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 <float.h> 34 #include <math.h> 35 36 #include "math_private.h" 37 38 /* For avoiding overflow for components >= DBL_MAX / (1 + sqrt(2)). */ 39 #define THRESH 0x1.a827999fcef32p+1022 40 41 double complex 42 csqrt(double complex z) 43 { 44 double complex result; 45 double a, b, rx, ry, scale, t; 46 47 a = creal(z); 48 b = cimag(z); 49 50 /* Handle special cases. */ 51 if (z == 0) 52 return (CMPLX(0, b)); 53 if (isinf(b)) 54 return (CMPLX(INFINITY, b)); 55 if (isnan(a)) { 56 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 57 return (CMPLX(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ 58 } 59 if (isinf(a)) { 60 /* 61 * csqrt(inf + NaN i) = inf + NaN i 62 * csqrt(inf + y i) = inf + 0 i 63 * csqrt(-inf + NaN i) = NaN +- inf i 64 * csqrt(-inf + y i) = 0 + inf i 65 */ 66 if (signbit(a)) 67 return (CMPLX(fabs(b - b), copysign(a, b))); 68 else 69 return (CMPLX(a, copysign(b - b, b))); 70 } 71 if (isnan(b)) { 72 t = (a - a) / (a - a); /* raise invalid */ 73 return (CMPLX(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ 74 } 75 76 /* Scale to avoid overflow. */ 77 if (fabs(a) >= THRESH || fabs(b) >= THRESH) { 78 /* 79 * Don't scale a or b if this might give (spurious) 80 * underflow. Then the unscaled value is an equivalent 81 * infinitesmal (or 0). 82 */ 83 if (fabs(a) >= 0x1p-1020) 84 a *= 0.25; 85 if (fabs(b) >= 0x1p-1020) 86 b *= 0.25; 87 scale = 2; 88 } else { 89 scale = 1; 90 } 91 92 /* Scale to reduce inaccuracies when both components are denormal. */ 93 if (fabs(a) < 0x1p-1022 && fabs(b) < 0x1p-1022) { 94 a *= 0x1p54; 95 b *= 0x1p54; 96 scale = 0x1p-27; 97 } 98 99 /* Algorithm 312, CACM vol 10, Oct 1967. */ 100 if (a >= 0) { 101 t = sqrt((a + hypot(a, b)) * 0.5); 102 rx = scale * t; 103 ry = scale * b / (2 * t); 104 } else { 105 t = sqrt((-a + hypot(a, b)) * 0.5); 106 rx = scale * fabs(b) / (2 * t); 107 ry = copysign(scale * t, b); 108 } 109 110 return (CMPLX(rx, ry)); 111 } 112 113 #if LDBL_MANT_DIG == 53 114 __weak_reference(csqrt, csqrtl); 115 #endif 116