musl/src/math/remquol.c

/* origin: FreeBSD /usr/src/lib/msun/src/s_remquol.c */
/*-
 * ====================================================
 * Copyright (C) 1993 by Sun Microsystems, Inc. All rights reserved.
 *
 * Developed at SunSoft, a Sun Microsystems, Inc. business.
 * Permission to use, copy, modify, and distribute this
 * software is freely granted, provided that this notice
 * is preserved.
 * ====================================================
 */

#include "libm.h"

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double remquol(long double x, long double y, int *quo)
{
	return remquo(x, y, quo);
}
#elif (LDBL_MANT_DIG == 64 || LDBL_MANT_DIG == 113) && LDBL_MAX_EXP == 16384

#define BIAS (LDBL_MAX_EXP - 1)

#if LDBL_MANL_SIZE > 32
typedef uint64_t manl_t;
#else
typedef uint32_t manl_t;
#endif

#if LDBL_MANH_SIZE > 32
typedef uint64_t manh_t;
#else
typedef uint32_t manh_t;
#endif

/*
 * These macros add and remove an explicit integer bit in front of the
 * fractional mantissa, if the architecture doesn't have such a bit by
 * default already.
 */
#ifdef LDBL_IMPLICIT_NBIT
#define SET_NBIT(hx)    ((hx) | (1ULL << LDBL_MANH_SIZE))
#define HFRAC_BITS      LDBL_MANH_SIZE
#else
#define SET_NBIT(hx)    (hx)
#define HFRAC_BITS      (LDBL_MANH_SIZE - 1)
#endif

#define MANL_SHIFT      (LDBL_MANL_SIZE - 1)

static const long double Zero[] = {0.0L, -0.0L};

/*
 * Return the IEEE remainder and set *quo to the last n bits of the
 * quotient, rounded to the nearest integer.  We choose n=31 because
 * we wind up computing all the integer bits of the quotient anyway as
 * a side-effect of computing the remainder by the shift and subtract
 * method.  In practice, this is far more bits than are needed to use
 * remquo in reduction algorithms.
 *
 * Assumptions:
 * - The low part of the mantissa fits in a manl_t exactly.
 * - The high part of the mantissa fits in an int64_t with enough room
 *   for an explicit integer bit in front of the fractional bits.
 */
long double remquol(long double x, long double y, int *quo)
{
	union IEEEl2bits ux, uy;
	int64_t hx,hz;  /* We need a carry bit even if LDBL_MANH_SIZE is 32. */
	manh_t hy;
	manl_t lx,ly,lz;
	int ix,iy,n,q,sx,sxy;

	ux.e = x;
	uy.e = y;
	sx = ux.bits.sign;
	sxy = sx ^ uy.bits.sign;
	ux.bits.sign = 0;       /* |x| */
	uy.bits.sign = 0;       /* |y| */
	x = ux.e;

	/* purge off exception values */
	if ((uy.bits.exp|uy.bits.manh|uy.bits.manl)==0 || /* y=0 */
	    (ux.bits.exp == BIAS + LDBL_MAX_EXP) ||       /* or x not finite */
	    (uy.bits.exp == BIAS + LDBL_MAX_EXP &&
		((uy.bits.manh&~LDBL_NBIT)|uy.bits.manl)!=0)) /* or y is NaN */
		return (x*y)/(x*y);
	if (ux.bits.exp <= uy.bits.exp) {
		if ((ux.bits.exp < uy.bits.exp) ||
		    (ux.bits.manh <= uy.bits.manh &&
		     (ux.bits.manh < uy.bits.manh ||
		      ux.bits.manl < uy.bits.manl))) {
			q = 0;
			goto fixup;       /* |x|<|y| return x or x-y */
		}
		if (ux.bits.manh == uy.bits.manh && ux.bits.manl == uy.bits.manl) {
			*quo = 1;
			return Zero[sx];  /* |x|=|y| return x*0*/
		}
	}

	/* determine ix = ilogb(x) */
	if (ux.bits.exp == 0) {  /* subnormal x */
		ux.e *= 0x1.0p512;
		ix = ux.bits.exp - (BIAS + 512);
	} else {
		ix = ux.bits.exp - BIAS;
	}

	/* determine iy = ilogb(y) */
	if (uy.bits.exp == 0) {  /* subnormal y */
		uy.e *= 0x1.0p512;
		iy = uy.bits.exp - (BIAS + 512);
	} else {
		iy = uy.bits.exp - BIAS;
	}

	/* set up {hx,lx}, {hy,ly} and align y to x */
	hx = SET_NBIT(ux.bits.manh);
	hy = SET_NBIT(uy.bits.manh);
	lx = ux.bits.manl;
	ly = uy.bits.manl;

	/* fix point fmod */
	n = ix - iy;
	q = 0;

	while (n--) {
		hz = hx - hy;
		lz = lx - ly;
		if (lx < ly)
			hz -= 1;
		if (hz < 0) {
			hx = hx + hx + (lx>>MANL_SHIFT);
			lx = lx + lx;
		} else {
			hx = hz + hz + (lz>>MANL_SHIFT);
			lx = lz + lz;
			q++;
		}
		q <<= 1;
	}
	hz = hx - hy;
	lz = lx - ly;
	if (lx < ly)
		hz -= 1;
	if (hz >= 0) {
		hx = hz;
		lx = lz;
		q++;
	}

	/* convert back to floating value and restore the sign */
	if ((hx|lx) == 0) {  /* return sign(x)*0 */
		*quo = sxy ? -q : q;
		return Zero[sx];
	}
	while (hx < (1ULL<<HFRAC_BITS)) {  /* normalize x */
		hx = hx + hx + (lx>>MANL_SHIFT);
		lx = lx + lx;
		iy -= 1;
	}
	ux.bits.manh = hx; /* The integer bit is truncated here if needed. */
	ux.bits.manl = lx;
	if (iy < LDBL_MIN_EXP) {
		ux.bits.exp = iy + (BIAS + 512);
		ux.e *= 0x1p-512;
	} else {
		ux.bits.exp = iy + BIAS;
	}
	ux.bits.sign = 0;
	x = ux.e;
fixup:
	y = fabsl(y);
	if (y < LDBL_MIN * 2) {
		if (x + x > y || (x + x == y && (q & 1))) {
			q++;
			x-=y;
		}
	} else if (x > 0.5*y || (x == 0.5*y && (q & 1))) {
		q++;
		x-=y;
	}

	ux.e = x;
	ux.bits.sign ^= sx;
	x = ux.e;

	q &= 0x7fffffff;
	*quo = sxy ? -q : q;
	return x;
}
#endif