feat: optimize checked_to_unchecked to take into account multiplications

[asterite]

Description

Problem

Another try at #8111 but this time memoizing values max bit sizes to see if it doesn't make performance worse.

Summary

If we have code like this:

fn main(x: u1, z: u32) -> pub u32 {
    let m = x as u32;
    z * m
}

then we don't check for overflow in that multiplication because we know m was casted from u1 which can only be 0 or 1.

If we have code like this:

fn main(x: u1, y: u1, z: u32) -> pub u32 {
    let x = x as u32;
    let y = y as u32;
    let m = x * y;
    z * m
}

then we shouldn't need to check for overflow either as we know x * y can be 1 or 0. However, there was no such check in our code so that's what this PR does.

Additional Context

I tried this in the past in #8111 but it turned out to be slow. The likely reason is that it was recursing without memoizing so hitting the same logic over and over. With memoization this seems to be solved and it maybe opens the door to more optimizations.

Documentation

Check one:

• No documentation needed.
• Documentation included in this PR.
• [For Experimental Features] Documentation to be submitted in a separate PR.

PR Checklist

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

[github-actions]

⚠️ Performance Alert ⚠️

Possible performance regression was detected for benchmark 'Test Suite Duration'.
Benchmark result of this commit is worse than the previous benchmark result exceeding threshold 1.20.

Benchmark suite	Current: 63a8dfb	Previous: 9845edc	Ratio
test_report_noir-lang_noir-bignum_	505 s	405 s	1.25

This comment was automatically generated by workflow using github-action-benchmark.

CC: @TomAFrench

[github-actions]

ACVM Benchmarks

Details

Benchmark suite	Current: b6ab48a	Previous: 7c6ab0c	Ratio
purely_sequential_opcodes	267385 ns/iter (± 382)	263545 ns/iter (± 1359)	1.01
perfectly_parallel_opcodes	237552 ns/iter (± 2021)	236787 ns/iter (± 4213)	1.00
perfectly_parallel_batch_inversion_opcodes	3583960 ns/iter (± 12547)	3581886 ns/iter (± 7418)	1.00

This comment was automatically generated by workflow using github-action-benchmark.

[github-actions]

Execution Time

Details

Benchmark suite	Current: b6ab48a	Previous: 7c6ab0c	Ratio
private-kernel-inner	0.028 s	0.029 s	0.97
private-kernel-reset	0.16 s	0.16 s	1
private-kernel-tail	0.017 s	0.017 s	1
rollup-base-private	0.333 s	0.335 s	0.99
rollup-base-public	0.213 s	0.211 s	1.01
rollup-block-root	11 s	11.2 s	0.98
rollup-merge	0.004 s	0.004 s	1
rollup-root	0.013 s	0.014 s	0.93

This comment was automatically generated by workflow using github-action-benchmark.

[github-actions]

Compilation Time

Details

Benchmark suite	Current: b6ab48a	Previous: 7c6ab0c	Ratio
regression_4709	0.663 s	0.665 s	1.00
ram_blowup_regression	12.6 s	12.8 s	0.98
global_var_regression_entry_points	0.464 s	0.458 s	1.01
private-kernel-inner	2.218 s	2.258 s	0.98
private-kernel-reset	6.518 s	6.422 s	1.01
private-kernel-tail	1.092 s	1.02 s	1.07
rollup-base-private	18.2 s	18.6 s	0.98
rollup-base-public	13.7 s	13.24 s	1.03
rollup-block-root-empty	0.903 s	0.879 s	1.03
rollup-block-root-single-tx	124 s	118 s	1.05
rollup-block-root	124 s	131 s	0.95
rollup-merge	0.864 s	0.859 s	1.01
rollup-root	1.36 s	1.358 s	1.00

This comment was automatically generated by workflow using github-action-benchmark.

[github-actions]

Test Suite Duration

Details

Benchmark suite	Current: b6ab48a	Previous: 7c6ab0c	Ratio
test_report_AztecProtocol_aztec-packages_noir-projects_aztec-nr	50 s	49 s	1.02
test_report_AztecProtocol_aztec-packages_noir-projects_noir-contracts	88 s	90 s	0.98
test_report_AztecProtocol_aztec-packages_noir-projects_noir-protocol-circuits_crates_blob	40 s	39 s	1.03
test_report_AztecProtocol_aztec-packages_noir-projects_noir-protocol-circuits_crates_private-kernel-lib	171 s	175 s	0.98
test_report_AztecProtocol_aztec-packages_noir-projects_noir-protocol-circuits_crates_rollup-lib	153 s	160 s	0.96
test_report_AztecProtocol_aztec-packages_noir-projects_noir-protocol-circuits_crates_types	51 s	51 s	1
test_report_noir-lang_noir-bignum_	407 s	414 s	0.98
test_report_noir-lang_noir_bigcurve_	235 s	275 s	0.85
test_report_noir-lang_sha512_	28 s	28 s	1

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[github-actions]

Execution Memory

Details

Benchmark suite	Current: b6ab48a	Previous: 7c6ab0c	Ratio
private-kernel-inner	203.28 MB	203.28 MB	1
private-kernel-reset	227.03 MB	227.03 MB	1
private-kernel-tail	181.3 MB	181.3 MB	1
rollup-base-private	433.5 MB	433.5 MB	1
rollup-base-public	425.68 MB	425.68 MB	1
rollup-block-root	1420 MB	1420 MB	1
rollup-merge	254.29 MB	254.29 MB	1
rollup-root	260.03 MB	260.03 MB	1

This comment was automatically generated by workflow using github-action-benchmark.

[github-actions]

Compilation Memory

Details

Benchmark suite	Current: b6ab48a	Previous: 7c6ab0c	Ratio
private-kernel-inner	270.75 MB	270.74 MB	1.00
private-kernel-reset	535.37 MB	535.37 MB	1
private-kernel-tail	200.14 MB	200.12 MB	1.00
rollup-base-private	1330 MB	1330 MB	1
rollup-base-public	1350 MB	1350 MB	1
rollup-block-root-empty	270.76 MB	270.77 MB	1.00
rollup-block-root-single-tx	7770 MB	7770 MB	1
rollup-block-root	7780 MB	7780 MB	1
rollup-merge	271.94 MB	271.94 MB	1
rollup-root	322.45 MB	322.44 MB	1.00

This comment was automatically generated by workflow using github-action-benchmark.

[asterite]

I think the performance alert might have been an outlier as bench-show shows similar times now.