powill.c

128位长双精度型数字运算包

/*							powil.c
 *
 *	Real raised to integer power, long double precision
 *
 *
 *
 * SYNOPSIS:
 *
 * long double x, y, powil();
 * int n;
 *
 * y = powil( 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
 *    IEEE     .001,1000  -1022,1023  100,000     7.5e-32     1.4e-32
 *    IEEE     .99,1.01     0,8700    100,000     4.6e-31     9.1e-32
 *
 * Returns MAXNUM on overflow, zero on underflow.
 *
 */

/*							powil.c	*/

/*
Cephes Math Library Release 2.2:  December, 1990
Copyright 1984, 1990 by Stephen L. Moshier
Direct inquiries to 30 Frost Street, Cambridge, MA 02140
*/

#include "mconf.h"
extern long double MAXNUML, MAXLOGL, MINLOGL;
extern long double LOGE2L;

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

if( x == 0.0L )
	{
	if( nn == 0 )
		return( 1.0L );
	else if( nn < 0 )
		return( MAXNUML );
	else
		return( 0.0L );
	}

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


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


if( nn < 0 )
	{
	sign = -1;
	n = -nn;
/*
	x = 1.0/x;
*/
	}
else
	{
	sign = 0;
	n = nn;
	}

/* Overflow detection */

/* Calculate approximate logarithm of answer */
s = x;
s = frexpl( s, &lx );
e = (lx - 1)*n;
if( (e == 0) || (e > 64) || (e < -64) )
	{
	s = (s - 7.0710678118654752e-1L) / (s +  7.0710678118654752e-1L);
	s = (2.9142135623730950L * s - 0.5L + lx) * nn * LOGE2L;
	}
else
	{
	s = LOGE2L * e;
	}

if( s > MAXLOGL )
	{
	mtherr( "powil", OVERFLOW );
	y = MAXNUML;
	goto done;
	}

if( s < MINLOGL )
	return(0.0L);

/* 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 < (-MAXLOGL+2.0L) )
	{
	x = 1.0L/x;
	sign = 0;
	}

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


done:

if( asign )
	y = -y; /* odd power of negative number */
if( sign )
	y = 1.0L/y;
return(y);
}