## The history of Calc

I'm taking some time off from cramming my KMD2004 project to write a review of Emacs 22 prerelease for Don Marti. It's a great excuse to look at all the cool new features I'd been taking for granted in my Emacs CVS.

I love the stories people tell through their code and their documentation! For example, take Calc mode. You'd expect it to be a simple desk calculator, right? No, it can do "arithmetic on rational numbers, complex numbers (rectangular and polar), error forms with standard deviations, open and closed intervals, vectors and matrices, dates and times, infinities, sets, quantities with units, and algebraic formulas." It has tons of other features, too.

How did a calculator get so big, the way all Emacs features seem to grow and grow and grow? Check out the History and Acknowledgements section of the info manual for Calc. Here's the story from David Gillespie in the manual:

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 doesn't have built-in floating point math, so it had to be simulated in software. In fact, Emacs integers will only comfortably fit six decimal digits or so—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; Francois 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; Robert J. Chassell, who suggested the Calc Tutorial and exercises; and Juha Sarlin, who first worked out how to split Calc into quickly-loading parts. Bob Weiner helped immensely with the Lucid Emacs port.

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.

I've had a lot of these two week projects. I wasn't supposed to get hooked on Planner. It was just supposed to be one of the components of my fourth-year undergrad project. It turned into a way of life and my main open source project for almost three years.

Most people look at Emacs and they see an editor with way, way, way too many features. How many people need to do in-line matrix calculations, anyway? I might never use it (then again, who knows?), but I think it's terrific that someone just sat down one day and put it in. When I look at Emacs, I see more than a text editor. I see a community of hackers and a tradition of tinkerers. It's awesome. =)

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History and Acknowledgements

Random Emacs symbol: enable-kinsoku - Variable: *Non-nil means enable "kinsoku" processing on filling paragraphs.