Analog Angle Article

Let us now praise famous. . . . algorithms

When you spend a lot of your time thinking analog thoughts, it's easy to neglect the importance of algorithms and numerical processing (however and wherever executed). What reminded me of this was the announcement a few months ago of the 35th anniversary of the legendary HP-35 scientific calculator (“Calculator longevity yields vital lessons,” click here).

One of the less-obvious developments which made the HP-35 practical was the COordinate Rotation Digital Computer (CORDIC) algorithm developed by Jack E. Volder in 1959 (“The Cordic Trigonometric Computing Technique”, IEEE Transactions on Electronic Computers, Sept. 1959, for use in digital computer of the Convair B-58 bomber navigation system that was replacing an analog computer (yes, folks, analog circuits can be very effective computers!).

He showed how to use just a shifter and adder to solve trigonometric and transcendental functions, instead of a dedicated multiplier, and with quick, efficient convergence. Although Volder's work built on thousands of years of numerical analysis, a large part of the CORDIC credit is his. In addition to the original CORDIC paper, References 1 through 3 are stimulating and worth reading; there are many other excellent and readable papers available online.

The interplay between analog input/output (I/O) channels and the digital processors which transform the raw data into intelligent insight has been a boon to the industry and analog markets. Well-designed, innovative algorithms for analysis, encoding, encryption, and control are a vital to driving the analog world.


1. “The Secret of the Algorithms,”

2. Ray Andraka, “A survey of CORDIC algorithms for FPGA based computers,”

3. J.S. Walther, “A unified algorithm for elementary functions,” Spring Joint Computer Conf., 1971, proc., pp 379-385,

-x x x-

0 comments on “Let us now praise famous. . . . algorithms

Leave a Reply

This site uses Akismet to reduce spam. Learn how your comment data is processed.