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  * $NetBSD: e_fmod.c,v 1.11 2002/05/26 22:01:49 wiz Exp $
  13  * $DragonFly: src/lib/libm/src/e_fmod.c,v 1.1 2005/07/26 21:15:20 joerg Exp $
  14  */
  15
  16 /*
  17  * fmod(x,y)
  18  * Return x mod y in exact arithmetic
  19  * Method: shift and subtract
  20  */
  21
  22 #include <math.h>
  23 #include "math_private.h"
  24
  25 static const double one = 1.0, Zero[] = {0.0, -0.0,};
  26
  27 double
  28 fmod(double x, double y)
  29 {
  30         int32_t n,hx,hy,hz,ix,iy,sx,i;
  31         u_int32_t lx,ly,lz;
  32
  33         EXTRACT_WORDS(hx,lx,x);
  34         EXTRACT_WORDS(hy,ly,y);
  35         sx = hx&0x80000000;             /* sign of x */
  36         hx ^=sx;                /* |x| */
  37         hy &= 0x7fffffff;       /* |y| */
  38
  39     /* purge off exception values */
  40         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  41           ((hy|((ly|-ly)>>31))>0x7ff00000))     /* or y is NaN */
  42             return (x*y)/(x*y);
  43         if(hx<=hy) {
  44             if((hx<hy)||(lx<ly)) return x;      /* |x|<|y| return x */
  45             if(lx==ly)
  46                 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
  47         }
  48
  49     /* determine ix = ilogb(x) */
  50         if(hx<0x00100000) {     /* subnormal x */
  51             if(hx==0) {
  52                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  53             } else {
  54                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  55             }
  56         } else ix = (hx>>20)-1023;
  57
  58     /* determine iy = ilogb(y) */
  59         if(hy<0x00100000) {     /* subnormal y */
  60             if(hy==0) {
  61                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
  62             } else {
  63                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
  64             }
  65         } else iy = (hy>>20)-1023;
  66
  67     /* set up {hx,lx}, {hy,ly} and align y to x */
  68         if(ix >= -1022)
  69             hx = 0x00100000|(0x000fffff&hx);
  70         else {          /* subnormal x, shift x to normal */
  71             n = -1022-ix;
  72             if(n<=31) {
  73                 hx = (hx<<n)|(lx>>(32-n));
  74                 lx <<= n;
  75             } else {
  76                 hx = lx<<(n-32);
  77                 lx = 0;
  78             }
  79         }
  80         if(iy >= -1022)
  81             hy = 0x00100000|(0x000fffff&hy);
  82         else {          /* subnormal y, shift y to normal */
  83             n = -1022-iy;
  84             if(n<=31) {
  85                 hy = (hy<<n)|(ly>>(32-n));
  86                 ly <<= n;
  87             } else {
  88                 hy = ly<<(n-32);
  89                 ly = 0;
  90             }
  91         }
  92
  93     /* fix point fmod */
  94         n = ix - iy;
  95         while(n--) {
  96             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
  97             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
  98             else {
  99                 if((hz|lz)==0)          /* return sign(x)*0 */
 100                     return Zero[(u_int32_t)sx>>31];
 101                 hx = hz+hz+(lz>>31); lx = lz+lz;
 102             }
 103         }
 104         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 105         if(hz>=0) {hx=hz;lx=lz;}
 106
 107     /* convert back to floating value and restore the sign */
 108         if((hx|lx)==0)                  /* return sign(x)*0 */
 109             return Zero[(u_int32_t)sx>>31];
 110         while(hx<0x00100000) {          /* normalize x */
 111             hx = hx+hx+(lx>>31); lx = lx+lx;
 112             iy -= 1;
 113         }
 114         if(iy>= -1022) {        /* normalize output */
 115             hx = ((hx-0x00100000)|((iy+1023)<<20));
 116             INSERT_WORDS(x,hx|sx,lx);
 117         } else {                /* subnormal output */
 118             n = -1022 - iy;
 119             if(n<=20) {
 120                 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
 121                 hx >>= n;
 122             } else if (n<=31) {
 123                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 124             } else {
 125                 lx = hx>>(n-32); hx = sx;
 126             }
 127             INSERT_WORDS(x,hx|sx,lx);
 128             x *= one;           /* create necessary signal */
 129         }
 130         return x;               /* exact output */
 131 }