The Turning Point: How `perf` Revealed the True Bottleneck in Groth16 Synthesis

Introduction

In the high-stakes world of Filecoin proof generation, every millisecond counts. The cuzk proving engine, a GPU-accelerated Groth16 prover for Filecoin's Proof-of-Replication (PoRep), had already undergone extensive optimization across multiple phases. Phase 4 targeted compute-level micro-optimizations in the CPU synthesis pipeline — the stage where circuit constraints are evaluated to produce the A, B, and C polynomials needed for the prover. Three optimizations had been implemented: a Vec recycling pool to eliminate heap allocations, an interleaved A+B evaluation loop for better instruction-level parallelism, and software prefetch intrinsics to reduce cache misses. Yet when the microbenchmark ran, the result was a crushing disappointment: only a 0.7% improvement, far below the expected 15–25%.

Message [msg 1167] captures the moment the assistant turned from speculation to evidence. It is a single command — a perf report invocation — but the data it returns fundamentally reshapes the optimization strategy. This article examines that message in depth: why it was written, what it reveals about the assistant's assumptions and reasoning, and how the output knowledge it creates drives the next phase of the project.

The Message: A `perf` Deep Dive

The message itself is brief but dense:

Critical data. Let me see more of the top functions: ``bash perf report -i /tmp/perf-synth.data -n --stdio --no-children --percent-limit 1 2>&1 | grep -E '^\s+[0-9]+\.[0-9]+%' | head -25 ` **Output:** ` 11.14% 25008 cuzk-bench cuzk-bench [.] <bellperson::groth16::prover::ProvingAssignment<Scalar> as bellpepper_core::constraint_system::ConstraintSystem<Scalar>>::enforce 8.52% 18781 cuzk-bench cuzk-bench [.] __mulx_mont_sparse_256 6.82% 15284 cuzk-bench cuzk-bench [.] bellperson::gadgets::uint32::UInt32::addmany 6.51% 14599 cuzk-bench cuzk-bench [.] bellpepper_core::gadgets::... ``

The assistant's opening words — "Critical data" — signal that this is not a routine measurement. The tone is one of discovery, the recognition that the numbers on the screen contradict prior assumptions and demand a new direction.

Why This Message Was Written: The Context of Disappointment

To understand why this perf report was necessary, we must trace the chain of reasoning that preceded it.

The assistant had spent several rounds implementing three optimizations derived from a prior perf stat analysis (see [msg 1155]). That analysis had shown that approximately 34% of synthesis runtime was spent on jemalloc allocation and deallocation in the enforce hot loop. The logical conclusion was that a Vec recycling pool — reusing the six Vec<Indexer> objects created per constraint — would eliminate those allocations and deliver a substantial speedup.

The implementation was clean and thorough:

Vec recycling pool (VecPool): Added to ProvingAssignment, this pool maintains a collection of pre-allocated Vec<Indexer> buffers. Each enforce call takes three pairs of Vecs (one pair per LinearCombination for A, B, C) and returns them after use, avoiding malloc/free calls.
Interleaved A+B eval (eval_ab_interleaved): Instead of evaluating the A and B linear combinations sequentially, this combined function processes terms from both LCs in a round-robin fashion, designed to improve instruction-level parallelism by keeping the CPU's execution units fed with independent arithmetic chains.
Software prefetch (_mm_prefetch): Added to the inner loops of eval and eval_with_trackers, these x86 intrinsics hint the CPU to bring cache lines into L1 data cache before they are needed. The microbenchmark results were devastating. The combined optimizations yielded an average of 54.9 seconds versus a baseline of 55.5 seconds — a mere 1.1% improvement. The assistant's own commentary captures the frustration: "That's only a 0.7% improvement — disappointing. The recycling pool should have had a bigger impact." The assistant then attempted to isolate the interleaved eval as the possible culprit. Reverting to separate eval_with_trackers calls while keeping the pool and prefetch produced an average of 55.5 seconds — actually slightly worse than the baseline. Something was fundamentally wrong with the optimization model. This is the moment that [msg 1167] addresses. The assistant needs hard data — not aggregate counter summaries from perf stat, but a detailed breakdown of where the CPU cycles are actually going. The perf stat counters from [msg 1156] had shown that instructions dropped 4.1% but IPC (instructions per cycle) also fell from 2.60 to 2.53, suggesting the interleaved eval's complex control flow was hurting pipeline utilization. But that analysis was speculative. The assistant now needs to see the actual hotspot functions to understand why the expected savings didn't materialize.

The Input Knowledge Required

To interpret this message, one must understand several layers of context:

The Groth16 synthesis pipeline: In Filecoin's PoRep circuit, the prover must evaluate hundreds of millions of constraints. Each constraint produces three linear combinations (A, B, C) that are evaluated against the witness assignments. The enforce method on ProvingAssignment is the central hot loop — it processes each constraint by calling closure functions that build up these linear combinations term by term.

