lib/libm/src/e_fmod.c

   1 /* @(#)e_fmod.c 5.1 93/09/24 */
   2 /*
   3  * ====================================================
   4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   5  *
   6  * Developed at SunPro, 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 #if defined(LIBM_SCCS) && !defined(lint)
  15 __RCSID("$NetBSD: e_fmod.c,v 1.11 2002/05/26 22:01:49 wiz Exp $");
  16 #endif
  17
  18 /*
  19  * __ieee754_fmod(x,y)
  20  * Return x mod y in exact arithmetic
  21  * Method: shift and subtract
  22  */
  23
  24 #include "math.h"
  25 #include "math_private.h"
  26
  27 static const double one = 1.0, Zero[] = {0.0, -0.0,};
  28
  29 double
  30 __ieee754_fmod(double x, double y)
  31 {
  32         int32_t n,hx,hy,hz,ix,iy,sx,i;
  33         u_int32_t lx,ly,lz;
  34
  35         EXTRACT_WORDS(hx,lx,x);
  36         EXTRACT_WORDS(hy,ly,y);
  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)) return x;      /* |x|<|y| return x */
  47             if(lx==ly)
  48                 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
  49         }
  50
  51     /* determine ix = ilogb(x) */
  52         if(hx<0x00100000) {     /* subnormal x */
  53             if(hx==0) {
  54                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  55             } else {
  56                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  57             }
  58         } else ix = (hx>>20)-1023;
  59
  60     /* determine iy = ilogb(y) */
  61         if(hy<0x00100000) {     /* subnormal y */
  62             if(hy==0) {
  63                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
  64             } else {
  65                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
  66             }
  67         } else iy = (hy>>20)-1023;
  68
  69     /* set up {hx,lx}, {hy,ly} and align y to x */
  70         if(ix >= -1022)
  71             hx = 0x00100000|(0x000fffff&hx);
  72         else {          /* subnormal x, shift x to normal */
  73             n = -1022-ix;
  74             if(n<=31) {
  75                 hx = (hx<<n)|(lx>>(32-n));
  76                 lx <<= n;
  77             } else {
  78                 hx = lx<<(n-32);
  79                 lx = 0;
  80             }
  81         }
  82         if(iy >= -1022)
  83             hy = 0x00100000|(0x000fffff&hy);
  84         else {          /* subnormal y, shift y to normal */
  85             n = -1022-iy;
  86             if(n<=31) {
  87                 hy = (hy<<n)|(ly>>(32-n));
  88                 ly <<= n;
  89             } else {
  90                 hy = ly<<(n-32);
  91                 ly = 0;
  92             }
  93         }
  94
  95     /* fix point fmod */
  96         n = ix - iy;
  97         while(n--) {
  98             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
  99             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
 100             else {
 101                 if((hz|lz)==0)          /* return sign(x)*0 */
 102                     return Zero[(u_int32_t)sx>>31];
 103                 hx = hz+hz+(lz>>31); lx = lz+lz;
 104             }
 105         }
 106         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 107         if(hz>=0) {hx=hz;lx=lz;}
 108
 109     /* convert back to floating value and restore the sign */
 110         if((hx|lx)==0)                  /* return sign(x)*0 */
 111             return Zero[(u_int32_t)sx>>31];
 112         while(hx<0x00100000) {          /* normalize x */
 113             hx = hx+hx+(lx>>31); lx = lx+lx;
 114             iy -= 1;
 115         }
 116         if(iy>= -1022) {        /* normalize output */
 117             hx = ((hx-0x00100000)|((iy+1023)<<20));
 118             INSERT_WORDS(x,hx|sx,lx);
 119         } else {                /* subnormal output */
 120             n = -1022 - iy;
 121             if(n<=20) {
 122                 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
 123                 hx >>= n;
 124             } else if (n<=31) {
 125                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 126             } else {
 127                 lx = hx>>(n-32); hx = sx;
 128             }
 129             INSERT_WORDS(x,hx|sx,lx);
 130             x *= one;           /* create necessary signal */
 131         }
 132         return x;               /* exact output */
 133 }