1 /*- 2 * Copyright (c) 2007 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 //__FBSDID("$FreeBSD: src/lib/msun/src/s_csqrt.c,v 1.4 2008/08/08 00:15:16 das Exp $"); 29 30 #include <complex.h> 31 #include <float.h> 32 #include <openlibm.h> 33 34 #include "math_private.h" 35 36 /* 37 * gcc doesn't implement complex multiplication or division correctly, 38 * so we need to handle infinities specially. We turn on this pragma to 39 * notify conforming c99 compilers that the fast-but-incorrect code that 40 * gcc generates is acceptable, since the special cases have already been 41 * handled. 42 */ 43 #ifndef __GNUC__ 44 #pragma STDC CX_LIMITED_RANGE ON 45 #endif 46 47 /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */ 48 #define THRESH 0x1.a827999fcef32p+1022 49 50 DLLEXPORT double complex 51 csqrt(double complex z) 52 { 53 double complex result; 54 double a, b; 55 double t; 56 int scale; 57 58 a = creal(z); 59 b = cimag(z); 60 61 /* Handle special cases. */ 62 if (z == 0) 63 return (cpack(0, b)); 64 if (isinf(b)) 65 return (cpack(INFINITY, b)); 66 if (isnan(a)) { 67 t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ 68 return (cpack(a, t)); /* return NaN + NaN i */ 69 } 70 if (isinf(a)) { 71 /* 72 * csqrt(inf + NaN i) = inf + NaN i 73 * csqrt(inf + y i) = inf + 0 i 74 * csqrt(-inf + NaN i) = NaN +- inf i 75 * csqrt(-inf + y i) = 0 + inf i 76 */ 77 if (signbit(a)) 78 return (cpack(fabs(b - b), copysign(a, b))); 79 else 80 return (cpack(a, copysign(b - b, b))); 81 } 82 /* 83 * The remaining special case (b is NaN) is handled just fine by 84 * the normal code path below. 85 */ 86 87 /* Scale to avoid overflow. */ 88 if (fabs(a) >= THRESH || fabs(b) >= THRESH) { 89 a *= 0.25; 90 b *= 0.25; 91 scale = 1; 92 } else { 93 scale = 0; 94 } 95 96 /* Algorithm 312, CACM vol 10, Oct 1967. */ 97 if (a >= 0) { 98 t = sqrt((a + hypot(a, b)) * 0.5); 99 result = cpack(t, b / (2 * t)); 100 } else { 101 t = sqrt((-a + hypot(a, b)) * 0.5); 102 result = cpack(fabs(b) / (2 * t), copysign(t, b)); 103 } 104 105 /* Rescale. */ 106 if (scale) 107 return (result * 2); 108 else 109 return (result); 110 } 111 112 #if LDBL_MANT_DIG == 53 113 __weak_reference(csqrt, csqrtl); 114 #endif 115