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