1 /*- 2 * Copyright (c) 2007 David Schultz <das (at) 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 } 89
