Return overflowing value when multiplying for UInt256 and Int256

[quocle108]

Issue to be solved

There are some cases in which we need to get the overflowing value instead of the maximum value when the overflow happens. For example this case mulDiv(uint256 x, uint256 y, uint256 denominator).

In order to multiply a and b and get the result in 512 bits, we need to get the overflowing value when it happens.

Suggested Solution

No response

[turbolent]

Related: https://forum.onflow.org/t/addmod-mulmod-as-built-in-functions/3973/5

[darkdrag00nv2]

@turbolent If I understand correctly, we want to implement Word128 and Word256?

The title of this issue is a little confusing. We wouldn't want to change the behavior of UInt256 and Int256 I presume. They should still raise runtime errors on overflow. Please correct me if I am wrong.

[turbolent]

@darkdrag00nv2 Good question and good idea!

I initially thought it might make sense to add a "modular multiplication" operation ((x * y) % k; like mulmod in Solidity).

Though maybe there is no need for arbitrary k here, in which case, like you pointed out, Word* types already wrap around, so we would just need to add Word256 (and maybe Word128 while at it / for consistency).

Integer values can be converted between each other, so UInt256 would then also be convertible to Word256.

@quocle108 Would that be sufficient?

[darkdrag00nv2]

Thanks @turbolent

I think we can implement Word128 and Word256 for starters. We can add more functions further if it is insufficient for @quocle108.

[turbolent]

@darkdrag00nv2 Sounds good!