text: /*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
  │vi: set et ft=c ts=8 tw=8 fenc=utf-8                                       :vi│
  ╚──────────────────────────────────────────────────────────────────────────────╝
  │                                                                              │
  │  Musl Libc                                                                   │
  │  Copyright © 2005-2014 Rich Felker, et al.                                   │
  │                                                                              │
  │  Permission is hereby granted, free of charge, to any person obtaining       │
  │  a copy of this software and associated documentation files (the             │
  │  "Software"), to deal in the Software without restriction, including         │
  │  without limitation the rights to use, copy, modify, merge, publish,         │
  │  distribute, sublicense, and/or sell copies of the Software, and to          │
  │  permit persons to whom the Software is furnished to do so, subject to       │
  │  the following conditions:                                                   │
  │                                                                              │
  │  The above copyright notice and this permission notice shall be              │
  │  included in all copies or substantial portions of the Software.             │
  │                                                                              │
  │  THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND,             │
  │  EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF          │
  │  MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.      │
  │  IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY        │
  │  CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT,        │
  │  TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE           │
  │  SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.                      │
  │                                                                              │
  ╚─────────────────────────────────────────────────────────────────────────────*/
  #include "libc/complex.h"
  #include "libc/math.h"
  #include "libc/tinymath/complex.internal.h"
  
  asm(".ident\t\"\\n\\n\
  Musl libc (MIT License)\\n\
  Copyright 2005-2014 Rich Felker, et. al.\"");
  asm(".include \"libc/disclaimer.inc\"");
  /* clang-format off */
  
  /* 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.
   */
  
  /*
   * 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.
   */
  // TODO(elimisteve): write test proving why we do / don't need it
  // #pragma STDC CX_LIMITED_RANGE ON
  
  /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
  #define THRESH  0x1.a827999fcef32p+1022
  
  /**
   * Returns complex square root.
   */
  complex double csqrt(complex double z)
  {
  	complex double 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;
  }
  