[444] | 1 | /* Adapted for Newlib, 2009. (Allow for int < 32 bits; return *quo=0 during |
---|
| 2 | * errors to make test scripts easier.) */ |
---|
| 3 | /* @(#)e_fmod.c 1.3 95/01/18 */ |
---|
| 4 | /*- |
---|
| 5 | * ==================================================== |
---|
| 6 | * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved. |
---|
| 7 | * |
---|
| 8 | * Developed at SunSoft, a Sun Microsystems, Inc. business. |
---|
| 9 | * Permission to use, copy, modify, and distribute this |
---|
| 10 | * software is freely granted, provided that this notice |
---|
| 11 | * is preserved. |
---|
| 12 | * ==================================================== |
---|
| 13 | */ |
---|
| 14 | /* |
---|
| 15 | FUNCTION |
---|
| 16 | <<remquo>>, <<remquof>>---remainder and part of quotient |
---|
| 17 | INDEX |
---|
| 18 | remquo |
---|
| 19 | INDEX |
---|
| 20 | remquof |
---|
| 21 | |
---|
| 22 | SYNOPSIS |
---|
| 23 | #include <math.h> |
---|
| 24 | double remquo(double <[x]>, double <[y]>, int *<[quo]>); |
---|
| 25 | float remquof(float <[x]>, float <[y]>, int *<[quo]>); |
---|
| 26 | |
---|
| 27 | DESCRIPTION |
---|
| 28 | The <<remquo>> functions compute the same remainder as the <<remainder>> |
---|
| 29 | functions; this value is in the range -<[y]>/2 ... +<[y]>/2. In the object |
---|
| 30 | pointed to by <<quo>> they store a value whose sign is the sign of <<x>>/<<y>> |
---|
| 31 | and whose magnitude is congruent modulo 2**n to the magnitude of the integral |
---|
| 32 | quotient of <<x>>/<<y>>. (That is, <<quo>> is given the n lsbs of the |
---|
| 33 | quotient, not counting the sign.) This implementation uses n=31 if int is 32 |
---|
| 34 | bits or more, otherwise, n is 1 less than the width of int. |
---|
| 35 | |
---|
| 36 | For example: |
---|
| 37 | . remquo(-29.0, 3.0, &<[quo]>) |
---|
| 38 | returns -1.0 and sets <[quo]>=10, and |
---|
| 39 | . remquo(-98307.0, 3.0, &<[quo]>) |
---|
| 40 | returns -0.0 and sets <[quo]>=-32769, although for 16-bit int, <[quo]>=-1. In |
---|
| 41 | the latter case, the actual quotient of -(32769=0x8001) is reduced to -1 |
---|
| 42 | because of the 15-bit limitation for the quotient. |
---|
| 43 | |
---|
| 44 | RETURNS |
---|
| 45 | When either argument is NaN, NaN is returned. If <[y]> is 0 or <[x]> is |
---|
| 46 | infinite (and neither is NaN), a domain error occurs (i.e. the "invalid" |
---|
| 47 | floating point exception is raised or errno is set to EDOM), and NaN is |
---|
| 48 | returned. |
---|
| 49 | Otherwise, the <<remquo>> functions return <[x]> REM <[y]>. |
---|
| 50 | |
---|
| 51 | BUGS |
---|
| 52 | IEEE754-2008 calls for <<remquo>>(subnormal, inf) to cause the "underflow" |
---|
| 53 | floating-point exception. This implementation does not. |
---|
| 54 | |
---|
| 55 | PORTABILITY |
---|
| 56 | C99, POSIX. |
---|
| 57 | |
