From aedc7118fc0b7103982f544ad737e12d66f4f8bd Mon Sep 17 00:00:00 2001 From: Aditya Upadhyay Date: Mon, 26 Jun 2017 14:38:38 +0530 Subject: [PATCH] Importing some long double complex methods from NetBSD. --- newlib/libm/complex/Makefile.am | 4 +- newlib/libm/complex/cacoshl.c | 45 +++++++++++++ newlib/libm/complex/cacosl.c | 45 +++++++++++++ newlib/libm/complex/cargl.c | 18 ++++++ newlib/libm/complex/ccosl.c | 45 +++++++++++++ newlib/libm/complex/cephes_subrl.c | 128 +++++++++++++++++++++++++++++++++++++ newlib/libm/complex/cephes_subrl.h | 9 +++ newlib/libm/complex/cexpl.c | 46 +++++++++++++ newlib/libm/complex/clogl.c | 46 +++++++++++++ newlib/libm/complex/cprojl.c | 64 +++++++++++++++++++ newlib/libm/complex/csqrtl.c | 112 ++++++++++++++++++++++++++++++++ 11 files changed, 560 insertions(+), 2 deletions(-) create mode 100644 newlib/libm/complex/cacoshl.c create mode 100644 newlib/libm/complex/cacosl.c create mode 100644 newlib/libm/complex/cargl.c create mode 100644 newlib/libm/complex/ccosl.c create mode 100644 newlib/libm/complex/cephes_subrl.c create mode 100644 newlib/libm/complex/cephes_subrl.h create mode 100644 newlib/libm/complex/cexpl.c create mode 100644 newlib/libm/complex/clogl.c create mode 100644 newlib/libm/complex/cprojl.c create mode 100644 newlib/libm/complex/csqrtl.c diff --git a/newlib/libm/complex/Makefile.am b/newlib/libm/complex/Makefile.am index 402053f..bb3ffef 100644 --- a/newlib/libm/complex/Makefile.am +++ b/newlib/libm/complex/Makefile.am @@ -10,7 +10,7 @@ src = cabs.c cacos.c cacosh.c carg.c casin.c casinh.c \ cpow.c cproj.c creal.c \ csin.c csinh.c csqrt.c ctan.c ctanh.c -lsrc = cabsl.c creall.c cimagl.c ccoshl.c +lsrc = cabsl.c creall.c cimagl.c ccoshl.c cacoshl.c csqrtl.c clogl.c cephes_subrl.c cargl.c cprojl.c cexpl.c cacosl.c ccosl.c fsrc = cabsf.c casinf.c ccosf.c cimagf.c cprojf.c \ csqrtf.c cacosf.c casinhf.c ccoshf.c clogf.c clog10f.c \ @@ -43,4 +43,4 @@ CHAPTERS = complex.tex # A partial dependency list. -$(lib_a_OBJECTS): $(srcdir)/../../libc/include/complex.h $(srcdir)/cephes_subr.h $(srcdir)/cephes_subrf.h +$(lib_a_OBJECTS): $(srcdir)/../../libc/include/complex.h $(srcdir)/cephes_subr.h $(srcdir)/cephes_subrf.h $(srcdir)/cephes_subrl.h diff --git a/newlib/libm/complex/cacoshl.c b/newlib/libm/complex/cacoshl.c new file mode 100644 index 0000000..4e4e006 --- /dev/null +++ b/newlib/libm/complex/cacoshl.c @@ -0,0 +1,45 @@ +/* $NetBSD: cacoshl.c,v 1.1 2014/10/10 00:48:18 christos Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * 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 NETBSD FOUNDATION, INC. 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 FOUNDATION 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 + +long double complex +cacoshl(long double complex z) +{ + long double complex w; + +#if 0 /* does not give the principal value */ + w = I * cacosl(z); +#else + w = clogl(z + csqrtl(z + 1) * csqrtl(z - 1)); +#endif + return w; +} diff --git a/newlib/libm/complex/cacosl.c b/newlib/libm/complex/cacosl.c new file mode 100644 index 0000000..6a05c8c --- /dev/null +++ b/newlib/libm/complex/cacosl.c @@ -0,0 +1,45 @@ +/* $NetBSD: cacosl.c,v 1.1 2014/10/10 00:48:18 christos Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * 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 NETBSD FOUNDATION, INC. 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 FOUNDATION 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 +#include +#include "cephes_subrl.h" + +long double complex +cacosl(long double complex z) +{ + long double complex w; + + w = casinl(z); + w = (M_PI_2L - creall(w)) - cimagl(w) * I; + return w; +} + diff --git a/newlib/libm/complex/cargl.c b/newlib/libm/complex/cargl.c new file mode 100644 index 0000000..d2885a4 --- /dev/null +++ b/newlib/libm/complex/cargl.c @@ -0,0 +1,18 @@ +/* $NetBSD: cargl.c,v 1.1 2014/10/10 00:48:18 christos Exp $ */ + +/* + * Public domain. + */ + +#include +#include + +long double +cargl(long double complex z) +{ + #ifdef _LDBL_EQ_DBL + return carg (z); + #else + return atan2l (imag (z), real (z)); + #endif +} diff --git a/newlib/libm/complex/ccosl.c b/newlib/libm/complex/ccosl.c new file mode 100644 index 0000000..c310f40 --- /dev/null +++ b/newlib/libm/complex/ccosl.c @@ -0,0 +1,45 @@ +/* $NetBSD: ccosl.c,v 1.1 2014/10/10 00:48:18 christos Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * 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 NETBSD FOUNDATION, INC. 