Generalize IsMontgomeryConfiguration and MontgomeryBackendPrimeField

[GianfrancoBazzani]

In order to solve #95 without repeat code i tried to generalize IsMontgomeryConfiguration trait and MontgomeryBackendPrimeField struct to allow usage with any UnsignedInteger.

Tried something like this:

If i use a generic U: IsUnsignedInteger :

Any idea to define a generic to generalize any type UnsignedInteger<_> struct like?

[MauroToscano]

Don't generalize it over the trait, we just need it to work with UnsignedInteger<u: usize> for now. This will enable the auto paramater generator we added to work smoothly, since rust don't like const functions in traits.

[MauroToscano]

This backend is to make generally optimized code and enable a fast implementation of any field. The IsUnsignedInteger is for everything to keep working if you want to make a really specific optimization, or swap the native type for another one.

[MauroToscano]

Leaving that aside, the problem there is that you are using a trait, so you can't use UnsignedInteger functions directly if you define the variable as U. You are limited to the trait functions, because the U could be something different.

[GianfrancoBazzani]

Tanks a lot Mauro, you are truly a Rust warlock. So instead of generalize for any object with IsUnsignedInteger trait implementation, I generalized for any NUM_LIMBS constant value and used UnsignedInteger<NUM_LIMBS> to generalize for any object following custom multiprecision unsigned integer struct like (Types: U256, U384,....). Seems Works and passes the tests:

[GianfrancoBazzani]

Leaving that aside, the problem there is that you are using a trait, so you can't use UnsignedInteger functions directly if you define the variable as U. You are limited to the trait functions, because the U could be something different.

I see the difference, thanks a lot. Generalizing through NUM_LIMS I can access all methods of UnsignedInteger that is what I wanted.