Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : POWIL.C

 
Output of file : POWIL.C contained in archive : CEPHES22.ZIP
/* 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 "mconf.h"
extern long double MAXNUML, MAXLOGL, MINLOGL;
extern double LOGE2;

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

if( x == 0.0L )
{
if( nn == 0 )
return( 1.0 );
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 = (double )x;
s = frexp( s, &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 > MAXLOGL )
{
mtherr( "powil", OVERFLOW );
y = MAXNUML;
goto done;
}

if( s < MINLOGL )
return(0.0);

/* 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+2.0) )
{
x = 1.0/x;
sign = 0;
}

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

else
{
y = 1.0;
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 = 1.0/y;
return(y);
}


  3 Responses to “Category : C Source Code
Archive   : CEPHES22.ZIP
Filename : POWIL.C

  1. Very nice! Thank you for this wonderful archive. I wonder why I found it only now. Long live the BBS file archives!

  2. This is so awesome! 😀 I’d be cool if you could download an entire archive of this at once, though.

  3. But one thing that puzzles me is the “mtswslnkmcjklsdlsbdmMICROSOFT” string. There is an article about it here. It is definitely worth a read: http://www.os2museum.com/wp/mtswslnk/