1 | /* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during |
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2 | * errors to make test scripts easier.) */ |
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3 | /* @(#)e_fmod.c 1.3 95/01/18 */ |
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4 | /*- |
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5 | * ==================================================== |
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6 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
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7 | * |
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8 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
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9 | * Permission to use, copy, modify, and distribute this |
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10 | * software is freely granted, provided that this notice |
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11 | * is preserved. |
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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 | <<remquo>>, <<remquof>>---remainder and part of quotient |
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17 | INDEX |
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18 | remquo |
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19 | INDEX |
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20 | remquof |
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21 | |
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22 | SYNOPSIS |
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23 | #include <math.h> |
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24 | double remquo(double <[x]>, double <[y]>, int *<[quo]>); |
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25 | float remquof(float <[x]>, float <[y]>, int *<[quo]>); |
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26 | |
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27 | DESCRIPTION |
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28 | The <<remquo>> functions compute the same remainder as the <<remainder>> |
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29 | functions; this value is in the range -<[y]>/2 ... +<[y]>/2. In the object |
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30 | pointed to by <<quo>> they store a value whose sign is the sign of <<x>>/<<y>> |
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31 | and whose magnitude is congruent modulo 2**n to the magnitude of the integral |
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32 | quotient of <<x>>/<<y>>. (That is, <<quo>> is given the n lsbs of the |
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33 | quotient, not counting the sign.) This implementation uses n=31 if int is 32 |
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34 | bits or more, otherwise, n is 1 less than the width of int. |
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35 | |
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36 | For example: |
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37 | . remquo(-29.0, 3.0, &<[quo]>) |
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38 | returns -1.0 and sets <[quo]>=10, and |
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39 | . remquo(-98307.0, 3.0, &<[quo]>) |
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40 | returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1. In |
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41 | the latter case, the actual quotient of -(32769=0x8001) is reduced to -1 |
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42 | because of the 15-bit limitation for the quotient. |
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43 | |
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44 | RETURNS |
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45 | When either argument is NaN, NaN is returned. If <[y]> is 0 or <[x]> is |
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46 | infinite (and neither is NaN), a domain error occurs (i.e. the "invalid" |
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47 | floating point exception is raised or errno is set to EDOM), and NaN is |
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48 | returned. |
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49 | Otherwise, the <<remquo>> functions return <[x]> REM <[y]>. |
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50 | |
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51 | BUGS |
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52 | IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow" |
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53 | floating-point exception. This implementation does not. |
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54 | |
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55 | PORTABILITY |
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56 | C99, POSIX. |
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57 | |
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58 | */ |
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59 | |
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60 | #include <limits.h> |
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61 | #include <math.h> |
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62 | #include "fdlibm.h" |
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63 | |
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64 | /* For quotient, return either all 31 bits that can from calculation (using |
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65 | * int32_t), or as many as can fit into an int that is smaller than 32 bits. */ |
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66 | #if INT_MAX > 0x7FFFFFFFL |
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67 | #define QUO_MASK 0x7FFFFFFF |
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68 | # else |
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69 | #define QUO_MASK INT_MAX |
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70 | #endif |
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71 | |
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72 | static const double Zero[] = {0.0, -0.0,}; |
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73 | |
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74 | /* |
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75 | * Return the IEEE remainder and set *quo to the last n bits of the |
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76 | * quotient, rounded to the nearest integer. We choose n=31--if that many fit-- |
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77 | * because we wind up computing all the integer bits of the quotient anyway as |
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78 | * a side-effect of computing the remainder by the shift and subtract |
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79 | * method. In practice, this is far more bits than are needed to use |
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80 | * remquo in reduction algorithms. |
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81 | */ |
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82 | double |
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83 | remquo(double x, double y, int *quo) |
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84 | { |
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85 | __int32_t n,hx,hy,hz,ix,iy,sx,i; |
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86 | __uint32_t lx,ly,lz,q,sxy; |
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87 | |
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88 | EXTRACT_WORDS(hx,lx,x); |
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89 | EXTRACT_WORDS(hy,ly,y); |
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90 | sxy = (hx ^ hy) & 0x80000000; |
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91 | sx = hx&0x80000000; /* sign of x */ |
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92 | hx ^=sx; /* |x| */ |
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93 | hy &= 0x7fffffff; /* |y| */ |
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94 | |
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95 | /* purge off exception values */ |
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96 | if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ |
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97 | ((hy|((ly|-ly)>>31))>0x7ff00000)) { /* or y is NaN */ |
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98 | *quo = 0; /* Not necessary, but return consistent value */ |
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99 | return (x*y)/(x*y); |
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100 | } |
