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/* 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 50000 4.3e-17 7.8e-18
* IEEE 1,2 -1022,1023 20000 3.9e-17 7.6e-18
* IEEE .99,1.01 0,8700 10000 3.6e-16 7.2e-17
*
* 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 <math.h>
extern long double MAXNUML, MAXLOGL, MINLOGL;
extern long double LOGE2L;
#ifdef ANSIPROT
extern long double frexpl ( long double, int * );
#else
long double frexpl();
#endif
long double powil( x, nn )
long double x;
int nn;
{
long double w, y;
long double s;
int n, e, sign, asign, lx;
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;
}
else
{
sign = 1;
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 )
{
mtherr( "powil", UNDERFLOW );
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 = -sign;
}
/* 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 < 0 )
y = 1.0L/y;
return(y);
}
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