When I first got a summer job at MIT's Project MAC almost 30 years ago, I was delighted to be able to work with the DEC PDP-10 computer, which was more fun to program in assembly language than any other computer, bar none, because of its rich yet tractable set of instructions for performing bit tests, bit masking, field manipulation, and operations on integers. Though the PDP-10 has not been manufactured for quite some years, there remains a thriving cult of enthusiasts who keep old PDP-10 hardware running and who run old PDP-10 software梕ntire operating systems and their applications梑y using personal computers to simulate the PDP-10 instruction set. They even write new software; there is now at least one Web site whose pages are served up by a simulated PDP-10. (Come on, stop laughing梚t's no sillier than keeping antique cars running.)

I also enjoyed, in that summer of 1972, reading a brand-new MIT research memo called HAKMEM, a bizarre and eclectic potpourri of technical trivia.[1] The subject matter ranged from electrical circuits to number theory, but what intrigued me most was its small catalog of ingenious little programming tricks. Each such gem would typically describe some plausible yet unusual operation on integers or bit strings (such as counting the 1-bits in a word) that could easily be programmed using either a longish fixed sequence of machine instructions or a loop, and then show how the same thing might be done much more cleverly, using just four or three or two carefully chosen instructions whose interactions are not at all obvious until explained or fathomed. For me, devouring these little programming nuggets was like eating peanuts, or rather bonbons桰 just couldn't stop梐nd there was a certain richness to them, a certain intellectual depth, elegance, even poetry.

[1] Why "HAKMEM"? Short for "hacks memo"; one 36-bit PDP-10 word could hold six 6-bit characters, so a lot of the names PDP-10 hackers worked with were limited to six characters. We were used to glancing at a six-character abbreviated name and instantly decoding the contractions. So naming the memo "HAKMEM" made sense at the time梐t least to the hackers.

"Surely," I thought, "there must be more of these," and indeed over the years I collected, and in some cases discovered, a few more. "There ought to be a book of them."

I was genuinely thrilled when I saw Hank Warren's manuscript. He has systematically collected these little programming tricks, organized them thematically, and explained them clearly. While some of them may be described in terms of machine instructions, this is not a book only for assembly language programmers. The subject matter is basic structural relationships among integers and bit strings in a computer and efficient techniques for performing useful operations on them.

These techniques are just as useful in the C or Java programming languages as they are in assembly language.

Many books on algorithms and data structures teach complicated techniques for sorting and searching, for maintaining hash tables and binary trees, for dealing with records and pointers. They overlook what can be done with very tiny pieces of data梑its and arrays of bits. It is amazing what can be done with just binary addition and subtraction and maybe some bitwise operations; the fact that the carry chain allows a single bit to affect all the bits to its left makes addition a peculiarly powerful data manipulation operation in ways that are not widely appreciated.

Yes, there ought to be a book about these techniques. Now it is in your hands, and it's terrific. If you write optimizing compilers or high-performance code, you must read this book. You otherwise might not use this bag of tricks every single day梑ut if you find yourself stuck in some situation where you apparently need to loop over the bits in a word, or to perform some operation on integers and it just seems harder to code than it ought, or you really need the inner loop of some integer or bit-fiddly computation to run twice as fast, then this is the place to look. Or maybe you'll just find yourself reading it straight through out of sheer pleasure.

Guy L. Steele, Jr.
Burlington, Massachusetts
April 2002