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Asked: 2026-05-26T09:21:32+00:00

I am trying to do modular exponentiation of integers with a very large modulus

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I am trying to do modular exponentiation of integers with a very large modulus by repetitive squaring (the power is always a power of 2 in my case, so I believe this is the most efficient way). Thanks to a nice property of my modulus, computing remainder is cheap; the hard part is multiplication.

Currently I run GMP on Intel Core 2 Quad. I would like to make efficient use of the four cores of the processor, but GMP does not scale on SMP environments, so I am looking for a substitute arbitrary-precision arithmetic library. I have found some libraries for parallel computation on matrices, but what I really need is a library for integers.

Does what I am looking for exist?

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  1. Editorial Team

    The answer is yes, multi-threaded arbitrary-precision libraries do exist. But I’m not aware of a single one that is actually public. (with comparable speed to GMP)

    For example, the arbitrary-precision libraries that are used in the Pi-computing programs, TachusPi and y-cruncher are capable of multi-threaded arithmetic on large numbers.

    However, both libraries are closed source and are not available to the public for use.

    Affiliation Disclosure: I’m the author of y-cruncher. So I have written one of such multi-threaded arbitrary-precision libraries myself.

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