The RESIDUE_INT Software Package: Documentation
The Chinese Remainder Theorem and Object-Oriented Programming
Certain computations result in integer values that exceed the word size of conventional 32-bit computers. A package is being written in the C++ language to enable the programmer to use very large integers without altering existing code. If all calculations are done in residue arithmetic modulo a list of large relatively prime integers, the very large integer result can be reconstituted at the end by the Chinese Remainder Theorem. The capability of C++ to overload arithmetic operators is used to make the transition from integer type variables to RESIDUE_INT type variables transparent.
This work, "The Chinese Remainder Theorem and Object Oriented Programming" presented at both the Texas Section MAA Annual Meeting 1994 and the National Meeting of the MAA in 1994.
- The Overheads from this Talk crtoop2.doc (MS Word Document)
- The Overheads from this Talk crtoop2.doc.gz (GZip-ed MS Word Document)
- The Overheads from this Talk crtoop2.ps (PostScript) [not yet available]
- Unfortunately, looking back over these overheads, I find them rather lacking without the sound of the speaker's voice behind them. I strongly recommend that interested parties refer to Donald E. Knuth's "The Art of Computer Programming" Volume II. After all, this is where I started to learn about residue number systems, it has the clearest introduction and development of the subject, and is arguably the definitive reference on the subject of computational implementations of modular arithmetic. Knuth's explanations (at least on this subject) really do not need to be improved upon.
Davin M. Potts
davin@discontinuity.net