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/* $OpenBSD: elog.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.
*/
/* xlog.c */
/* natural logarithm */
/* by Stephen L. Moshier. */
#include "mconf.h"
#include "ehead.h"
void elog( x, y )
unsigned short *x, *y;
{
unsigned short xx[NE], z[NE], a[NE], b[NE], t[NE], qj[NE];
long ex;
int fex;
if( x[NE-1] & (unsigned short )0x8000 )
{
eclear(y);
mtherr( "elog", DOMAIN );
return;
}
if( ecmp( x, ezero ) == 0 )
{
einfin( y );
eneg(y);
mtherr( "elog", SING );
return;
}
if( ecmp( x, eone ) == 0 )
{
eclear( y );
return;
}
/* range reduction: log x = log( 2**ex * m ) = ex * log2 + log m */
efrexp( x, &fex, xx );
/*
emov(x, xx );
ex = xx[NX-1] & 0x7fff;
ex -= 0x3ffe;
xx[NX-1] = 0x3ffe;
*/
/* Adjust range to 1/sqrt(2), sqrt(2) */
esqrt2[NE-1] -= 1;
if( ecmp( xx, esqrt2 ) < 0 )
{
fex -= 1;
emul( xx, etwo, xx );
}
esqrt2[NE-1] += 1;
esub( eone, xx, a );
if( a[NE-1] == 0 )
{
eclear( y );
goto logdon;
}
eadd( eone, xx, b );
ediv( b, a, y ); /* store (x-1)/(x+1) in y */
emul( y, y, z );
emov( eone, a );
emov( eone, b );
emov( eone, qj );
do
{
eadd( etwo, qj, qj ); /* 2 * i + 1 */
emul( z, a, a );
ediv( qj, a, t );
eadd( t, b, b );
}
while( ((b[NE-1] & 0x7fff) - (t[NE-1] & 0x7fff)) < NBITS );
emul( b, y, y );
emul( y, etwo, y );
logdon:
/* now add log of 2**ex */
if( fex != 0 )
{
ex = fex;
ltoe( &ex, b );
emul( elog2, b, b );
eadd( b, y, y );
}
}
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