private static void Main()
//****************************************************************************80
//
// Purpose:
//
// MAIN is the main program for TOMS743_TEST.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 June 2014
//
// Author:
//
// Original FORTRAN77 version by Andrew Barry, S. J. Barry,
// Patricia Culligan-Hensley.
// C++ version by John Burkardt.
//
// Reference:
//
// Andrew Barry, S. J. Barry, Patricia Culligan-Hensley,
// Algorithm 743: WAPR - A Fortran routine for calculating real
// values of the W-function,
// ACM Transactions on Mathematical Software,
// Volume 21, Number 2, June 1995, pages 172-181.
//
{
Console.WriteLine("");
Console.WriteLine("TOMS743_TEST");
Console.WriteLine(" Test the TOMS743 library.");
int nbits = NBITS.nbits_compute();
Console.WriteLine("");
Console.WriteLine(" Number of bits in mantissa - 1 = " + nbits + "");
test01(nbits);
const double dx = +1.0E-09;
int n = 10;
test02(nbits, dx, n);
const double xmin = 0.0;
const double xmax = 1.0E+20;
n = 20;
test03(nbits, xmin, xmax, n);
Console.WriteLine("");
Console.WriteLine("TOMS743_TEST");
Console.WriteLine(" Normal end of execution.");
Console.WriteLine("");
}
public static double wapr(ref WAPRData data, double x, int nb, ref int nerror, int l)
//****************************************************************************80
//
// WAPR approximates the W function.
//
// Discussion:
//
// The call will fail if the input value X is out of range.
// The range requirement for the upper branch is:
// -Math.Exp(-1) <= X.
// The range requirement for the lower branch is:
// -Math.Exp(-1) < X < 0.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 June 2014
//
// Author:
//
// Original FORTRAN77 version by Andrew Barry, S. J. Barry,
// Patricia Culligan-Hensley.
// C++ version by John Burkardt.
//
// Reference:
//
// Andrew Barry, S. J. Barry, Patricia Culligan-Hensley,
// Algorithm 743: WAPR - A Fortran routine for calculating real
// values of the W-function,
// ACM Transactions on Mathematical Software,
// Volume 21, Number 2, June 1995, pages 172-181.
//
// Parameters:
//
// Input, double X, the argument.
//
// Input, int NB, indicates the desired branch.
// * 0, the upper branch;
// * nonzero, the lower branch.
//
// Output, int &NERROR, the error flag.
// * 0, successful call.
// * 1, failure, the input X is out of range.
//
// Input, int L, indicates the interpretation of X.
// * 1, X is actually the offset from -(Math.Exp-1), so compute W(X-Math.Exp(-1)).
// * not 1, X is the argument; compute W(X);
//
// Output, double WAPR, the approximate value of W(X).
//
{
double delx;
int i;
double reta;
double xx;
double zl;
double value = 0.0;
nerror = 0;
switch (data.init)
{
case 0:
{
data.init = 1;
data.nbits = NBITS.nbits_compute();
data.niter = data.nbits switch
{
>= 56 => 2,
_ => data.niter
};
//
// Various mathematical constants.
//
data.em = -Math.Exp(-1.0);
data.em9 = -Math.Exp(-9.0);
data.c13 = 1.0 / 3.0;
data.c23 = 2.0 * data.c13;
data.em2 = 2.0 / data.em;
data.d12 = -data.em2;
data.tb = Math.Pow(0.5, data.nbits);
data.x0 = Math.Pow(data.tb, 1.0 / 6.0) * 0.5;
data.x1 = (1.0 - 17.0 * Math.Pow(data.tb, 2.0 / 7.0)) * data.em;
data.an3 = 8.0 / 3.0;
data.an4 = 135.0 / 83.0;
data.an5 = 166.0 / 39.0;
data.an6 = 3167.0 / 3549.0;
data.s2 = Math.Sqrt(2.0);
data.s21 = 2.0 * data.s2 - 3.0;
data.s22 = 4.0 - 3.0 * data.s2;
data.s23 = data.s2 - 2.0;
break;
}
public static double bisect(ref BisectData data, double xx, int nb, ref int ner, int l)
//****************************************************************************80
//
// Purpose:
//
// BISECT approximates the W function using bisection.
