Systems and methods for efficient fixed-base multi-precision exponentiation
First Claim
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1. A method, comprising:
- determining, via a processor, that a base number has a size that exceeds a size threshold, wherein the size threshold is greater than 64 bits; and
applying, via the processor, a multi-precision exponentiation algorithm to the base number, the multi-precision exponentiation algorithm comprising a pre-generated lookup table used to perform calculations on the base number, the pre-generated lookup table comprising pre-calculated exponentiated values of the base number, wherein the pre-generated lookup table is stored in a memory, the memory being coupled to the processor;
wherein an exponent size parameter of each of the pre-calculated exponentiated values in the pre-generated lookup table is selected by the processor based on a size limitation of a memory portion dedicated in the memory to the multi-precision exponentiation algorithm to prevent the pre-generated lookup table from growing to a size at which the memory portion dedicated in the memory to the multi-precision exponentiation algorithm is exhausted.
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Abstract
Systems and methods for efficient fixed-base multi-precision exponentiation are disclosed herein. An example method includes applying a multi-precision exponentiation algorithm to a base number, the multi-precision exponentiation algorithm comprises a pre-generated lookup table used to perform calculations on the base number, the pre-generated lookup table comprising pre-calculated exponentiated values of the base number.
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Citations
12 Claims
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1. A method, comprising:
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determining, via a processor, that a base number has a size that exceeds a size threshold, wherein the size threshold is greater than 64 bits; and applying, via the processor, a multi-precision exponentiation algorithm to the base number, the multi-precision exponentiation algorithm comprising a pre-generated lookup table used to perform calculations on the base number, the pre-generated lookup table comprising pre-calculated exponentiated values of the base number, wherein the pre-generated lookup table is stored in a memory, the memory being coupled to the processor; wherein an exponent size parameter of each of the pre-calculated exponentiated values in the pre-generated lookup table is selected by the processor based on a size limitation of a memory portion dedicated in the memory to the multi-precision exponentiation algorithm to prevent the pre-generated lookup table from growing to a size at which the memory portion dedicated in the memory to the multi-precision exponentiation algorithm is exhausted. - View Dependent Claims (2, 3, 4, 5, 6, 7)
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8. A system, comprising:
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a processor; and a memory for storing executable instructions, the memory being coupled to the processor, the processor executing the instructions to; determine if a time required for using a multi-precision exponentiation algorithm to exponentiate a base number is less than a time required to perform exponentiation of the base number directly using exponents; apply a multi-precision exponentiation algorithm to the base number, wherein the multi-precision exponentiation algorithm comprises a pre-generated lookup table used to perform calculations on the base number, the pre-generated lookup table comprising pre-calculated exponentiated values of the base number, wherein the pre-generated lookup table is stored in the memory; wherein an exponent size parameter of each of the pre-calculated exponentiated values in the pre-generated lookup table is selected by the processor based on a size limitation of a memory portion dedicated in the memory to the multi-precision exponentiation algorithm to prevent the pre-generated lookup table from growing to a size at which the memory portion dedicated in the memory to the multi-precision exponentiation algorithm is exhausted; and return a calculated value for the base number. - View Dependent Claims (9, 10, 11, 12)
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Specification