Applications of and techniques for quickly computing a modulo operation by a Mersenne or a Fermat number

A modulo operation generator, comprising:

• an accumulation circuit that:
• performs a first set of summations on an input value to generate a first sum;
• a lookup and correction circuit that:
• accesses a correction value associated with a first portion of the first sum, and
• performs a second set of summations on the correction value and a second portion of the first sum to generate a second sum;
• and
• a test and correct circuit that:
• generates a result of a modulo operation based on the second sum.

A system, comprising:

• a processor that transmits a memory address and a data value to a memory management unit (MMU);
• a cache memory that comprises a plurality of cache memory slices;
• and
• the MMU that:
• receives the memory address and the data value from the processor,
• performs a first set of summations on the memory address to generate a first sum,
• accesses a correction value associated with a first portion of the first sum,
• performs a second set of summations on the correction value and a second portion of the first sum to generate a second sum,
• generates a result of a modulo operation based on the second sum, wherein the result of the modulo operation identifies a first cache memory slice in the plurality of cache memory slices;
• and
• stores the data value in the first cache memory slice.