1 /*- 2 * SPDX-License-Identifier: BSD-2-Clause 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 * Several thresholds require a 15-bit exponent and also the usual bias. 40 * s_logl.c and e_hypotl have less hard-coding but end up requiring the 41 * same for the exponent and more for the mantissa. 42 */ 43 #if LDBL_MAX_EXP != 0x4000 44 #error "Unsupported long double format" 45 #endif 46 47 /* 48 * Overflow must be avoided for components >= LDBL_MAX / (1 + sqrt(2)). 49 * The precise threshold is nontrivial to determine and spell, so use a 50 * lower threshold of approximaely LDBL_MAX / 4, and don't use LDBL_MAX 51 * to spell this since LDBL_MAX is broken on i386 (it overflows in 53-bit 52 * precision). 53 */ 54 #define THRESH 0x1p16382L 55 56 long double complex 57 csqrtl(long double complex z) 58 { 59 long double complex result; 60 long double a, b, rx, ry, scale, t; 61 62 a = creall(z); 63 b = cimagl(z); 64 65 /* Handle special cases. */ 66 if (z == 0) 67 return (CMPLXL(0, b)); 68 if (isinf(b)) 69 return (CMPLXL(INFINITY, b)); 70 if (isnan(a)) { 71 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 72 return (CMPLXL(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ 73 } 74 if (isinf(a)) { 75 /* 76 * csqrt(inf + NaN i) = inf + NaN i 77 * csqrt(inf + y i) = inf + 0 i 78 * csqrt(-inf + NaN i) = NaN +- inf i 79 * csqrt(-inf + y i) = 0 + inf i 80 */ 81 if (signbit(a)) 82 return (CMPLXL(fabsl(b - b), copysignl(a, b))); 83 else 84 return (CMPLXL(a, copysignl(b - b, b))); 85 } 86 if (isnan(b)) { 87 t = (a - a) / (a - a); /* raise invalid */ 88 return (CMPLXL(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ 89 } 90 91 /* Scale to avoid overflow. */ 92 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { 93 /* 94 * Don't scale a or b if this might give (spurious) 95 * underflow. Then the unscaled value is an equivalent 96 * infinitesmal (or 0). 97 */ 98 if (fabsl(a) >= 0x1p-16380L) 99 a *= 0.25; 100 if (fabsl(b) >= 0x1p-16380L) 101 b *= 0.25; 102 scale = 2; 103 } else { 104 scale = 1; 105 } 106 107 /* Scale to reduce inaccuracies when both components are denormal. */ 108 if (fabsl(a) < 0x1p-16382L && fabsl(b) < 0x1p-16382L) { 109 a *= 0x1p64; 110 b *= 0x1p64; 111 scale = 0x1p-32; 112 } 113 114 /* Algorithm 312, CACM vol 10, Oct 1967. */ 115 if (a >= 0) { 116 t = sqrtl((a + hypotl(a, b)) * 0.5); 117 rx = scale * t; 118 ry = scale * b / (2 * t); 119 } else { 120 t = sqrtl((-a + hypotl(a, b)) * 0.5); 121 rx = scale * fabsl(b) / (2 * t); 122 ry = copysignl(scale * t, b); 123 } 124 125 return (CMPLXL(rx, ry)); 126 } 127