/*
 * 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 __acosh = acosh

/* INDENT OFF */
/*
 * acosh(x)
 * Method :
 *      Based on
 *              acosh(x) = log [ x + sqrt(x*x-1) ]
 *      we have
 *              acosh(x) := log(x)+ln2, if x is large; else
 *              acosh(x) := log(2x-1/(sqrt(x*x-1)+x)) if x > 2; else
 *              acosh(x) := log1p(t+sqrt(2.0*t+t*t)); where t = x-1.
 *
 * Special cases:
 *      acosh(x) is NaN with signal if x < 1.
 *      acosh(NaN) is NaN without signal.
 */
/* INDENT ON */

#include "libm_protos.h"        /* _SVID_libm_error */
#include "libm_macros.h"
#include <math.h>

static const double
        one = 1.0,
        ln2 = 6.93147180559945286227e-01;       /* 3FE62E42, FEFA39EF */

double
acosh(double x) {
        double t;
        int hx;

        hx = ((int *) &x)[HIWORD];
        if (hx < 0x3ff00000) {  /* x < 1 */
                if (isnan(x))
#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
                        return (hx >= 0xfff80000 ? x : (x - x) / (x - x));
                        /* assumes sparc-like QNaN */
#else
                        return (x - x) / (x - x);
#endif
                else
                        return (_SVID_libm_err(x, x, 29));
        } else if (hx >= 0x41b00000) {
                /* x > 2**28 */
                if (hx >= 0x7ff00000) { /* x is inf of NaN */
#if defined(FPADD_TRAPS_INCOMPLETE_ON_NAN)
                        return (hx >= 0x7ff80000 ? x : x + x);
                        /* assumes sparc-like QNaN */
#else
                        return (x + x);
#endif
                } else  /* acosh(huge)=log(2x) */
                        return (log(x) + ln2);
        } else if (((hx - 0x3ff00000) | ((int *) &x)[LOWORD]) == 0) {
                return (0.0);   /* acosh(1) = 0 */
        } else if (hx > 0x40000000) {
                /* 2**28 > x > 2 */
                t = x * x;
                return (log(2.0 * x - one / (x + sqrt(t - one))));
        } else {
                /* 1 < x < 2 */
                t = x - one;
                return (log1p(t + sqrt(2.0 * t + t * t)));
        }
}