chore: Rework DIE pass to operate on a postorder SCC CFG

[jfecher]

Description

Problem*

This is currently preventing DIE from being able to remove side-effectful instructions like stores or increment_rcs directly. Instead we rely on either special checks in mem2reg (for stores) or special checks in DIE for inc/decrement rcs.

Summary*

This is part of a breakout change for #6460 since that PR changes mem2reg to use DIE to remove stores, but it needs this change to handle side-effectful instructions in the presence of loops. When loops are in the program and DIE is run, it previously could remove a store that would be used again next iteration of the loop.

This PR changes DIE to use a graph of strongly-connected components of blocks and to operate on every block within an SCC all at once. This requires a more traditional DIE algorithm which repeats until there are no more changes. This isn't necessary in ours currently since acir is always 1 block and normal scoping semantics prevent creating brillig programs which refer to the same instruction across multiple blocks (unless it is a store).

Additional Context

Currently a draft while I just verify it does work while merged into #6460, and to see if this has any brillig opcode regressions.

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: d6d9f2e2d2e7f85465a8893e7935d82afea2fb65, compared to commit: 713df69aad56fc5aaefd5d140275a3217de4d866

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
slice_regex	+156 ❌	+6.05%
regression_4449	+36 ❌	+4.19%
brillig_hash_to_field	+6 ❌	+4.03%
hash_to_field	+6 ❌	+4.03%
check_large_field_bits	-12 ✅	-4.18%
cast_and_shift_global	-8 ✅	-11.27%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
slice_regex	2,733 (+156)	+6.05%
regression_4449	896 (+36)	+4.19%
brillig_hash_to_field	155 (+6)	+4.03%
hash_to_field	155 (+6)	+4.03%
regression_5252	5,059 (+167)	+3.41%
sha256_var_size_regression	2,114 (+66)	+3.22%
wildcard_type	294 (+9)	+3.16%
array_dynamic_blackbox_input	1,199 (+21)	+1.78%
ram_blowup_regression	1,028 (+18)	+1.78%
poseidonsponge_x5_254	4,565 (+71)	+1.58%
sha256_var_padding_regression	5,326 (+72)	+1.37%
keccak256	1,806 (+24)	+1.35%
brillig_keccak	1,806 (+24)	+1.35%
brillig_cow_regression	2,445 (+29)	+1.20%
no_predicates_numeric_generic_poseidon	815 (+9)	+1.12%
fold_numeric_generic_poseidon	815 (+9)	+1.12%
sha256_regression	7,344 (+66)	+0.91%
6	1,381 (+12)	+0.88%
sha256	2,074 (+18)	+0.88%
slice_loop	352 (+3)	+0.86%
sha256_var_witness_const_regression	1,417 (+12)	+0.85%
conditional_regression_short_circuit	1,451 (+12)	+0.83%
brillig_sha256	803 (+6)	+0.75%
merkle_insert	820 (+6)	+0.74%
6_array	436 (+3)	+0.69%
hashmap	27,784 (+190)	+0.69%
poseidon_bn254_hash_width_3	5,722 (+38)	+0.67%
poseidon_bn254_hash	5,722 (+38)	+0.67%
array_dynamic_nested_blackbox_input	1,001 (+6)	+0.60%
ecdsa_secp256k1	1,020 (+6)	+0.59%
regression_4709	134,507 (+774)	+0.58%
eddsa	11,180 (+60)	+0.54%
sha2_byte	3,406 (+18)	+0.53%
conditional_1	1,348 (+6)	+0.45%
simple_shield	900 (+3)	+0.33%
uhashmap	16,750 (+34)	+0.20%
references	307 (-4)	-1.29%
fold_complex_outputs	580 (-8)	-1.36%
regression_struct_array_conditional	549 (-9)	-1.61%
generics	204 (-4)	-1.92%
side_effects_constrain_array	119 (-4)	-3.25%
check_large_field_bits	275 (-12)	-4.18%
cast_and_shift_global	63 (-8)	-11.27%

[github-actions]

Changes to number of Brillig opcodes executed

Generated at commit: d6d9f2e2d2e7f85465a8893e7935d82afea2fb65, compared to commit: 713df69aad56fc5aaefd5d140275a3217de4d866

🧾 Summary (10% most significant diffs)

Program	Brillig opcodes (+/-)	%
regression_4449	+23,240 ❌	+10.57%
slice_regex	+261 ❌	+6.78%
wildcard_type	+25 ❌	+5.09%
side_effects_constrain_array	-6 ✅	-7.14%
check_large_field_bits	-210 ✅	-7.67%
cast_and_shift_global	-30 ✅	-14.71%

---

Full diff report 👇

Program	Brillig opcodes (+/-)	%
regression_4449	243,063 (+23,240)	+10.57%
slice_regex	4,110 (+261)	+6.78%
wildcard_type	516 (+25)	+5.09%
sha256_var_witness_const_regression	7,134 (+96)	+1.36%
fold_numeric_generic_poseidon	5,486 (+72)	+1.33%
no_predicates_numeric_generic_poseidon	5,486 (+72)	+1.33%
sha256	10,991 (+144)	+1.33%
6	7,455 (+96)	+1.30%
conditional_regression_short_circuit	7,530 (+96)	+1.29%
brillig_sha256	4,249 (+48)	+1.14%
array_dynamic_nested_blackbox_input	4,678 (+48)	+1.04%
sha256_var_size_regression	18,489 (+156)	+0.85%
6_array	1,855 (+15)	+0.82%
conditional_1	5,949 (+48)	+0.81%
slice_loop	1,225 (+9)	+0.74%
ecdsa_secp256k1	7,124 (+48)	+0.68%
brillig_hash_to_field	958 (+6)	+0.63%
hash_to_field	958 (+6)	+0.63%
regression_5252	985,891 (+6,122)	+0.62%
array_dynamic_blackbox_input	20,894 (+126)	+0.61%
poseidonsponge_x5_254	197,365 (+1,165)	+0.59%
hashmap	60,320 (+318)	+0.53%
poseidon_bn254_hash	178,792 (+867)	+0.49%
poseidon_bn254_hash_width_3	178,792 (+867)	+0.49%
merkle_insert	3,977 (+18)	+0.45%
sha256_regression	126,722 (+462)	+0.37%
simple_shield	2,873 (+9)	+0.31%
eddsa	751,520 (+2,307)	+0.31%
brillig_cow_regression	585,490 (+1,608)	+0.28%
ram_blowup_regression	879,757 (+2,352)	+0.27%
brillig_keccak	37,199 (+96)	+0.26%
keccak256	37,199 (+96)	+0.26%
sha256_var_padding_regression	235,407 (+564)	+0.24%
sha2_byte	53,644 (+96)	+0.18%
uhashmap	156,483 (+108)	+0.07%
generics	234 (-2)	-0.85%
regression_struct_array_conditional	1,573 (-14)	-0.88%
references	423 (-4)	-0.94%
fold_complex_outputs	890 (-14)	-1.55%
side_effects_constrain_array	78 (-6)	-7.14%
check_large_field_bits	2,528 (-210)	-7.67%
cast_and_shift_global	174 (-30)	-14.71%

[jfecher]

Closing this to work on an alternate solution for mem2reg (this was only needed for #6460)