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101 | if(hx<=hy) { |
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102 | if((hx<hy)||(lx<ly)) { |
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103 | q = 0; |
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104 | goto fixup; /* |x|<|y| return x or x-y */ |
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105 | } |
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106 | if(lx==ly) { |
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107 | *quo = (sxy ? -1 : 1); |
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108 | return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0 */ |
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109 | } |
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110 | } |
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111 | |
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112 | /* determine ix = ilogb(x) */ |
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113 | if(hx<0x00100000) { /* subnormal x */ |
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114 | if(hx==0) { |
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115 | for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; |
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116 | } else { |
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117 | for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; |
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118 | } |
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119 | } else ix = (hx>>20)-1023; |
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120 | |
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121 | /* determine iy = ilogb(y) */ |
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122 | if(hy<0x00100000) { /* subnormal y */ |
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123 | if(hy==0) { |
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124 | for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; |
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125 | } else { |
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126 | for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; |
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127 | } |
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128 | } else iy = (hy>>20)-1023; |
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129 | |
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130 | /* set up {hx,lx}, {hy,ly} and align y to x */ |
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131 | if(ix >= -1022) |
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132 | hx = 0x00100000|(0x000fffff&hx); |
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133 | else { /* subnormal x, shift x to normal */ |
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134 | n = -1022-ix; |
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135 | if(n<=31) { |
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136 | hx = (hx<<n)|(lx>>(32-n)); |
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137 | lx <<= n; |
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138 | } else { |
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139 | hx = lx<<(n-32); |
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140 | lx = 0; |
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141 | } |
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142 | } |
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143 | if(iy >= -1022) |
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144 | hy = 0x00100000|(0x000fffff&hy); |
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145 | else { /* subnormal y, shift y to normal */ |
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146 | n = -1022-iy; |
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147 | if(n<=31) { |
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148 | hy = (hy<<n)|(ly>>(32-n)); |
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149 | ly <<= n; |
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150 | } else { |
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151 | hy = ly<<(n-32); |
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152 | ly = 0; |
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153 | } |
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154 | } |
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155 | |
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156 | /* fix point fmod */ |
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157 | n = ix - iy; |
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158 | q = 0; |
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159 | while(n--) { |
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160 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
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161 | if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} |
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162 | else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} |
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163 | q <<= 1; |
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164 | } |
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165 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
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166 | if(hz>=0) {hx=hz;lx=lz;q++;} |
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167 | |
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168 | /* convert back to floating value and restore the sign */ |
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169 | if((hx|lx)==0) { /* return sign(x)*0 */ |
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170 | q &= QUO_MASK; |
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171 | *quo = (sxy ? -q : q); |
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172 | return Zero[(__uint32_t)sx>>31]; |
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173 | } |
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174 | while(hx<0x00100000) { /* normalize x */ |
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175 | hx = hx+hx+(lx>>31); lx = lx+lx; |
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176 | iy -= 1; |
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177 | } |
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178 | if(iy>= -1022) { /* normalize output */ |
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179 | hx = ((hx-0x00100000)|((iy+1023)<<20)); |
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180 | } else { /* subnormal output */ |
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181 | n = -1022 - iy; |
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182 | if(n<=20) { |
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183 | lx = (lx>>n)|((__uint32_t)hx<<(32-n)); |
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184 | hx >>= n; |
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185 | } else if (n<=31) { |
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186 | lx = (hx<<(32-n))|(lx>>n); hx = sx; |
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187 | } else { |
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188 | lx = hx>>(n-32); hx = sx; |
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189 | } |
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190 | } |
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191 | fixup: |
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192 | INSERT_WORDS(x,hx,lx); |
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193 | y = fabs(y); |
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194 | if (y < 0x1p-1021) { |
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195 | if (x+x>y || (x+x==y && (q & 1))) { |
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196 | q++; |
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197 | x-=y; |
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198 | } |
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199 | } else if (x>0.5*y || (x==0.5*y && (q & 1))) { |
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200 | q++; |
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201 | x-=y; |
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202 | } |
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203 | GET_HIGH_WORD(hx,x); |
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204 | SET_HIGH_WORD(x,hx^sx); |
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205 | q &= QUO_MASK; |
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206 | *quo = (sxy ? -q : q); |
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207 | return x; |
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208 | } |
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