acosh.c revision 25c28e83beb90e7c80452a7c818c5e6f73a07dc8
/*
* 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
* 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.
*/
/* 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_synonyms.h" /* __acosh, __log, __log1p */
#include "libm_protos.h" /* _SVID_libm_error */
#include "libm_macros.h"
#include <math.h>
static const double
one = 1.0,
double
acosh(double x) {
double t;
int hx;
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 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 (0.0); /* acosh(1) = 0 */
} else if (hx > 0x40000000) {
/* 2**28 > x > 2 */
t = x * x;
} else {
/* 1 < x < 2 */
t = x - one;
}
}