Multiplication Algorithm Based on Collatz Function

Abstract

This article presents a new multiplication algorithm based on the Collatz function. Assuming the validity of the Collatz conjecture, the time complexity of multiplying two n-digit numbers is O(kn), where the k is the number of odd steps in the Collatz trajectory of the first multiplicand. Most likely, the algorithm is only of theoretical interest.

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Acknowledgments

Computational resources were supplied by the project “e-Infrastruktura CZ” (e-INFRA LM2018140) provided within the program Projects of Large Research, Development and Innovations Infrastructures. This work was supported by The Ministry of Education, Youth and Sports from the National Programme of Sustainability (NPU II) project IT4Innovations excellence in science – LQ1602 and by the IT4Innovations infrastructure which is supported from the Large Infrastructures for Research, Experimental Development and Innovations project IT4Innovations National Supercomputing Center – LM2015070.

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Correspondence to David Barina.

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Barina, D. Multiplication Algorithm Based on Collatz Function. Theory Comput Syst 64, 1331–1337 (2020). https://doi.org/10.1007/s00224-020-09986-5

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Keywords

  • Multiplication algorithm
  • Division algorithm
  • Computer arithmetic
  • Collatz conjecture