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 1.12 2013/11/19 14:02:59 joerg 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 #ifndef __HAVE_LONG_DOUBLE
  30 __strong_alias(__ieee754_fmodl, __ieee754_fmod)
  31 #endif
  32
  33 double
  34 __ieee754_fmod(double x, double y)
  35 {
  36         int32_t n,hx,hy,hz,ix,iy,sx,i;
  37         u_int32_t lx,ly,lz;
  38
  39         EXTRACT_WORDS(hx,lx,x);
  40         EXTRACT_WORDS(hy,ly,y);
  41         sx = hx&0x80000000;             /* sign of x */
  42         hx ^=sx;                /* |x| */
  43         hy &= 0x7fffffff;       /* |y| */
  44
  45     /* purge off exception values */
  46         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  47           ((hy|((ly|-ly)>>31))>0x7ff00000))     /* or y is NaN */
  48             return (x*y)/(x*y);
  49         if(hx<=hy) {
  50             if((hx<hy)||(lx<ly)) return x;      /* |x|<|y| return x */
  51             if(lx==ly)
  52                 return Zero[(u_int32_t)sx>>31]; /* |x|=|y| return x*0*/
  53         }
  54
  55     /* determine ix = ilogb(x) */
  56         if(hx<0x00100000) {     /* subnormal x */
  57             if(hx==0) {
  58                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  59             } else {
  60                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  61             }
  62         } else ix = (hx>>20)-1023;
  63
  64     /* determine iy = ilogb(y) */
  65         if(hy<0x00100000) {     /* subnormal y */
  66             if(hy==0) {
  67                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
  68             } else {
  69                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
  70             }
  71         } else iy = (hy>>20)-1023;
  72
  73     /* set up {hx,lx}, {hy,ly} and align y to x */
  74         if(ix >= -1022)
  75             hx = 0x00100000|(0x000fffff&hx);
  76         else {          /* subnormal x, shift x to normal */
  77             n = -1022-ix;
  78             if(n<=31) {
  79                 hx = (hx<<n)|(lx>>(32-n));
  80                 lx <<= n;
  81             } else {
  82                 hx = lx<<(n-32);
  83                 lx = 0;
  84             }
  85         }
  86         if(iy >= -1022)
  87             hy = 0x00100000|(0x000fffff&hy);
  88         else {          /* subnormal y, shift y to normal */
  89             n = -1022-iy;
  90             if(n<=31) {
  91                 hy = (hy<<n)|(ly>>(32-n));
  92                 ly <<= n;
  93             } else {
  94                 hy = ly<<(n-32);
  95                 ly = 0;
  96             }
  97         }
  98
  99     /* fix point fmod */
 100         n = ix - iy;
 101         while(n--) {
 102             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 103             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
 104             else {
 105                 if((hz|lz)==0)          /* return sign(x)*0 */
 106                     return Zero[(u_int32_t)sx>>31];
 107                 hx = hz+hz+(lz>>31); lx = lz+lz;
 108             }
 109         }
 110         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 111         if(hz>=0) {hx=hz;lx=lz;}
 112
 113     /* convert back to floating value and restore the sign */
 114         if((hx|lx)==0)                  /* return sign(x)*0 */
 115             return Zero[(u_int32_t)sx>>31];
 116         while(hx<0x00100000) {          /* normalize x */
 117             hx = hx+hx+(lx>>31); lx = lx+lx;
 118             iy -= 1;
 119         }
 120         if(iy>= -1022) {        /* normalize output */
 121             hx = ((hx-0x00100000)|((iy+1023)<<20));
 122             INSERT_WORDS(x,hx|sx,lx);
 123         } else {                /* subnormal output */
 124             n = -1022 - iy;
 125             if(n<=20) {
 126                 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
 127                 hx >>= n;
 128             } else if (n<=31) {
 129                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 130             } else {
 131                 lx = hx>>(n-32); hx = sx;
 132             }
 133             INSERT_WORDS(x,hx|sx,lx);
 134             x *= one;           /* create necessary signal */
 135         }
 136         return x;               /* exact output */
 137 }