/*-*- mode:c;indent-tabs-mode:t;c-basic-offset:8;tab-width:8;coding:utf-8   -*-│
│ vi: set noet ft=c ts=8 sw=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"
#include "libc/tinymath/expo.internal.h"
__static_yoink("musl_libc_notice");


#define asdouble(i) ((union{uint64_t _i; double _f;}){i})._f
#define INSERT_WORDS(d,hi,lo)                     \
do {                                              \
  (d) = asdouble(((uint64_t)(hi)<<32) | (uint32_t)(lo)); \
} while (0)

/* k is such that k*ln2 has minimal relative error and x - kln2 > log(DBL_MIN) */
static const int k = 2043;
static const double kln2 = 0x1.62066151add8bp+10;

/* exp(x)/2 for x >= log(DBL_MAX), slightly better than 0.5*exp(x/2)*exp(x/2) */
double __expo2(double x, double sign)
{
	double scale;

	/* note that k is odd and scale*scale overflows */
	INSERT_WORDS(scale, (uint32_t)(0x3ff + k/2) << 20, 0);
	/* exp(x - k ln2) * 2**(k-1) */
	/* in directed rounding correct sign before rounding or overflow is important */
	return exp(x - kln2) * (sign * scale) * scale;
}
