Division-Free Binary-to-Decimal Conversion

Cyril Bouvier 1 Paul Zimmermann 1
1 CARAMEL - Cryptology, Arithmetic: Hardware and Software
Inria Nancy - Grand Est, LORIA - ALGO - Department of Algorithms, Computation, Image and Geometry
Abstract : This article presents algorithms that convert multiple precision integer or floating-point numbers from radix $2$ to radix $10$ (or to any radix $b > 2$). Those algorithms, based on the ''scaled remainder tree'' technique, use multiplications instead of divisions in their critical part. Both quadratic and subquadratic algorithms are detailed, with proofs of correctness. Experimental results show that our implementation of those algorithms outperforms the GMP library by up to 50\%.
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Cyril Bouvier, Paul Zimmermann. Division-Free Binary-to-Decimal Conversion. IEEE Transactions on Computers, Institute of Electrical and Electronics Engineers, 2014, 63 (8), pp.1895-1901. ⟨10.1109/TC.2014.2315621⟩. ⟨hal-00864293v2⟩

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