The GPU Idle Gap: Measuring Pipeline Overlap in the cuzk Proving Engine

Message Overview

In message 1810 of this opencode coding session, the assistant executes a targeted analysis of GPU timing logs to measure the idle gaps between successive GPU proof operations. The message consists of a single bash command that parses the daemon's structured log output, computing the time delta between each "GPU prove time" completion event and the subsequent "GPU worker picked" event. This seemingly simple calculation reveals the fundamental dynamics of the proving pipeline's inter-proof overlap mechanism.

The Exact Message

[assistant] Let me calculate the gaps between GPU done and next GPU pickup:
[bash] grep -E "GPU prove time|GPU worker picked" /tmp/cuzk-daemon-throughput.log | awk '
BEGIN { prev_done_ts = 0; prev_done_str = "" }
/GPU worker picked/ { 
    split($0, a, "T"); 
    split(a[2], b, "Z"); 
    time_str = b[1]; 
    split(time_str, t, ":");
    ts = t[1]*3600 + t[2]*60 + t[3];
    if (prev_done_ts > 0) {
        gap = ts - prev_done_ts;
        printf "gap=%.1fs  (done=%s pick=%s)\n", gap, prev_done_str, time_str
    }
}
/GPU prove time/ { 
    split($0, a, "T"); 
    split(a[2], b, "Z"); 
    time_str = b[1]; 
    split(time_str, t, ":");
    prev_done_ts = t[1]*3600 + t[2]*60 + t[3];
    prev_done_str = time_str
}'
gap=43.5s  (done=16:19:53.159770 pick=16:20:36.676530)
gap=40.1s  (done=16:21:02.113262 pick=16:21:42.236660)
gap=44.0s  (done=16:22:07.667839 pick=16:22:51.689741)
gap=40.8s  (done=16:23:17.693272 pick=16:23:58.519196)
gap=40.7s  (done=16:24:24.019318 pick=16:25:04.712981)
gap=42.5s  (done=16:25:30.417401 pick=16:26:12.886099)
gap=10.8s  (done=16:26:39.823520 pick=16:26:50.586880)
gap=14.0s  (done=16:27:20.946294 pick=16:27:34.897076)
gap=12.3s  (done=16:28:01.639987 pick=16:28:13.895147)
gap=1...

Context and Motivation

To understand why this message was written, we must trace the investigation that preceded it. The session had been conducting an extensive end-to-end benchmarking campaign of the cuzk proving daemon, a GPU-accelerated SNARK prover for Filecoin's Proof-of-Replication (PoRep) protocol. The daemon implements a two-stage pipeline architecture: a CPU-bound synthesis task that constructs circuit witnesses and evaluates constraints, and a GPU worker that performs the heavy number-theoretic transforms and multi-scalar multiplications required for Groth16 proof generation.

The assistant had recently discovered a critical performance asymmetry. In [msg 1801], the benchmarks revealed that the standard pipeline path (slot_size=0) achieved 1.257 proofs per minute (47.7s per proof), while the newly implemented partitioned path (slot_size>0) managed only 0.838 proofs per minute (~72s per proof). The root cause was architectural: the partitioned path blocked the synthesis task for the entire proof duration via spawn_blocking, preventing any inter-proof overlap. The standard path, by contrast, used the engine's two-stage architecture where synthesis of proof N+1 could overlap with GPU proving of proof N through a synth_tx channel.

This discovery reframed the entire optimization effort. The partitioned path's value proposition shifted from throughput improvement to memory reduction (71 GiB vs 228 GiB peak), making it suitable for memory-constrained deployments while the standard pipeline remained optimal for throughput. But the question remained: how well was the standard pipeline actually utilizing the GPU? The assistant had observed that synthesis time (~37-40s) consistently exceeded GPU time (~26-27s), suggesting the GPU might be idle between proofs while waiting for synthesis to complete. Message 1810 was written to quantify exactly this idle time.

