/*-*- 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"
#include "libc/tinymath/internal.h"

asm(".ident\t\"\\n\\n\
OpenBSD libm (MIT License)\\n\
Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>\"");
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

/* origin: OpenBSD /usr/src/lib/libm/src/ld80/e_expl.c */
/*
 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
 *
 * Permission to use, copy, modify, and distribute this software for any
 * purpose with or without fee is hereby granted, provided that the above
 * copyright notice and this permission notice appear in all copies.
 *
 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
 */
/*
 *      Exponential function, long double precision
 *
 *
 * SYNOPSIS:
 *
 * long double x, y, expl();
 *
 * y = expl( x );
 *
 *
 * DESCRIPTION:
 *
 * Returns e (2.71828...) raised to the x power.
 *
 * Range reduction is accomplished by separating the argument
 * into an integer k and fraction f such that
 *
 *     x    k  f
 *    e  = 2  e.
 *
 * A Pade' form of degree 5/6 is used to approximate exp(f) - 1
 * in the basic range [-0.5 ln 2, 0.5 ln 2].
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 * arithmetic   domain     # trials      peak         rms
 *    IEEE      +-10000     50000       1.12e-19    2.81e-20
 *
 *
 * Error amplification in the exponential function can be
 * a serious matter.  The error propagation involves
 * exp( X(1+delta) ) = exp(X) ( 1 + X*delta + ... ),
 * which shows that a 1 lsb error in representing X produces
 * a relative error of X times 1 lsb in the function.
 * While the routine gives an accurate result for arguments
 * that are exactly represented by a long double precision
 * computer number, the result contains amplified roundoff
 * error for large arguments not exactly represented.
 *
 *
 * ERROR MESSAGES:
 *
 *   message         condition      value returned
 * exp underflow    x < MINLOG         0.0
 * exp overflow     x > MAXLOG         MAXNUM
 *
 */

#if LDBL_MANT_DIG == 53 && LDBL_MAX_EXP == 1024
long double expl(long double x)
{
	return exp(x);
}
#elif LDBL_MANT_DIG == 64 && LDBL_MAX_EXP == 16384

static const long double P[3] = {
 1.2617719307481059087798E-4L,
 3.0299440770744196129956E-2L,
 9.9999999999999999991025E-1L,
};
static const long double Q[4] = {
 3.0019850513866445504159E-6L,
 2.5244834034968410419224E-3L,
 2.2726554820815502876593E-1L,
 2.0000000000000000000897E0L,
};
static const long double
LN2HI = 6.9314575195312500000000E-1L,
LN2LO = 1.4286068203094172321215E-6L,
LOG2E = 1.4426950408889634073599E0L;

long double expl(long double x)
{
	long double px, xx;
	int k;

	if (isnan(x))
		return x;
	if (x > 11356.5234062941439488L) /* x > ln(2^16384 - 0.5) */
		return x * 0x1p16383L;
	if (x < -11399.4985314888605581L) /* x < ln(2^-16446) */
		return -0x1p-16445L/x;

	/* Express e**x = e**f 2**k
	 *   = e**(f + k ln(2))
	 */
	px = floorl(LOG2E * x + 0.5);
	k = px;
	x -= px * LN2HI;
	x -= px * LN2LO;

	/* rational approximation of the fractional part:
	 * e**x =  1 + 2x P(x**2)/(Q(x**2) - x P(x**2))
	 */
	xx = x * x;
	px = x * __polevll(xx, P, 2);
	x = px/(__polevll(xx, Q, 3) - px);
	x = 1.0 + 2.0 * x;
	return scalbnl(x, k);
}
#elif LDBL_MANT_DIG == 113 && LDBL_MAX_EXP == 16384
// TODO: broken implementation to make things compile
long double expl(long double x)
{
	return exp(x);
}
#else
#error "architecture unsupported"
#endif