musl/src/math/fmodl.c

/* origin: FreeBSD /usr/src/lib/msun/src/e_fmodl.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 fmodl(long double x, long double y)
{
	return fmod(x, y);
}
#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[] = {0.0, -0.0,};

/*
 * fmodl(x,y)
 * Return x mod y in exact arithmetic
 * Method: shift and subtract
 *
 * 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 fmodl(long double x, long double y)
{
	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,sx;

	ux.e = x;
	uy.e = y;
	sx = ux.bits.sign;

	/* 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)))  /* |x|<|y| return x or x-y */
			return x;
		if (ux.bits.manh==uy.bits.manh && ux.bits.manl==uy.bits.manl)
			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;

	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 {
			if ((hz|lz)==0)   /* return sign(x)*0 */
				return Zero[sx];
			hx = hz+hz+(lz>>MANL_SHIFT);
			lx = lz+lz;
		}
	}
	hz = hx-hy;
	lz = lx-ly;
	if (lx < ly)
		hz -= 1;
	if (hz >= 0) {
		hx = hz;
		lx = lz;
	}

	/* convert back to floating value and restore the sign */
	if ((hx|lx) == 0)   /* return sign(x)*0 */
		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 mantissa 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;
	}
	return ux.e;       /* exact output */
}
#endif