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      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 }
    138