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Fast vector arithmetic over \(\mathbb{F}_3\). (English) Zbl 1277.65121

The author discusses a new implementation of a fast vector arithmetic over the finite field \(\mathbb F_3\) based on inherent parallel 64-bit operations of modern CPUs. The vector operations are parallelized using a special trick, where every element of the field can be represented as a pair of bits. Moreover, the field operations can be emulated as combinations of standard machine instructions. Numerical tests show that the new implementation can be 10 times faster than the standard method using modular arithmetic on arrays of bytes.

MSC:

65Y04 Numerical algorithms for computer arithmetic, etc.
12E30 Field arithmetic
65Y05 Parallel numerical computation
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Full Text: Euclid