/*
 * CDDL HEADER START
 *
 * The contents of this file are subject to the terms of the
 * Common Development and Distribution License (the "License").
 * You may not use this file except in compliance with the License.
 *
 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
 * or http://www.opensolaris.org/os/licensing.
 * See the License for the specific language governing permissions
 * and limitations under the License.
 *
 * When distributing Covered Code, include this CDDL HEADER in each
 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
 * If applicable, add the following below this CDDL HEADER, with the
 * fields enclosed by brackets "[]" replaced with your own identifying
 * information: Portions Copyright [yyyy] [name of copyright owner]
 *
 * CDDL HEADER END
 */

/*
 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
 */
/*
 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
 * Use is subject to license terms.
 */

#pragma weak __coshl = coshl

#include "libm.h"
#include "longdouble.h"


/*
 * coshl(X)
 * RETURN THE HYPERBOLIC COSINE OF X
 *
 * Method :
 *      1. Replace x by |x| (coshl(x) = coshl(-x)).
 *      2.
 *                                                     [ expl(x) - 1 ]^2
 *          0        <= x <= 0.3465 : coshl(x) := 1 + -------------------
 *                                                          2*expl(x)
 *
 *                                                expl(x) + 1/expl(x)
 *          0.3465   <= x <= thresh : coshl(x) := -------------------
 *                                                         2
 *          thresh   <= x <= lnovft : coshl(x) := expl(x)/2
 *          lnovft   <= x <  INF    : coshl(x) := scalbnl(expl(x-1024*ln2),1023)
 *
 * here
 *      thr1            a number that is near one half of ln2.
 *      thr2            a number such that
 *                              expl(thresh)+expl(-thresh)=expl(thresh)
 *      lnovft:         logrithm of the overflow threshold
 *                      = MEP1*ln2 chopped to machine precision.
 *      ME              maximum exponent
 *      MEP1            maximum exponent plus 1
 *
 * Special cases:
 *      coshl(x) is |x| if x is +INF, -INF, or NaN.
 *      only coshl(0)=1 is exact for finite x.
 */

#define ME      16383
#define MEP1    16384
#define LNOVFT  1.135652340629414394949193107797076342845e+4L
                /* last 32 bits of LN2HI is zero */
#define LN2HI   6.931471805599453094172319547495844850203e-0001L
#define LN2LO   1.667085920830552208890449330400379754169e-0025L
#define THR1    0.3465L
#define THR2    45.L

static const long double
        half    = 0.5L,
        tinyl   = 7.5e-37L,
        one     = 1.0L,
        ln2hi   = LN2HI,
        ln2lo   = LN2LO,
        lnovftL = LNOVFT,
        thr1    = THR1,
        thr2    = THR2;

long double
coshl(long double x) {
        long double t, w;

        w = fabsl(x);
        if (!finitel(w))
                return (w + w);         /* x is INF or NaN */
        if (w < thr1) {
                t = w < tinyl ? w : expm1l(w);
                w = one + t;
                if (w != one)
                        w = one + (t * t) / (w + w);
                return (w);
        } else if (w < thr2) {
                t = expl(w);
                return (half * (t + one / t));
        } else if (w <= lnovftL)
                return (half * expl(w));
        else {
                return (scalbnl(expl((w - MEP1 * ln2hi) - MEP1 * ln2lo), ME));
        }
}