xref: /src/lib/libm/ld80/s_cexpl.c

/*-
 * SPDX-License-Identifier: BSD-2-Clause
 *
 * Copyright (c) 2011 David Schultz <das (at) FreeBSD.ORG>
 * All rights reserved.
 *
 * Redistribution and use in source and binary forms, with or without
 * modification, are permitted provided that the following conditions
 * are met:
 * 1. Redistributions of source code must retain the above copyright
 *    notice, this list of conditions and the following disclaimer.
 * 2. Redistributions in binary form must reproduce the above copyright
 *    notice, this list of conditions and the following disclaimer in the
 *    documentation and/or other materials provided with the distribution.
 *
 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 * SUCH DAMAGE.
 *
 * src/s_cexp.c converted to long double complex by Steven G. Kargl
 */

#include <sys/cdefs.h>
#include <complex.h>
#include <float.h>

#include "fpmath.h"
#include "math.h"
#include "math_private.h"
#include "k_expl.h"

long double complex
cexpl (long double complex z)
{
	long double c, exp_x, s, x, y;
	uint64_t lx, ly;
	uint16_t hx, hy;

	ENTERI();

	x = creall(z);
	y = cimagl(z);

	EXTRACT_LDBL80_WORDS(hy, ly, y);
	hy &= 0x7fff;

	/* cexp(x + I 0) = exp(x) + I 0 */
	if ((hy | ly) == 0)
		RETURNI(CMPLXL(expl(x), y));
	EXTRACT_LDBL80_WORDS(hx, lx, x);
	/* cexp(0 + I y) = cos(y) + I sin(y) */
	if (((hx & 0x7fff) | lx) == 0) {
		sincosl(y, &s, &c);
		RETURNI(CMPLXL(c, s));
	}

	if (hy >= 0x7fff) {
		if ((hx & 0x7fff) < 0x7fff || ((hx & 0x7fff) == 0x7fff &&
		    (lx & 0x7fffffffffffffffULL) != 0)) {
			/* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
			RETURNI(CMPLXL(y - y, y - y));
		} else if (hx & 0x8000) {
			/* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
			RETURNI(CMPLXL(0.0, 0.0));
		} else {
			/* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
			RETURNI(CMPLXL(x, y - y));
		}
	}

	/*
	 *  exp_ovfl = 11356.5234062941439497
	 * cexp_ovfl = 22755.3287906024445633
	 */
	if ((hx == 0x400c && lx > 0xb17217f7d1cf79acULL) ||
	    (hx == 0x400d && lx < 0xb1c6a8573de9768cULL)) {
		/*
		 * x is between exp_ovfl and cexp_ovfl, so we must scale to
		 * avoid overflow in exp(x).
		 */
		RETURNI(__ldexp_cexpl(z, 0));
	} else {
		/*
		 * Cases covered here:
		 *  -  x < exp_ovfl and exp(x) won't overflow (common case)
		 *  -  x > cexp_ovfl, so exp(x) * s overflows for all s > 0
		 *  -  x = +-Inf (generated by exp())
		 *  -  x = NaN (spurious inexact exception from y)
		 */
		exp_x = expl(x);
		sincosl(y, &s, &c);
		RETURNI(CMPLXL(exp_x * c, exp_x * s));
	}
}