1 | |
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2 | /* @(#)z_fmod.c 1.0 98/08/13 */ |
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3 | /* |
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4 | * ==================================================== |
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5 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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6 | * |
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7 | * Developed at SunPro, a Sun Microsystems, Inc. business. |
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8 | * Permission to use, copy, modify, and distribute this |
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9 | * software is freely granted, provided that this notice |
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10 | * is preserved. |
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11 | * ==================================================== |
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12 | */ |
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13 | |
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14 | /* |
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15 | FUNCTION |
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16 | <<fmod>>, <<fmodf>>---floating-point remainder (modulo) |
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17 | |
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18 | INDEX |
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19 | fmod |
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20 | INDEX |
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21 | fmodf |
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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 fmod(double <[x]>, double <[y]>); |
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26 | float fmodf(float <[x]>, float <[y]>); |
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27 | |
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28 | DESCRIPTION |
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29 | The <<fmod>> and <<fmodf>> functions compute the floating-point |
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30 | remainder of <[x]>/<[y]> (<[x]> modulo <[y]>). |
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31 | |
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32 | RETURNS |
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33 | The <<fmod>> function returns the value |
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34 | @ifnottex |
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35 | <[x]>-<[i]>*<[y]>, |
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36 | @end ifnottex |
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37 | @tex |
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38 | $x-i\times y$, |
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39 | @end tex |
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40 | for the largest integer <[i]> such that, if <[y]> is nonzero, the |
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41 | result has the same sign as <[x]> and magnitude less than the |
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42 | magnitude of <[y]>. |
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43 | |
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44 | <<fmod(<[x]>,0)>> returns NaN, and sets <<errno>> to <<EDOM>>. |
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45 | |
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46 | You can modify error treatment for these functions using <<matherr>>. |
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47 | |
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48 | PORTABILITY |
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49 | <<fmod>> is ANSI C. <<fmodf>> is an extension. |
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50 | */ |
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51 | |
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52 | /* |
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53 | * fmod(x,y) |
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54 | * Return x mod y in exact arithmetic |
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55 | * Method: shift and subtract |
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56 | */ |
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57 | |
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58 | #include "fdlibm.h" |
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59 | #include "zmath.h" |
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60 | |
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61 | #ifndef _DOUBLE_IS_32BITS |
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62 | |
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63 | #ifdef __STDC__ |
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64 | static const double one = 1.0, Zero[] = {0.0, -0.0,}; |
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65 | #else |
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66 | static double one = 1.0, Zero[] = {0.0, -0.0,}; |
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67 | #endif |
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68 | |
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69 | #ifdef __STDC__ |
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70 | double fmod(double x, double y) |
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71 | #else |
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72 | double fmod(x,y) |
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73 | double x,y ; |
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74 | #endif |
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75 | { |
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76 | __int32_t n,hx,hy,hz,ix,iy,sx,i; |
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77 | __uint32_t lx,ly,lz; |
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78 | |
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79 | EXTRACT_WORDS(hx,lx,x); |
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80 | EXTRACT_WORDS(hy,ly,y); |
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81 | sx = hx&0x80000000; /* sign of x */ |
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82 | hx ^=sx; /* |x| */ |
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83 | hy &= 0x7fffffff; /* |y| */ |
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84 | |
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85 | /* purge off exception values */ |
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86 | if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ |
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87 | ((hy|((ly|-ly)>>31))>0x7ff00000)) /* or y is NaN */ |
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88 | return (x*y)/(x*y); |
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89 | if(hx<=hy) { |
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90 | if((hx<hy)||(lx<ly)) return x; /* |x|<|y| return x */ |
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91 | if(lx==ly) |
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92 | return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0*/ |
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93 | } |
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94 | |
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95 | /* determine ix = ilogb(x) */ |
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96 | if(hx<0x00100000) { /* subnormal x */ |
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97 | if(hx==0) { |
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98 | for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; |
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99 | } else { |
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100 | for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; |
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101 | } |
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102 | } else ix = (hx>>20)-1023; |
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103 | |
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104 | /* determine iy = ilogb(y) */ |
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105 | if(hy<0x00100000) { /* subnormal y */ |
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106 | if(hy==0) { |
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107 | for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; |
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108 | } else { |
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109 | for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; |
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110 | } |
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111 | } else iy = (hy>>20)-1023; |
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112 | |
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113 | /* set up {hx,lx}, {hy,ly} and align y to x */ |
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114 | if(ix >= -1022) |
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115 | hx = 0x00100000|(0x000fffff&hx); |
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116 | else { /* subnormal x, shift x to normal */ |
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117 | n = -1022-ix; |
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118 | if(n<=31) { |
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119 | hx = (hx<<n)|(lx>>(32-n)); |
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120 | lx <<= n; |
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121 | } else { |
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122 | hx = lx<<(n-32); |
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123 | lx = 0; |
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124 | } |
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125 | } |
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126 | if(iy >= -1022) |
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127 | hy = 0x00100000|(0x000fffff&hy); |
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128 | else { /* subnormal y, shift y to normal */ |
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129 | n = -1022-iy; |
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130 | if(n<=31) { |
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131 | hy = (hy<<n)|(ly>>(32-n)); |
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132 | ly <<= n; |
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133 | } else { |
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134 | hy = ly<<(n-32); |
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135 | ly = 0; |
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136 | } |
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137 | } |
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138 | |
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139 | /* fix point fmod */ |
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140 | n = ix - iy; |
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141 | while(n--) { |
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142 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
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143 | if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} |
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144 | else { |
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145 | if((hz|lz)==0) /* return sign(x)*0 */ |
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146 | return Zero[(__uint32_t)sx>>31]; |
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147 | hx = hz+hz+(lz>>31); lx = lz+lz; |
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148 | } |
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149 | } |
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150 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
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151 | if(hz>=0) {hx=hz;lx=lz;} |
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152 | |
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153 | /* convert back to floating value and restore the sign */ |
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154 | if((hx|lx)==0) /* return sign(x)*0 */ |
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155 | return Zero[(__uint32_t)sx>>31]; |
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156 | while(hx<0x00100000) { /* normalize x */ |
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157 | hx = hx+hx+(lx>>31); lx = lx+lx; |
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158 | iy -= 1; |
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159 | } |
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160 | if(iy>= -1022) { /* normalize output */ |
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161 | hx = ((hx-0x00100000)|((iy+1023)<<20)); |
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162 | INSERT_WORDS(x,hx|sx,lx); |
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163 | } else { /* subnormal output */ |
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164 | n = -1022 - iy; |
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165 | if(n<=20) { |
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166 | lx = (lx>>n)|((__uint32_t)hx<<(32-n)); |
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167 | hx >>= n; |
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168 | } else if (n<=31) { |
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169 | lx = (hx<<(32-n))|(lx>>n); hx = sx; |
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170 | } else { |
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171 | lx = hx>>(n-32); hx = sx; |
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172 | } |
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173 | INSERT_WORDS(x,hx|sx,lx); |
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174 | x *= one; /* create necessary signal */ |
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175 | } |
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176 | return x; /* exact output */ |
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177 | } |
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178 | |
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179 | #endif /* defined(_DOUBLE_IS_32BITS) */ |
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