/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
/*-
 * Copyright (c) 2007 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 "libm.h"

/*
 * gcc doesn't implement complex multiplication or division correctly,
 * so we need to handle infinities specially. We turn on this pragma to
 * notify conforming c99 compilers that the fast-but-incorrect code that
 * gcc generates is acceptable, since the special cases have already been
 * handled.
 */
#pragma STDC CX_LIMITED_RANGE ON

/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
#define THRESH 0x1.a827999fcef32p+1022

double complex csqrt(double complex z) {
  double complex result;
  double a, b;
  double t;
  int scale;

  a = creal(z);
  b = cimag(z);

  /* Handle special cases. */
  if (z == 0)
    return CMPLX(0, b);
  if (isinf(b))
    return CMPLX(INFINITY, b);
  if (isnan(a)) {
    t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
    return CMPLX(a, t);    /* return NaN + NaN i */
  }
  if (isinf(a)) {
    /*
     * csqrt(inf + NaN i)  = inf +  NaN i
     * csqrt(inf + y i)    = inf +  0 i
     * csqrt(-inf + NaN i) = NaN +- inf i
     * csqrt(-inf + y i)   = 0   +  inf i
     */
    if (signbit(a))
      return CMPLX(fabs(b - b), copysign(a, b));
    else
      return CMPLX(a, copysign(b - b, b));
  }
  /*
   * The remaining special case (b is NaN) is handled just fine by
   * the normal code path below.
   */

  /* Scale to avoid overflow. */
  if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
    a *= 0.25;
    b *= 0.25;
    scale = 1;
  } else {
    scale = 0;
  }

  /* Algorithm 312, CACM vol 10, Oct 1967. */
  if (a >= 0) {
    t = sqrt((a + hypot(a, b)) * 0.5);
    result = CMPLX(t, b / (2 * t));
  } else {
    t = sqrt((-a + hypot(a, b)) * 0.5);
    result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
  }

  /* Rescale. */
  if (scale)
    result *= 2;
  return result;
}