Branch data Line data Source code
1 : : /*-
2 : : * Copyright (c) 2007-2008 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 "cdefs-compat.h"
28 : :
29 : : #include <float.h>
30 : : #include <openlibm_complex.h>
31 : : #include <openlibm_math.h>
32 : :
33 : : #include "math_private.h"
34 : :
35 : : /*
36 : : * gcc doesn't implement complex multiplication or division correctly,
37 : : * so we need to handle infinities specially. We turn on this pragma to
38 : : * notify conforming c99 compilers that the fast-but-incorrect code that
39 : : * gcc generates is acceptable, since the special cases have already been
40 : : * handled.
41 : : */
42 : : #ifndef __GNUC__
43 : : #pragma STDC CX_LIMITED_RANGE ON
44 : : #endif
45 : :
46 : : /* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */
47 : : #define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L)
48 : :
49 : : OLM_DLLEXPORT long double complex
50 : 0 : csqrtl(long double complex z)
51 : : {
52 : : long double complex result;
53 : : long double a, b;
54 : : long double t;
55 : : int scale;
56 : :
57 : 0 : a = creall(z);
58 : 0 : b = cimagl(z);
59 : :
60 : : /* Handle special cases. */
61 [ # # ]: 0 : if (z == 0)
62 : 0 : return (CMPLXL(0, b));
63 [ # # ]: 0 : if (isinf(b))
64 : 0 : return (CMPLXL(INFINITY, b));
65 [ # # ]: 0 : if (isnan(a)) {
66 : 0 : t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
67 : 0 : return (CMPLXL(a, t)); /* return NaN + NaN i */
68 : : }
69 [ # # ]: 0 : if (isinf(a)) {
70 : : /*
71 : : * csqrt(inf + NaN i) = inf + NaN i
72 : : * csqrt(inf + y i) = inf + 0 i
73 : : * csqrt(-inf + NaN i) = NaN +- inf i
74 : : * csqrt(-inf + y i) = 0 + inf i
75 : : */
76 [ # # ]: 0 : if (signbit(a))
77 : 0 : return (CMPLXL(fabsl(b - b), copysignl(a, b)));
78 : : else
79 : 0 : return (CMPLXL(a, copysignl(b - b, b)));
80 : : }
81 : : /*
82 : : * The remaining special case (b is NaN) is handled just fine by
83 : : * the normal code path below.
84 : : */
85 : :
86 : : /* Scale to avoid overflow. */
87 [ # # # # ]: 0 : if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) {
88 : 0 : a *= 0.25;
89 : 0 : b *= 0.25;
90 : 0 : scale = 1;
91 : : } else {
92 : 0 : scale = 0;
93 : : }
94 : :
95 : : /* Algorithm 312, CACM vol 10, Oct 1967. */
96 [ # # ]: 0 : if (a >= 0) {
97 : 0 : t = sqrtl((a + hypotl(a, b)) * 0.5);
98 : 0 : result = CMPLXL(t, b / (2 * t));
99 : : } else {
100 : 0 : t = sqrtl((-a + hypotl(a, b)) * 0.5);
101 : 0 : result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b));
102 : : }
103 : :
104 : : /* Rescale. */
105 [ # # ]: 0 : if (scale)
106 : 0 : return (result * 2);
107 : : else
108 : 0 : return (result);
109 : : }
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