1/*	$OpenBSD: eexp.c,v 1.1 2011/07/02 18:11:01 martynas Exp $	*/
2
3/*
4 * Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
5 *
6 * Permission to use, copy, modify, and distribute this software for any
7 * purpose with or without fee is hereby granted, provided that the above
8 * copyright notice and this permission notice appear in all copies.
9 *
10 * THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
11 * WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
12 * MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
13 * ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
14 * WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
15 * ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
16 * OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
17 */
18
19/*							xexp.c		*/
20/* exponential function check routine */
21/* by Stephen L. Moshier. */
22
23
24#include "ehead.h"
25
26void eexp( x, y )
27unsigned short *x, *y;
28{
29unsigned short num[NE], den[NE], x2[NE];
30long i;
31unsigned short sign, expchk;
32
33/* range reduction theory: x = i + f, 0<=f<1;
34 * e**x = e**i * e**f
35 * e**i = 2**(i/log 2).
36 * Let i/log2 = i1 + f1, 0<=f1<1.
37 * Then e**i = 2**i1 * 2**f1, so
38 * e**x = 2**i1 * e**(log 2 * f1) * e**f.
39 */
40if( ecmp(x, ezero) == 0 )
41	{
42	emov( eone, y );
43	return;
44	}
45emov(x, x2);
46expchk = x2[NE-1];
47sign = expchk & 0x8000;
48x2[NE-1] &= 0x7fff;
49
50/* Test for excessively large argument */
51expchk &= 0x7fff;
52if( expchk > (EXONE + 15) )
53	{
54	eclear( y );
55	if( sign == 0 )
56		einfin( y );
57	return;
58	}
59
60eifrac( x2, &i, num );		/* x = i + f		*/
61
62if( i != 0 )
63 {
64 ltoe( &i, den );		/* floating point i	*/
65 ediv( elog2, den, den );	/* i/log 2		*/
66 eifrac( den, &i, den );	/* i/log 2  =  i1 + f1	*/
67 emul( elog2, den, den );	/* log 2 * f1		*/
68 eadd( den, num, x2 );		/* log 2 * f1  + f	*/
69 }
70
71/*x2[NE-1] -= 1;*/
72eldexp( x2, -1L, x2 ); /* divide by 2 */
73etanh( x2, x2 );	/* tanh( x/2 )			*/
74eadd( x2, eone, num );	/* 1 + tanh			*/
75eneg( x2 );
76eadd( x2, eone, den );	/* 1 - tanh			*/
77ediv( den, num, y );	/* (1 + tanh)/(1 - tanh)	*/
78
79/*y[NE-1] += i;*/
80if( sign )
81	{
82	ediv( y, eone, y );
83	i = -i;
84	}
85eldexp( y, i, y );	/* multiply by 2**i */
86}
87