Modulus functionality for field element

[sameersubudhi]

Hi,

Is it possible to extend the FieldPrime implementation to include the support for modulus operator for determining the remainder? Ref: https://doc.rust-lang.org/std/ops/trait.Rem.html

Is it not implemented on purpose? If so, could you please offer a brief explanation?

Best regards, Sameer

[Schaeff]

Hi Sameer,

Yes this is on purpose as arbitrary modulo operations are expensive on prime fields, as they require a range check: a = q*b + r s.t. r < b which is expensive.

Can you share your use case here?

[sameersubudhi]

Hi Thibaut ( @Schaeff ),

In my program, I need to determine the exact quotient value for further processing and the remainder part doesn't have any impact on the logic. Thus, I can afford to sacrifice some accuracy.

But since FieldPrime implements the division method as a multiplication of numerator and the multiplicative inverse mod P of the denominator, the combinations that have non-zero remainder cause huge numbers and thus do not really work out in my use-case.

Alternatively, a floor division implementation (similar to // operator in Python) could be of great help to me. Or could you suggest me an approach to handle this scenario with ZoKrates in its current state?

Regards, Sameer

[sameersubudhi]

@nono2357 As per my understanding (FieldPrime implementation in ZoKrates), your recommended solution will always return 0, no matter what input values you provide.

d*(nb/d) will always evaluate to nb.