Math-Cephes

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lib/Math/Cephes.pm  view on Meta::CPAN

    my $h = ($b - $a) / $n / 8;
    my $f = [];
    for($count=0; $count <= 8*$n; $count++, $x+=$h) {
      $f->[$count] = &$r($x);
    }
    $sum = Math::Cephes::simpsn_wrap($f, $count-1, $h);
    my $test = abs($sum - $sumold);
    return $sum if ($test < $abs or abs($test/$sum) < $rel);
    $sumold = $sum;
  }
  warn("Math::Cephes::simpson: Maximum number $nmax of iterations reached");
  return undef;
}

sub bernum {
  my $i = shift;
  die "Cannot exceed i=30" if (defined $i and $i > 30);
  my $num = [split //, 0 x 30 ];
  my $den = [split //, 0 x 30 ];
  Math::Cephes::bernum_wrap($num, $den);
  return defined $i ? (int($num->[$i]), int($den->[$i])) : ($num, $den);

lib/Math/Cephes.pod  view on Meta::CPAN

  x = a t

  where

  t = 1 - d - ndtri(p) sqrt(d)

 and

  d = 1/9a,

 the routine performs up to 10 Newton iterations to find the
 root of igamc(a,x) - p = 0.

 ACCURACY:

 Tested at random a, p in the intervals indicated.

                a        p                      Relative error:
 arithmetic   domain   domain     # trials      peak         rms
    IEEE     0.5,100   0,0.5       100000       1.0e-14     1.7e-15
    IEEE     0.01,0.5  0,0.5       100000       9.0e-14     3.4e-15

lib/Math/Cephes.pod  view on Meta::CPAN

 # double a, b, x, y, incbi();

 $x = incbi( $a, $b, $y );

 DESCRIPTION:

 Given y, the function finds x such that

  incbet( a, b, x ) = y .

 The routine performs interval halving or Newton iterations to find the
 root of incbet(a,b,x) - y = 0.

 ACCURACY:

                      Relative error:
                x     a,b
 arithmetic   domain  domain  # trials    peak       rms
    IEEE      0,1    .5,10000   50000    5.8e-12   1.3e-13
    IEEE      0,1   .25,100    100000    1.8e-13   3.9e-15
    IEEE      0,1     0,5       50000    1.1e-12   5.5e-15

lib/Math/Cephes.pod  view on Meta::CPAN

 This evaluates the area under the graph of a function,
 represented in a subroutine, from $a to $b, using an 8-point
 Newton-Cotes formula. The routine divides up the interval into
 equal segments, evaluates the integral, then compares that
 to the result with double the number of segments. If the two
 results agree, to within an absolute error $abs_err or a
 relative error $rel_err, the result is returned; otherwise,
 the number of segments is doubled again, and the results
 compared. This continues until the desired accuracy is attained,
 or until the maximum number of iterations $nmax is reached.

=item I<vecang>: angle between two vectors

 SYNOPSIS:

 # double p[3], q[3], vecang();

    $y = vecang( $p, $q );

 DESCRIPTION:

libmd/igami.c  view on Meta::CPAN

 *  x = a t
 *
 *  where
 *
 *  t = 1 - d - ndtri(p) sqrt(d)
 * 
 * and
 *
 *  d = 1/9a,
 *
 * the routine performs up to 10 Newton iterations to find the
 * root of igamc(a,x) - p = 0.
 *
 * ACCURACY:
 *
 * Tested at random a, p in the intervals indicated.
 *
 *                a        p                      Relative error:
 * arithmetic   domain   domain     # trials      peak         rms
 *    IEEE     0.5,100   0,0.5       100000       1.0e-14     1.7e-15
 *    IEEE     0.01,0.5  0,0.5       100000       9.0e-14     3.4e-15

libmd/incbi.c  view on Meta::CPAN

 * x = incbi( a, b, y );
 *
 *
 *
 * DESCRIPTION:
 *
 * Given y, the function finds x such that
 *
 *  incbet( a, b, x ) = y .
 *
 * The routine performs interval halving or Newton iterations to find the
 * root of incbet(a,b,x) - y = 0.
 *
 *
 * ACCURACY:
 *
 *                      Relative error:
 *                x     a,b
 * arithmetic   domain  domain  # trials    peak       rms
 *    IEEE      0,1    .5,10000   50000    5.8e-12   1.3e-13
 *    IEEE      0,1   .25,100    100000    1.8e-13   3.9e-15

libmd/polmisc.c  view on Meta::CPAN

  /* If first nonzero coefficient was at degree n > 0, multiply by
     x^(n/2).  */
  if (n > 0)
    {
      polclr (x, MAXPOL);
      x[n/2] = 1.0;
      polmul (x, nn, y, nn, y);
    }
#if 0
/* Newton iterations */
for( n=0; n<10; n++ )
	{
	poldiv( y, nn, pol, nn, z );
	poladd( y, nn, z, nn, y );
	for( i=0; i<=nn; i++ )
		y[i] *= 0.5;
	for( i=0; i<=nn; i++ )
		{
		u = md_fabs( y[i] - z[i] );
		if( u > 1.0e-15 )

libmd/sqrt.c  view on Meta::CPAN

*/
#endif
#ifdef MIEEE
x = ldexp( x, (e >> 1) );
/*
*q += ((e >>1) & 0x7ff) << 4;
*q &= 077777;
*/
#endif

/* Newton iterations: */
#ifdef UNK
x = 0.5*(x + w/x);
x = 0.5*(x + w/x);
x = 0.5*(x + w/x);
#endif

/* Note, assume the square root cannot be denormal,
 * so it is safe to use integer exponent operations here.
 */
#ifdef DEC

libmd/sqrt.c.src  view on Meta::CPAN

*/
#endif
#ifdef MIEEE
x = ldexp( x, (e >> 1) );
/*
*q += ((e >>1) & 0x7ff) << 4;
*q &= 077777;
*/
#endif

/* Newton iterations: */
#ifdef UNK
x = 0.5*(x + w/x);
x = 0.5*(x + w/x);
x = 0.5*(x + w/x);
#endif

/* Note, assume the square root cannot be denormal,
 * so it is safe to use integer exponent operations here.
 */
#ifdef DEC

pmath  view on Meta::CPAN

  x = a t

  where

  t = 1 - d - ndtri(p) sqrt(d)
 
 and

  d = 1/9a,

 the routine performs up to 10 Newton iterations to find the
 root of igamc(a,x) - p = 0.

 ',
          'catan' => 'catan:  Complex circular arc tangent

SYNOPSIS:

 # void catan();
 # cmplx z, w;

pmath  view on Meta::CPAN

 # double a, b, x, y, incbi();

 $x = incbi( $a, $b, $y );

DESCRIPTION:

 Given y, the function finds x such that

  incbet( a, b, x ) = y .

 The routine performs interval halving or Newton iterations to find the
 root of incbet(a,b,x) - y = 0.

 ',
          'round' => 'round:  Round double to nearest or even integer valued double

SYNOPSIS:

 # double x, y, round();

 $y = round( $x );