2021-08-16 22:26:31 +00:00
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/*-*- 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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2021-02-28 09:06:00 +00:00
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│ │
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2021-08-16 22:26:31 +00:00
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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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2021-02-28 09:06:00 +00:00
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│ │
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╚─────────────────────────────────────────────────────────────────────────────*/
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#include "libc/math.h"
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2021-08-16 22:26:31 +00:00
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#include "libc/tinymath/expo.internal.h"
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#include "libc/tinymath/feval.internal.h"
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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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2021-02-28 09:06:00 +00:00
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/**
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* Returns hyperbolic cosine of 𝑥.
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2021-08-16 22:26:31 +00:00
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*
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* cosh(x) = (exp(x) + 1/exp(x))/2
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* = 1 + 0.5*(exp(x)-1)*(exp(x)-1)/exp(x)
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* = 1 + x*x/2 + o(x^4)
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2021-02-28 09:06:00 +00:00
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*/
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2021-08-16 22:26:31 +00:00
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double cosh(double x)
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{
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union {double f; uint64_t i;} u = {.f = x};
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uint32_t w;
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double t;
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/* |x| */
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u.i &= (uint64_t)-1/2;
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x = u.f;
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w = u.i >> 32;
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/* |x| < log(2) */
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if (w < 0x3fe62e42) {
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if (w < 0x3ff00000 - (26<<20)) {
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/* raise inexact if x!=0 */
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feval(x + 0x1p120f);
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return 1;
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}
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t = expm1(x);
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return 1 + t*t/(2*(1+t));
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}
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/* |x| < log(DBL_MAX) */
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if (w < 0x40862e42) {
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t = exp(x);
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/* note: if x>log(0x1p26) then the 1/t is not needed */
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return 0.5*(t + 1/t);
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}
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/* |x| > log(DBL_MAX) or nan */
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/* note: the result is stored to handle overflow */
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t = __expo2(x, 1.0);
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return t;
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2021-02-28 09:06:00 +00:00
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}
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