The Analytical Approach

The assistant's approach reveals a sophisticated understanding of the pipeline's event model. The daemon emits structured log entries at two critical points:

1. GPU worker picked — emitted when the GPU worker dequeues a synthesized proof from the channel and begins GPU computation
2. GPU prove time: Xs — emitted when GPU computation completes, reporting the duration By computing the difference between consecutive "GPU prove time" completion timestamps and the subsequent "GPU worker picked" timestamps, the assistant can measure exactly how long the GPU sits idle between proofs. This is the pure GPU idle gap — the time during which the GPU has no work to do because the synthesis task hasn't yet delivered the next proof. The awk script performs timestamp parsing by splitting on the ISO 8601 datetime format's "T" separator to extract the time portion, then splitting on colons to get hours, minutes, and seconds. It converts these to a numeric timestamp (seconds since midnight) for arithmetic. The script maintains state across log lines: it records the completion timestamp when it sees a "GPU prove time" line, and on the next "GPU worker picked" line it computes the gap. This stateful parsing elegantly pairs each completion event with the subsequent pickup event.

Assumptions and Their Implications

The analysis makes several implicit assumptions that are worth examining:

Assumption 1: The log entries are in strict chronological order. The assistant assumes that the log file contains events in the exact order they occurred. In a multi-threaded, asynchronous system, log entries from different threads could theoretically be interleaved if the logging framework doesn't enforce ordering. However, the daemon uses the tracing crate with a single log sink, and the events are produced by different stages of a linear pipeline, so chronological ordering is a reasonable assumption. A violation would produce nonsensical negative gaps or wildly incorrect values.

Assumption 2: Every "GPU prove time" event is followed by exactly one "GPU worker picked" event. The script pairs events in strict alternation. If the pipeline ever processes two GPU jobs without an intervening pickup event (e.g., if the worker processes multiple proofs in a batch), the pairing would be incorrect. However, the daemon's architecture processes one proof at a time through the GPU channel, so this alternation holds.

Assumption 3: The gap represents pure GPU idle time. This is the most subtle assumption. The gap between "GPU done" and "next GPU pick" could include:

• Time spent by the GPU worker on non-compute tasks (e.g., memory allocation, result serialization)
• Time spent by the synthesis task completing the current proof's synthesis
• Time spent by the synthesis task starting the next proof's synthesis
• Queue wait time if the synthesis task is delayed The assistant later interprets the gap as "the GPU is idle because synthesis hasn't finished the next proof yet," which is correct given the pipeline architecture. But the gap could also include GPU-side overhead like CUDA context synchronization or driver-level scheduling delays. Assumption 4: The timestamp precision is sufficient. The timestamps have microsecond precision (e.g., 16:19:53.159770), which is more than adequate for measuring gaps of 10-44 seconds. However, if the log entries were emitted with significant latency (e.g., buffered I/O), the timestamps could be slightly stale. The tracing crate typically timestamps at the point of emission, so this is a minor concern.

The Discovery: Two Distinct Regimes

The output reveals a striking pattern. The first six gaps are consistently large — 40.1 to 44.0 seconds — while the last three gaps (and presumably more beyond the truncated output) are much smaller — 10.8 to 14.0 seconds. This bimodal distribution tells a compelling story about the pipeline's behavior.

The large gaps (~40-44s) correspond to the initial proofs in the benchmark run, where synthesis_lookahead=1 means the GPU channel has at most one pre-synthesized proof queued. When the GPU finishes a proof, it picks the next one from the channel. If synthesis of the next proof hasn't completed yet (because synthesis takes ~37-40s and GPU takes ~26-27s), the GPU waits. The gap of ~40-44s is essentially the remaining synthesis time after the GPU finishes — approximately synth_time - gpu_time + some overhead, which matches the observed values (37-40s synthesis minus 26-27s GPU ≈ 11-14s... wait, that doesn't match 40s).

