/*-
 * SPDX-License-Identifier: BSD-2-Clause
 *
 * Copyright (c) 2005-2025 Bruce D. Evans and Steven G. Kargl
 * 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 unmodified, 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 ``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 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.
 */

/*
 * Hyperbolic cosine of a complex argument z = x + i y.
 *
 * cosh(z) = cosh(x+iy)
 *         = cosh(x) cos(y) + i sinh(x) sin(y).
 *
 * Exceptional values are noted in the comments within the source code.
 * These values and the return value were taken from n1124.pdf.
 * The sign of the result for some exceptional values is unspecified but
 * must satisfy both cosh(conj(z)) == conj(cosh(z)) and cosh(-z) == cosh(z).
 */

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

#include "math_private.h"

static const double huge = 0x1p1023;

double complex
ccosh(double complex z)
{
        double c, h, s, x, y;
        int32_t hx, hy, ix, iy, lx, ly;

        x = creal(z);
        y = cimag(z);

        EXTRACT_WORDS(hx, lx, x);
        EXTRACT_WORDS(hy, ly, y);

        ix = 0x7fffffff & hx;
        iy = 0x7fffffff & hy;

        /* Handle the nearly-non-exceptional cases where x and y are finite. */
        if (ix < 0x7ff00000 && iy < 0x7ff00000) {
                if ((iy | ly) == 0)
                        return (CMPLX(cosh(x), x * y));

                sincos(y, &s, &c);
                if (ix < 0x40360000)    /* |x| < 22: normal case */
                        return (CMPLX(cosh(x) * c, sinh(x) * s));

                /* |x| >= 22, so cosh(x) ~= exp(|x|) */
                if (ix < 0x40862e42) {
                        /* x < 710: exp(|x|) won't overflow */
                        h = exp(fabs(x)) / 2;
                        return (CMPLX(h * c, copysign(h, x) * s));
                } else if (ix < 0x4096bbaa) {
                        /* x < 1455: scale to avoid overflow */
                        z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
                        return (CMPLX(creal(z), cimag(z) * copysign(1, x)));
                } else {
                        /* x >= 1455: the result always overflows */
                        h = huge * x;
                        return (CMPLX(h * h * c, h * s));
                }
        }

        /*
         * cosh(+-0 +- I Inf) = dNaN + I (+-)(+-)0.
         * The sign of 0 in the result is unspecified.  Choice = product
         * of the signs of the argument.  Raise the invalid floating-point
         * exception.
         *
         * cosh(+-0 +- I NaN) = d(NaN) + I (+-)(+-)0.
         * The sign of 0 in the result is unspecified.  Choice = product
         * of the signs of the argument.
         */
        if ((ix | lx) == 0)             /* && iy >= 0x7ff00000 */
                return (CMPLX(y - y, x * copysign(0, y)));

        /*
         * cosh(+-Inf +- I 0) = +Inf + I (+-)(+-)0.
         *
         * cosh(NaN +- I 0)   = d(NaN) + I (+-)(+-)0.
         * The sign of 0 in the result is unspecified.  Choice = product
         * of the signs of the argument.
         */
        if ((iy | ly) == 0)             /* && ix >= 0x7ff00000 */
                return (CMPLX(x * x, copysign(0, x) * y));

        /*
         * cosh(x +- I Inf) = dNaN + I dNaN.
         * Raise the invalid floating-point exception for finite nonzero x.
         *
         * cosh(x + I NaN) = d(NaN) + I d(NaN).
         * Optionally raises the invalid floating-point exception for finite
         * nonzero x.  Choice = don't raise (except for signaling NaNs).
         */
        if (ix < 0x7ff00000)            /* && iy >= 0x7ff00000 */
                return (CMPLX(y - y, x * (y - y)));

        /*
         * cosh(+-Inf + I NaN)  = +Inf + I d(NaN).
         *
         * cosh(+-Inf +- I Inf) = +Inf + I dNaN.
         * The sign of Inf in the result is unspecified.  Choice = always +.
         * Raise the invalid floating-point exception.
         *
         * cosh(+-Inf + I y)   = +Inf cos(y) +- I Inf sin(y)
         */
        if (ix == 0x7ff00000 && lx == 0) {
                if (iy >= 0x7ff00000)
                        return (CMPLX(INFINITY, x * (y - y)));

                sincos(y, &s, &c);
                return (CMPLX(INFINITY * c, x * s));
        }

        /*
         * cosh(NaN + I NaN)  = d(NaN) + I d(NaN).
         *
         * cosh(NaN +- I Inf) = d(NaN) + I d(NaN).
         * Optionally raises the invalid floating-point exception.
         * Choice = raise.
         *
         * cosh(NaN + I y)    = d(NaN) + I d(NaN).
         * Optionally raises the invalid floating-point exception for finite
         * nonzero y.  Choice = don't raise (except for signaling NaNs).
         */
        return (CMPLX(((long double)x * x) * (y - y),
            ((long double)x + x) * (y - y)));
}

double complex
ccos(double complex z)
{

        /* ccos(z) = ccosh(I * z) */
        return (ccosh(CMPLX(-cimag(z), creal(z))));
}

#if (LDBL_MANT_DIG == 53)
__weak_reference(ccosh, ccoshl);
__weak_reference(ccos, ccosl);
#endif