libm/e_fmod.c

   1 /*
   2  * ====================================================
   3  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   4  *
   5  * Developed at SunPro, a Sun Microsystems, Inc. business.
   6  * Permission to use, copy, modify, and distribute this
   7  * software is freely granted, provided that this notice
   8  * is preserved.
   9  * ====================================================
  10  */
  11
  12 /*
  13  * __ieee754_fmod(x,y)
  14  * Return x mod y in exact arithmetic
  15  * Method: shift and subtract
  16  */
  17
  18 #include "math.h"
  19 #include "math_private.h"
  20
  21 static const double one = 1.0, Zero[] = {0.0, -0.0,};
  22
  23 double __ieee754_fmod(double x, double y)
  24 {
  25         int32_t n,hx,hy,hz,ix,iy,sx,i;
  26         u_int32_t lx,ly,lz;
  27
  28         EXTRACT_WORDS(hx,lx,x);
  29         EXTRACT_WORDS(hy,ly,y);
  30         sx = hx&0x80000000;             /* sign of x */
  31         hx ^=sx;                /* |x| */
  32         hy &= 0x7fffffff;       /* |y| */
  33
  34     /* purge off exception values */
  35         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  36           ((hy|((ly|-ly)>>31))>0x7ff00000))     /* or y is NaN */
  37             return (x*y)/(x*y);
  38         if(hx<=hy) {
  39             if((hx<hy)||(lx<ly)) return x;      /* |x|<|y| return x */
  40             if(lx==ly)
  41                 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
  42         }
  43
  44     /* determine ix = ilogb(x) */
  45         if(hx<0x00100000) {     /* subnormal x */
  46             if(hx==0) {
  47                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  48             } else {
  49                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  50             }
  51         } else ix = (hx>>20)-1023;
  52
  53     /* determine iy = ilogb(y) */
  54         if(hy<0x00100000) {     /* subnormal y */
  55             if(hy==0) {
  56                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
  57             } else {
  58                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
  59             }
  60         } else iy = (hy>>20)-1023;
  61
  62     /* set up {hx,lx}, {hy,ly} and align y to x */
  63         if(ix >= -1022)
  64             hx = 0x00100000|(0x000fffff&hx);
  65         else {          /* subnormal x, shift x to normal */
  66             n = -1022-ix;
  67             if(n<=31) {
  68                 hx = (hx<<n)|(lx>>(32-n));
  69                 lx <<= n;
  70             } else {
  71                 hx = lx<<(n-32);
  72                 lx = 0;
  73             }
  74         }
  75         if(iy >= -1022)
  76             hy = 0x00100000|(0x000fffff&hy);
  77         else {          /* subnormal y, shift y to normal */
  78             n = -1022-iy;
  79             if(n<=31) {
  80                 hy = (hy<<n)|(ly>>(32-n));
  81                 ly <<= n;
  82             } else {
  83                 hy = ly<<(n-32);
  84                 ly = 0;
  85             }
  86         }
  87
  88     /* fix point fmod */
  89         n = ix - iy;
  90         while(n--) {
  91             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
  92             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
  93             else {
  94                 if((hz|lz)==0)          /* return sign(x)*0 */
  95                     return Zero[(u_int32_t)sx>>31];
  96                 hx = hz+hz+(lz>>31); lx = lz+lz;
  97             }
  98         }
  99         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 100         if(hz>=0) {hx=hz;lx=lz;}
 101
 102     /* convert back to floating value and restore the sign */
 103         if((hx|lx)==0)                  /* return sign(x)*0 */
 104             return Zero[(u_int32_t)sx>>31];
 105         while(hx<0x00100000) {          /* normalize x */
 106             hx = hx+hx+(lx>>31); lx = lx+lx;
 107             iy -= 1;
 108         }
 109         if(iy>= -1022) {        /* normalize output */
 110             hx = ((hx-0x00100000)|((iy+1023)<<20));
 111             INSERT_WORDS(x,hx|sx,lx);
 112         } else {                /* subnormal output */
 113             n = -1022 - iy;
 114             if(n<=20) {
 115                 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
 116                 hx >>= n;
 117             } else if (n<=31) {
 118                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 119             } else {
 120                 lx = hx>>(n-32); hx = sx;
 121             }
 122             INSERT_WORDS(x,hx|sx,lx);
 123             x *= one;           /* create necessary signal */
 124         }
 125         return x;               /* exact output */
 126 }