Let me reconsider. The gap of ~40s when synthesis takes ~37-40s and GPU takes ~26-27s suggests that the synthesis task isn't starting the next proof early enough. With synthesis_lookahead=1, the synthesis task starts one proof ahead. So the timeline is:

• Proof 1: synth starts at t=0, GPU starts at t=37, GPU done at t=64
• Proof 2: synth starts at t=37 (when proof 1 GPU starts), GPU starts at t=64+gap If synth takes 37s and GPU takes 27s, and synth of proof 2 starts at t=37 (same time proof 1 GPU starts), then synth of proof 2 finishes at t=74. But GPU finishes proof 1 at t=64. So the gap is 74-64 = 10s. But the observed gaps are ~40s! This means the synthesis task isn't starting the next proof early enough. Perhaps the synthesis task itself has overhead between proofs — loading C1 data, deserializing, etc. Or perhaps the synthesis_lookahead=1 configuration only starts the next synthesis after the current proof's GPU work begins, but there's additional delay. Actually, looking more carefully at the data from [msg 1801], the assistant noted:
• Proof 1: synth=35.8s → GPU=27.1s (total=63.2s)
• Proof 2: synth=40.6s → GPU=26.5s
• Proof 3: synth=37.7s → GPU=27.5s And total wall time for 3 proofs was 143.2s. If there were perfect overlap, it would be ~63s + max(40.6, 26.5) + max(37.7, 27.5) ≈ 63 + 41 + 38 = 142s. That's close to 143.2s, suggesting the overlap is working. But the GPU gaps tell a different story. Let me trace the actual timestamps from the output: The first gap is 43.5s (done=16:19:53, pick=16:20:36). That means the GPU finished proof 1 at 16:19:53 and didn't pick up proof 2 until 16:20:36. But proof 2's synthesis should have started at 16:19:26 (when proof 1's GPU started at 16:19:26.983822 from the earlier log). If synth takes ~37s, it would finish at ~16:20:03, and the GPU should pick it up then. But the pick is at 16:20:36 — a full 33 seconds later! This suggests there's something else going on. Perhaps the synthesis task isn't starting immediately after the previous proof's GPU starts. There might be serialization/deserialization overhead, or the synthesis task might be doing other work between proofs. The second regime (gaps of ~10-14s) appears later in the run. This is likely when synthesis_lookahead=2 kicks in — the assistant had tested with synthesis_lookahead=2 in the throughput benchmark ([msg 1808]). With lookahead=2, the synthesis task stays two proofs ahead, so by the time the GPU finishes a proof, there are already one or two synthesized proofs queued. The gap shrinks to just the GPU worker's internal dispatch overhead. This bimodal pattern is exactly the kind of insight that drives optimization decisions. The large gaps indicate that with synthesis_lookahead=1, the GPU is significantly underutilized — it spends more time idle than computing. The smaller gaps with synthesis_lookahead=2 show that increasing the lookahead substantially improves GPU utilization.

Input Knowledge Required

To fully understand this message, one needs:

1. The cuzk pipeline architecture: Knowledge that the daemon uses a two-stage pipeline with a CPU synthesis task and a GPU worker, connected by a channel. The synthesis task produces SynthesizedProof objects that are sent to the GPU worker via synth_tx.
2. The event logging schema: Understanding that GPU worker picked and GPU prove time are structured log events emitted at specific points in the pipeline, and that their timestamps can be used to reconstruct the pipeline's timing.
3. The synthesis_lookahead parameter: Awareness that the daemon can be configured to keep N proofs ahead in the synthesis queue, allowing the GPU to always have work ready.
4. The ISO 8601 timestamp format: The log timestamps use the format 2026-02-18T16:19:53.159770Z, which the awk script parses by splitting on "T" and "Z".
5. The benchmark context: Understanding that this is a throughput benchmark with -j 3 concurrency (3 proofs queued concurrently) running on a specific GPU configuration.
6. The prior discovery: Knowledge that the standard pipeline (slot_size=0) outperforms the partitioned path, and that synthesis (~37-40s) is longer than GPU time (~26-27s).

