cosmopolitan/libc/tinymath/remquol.c

/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│ vi: set noet ft=c ts=8 sw=8 fenc=utf-8                                   :vi │
╚──────────────────────────────────────────────────────────────────────────────╝
│                                                                              │
│  Musl Libc                                                                   │
│  Copyright © 2005-2020 Rich Felker, et al.                                   │
│                                                                              │
│  Permission is hereby granted, free of charge, to any person obtaining       │
│  a copy of this software and associated documentation files (the             │
│  "Software"), to deal in the Software without restriction, including         │
│  without limitation the rights to use, copy, modify, merge, publish,         │
│  distribute, sublicense, and/or sell copies of the Software, and to          │
│  permit persons to whom the Software is furnished to do so, subject to       │
│  the following conditions:                                                   │
│                                                                              │
│  The above copyright notice and this permission notice shall be              │
│  included in all copies or substantial portions of the Software.             │
│                                                                              │
│  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             │
│  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          │
│  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      │
│  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        │
│  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        │
│  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           │
│  SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                      │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"
#include "libc/tinymath/ldshape.internal.h"
#if !(LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024)

asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
// clang-format off

/**
 * Computes remainder and part of quotient.
 */
long double remquol(long double x, long double y, int *quo)
{
	union ldshape ux = {x}, uy = {y};
	int ex = ux.i.se & 0x7fff;
	int ey = uy.i.se & 0x7fff;
	int sx = ux.i.se >> 15;
	int sy = uy.i.se >> 15;
	uint32_t q;

	*quo = 0;
	if (y == 0 || isnan(y) || ex == 0x7fff)
		return (x*y)/(x*y);
	if (x == 0)
		return x;

	/* normalize x and y */
	if (!ex) {
		ux.i.se = ex;
		ux.f *= 0x1p120f;
		ex = ux.i.se - 120;
	}
	if (!ey) {
		uy.i.se = ey;
		uy.f *= 0x1p120f;
		ey = uy.i.se - 120;
	}

	q = 0;
	if (ex >= ey) {
		/* x mod y */
#if LDBL_MANT_DIG == 64
		uint64_t i, mx, my;
		mx = ux.i.m;
		my = uy.i.m;
		for (; ex > ey; ex--) {
			i = mx - my;
			if (mx >= my) {
				mx = 2*i;
				q++;
				q <<= 1;
			} else if (2*mx < mx) {
				mx = 2*mx - my;
				q <<= 1;
				q++;
			} else {
				mx = 2*mx;
				q <<= 1;
			}
		}
		i = mx - my;
		if (mx >= my) {
			mx = i;
			q++;
		}
		if (mx == 0)
			ex = -120;
		else
			for (; mx >> 63 == 0; mx *= 2, ex--);
		ux.i.m = mx;
#elif LDBL_MANT_DIG == 113
		uint64_t hi, lo, xhi, xlo, yhi, ylo;
		xhi = (ux.i2.hi & -1ULL>>16) | 1ULL<<48;
		yhi = (uy.i2.hi & -1ULL>>16) | 1ULL<<48;
		xlo = ux.i2.lo;
		ylo = ux.i2.lo;
		for (; ex > ey; ex--) {
			hi = xhi - yhi;
			lo = xlo - ylo;
			if (xlo < ylo)
				hi -= 1;
			if (hi >> 63 == 0) {
				xhi = 2*hi + (lo>>63);
				xlo = 2*lo;
				q++;
			} else {
				xhi = 2*xhi + (xlo>>63);
				xlo = 2*xlo;
			}
			q <<= 1;
		}
		hi = xhi - yhi;
		lo = xlo - ylo;
		if (xlo < ylo)
			hi -= 1;
		if (hi >> 63 == 0) {
			xhi = hi;
			xlo = lo;
			q++;
		}
		if ((xhi|xlo) == 0)
			ex = -120;
		else
			for (; xhi >> 48 == 0; xhi = 2*xhi + (xlo>>63), xlo = 2*xlo, ex--);
		ux.i2.hi = xhi;
		ux.i2.lo = xlo;
#endif
	}

	/* scale result and decide between |x| and |x|-|y| */
	if (ex <= 0) {
		ux.i.se = ex + 120;
		ux.f *= 0x1p-120f;
	} else
		ux.i.se = ex;
	x = ux.f;
	if (sy)
		y = -y;
	if (ex == ey || (ex+1 == ey && (2*x > y || (2*x == y && q%2)))) {
		x -= y;
		q++;
	}
	q &= 0x7fffffff;
	*quo = sx^sy ? -(int)q : (int)q;
	return sx ? -x : x;
}

#endif /* long double is long */