1.6 History and Acknowledgments

Calc was originally started as a two-week project to occupy a lull in the author’s schedule. Basically, a friend asked if I remembered the value of ‘2^32’. I didn’t offhand, but I said, “that’s easy, just call up an xcalc.” Xcalc duly reported that the answer to our question was ‘4.294967e+09’—with no way to see the full ten digits even though we knew they were there in the program’s memory! I was so annoyed, I vowed to write a calculator of my own, once and for all.

I chose Emacs Lisp, a) because I had always been curious about it and b) because, being only a text editor extension language after all, Emacs Lisp would surely reach its limits long before the project got too far out of hand.

To make a long story short, Emacs Lisp turned out to be a distressingly solid implementation of Lisp, and the humble task of calculating turned out to be more open-ended than one might have expected.

Emacs Lisp didn’t have built-in floating point math (now it does), so this had to be simulated in software. In fact, Emacs integers would only comfortably fit six decimal digits or so (at the time)—not enough for a decent calculator. So I had to write my own high-precision integer code as well, and once I had this I figured that arbitrary-size integers were just as easy as large integers. Arbitrary floating-point precision was the logical next step. Also, since the large integer arithmetic was there anyway it seemed only fair to give the user direct access to it, which in turn made it practical to support fractions as well as floats. All these features inspired me to look around for other data types that might be worth having.

Around this time, my friend Rick Koshi showed me his nifty new HP-28 calculator. It allowed the user to manipulate formulas as well as numerical quantities, and it could also operate on matrices. I decided that these would be good for Calc to have, too. And once things had gone this far, I figured I might as well take a look at serious algebra systems for further ideas. Since these systems did far more than I could ever hope to implement, I decided to focus on rewrite rules and other programming features so that users could implement what they needed for themselves.

Rick complained that matrices were hard to read, so I put in code to format them in a 2D style. Once these routines were in place, Big mode was obligatory. Gee, what other language modes would be useful?

Scott Hemphill and Allen Knutson, two friends with a strong mathematical bent, contributed ideas and algorithms for a number of Calc features including modulo forms, primality testing, and float-to-fraction conversion.

Units were added at the eager insistence of Mass Sivilotti. Later, Ulrich Mueller at CERN and Przemek Klosowski at NIST provided invaluable expert assistance with the units table. As far as I can remember, the idea of using algebraic formulas and variables to represent units dates back to an ancient article in Byte magazine about muMath, an early algebra system for microcomputers.

Many people have contributed to Calc by reporting bugs and suggesting features, large and small. A few deserve special mention: Tim Peters, who helped develop the ideas that led to the selection commands, rewrite rules, and many other algebra features; François Pinard, who contributed an early prototype of the Calc Summary appendix as well as providing valuable suggestions in many other areas of Calc; Carl Witty, whose eagle eyes discovered many typographical and factual errors in the Calc manual; Tim Kay, who drove the development of Embedded mode; Ove Ewerlid, who made many suggestions relating to the algebra commands and contributed some code for polynomial operations; Randal Schwartz, who suggested the calc-eval function; Juha Sarlin, who first worked out how to split Calc into quickly-loading parts; Bob Weiner, who helped immensely with the Lucid Emacs port; and Robert J. Chassell, who suggested the Calc Tutorial and exercises as well as many other things.

Among the books used in the development of Calc were Knuth’s Art of Computer Programming (especially volume II, Seminumerical Algorithms); Numerical Recipes by Press, Flannery, Teukolsky, and Vetterling; Bevington’s Data Reduction and Error Analysis for the Physical Sciences; Concrete Mathematics by Graham, Knuth, and Patashnik; Steele’s Common Lisp, the Language; the CRC Standard Math Tables (William H. Beyer, ed.); and Abramowitz and Stegun’s venerable Handbook of Mathematical Functions. Also, of course, Calc could not have been written without the excellent GNU Emacs Lisp Reference Manual, by Bil Lewis and Dan LaLiberte.

Final thanks go to Richard Stallman, without whose fine implementations of the Emacs editor, language, and environment, Calc would have been finished in two weeks.