feat: potentially set brillig functions to pure if not entry points

[jialinli98]

Description

Problem

same changes as #9659

Noir and avm-transpiler build were successful. Noir projects can also be compiled with no error.

Summary

Additional Context

User Documentation

Check one:

• No user documentation needed.
• Changes in docs/ included in this PR.
• [For Experimental Features] Changes in docs/ 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]

Changes to Brillig bytecode sizes

Generated at commit: f64b028de8ddaf47fb4148097688762a3b957d4c, compared to commit: 13ce5c89c1edbfbf5e92c4cbf2258ea6e63f46b5

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
regression_8739_inliner_min	-39 ✅	-66.10%
regression_8739_inliner_zero	-39 ✅	-66.10%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
array_sort_inliner_min	472 (-10)	-2.07%
reference_alias_in_array_inliner_zero	20 (-18)	-47.37%
regression_8739_inliner_max	20 (-32)	-61.54%
regression_8739_inliner_min	20 (-39)	-66.10%
regression_8739_inliner_zero	20 (-39)	-66.10%

[github-actions]

Changes to number of Brillig opcodes executed

Generated at commit: f64b028de8ddaf47fb4148097688762a3b957d4c, compared to commit: 13ce5c89c1edbfbf5e92c4cbf2258ea6e63f46b5

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
regression_8739_inliner_min	-40 ✅	-68.97%
regression_8739_inliner_zero	-40 ✅	-68.97%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
reference_alias_in_array_inliner_zero	18 (-24)	-57.14%
regression_8739_inliner_max	18 (-29)	-61.70%
regression_8739_inliner_min	18 (-40)	-68.97%
regression_8739_inliner_zero	18 (-40)	-68.97%

[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: ffe2817	Previous: e48a0d8	Ratio
test_report_zkpassport_noir-ecdsa_	3 s	1 s	3

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

CC: @TomAFrench

[github-actions]

⚠️ Performance Alert ⚠️

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

Benchmark suite	Current: 09f6b06	Previous: 13ce5c8	Ratio
rollup-block-root	0.005 s	0.004 s	1.25

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

CC: @TomAFrench

[vezenovm]

@asterite if I remember correctly this change started causes failures on aztec-packages once Noir got synced. Do you remember?

@jialinli98 it may be a good idea to mirror these changes onto aztec-packages to see if we get any test failures before merging.

[TomAFrench]

I've opened a PR to run the full CI on this change in AztecProtocol/aztec-packages#19802

[TomAFrench]

Interesting that there's regressions in fold_numeric_generic_poseidon_inliner_zero and no_predicates_numeric_generic_poseidon_inliner_zero.