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Check new bounded_int_mul implementation #1478

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@DiegoCivi

We have C = A * B, where all of them are BoundedInt. We represent the BoundedInt as:

  • X = Xo + Xd, where
    • X is a BoundedInt.
    • Xo is the lower bound of the BoundedInt range.
    • Xd is the offset.

So we have:
Cd = (Ad + Ao) * (Bd + Bo) - Co -> Cd = (Ad * Bd) + (Ad * Bo) + (Bd * Ao) + (Ao * Bo - Co)

We can separate it into run-time values:

  • Ad with P bits.
  • Bd with Q bits.
  • Ad * Bd with X = max(P, Q) * 2 bits
  • Ad * Bo with Y = max(P, S) * 2 bits
  • Bd * Ao with Z = max(Q, R) * 2 bits
    And compile-time values:
  • Ao with R bits.
  • Bo with S bits.
  • Ao * Bo - Co with W bits.

We should check if this new implementation is more performant than what we have now. This algorithm implementation can be seen here.

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