| Elliott Hughes | a0ee078 | 2013-01-30 19:06:37 -0800 | [diff] [blame^] | 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("$FreeBSD$"); |
| 29 | |
| 30 | #include <complex.h> |
| 31 | #include <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 | #pragma STDC CX_LIMITED_RANGE ON |
| 43 | |
| 44 | float complex |
| 45 | csqrtf(float complex z) |
| 46 | { |
| 47 | float a = crealf(z), b = cimagf(z); |
| 48 | double t; |
| 49 | |
| 50 | /* Handle special cases. */ |
| 51 | if (z == 0) |
| 52 | return (cpackf(0, b)); |
| 53 | if (isinf(b)) |
| 54 | return (cpackf(INFINITY, b)); |
| 55 | if (isnan(a)) { |
| 56 | t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ |
| 57 | return (cpackf(a, t)); /* return NaN + NaN i */ |
| 58 | } |
| 59 | if (isinf(a)) { |
| 60 | /* |
| 61 | * csqrtf(inf + NaN i) = inf + NaN i |
| 62 | * csqrtf(inf + y i) = inf + 0 i |
| 63 | * csqrtf(-inf + NaN i) = NaN +- inf i |
| 64 | * csqrtf(-inf + y i) = 0 + inf i |
| 65 | */ |
| 66 | if (signbit(a)) |
| 67 | return (cpackf(fabsf(b - b), copysignf(a, b))); |
| 68 | else |
| 69 | return (cpackf(a, copysignf(b - b, b))); |
| 70 | } |
| 71 | /* |
| 72 | * The remaining special case (b is NaN) is handled just fine by |
| 73 | * the normal code path below. |
| 74 | */ |
| 75 | |
| 76 | /* |
| 77 | * We compute t in double precision to avoid overflow and to |
| 78 | * provide correct rounding in nearly all cases. |
| 79 | * This is Algorithm 312, CACM vol 10, Oct 1967. |
| 80 | */ |
| 81 | if (a >= 0) { |
| 82 | t = sqrt((a + hypot(a, b)) * 0.5); |
| 83 | return (cpackf(t, b / (2.0 * t))); |
| 84 | } else { |
| 85 | t = sqrt((-a + hypot(a, b)) * 0.5); |
| 86 | return (cpackf(fabsf(b) / (2.0 * t), copysignf(t, b))); |
| 87 | } |
| 88 | } |