1 /* origin: FreeBSD /usr/src/lib/msun/src/s_csqrtf.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 float complex csqrtf(float complex z)
40 {
41 float a = crealf(z), b = cimagf(z);
42 double t;
43 44 /* Handle special cases. */
45 if (z == 0)
46 return CMPLXF(0, b);
47 if (isinf(b))
48 return CMPLXF(INFINITY, b);
49 if (isnan(a)) {
50 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */
51 return CMPLXF(a, t); /* return NaN + NaN i */
52 }
53 if (isinf(a)) {
54 /*
55 * csqrtf(inf + NaN i) = inf + NaN i
56 * csqrtf(inf + y i) = inf + 0 i
57 * csqrtf(-inf + NaN i) = NaN +- inf i
58 * csqrtf(-inf + y i) = 0 + inf i
59 */
60 if (signbit(a))
61 return CMPLXF(fabsf(b - b), copysignf(a, b));
62 else
63 return CMPLXF(a, copysignf(b - b, b));
64 }
65 /*
66 * The remaining special case (b is NaN) is handled just fine by
67 * the normal code path below.
68 */
69 70 /*
71 * We compute t in double precision to avoid overflow and to
72 * provide correct rounding in nearly all cases.
73 * This is Algorithm 312, CACM vol 10, Oct 1967.
74 */
75 if (a >= 0) {
76 t = sqrt((a + hypot(a, b)) * 0.5);
77 return CMPLXF(t, b / (2.0 * t));
78 } else {
79 t = sqrt((-a + hypot(a, b)) * 0.5);
80 return CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b));
81 }
82 }
83