Expand benchmark coverage with new modules and comprehensive workloads

[shakayami]

Summary

This PR significantly expands the benchmark suite by adding workloads for five new modules (fenwicktree, acl_math, acl_string, prime_fact, two_sat) and enhancing existing benchmarks to exercise all public methods of their respective modules. The changes ensure more comprehensive performance regression detection across the codebase.

Key Changes

• Enhanced module documentation: Updated the workloads module docstring to explain the philosophy of using large data sizes and exercising all public methods to catch regressions in any single method.

• New module imports: Added imports for fenwicktree, acl_math, acl_string, prime_fact, and two_sat modules.

• Expanded segtree benchmark:

  • Increased problem size from 50K to 200K elements
  • Added coverage for all public methods: get(), all_prod(), max_right(), and min_left() in addition to existing set() and prod()

• Expanded lazysegtree benchmark:

  • Increased problem size from 50K to 100K elements
  • Added coverage for set(), get(), all_prod(), apply_point(), max_right(), and min_left() methods

• Expanded dsu benchmark:

  • Increased problem size from 100K to 300K elements
  • Restructured to exercise all public methods: leader(), merge(), same(), size(), and groups()

• Expanded maxflow benchmark:

  • Increased problem size from 2K nodes/8K edges to 50K nodes/200K edges
  • Added coverage for get_edge(), edges(), change_edge(), and min_cut() methods

• Expanded mincostflow benchmark:

  • Increased problem size from 300 nodes/1.5K edges to 5K nodes/25K edges
  • Added coverage for slope(), get_edge(), and edges() methods

• Enhanced scc benchmark: Increased problem size from 50K to 120K nodes with proportional edge increase

• Enhanced fps benchmark: Added coverage for diff(), integral(), addition, and subtraction operations

• New fenwicktree benchmark: Comprehensive workload exercising add() and sum() operations on 300K elements with 300K queries

• New acl_math benchmark: Batch queries for inv_mod(), inv_gcd(), crt(), and floor_sum() functions with 100K queries each

• New acl_string benchmark: Workload for suffix_array(), lcp_array(), z_algorithm() and string operations on 100K character string

• New prime_fact benchmark: Comprehensive testing of is_probable_prime(), prime_fact(), divisors(), totient(), and lcm() functions

• New two_sat benchmark: Large random 2-SAT instance with 200K variables and 400K clauses

Implementation Details

• All new benchmarks follow the established pattern of separate build and run functions
• Workloads use deterministic seeding (via _rng()) for reproducibility
• Query distributions are carefully chosen to exercise different code paths (e.g., segtree uses 30% set, 20% get, 25% prod, etc.)
• All benchmarks are registered in the BENCHMARKS list for integration with the test framework

https://claude.ai/code/session_01CZ5PzQCeMYkhV9xUhfZmxP

[github-actions]

📊 Performance Benchmark Results

⏱️ Execution time (mean, lower is better)

Benchmark	Base	PR	Delta
acl_math	n/a	1.568s	n/a
acl_string	n/a	212.19ms	n/a
convolution	763.62ms	822.63ms	+7.7% ⚠️
dsu	81.36ms	613.32ms	+653.9% ⚠️
fenwicktree	n/a	1.112s	n/a
fps	457.81ms	506.19ms	+10.6% ⚠️
lazysegtree	1.210s	2.124s	+75.5% ⚠️
maxflow	7.60ms	799.27ms	+10414.0% ⚠️
mincostflow	3.41ms	39.24ms	+1049.7% ⚠️
prime_fact	n/a	1.691s	n/a
scc	121.63ms	438.33ms	+260.4% ⚠️
segtree	176.97ms	606.73ms	+242.9% ⚠️
two_sat	n/a	1.357s	n/a

💾 Peak memory (lower is better)

Benchmark	Base	PR	Delta
acl_math	n/a	4.9KiB	n/a
acl_string	n/a	13.5MiB	n/a
convolution	16.1MiB	16.1MiB	+0.0%
dsu	849.2KiB	40.4MiB	+4773.7% ⚠️
fenwicktree	n/a	8.9MiB	n/a
fps	3.9MiB	3.9MiB	+0.0%
lazysegtree	5.0MiB	9.8MiB	+97.2% ⚠️
maxflow	2.3MiB	97.0MiB	+4133.3% ⚠️
mincostflow	662.2KiB	16.3MiB	+2423.4% ⚠️
prime_fact	n/a	8.5KiB	n/a
scc	13.8MiB	32.7MiB	+137.4% ⚠️
segtree	1.5MiB	6.0MiB	+308.0% ⚠️
two_sat	n/a	174.0MiB	n/a

_{Base = target branch, PR = this branch. Negative delta = improvement. ✅ improvement ≥ 1%, ⚠️ regression > 5%. "n/a" base entries mean the target branch has no benchmark suite yet.}