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We demonstrate a multiplication method based on numbers represented as set ofpolynomial radix 2 indices stored as an integer list. The 'polynomial integerindex multiplication' method is a set of algorithms implemented in python code.We demonstrate the method to be faster than both the Number Theoretic Transform(NTT) and Karatsuba for multiplication within a certain bit range. Alsoimplemented in python code for comparison purposes with the polynomial radix 2integer method. We demonstrate that it is possible to express any integer orreal number as a list of integer indices, representing a finite series in basetwo. The finite series of integer index representation of a number can then bestored and distributed across multiple CPUs / GPUs. We show that operations ofaddition and multiplication can be applied as two's complement additionsoperating on the index integer representations and can be fully distributedacross a given CPU / GPU architecture. We demonstrate fully distributedarithmetic operations such that the 'polynomial integer index multiplication'method overcomes the current limitation of parallel multiplication methods. Ie,the need to share common core memory and common disk for the calculation ofresults and intermediate results.

Fast multiplication by two's complement addition of numbers represented  as a set of polynomial radix 2 indexes, stored as an integer list for  massively parallel computation