---|
| 58 | */ |
---|
| 59 | |
---|
| 60 | #include <limits.h> |
---|
| 61 | #include <math.h> |
---|
| 62 | #include "fdlibm.h" |
---|
| 63 | |
---|
| 64 | /* For quotient, return either all 31 bits that can from calculation (using |
---|
| 65 | * int32_t), or as many as can fit into an int that is smaller than 32 bits. */ |
---|
| 66 | #if INT_MAX > 0x7FFFFFFFL |
---|
| 67 | #define QUO_MASK 0x7FFFFFFF |
---|
| 68 | # else |
---|
| 69 | #define QUO_MASK INT_MAX |
---|
| 70 | #endif |
---|
| 71 | |
---|
| 72 | static const double Zero[] = {0.0, -0.0,}; |
---|
| 73 | |
---|
| 74 | /* |
---|
| 75 | * Return the IEEE remainder and set *quo to the last n bits of the |
---|
| 76 | * quotient, rounded to the nearest integer. We choose n=31--if that many fit-- |
---|
| 77 | * because we wind up computing all the integer bits of the quotient anyway as |
---|
| 78 | * a side-effect of computing the remainder by the shift and subtract |
---|
| 79 | * method. In practice, this is far more bits than are needed to use |
---|
| 80 | * remquo in reduction algorithms. |
---|
| 81 | */ |
---|
| 82 | double |
---|
| 83 | remquo(double x, double y, int *quo) |
---|
| 84 | { |
---|
| 85 | __int32_t n,hx,hy,hz,ix,iy,sx,i; |
---|
| 86 | __uint32_t lx,ly,lz,q,sxy; |
---|
| 87 | |
---|
| 88 | EXTRACT_WORDS(hx,lx,x); |
---|
| 89 | EXTRACT_WORDS(hy,ly,y); |
---|
| 90 | sxy = (hx ^ hy) & 0x80000000; |
---|
| 91 | sx = hx&0x80000000; /* sign of x */ |
---|
| 92 | hx ^=sx; /* |x| */ |
---|
| 93 | hy &= 0x7fffffff; /* |y| */ |
---|
| 94 | |
---|
| 95 | /* purge off exception values */ |
---|
| 96 | if((hy|ly)==0||(hx>=0x7ff00000)|| /* y=0,or x not finite */ |
---|
| 97 | ((hy|((ly|-ly)>>31))>0x7ff00000)) { /* or y is NaN */ |
---|
| 98 | *quo = 0; /* Not necessary, but return consistent value */ |
---|
| 99 | return (x*y)/(x*y); |
---|
| 100 | } |
---|
| 101 | if(hx<=hy) { |
---|
| 102 | if((hx<hy)||(lx<ly)) { |
---|
| 103 | q = 0; |
---|
| 104 | goto fixup; /* |x|<|y| return x or x-y */ |
---|
| 105 | } |
---|
| 106 | if(lx==ly) { |
---|
| 107 | *quo = (sxy ? -1 : 1); |
---|
| 108 | return Zero[(__uint32_t)sx>>31]; /* |x|=|y| return x*0 */ |
---|
| 109 | } |
---|
| 110 | } |
---|
| 111 | |
---|
| 112 | /* determine ix = ilogb(x) */ |
---|
| 113 | if(hx<0x00100000) { /* subnormal x */ |
---|
| 114 | if(hx==0) { |
---|
| 115 | for (ix = -1043, i=lx; i>0; i<<=1) ix -=1; |
---|
| 116 | } else { |
---|
| 117 | for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1; |
---|
| 118 | } |
---|
| 119 | } else ix = (hx>>20)-1023; |
---|
| 120 | |
---|
| 121 | /* determine iy = ilogb(y) */ |
---|
| 122 | if(hy<0x00100000) { /* subnormal y */ |
---|
| 123 | if(hy==0) { |
---|
| 124 | for (iy = -1043, i=ly; i>0; i<<=1) iy -=1; |
---|
| 125 | } else { |
---|
| 126 | for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1; |
