Contributors

Borrowed Code

The Internet is a great resource, especially for software developers who need expert help in the guise of well-crafted code and useful ideas. This project is no exception having borrowed with great thanks from the following sources:

• GNU Scientific Library for the factorial/binomial functions for both Real and Complex numbers as well as matrix inverse/matrix divide functions (using Singular Value Decomposition) and the Determinant Operator (e.g., -.×).
• Bob Jenkins' Hash routines were used in the Hash table.
• The Wine library of Windows Emulation routines contributed an implementation of the Windows Edit Control when I couldn't get the one in Windows to do what I wanted.
• David M. Gay's Numeric input/output conversion routines were invaluable for full numeric precision conversion (good to the last ULP!).
• Bob Bernecky's APEX project contributed many test cases of APL code through which numerous bugs in NARS were found.
• Nicolas Devillard's iniparser code was an invaluable resource after I found that the Win32 API has an undocumented limit on the size of a string returned by the GetPrivateProfileString API.
• Jason Papadopoulos' excellent msieve project provided the necessary code to factor integers of arbitrary precision.
• The MPC team contributed their Multiple Precision Floating Point Complex Numbers code.
• The MPIR team contributed their Multiple Precision Integers and Rationals code.
• The MPFR team contributed their Multiple Precision Floating-Point Reliable Library code.
• The GMP ECM team contributed their Elliptic Curve Method for Integer Factorization code.
• The FLINT team contributed their Fast Library for Number Theory code.
• The ARB team contributed their Arbitrary Precision Ball Arithmetic code.
• Mattias Andrée contributed his implementation of Kuhn's Hungarian Algorithm.
• Dave Barber contributed his implementation of A Quaternion Postfix Calculator from which I extracted numerous algorithms of the elementary functions on Quaternions, all written in Javascript. This allowed me to generalize them, trivially, to the other Hypercomplex numbers.
• Paul Godfrey contributed his explanation of how to calculate the coefficients of the Lanczos approximation to the Gamma function to an arbitrary degree of precision. This allowed me to implement the Factorial and Binomial primitive functions on multiple-precision Hypercomplex arguments.
• Donald E. Knuth contributed many excellent Combinatorial Algorithms to the Combinatorial Operator through his "The Art of Computer Programming", Volume 4A, "Combinatorial Algorithms", Addison Wesley, 2011.
• The user who goes by the name urrfinjuss contributed the MPFFT library.
• Laurent Fousse contributed his Numerical Integration code as documented here.

Borrowed Ideas

• The Hash Table and Symbol Table code was created using the ideas in "Linear hashing: A new tool for file and table addressing", by Witold Litwin, Proc. 6th Conference on Very Large Databases, pp. 212-223, 1980.
• The LALR(n) Parser is based upon The Syntax of APL: An Old Approach Revisited" by Jean Jacques Giardot & Florence Rollin, ACM SIGAPL APL87 Conference Proceedings, pp. 441-449.
• The Syntax Analyzer (which replaced the above LALR(n) Parser) is based upon the paper "APL two by two-syntax analysis by pairwise reduction", Gerth, John A. and Bunda, John D., in ACM SIGAPL APL Quote Quad 06/1984; 14(4):85-94.
• The algorithm for the character grade functions was taken from "Sorting - A New/Old Problem" by Howard J. Smith, Jr., ACM SIGAPL APL79 Conference Proceedings, pp. 123-127.
• The algorithm for the roll function was taken from "How the Roll Function Works" by E. E. McDonnell, APL Quote Quad, Vol. 8, Number 3, p. 42.
• The algorithm for the deal function was taken from "APLGOL, an Experimental Structured Programming Language" by R. A. Kelley, IBM Journal of Research and Delvelopment, January 1973, pp. 69-73.
• The algorithm for the Fast Boolean functions was taken from "The Caret Functions" by E. E. McDonnell, Proceedings of The Sixth International Conference on APL, 1974, pp. 316-323.
• The idea for Array Predicates was taken from Bob Bernecky's APEX project.
• The idea for Point Notation was taken from the designers of J.
• The idea for Trains was taken from the designers of J.
• The idea for grouping of rows in width-limited output came from Larry Breed in a private communication sometime in the early 1980s.
• The algorithm for Numerical Differentiation came from a series of papers by Ishtiaq Rasool Khan and Ryoji Ohba, principally in this paper.
• This project benefited greatly by discussions (across several decades) with some of the many great APL implementors and language designers who went before me. To name but a few: Ken Iverson, Larry Breed, Gene McDonnell, Jim Brown, Bob Bernecky, Jim Ryan, John Scholes, etc.

Font

Phil Chastney built a special version of his SImPL font, adding the infinity symbol as well as making other changes, and then graciously allowed it to be bundled with NARS2000. Note that this font is licensed for distribution with NARS2000 only.

Contributors

• Dave Durgee was especially helpful in testing the early beta release of NARS, particularly with PC/3270 translations.
• Paul Robinson greatly improved the Wiki with numerous excellent design ideas.
• David A. Rabenhorst has been and continues to be extremely helpful contributing both design ideas as well as a wealth of bug reports. Excellent job, Dave!

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