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Replacing Square Roots by Pythagorean Sums

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2 Author(s)
Moler, C. ; Department of Computer Science, University of New Mexico, Albuquerque, New Mexico 87131, USA ; Morrison, Donald

An algorithm is presented for computing a “Pythagorean sum” a ⊕ b = √(a2 + b2) directly from a and b without computing their squares or taking a square root. No destructive floating point overflows or underflows are possible. The algorithm can be extended to compute the Euclidean norm of a vector. The resulting subroutine is short, portable, robust, and accurate, but not as efficient as some other possibilities. The algorithm is particularly attractive for computers where space and reliability are more important than speed.

Note: The Institute of Electrical and Electronics Engineers, Incorporated is distributing this Article with permission of the International Business Machines Corporation (IBM) who is the exclusive owner. The recipient of this Article may not assign, sublicense, lease, rent or otherwise transfer, reproduce, prepare derivative works, publicly display or perform, or distribute the Article.  

Published in:

IBM Journal of Research and Development  (Volume:27 ,  Issue: 6 )