1/*- 2 * Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG> 3 * All rights reserved. 4 * 5 * Redistribution and use in source and binary forms, with or without 6 * modification, are permitted provided that the following conditions 7 * are met: 8 * 1. Redistributions of source code must retain the above copyright 9 * notice, this list of conditions and the following disclaimer. 10 * 2. Redistributions in binary form must reproduce the above copyright 11 * notice, this list of conditions and the following disclaimer in the 12 * documentation and/or other materials provided with the distribution. 13 * 14 * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15 * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16 * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17 * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18 * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19 * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20 * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21 * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23 * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24 * SUCH DAMAGE. 25 */ 26 27#include <sys/cdefs.h> 28#if 0 29__FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $"); 30#else 31__RCSID("$NetBSD: csqrtl.c,v 1.1 2014/10/10 00:48:18 christos Exp $"); 32#endif 33 34#include "../src/namespace.h" 35#include <complex.h> 36#include <float.h> 37#include <math.h> 38#include <stdbool.h> 39 40/* 41 * gcc doesn't implement complex multiplication or division correctly, 42 * so we need to handle infinities specially. We turn on this pragma to 43 * notify conforming c99 compilers that the fast-but-incorrect code that 44 * gcc generates is acceptable, since the special cases have already been 45 * handled. 46 */ 47// #pragma STDC CX_LIMITED_RANGE ON 48 49/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ 50#define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) 51 52#define cpackl(r, i) ((r) + (i) * I) 53 54long double complex 55csqrtl(long double complex z) 56{ 57 long double complex result; 58 long double a, b; 59 long double t; 60 bool scale; 61 62 a = creall(z); 63 b = cimagl(z); 64 65 /* Handle special cases. */ 66 if (z == 0.0L) 67 return (cpackl(0.0L, b)); 68 if (isinf(b)) 69 return (cpackl(INFINITY, b)); 70 if (isnan(a)) { 71 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 72 return (cpackl(a, t)); /* return 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 (cpackl(fabsl(b - b), copysignl(a, b))); 83 else 84 return (cpackl(a, copysignl(b - b, b))); 85 } 86 /* 87 * The remaining special case (b is NaN) is handled just fine by 88 * the normal code path below. 89 */ 90 91 /* Scale to avoid overflow. */ 92 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { 93 a *= 0.25L; 94 b *= 0.25L; 95 scale = true; 96 } else { 97 scale = false; 98 } 99 100 /* Algorithm 312, CACM vol 10, Oct 1967. */ 101 if (a >= 0L) { 102 t = sqrtl((a + hypotl(a, b)) * 0.5L); 103 result = cpackl(t, b / (2.0L * t)); 104 } else { 105 t = sqrtl((-a + hypotl(a, b)) * 0.5L); 106 result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b)); 107 } 108 109 /* Rescale. */ 110 if (scale) 111 return (result * 2.0L); 112 else 113 return (result); 114} 115