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 <complex.h> 30 #include <float.h> 31 #include <math.h> 32 33 #include "math_private.h" 34 35 /* 36 * Several thresholds require a 15-bit exponent and also the usual bias. 37 * s_logl.c and e_hypotl have less hard-coding but end up requiring the 38 * same for the exponent and more for the mantissa. 39 */ 40 #if LDBL_MAX_EXP != 0x4000 41 #error "Unsupported long double format" 42 #endif 43 44 /* 45 * Overflow must be avoided for components >= LDBL_MAX / (1 + sqrt(2)). 46 * The precise threshold is nontrivial to determine and spell, so use a 47 * lower threshold of approximaely LDBL_MAX / 4, and don't use LDBL_MAX 48 * to spell this since LDBL_MAX is broken on i386 (it overflows in 53-bit 49 * precision). 50 */ 51 #define THRESH 0x1p16382L 52 53 long double complex 54 csqrtl(long double complex z) 55 { 56 long double complex result; 57 long double a, b, rx, ry, scale, t; 58 59 a = creall(z); 60 b = cimagl(z); 61 62 /* Handle special cases. */ 63 if (z == 0) 64 return (CMPLXL(0, b)); 65 if (isinf(b)) 66 return (CMPLXL(INFINITY, b)); 67 if (isnan(a)) { 68 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 69 return (CMPLXL(a + 0.0L + t, a + 0.0L + t)); /* NaN + NaN i */ 70 } 71 if (isinf(a)) { 72 /* 73 * csqrt(inf + NaN i) = inf + NaN i 74 * csqrt(inf + y i) = inf + 0 i 75 * csqrt(-inf + NaN i) = NaN +- inf i 76 * csqrt(-inf + y i) = 0 + inf i 77 */ 78 if (signbit(a)) 79 return (CMPLXL(fabsl(b - b), copysignl(a, b))); 80 else 81 return (CMPLXL(a, copysignl(b - b, b))); 82 } 83 if (isnan(b)) { 84 t = (a - a) / (a - a); /* raise invalid */ 85 return (CMPLXL(b + 0.0L + t, b + 0.0L + t)); /* NaN + NaN i */ 86 } 87 88 /* Scale to avoid overflow. */ 89 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { 90 /* 91 * Don't scale a or b if this might give (spurious) 92 * underflow. Then the unscaled value is an equivalent 93 * infinitesmal (or 0). 94 */ 95 if (fabsl(a) >= 0x1p-16380L) 96 a *= 0.25; 97 if (fabsl(b) >= 0x1p-16380L) 98 b *= 0.25; 99 scale = 2; 100 } else { 101 scale = 1; 102 } 103 104 /* Scale to reduce inaccuracies when both components are denormal. */ 105 if (fabsl(a) < 0x1p-16382L && fabsl(b) < 0x1p-16382L) { 106 a *= 0x1p64; 107 b *= 0x1p64; 108 scale = 0x1p-32; 109 } 110 111 /* Algorithm 312, CACM vol 10, Oct 1967. */ 112 if (a >= 0) { 113 t = sqrtl((a + hypotl(a, b)) * 0.5); 114 rx = scale * t; 115 ry = scale * b / (2 * t); 116 } else { 117 t = sqrtl((-a + hypotl(a, b)) * 0.5); 118 rx = scale * fabsl(b) / (2 * t); 119 ry = copysignl(scale * t, b); 120 } 121 122 return (CMPLXL(rx, ry)); 123 } 124