1/*-
2 * SPDX-License-Identifier: BSD-2-Clause
3 *
4 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
5 * All rights reserved.
6 *
7 * Redistribution and use in source and binary forms, with or without
8 * modification, are permitted provided that the following conditions
9 * are met:
10 * 1. Redistributions of source code must retain the above copyright
11 *    notice, this list of conditions and the following disclaimer.
12 * 2. Redistributions in binary form must reproduce the above copyright
13 *    notice, this list of conditions and the following disclaimer in the
14 *    documentation and/or other materials provided with the distribution.
15 *
16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
19 * ARE DISCLAIMED.  IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
26 * SUCH DAMAGE.
27 */
28
29#include <complex.h>
30#include <float.h>
31#include <math.h>
32
33#include "math_private.h"
34
35/* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */
36#define	THRESH	0x1.a827999fcef32p+1022
37
38double complex
39csqrt(double complex z)
40{
41	double complex result;
42	double a, b, rx, ry, scale, t;
43
44	a = creal(z);
45	b = cimag(z);
46
47	/* Handle special cases. */
48	if (z == 0)
49		return (CMPLX(0, b));
50	if (isinf(b))
51		return (CMPLX(INFINITY, b));
52	if (isnan(a)) {
53		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
54		return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
55	}
56	if (isinf(a)) {
57		/*
58		 * csqrt(inf + NaN i)  = inf +  NaN i
59		 * csqrt(inf + y i)    = inf +  0 i
60		 * csqrt(-inf + NaN i) = NaN +- inf i
61		 * csqrt(-inf + y i)   = 0   +  inf i
62		 */
63		if (signbit(a))
64			return (CMPLX(fabs(b - b), copysign(a, b)));
65		else
66			return (CMPLX(a, copysign(b - b, b)));
67	}
68	if (isnan(b)) {
69		t = (a - a) / (a - a);	/* raise invalid */
70		return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
71	}
72
73	/* Scale to avoid overflow. */
74	if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
75		/*
76		 * Don't scale a or b if this might give (spurious)
77		 * underflow.  Then the unscaled value is an equivalent
78		 * infinitesmal (or 0).
79		 */
80		if (fabs(a) >= 0x1p-1020)
81			a *= 0.25;
82		if (fabs(b) >= 0x1p-1020)
83			b *= 0.25;
84		scale = 2;
85	} else {
86		scale = 1;
87	}
88
89	/* Scale to reduce inaccuracies when both components are denormal. */
90	if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) {
91		a *= 0x1p54;
92		b *= 0x1p54;
93		scale = 0x1p-27;
94	}
95
96	/* Algorithm 312, CACM vol 10, Oct 1967. */
97	if (a >= 0) {
98		t = sqrt((a + hypot(a, b)) * 0.5);
99		rx = scale * t;
100		ry = scale * b / (2 * t);
101	} else {
102		t = sqrt((-a + hypot(a, b)) * 0.5);
103		rx = scale * fabs(b) / (2 * t);
104		ry = copysign(scale * t, b);
105	}
106
107	return (CMPLX(rx, ry));
108}
109
110#if LDBL_MANT_DIG == 53
111__weak_reference(csqrt, csqrtl);
112#endif
113