The perf toolchain: The assistant uses perf record (in [msg 1165]) to capture 229,841 samples of CPU cycle events, then perf report to analyze them. The --no-children flag is critical: it attributes samples to the function where the sample was taken, not its callers. The --percent-limit 1 filters to functions consuming at least 1% of cycles. The grep pipeline extracts only the percentage lines for readability.

The function symbols: The output shows four top hotspots. The first, enforce, at 11.14%, is the main constraint loop itself — this is expected for any synthesis workload. The second, __mulx_mont_sparse_256 at 8.52%, is the field multiplication routine (using MULX for accelerated Montgomery multiplication on Zen4). This is also expected — field arithmetic is the bread and butter of constraint evaluation.

The third and fourth entries are where the story changes. UInt32::addmany at 6.82% is a gadget for 32-bit addition with carry constraints — used heavily in SHA-256 hash computation, which is a major component of Filecoin's PoRep circuit. The fourth entry, truncated at 6.51%, is bellpepper_core::gadgets::... — specifically Boolean::lc(), the method that creates a LinearCombination from a boolean variable.

The significance of Boolean::lc(): In the bellpepper constraint system, Boolean is a wrapper around a variable that is constrained to be 0 or 1. The lc() method creates a new LinearCombination containing that variable with a coefficient. This is used extensively in circuit closures like:

|lc| lc + &bits[0].lc::<Scalar>(one, Scalar::ONE),

Each call to lc() allocates a new LinearCombination on the heap. The assistant's recycling pool only recycled the six Vecs per enforce call — but the closures themselves create dozens of temporary LCs per constraint through Boolean::lc() and similar methods.

The Assumptions That Were Wrong

The perf data in [msg 1167] exposes two critical incorrect assumptions:

Assumption 1: The 6 Vecs per enforce are the dominant allocation cost. The assistant had estimated that ~34% of synthesis time was spent on jemalloc alloc/dealloc, based on perf stat counter analysis. The reasoning was that each enforce creates 3 LinearCombinations with 2 Indexers each (inputs + aux), totaling 6 Vec allocations per constraint. With ~130 million constraints, that's ~780 million malloc/free calls.

The perf report data shows this assumption was wrong — or at least incomplete. While enforce itself is 11.14% of cycles, the allocation cost within it is distributed across many more allocation sites than just the 6 Vecs. The Boolean::lc() method at 6.51% is a single allocation site that was completely invisible in the perf stat aggregate counters. The recycling pool, which only addressed the 6 Vecs, missed the dozens of temporary LCs created per constraint inside the closures.

Assumption 2: The interleaved A+B eval would improve IPC. The assistant had hypothesized that processing A and B terms in a combined loop would allow the CPU to overlap independent arithmetic chains, improving instruction-level parallelism. The perf stat counters in [msg 1156] showed the opposite: IPC dropped from 2.60 to 2.53. The interleaved loop's more complex control flow — with min/max calculations for term counts, two sets of prefetch operations, and conditional branches — was actually hurting pipeline utilization. The perf report data doesn't directly address this (since the interleaved eval was already reverted by [msg 1157]), but it confirms that the assistant's intuition about the bottleneck was misdirected.

Assumption 3: The recycling pool operations are negligible. The assistant correctly noted that Vec::pop(), Vec::clear(), and Vec::push() are each ~10-15 instructions. But the pool also introduces branch mispredictions: each take() must check if the pool is empty and potentially allocate a new Vec; each give() must check if the pool is at capacity. These branches, while individually cheap, add up across 130 million constraints. More importantly, the pool's existence doesn't eliminate the real allocation bottleneck — the temporary LCs inside closures — so the pool's savings are swamped by the unaddressed overhead.

The Output Knowledge Created

The perf report output in [msg 1167] creates several pieces of actionable knowledge:

1. A prioritized hotspot list. The assistant now knows the exact functions consuming CPU cycles, ranked by overhead. This is vastly more informative than the aggregate perf stat counters from [msg 1156]. The top four entries — enforce (11.14%), field multiplication (8.52%), UInt32::addmany (6.82%), and Boolean::lc() (6.51%) — define the optimization frontier.

2. The true allocation bottleneck. The 6.51% attributed to Boolean::lc() (and the truncated gadget name that follows) reveals that temporary LinearCombination creation inside circuit closures is a major cost center. This is a fundamentally different problem from the 6 Vecs per enforce that the recycling pool addressed. The temporary LCs are created and destroyed within each closure invocation, often multiple times per constraint.