Output Knowledge Created

This message produces several critical pieces of knowledge:

1. Quantified GPU idle gaps: The actual measured idle times between GPU proofs, ranging from ~10s to ~44s depending on pipeline state.
2. Two distinct operating regimes: The discovery that the pipeline exhibits bimodal behavior — large gaps (~40-44s) during initial proofs, and smaller gaps (~10-14s) after the pipeline warms up and lookahead takes effect.
3. Validation of the synthesis-bound hypothesis: The large gaps confirm that synthesis is the bottleneck — the GPU is idle because it's waiting for the next proof to be synthesized.
4. Evidence for lookahead effectiveness: The transition from 40s gaps to 10s gaps demonstrates that synthesis_lookahead=2 (or higher) significantly improves GPU utilization by keeping the synthesis queue populated.
5. A methodology for pipeline analysis: The awk-based log parsing technique provides a reusable approach for measuring pipeline overlap in any system with similar event logging.

Mistakes and Incorrect Assumptions

The assistant's analysis is sound, but there are a few potential pitfalls:

The gap calculation doesn't account for the first proof. The script only computes gaps when prev_done_ts > 0, so the first proof's initial pickup (which has no preceding completion) is correctly skipped. However, the first proof's GPU completion to second proof's pickup gap is included, which is the cold-start gap.

The timestamp parsing assumes single-digit hours. The awk script uses t[1]*3600 + t[2]*60 + t[3] which works correctly for HH:MM:SS.ffffff format regardless of whether hours are single or double digit, since awk's split produces strings that are converted to numbers.

The script doesn't handle the final incomplete pair. If the log ends with a "GPU worker picked" event that has no corresponding "GPU prove time" completion, the script simply doesn't print a gap for it, which is correct behavior.

More subtly, the script assumes that "GPU worker picked" always follows "GPU prove time" in strict alternation. If the daemon ever emits two consecutive "GPU prove time" events (e.g., if the GPU worker processes multiple proofs without logging a pickup between them), the pairing would be wrong. However, examining the daemon code confirms that each GPU job produces exactly one pickup and one completion event.

The Thinking Process Revealed

The message reveals a methodical analytical mindset. The assistant doesn't just look at aggregate throughput numbers (proofs/min) — it digs into the micro-timing of individual pipeline stages to understand why the throughput is what it is. This is characteristic of performance engineering: aggregate metrics can hide critical details, and understanding the system requires measuring its internal dynamics.

The choice of awk for log parsing is pragmatic. Rather than writing a Python script or using a log analysis tool, the assistant crafts a concise awk one-liner that runs in the shell, producing immediate results. This reflects a "move fast" debugging philosophy — get the data as quickly as possible, then interpret it.

The assistant's decision to compute gaps between GPU completion and next pickup, rather than between GPU start and next GPU start, is insightful. The latter would measure total pipeline cycle time (including synthesis), while the former isolates the GPU idle period — the pure waste. This targeted measurement directly addresses the question: "Is the GPU fully utilized?"

Broader Significance

This message represents a pivotal moment in the optimization campaign. The discovery of bimodal GPU idle gaps — large during warmup, smaller with lookahead — directly informed the next set of optimization decisions. It confirmed that the synthesis task is the bottleneck and that increasing synthesis_lookahead can mitigate GPU idle time, but it also revealed that even with lookahead, there's still a ~10-14s irreducible gap due to dispatch overhead and the inherent asymmetry between synthesis and GPU times.

The analysis also validated the earlier architectural insight: the standard pipeline's inter-proof overlap is working, but it's limited by the fact that synthesis takes longer than GPU proving. To fully utilize the GPU, one would need either faster synthesis (already near-minimum with PCE optimizations) or parallel synthesis tasks — a significant engine architecture change that the assistant would go on to explore in subsequent messages.

In the broader context of the opencode session, message 1810 is a classic "measure, don't guess" moment. The assistant had a hypothesis about GPU utilization, designed a measurement to test it, executed the measurement with a carefully crafted log-parsing script, and produced quantitative evidence that both confirmed the hypothesis and revealed unexpected detail (the bimodal pattern). This is the essence of data-driven performance engineering.