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 #include <sys/cdefs.h>
  14 __FBSDID("$FreeBSD: src/lib/msun/src/s_remquo.c,v 1.1 2005/03/25 04:40:44 das Exp $");
  15
  16 #include "math.h"
  17 #include "math_private.h"
  18
  19 static const double Zero[] = {0.0, -0.0,};
  20
  21 /*
  22  * Return the IEEE remainder and set *quo to the last n bits of the
  23  * quotient, rounded to the nearest integer.  We choose n=31 because
  24  * we wind up computing all the integer bits of the quotient anyway as
  25  * a side-effect of computing the remainder by the shift and subtract
  26  * method.  In practice, this is far more bits than are needed to use
  27  * remquo in reduction algorithms.
  28  */
  29 double
  30 remquo(double x, double y, int *quo)
  31 {
  32         int32_t n,hx,hy,hz,ix,iy,sx,i;
  33         u_int32_t lx,ly,lz,q,sxy;
  34
  35         EXTRACT_WORDS(hx,lx,x);
  36         EXTRACT_WORDS(hy,ly,y);
  37         sxy = (hx ^ hy) & 0x80000000;
  38         sx = hx&0x80000000;             /* sign of x */
  39         hx ^=sx;                /* |x| */
  40         hy &= 0x7fffffff;       /* |y| */
  41
  42     /* purge off exception values */
  43         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  44           ((hy|((ly|-ly)>>31))>0x7ff00000))     /* or y is NaN */
  45             return (x*y)/(x*y);
  46         if(hx<=hy) {
  47             if((hx<hy)||(lx<ly)) {
  48                 q = 0;
  49                 goto fixup;     /* |x|<|y| return x or x-y */
  50             }
  51             if(lx==ly) {
  52                 *quo = 1;
  53                 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
  54             }
  55         }
  56
  57     /* determine ix = ilogb(x) */
  58         if(hx<0x00100000) {     /* subnormal x */
  59             if(hx==0) {
  60                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  61             } else {
  62                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  63             }
  64         } else ix = (hx>>20)-1023;
  65
  66     /* determine iy = ilogb(y) */
  67         if(hy<0x00100000) {     /* subnormal y */
  68             if(hy==0) {
  69                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
  70             } else {
  71                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
  72             }
  73         } else iy = (hy>>20)-1023;
  74
  75     /* set up {hx,lx}, {hy,ly} and align y to x */
  76         if(ix >= -1022)
  77             hx = 0x00100000|(0x000fffff&hx);
  78         else {          /* subnormal x, shift x to normal */
  79             n = -1022-ix;
  80             if(n<=31) {
  81                 hx = (hx<<n)|(lx>>(32-n));
  82                 lx <<= n;
  83             } else {
  84                 hx = lx<<(n-32);
  85                 lx = 0;
  86             }
  87         }
  88         if(iy >= -1022)
  89             hy = 0x00100000|(0x000fffff&hy);
  90         else {          /* subnormal y, shift y to normal */
  91             n = -1022-iy;
  92             if(n<=31) {
  93                 hy = (hy<<n)|(ly>>(32-n));
  94                 ly <<= n;
  95             } else {
  96                 hy = ly<<(n-32);
  97                 ly = 0;
  98             }
  99         }
 100
 101     /* fix point fmod */
 102         n = ix - iy;
 103         q = 0;
 104         while(n--) {
 105             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 106             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
 107             else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
 108             q <<= 1;
 109         }
 110         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 111         if(hz>=0) {hx=hz;lx=lz;q++;}
 112
 113     /* convert back to floating value and restore the sign */
 114         if((hx|lx)==0) {                        /* return sign(x)*0 */
 115             *quo = (sxy ? -q : q);
 116             return Zero[(u_int32_t)sx>>31];
 117         }
 118         while(hx<0x00100000) {          /* normalize x */
 119             hx = hx+hx+(lx>>31); lx = lx+lx;
 120             iy -= 1;
 121         }
 122         if(iy>= -1022) {        /* normalize output */
 123             hx = ((hx-0x00100000)|((iy+1023)<<20));
 124         } else {                /* subnormal output */
 125             n = -1022 - iy;
 126             if(n<=20) {
 127                 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
 128                 hx >>= n;
 129             } else if (n<=31) {
 130                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 131             } else {
 132                 lx = hx>>(n-32); hx = sx;
 133             }
 134         }
 135 fixup:
 136         INSERT_WORDS(x,hx,lx);
 137         y = fabs(y);
 138         if (y < 0x1p-1021) {
 139             if (x+x>y || (x+x==y && (q & 1))) {
 140                 q++;
 141                 x-=y;
 142             }
 143         } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
 144             q++;
 145             x-=y;
 146         }
 147         GET_HIGH_WORD(hx,x);
 148         SET_HIGH_WORD(x,hx^sx);
 149         q &= 0x7fffffff;
 150         *quo = (sxy ? -q : q);
 151         return x;
 152 }