3. A new optimization direction. The data suggests that instead of recycling Vecs, the assistant should eliminate the temporary LC allocations entirely by adding in-place methods to Boolean and Num — methods that directly add or subtract a boolean's term(s) to an existing LinearCombination without creating a temporary. This is exactly what the assistant proceeds to implement in the subsequent chunk ([chunk 14.1]): add_to_lc, sub_from_lc on Boolean, and add_lc on Num, followed by patching the hottest call sites in UInt32::addmany, SHA-256 gadgets, and lookup closures.

4. Validation of the measurement methodology. The perf report confirms that the assistant's benchmarking infrastructure is working correctly. The data is consistent, the sample count is sufficient (229,841 samples), and the hotspot ranking matches expectations for a synthesis workload. This gives confidence that future optimizations can be accurately measured.

The Thinking Process: From Aggregate to Granular

The assistant's thinking process across messages [msg 1155] through [msg 1167] reveals a methodical, evidence-driven approach to performance optimization.

The initial hypothesis (the 6 Vecs are the bottleneck) was based on reasonable inference from perf stat counters showing high allocation/deallocation overhead. When the microbenchmark contradicted that hypothesis, the assistant didn't double down or tweak parameters — it went back to measurement.

The first diagnostic step was perf stat with detailed counters ([msg 1156]), which showed the IPC regression. This led to reverting the interleaved eval to isolate its effect ([msg 1157]). When the pool+prefetch configuration still showed no improvement (<msg id=1159-1160>), the assistant engaged in a detailed thought process about why:

"The issue might be that jemalloc's thread-local cache is SO fast on Zen4 that the recycling pool's Vec::clear() + Vec::pop()/push() on the pool itself has similar overhead."

This speculation was reasonable but ultimately wrong. The assistant then considered alternative explanations: that most LCs are very small (1-2 terms), that jemalloc's tcache is even faster than estimated, that the pool operations have hidden overhead. Each of these was a plausible hypothesis, but none could be confirmed without deeper data.

The decision to run perf record with call-graph data ([msg 1165]) was the correct next step. The 3.6 GB perf.data file with 229,841 samples provides enough resolution to identify hotspots at the function level. The --call-graph dwarf,16384 flag captures stack traces using DWARF debug info with a maximum depth of 16384 frames, ensuring that even deeply nested gadget calls are captured.

The perf report command in [msg 1167] is the payoff. The assistant filters to functions above 1% overhead and extracts the top entries. The data immediately refutes the earlier hypothesis: Boolean::lc() at 6.51% is a clear smoking gun. The assistant's response — "Critical data" — reflects the recognition that the optimization strategy must pivot.

The Broader Significance

This message is a textbook example of the measurement-driven optimization loop: hypothesize, implement, measure, analyze, and pivot based on evidence. The assistant could have easily spent more time tweaking the recycling pool — trying fixed-size arrays, inline buffers, or thread-local caches. Instead, the perf data provided a clear signal to change direction.

The insight that temporary LCs inside closures are the real bottleneck is non-obvious without profiling. The circuit code patterns that create these temporaries are spread across dozens of gadget implementations — UInt32::addmany, SHA-256 ch and maj functions, lookup table gadgets, and more. Each individual allocation is tiny (one or two Indexer entries), but multiplied by hundreds of millions of constraints, they dominate the runtime.

The solution that the assistant implements in the following chunk — adding add_to_lc and sub_from_lc methods to Boolean and patching the hot call sites — is a direct response to the evidence in [msg 1167]. It's a surgical optimization that targets the exact bottleneck identified by perf, rather than the speculative bottleneck that the recycling pool addressed.

Conclusion

Message [msg 1167] is the turning point in a multi-round optimization effort. A single perf report command, producing just four lines of output, fundamentally reshapes the assistant's understanding of where CPU cycles are spent during Groth16 synthesis. The data reveals that the assistant's prior hypothesis — that the 6 Vecs per enforce call were the dominant allocation cost — was incorrect. The real bottleneck is the dozens of temporary LinearCombination objects created inside circuit closures via Boolean::lc() and similar methods.

This message demonstrates the critical importance of granular profiling data in performance optimization. Aggregate counters from perf stat can suggest hypotheses, but only function-level hotspot analysis from perf record/perf report can confirm or refute them. The assistant's willingness to abandon a carefully implemented optimization (the recycling pool) in favor of a new direction based on evidence is the hallmark of effective engineering.

The output knowledge created by this message — the prioritized hotspot list and the identification of Boolean::lc() as a major cost center — directly drives the next phase of optimization. The assistant proceeds to implement in-place methods that eliminate temporary LC allocations at the hottest call sites, targeting the exact bottleneck revealed by the data. Without this message, the optimization effort would have continued chasing the wrong problem, wasting time on a recycling pool that could never deliver the expected gains.

The Turning Point: How perf Revealed the True Bottleneck in Groth16 Synthesis