I've recently started development on a continued fraction based exact arithmetic computational package. This is work based on Bill Gosper's HACMEM algorithm and Peter Potts' Mobius transforms with significant modifications. These algorithms have some remarkable properties and can be made much more efficient. Some enhancements I've developed include the ability to detect patterns which define exact solutions when they exist and a method to automatically compose operations (reducing operation counts significantly).(adsbygoogle = window.adsbygoogle || []).push({});

While these algorithms have been around since the early 70's (HACMEM was written in 1972), they don't seem to be commonly implemented commercially. Are these algorithms used in proprietary software (e.g. Mathematica )? I've seen some simple implementations, but most fail to address some of the issues Bill identified (e.g. non-termination when computing the square of a root).

I intend to release a version of this system to the public domain at some point, but was curious about similar systems that might exist. I'm also interested in applying these algorithms with complex numbers (which should be reasonably straightforward), and wondered if anyone had done this.

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# Exact Arithmetic using Continued Fractions

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