125c28e83SPiotr Jasiukajtis /*
225c28e83SPiotr Jasiukajtis * CDDL HEADER START
325c28e83SPiotr Jasiukajtis *
425c28e83SPiotr Jasiukajtis * The contents of this file are subject to the terms of the
525c28e83SPiotr Jasiukajtis * Common Development and Distribution License (the "License").
625c28e83SPiotr Jasiukajtis * You may not use this file except in compliance with the License.
725c28e83SPiotr Jasiukajtis *
825c28e83SPiotr Jasiukajtis * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
925c28e83SPiotr Jasiukajtis * or http://www.opensolaris.org/os/licensing.
1025c28e83SPiotr Jasiukajtis * See the License for the specific language governing permissions
1125c28e83SPiotr Jasiukajtis * and limitations under the License.
1225c28e83SPiotr Jasiukajtis *
1325c28e83SPiotr Jasiukajtis * When distributing Covered Code, include this CDDL HEADER in each
1425c28e83SPiotr Jasiukajtis * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
1525c28e83SPiotr Jasiukajtis * If applicable, add the following below this CDDL HEADER, with the
1625c28e83SPiotr Jasiukajtis * fields enclosed by brackets "[]" replaced with your own identifying
1725c28e83SPiotr Jasiukajtis * information: Portions Copyright [yyyy] [name of copyright owner]
1825c28e83SPiotr Jasiukajtis *
1925c28e83SPiotr Jasiukajtis * CDDL HEADER END
2025c28e83SPiotr Jasiukajtis */
2125c28e83SPiotr Jasiukajtis
2225c28e83SPiotr Jasiukajtis /*
2325c28e83SPiotr Jasiukajtis * Copyright 2011 Nexenta Systems, Inc. All rights reserved.
2425c28e83SPiotr Jasiukajtis */
2525c28e83SPiotr Jasiukajtis /*
2625c28e83SPiotr Jasiukajtis * Copyright 2006 Sun Microsystems, Inc. All rights reserved.
2725c28e83SPiotr Jasiukajtis * Use is subject to license terms.
2825c28e83SPiotr Jasiukajtis */
2925c28e83SPiotr Jasiukajtis
30*ddc0e0b5SRichard Lowe #pragma weak __coshl = coshl
3125c28e83SPiotr Jasiukajtis
3225c28e83SPiotr Jasiukajtis #include "libm.h"
3325c28e83SPiotr Jasiukajtis #include "longdouble.h"
3425c28e83SPiotr Jasiukajtis
3525c28e83SPiotr Jasiukajtis
3625c28e83SPiotr Jasiukajtis /*
3725c28e83SPiotr Jasiukajtis * coshl(X)
3825c28e83SPiotr Jasiukajtis * RETURN THE HYPERBOLIC COSINE OF X
3925c28e83SPiotr Jasiukajtis *
4025c28e83SPiotr Jasiukajtis * Method :
4125c28e83SPiotr Jasiukajtis * 1. Replace x by |x| (coshl(x) = coshl(-x)).
4225c28e83SPiotr Jasiukajtis * 2.
4325c28e83SPiotr Jasiukajtis * [ expl(x) - 1 ]^2
4425c28e83SPiotr Jasiukajtis * 0 <= x <= 0.3465 : coshl(x) := 1 + -------------------
4525c28e83SPiotr Jasiukajtis * 2*expl(x)
4625c28e83SPiotr Jasiukajtis *
4725c28e83SPiotr Jasiukajtis * expl(x) + 1/expl(x)
4825c28e83SPiotr Jasiukajtis * 0.3465 <= x <= thresh : coshl(x) := -------------------
4925c28e83SPiotr Jasiukajtis * 2
5025c28e83SPiotr Jasiukajtis * thresh <= x <= lnovft : coshl(x) := expl(x)/2
5125c28e83SPiotr Jasiukajtis * lnovft <= x < INF : coshl(x) := scalbnl(expl(x-1024*ln2),1023)
5225c28e83SPiotr Jasiukajtis *
5325c28e83SPiotr Jasiukajtis * here
5425c28e83SPiotr Jasiukajtis * thr1 a number that is near one half of ln2.
