Fastest way to calculate a 128-bit integer modulo a 64-bit integer?

You can use the division version of Russian Peasant Multiplication .

Perhaps you're looking for a finished program, but the basic algorithms for multi-precision arithmetic can be found in Knuth's Art of Computer Programming, Volume 2. You can find the division algorithm described online here. The algorithms deal with arbitrary multi-precision arithmetic, and so are more general than you need, but you should be able to simplify them for 128 bit arithmetic done on 64- or 32-bit digits.

Be prepared for a reasonable amount of work (a) understanding the algorithm, and (b) converting it to C or assembler.

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