compiler/mlib/s_remquo.c

   1 /* @(#)e_fmod.c 1.3 95/01/18 */
   2 /*-
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunSoft, a Sun Microsystems, Inc. business.
   7  * Permission to use, copy, modify, and distribute this
   8  * software is freely granted, provided that this notice
   9  * is preserved.
  10  * ====================================================
  11  */
  12
  13 __FBSDID("$FreeBSD: src/lib/msun/src/s_remquo.c,v 1.1 2005/03/25 04:40:44 das Exp $");
  14
  15 #include "math.h"
  16 #include "math_private.h"
  17
  18 static const double Zero[] = {0.0, -0.0,};
  19
  20 /*
  21  * Return the IEEE remainder and set *quo to the last n bits of the
  22  * quotient, rounded to the nearest integer.  We choose n=31 because
  23  * we wind up computing all the integer bits of the quotient anyway as
  24  * a side-effect of computing the remainder by the shift and subtract
  25  * method.  In practice, this is far more bits than are needed to use
  26  * remquo in reduction algorithms.
  27  */
  28 double
  29 remquo(double x, double y, int *quo)
  30 {
  31         int32_t n,hx,hy,hz,ix,iy,sx,i;
  32         uint32_t lx,ly,lz,q,sxy;
  33
  34         EXTRACT_WORDS(hx,lx,x);
  35         EXTRACT_WORDS(hy,ly,y);
  36         sxy = (hx ^ hy) & 0x80000000;
  37         sx = hx&0x80000000;             /* sign of x */
  38         hx ^=sx;                /* |x| */
  39         hy &= 0x7fffffff;       /* |y| */
  40
  41     /* purge off exception values */
  42         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  43           ((hy|((ly|-ly)>>31))>0x7ff00000))     /* or y is NaN */
  44             return (x*y)/(x*y);
  45         if(hx<=hy) {
  46             if((hx<hy)||(lx<ly)) {
  47                 q = 0;
  48                 goto fixup;     /* |x|<|y| return x or x-y */
  49             }
  50             if(lx==ly) {
  51                 *quo = 1;
  52                 return Zero[(uint32_t)sx>>31];  /* |x|=|y| return x*0*/
  53             }
  54         }
  55
  56     /* determine ix = ilogb(x) */
  57         if(hx<0x00100000) {     /* subnormal x */
  58             if(hx==0) {
  59                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  60             } else {
  61                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  62             }
  63         } else ix = (hx>>20)-1023;
  64
  65     /* determine iy = ilogb(y) */
  66         if(hy<0x00100000) {     /* subnormal y */
  67             if(hy==0) {
  68                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
  69             } else {
  70                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
  71             }
  72         } else iy = (hy>>20)-1023;
  73
  74     /* set up {hx,lx}, {hy,ly} and align y to x */
  75         if(ix >= -1022)
  76             hx = 0x00100000|(0x000fffff&hx);
  77         else {          /* subnormal x, shift x to normal */
  78             n = -1022-ix;
  79             if(n<=31) {
  80                 hx = (hx<<n)|(lx>>(32-n));
  81                 lx <<= n;
  82             } else {
  83                 hx = lx<<(n-32);
  84                 lx = 0;
  85             }
  86         }
  87         if(iy >= -1022)
  88             hy = 0x00100000|(0x000fffff&hy);
  89         else {          /* subnormal y, shift y to normal */
  90             n = -1022-iy;
  91             if(n<=31) {
  92                 hy = (hy<<n)|(ly>>(32-n));
  93                 ly <<= n;
  94             } else {
  95                 hy = ly<<(n-32);
  96                 ly = 0;
  97             }
  98         }
  99
 100     /* fix point fmod */
 101         n = ix - iy;
 102         q = 0;
 103         while(n--) {
 104             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 105             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
 106             else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
 107             q <<= 1;
 108         }
 109         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 110         if(hz>=0) {hx=hz;lx=lz;q++;}
 111
 112     /* convert back to floating value and restore the sign */
 113         if((hx|lx)==0) {                        /* return sign(x)*0 */
 114             *quo = (sxy ? -q : q);
 115             return Zero[(uint32_t)sx>>31];
 116         }
 117         while(hx<0x00100000) {          /* normalize x */
 118             hx = hx+hx+(lx>>31); lx = lx+lx;
 119             iy -= 1;
 120         }
 121         if(iy>= -1022) {        /* normalize output */
 122             hx = ((hx-0x00100000)|((iy+1023)<<20));
 123         } else {                /* subnormal output */
 124             n = -1022 - iy;
 125             if(n<=20) {
 126                 lx = (lx>>n)|((uint32_t)hx<<(32-n));
 127                 hx >>= n;
 128             } else if (n<=31) {
 129                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 130             } else {
 131                 lx = hx>>(n-32); hx = sx;
 132             }
 133         }
 134 fixup:
 135         INSERT_WORDS(x,hx,lx);
 136         y = fabs(y);
 137         if (y < 0x1p-1021) {
 138             if (x+x>y || (x+x==y && (q & 1))) {
 139                 q++;
 140                 x-=y;
 141             }
 142         } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
 143             q++;
 144             x-=y;
 145         }
 146         GET_HIGH_WORD(hx,x);
 147         SET_HIGH_WORD(x,hx^sx);
 148         q &= 0x7fffffff;
 149         *quo = (sxy ? -q : q);
 150         return x;
 151 }