feat: reduced number of u128 ops in serialization

[zac-williamson]

Description

calling fn from_be_bytes calls a large number of u128 operations as byte sums are being computed. This PR constructs bignum limbs out of byte arrays using Field arithmetic operations, converting the result to u128.

Problem*

u128 ops are expensive and from_be_bytes was using a lot of them, making from_be_bytes cost ~1,000 gates more than neccessary

Summary*

PR changes from_be_bytes to evaluate most of its arithmetic operations using Field arithmetic. This is safe as we are computing sums of u8 objects and implicitly know that the output is range constrained.

Additional Context

This PR should not create any breaking changes.

PR Checklist*

• I have tested the changes locally.
• I have formatted the changes with Prettier and/or cargo fmt on default settings.

[kashbrti]

Thanks for catching this! benchmarks for from_be_bytes were not implemented, so this went unnoticed. I'll add some benchmarks for the operation in this PR.

[kashbrti]

noticed we even don't have tests for to_be_bytes

[TomAFrench]

The beta.4 release of noir will make the most efficient implementation of this to be

limb.assert_max_bit_size::<128>()
result[N - i - 1] = limb;

We should avoid using an unconstrained function to do this.

[kashbrti]

@zac-williamson @TomAFrench I have another PR open #157, that replicates this PR and also adds some other serialization methods. Should we close this branch and switch to the other PR?

[kashbrti]

closing this as it's done in #157