1177761Sdas/*- 2177761Sdas * Copyright (c) 2007-2008 David Schultz <das@FreeBSD.ORG> 3177761Sdas * All rights reserved. 4177761Sdas * 5177761Sdas * Redistribution and use in source and binary forms, with or without 6177761Sdas * modification, are permitted provided that the following conditions 7177761Sdas * are met: 8177761Sdas * 1. Redistributions of source code must retain the above copyright 9177761Sdas * notice, this list of conditions and the following disclaimer. 10177761Sdas * 2. Redistributions in binary form must reproduce the above copyright 11177761Sdas * notice, this list of conditions and the following disclaimer in the 12177761Sdas * documentation and/or other materials provided with the distribution. 13177761Sdas * 14177761Sdas * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND 15177761Sdas * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE 16177761Sdas * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE 17177761Sdas * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE 18177761Sdas * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL 19177761Sdas * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS 20177761Sdas * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) 21177761Sdas * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT 22177761Sdas * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY 23177761Sdas * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF 24177761Sdas * SUCH DAMAGE. 25177761Sdas */ 26177761Sdas 27177761Sdas#include <sys/cdefs.h> 28177761Sdas__FBSDID("$FreeBSD: releng/10.2/lib/msun/src/s_csqrtl.c 284810 2015-06-25 13:01:10Z tijl $"); 29177761Sdas 30177761Sdas#include <complex.h> 31177761Sdas#include <float.h> 32177761Sdas#include <math.h> 33177761Sdas 34177761Sdas#include "math_private.h" 35177761Sdas 36177761Sdas/* 37177761Sdas * gcc doesn't implement complex multiplication or division correctly, 38177761Sdas * so we need to handle infinities specially. We turn on this pragma to 39177761Sdas * notify conforming c99 compilers that the fast-but-incorrect code that 40177761Sdas * gcc generates is acceptable, since the special cases have already been 41177761Sdas * handled. 42177761Sdas */ 43181402Sdas#pragma STDC CX_LIMITED_RANGE ON 44177761Sdas 45177761Sdas/* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ 46177761Sdas#define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) 47177761Sdas 48177761Sdaslong double complex 49177761Sdascsqrtl(long double complex z) 50177761Sdas{ 51177761Sdas long double complex result; 52177761Sdas long double a, b; 53177761Sdas long double t; 54177761Sdas int scale; 55177761Sdas 56177761Sdas a = creall(z); 57177761Sdas b = cimagl(z); 58177761Sdas 59177761Sdas /* Handle special cases. */ 60177761Sdas if (z == 0) 61284810Stijl return (CMPLXL(0, b)); 62177761Sdas if (isinf(b)) 63284810Stijl return (CMPLXL(INFINITY, b)); 64177761Sdas if (isnan(a)) { 65177761Sdas t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 66284810Stijl return (CMPLXL(a, t)); /* return NaN + NaN i */ 67177761Sdas } 68177761Sdas if (isinf(a)) { 69177761Sdas /* 70177761Sdas * csqrt(inf + NaN i) = inf + NaN i 71177761Sdas * csqrt(inf + y i) = inf + 0 i 72177761Sdas * csqrt(-inf + NaN i) = NaN +- inf i 73177761Sdas * csqrt(-inf + y i) = 0 + inf i 74177761Sdas */ 75177761Sdas if (signbit(a)) 76284810Stijl return (CMPLXL(fabsl(b - b), copysignl(a, b))); 77177761Sdas else 78284810Stijl return (CMPLXL(a, copysignl(b - b, b))); 79177761Sdas } 80177761Sdas /* 81177761Sdas * The remaining special case (b is NaN) is handled just fine by 82177761Sdas * the normal code path below. 83177761Sdas */ 84177761Sdas 85177761Sdas /* Scale to avoid overflow. */ 86177761Sdas if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { 87177761Sdas a *= 0.25; 88177761Sdas b *= 0.25; 89177761Sdas scale = 1; 90177761Sdas } else { 91177761Sdas scale = 0; 92177761Sdas } 93177761Sdas 94177761Sdas /* Algorithm 312, CACM vol 10, Oct 1967. */ 95177761Sdas if (a >= 0) { 96177761Sdas t = sqrtl((a + hypotl(a, b)) * 0.5); 97284810Stijl result = CMPLXL(t, b / (2 * t)); 98177761Sdas } else { 99177761Sdas t = sqrtl((-a + hypotl(a, b)) * 0.5); 100284810Stijl result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b)); 101177761Sdas } 102177761Sdas 103177761Sdas /* Rescale. */ 104177761Sdas if (scale) 105177761Sdas return (result * 2); 106177761Sdas else 107177761Sdas return (result); 108177761Sdas} 109