text: /*-
   * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
   *
   * 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 <sys/cdefs.h>
  __FBSDID("$FreeBSD$");
  
  #include <complex.h>
  #include <float.h>
  #include <math.h>
  
  #include "math_private.h"
  
  /* For avoiding 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, rx, ry, scale, t;
  
  	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 + 0.0L + t, a + 0.0L + t)); /* 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)));
  	}
  	if (isnan(b)) {
  		t = (a - a) / (a - a);	/* raise invalid */
  		return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
  	}
  
  	/* Scale to avoid overflow. */
  	if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
  		/*
  		 * Don't scale a or b if this might give (spurious)
  		 * underflow.  Then the unscaled value is an equivalent
  		 * infinitesmal (or 0).
  		 */
  		if (fabs(a) >= 0x1p-1020)
  			a *= 0.25;
  		if (fabs(b) >= 0x1p-1020)
  			b *= 0.25;
  		scale = 2;
  	} else {
  		scale = 1;
  	}
  
  	/* Scale to reduce inaccuracies when both components are denormal. */
  	if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) {
  		a *= 0x1p54;
  		b *= 0x1p54;
  		scale = 0x1p-27;
  	}
  
  	/* Algorithm 312, CACM vol 10, Oct 1967. */
  	if (a >= 0) {
  		t = sqrt((a + hypot(a, b)) * 0.5);
  		rx = scale * t;
  		ry = scale * b / (2 * t);
  	} else {
  		t = sqrt((-a + hypot(a, b)) * 0.5);
  		rx = scale * fabs(b) / (2 * t);
  		ry = copysign(scale * t, b);
  	}
  
  	return (CMPLX(rx, ry));
  }
  
  #if LDBL_MANT_DIG == 53
  __weak_reference(csqrt, csqrtl);
  #endif
  