1/*-
2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD
3 *
4 * Copyright (c) 2007-2008 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 <sys/cdefs.h>
30__FBSDID("$FreeBSD$");
31
32#include <complex.h>
33#include <float.h>
34#include <math.h>
35
36#include "math_private.h"
37
38/*
39 * Several thresholds require a 15-bit exponent and also the usual bias.
40 * s_logl.c and e_hypotl have less hard-coding but end up requiring the
41 * same for the exponent and more for the mantissa.
42 */
43#if LDBL_MAX_EXP != 0x4000
44#error "Unsupported long double format"
45#endif
46
47/*
48 * Overflow must be avoided for components >= LDBL_MAX / (1 + sqrt(2)).
49 * The precise threshold is nontrivial to determine and spell, so use a
50 * lower threshold of approximaely LDBL_MAX / 4, and don't use LDBL_MAX
51 * to spell this since LDBL_MAX is broken on i386 (it overflows in 53-bit
52 * precision).
53 */
54#define	THRESH	0x1p16382L
55
56long double complex
57csqrtl(long double complex z)
58{
59	long double complex result;
60	long double a, b, rx, ry, scale, t;
61
62	a = creall(z);
63	b = cimagl(z);
64
65	/* Handle special cases. */
66	if (z == 0)
67		return (CMPLXL(0, b));
68	if (isinf(b))
69		return (CMPLXL(INFINITY, b));
70	if (isnan(a)) {
71		t = (b - b) / (b - b);	/* raise invalid if b is not a NaN */
72		return (CMPLXL(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */
73	}
74	if (isinf(a)) {
75		/*
76		 * csqrt(inf + NaN i)  = inf +  NaN i
77		 * csqrt(inf + y i)    = inf +  0 i
78		 * csqrt(-inf + NaN i) = NaN +- inf i
79		 * csqrt(-inf + y i)   = 0   +  inf i
80		 */
81		if (signbit(a))
82			return (CMPLXL(fabsl(b - b), copysignl(a, b)));
83		else
84			return (CMPLXL(a, copysignl(b - b, b)));
85	}
86	if (isnan(b)) {
87		t = (a - a) / (a - a);	/* raise invalid */
88		return (CMPLXL(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */
89	}
90
91	/* Scale to avoid overflow. */
92	if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
93		/*
94		 * Don't scale a or b if this might give (spurious)
95		 * underflow.  Then the unscaled value is an equivalent
96		 * infinitesmal (or 0).
97		 */
98		if (fabsl(a) >= 0x1p-16380L)
99			a *= 0.25;
100		if (fabsl(b) >= 0x1p-16380L)
101			b *= 0.25;
102		scale = 2;
103	} else {
104		scale = 1;
105	}
106
107	/* Scale to reduce inaccuracies when both components are denormal. */
108	if (fabsl(a) < 0x1p-16382L && fabsl(b) < 0x1p-16382L) {
109		a *= 0x1p64;
110		b *= 0x1p64;
111		scale = 0x1p-32;
112	}
113
114	/* Algorithm 312, CACM vol 10, Oct 1967. */
115	if (a >= 0) {
116		t = sqrtl((a + hypotl(a, b)) * 0.5);
117		rx = scale * t;
118		ry = scale * b / (2 * t);
119	} else {
120		t = sqrtl((-a + hypotl(a, b)) * 0.5);
121		rx = scale * fabsl(b) / (2 * t);
122		ry = copysignl(scale * t, b);
123	}
124
125	return (CMPLXL(rx, ry));
126}
127