raze/source/common/thirdparty/math/powi.c

/*							powi.c
 *
 *	Real raised to integer power
 *
 *
 *
 * SYNOPSIS:
 *
 * double x, y, powi();
 * int n;
 *
 * y = powi( x, n );
 *
 *
 *
 * DESCRIPTION:
 *
 * Returns argument x raised to the nth power.
 * The routine efficiently decomposes n as a sum of powers of
 * two. The desired power is a product of two-to-the-kth
 * powers of x.  Thus to compute the 32767 power of x requires
 * 28 multiplications instead of 32767 multiplications.
 *
 *
 *
 * ACCURACY:
 *
 *
 *                      Relative error:
 * arithmetic   x domain   n domain  # trials      peak         rms
 *    DEC       .04,26     -26,26    100000       2.7e-16     4.3e-17
 *    IEEE      .04,26     -26,26     50000       2.0e-15     3.8e-16
 *    IEEE        1,2    -1022,1023   50000       8.6e-14     1.6e-14
 *
 * Returns MAXNUM on overflow, zero on underflow.
 *
 */

/*							powi.c	*/

/*
Cephes Math Library Release 2.8:  June, 2000
Copyright 1984, 1995, 2000 by Stephen L. Moshier

Redistribution and use in source and binary forms, with or without
modification, are permitted provided that the following conditions are met:

1. Redistributions of source code must retain the above copyright notice,
   this list of conditions and the following disclaimer.
2. Redistributions in binary form must reproduce the above copyright
   notice, this list of conditions and the following disclaimer in the
   documentation and/or other materials provided with the distribution.
3. Neither the name of the <ORGANIZATION> nor the names of its
   contributors may be used to endorse or promote products derived from
   this software without specific prior written permission.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS "AS IS"
AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE
IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE
ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT OWNER OR CONTRIBUTORS BE
LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR
CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF
SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS
INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN
CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE)
ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
POSSIBILITY OF SUCH DAMAGE.
*/

#include "mconf.h"
#ifdef ANSIPROT
extern double log ( double );
extern double frexp ( double, int * );
extern int signbit ( double );
#else
double log(), frexp();
int signbit();
#endif
extern double NEGZERO, INFINITY, MAXNUM, MAXLOG, MINLOG, LOGE2;

double c_powi( x, nn )
double x;
int nn;
{
int n, e, sign, asign, lx;
double w, y, s;

/* See pow.c for these tests.  */
if( x == 0.0 )
	{
	if( nn == 0 )
		return( 1.0 );
	else if( nn < 0 )
	    return( INFINITY );
	else
	  {
	    if( nn & 1 )
	      return( x );
	    else
	      return( 0.0 );
	  }
	}

if( nn == 0 )
	return( 1.0 );

if( nn == -1 )
	return( 1.0/x );

if( x < 0.0 )
	{
	asign = -1;
	x = -x;
	}
else
	asign = 0;


if( nn < 0 )
	{
	sign = -1;
	n = -nn;
	}
else
	{
	sign = 1;
	n = nn;
	}

/* Even power will be positive. */
if( (n & 1) == 0 )
	asign = 0;

/* Overflow detection */

/* Calculate approximate logarithm of answer */
s = frexp( x, &lx );
e = (lx - 1)*n;
if( (e == 0) || (e > 64) || (e < -64) )
	{
	s = (s - 7.0710678118654752e-1) / (s +  7.0710678118654752e-1);
	s = (2.9142135623730950 * s - 0.5 + lx) * nn * LOGE2;
	}
else
	{
	s = LOGE2 * e;
	}

if( s > MAXLOG )
	{
	mtherr( "powi", OVERFLOW );
	y = INFINITY;
	goto done;
	}

#if DENORMAL
if( s < MINLOG )
	{
	y = 0.0;
	goto done;
	}

/* Handle tiny denormal answer, but with less accuracy
 * since roundoff error in 1.0/x will be amplified.
 * The precise demarcation should be the gradual underflow threshold.
 */
if( (s < (-MAXLOG+2.0)) && (sign < 0) )
	{
	x = 1.0/x;
	sign = -sign;
	}
#else
/* do not produce denormal answer */
if( s < -MAXLOG )
	return(0.0);
#endif


/* First bit of the power */
if( n & 1 )
	y = x;
		
else
	y = 1.0;

w = x;
n >>= 1;
while( n )
	{
	w = w * w;	/* arg to the 2-to-the-kth power */
	if( n & 1 )	/* if that bit is set, then include in product */
		y *= w;
	n >>= 1;
	}

if( sign < 0 )
	y = 1.0/y;

done:

if( asign )
	{
	/* odd power of negative number */
	if( y == 0.0 )
		y = NEGZERO;
	else
		y = -y;
	}
return(y);
}