---|
| 127 | } |
---|
| 128 | } else iy = (hy>>20)-1023; |
---|
| 129 | |
---|
| 130 | /* set up {hx,lx}, {hy,ly} and align y to x */ |
---|
| 131 | if(ix >= -1022) |
---|
| 132 | hx = 0x00100000|(0x000fffff&hx); |
---|
| 133 | else { /* subnormal x, shift x to normal */ |
---|
| 134 | n = -1022-ix; |
---|
| 135 | if(n<=31) { |
---|
| 136 | hx = (hx<<n)|(lx>>(32-n)); |
---|
| 137 | lx <<= n; |
---|
| 138 | } else { |
---|
| 139 | hx = lx<<(n-32); |
---|
| 140 | lx = 0; |
---|
| 141 | } |
---|
| 142 | } |
---|
| 143 | if(iy >= -1022) |
---|
| 144 | hy = 0x00100000|(0x000fffff&hy); |
---|
| 145 | else { /* subnormal y, shift y to normal */ |
---|
| 146 | n = -1022-iy; |
---|
| 147 | if(n<=31) { |
---|
| 148 | hy = (hy<<n)|(ly>>(32-n)); |
---|
| 149 | ly <<= n; |
---|
| 150 | } else { |
---|
| 151 | hy = ly<<(n-32); |
---|
| 152 | ly = 0; |
---|
| 153 | } |
---|
| 154 | } |
---|
| 155 | |
---|
| 156 | /* fix point fmod */ |
---|
| 157 | n = ix - iy; |
---|
| 158 | q = 0; |
---|
| 159 | while(n--) { |
---|
| 160 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
---|
| 161 | if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;} |
---|
| 162 | else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;} |
---|
| 163 | q <<= 1; |
---|
| 164 | } |
---|
| 165 | hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1; |
---|
| 166 | if(hz>=0) {hx=hz;lx=lz;q++;} |
---|
| 167 | |
---|
| 168 | /* convert back to floating value and restore the sign */ |
---|
| 169 | if((hx|lx)==0) { /* return sign(x)*0 */ |
---|
| 170 | q &= QUO_MASK; |
---|
| 171 | *quo = (sxy ? -q : q); |
---|
| 172 | return Zero[(__uint32_t)sx>>31]; |
---|
| 173 | } |
---|
| 174 | while(hx<0x00100000) { /* normalize x */ |
---|
| 175 | hx = hx+hx+(lx>>31); lx = lx+lx; |
---|
| 176 | iy -= 1; |
---|
| 177 | } |
---|
| 178 | if(iy>= -1022) { /* normalize output */ |
---|
| 179 | hx = ((hx-0x00100000)|((iy+1023)<<20)); |
---|
| 180 | } else { /* subnormal output */ |
---|
| 181 | n = -1022 - iy; |
---|
| 182 | if(n<=20) { |
---|
| 183 | lx = (lx>>n)|((__uint32_t)hx<<(32-n)); |
---|
| 184 | hx >>= n; |
---|
| 185 | } else if (n<=31) { |
---|
| 186 | lx = (hx<<(32-n))|(lx>>n); hx = sx; |
---|
| 187 | } else { |
---|
| 188 | lx = hx>>(n-32); hx = sx; |
---|
| 189 | } |
---|
| 190 | } |
---|
| 191 | fixup: |
---|
| 192 | INSERT_WORDS(x,hx,lx); |
---|
| 193 | y = fabs(y); |
---|
| 194 | if (y < 0x1p-1021) { |
---|
| 195 | if (x+x>y || (x+x==y && (q & 1))) { |
---|
| 196 | q++; |
---|
| 197 | x-=y; |
---|
| 198 | } |
---|
| 199 | } else if (x>0.5*y || (x==0.5*y && (q & 1))) { |
---|
| 200 | q++; |
---|
| 201 | x-=y; |
---|
| 202 | } |
---|
| 203 | GET_HIGH_WORD(hx,x); |
---|
| 204 | SET_HIGH_WORD(x,hx^sx); |
---|
| 205 | q &= QUO_MASK; |
---|
| 206 | *quo = (sxy ? -q : q); |
---|
| 207 | return x; |
---|
| 208 | } |
---|