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 * gcc doesn't implement complex multiplication or division correctly, 40 * so we need to handle infinities specially. We turn on this pragma to 41 * notify conforming c99 compilers that the fast-but-incorrect code that 42 * gcc generates is acceptable, since the special cases have already been 43 * handled. 44 */ 45 #pragma STDC CX_LIMITED_RANGE ON 46 47 /* 48 * We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). 49 * Rather than determining the fully precise value at which we might 50 * overflow, just use a threshold of approximately LDBL_MAX / 4. 51 */ 52 #if LDBL_MAX_EXP != 0x4000 53 #error "Unsupported long double format" 54 #else 55 #define THRESH 0x1p16382L 56 #endif 57 58 long double complex 59 csqrtl(long double complex z) 60 { 61 long double complex result; 62 long double a, b; 63 long double t; 64 int scale; 65 66 a = creall(z); 67 b = cimagl(z); 68 69 /* Handle special cases. */ 70 if (z == 0) 71 return (CMPLXL(0, b)); 72 if (isinf(b)) 73 return (CMPLXL(INFINITY, b)); 74 if (isnan(a)) { 75 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 76 return (CMPLXL(a, t)); /* return NaN + NaN i */ 77 } 78 if (isinf(a)) { 79 /* 80 * csqrt(inf + NaN i) = inf + NaN i 81 * csqrt(inf + y i) = inf + 0 i 82 * csqrt(-inf + NaN i) = NaN +- inf i 83 * csqrt(-inf + y i) = 0 + inf i 84 */ 85 if (signbit(a)) 86 return (CMPLXL(fabsl(b - b), copysignl(a, b))); 87 else 88 return (CMPLXL(a, copysignl(b - b, b))); 89 } 90 /* 91 * The remaining special case (b is NaN) is handled just fine by 92 * the normal code path below. 93 */ 94 95 /* Scale to avoid overflow. */ 96 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { 97 a *= 0.25; 98 b *= 0.25; 99 scale = 1; 100 } else { 101 scale = 0; 102 } 103 104 /* Algorithm 312, CACM vol 10, Oct 1967. */ 105 if (a >= 0) { 106 t = sqrtl((a + hypotl(a, b)) * 0.5); 107 result = CMPLXL(t, b / (2 * t)); 108 } else { 109 t = sqrtl((-a + hypotl(a, b)) * 0.5); 110 result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b)); 111 } 112 113 /* Rescale. */ 114 if (scale) 115 return (result * 2); 116 else 117 return (result); 118 } 119