gonzui

    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: /* LINTLIBRARY */
   14: 
   15: /* 
   16:  * fmod(x,y)
   17:  * Return x mod y in exact arithmetic
   18:  * Method: shift and subtract
   19:  */
   20: 
   21: #include <sys/cdefs.h>
   22: #include <float.h>
   23: #include <math.h>
   24: 
   25: #include "math_private.h"
   26: 
   27: static const double one = 1.0, Zero[] = {0.0, -0.0,};
   28: 
   29: double
   30: fmod(double x, double y)
   31: {
   32:         int32_t n,hx,hy,hz,ix,iy,sx,i;
   33:         u_int32_t lx,ly,lz;
   34: 
   35:         EXTRACT_WORDS(hx,lx,x);
   36:         EXTRACT_WORDS(hy,ly,y);
   37:         sx = hx&0x80000000;            /* sign of x */
   38:         hx ^=sx;               /* |x| */
   39:         hy &= 0x7fffffff;      /* |y| */
   40: 
   41:     /* purge off exception values */
   42:         if((hy|ly)==0||(hx>=0x7ff00000)||      /* y=0,or x not finite */
   43:           ((hy|((ly|-ly)>>31))>0x7ff00000))    /* or y is NaN */
   44:             return (x*y)/(x*y);
   45:         if(hx<=hy) {
   46:             if((hx<hy)||(lx<ly)) return x;     /* |x|<|y| return x */
   47:             if(lx==ly) 
   48:                 return Zero[(u_int32_t)sx>>31];       /* |x|=|y| return x*0*/
   49:         }
   50: 
   51:     /* determine ix = ilogb(x) */
   52:         if(hx<0x00100000) {    /* subnormal x */
   53:             if(hx==0) {
   54:                 for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
   55:             } else {
   56:                 for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
   57:             }
   58:         } else ix = (hx>>20)-1023;
   59: 
   60:     /* determine iy = ilogb(y) */
   61:         if(hy<0x00100000) {    /* subnormal y */
   62:             if(hy==0) {
   63:                 for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
   64:             } else {
   65:                 for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
   66:             }
   67:         } else iy = (hy>>20)-1023;
   68: 
   69:     /* set up {hx,lx}, {hy,ly} and align y to x */
   70:         if(ix >= -1022) 
   71:             hx = 0x00100000|(0x000fffff&hx);
   72:         else {         /* subnormal x, shift x to normal */
   73:             n = -1022-ix;
   74:             if(n<=31) {
   75:                 hx = (hx<<n)|(lx>>(32-n));
   76:                 lx <<= n;
   77:             } else {
   78:                 hx = lx<<(n-32);
   79:                 lx = 0;
   80:             }
   81:         }
   82:         if(iy >= -1022) 
   83:             hy = 0x00100000|(0x000fffff&hy);
   84:         else {         /* subnormal y, shift y to normal */
   85:             n = -1022-iy;
   86:             if(n<=31) {
   87:                 hy = (hy<<n)|(ly>>(32-n));
   88:                 ly <<= n;
   89:             } else {
   90:                 hy = ly<<(n-32);
   91:                 ly = 0;
   92:             }
   93:         }
   94: 
   95:     /* fix point fmod */
   96:         n = ix - iy;
   97:         while(n--) {
   98:             hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
   99:             if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
  100:             else {
  101:                if((hz|lz)==0)            /* return sign(x)*0 */
  102:                     return Zero[(u_int32_t)sx>>31];
  103:                hx = hz+hz+(lz>>31); lx = lz+lz;
  104:             }
  105:         }
  106:         hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
  107:         if(hz>=0) {hx=hz;lx=lz;}
  108: 
  109:     /* convert back to floating value and restore the sign */
  110:         if((hx|lx)==0)                         /* return sign(x)*0 */
  111:             return Zero[(u_int32_t)sx>>31];    
  112:         while(hx<0x00100000) {         /* normalize x */
  113:             hx = hx+hx+(lx>>31); lx = lx+lx;
  114:             iy -= 1;
  115:         }
  116:         if(iy>= -1022) {       /* normalize output */
  117:             hx = ((hx-0x00100000)|((iy+1023)<<20));
  118:             INSERT_WORDS(x,hx|sx,lx);
  119:         } else {               /* subnormal output */
  120:             n = -1022 - iy;
  121:             if(n<=20) {
  122:                 lx = (lx>>n)|((u_int32_t)hx<<(32-n));
  123:                 hx >>= n;
  124:             } else if (n<=31) {
  125:                 lx = (hx<<(32-n))|(lx>>n); hx = sx;
  126:             } else {
  127:                 lx = hx>>(n-32); hx = sx;
  128:             }
  129:             INSERT_WORDS(x,hx|sx,lx);
  130:             x *= one;          /* create necessary signal */
  131:         }
  132:         return x;              /* exact output */
  133: }
  134: 
  135: #if     LDBL_MANT_DIG == 53
  136: #ifdef  lint
  137: /* PROTOLIB1 */
  138: long double fmodl(long double, long double);
  139: #else   /* lint */
  140: __weak_alias(fmodl, fmod);
  141: #endif  /* lint */
  142: #endif  /* LDBL_MANT_DIG == 53 */