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 "cdefs-compat.h" 28 29 #include <float.h> 30 #include <openlibm_complex.h> 31 #include <openlibm_math.h> 32 33 #include "math_private.h" 34 35 /* 36 * gcc doesn't implement complex multiplication or division correctly, 37 * so we need to handle infinities specially. We turn on this pragma to 38 * notify conforming c99 compilers that the fast-but-incorrect code that 39 * gcc generates is acceptable, since the special cases have already been 40 * handled. 41 */ 42 #ifndef __GNUC__ 43 #pragma STDC CX_LIMITED_RANGE ON 44 #endif 45 46 /* We risk spurious overflow for components >= LDBL_MAX / (1 + sqrt(2)). */ 47 #define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) 48 49 OLM_DLLEXPORT long double complex 50 csqrtl(long double complex z) 51 { 52 long double complex result; 53 long double a, b; 54 long double t; 55 int scale; 56 57 a = creall(z); 58 b = cimagl(z); 59 60 /* Handle special cases. */ 61 if (z == 0) 62 return (CMPLXL(0, b)); 63 if (isinf(b)) 64 return (CMPLXL(INFINITY, b)); 65 if (isnan(a)) { 66 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 67 return (CMPLXL(a, t)); /* return NaN + NaN i */ 68 } 69 if (isinf(a)) { 70 /* 71 * csqrt(inf + NaN i) = inf + NaN i 72 * csqrt(inf + y i) = inf + 0 i 73 * csqrt(-inf + NaN i) = NaN +- inf i 74 * csqrt(-inf + y i) = 0 + inf i 75 */ 76 if (signbit(a)) 77 return (CMPLXL(fabsl(b - b), copysignl(a, b))); 78 else 79 return (CMPLXL(a, copysignl(b - b, b))); 80 } 81 /* 82 * The remaining special case (b is NaN) is handled just fine by 83 * the normal code path below. 84 */ 85 86 /* Scale to avoid overflow. */ 87 if (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { 88 a *= 0.25; 89 b *= 0.25; 90 scale = 1; 91 } else { 92 scale = 0; 93 } 94 95 /* Algorithm 312, CACM vol 10, Oct 1967. */ 96 if (a >= 0) { 97 t = sqrtl((a + hypotl(a, b)) * 0.5); 98 result = CMPLXL(t, b / (2 * t)); 99 } else { 100 t = sqrtl((-a + hypotl(a, b)) * 0.5); 101 result = CMPLXL(fabsl(b) / (2 * t), copysignl(t, b)); 102 } 103 104 /* Rescale. */ 105 if (scale) 106 return (result * 2); 107 else 108 return (result); 109 } 110