//
// Discussion:
//
// The parameter TOL, which determines the accuracy of the bisection
// method, is calculated using NBITS (assuming the final bit is lost
// due to rounding error).
//
// N0 is the maximum number of iterations used in the bisection
// method.
//
// For XX close to 0 for Wp, the exponential approximation is used.
// The approximation is exact to O(XX^8) so, depending on the value
// of NBITS, the range of application of this formula varies. Outside
// this range, the usual bisection method is used.
//
// Licensing:
//
// This code is distributed under the GNU LGPL license.
//
// Modified:
//
// 17 June 2014
//
// Author:
//
// Original FORTRAN77 version by Andrew Barry, S. J. Barry,
// Patricia Culligan-Hensley.
// C++ version by John Burkardt.
//
// Reference:
//
// Andrew Barry, S. J. Barry, Patricia Culligan-Hensley,
// Algorithm 743: WAPR - A Fortran routine for calculating real
// values of the W-function,
// ACM Transactions on Mathematical Software,
// Volume 21, Number 2, June 1995, pages 172-181.
//
// Parameters:
//
// Input, double XX, the argument.
//
// Input, int NB, indicates the branch of the W function.
// 0, the upper branch;
// nonzero, the lower branch.
//
// Output, int &NER, the error flag.
// 0, success;
// 1, the routine did not converge. Perhaps reduce NBITS and try again.
//
// Input, int L, the offset indicator.
// 1, XX represents the offset of the argument from -Math.Exp(-1).
// not 1, XX is the actual argument.
//
// Output, double BISECT, the value of W(X), as determined
//
{
double d;
double f;
double fd;
int i;
const int n0 = 500;
double r;
double tol;
double u;
double value = 0.0;
ner = 0;
data.nbits = data.nbits switch
{
0 => NBITS.nbits_compute(),
_ => data.nbits
};
double x = l switch
{
1 => xx - Math.Exp(-1.0),
_ => xx
};
switch (nb)
{
case 0:
{
double test = 1.0 / Math.Pow(Math.Pow(2.0, data.nbits), 1.0 / 7.0);
if (Math.Abs(x) < test)
{
value = x
* Math.Exp(-x
* Math.Exp(-x
* Math.Exp(-x
* Math.Exp(-x
* Math.Exp(-x
* Math.Exp(-x))))));
return(value);
}
u = Crude.crude(ref data.data, x, nb) + 1.0E-03;
tol = Math.Abs(u) / Math.Pow(2.0, data.nbits);
d = Math.Max(u - 2.0E-03, -1.0);
for (i = 1; i <= n0; i++)
{
r = 0.5 * (u - d);
value = d + r;
//
// Find root using w*Math.Exp(w)-x to avoid ln(0) error.
//
if (x < Math.Exp(1.0))
{
f = value * Math.Exp(value) - x;
fd = d * Math.Exp(d) - x;
}
//
// Find root using ln(w/x)+w to avoid overflow error.
//
else
{
f = Math.Log(value / x) + value;
fd = Math.Log(d / x) + d;
}
switch (f)
{
case 0.0:
return(value);
}
if (Math.Abs(r) <= tol)
{
return(value);
}
switch (fd * f)
{
case > 0.0:
d = value;
break;
default:
u = value;
break;
}
}
break;
}
default:
{
d = Crude.crude(ref data.data, x, nb) - 1.0E-03;
u = Math.Min(d + 2.0E-03, -1.0);
tol = Math.Abs(u) / Math.Pow(2.0, data.nbits);
for (i = 1; i <= n0; i++)
{
r = 0.5 * (u - d);
value = d + r;
f = value * Math.Exp(value) - x;
switch (f)
{
case 0.0:
return(value);
}
if (Math.Abs(r) <= tol)
{
return(value);
}
fd = d * Math.Exp(d) - x;
switch (fd * f)
{
case > 0.0:
d = value;
break;
default:
u = value;
break;
}
}
break;
}
}
//
// The iteration did not converge.
//
ner = 1;
return(value);
}
}