Workshop on computer arithmetic

Original version: Tue Nov 5 08:13:32 2019 Updates: Mon Nov 11 05:54:50 2019 Wed Nov 13 16:47:32 2019

Attendees received a folder with several documents. For copyright reasons, only the first three can be placed here for free download. Links are provided to commercial sources for the remaining ones.

Computer Arithmetic — Perils, Pitfalls, and Practices. This is a chapter that forms the basis for material in a forthcoming book by authors in the GNU Project on the C programming language. It is available here with their permission.
Highlights of Computer Arithmetic. This document is a supplement to the first one, and takes the reader into applications of floating-point arithmetic, and issues of computer performance.
Manual pages for hoc (high-order calculator). This tool provides convenient interactive access to features of IEEE 754 floating-point arithmetic in 32-, 64-, 80, and 128-bit binary arithmetic, and in 32-, 64-, and 128-bit decimal arithmetic.
Appendix D: Decimal arithmetic from the author's The Mathematical-Function Computation Handbook: Programming Using the MathCW Portable Software Library.
Appendix G: Go interface. This appendix was written after the book was published; it is still in development, but a recent snapshot is available here.
Appendix H: Historical floating-point architectures.
Appendix I: Integer arithmetic.
Jerome T. Coonen's Underflow and the Denormalized Numbers, Computer 14(3), 75--87, March 1981.

Participants were told about the various IEEE 754 floating-point standards. Here is a link to the latest one. They were also recommended to read David Goldberg's What Every Computer Scientist Should Know About Floating-Point Arithmetic, ACM Computing Surveys 23(1) 5--48 March 1991, with corrections from 23(3) 413 September 1991. The latter is regrettably not available at the publisher's Web site, but I have a journal subscription, and personal archives of all issues of that journal. A PDF file of the corrections page is available here.

David Goldberg has also written a longer document on computer arithmetic with more details of low-level hardware implementation; it appears as appendices in successive editions of John Hennessey and David Patterson's famous book series Computer Architecture: a Quantitative Approach. Goldberg's Appendix J: Computer Arithmetic from the fifth edition in 2012 is available here. The sixth edition of the book appeared in 2019, and its appendices are bundled in a single InfoZIP file. The material in its Appendix J appears to be largely similar to that in the previous book edition.

I maintain an extensive, and frequently updated, bibliography on floating-point and integer arithmetic. It is freely available in several formats: BibTeX, HTML (similar appearance, but with live hyperlinks), and as an SQLite3 database. If you are unfamiliar with SQL (Structured Query Language) for database access, you can find many examples in the bibsql paper available at a link from this site.