newlib/libm/mathfp/s_fmod.c

   1
   2 /* @(#)z_fmod.c 1.0 98/08/13 */
   3 /*
   4  * ====================================================
   5  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
   6  *
   7  * Developed at SunPro, a Sun Microsystems, Inc. business.
   8  * Permission to use, copy, modify, and distribute this
   9  * software is freely granted, provided that this notice
  10  * is preserved.
  11  * ====================================================
  12  */
  13
  14 /*
  15 FUNCTION
  16 <<fmod>>, <<fmodf>>---floating-point remainder (modulo)
  17
  18 INDEX
  19 fmod
  20 INDEX
  21 fmodf
  22
  23 SYNOPSIS
  24 #include <math.h>
  25 double fmod(double <[x]>, double <[y]>);
  26 float fmodf(float <[x]>, float <[y]>);
  27
  28 DESCRIPTION
  29 The <<fmod>> and <<fmodf>> functions compute the floating-point
  30 remainder of <[x]>/<[y]> (<[x]> modulo <[y]>).
  31
  32 RETURNS
  33 The <<fmod>> function returns the value
  34 @ifnottex
  35 <[x]>-<[i]>*<[y]>,
  36 @end ifnottex
  37 @tex
  38 $x-i\times y$,
  39 @end tex
  40 for the largest integer <[i]> such that, if <[y]> is nonzero, the
  41 result has the same sign as <[x]> and magnitude less than the
  42 magnitude of <[y]>.
  43
  44 <<fmod(<[x]>,0)>> returns NaN, and sets <<errno>> to <<EDOM>>.
  45
  46 PORTABILITY
  47 <<fmod>> is ANSI C. <<fmodf>> is an extension.
  48 */
  49
  50 /*
  51  * fmod(x,y)
  52  * Return x mod y in exact arithmetic
  53  * Method: shift and subtract
  54  */
  55
  56 #include "fdlibm.h"
  57 #include "zmath.h"
  58
  59 #ifndef _DOUBLE_IS_32BITS
  60
  61 #ifdef __STDC__
  62 static const double one = 1.0, Zero[] = {0.0, -0.0,};
  63 #else
  64 static double one = 1.0, Zero[] = {0.0, -0.0,};
  65 #endif
  66
  67 #ifdef __STDC__
  68         double fmod(double x, double y)
  69 #else
  70         double fmod(x,y)
  71         double x,y ;
  72 #endif
  73 {
  74         __int32_t n,hx,hy,hz,ix,iy,sx,i;
  75         __uint32_t lx,ly,lz;
  76
  77         EXTRACT_WORDS(hx,lx,x);
  78         EXTRACT_WORDS(hy,ly,y);
  79         sx = hx&0x80000000;             /* sign of x */
  80         hx ^=sx;                /* |x| */
  81         hy &= 0x7fffffff;       /* |y| */
  82
  83     /* purge off exception values */
  84         if((hy|ly)==0||(hx>=0x7ff00000)||       /* y=0,or x not finite */
  85           ((hy|((ly|-ly)>>31))>0x7ff00000))     /* or y is NaN */
  86             return (x*y)/(x*y);
  87         if(hx<=hy) {
  88             if((hx<hy)||(lx<ly)) return x;      /* |x|<|y| return x */
  89             if(lx==ly)
  90                 return Zero[(__uint32_t)sx>>31];        /* |x|=|y| return x*0*/
  91         }
  92
  93     /* determine ix = ilogb(x) */
  94         if(hx<0x00100000) {     /* subnormal x */
  95             if(hx==0) {
  96                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
  97             } else {
  98                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
  99             }
 100         } else ix = (hx>>20)-1023;
 101
 102     /* determine iy = ilogb(y) */
 103         if(hy<0x00100000) {     /* subnormal y */
 104             if(hy==0) {
 105                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
 106             } else {
 107                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
 108             }
 109         } else iy = (hy>>20)-1023;
 110
 111     /* set up {hx,lx}, {hy,ly} and align y to x */
 112         if(ix >= -1022)
 113             hx = 0x00100000|(0x000fffff&hx);
 114         else {          /* subnormal x, shift x to normal */
 115             n = -1022-ix;
 116             if(n<=31) {
 117                 hx = (hx<<n)|(lx>>(32-n));
 118                 lx <<= n;
 119             } else {
 120                 hx = lx<<(n-32);
 121                 lx = 0;
 122             }
 123         }
 124         if(iy >= -1022)
 125             hy = 0x00100000|(0x000fffff&hy);
 126         else {          /* subnormal y, shift y to normal */
 127             n = -1022-iy;
 128             if(n<=31) {
 129                 hy = (hy<<n)|(ly>>(32-n));
 130                 ly <<= n;
 131             } else {
 132                 hy = ly<<(n-32);
 133                 ly = 0;
 134             }
 135         }
 136
 137     /* fix point fmod */
 138         n = ix - iy;
 139         while(n--) {
 140             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 141             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
 142             else {
 143                 if((hz|lz)==0)          /* return sign(x)*0 */
 144                     return Zero[(__uint32_t)sx>>31];
 145                 hx = hz+hz+(lz>>31); lx = lz+lz;
 146             }
 147         }
 148         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
 149         if(hz>=0) {hx=hz;lx=lz;}
 150
 151     /* convert back to floating value and restore the sign */
 152         if((hx|lx)==0)                  /* return sign(x)*0 */
 153             return Zero[(__uint32_t)sx>>31];
 154         while(hx<0x00100000) {          /* normalize x */
 155             hx = hx+hx+(lx>>31); lx = lx+lx;
 156             iy -= 1;
 157         }
 158         if(iy>= -1022) {        /* normalize output */
 159             hx = ((hx-0x00100000)|((iy+1023)<<20));
 160             INSERT_WORDS(x,hx|sx,lx);
 161         } else {                /* subnormal output */
 162             n = -1022 - iy;
 163             if(n<=20) {
 164                 lx = (lx>>n)|((__uint32_t)hx<<(32-n));
 165                 hx >>= n;
 166             } else if (n<=31) {
 167                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
 168             } else {
 169                 lx = hx>>(n-32); hx = sx;
 170             }
 171             INSERT_WORDS(x,hx|sx,lx);
 172             x *= one;           /* create necessary signal */
 173         }
 174         return x;               /* exact output */
 175 }
 176
 177 #endif /* defined(_DOUBLE_IS_32BITS) */