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      1 /* @(#)e_fmod.c 1.3 95/01/18 */
      2 /*-
      3  * ====================================================
      4  * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
      5  *
      6  * Developed at SunSoft, 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 
     15 #include "namespace.h"
     16 
     17 #include <float.h>
     18 
     19 #include "math.h"
     20 #include "math_private.h"
     21 
     22 #ifdef __weak_alias
     23 __weak_alias(remquo, _remquo)
     24 #endif
     25 
     26 static const double Zero[] = {0.0, -0.0,};
     27 
     28 /*
     29  * Return the IEEE remainder and set *quo to the last n bits of the
     30  * quotient, rounded to the nearest integer.  We choose n=31 because
     31  * we wind up computing all the integer bits of the quotient anyway as
     32  * a side-effect of computing the remainder by the shift and subtract
     33  * method.  In practice, this is far more bits than are needed to use
     34  * remquo in reduction algorithms.
     35  */
     36 double
     37 remquo(double x, double y, int *quo)
     38 {
     39 	int32_t n,hx,hy,hz,ix,iy,sx,i;
     40 	u_int32_t lx,ly,lz,q,sxy;
     41 
     42 	EXTRACT_WORDS(hx,lx,x);
     43 	EXTRACT_WORDS(hy,ly,y);
     44 	sxy = (hx ^ hy) & 0x80000000;
     45 	sx = hx&0x80000000;		/* sign of x */
     46 	hx ^=sx;		/* |x| */
     47 	hy &= 0x7fffffff;	/* |y| */
     48 
     49     /* purge off exception values */
     50 	if((hy|ly)==0||(hx>=0x7ff00000)||	/* y=0,or x not finite */
     51 	  ((hy|((ly|-ly)>>31))>0x7ff00000))	/* or y is NaN */
     52 	    return (x*y)/(x*y);
     53 	if(hx<=hy) {
     54 	    if((hx<hy)||(lx<ly)) {
     55 		q = 0;
     56 		goto fixup;	/* |x|<|y| return x or x-y */
     57 	    }
     58 	    if(lx==ly) {
     59 		*quo = (sxy ? -1 : 1);
     60 		return Zero[(u_int32_t)sx>>31];	/* |x|=|y| return x*0*/
     61 	    }
     62 	}
     63 
     64     /* determine ix = ilogb(x) */
     65 	if(hx<0x00100000) {	/* subnormal x */
     66 	    if(hx==0) {
     67 		for (ix = -1043, i=lx; i>0; i<<=1) ix -=1;
     68 	    } else {
     69 		for (ix = -1022,i=(hx<<11); i>0; i<<=1) ix -=1;
     70 	    }
     71 	} else ix = (hx>>20)-1023;
     72 
     73     /* determine iy = ilogb(y) */
     74 	if(hy<0x00100000) {	/* subnormal y */
     75 	    if(hy==0) {
     76 		for (iy = -1043, i=ly; i>0; i<<=1) iy -=1;
     77 	    } else {
     78 		for (iy = -1022,i=(hy<<11); i>0; i<<=1) iy -=1;
     79 	    }
     80 	} else iy = (hy>>20)-1023;
     81 
     82     /* set up {hx,lx}, {hy,ly} and align y to x */
     83 	if(ix >= -1022)
     84 	    hx = 0x00100000|(0x000fffff&hx);
     85 	else {		/* subnormal x, shift x to normal */
     86 	    n = -1022-ix;
     87 	    if(n<=31) {
     88 	        hx = (hx<<n)|(lx>>(32-n));
     89 	        lx <<= n;
     90 	    } else {
     91 		hx = lx<<(n-32);
     92 		lx = 0;
     93 	    }
     94 	}
     95 	if(iy >= -1022)
     96 	    hy = 0x00100000|(0x000fffff&hy);
     97 	else {		/* subnormal y, shift y to normal */
     98 	    n = -1022-iy;
     99 	    if(n<=31) {
    100 	        hy = (hy<<n)|(ly>>(32-n));
    101 	        ly <<= n;
    102 	    } else {
    103 		hy = ly<<(n-32);
    104 		ly = 0;
    105 	    }
    106 	}
    107 
    108     /* fix point fmod */
    109 	n = ix - iy;
    110 	q = 0;
    111 	while(n--) {
    112 	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
    113 	    if(hz<0){hx = hx+hx+(lx>>31); lx = lx+lx;}
    114 	    else {hx = hz+hz+(lz>>31); lx = lz+lz; q++;}
    115 	    q <<= 1;
    116 	}
    117 	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
    118 	if(hz>=0) {hx=hz;lx=lz;q++;}
    119 
    120     /* convert back to floating value and restore the sign */
    121 	if((hx|lx)==0) {			/* return sign(x)*0 */
    122 	    q &= 0x7fffffff;
    123 	    *quo = (sxy ? -q : q);
    124 	    return Zero[(u_int32_t)sx>>31];
    125 	}
    126 	while(hx<0x00100000) {		/* normalize x */
    127 	    hx = hx+hx+(lx>>31); lx = lx+lx;
    128 	    iy -= 1;
    129 	}
    130 	if(iy>= -1022) {	/* normalize output */
    131 	    hx = ((hx-0x00100000)|((iy+1023)<<20));
    132 	} else {		/* subnormal output */
    133 	    n = -1022 - iy;
    134 	    if(n<=20) {
    135 		lx = (lx>>n)|((u_int32_t)hx<<(32-n));
    136 		hx >>= n;
    137 	    } else if (n<=31) {
    138 		lx = (hx<<(32-n))|(lx>>n); hx = 0;
    139 	    } else {
    140 		lx = hx>>(n-32); hx = 0;
    141 	    }
    142 	}
    143 fixup:
    144 	INSERT_WORDS(x,hx,lx);
    145 	y = fabs(y);
    146 	if (y < 0x1p-1021) {
    147 	    if (x+x>y || (x+x==y && (q & 1))) {
    148 		q++;
    149 		x-=y;
    150 	    }
    151 	} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
    152 	    q++;
    153 	    x-=y;
    154 	}
    155 	GET_HIGH_WORD(hx,x);
    156 	SET_HIGH_WORD(x,hx^sx);
    157 	q &= 0x7fffffff;
    158 	*quo = (sxy ? -q : q);
    159 	/*
    160 	 * If q is 0 and we need to return negative, we have to choose
    161 	 * the largest negative number (in 32 bits) because it is the
    162 	 * only value that is negative and congruent to 0 mod 2^31.
    163 	 */
    164 	if (q == 0 && sxy)
    165 	  *quo = 0x80000000;
    166 	return x;
    167 }
    168