I'm replying to your question about division an modulo together.

In perl, there's no reason to do this, as the opcodes to do the separating of the two results would take much more time than what you'd gain from calculating the two together. However, this might not be the case with big integers, and indeed, the Math::BigInt module defined the bdiv method in such a way that it can store the remainder at once. (Btw the iquo function of Maple works the same way: it stores the other result. This is not surprising as Maple handles big integers.)

In C, you can hope that the compiler notices that you use division and modulus on the same number and will optimize them to use just one operation if that helps. If you don't trust the compiler, you can also use the div (or ldiv, lldiv, imaxdiv) functions of the C library, which return both the quotient and the remainder. I think this doesn't have much merit anyway, as if the compiler cannot do the optimization of a division and a modulus together, then either it wouldn't give any speed gain in the particular case (eg because there's no free register to store the other result) or your compiler is crap and you'd gain more speed by installing a new compiler or fiddling with the compiler flags than doing micro-optimizations on division.