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