, <<atangentf>>---arc tangent |
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13 | |
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14 | INDEX |
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15 | atan2 |
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16 | INDEX |
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17 | atan2f |
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18 | INDEX |
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19 | atan |
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20 | INDEX |
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21 | atanf |
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22 | |
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23 | SYNOPSIS |
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24 | #include <math.h> |
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25 | double atan(double <[x]>); |
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26 | float atan(float <[x]>); |
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27 | double atan2(double <[y]>,double <[x]>); |
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28 | float atan2f(float <[y]>,float <[x]>); |
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29 | |
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30 | DESCRIPTION |
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31 | |
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32 | <<atan2>> computes the inverse tangent (arc tangent) of y / x. |
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33 | |
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34 | <<atan2f>> is identical to <<atan2>>, save that it operates on <<floats>>. |
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35 | |
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36 | <<atan>> computes the inverse tangent (arc tangent) of the input value. |
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37 | |
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38 | <<atanf>> is identical to <<atan>>, save that it operates on <<floats>>. |
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39 | |
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40 | RETURNS |
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41 | @ifnottex |
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42 | <<atan>> returns a value in radians, in the range of -pi/2 to pi/2. |
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43 | <<atan2>> returns a value in radians, in the range of -pi/2 to pi/2. |
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44 | @end ifnottex |
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45 | @tex |
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46 | <<atan>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$. |
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47 | <<atan2>> returns a value in radians, in the range of $-\pi/2$ to $\pi/2$. |
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48 | @end tex |
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49 | |
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50 | PORTABILITY |
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51 | <<atan>> is ANSI C. <<atanf>> is an extension. |
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52 | <<atan2>> is ANSI C. <<atan2f>> is an extension. |
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53 | |
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54 | */ |
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55 | |
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56 | /****************************************************************** |
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57 | * Arctangent |
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58 | * |
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59 | * Input: |
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60 | * x - floating point value |
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61 | * |
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62 | * Output: |
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63 | * arctangent of x |
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64 | * |
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65 | * Description: |
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66 | * This routine calculates arctangents. |
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67 | * |
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68 | *****************************************************************/ |
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69 | #include <float.h> |
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70 | #include "fdlibm.h" |
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71 | #include "zmath.h" |
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72 | |
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73 | #ifndef _DOUBLE_IS_32BITS |
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74 | |
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75 | static const double ROOT3 = 1.73205080756887729353; |
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76 | static const double a[] = { 0.0, 0.52359877559829887308, 1.57079632679489661923, |
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77 | 1.04719755119659774615 }; |
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78 | static const double q[] = { 0.41066306682575781263e+2, |
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79 | 0.86157349597130242515e+2, |
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80 | 0.59578436142597344465e+2, |
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81 | 0.15024001160028576121e+2 }; |
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82 | static const double p[] = { -0.13688768894191926929e+2, |
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83 | -0.20505855195861651981e+2, |
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84 | -0.84946240351320683534e+1, |
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85 | -0.83758299368150059274 }; |
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86 | |
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87 | double |
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88 | atangent (double x, |
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89 | double v, |
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90 | double u, |
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91 | int arctan2) |
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92 | { |
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93 | double f, g, R, P, Q, A, res; |
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94 | int N; |
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95 | int branch = 0; |
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96 | int expv, expu; |
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97 | |
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98 | /* Preparation for calculating arctan2. */ |
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99 | if (arctan2) |
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100 | { |
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101 | if (u == 0.0) |
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102 | if (v == 0.0) |
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103 | { |
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104 | errno = ERANGE; |
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105 | return (z_notanum.d); |
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106 | } |
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107 | else |
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108 | { |
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109 | branch = 1; |
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110 | res = __PI_OVER_TWO; |
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111 | } |
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112 | |
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113 | if (!branch) |
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114 | { |
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115 | int e; |
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116 | /* Get the exponent values of the inputs. */ |
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117 | g = frexp (v, &expv); |
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118 | g = frexp (u, &expu); |
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119 | |
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120 | /* See if a divide will overflow. */ |
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121 | e = expv - expu; |
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122 | if (e > DBL_MAX_EXP) |
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123 | { |
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124 | branch = 1; |
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125 | res = __PI_OVER_TWO; |
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126 | } |
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127 | |
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128 | /* Also check for underflow. */ |
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129 | else if (e < DBL_MIN_EXP) |
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130 | { |
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131 | branch = 2; |
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132 | res = 0.0; |
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133 | } |
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134 | } |
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135 | } |
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136 | |
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137 | if (!branch) |
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138 | { |
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139 | if (arctan2) |
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140 | f = fabs (v / u); |
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141 | else |
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142 | f = fabs (x); |
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143 | |
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144 | if (f > 1.0) |
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145 | { |
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146 | f = 1.0 / f; |
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147 | N = 2; |
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148 | } |
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149 | else |
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150 | N = 0; |
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151 | |
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152 | if (f > (2.0 - ROOT3)) |
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153 | { |
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154 | A = ROOT3 - 1.0; |
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155 | f = (((A * f - 0.5) - 0.5) + f) / (ROOT3 + f); |
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156 | N++; |
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157 | } |
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158 | |
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159 | /* Check for values that are too small. */ |
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160 | if (-z_rooteps < f && f < z_rooteps) |
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161 | res = f; |
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162 | |
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163 | /* Calculate the Taylor series. */ |
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164 | else |
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165 | { |
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166 | g = f * f; |
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167 | P = (((p[3] * g + p[2]) * g + p[1]) * g + p[0]) * g; |
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168 | Q = (((g + q[3]) * g + q[2]) * g + q[1]) * g + q[0]; |
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169 | R = P / Q; |
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170 | |
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171 | res = f + f * R; |
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172 | } |
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173 | |
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174 | if (N > 1) |
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175 | res = -res; |
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176 | |
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177 | res += a[N]; |
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178 | } |
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179 | |
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180 | if (arctan2) |
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181 | { |
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182 | if (u < 0.0) |
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183 | res = __PI - res; |
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184 | if (v < 0.0) |
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185 | res = -res; |
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186 | } |
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187 | else if (x < 0.0) |
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188 | { |
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189 | res = -res; |
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190 | } |
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191 | |
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192 | return (res); |
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193 | } |
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194 | |
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195 | #endif /* _DOUBLE_IS_32BITS */ |
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