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/* $OpenBSD: eexp.c,v 1.1 2011/07/02 18:11:01 martynas Exp $ */
/*
* Copyright (c) 2008 Stephen L. Moshier <steve@moshier.net>
*
* Permission to use, copy, modify, and distribute this software for any
* purpose with or without fee is hereby granted, provided that the above
* copyright notice and this permission notice appear in all copies.
*
* THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES
* WITH REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF
* MERCHANTABILITY AND FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR
* ANY SPECIAL, DIRECT, INDIRECT, OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES
* WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER IN AN
* ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS ACTION, ARISING OUT OF
* OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS SOFTWARE.
*/
/* xexp.c */
/* exponential function check routine */
/* by Stephen L. Moshier. */
#include "ehead.h"
void eexp( x, y )
unsigned short *x, *y;
{
unsigned short num[NE], den[NE], x2[NE];
long i;
unsigned short sign, expchk;
/* range reduction theory: x = i + f, 0<=f<1;
* e**x = e**i * e**f
* e**i = 2**(i/log 2).
* Let i/log2 = i1 + f1, 0<=f1<1.
* Then e**i = 2**i1 * 2**f1, so
* e**x = 2**i1 * e**(log 2 * f1) * e**f.
*/
if( ecmp(x, ezero) == 0 )
{
emov( eone, y );
return;
}
emov(x, x2);
expchk = x2[NE-1];
sign = expchk & 0x8000;
x2[NE-1] &= 0x7fff;
/* Test for excessively large argument */
expchk &= 0x7fff;
if( expchk > (EXONE + 15) )
{
eclear( y );
if( sign == 0 )
einfin( y );
return;
}
eifrac( x2, &i, num ); /* x = i + f */
if( i != 0 )
{
ltoe( &i, den ); /* floating point i */
ediv( elog2, den, den ); /* i/log 2 */
eifrac( den, &i, den ); /* i/log 2 = i1 + f1 */
emul( elog2, den, den ); /* log 2 * f1 */
eadd( den, num, x2 ); /* log 2 * f1 + f */
}
/*x2[NE-1] -= 1;*/
eldexp( x2, -1L, x2 ); /* divide by 2 */
etanh( x2, x2 ); /* tanh( x/2 ) */
eadd( x2, eone, num ); /* 1 + tanh */
eneg( x2 );
eadd( x2, eone, den ); /* 1 - tanh */
ediv( den, num, y ); /* (1 + tanh)/(1 - tanh) */
/*y[NE-1] += i;*/
if( sign )
{
ediv( y, eone, y );
i = -i;
}
eldexp( y, i, y ); /* multiply by 2**i */
}
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