coshl.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.
*/
#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,
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) {
w = one + t;
if (w != one)
w = one + (t * t) / (w + w);
return (w);
} else if (w < thr2) {
t = expl(w);
} else if (w <= lnovftL)
else {
}
}