/* origin: FreeBSD /usr/src/lib/msun/src/s_csinh.c */
/*-
 * Copyright (c) 2005 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 sine of a complex argument z = x + i y.
 *
 * sinh(z) = sinh(x+iy)
 *         = sinh(x) cos(y) + i cosh(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.
 */

#include "libm.h"

static const double huge = 0x1p1023;

double complex csinh(double complex z) {
  double x, y, h;
  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(sinh(x), y);
    if (ix < 0x40360000) /* small x: normal case */
      return CMPLX(sinh(x) * cos(y), cosh(x) * sin(y));

    /* |x| >= 22, so cosh(x) ~= exp(|x|) */
    if (ix < 0x40862e42) {
      /* x < 710: exp(|x|) won't overflow */
      h = exp(fabs(x)) * 0.5;
      return CMPLX(copysign(h, x) * cos(y), h * sin(y));
    } else if (ix < 0x4096bbaa) {
      /* x < 1455: scale to avoid overflow */
      z = __ldexp_cexp(CMPLX(fabs(x), y), -1);
      return CMPLX(creal(z) * copysign(1, x), cimag(z));
    } else {
      /* x >= 1455: the result always overflows */
      h = huge * x;
      return CMPLX(h * cos(y), h * h * sin(y));
    }
  }

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

  /*
   * sinh(+-Inf +- I 0) = +-Inf + I +-0.
   *
   * sinh(NaN +- I 0)   = d(NaN) + I +-0.
   */
  if ((iy | ly) == 0 && ix >= 0x7ff00000) {
    if (((hx & 0xfffff) | lx) == 0)
      return CMPLX(x, y);
    return CMPLX(x, copysign(0, y));
  }

  /*
   * sinh(x +- I Inf) = dNaN + I dNaN.
   * Raise the invalid floating-point exception for finite nonzero x.
   *
   * sinh(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));

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

  /*
   * sinh(NaN + I NaN)  = d(NaN) + I d(NaN).
   *
   * sinh(NaN +- I Inf) = d(NaN) + I d(NaN).
   * Optionally raises the invalid floating-point exception.
   * Choice = raise.
   *
   * sinh(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((x * x) * (y - y), (x + x) * (y - y));
}