lib/libm/src/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
  15 #include <float.h>
  16
  17 #include "math.h"
  18 #include "math_private.h"
  19
  20 static const double Zero[] = {0.0, -0.0,};
  21
  22 /*
  23  * Return the IEEE remainder and set *quo to the last n bits of the
  24  * quotient, rounded to the nearest integer.  We choose n=31 because
  25  * we wind up computing all the integer bits of the quotient anyway as
  26  * a side-effect of computing the remainder by the shift and subtract
  27  * method.  In practice, this is far more bits than are needed to use
  28  * remquo in reduction algorithms.
  29  */
  30 double
  31 remquo(double x, double y, int *quo)
  32 {
  33         int32_t n,hx,hy,hz,ix,iy,sx,i;
  34         u_int32_t lx,ly,lz,q,sxy;
  35
  36         EXTRACT_WORDS(hx,lx,x);
  37         EXTRACT_WORDS(hy,ly,y);
  38         sxy = (hx ^ hy) & 0x80000000;
  39         sx = hx&0x80000000;             /* sign of x */
  40         hx ^=sx;                /* |x| */
  41         hy &= 0x7fffffff;       /* |y| */
  42
  43     /* purge off exception values */
  44         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  45           ((hy|((ly|-ly)>>31))>0x7ff00000))     /* or y is NaN */
  46             return (x*y)/(x*y);
  47         if(hx<=hy) {
  48             if((hx<hy)||(lx<ly)) {
  49                 q = 0;
  50                 goto fixup;     /* |x|<|y| return x or x-y */
  51             }
  52             if(lx==ly) {
  53                 *quo = 1;
  54                 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
  55             }
  56         }
  57
  58     /* determine ix = ilogb(x) */
  59         if(hx<0x00100000) {     /* subnormal x */
  60             if(hx==0) {
  61                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  62             } else {
  63                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  64             }
  65         } else ix = (hx>>20)-1023;
  66
  67     /* determine iy = ilogb(y) */
  68         if(hy<0x00100000) {     /* subnormal y */
  69             if(hy==0) {
  70                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
  71             } else {
  72                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
  73             }
  74         } else iy = (hy>>20)-1023;
  75
  76     /* set up {hx,lx}, {hy,ly} and align y to x */
  77         if(ix >= -1022)
  78             hx = 0x00100000|(0x000fffff&hx);
  79         else {          /* subnormal x, shift x to normal */
  80             n = -1022-ix;
  81             if(n<=31) {
  82                 hx = (hx<<n)|(lx>>(32-n));
  83                 lx <<= n;
  84             } else {
  85                 hx = lx<<(n-32);
  86                 lx = 0;
  87             }
  88         }
  89         if(iy >= -1022)
  90             hy = 0x00100000|(0x000fffff&hy);
  91         else {          /* subnormal y, shift y to normal */
  92             n = -1022-iy;
  93             if(n<=31) {
  94                 hy = (hy<<n)|(ly>>(32-n));
  95                 ly <<= n;
  96             } else {
  97                 hy = ly<<(n-32);
  98                 ly = 0;
  99             }
 100         }
 101
 102     /* fix point fmod */
 103         n = ix - iy;
 104         q = 0;
 105         while(n--) {
 106             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 107             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
 108             else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
 109             q <<= 1;
 110         }
 111         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 112         if(hz>=0) {hx=hz;lx=lz;q++;}
 113
 114     /* convert back to floating value and restore the sign */
 115         if((hx|lx)==0) {                        /* return sign(x)*0 */
 116             *quo = (sxy ? -q : q);
 117             return Zero[(u_int32_t)sx>>31];
 118         }
 119         while(hx<0x00100000) {          /* normalize x */
 120             hx = hx+hx+(lx>>31); lx = lx+lx;
 121             iy -= 1;
 122         }
 123         if(iy>= -1022) {        /* normalize output */
 124             hx = ((hx-0x00100000)|((iy+1023)<<20));
 125         } else {                /* subnormal output */
 126             n = -1022 - iy;
 127             if(n<=20) {
 128                 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
 129                 hx >>= n;
 130             } else if (n<=31) {
 131                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 132             } else {
 133                 lx = hx>>(n-32); hx = sx;
 134             }
 135         }
 136 fixup:
 137         INSERT_WORDS(x,hx,lx);
 138         y = fabs(y);
 139         if (y < 0x1p-1021) {
 140             if (x+x>y || (x+x==y && (q & 1))) {
 141                 q++;
 142                 x-=y;
 143             }
 144         } else if (x>0.5*y || (x==0.5*y && (q & 1))) {
 145             q++;
 146             x-=y;
 147         }
 148         GET_HIGH_WORD(hx,x);
 149         SET_HIGH_WORD(x,hx^sx);
 150         q &= 0x7fffffff;
 151         *quo = (sxy ? -q : q);
 152         return x;
 153 }