1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 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 #include <complex.h> 31 #include <float.h> 32 #include <math.h> 33 34 #include "math_private.h" 35 36 /* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */ 37 #define THRESH 0x1.a827999fcef32p+1022 38 39 double complex 40 csqrt(double complex z) 41 { 42 double complex result; 43 double a, b, rx, ry, scale, t; 44 45 a = creal(z); 46 b = cimag(z); 47 48 /* Handle special cases. */ 49 if (z == 0) 50 return (CMPLX(0, b)); 51 if (isinf(b)) 52 return (CMPLX(INFINITY, b)); 53 if (isnan(a)) { 54 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 55 return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ 56 } 57 if (isinf(a)) { 58 /* 59 * csqrt(inf + NaN i) = inf + NaN i 60 * csqrt(inf + y i) = inf + 0 i 61 * csqrt(-inf + NaN i) = NaN +- inf i 62 * csqrt(-inf + y i) = 0 + inf i 63 */ 64 if (signbit(a)) 65 return (CMPLX(fabs(b - b), copysign(a, b))); 66 else 67 return (CMPLX(a, copysign(b - b, b))); 68 } 69 if (isnan(b)) { 70 t = (a - a) / (a - a); /* raise invalid */ 71 return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ 72 } 73 74 /* Scale to avoid overflow. */ 75 if (fabs(a) >= THRESH || fabs(b) >= THRESH) { 76 /* 77 * Don't scale a or b if this might give (spurious) 78 * underflow. Then the unscaled value is an equivalent 79 * infinitesmal (or 0). 80 */ 81 if (fabs(a) >= 0x1p-1020) 82 a *= 0.25; 83 if (fabs(b) >= 0x1p-1020) 84 b *= 0.25; 85 scale = 2; 86 } else { 87 scale = 1; 88 } 89 90 /* Scale to reduce inaccuracies when both components are denormal. */ 91 if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) { 92 a *= 0x1p54; 93 b *= 0x1p54; 94 scale = 0x1p-27; 95 } 96 97 /* Algorithm 312, CACM vol 10, Oct 1967. */ 98 if (a >= 0) { 99 t = sqrt((a + hypot(a, b)) * 0.5); 100 rx = scale * t; 101 ry = scale * b / (2 * t); 102 } else { 103 t = sqrt((-a + hypot(a, b)) * 0.5); 104 rx = scale * fabs(b) / (2 * t); 105 ry = copysign(scale * t, b); 106 } 107 108 return (CMPLX(rx, ry)); 109 } 110 111 #if LDBL_MANT_DIG == 53 112 __weak_reference(csqrt, csqrtl); 113 #endif 114