1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause-FreeBSD 3 * 4 * Copyright (c) 2007-2008 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 /* 39 * THRESH is now calculated portably (up to 113-bit precision). However, 40 * the denormal threshold is hard-coded for a 15-bit exponent with the usual 41 * bias. s_logl.c and e_hypotl have less hard-coding but end up requiring 42 * the same for the exponent and more for the mantissa. 43 */ 44 #if LDBL_MAX_EXP != 0x4000 45 #error "Unsupported long double format" 46 #endif 47 48 /* For avoiding overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ 49 #define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) 50 51 long double complex 52 csqrtl(long double complex z) 53 { 54 long double complex result; 55 long double a, b, rx, ry, scale, t; 56 57 a = creall(z); 58 b = cimagl(z); 59 60 /* Handle special cases. */ 61 if (z == 0) 62 return (CMPLXL(0, b)); 63 if (isinf(b)) 64 return (CMPLXL(INFINITY, b)); 65 if (isnan(a)) { 66 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 67 return (CMPLXL(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ 68 } 69 if (isinf(a)) { 70 /* 71 * csqrt(inf + NaN i) = inf + NaN i 72 * csqrt(inf + y i) = inf + 0 i 73 * csqrt(-inf + NaN i) = NaN +- inf i 74 * csqrt(-inf + y i) = 0 + inf i 75 */ 76 if (signbit(a)) 77 return (CMPLXL(fabsl(b - b), copysignl(a, b))); 78 else 79 return (CMPLXL(a, copysignl(b - b, b))); 80 } 81 if (isnan(b)) { 82 t = (a - a) / (a - a); /* raise invalid */ 83 return (CMPLXL(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ 84 } 85 86 /* Scale to avoid overflow. */ 87 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { 88 /* 89 * Don't scale a or b if this might give (spurious) 90 * underflow. Then the unscaled value is an equivalent 91 * infinitesmal (or 0). 92 */ 93 if (fabsl(a) >= 0x1p-16380L) 94 a *= 0.25; 95 if (fabsl(b) >= 0x1p-16380L) 96 b *= 0.25; 97 scale = 2; 98 } else { 99 scale = 1; 100 } 101 102 /* Scale to reduce inaccuracies when both components are denormal. */ 103 if (fabsl(a) < 0x1p-16382L && fabsl(b) < 0x1p-16382L) { 104 a *= 0x1p64; 105 b *= 0x1p64; 106 scale = 0x1p-32; 107 } 108 109 /* Algorithm 312, CACM vol 10, Oct 1967. */ 110 if (a >= 0) { 111 t = sqrtl((a + hypotl(a, b)) * 0.5); 112 rx = t; 113 ry = b / (2 * t); 114 } else { 115 t = sqrtl((-a + hypotl(a, b)) * 0.5); 116 rx = fabsl(b) / (2 * t); 117 ry = copysignl(t, b); 118 } 119 120 return (CMPLXL(rx * scale, ry * scale)); 121 } 122