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 FOUNDATION 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 +#include +#include "cephes_subrl.h" + +long double complex +ccosl(long double complex z) +{ + long double complex w; + long double ch, sh; + + _cchshl(cimagl(z), &ch, &sh); + w = cosl(creall(z)) * ch - (sinl(creall(z)) * sh) * I; + return w; +} diff --git a/newlib/libm/complex/cephes_subrl.c b/newlib/libm/complex/cephes_subrl.c new file mode 100644 index 0000000..8af11df --- /dev/null +++ b/newlib/libm/complex/cephes_subrl.c @@ -0,0 +1,128 @@ +/* $NetBSD: cephes_subrl.c,v 1.2 2014/10/10 14:06:40 christos Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * 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 NETBSD FOUNDATION, INC. 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 FOUNDATION 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 +#include +#include "cephes_subrl.h" + +/* calculate cosh and sinh */ + +void +_cchshl(long double x, long double *c, long double *s) +{ + long double e, ei; + + if (fabsl(x) <= 0.5L) { + *c = coshl(x); + *s = sinhl(x); + } else { + e = expl(x); + ei = 0.5L / e; + e = 0.5L * e; + *s = e - ei; + *c = e + ei; + } +} + +/* Program to subtract nearest integer multiple of PI */ + +/* extended precision value of PI: */ +static const long double DP1 = 3.14159265358979323829596852490908531763125L; +static const long double DP2 = 1.6667485837041756656403424829301998703007e-19L; +#ifndef __vax__ +static const long double DP3 = 1.8830410776607851167459095484560349402753e-39L; +#define MACHEPL 1.1e-38L +#else +static const long double DP3 = 0L; +#define MACHEPL 1.1e-19L +#endif + +long double +_redupil(long double x) +{ + long double t; + long long i; + + t = x / M_PIL; + if (t >= 0.0L) + t += 0.5L; + else + t -= 0.5L; + + i = t; /* the multiple */ + t = i; + t = ((x - t * DP1) - t * DP2) - t * DP3; + return t; +} + +/* Taylor series expansion for cosh(2y) - cos(2x) */ + +long double +_ctansl(long double complex z) +{ + long double f, x, x2, y, y2, rn, t; + long double d; + + x = fabsl(2.0L * creall(z)); + y = fabsl(2.0L * cimagl(z)); + + x = _redupil(x); + + x = x * x; + y = y * y; + x2 = 1.0; + y2 = 1.0; + f = 1.0; + rn = 0.0; + d = 0.0; + do { + rn += 1.0L; + f *= rn; + rn += 1.0L; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 + x2; + t /= f; + d += t; + + rn += 1.0L; + f *= rn; + rn += 1.0L; + f *= rn; + x2 *= x; + y2 *= y; + t = y2 - x2; + t /= f; + d += t; + } while (fabsl(t/d) > MACHEPL); + return d; +} diff --git a/newlib/libm/complex/cephes_subrl.h b/newlib/libm/complex/cephes_subrl.h new file mode 100644 index 0000000..6354b23 --- /dev/null +++ b/newlib/libm/complex/cephes_subrl.h @@ -0,0 +1,9 @@ +/* $NetBSD: cephes_subrl.h,v 1.1 2014/10/10 00:48:18 christos Exp $ */ + +void _cchshl(long double, long double *, long double *); +long double _redupil(long double); +long double _ctansl(long double complex); + +#define M_PIL 3.14159265358979323846264338327950280e+00L +#define M_PI_2L 1.57079632679489661923132169163975140e+00L + diff --git a/newlib/libm/complex/cexpl.c b/newlib/libm/complex/cexpl.c new file mode 100644 index 0000000..8b56634 --- /dev/null +++ b/newlib/libm/complex/cexpl.c @@ -0,0 +1,46 @@ +/* $NetBSD: cexpl.c,v 1.1 2014/10/10 00:48:18 christos Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * 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 NETBSD FOUNDATION, INC. 