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394d998315
At least in neovim, `│vi:` is not recognized as a modeline because it has no preceding whitespace. After fixing this, opening a file yields an error because `net` is not an option. (`noet`, however, is.)
169 lines
7 KiB
C
169 lines
7 KiB
C
/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8 -*-│
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│ vi: set et ft=c ts=8 tw=8 fenc=utf-8 :vi │
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╚──────────────────────────────────────────────────────────────────────────────╝
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│ │
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│ Musl Libc │
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│ Copyright © 2005-2014 Rich Felker, et al. │
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│ │
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│ Permission is hereby granted, free of charge, to any person obtaining │
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│ a copy of this software and associated documentation files (the │
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│ "Software"), to deal in the Software without restriction, including │
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│ without limitation the rights to use, copy, modify, merge, publish, │
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│ distribute, sublicense, and/or sell copies of the Software, and to │
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│ permit persons to whom the Software is furnished to do so, subject to │
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│ the following conditions: │
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│ │
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│ The above copyright notice and this permission notice shall be │
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│ included in all copies or substantial portions of the Software. │
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│ │
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│ THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, │
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│ EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF │
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│ MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. │
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│ IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY │
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│ CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, │
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│ TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE │
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│ SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE. │
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/complex.h"
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#include "libc/math.h"
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#include "libc/tinymath/complex.internal.h"
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asm(".ident\t\"\\n\\n\
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ctahnh (BSD-2 License)\\n\
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Copyright (c) 2011 David Schultz <das@FreeBSD.ORG>\"");
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asm(".ident\t\"\\n\\n\
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Musl libc (MIT License)\\n\
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Copyright 2005-2014 Rich Felker, et. al.\"");
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asm(".include \"libc/disclaimer.inc\"");
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/* clang-format off */
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/* origin: FreeBSD /usr/src/lib/msun/src/s_ctanh.c */
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/*-
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* Copyright (c) 2011 David Schultz
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* All rights reserved.
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* 1. Redistributions of source code must retain the above copyright
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* notice unmodified, this list of conditions, and the following
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* disclaimer.
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* 2. Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in the
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* documentation and/or other materials provided with the distribution.
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*
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* THIS SOFTWARE IS PROVIDED BY THE AUTHOR ``AS IS'' AND ANY EXPRESS OR
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* IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES
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* OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED.
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* IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT
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* NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
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* DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
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* THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
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* (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF
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* THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
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*/
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/*
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* Hyperbolic tangent of a complex argument z = x + i y.
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*
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* The algorithm is from:
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*
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* W. Kahan. Branch Cuts for Complex Elementary Functions or Much
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* Ado About Nothing's Sign Bit. In The State of the Art in
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* Numerical Analysis, pp. 165 ff. Iserles and Powell, eds., 1987.
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*
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* Method:
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*
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* Let t = tan(x)
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* beta = 1/cos^2(y)
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* s = sinh(x)
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* rho = cosh(x)
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*
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* We have:
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*
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* tanh(z) = sinh(z) / cosh(z)
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*
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* sinh(x) cos(y) + i cosh(x) sin(y)
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* = ---------------------------------
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* cosh(x) cos(y) + i sinh(x) sin(y)
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*
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* cosh(x) sinh(x) / cos^2(y) + i tan(y)
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* = -------------------------------------
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* 1 + sinh^2(x) / cos^2(y)
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*
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* beta rho s + i t
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* = ----------------
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* 1 + beta s^2
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*
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* Modifications:
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*
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* I omitted the original algorithm's handling of overflow in tan(x) after
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* verifying with nearpi.c that this can't happen in IEEE single or double
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* precision. I also handle large x differently.
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*/
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double complex ctanh(double complex z)
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{
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double x, y;
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double t, beta, s, rho, denom;
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uint32_t hx, ix, lx;
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x = creal(z);
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y = cimag(z);
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EXTRACT_WORDS(hx, lx, x);
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ix = hx & 0x7fffffff;
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/*
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* ctanh(NaN + i 0) = NaN + i 0
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*
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* ctanh(NaN + i y) = NaN + i NaN for y != 0
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*
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* The imaginary part has the sign of x*sin(2*y), but there's no
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* special effort to get this right.
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*
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* ctanh(+-Inf +- i Inf) = +-1 +- 0
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*
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* ctanh(+-Inf + i y) = +-1 + 0 sin(2y) for y finite
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*
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* The imaginary part of the sign is unspecified. This special
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* case is only needed to avoid a spurious invalid exception when
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* y is infinite.
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*/
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if (ix >= 0x7ff00000) {
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if ((ix & 0xfffff) | lx) /* x is NaN */
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return CMPLX(x, (y == 0 ? y : x * y));
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SET_HIGH_WORD(x, hx - 0x40000000); /* x = copysign(1, x) */
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return CMPLX(x, copysign(0, isinf(y) ? y : sin(y) * cos(y)));
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}
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/*
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* ctanh(+-0 + i NAN) = +-0 + i NaN
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* ctanh(+-0 +- i Inf) = +-0 + i NaN
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* ctanh(x + i NAN) = NaN + i NaN
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* ctanh(x +- i Inf) = NaN + i NaN
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*/
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if (!isfinite(y))
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return CMPLX(x ? y - y : x, y - y);
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/*
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* ctanh(+-huge + i +-y) ~= +-1 +- i 2sin(2y)/exp(2x), using the
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* approximation sinh^2(huge) ~= exp(2*huge) / 4.
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* We use a modified formula to avoid spurious overflow.
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*/
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if (ix >= 0x40360000) { /* x >= 22 */
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double exp_mx = exp(-fabs(x));
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return CMPLX(copysign(1, x), 4 * sin(y) * cos(y) * exp_mx * exp_mx);
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}
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/* Kahan's algorithm */
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t = tan(y);
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beta = 1.0 + t * t; /* = 1 / cos^2(y) */
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s = sinh(x);
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rho = sqrt(1 + s * s); /* = cosh(x) */
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denom = 1 + beta * s * s;
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return CMPLX((beta * rho * s) / denom, t / denom);
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}
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