Nim operations

In mathematics, the nimbers, also called Grundy numbers, are introduced in combinatorial game theory, where they are defined as the values of nim heaps. They arise in a much larger class of games because of the Sprague–Grundy theorem. The nimbers are the ordinal numbers endowed with a new nimber addition and nimber multiplication, which are distinct from ordinal addition and ordinal multiplication. Visit the following page for more info on nimber addition and nimber multiplication: Nimber - Wikipedia, the free encyclopedia We also define Nimber square root such that it returns a number which, when the nimber multiplication applied to itself, returns the original number: s = Nim_sqrt(n) such that n = Nim_prod(s,s) Similarly Nimber inverse of a number is the one when the nimber multiplication is applied, returns 1: 1 = Nim_prod(n,Nim_inv(n)) Evaluate the following using the above mentioned operations from n=0x100000 (hex) to 0x110000 (inclusive) and find the sum of the results. Answer format: number (in decimal) [My timing: 6s]