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Diffstat (limited to 'src/complex/csqrt.c')
-rw-r--r-- | src/complex/csqrt.c | 100 |
1 files changed, 100 insertions, 0 deletions
diff --git a/src/complex/csqrt.c b/src/complex/csqrt.c new file mode 100644 index 00000000..21fb879d --- /dev/null +++ b/src/complex/csqrt.c @@ -0,0 +1,100 @@ +/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */ +/*- + * 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 "libm.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) + result *= 2; + return result; +} |