Systems, methods, and computer program products for parallelizing large number arithmetic

A system comprising:

• a multi-core processor;
• and
• a memory device in communication with said processor, wherein said memory device stores a plurality of processing instructions configured to direct said processor to cause the following:
• organizing a binary representation of a first number as a first number vector having a number of elements;
• organizing a binary representation of a second number as a number vector having the same number of elements as the first number vector;
• adding each element of the first number vector with a corresponding element of the second number vector, where the additions are performed in parallel, and storing each sum into a respective element of a results vector having the same number of elements as the first number vector;
• packing any resulting overflow bits, whether 0 or 1, into an overflow variable;
• left shifting the overflow variable bitwise;
• adding each element of the results vector with a corresponding bit of the overflow variable, storing each result into a corresponding element of the results vector and storing any resulting overflow bits into the overflow variable;
• and
• if the overflow variable is nonzero, repeating said left shift and said adding of each element of the results vector with a corresponding bit of the overflow variable.

A computer program product including non-transitory computer readable media having computer program logic stored therein, the computer program logic comprising:

• logic to cause a multi-core processor to organize a binary representation of a first number as a number vector having a number of elements;
• logic to cause the processor to organize a binary representation of a second number as a number vector having the same number of elements as the first number vector;
• logic to cause the processor to add each element of the first number vector with a corresponding element of the second number vector, where the additions are performed in parallel, and storing each sum into a respective element of a results vector having the same number of elements as the first number vector;
• logic to cause the processor to pack any resulting overflow bits, whether 0 or 1, into an overflow variable;
• logic to cause the processor to left shift the integer variable bitwise;
• logic to cause the processor to add each element of the results vector with a corresponding bit of the overflow variable, store each result into the corresponding element of the results vector, and store any resulting overflow bits into the overflow variable;
• and
• logic to cause the processor to repeat said left shift and said adding of each element of the results vector with a corresponding bit of the overflow variable, if the overflow variable is nonzero.

A system comprising:

• a multi-core processor;
• and
• a memory device in communication with said processor, wherein said memory device stores a plurality of processing instructions configured to direct said processor to cause the following,
• organizing the binary representation of a first number as a first number vector having a number of elements;
• organizing the binary representation of a second number as a second number vector having the same number of elements as the first number vector;
• comparing the value of each element of the first number vector with a corresponding value of a corresponding element of the second number vector, where the comparisons are performed in parallel;
• storing results of the comparisons into first and second comparison vectors each having the same number of elements as the first number vector, wherein for each comparison, if an element of the first number vector is greater than the corresponding element of the second number vector, the corresponding element of the first comparison vector is set to 1, and if the element of the first number vector is less than the corresponding element of the second number vector, the corresponding element of the second comparison vector is set to 1;
• and
• determining which of the first and second numbers is greater by treating the first and second comparison vectors as respective first and second integers, and comparing the values of the first and second integers.