feat(ssa): Hoist add and mul binary ops using known induction variables

[vezenovm]

Description

Problem*

Followup to #6848 whose largest regression was in brillig opcodes executed #6848 (comment).

Summary*

In #6848 we marked certain binary ops as not being able to be hoisted due to the overflow checks inside of ACIR gen and Brillig gen. However, if a binary operation has one variable that is from an outer loop's induction variable we can determine whether or not there would be an overflow. This re-uses logic introduced in #6639.

This PR currently just tries to hoist add and mul instructions as they are simpler. For example, Sub overflows depends on if the induction variable is on the lhs or the rhs (e.g. if it is the rhs we should check the induction variable's upper bound but if it is the lhs we should check the lower bound). These can be done in follow-ups if we are comfortable with this approach.

Additional Context

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]

Changes to Brillig bytecode sizes

Generated at commit: 6929ac3b93eab10080caa0ddbff637b8241edf12, compared to commit: 03b58fa2dfcc8acc8cf5198b1b23b55676fbdb02

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
poseidonsponge_x5_254	-10 ✅	-0.23%
sha2_byte	-8 ✅	-0.29%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
hashmap	21,798 (-12)	-0.06%
uhashmap	14,001 (-15)	-0.11%
poseidon_bn254_hash	5,425 (-10)	-0.18%
poseidon_bn254_hash_width_3	5,425 (-10)	-0.18%
regression_5252	4,594 (-10)	-0.22%
poseidonsponge_x5_254	4,254 (-10)	-0.23%
sha2_byte	2,767 (-8)	-0.29%

[github-actions]

Changes to number of Brillig opcodes executed

Generated at commit: 6929ac3b93eab10080caa0ddbff637b8241edf12, compared to commit: 03b58fa2dfcc8acc8cf5198b1b23b55676fbdb02

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
sha256_regression	-9,606 ✅	-7.49%
sha256_var_size_regression	-1,326 ✅	-7.49%
brillig_cow_regression	-64,620 ✅	-11.07%
ram_blowup_regression	-98,719 ✅	-11.25%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
uhashmap	145,546 (-62)	-0.04%
hashmap	54,140 (-62)	-0.11%
poseidon_bn254_hash	162,594 (-1,599)	-0.97%
poseidon_bn254_hash_width_3	162,594 (-1,599)	-0.97%
poseidonsponge_x5_254	183,753 (-2,274)	-1.22%
regression_5252	915,026 (-11,370)	-1.23%
regression_6674_3	1,615 (-30)	-1.82%
keccak256	34,777 (-700)	-1.97%
conditional_1	5,717 (-201)	-3.40%
loop_invariant_regression	1,164 (-42)	-3.48%
array_dynamic_nested_blackbox_input	4,550 (-180)	-3.81%
sha2_byte	47,309 (-2,223)	-4.49%
sha256	14,996 (-720)	-4.58%
sha256_var_witness_const_regression	7,200 (-360)	-4.76%
conditional_regression_short_circuit	7,528 (-402)	-5.07%
6	7,450 (-402)	-5.12%
ecdsa_secp256k1	6,789 (-369)	-5.16%
array_dynamic_blackbox_input	18,209 (-990)	-5.16%
sha256_brillig_performance_regression	23,194 (-1,524)	-6.17%
sha256_var_padding_regression	222,216 (-15,066)	-6.35%
regression_4449	200,857 (-14,070)	-6.55%
sha256_regression	118,704 (-9,606)	-7.49%
sha256_var_size_regression	16,377 (-1,326)	-7.49%
brillig_cow_regression	519,086 (-64,620)	-11.07%
ram_blowup_regression	778,650 (-98,719)	-11.25%

[github-actions]

Compilation Sample

Program	Compilation Time	%
sha256_regression	1.373s	3%
regression_4709	0.780s	0%
ram_blowup_regression	15.472s	1%
rollup-base-public	116.085s	1%
rollup-base-private	95.825s	-2%
private-kernel-tail	1.078s	5%
private-kernel-reset	7.137s	-2%
private-kernel-inner	2.192s	4%
parity-root	0.713s	-8%
noir-contracts	87.283s	1%

[github-actions]

Execution Sample

Program	Execution Time	%
sha256_regression	0.618s	0%
regression_4709	0.391s	3%
ram_blowup_regression	4.451s	0%
rollup-base-public	21.356s	0%
rollup-base-private	19.487s	0%
private-kernel-tail	0.691s	-1%
private-kernel-reset	1.468s	-2%
private-kernel-inner	0.973s	1%
parity-root	0.527s	-5%

[github-actions]

Peak Memory Sample

Program	Peak Memory
keccak256	78.48M
workspace	123.81M
regression_4709	422.91M
ram_blowup_regression	1.58G
private-kernel-tail	201.60M
private-kernel-reset	716.87M
private-kernel-inner	291.67M
parity-root	171.93M