diff --git a/libc/tinymath/csqrt.c b/libc/tinymath/csqrt.c new file mode 100644 index 000000000..61c042fb9 --- /dev/null +++ b/libc/tinymath/csqrt.c @@ -0,0 +1,127 @@ +/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│ +│vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi│ +╚──────────────────────────────────────────────────────────────────────────────╝ +│ │ +│ Musl Libc │ +│ Copyright © 2005-2014 Rich Felker, et al. │ +│ │ +│ Permission is hereby granted, free of charge, to any person obtaining │ +│ a copy of this software and associated documentation files (the │ +│ "Software"), to deal in the Software without restriction, including │ +│ without limitation the rights to use, copy, modify, merge, publish, │ +│ distribute, sublicense, and/or sell copies of the Software, and to │ +│ permit persons to whom the Software is furnished to do so, subject to │ +│ the following conditions: │ +│ │ +│ The above copyright notice and this permission notice shall be │ +│ included in all copies or substantial portions of the Software. │ +│ │ +│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │ +│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │ +│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │ +│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │ +│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │ +│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │ +│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │ +│ │ +╚─────────────────────────────────────────────────────────────────────────────*/ +/* origin: FreeBSD /usr/src/lib/msun/src/s_csqrt.c */ +/*- + * Copyright (c) 2007 David Schultz + * 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 "complex_impl.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 CMPLX(0, b); + if (isinf(b)) + return CMPLX(INFINITY, b); + if (isnan(a)) { + t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ + return CMPLX(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 CMPLX(fabs(b - b), copysign(a, b)); + else + return CMPLX(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 = CMPLX(t, b / (2 * t)); + } else { + t = sqrt((-a + hypot(a, b)) * 0.5); + result = CMPLX(fabs(b) / (2 * t), copysign(t, b)); + } + + /* Rescale. */ + if (scale) + result *= 2; + return result; +}