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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 #include <stdint.h>
     18 
     19 #include "fpmath.h"
     20 #include "math.h"
     21 #include "math_private.h"
     22 
     23 #define	BIAS (LDBL_MAX_EXP - 1)
     24 
     25 #if LDBL_MANL_SIZE > 32
     26 typedef	uint64_t manl_t;
     27 #else
     28 typedef	uint32_t manl_t;
     29 #endif
     30 
     31 #if LDBL_MANH_SIZE > 32
     32 typedef	uint64_t manh_t;
     33 #else
     34 typedef	uint32_t manh_t;
     35 #endif
     36 
     37 /*
     38  * These macros add and remove an explicit integer bit in front of the
     39  * fractional mantissa, if the architecture doesn't have such a bit by
     40  * default already.
     41  */
     42 #ifdef LDBL_IMPLICIT_NBIT
     43 #define	SET_NBIT(hx)	((hx) | (1ULL << LDBL_MANH_SIZE))
     44 #define	HFRAC_BITS	LDBL_MANH_SIZE
     45 #else
     46 #define	SET_NBIT(hx)	(hx)
     47 #define	HFRAC_BITS	(LDBL_MANH_SIZE - 1)
     48 #endif
     49 
     50 #define	MANL_SHIFT	(LDBL_MANL_SIZE - 1)
     51 
     52 static const long double Zero[] = {0.0L, -0.0L};
     53 
     54 /*
     55  * Return the IEEE remainder and set *quo to the last n bits of the
     56  * quotient, rounded to the nearest integer.  We choose n=31 because
     57  * we wind up computing all the integer bits of the quotient anyway as
     58  * a side-effect of computing the remainder by the shift and subtract
     59  * method.  In practice, this is far more bits than are needed to use
     60  * remquo in reduction algorithms.
     61  *
     62  * Assumptions:
     63  * - The low part of the mantissa fits in a manl_t exactly.
     64  * - The high part of the mantissa fits in an int64_t with enough room
     65  *   for an explicit integer bit in front of the fractional bits.
     66  */
     67 long double
     68 remquol(long double x, long double y, int *quo)
     69 {
     70 	union IEEEl2bits ux, uy;
     71 	int64_t hx,hz;	/* We need a carry bit even if LDBL_MANH_SIZE is 32. */
     72 	manh_t hy;
     73 	manl_t lx,ly,lz;
     74 	int ix,iy,n,q,sx,sxy;
     75 
     76 	ux.e = x;
     77 	uy.e = y;
     78 	sx = ux.bits.sign;
     79 	sxy = sx ^ uy.bits.sign;
     80 	ux.bits.sign = 0;	/* |x| */
     81 	uy.bits.sign = 0;	/* |y| */
     82 	x = ux.e;
     83 
     84     /* purge off exception values */
     85 	if((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
     86 	   (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||	 /* or x not finite */
     87 	   (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
     88 	    ((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
     89 	    return (x*y)/(x*y);
     90 	if(ux.bits.exp<=uy.bits.exp) {
     91 	    if((ux.bits.exp<uy.bits.exp) ||
     92 	       (ux.bits.manh<=uy.bits.manh &&
     93 		(ux.bits.manh<uy.bits.manh ||
     94 		 ux.bits.manl<uy.bits.manl))) {
     95 		q = 0;
     96 		goto fixup;	/* |x|<|y| return x or x-y */
     97 	    }
     98 	    if(ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl) {
     99 		*quo = (sxy ? -1 : 1);
    100 		return Zero[sx];	/* |x|=|y| return x*0*/
    101 	    }
    102 	}
    103 
    104     /* determine ix = ilogb(x) */
    105 	if(ux.bits.exp == 0) {	/* subnormal x */
    106 	    ux.e *= 0x1.0p512;
    107 	    ix = ux.bits.exp - (BIAS + 512);
    108 	} else {
    109 	    ix = ux.bits.exp - BIAS;
    110 	}
    111 
    112     /* determine iy = ilogb(y) */
    113 	if(uy.bits.exp == 0) {	/* subnormal y */
    114 	    uy.e *= 0x1.0p512;
    115 	    iy = uy.bits.exp - (BIAS + 512);
    116 	} else {
    117 	    iy = uy.bits.exp - BIAS;
    118 	}
    119 
    120     /* set up {hx,lx}, {hy,ly} and align y to x */
    121 	hx = SET_NBIT(ux.bits.manh);
    122 	hy = SET_NBIT(uy.bits.manh);
    123 	lx = ux.bits.manl;
    124 	ly = uy.bits.manl;
    125 
    126     /* fix point fmod */
    127 	n = ix - iy;
    128 	q = 0;
    129 
    130 	while(n--) {
    131 	    hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
    132 	    if(hz<0){hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;}
    133 	    else {hx = hz+hz+(lz>>MANL_SHIFT); lx = lz+lz; q++;}
    134 	    q <<= 1;
    135 	}
    136 	hz=hx-hy;lz=lx-ly; if(lx<ly) hz -= 1;
    137 	if(hz>=0) {hx=hz;lx=lz;q++;}
    138 
    139     /* convert back to floating value and restore the sign */
    140 	if((hx|lx)==0) {			/* return sign(x)*0 */
    141 	    q &= 0x7fffffff;
    142 	    *quo = (sxy ? -q : q);
    143 	    return Zero[sx];
    144 	}
    145 	while(hx<(1ULL<<HFRAC_BITS)) {	/* normalize x */
    146 	    hx = hx+hx+(lx>>MANL_SHIFT); lx = lx+lx;
    147 	    iy -= 1;
    148 	}
    149 	ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
    150 	ux.bits.manl = lx;
    151 	if (iy < LDBL_MIN_EXP) {
    152 	    ux.bits.exp = iy + (BIAS + 512);
    153 	    ux.e *= 0x1p-512;
    154 	} else {
    155 	    ux.bits.exp = iy + BIAS;
    156 	}
    157 	ux.bits.sign = 0;
    158 	x = ux.e;
    159 fixup:
    160 	y = fabsl(y);
    161 	if (y < LDBL_MIN * 2) {
    162 	    if (x+x>y || (x+x==y && (q & 1))) {
    163 		q++;
    164 		x-=y;
    165 	    }
    166 	} else if (x>0.5*y || (x==0.5*y && (q & 1))) {
    167 	    q++;
    168 	    x-=y;
    169 	}
    170 
    171 	ux.e = x;
    172 	ux.bits.sign ^= sx;
    173 	x = ux.e;
    174 
    175 	q &= 0x7fffffff;
    176 	*quo = (sxy ? -q : q);
    177 	return x;
    178 }
    179