/*-
* Copyright (c) 2007-2008 David Schultz <[email protected]>
* 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 <sys/cdefs.h>
#if 0
__FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $");
#else
__RCSID("$NetBSD: csqrtl.c,v 1.2 2014/10/11 00:43:51 christos Exp $");
#endif

#include "../src/namespace.h"
#include <complex.h>
#include <float.h>
#include <math.h>
#include <stdbool.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 >= LDBL_MAX / (1 + sqrt(2)). */
#define THRESH  (LDBL_MAX / 2.414213562373095048801688724209698L)

#define cpackl(r, i) ((r) + (i) * I)

long double complex
csqrtl(long double complex z)
{
       long double complex result;
       long double a, b;
       long double t;
       bool scale;

       a = creall(z);
       b = cimagl(z);

       /* Handle special cases. */
       if (z == 0.0L)
               return (cpackl(0.0L, b));
       if (isinf(b))
               return (cpackl(INFINITY, b));
       if (isnan(a)) {
               t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
               return (cpackl(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 (cpackl(fabsl(b - b), copysignl(a, b)));
               else
                       return (cpackl(a, copysignl(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 (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
               a *= 0.25L;
               b *= 0.25L;
               scale = true;
       } else {
               scale = false;
       }

       /* Algorithm 312, CACM vol 10, Oct 1967. */
       if (a >= 0L) {
               t = sqrtl((a + hypotl(a, b)) * 0.5L);
               result = cpackl(t, b / (2.0L * t));
       } else {
               t = sqrtl((-a + hypotl(a, b)) * 0.5L);
               result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b));
       }

       /* Rescale. */
       if (scale)
               return (result * 2.0L);
       else
               return (result);
}