| /*- |
| * Copyright (c) 2007 David Schultz <das@FreeBSD.ORG> |
| * All rights reserved. |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * 1. Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * 2. Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in the |
| * documentation and/or other materials provided with the distribution. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE AUTHOR AND CONTRIBUTORS ``AS IS'' AND |
| * ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE |
| * IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE |
| * ARE DISCLAIMED. IN NO EVENT SHALL THE AUTHOR OR CONTRIBUTORS BE LIABLE |
| * FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL |
| * DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS |
| * OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) |
| * HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY |
| * OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF |
| * SUCH DAMAGE. |
| */ |
| |
| #include <sys/cdefs.h> |
| __FBSDID("$FreeBSD$"); |
| |
| #include <complex.h> |
| #include <float.h> |
| #include <math.h> |
| |
| #include "math_private.h" |
| |
| /* |
| * gcc doesn't implement complex multiplication or division correctly, |
| * so we need to handle infinities specially. We turn on this pragma to |
| * notify conforming c99 compilers that the fast-but-incorrect code that |
| * gcc generates is acceptable, since the special cases have already been |
| * handled. |
| */ |
| #pragma STDC CX_LIMITED_RANGE ON |
| |
| /* We risk spurious overflow for components >= DBL_MAX / (1 + sqrt(2)). */ |
| #define THRESH 0x1.a827999fcef32p+1022 |
| |
| double complex |
| csqrt(double complex z) |
| { |
| double complex result; |
| double a, b; |
| double t; |
| int scale; |
| |
| a = creal(z); |
| b = cimag(z); |
| |
| /* Handle special cases. */ |
| if (z == 0) |
| return (cpack(0, b)); |
| if (isinf(b)) |
| return (cpack(INFINITY, b)); |
| if (isnan(a)) { |
| t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ |
| return (cpack(a, t)); /* return NaN + NaN i */ |
| } |
| if (isinf(a)) { |
| /* |
| * csqrt(inf + NaN i) = inf + NaN i |
| * csqrt(inf + y i) = inf + 0 i |
| * csqrt(-inf + NaN i) = NaN +- inf i |
| * csqrt(-inf + y i) = 0 + inf i |
| */ |
| if (signbit(a)) |
| return (cpack(fabs(b - b), copysign(a, b))); |
| else |
| return (cpack(a, copysign(b - b, b))); |
| } |
| /* |
| * The remaining special case (b is NaN) is handled just fine by |
| * the normal code path below. |
| */ |
| |
| /* Scale to avoid overflow. */ |
| if (fabs(a) >= THRESH || fabs(b) >= THRESH) { |
| a *= 0.25; |
| b *= 0.25; |
| scale = 1; |
| } else { |
| scale = 0; |
| } |
| |
| /* Algorithm 312, CACM vol 10, Oct 1967. */ |
| if (a >= 0) { |
| t = sqrt((a + hypot(a, b)) * 0.5); |
| result = cpack(t, b / (2 * t)); |
| } else { |
| t = sqrt((-a + hypot(a, b)) * 0.5); |
| result = cpack(fabs(b) / (2 * t), copysign(t, b)); |
| } |
| |
| /* Rescale. */ |
| if (scale) |
| return (result * 2); |
| else |
| return (result); |
| } |
| |
| #if LDBL_MANT_DIG == 53 |
| __weak_reference(csqrt, csqrtl); |
| #endif |
