/*-
 * SPDX-License-Identifier: BSD-2-Clause
 *
 * Copyright (c) 2011 David Schultz <das@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.
 */

#include <complex.h>
#include <math.h>

#include "math_private.h"

static const uint32_t
exp_ovfl  = 0x42b17218,         /* MAX_EXP * ln2 ~= 88.722839355 */
cexp_ovfl = 0x43400074;         /* (MAX_EXP - MIN_DENORM_EXP) * ln2 */

float complex
cexpf(float complex z)
{
        float c, exp_x, s, x, y;
        uint32_t hx, hy;

        x = crealf(z);
        y = cimagf(z);

        GET_FLOAT_WORD(hy, y);
        hy &= 0x7fffffff;

        /* cexp(x + I 0) = exp(x) + I 0 */
        if (hy == 0)
                return (CMPLXF(expf(x), y));
        GET_FLOAT_WORD(hx, x);
        /* cexp(0 + I y) = cos(y) + I sin(y) */
        if ((hx & 0x7fffffff) == 0) {
                sincosf(y, &s, &c);
                return (CMPLXF(c, s));
        }

        if (hy >= 0x7f800000) {
                if ((hx & 0x7fffffff) != 0x7f800000) {
                        /* cexp(finite|NaN +- I Inf|NaN) = NaN + I NaN */
                        return (CMPLXF(y - y, y - y));
                } else if (hx & 0x80000000) {
                        /* cexp(-Inf +- I Inf|NaN) = 0 + I 0 */
                        return (CMPLXF(0.0, 0.0));
                } else {
                        /* cexp(+Inf +- I Inf|NaN) = Inf + I NaN */
                        return (CMPLXF(x, y - y));
                }
        }

        if (hx >= exp_ovfl && hx <= cexp_ovfl) {
                /*
                 * x is between 88.7 and 192, so we must scale to avoid
                 * overflow in expf(x).
                 */
                return (__ldexp_cexpf(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 = expf(x);
                sincosf(y, &s, &c);
                return (CMPLXF(exp_x * c, exp_x * s));
        }
}