5525c28e83SPiotr Jasiukajtis * thr2 a number such that
5625c28e83SPiotr Jasiukajtis * expl(thresh)+expl(-thresh)=expl(thresh)
5725c28e83SPiotr Jasiukajtis * lnovft: logrithm of the overflow threshold
5825c28e83SPiotr Jasiukajtis * = MEP1*ln2 chopped to machine precision.
5925c28e83SPiotr Jasiukajtis * ME maximum exponent
6025c28e83SPiotr Jasiukajtis * MEP1 maximum exponent plus 1
6125c28e83SPiotr Jasiukajtis *
6225c28e83SPiotr Jasiukajtis * Special cases:
6325c28e83SPiotr Jasiukajtis * coshl(x) is |x| if x is +INF, -INF, or NaN.
6425c28e83SPiotr Jasiukajtis * only coshl(0)=1 is exact for finite x.
6525c28e83SPiotr Jasiukajtis */
6625c28e83SPiotr Jasiukajtis
6725c28e83SPiotr Jasiukajtis #define ME 16383
6825c28e83SPiotr Jasiukajtis #define MEP1 16384
6925c28e83SPiotr Jasiukajtis #define LNOVFT 1.135652340629414394949193107797076342845e+4L
7025c28e83SPiotr Jasiukajtis /* last 32 bits of LN2HI is zero */
7125c28e83SPiotr Jasiukajtis #define LN2HI 6.931471805599453094172319547495844850203e-0001L
7225c28e83SPiotr Jasiukajtis #define LN2LO 1.667085920830552208890449330400379754169e-0025L
7325c28e83SPiotr Jasiukajtis #define THR1 0.3465L
7425c28e83SPiotr Jasiukajtis #define THR2 45.L
7525c28e83SPiotr Jasiukajtis
7625c28e83SPiotr Jasiukajtis static const long double
7725c28e83SPiotr Jasiukajtis half = 0.5L,
7825c28e83SPiotr Jasiukajtis tinyl = 7.5e-37L,
7925c28e83SPiotr Jasiukajtis one = 1.0L,
8025c28e83SPiotr Jasiukajtis ln2hi = LN2HI,
8125c28e83SPiotr Jasiukajtis ln2lo = LN2LO,
8225c28e83SPiotr Jasiukajtis lnovftL = LNOVFT,
8325c28e83SPiotr Jasiukajtis thr1 = THR1,
8425c28e83SPiotr Jasiukajtis thr2 = THR2;
8525c28e83SPiotr Jasiukajtis
8625c28e83SPiotr Jasiukajtis long double
coshl(long double x)8725c28e83SPiotr Jasiukajtis coshl(long double x) {
8825c28e83SPiotr Jasiukajtis long double t, w;
8925c28e83SPiotr Jasiukajtis
9025c28e83SPiotr Jasiukajtis w = fabsl(x);
9125c28e83SPiotr Jasiukajtis if (!finitel(w))
9225c28e83SPiotr Jasiukajtis return (w + w); /* x is INF or NaN */
9325c28e83SPiotr Jasiukajtis if (w < thr1) {
9425c28e83SPiotr Jasiukajtis t = w < tinyl ? w : expm1l(w);
9525c28e83SPiotr Jasiukajtis w = one + t;
9625c28e83SPiotr Jasiukajtis if (w != one)
9725c28e83SPiotr Jasiukajtis w = one + (t * t) / (w + w);
9825c28e83SPiotr Jasiukajtis return (w);
9925c28e83SPiotr Jasiukajtis } else if (w < thr2) {
10025c28e83SPiotr Jasiukajtis t = expl(w);
10125c28e83SPiotr Jasiukajtis return (half * (t + one / t));
10225c28e83SPiotr Jasiukajtis } else if (w <= lnovftL)
10325c28e83SPiotr Jasiukajtis return (half * expl(w));
10425c28e83SPiotr Jasiukajtis else {
10525c28e83SPiotr Jasiukajtis return (scalbnl(expl((w - MEP1 * ln2hi) - MEP1 * ln2lo), ME));
10625c28e83SPiotr Jasiukajtis }
10725c28e83SPiotr Jasiukajtis }
108