1/*
2 * CDDL HEADER START
3 *
4 * The contents of this file are subject to the terms of the
5 * Common Development and Distribution License (the "License").
6 * You may not use this file except in compliance with the License.
7 *
8 * You can obtain a copy of the license at usr/src/OPENSOLARIS.LICENSE
9 * or http://www.opensolaris.org/os/licensing.
10 * See the License for the specific language governing permissions
11 * and limitations under the License.
12 *
13 * When distributing Covered Code, include this CDDL HEADER in each
14 * file and include the License file at usr/src/OPENSOLARIS.LICENSE.
15 * If applicable, add the following below this CDDL HEADER, with the
16 * fields enclosed by brackets "[]" replaced with your own identifying
17 * information: Portions Copyright [yyyy] [name of copyright owner]
18 *
19 * CDDL HEADER END
20 */
21
22/*
23 * Copyright 2011 Nexenta Systems, Inc.  All rights reserved.
24 */
25/*
26 * Copyright 2006 Sun Microsystems, Inc.  All rights reserved.
27 * Use is subject to license terms.
28 */
29
30/*
31 * expl(x)
32 * Table driven method
33 * Written by K.C. Ng, November 1988.
34 * Algorithm :
35 *	1. Argument Reduction: given the input x, find r and integer k
36 *	   and j such that
37 *	             x = (32k+j)*ln2 + r,  |r| <= (1/64)*ln2 .
38 *
39 *	2. expl(x) = 2^k * (2^(j/32) + 2^(j/32)*expm1(r))
40 *	   Note:
41 *	   a. expm1(r) = (2r)/(2-R), R = r - r^2*(t1 + t2*r^2)
42 *	   b. 2^(j/32) is represented as
43 *			_TBL_expl_hi[j]+_TBL_expl_lo[j]
44 *         where
45 *		_TBL_expl_hi[j] = 2^(j/32) rounded
46 *		_TBL_expl_lo[j] = 2^(j/32) - _TBL_expl_hi[j].
47 *
48 * Special cases:
49 *	expl(INF) is INF, expl(NaN) is NaN;
50 *	expl(-INF)=  0;
51 *	for finite argument, only expl(0)=1 is exact.
52 *
53 * Accuracy:
54 *	according to an error analysis, the error is always less than
55 *	an ulp (unit in the last place).
56 *
57 * Misc. info.
58 *	For 113 bit long double
59 *		if x >  1.135652340629414394949193107797076342845e+4
60 *      then expl(x) overflow;
61 *		if x < -1.143346274333629787883724384345262150341e+4
62 *	then expl(x) underflow
63 *
64 * Constants:
65 * Only decimal values are given. We assume that the compiler will convert
66 * from decimal to binary accurately enough to produce the correct
67 * hexadecimal values.
68 */
69
70#pragma weak __expl = expl
71
72#include "libm.h"
73
74extern const long double _TBL_expl_hi[], _TBL_expl_lo[];
75
76static const long double
77one		=  1.0L,
78two		=  2.0L,
79ln2_64		=  1.083042469624914545964425189778400898568e-2L,
80ovflthreshold	=  1.135652340629414394949193107797076342845e+4L,
81unflthreshold	= -1.143346274333629787883724384345262150341e+4L,
82invln2_32	=  4.616624130844682903551758979206054839765e+1L,
83ln2_32hi	=  2.166084939249829091928849858592451515688e-2L,
84ln2_32lo	=  5.209643502595475652782654157501186731779e-27L;
85
86/* rational approximation coeffs for [-(ln2)/64,(ln2)/64] */
87static const long double
88t1 =   1.666666666666666666666666666660876387437e-1L,
89t2 =  -2.777777777777777777777707812093173478756e-3L,
90t3 =   6.613756613756613482074280932874221202424e-5L,
91t4 =  -1.653439153392139954169609822742235851120e-6L,
92t5 =   4.175314851769539751387852116610973796053e-8L;
93
94long double
95expl(long double x) {
96	int *px = (int *) &x, ix, j, k, m;
97	long double t, r;
98
99	ix = px[0];				/* high word of x */
100	if (ix >= 0x7fff0000)
101		return (x + x);			/* NaN of +inf */
102	if (((unsigned) ix) >= 0xffff0000)
103		return (-one / x);		/* NaN or -inf */
104	if ((ix & 0x7fffffff) < 0x3fc30000) {
105		if ((int) x < 1)
106			return (one + x);	/* |x|<2^-60 */
107	}
108	if (ix > 0) {
109		if (x > ovflthreshold)
110			return (scalbnl(x, 20000));
111		k = (int) (invln2_32 * (x + ln2_64));
112	} else {
113		if (x < unflthreshold)
114			return (scalbnl(-x, -40000));
115		k = (int) (invln2_32 * (x - ln2_64));
116	}
117	j  = k&0x1f;
118	m  = k>>5;
119	t  = (long double) k;
120	x  = (x - t * ln2_32hi) - t * ln2_32lo;
121	t  = x * x;
122	r  = (x - t * (t1 + t * (t2 + t * (t3 + t * (t4 + t * t5))))) - two;
123	x  = _TBL_expl_hi[j] - ((_TBL_expl_hi[j] * (x + x)) / r -
124		_TBL_expl_lo[j]);
125	return (scalbnl(x, m));
126}
127