Customer Reviews

The Art of Computer Programming, Volume 4, Fascicle 1: Bitwise Tricks & Techniques; Binary Decision Diagrams

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Much of Knuth's other works in his long running Art of Computer Programming series describe algorithms that might be useful by being implemented in high level languages like Fortran, C or java. (Though to be sure, he also offered MMIX as an assembler in which they could be done.)

In contrast, the first part of this book, on bitwise tricks, goes to the basics of all digital computing. It defines Boolean functions that operate directly on ones and zeros. It then goes on to extend these in various ways for arithmetic operations. How obvious and boring, you might think. Yet the book shows at even at such a low level, there are subtleties abounding.

Here, in terms of code implementation, some type of assembler can be the natural choice. But it could go deeper, into the silicon circuitry itself. Knuth points out possible applications in bitwise operations on long words. A SIMD approach, if you treat parallel operations on each bit as equivalent to having a small microprocessor dedicated to that bit. At this level, there may be prospects of new logic gate configurations, perhaps more efficiently run, inasmuch as they can keep more gates concurrently churning, instead of having many idle, as might be the case with current hardware.

Of course, semiconductor firms has spent billions on design, and all the obvious techniques for optimisation in that field must already be known. But how many of their engineers are in the habit of reading Knuth?

In this sense, this fascicle can be useful to VLSI designers.