1/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */
  2/*-
  3 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
  4 * All rights reserved.
  5 *
  6 * Redistribution and use in source and binary forms, with or without
  7 * modification, are permitted provided that the following conditions
  8 * are met:
  9 * 1. Redistributions of source code must retain the above copyright
 10 *    notice, this list of conditions and the following disclaimer.
 11 * 2. Redistributions in binary form must reproduce the above copyright
 12 *    notice, this list of conditions and the following disclaimer in the
 13 *    documentation and/or other materials provided with the distribution.
 14 *
 15 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
 16 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
 17 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
 18 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
 19 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
 20 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
 21 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
 22 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
 23 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
 24 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
 25 * SUCH DAMAGE.
 26 */
 27
 28#include "complex_impl.h"
 29
 30/*
 31 * gcc doesn't implement complex multiplication or division correctly,
 32 * so we need to handle infinities specially. We turn on this pragma to
 33 * notify conforming c99 compilers that the fast-but-incorrect code that
 34 * gcc generates is acceptable, since the special cases have already been
 35 * handled.
 36 */
 37#pragma STDC CX_LIMITED_RANGE ON
 38
 39/* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
 40#define THRESH  0x1.a827999fcef32p+1022
 41
 42double complex csqrt(double complex z)
 43{
 44	double complex result;
 45	double a, b;
 46	double t;
 47	int scale;
 48
 49	a = creal(z);
 50	b = cimag(z);
 51
 52	/* Handle special cases. */
 53	if (z == 0)
 54		return CMPLX(0, b);
 55	if (isinf(b))
 56		return CMPLX(INFINITY, b);
 57	if (isnan(a)) {
 58		t = (b - b) / (b - b);  /* raise invalid if b is not a NaN */
 59		return CMPLX(a, t);   /* return NaN + NaN i */
 60	}
 61	if (isinf(a)) {
 62		/*
 63		 * csqrt(inf + NaN i)  = inf +  NaN i
 64		 * csqrt(inf + y i)    = inf +  0 i
 65		 * csqrt(-inf + NaN i) = NaN +- inf i
 66		 * csqrt(-inf + y i)   = 0   +  inf i
 67		 */
 68		if (signbit(a))
 69			return CMPLX(fabs(b - b), copysign(a, b));
 70		else
 71			return CMPLX(a, copysign(b - b, b));
 72	}
 73	/*
 74	 * The remaining special case (b is NaN) is handled just fine by
 75	 * the normal code path below.
 76	 */
 77
 78	/* Scale to avoid overflow. */
 79	if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
 80		a *= 0.25;
 81		b *= 0.25;
 82		scale = 1;
 83	} else {
 84		scale = 0;
 85	}
 86
 87	/* Algorithm 312, CACM vol 10, Oct 1967. */
 88	if (a >= 0) {
 89		t = sqrt((a + hypot(a, b)) * 0.5);
 90		result = CMPLX(t, b / (2 * t));
 91	} else {
 92		t = sqrt((-a + hypot(a, b)) * 0.5);
 93		result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
 94	}
 95
 96	/* Rescale. */
 97	if (scale)
 98		result *= 2;
 99	return result;
100}