1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 3 * 4 * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG> 5 * All rights reserved. 6 * 7 * Redistribution and use in source and binary forms, with or without 8 * modification, are permitted provided that the following conditions 9 * are met: 10 * 1. Redistributions of source code must retain the above copyright 11 * notice, this list of conditions and the following disclaimer. 12 * 2. Redistributions in binary form must reproduce the above copyright 13 * notice, this list of conditions and the following disclaimer in the 14 * documentation and/or other materials provided with the distribution. 15 * 16 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 17 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 18 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 19 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 20 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 21 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 22 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 23 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 24 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 25 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 26 * SUCH DAMAGE. 27 */ 28 29 #include <sys/cdefs.h> 30 __FBSDID("$FreeBSD$"); 31 32 #include <complex.h> 33 #include <math.h> 34 35 #include "math_private.h" 36 37 /* 38 * gcc doesn't implement complex multiplication or division correctly, 39 * so we need to handle infinities specially. We turn on this pragma to 40 * notify conforming c99 compilers that the fast-but-incorrect code that 41 * gcc generates is acceptable, since the special cases have already been 42 * handled. 43 */ 44 #pragma STDC CX_LIMITED_RANGE ON 45 46 float complex 47 csqrtf(float complex z) 48 { 49 float a = crealf(z), b = cimagf(z); 50 double t; 51 52 /* Handle special cases. */ 53 if (z == 0) 54 return (CMPLXF(0, b)); 55 if (isinf(b)) 56 return (CMPLXF(INFINITY, b)); 57 if (isnan(a)) { 58 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 59 return (CMPLXF(a, t)); /* return NaN + NaN i */ 60 } 61 if (isinf(a)) { 62 /* 63 * csqrtf(inf + NaN i) = inf + NaN i 64 * csqrtf(inf + y i) = inf + 0 i 65 * csqrtf(-inf + NaN i) = NaN +- inf i 66 * csqrtf(-inf + y i) = 0 + inf i 67 */ 68 if (signbit(a)) 69 return (CMPLXF(fabsf(b - b), copysignf(a, b))); 70 else 71 return (CMPLXF(a, copysignf(b - b, b))); 72 } 73 /* 74 * The remaining special case (b is NaN) is handled just fine by 75 * the normal code path below. 76 */ 77 78 /* 79 * We compute t in double precision to avoid overflow and to 80 * provide correct rounding in nearly all cases. 81 * This is Algorithm 312, CACM vol 10, Oct 1967. 82 */ 83 if (a >= 0) { 84 t = sqrt((a + hypot(a, b)) * 0.5); 85 return (CMPLXF(t, b / (2.0 * t))); 86 } else { 87 t = sqrt((-a + hypot(a, b)) * 0.5); 88 return (CMPLXF(fabsf(b) / (2.0 * t), copysignf(t, b))); 89 } 90 } 91