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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, www.jacques-laporte.org/Volder_CORDIC.pdf) 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.

References

1. “The Secret of the Algorithms,” www.jacques-laporte.org/TheSecretOfTheAlgorithms.htm

2. Ray Andraka, “A survey of CORDIC algorithms for FPGA based computers,” www.fpga-guru.com/files/crdcsrvy.pdf

3. J.S. Walther, “A unified algorithm for elementary functions,” Spring Joint Computer Conf., 1971, proc., pp 379-385, www.jacques-laporte.org/Welther-Unified%20Algorithm.pdf

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