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 FOUNDATION 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 +#include + +long double complex +cexpl(long double complex z) +{ + long double complex w; + long double r, x, y; + + x = creall(z); + y = cimagl(z); + r = expl(x); + w = r * cosl(y) + r * sinl(y) * I; + return w; +} diff --git a/newlib/libm/complex/clogl.c b/newlib/libm/complex/clogl.c new file mode 100644 index 0000000..3644a44 --- /dev/null +++ b/newlib/libm/complex/clogl.c @@ -0,0 +1,46 @@ +/* $NetBSD: clogl.c,v 1.1 2014/10/10 00:48:18 christos Exp $ */ + +/*- + * Copyright (c) 2007 The NetBSD Foundation, Inc. + * All rights reserved. + * + * This code is derived from software written by Stephen L. Moshier. + * It is redistributed by the NetBSD Foundation by permission of the author. + * + * 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 NETBSD FOUNDATION, INC. 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 FOUNDATION 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 +#include + +long double complex +clogl(long double complex z) +{ + long double complex w; + long double p, rr; + + rr = cabsl(z); + p = logl(rr); + rr = atan2l(cimagl(z), creall(z)); + w = p + rr * I; + return w; +} diff --git a/newlib/libm/complex/cprojl.c b/newlib/libm/complex/cprojl.c new file mode 100644 index 0000000..e71c773 --- /dev/null +++ b/newlib/libm/complex/cprojl.c @@ -0,0 +1,64 @@ +/* $NetBSD: cprojl.c,v 1.7 2014/10/10 00:48:18 christos Exp $ */ + +/*- + * Copyright (c) 2010 The NetBSD Foundation, Inc. + * 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 NETBSD FOUNDATION, INC. 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 FOUNDATION 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 +__RCSID("$NetBSD: cprojl.c,v 1.7 2014/10/10 00:48:18 christos Exp $"); + +#include +#include + +#include "../common/fdlibm.h" + +/* + * cprojl(long double complex z) + * + * These functions return the value of the projection (not stereographic!) + * onto the Riemann sphere. + * + * z projects to z, except that all complex infinities (even those with one + * infinite part and one NaN part) project to positive infinity on the real axis. + * If z has an infinite part, then cproj(z) shall be equivalent to: + * + * INFINITY + I * copysign(0.0, cimag(z)) + */ +long double complex +cprojl(long double complex z) +{ + long_double_complex w = { .z = z }; + + /*CONSTCOND*/ + if (isinf(creall(z)) || isinf(cimagl(z))) { +#ifdef __INFINITY + REAL_PART(w) = HUGE_VAL; +#else + REAL_PART(w) = INFINITY; +#endif + IMAG_PART(w) = copysignl(0.0L, cimagl(z)); + } + + return (w.z); +} diff --git a/newlib/libm/complex/csqrtl.c b/newlib/libm/complex/csqrtl.c new file mode 100644 index 0000000..c10a126 --- /dev/null +++ b/newlib/libm/complex/csqrtl.c @@ -0,0 +1,112 @@ +/*- + * Copyright (c) 2007-2008 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 +#if 0 +__FBSDID("$FreeBSD: head/lib/msun/src/s_csqrtl.c 181402 2008-08-08 00:15:16Z das $"); +#else +__RCSID("$NetBSD: csqrtl.c,v 1.2 2014/10/11 00:43:51 christos Exp $"); +#endif + +#include +#include +#include +#include +/* + * 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 >= LDBL_MAX / (1 + sqrt(2)). */ +#define THRESH (LDBL_MAX / 2.414213562373095048801688724209698L) + +#define cpackl(r, i) ((r) + (i) * I) + +long double complex +csqrtl(long double complex z) +{ + long double complex result; + long double a, b; + long double t; + bool scale; + + a = creall(z); + b = cimagl(z); + + /* Handle special cases. */ + if (z == 0.0L) + return (cpackl(0.0L, b)); + if (isinf(b)) + return (cpackl(INFINITY, b)); + if (isnan(a)) { + t = (b - b) / (b - b); /* raise invalid if b is not a NaN */ + return (cpackl(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 (cpackl(fabsl(b - b), copysignl(a, b))); + else + return (cpackl(a, copysignl(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 (fabsl(a) >= THRESH || fabsl(b) >= THRESH) { + a *= 0.25L; + b *= 0.25L; + scale = true; + } else { + scale = false; + } + + /* Algorithm 312, CACM vol 10, Oct 1967. */ + if (a >= 0L) { + t = sqrtl((a + hypotl(a, b)) * 0.5L); + result = cpackl(t, b / (2.0L * t)); + } else { + t = sqrtl((-a + hypotl(a, b)) * 0.5L); + result = cpackl(fabsl(b) / (2.0L * t), copysignl(t, b)); + } + + /* Rescale. */ + if (scale) + return (result * 2.0L); + else + return (result); +} -- 2.7.4