Gamma Solution: An Application of Metrics to the Comparison of Complete Gamma Function Solution Algorithms

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The Gamma Function is a generalisation of the factorial for use with complex numbers. The plane of complex numbers subsumes fractions including transcendental numbers, some of which have especially elegant Gamma forms. The Gamma Function has a number of applications in advanced science including quantum physics, astrophysics and fluid dynamics An analytical and experimental study was undertaken to assess how theoretical and experimental code and performance metrics might assist the choice of published Complete Gamma Function ( CGF ) solution algorithms, or inform the development of new CGF methods. Accuracy, speed and component timing statistics were computed for thirteen methods or method variations, and new empirical metrics proposed. Empirical metrics and component time profiles disclosed significant algorithm properties and assisted coding optimisations. Halstead metrics did not apply, but code token ratios correlated with other CGF algorithm features. Further research could involve recently discovered Elliptic, Laplacian or Zeta Function avenues. Enjoy the work and I hope you find it useful as a starting point.

Extensive equations and diagrams are included, as well as program code in Visual Basic