/*-*- 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.                      │
│                                                                              │
╚─────────────────────────────────────────────────────────────────────────────*/
#include "libc/math.h"

asm(".ident\t\"\\n\\n\
Musl libc (MIT License)\\n\
Copyright 2005-2014 Rich Felker, et. al.\"");
asm(".include \"libc/disclaimer.inc\"");
/* clang-format off */

/**
 * Returns inverse hyperbolic cosine of 𝑥.
 * @define acosh(x) = log(x + sqrt(x*x-1))
 */
double acosh(double x)
{
	union {double f; uint64_t i;} u = {.f = x};
	unsigned e = u.i >> 52 & 0x7ff;

	/* x < 1 domain error is handled in the called functions */

	if (e < 0x3ff + 1)
		/* |x| < 2, up to 2ulp error in [1,1.125] */
		return log1p(x-1 + sqrt((x-1)*(x-1)+2*(x-1)));
	if (e < 0x3ff + 26)
		/* |x| < 0x1p26 */
		return log(2*x - 1/(x+sqrt(x*x-1)));
	/* |x| >= 0x1p26 or nan */
	return log(x) + 0.693147180559945309417232121458176568;
}