Correspondence between SpecialFunctions library names and GSL names

An example code fragment using the ZOOM SpecialFunctions wrappers around the GNU Scientific Library (aka GSL) looks like

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			.
	#include "SpecialFunctions/Bessel.h"
			.
			.
     // Compute J3(2.5) two different ways and compare

	double J3One = Bessel::Jn( 3, 2.5 );
	Dpair J3Pair = Bessel::JnErr( 3, -2.5 );
	double J3Two = J3Pair.first;
	double J3Err = J3Pair.second;
	if( abs(J3One-J3Two) > J3Err )  cerr << "Bad news, Bubba!" << endl;
			.
			.

The non-native return types shown here and in the tables below are all defined through typedef declarations in the relevant header files. For the record, they are also given here,

• typedef std::vector<double> Dvector;
• typedef std::pair<double,double> Dpair;
• typedef std::complex<double> Dcomplex;
• typedef std::pair<Dcomplex,Dcomplex> Cpair;

The GSL library makes heavy use of a two-member struct gsl_sf_result such that the first member is the numerical result and the second is the estimated error for that result, when requested. We have uniformly replaced that usage in the following way. When no error estimate is requested, the return value is either a simple double or a Dcomplex, as appropriate. When an error estimate is requested, we return a Dpair or, in the case of a complex result, a Cpair where the first member of the pair is the result and the second is the estimated error.

Note that the tables do not show return types for any of the GSL functions. In standard C fashion, the GSL functions all return an integer status code with a zero value to indicate success and something non-zero to indicate one of a number of possible error conditions as described in the GSL Reference Manual. The SpecialFunctions wrappers intercept the GSL error returns and turn them into ZMExceptions of varying severity levels. The user can select any of the several ZMException handlers or supply one of his/her own to deal with these error returns in the same way as any other ZMexception and does not need to build up special code to deal with the specifics of the GSL design. Note also that, except for the Chebyshev class, all our wrappers have been implemented in the form of static methods. In fact, rather than define classes, we have used structs instead. Consequently, there are no constructors, no destructors and no member data. There is nothing to instantiate and the methods are uniformly invoked as shown in the tables without reference to any object.

With this list of correspondences, the user can refer to the existing GNU Scientific Library Reference Manual (a PostScript file in the doc subdirectory of the ZOOM SpecialFunctions package) for most of the operational details. In large measure, this relieves us of the need to duplicate existing documentation and relieves the user of having to cope with two manuals that inevitably get out of synch with each other.

It is only fair to emphasize that the whole GSL is much larger than the portion we have wrapped here. The goal of this package was limited to making the set of special functions included in the GSL available to the C++ programmer. As it stands now, this package is based on what the GSL developers call release 0.5++. It is clear that GSL is a "work-in-progress." For instance, there are functions in various implementation files with no corresponding prototype in the associated header file and vice versa. All such anomalies have been excluded from the SpecialFunctions package at the cost of a small loss of functionality.

Some portions of this library, notably Exponential, IntegerPowers and Trigonometry are redundant in that the standard library is supposed to provide all that. They are present in the GSL partly to cover those cases where the standard library is deficient and, as noted in the GSL manual, to provide uniform semantics across platforms. For the most part, we have retained all that.

For the file Airy.h

For the file Bessel.h

For the file ClausenIntegral.h

For the file Coulomb.h

For the file DawsonIntegral.h

For the file DebyeIntegral.h

For for file DiLogarithm.h

For the file EllipticIntegrals.h

For the file ErrorFunction.h

For the file ExpIntegrals.h

From file Exponential.h

For the file FermiDirac.h

For the file Gamma.h

For the file Gegenbauer.h

For the file HyperGeometric.h

For the file IntegerPowers.h

For the file JacobiElliptics.h

For the file Laguerre.h

For the file Legendre.h

For the file Logarithm.h

For the file PolyGamma.h

For the file Synchrotron.h

For the file Transport.h

For the file Trigonometry.h

For the file Wigner.h

For the file Zeta.h