1 /*-
2 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG>
3 * All rights reserved.
4 *
5 * Redistribution and use in source and binary forms, with or without
6 * modification, are permitted provided that the following conditions
7 * are met:
8 * 1. Redistributions of source code must retain the above copyright
9 * notice, this list of conditions and the following disclaimer.
10 * 2. Redistributions in binary form must reproduce the above copyright
11 * notice, this list of conditions and the following disclaimer in the
12 * documentation and/or other materials provided with the distribution.
13 *
14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND
15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE
18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL
19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS
20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION)
21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY
23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF
24 * SUCH DAMAGE.
25 */
26
27 #include <sys/cdefs.h>
28 __FBSDID("$FreeBSD: head/lib/msun/src/s_csqrt.c 275819 2014-12-16 09:21:56Z ed $");
29
30 #include <complex.h>
31 #include <float.h>
32 #include <math.h>
33
34 #include "math_private.h"
35
36 /*
37 * gcc doesn't implement complex multiplication or division correctly,
38 * so we need to handle infinities specially. We turn on this pragma to
39 * notify conforming c99 compilers that the fast-but-incorrect code that
40 * gcc generates is acceptable, since the special cases have already been
41 * handled.
42 */
43 #pragma STDC CX_LIMITED_RANGE ON
44
45 /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */
46 #define THRESH 0x1.a827999fcef32p+1022
47
48 double complex
csqrt(double complex z)49 csqrt(double complex z)
50 {
51 double complex result;
52 double a, b;
53 double t;
54 int scale;
55
56 a = creal(z);
57 b = cimag(z);
58
59 /* Handle special cases. */
60 if (z == 0)
61 return (CMPLX(0, b));
62 if (isinf(b))
63 return (CMPLX(INFINITY, b));
64 if (isnan(a)) {
65 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
66 return (CMPLX(a, t)); /* return NaN + NaN i */
67 }
68 if (isinf(a)) {
69 /*
70 * csqrt(inf + NaN i) = inf + NaN i
71 * csqrt(inf + y i) = inf + 0 i
72 * csqrt(-inf + NaN i) = NaN +- inf i
73 * csqrt(-inf + y i) = 0 + inf i
74 */
75 if (signbit(a))
76 return (CMPLX(fabs(b - b), copysign(a, b)));
77 else
78 return (CMPLX(a, copysign(b - b, b)));
79 }
80 /*
81 * The remaining special case (b is NaN) is handled just fine by
82 * the normal code path below.
83 */
84
85 /* Scale to avoid overflow. */
86 if (fabs(a) >= THRESH || fabs(b) >= THRESH) {
87 a *= 0.25;
88 b *= 0.25;
89 scale = 1;
90 } else {
91 scale = 0;
92 }
93
94 /* Algorithm 312, CACM vol 10, Oct 1967. */
95 if (a >= 0) {
96 t = sqrt((a + hypot(a, b)) * 0.5);
97 result = CMPLX(t, b / (2 * t));
98 } else {
99 t = sqrt((-a + hypot(a, b)) * 0.5);
100 result = CMPLX(fabs(b) / (2 * t), copysign(t, b));
101 }
102
103 /* Rescale. */
104 if (scale)
105 return (result * 2);
106 else
107 return (result);
108 }
109
110 #if LDBL_MANT_DIG == 53
111 __weak_reference(csqrt, csqrtl);
112 #endif
113