Measure a regroup on the tablet, not just on the desktop

The GPU question needed a number nobody had: how a regroup divides on
the hardware whose CPU is weakest. dr-face carries no weights and
touches no display, and dr-catalog's example needs only a catalog file,
so both run under adb shell against a copy of a real library.

On the same 18,143 faces — desktop against the tablet — scan 0.96s /
2.61s, agglomerate 1.69s / 2.16s, score 0.26s / 0.40s. The scan is half
the pass on the tablet and under a third on the desktop, because twenty
cores of AVX2 pull ahead of NEON much further than the merge engine's
single-threaded hashing does. So a GPU GEMM is worth roughly 2× a
regroup on the tablet and 1.5× here, and it is the tablet that should
decide whether it is built.

The two architectures agree exactly: the same 1,531,969 evidence pairs,
the same 2,518 groups holding the same 16,246 faces, the same
reliability table. That is a better check on the NEON kernel than the
unit test can be.

Two instruments, both read-only: the example now prints its phases, and
dr-face gains scan_bench, which needs no library at all and so can
answer "how fast is this machine" on a device with nothing on it.

Co-Authored-By: Claude Opus 5 (1M context) <noreply@anthropic.com>

core/dr-catalog/examples/face_confidence.rs

@@ -305,6 +305,46 @@ fn full_library(
     candidates.sort_by_key(|c| c.face);
 
     println!("\nthe whole library, at the default merge probability:");
+
+    // The three phases, separately, because "a regroup takes n seconds" does
+    // not tell anyone which half to optimise — and the answer differs between
+    // a desktop and a tablet (docs/faces.md §9).
+    {
+        let dim = candidates.first().map(|c| c.embedding.len()).unwrap_or(0);
+        let flat: Vec<f32> = candidates.iter().flat_map(|c| c.embedding.clone()).collect();
+        let crop_px: Vec<f32> = candidates.iter().map(|c| c.crop_px).collect();
+        let images: Vec<u64> = candidates.iter().map(|c| c.image).collect();
+        let view = dr_face::neighbours::Faces {
+            embeddings: &flat,
+            dim,
+            crop_px: &crop_px,
+            images: &images,
+        };
+
+        let t = std::time::Instant::now();
+        let evidence = dr_face::neighbours::above_threshold(&view, cal, dr_face::RIVAL_FLOOR);
+        let scan = t.elapsed().as_secs_f64();
+
+        // `cluster` runs its own scan at the merge threshold, so the
+        // agglomeration is what is left after taking one scan off the total.
+        let t = std::time::Instant::now();
+        let clusters = dr_face::cluster(&candidates, cal, dr_face::DEFAULT_MERGE_PROBABILITY);
+        let agglomerate = t.elapsed().as_secs_f64() - scan;
+
+        let t = std::time::Instant::now();
+        let _ = dr_face::identity_shares(
+            candidates.len(),
+            &clusters,
+            &evidence,
+            dr_face::TOP_MATCHES,
+        );
+        println!(
+            "  scan {scan:.2}s ({} evidence pairs) · agglomerate {agglomerate:.2}s · score {:.2}s",
+            evidence.len(),
+            t.elapsed().as_secs_f64()
+        );
+    }
+
     let start = std::time::Instant::now();
     let grouping = dr_face::cluster_scored(&candidates, cal, dr_face::DEFAULT_MERGE_PROBABILITY);
     let real: Vec<_> = grouping

core/dr-face/examples/scan_bench.rs

@@ -0,0 +1,104 @@
+//! How fast this machine can scan a library for face pairs.
+//!
+//!   cargo run --release -p dr-face --example scan_bench [-- FACES…]
+//!
+//! Synthetic embeddings, because the scan's cost is `n²/2` dot products and
+//! does not care what the vectors mean — which is what makes this runnable on
+//! a phone with no library on it, over `adb shell`, beside
+//! `tools/face-tests-on-device.sh`.
+//!
+//! # What it is for
+//!
+//! docs/faces.md §9 has the desktop numbers and the question they leave open:
+//! a GPU GEMM is worth roughly 1.5× of a regroup on a twenty-core desktop,
+//! because the scan is under a third of the pass there. On a tablet the CPU is
+//! several times slower and the GPU is not, so the same optimisation is worth
+//! something different — and nobody had measured which.
+//!
+//! No weights, no catalog, no display: it needs nothing but the binary.
+
+use dr_face::neighbours::{above_threshold, Faces};
+use dr_face::{Calibration, EMBEDDING_DIM, RIVAL_FLOOR};
+
+/// Sizes to time, unless the command line names others.
+const DEFAULT_SIZES: [usize; 4] = [2_000, 4_000, 8_000, 18_000];
+
+fn main() {
+    let sizes: Vec<usize> = {
+        let given: Vec<usize> = std::env::args().skip(1).filter_map(|a| a.parse().ok()).collect();
+        if given.is_empty() {
+            DEFAULT_SIZES.to_vec()
+        } else {
+            given
+        }
+    };
+
+    // The reference curve, so the cosine floor is the one a real library with
+    // no fit of its own would scan at.
+    let cal = Calibration::default();
+
+    println!("{:>8}  {:>9}  {:>10}  {:>9}", "faces", "scan", "pairs", "GFLOP/s");
+    for n in sizes {
+        let (embeddings, crop_px, images) = population(n);
+        let faces = Faces {
+            embeddings: &embeddings,
+            dim: EMBEDDING_DIM,
+            crop_px: &crop_px,
+            images: &images,
+        };
+
+        let start = std::time::Instant::now();
+        let pairs = above_threshold(&faces, &cal, RIVAL_FLOOR);
+        let secs = start.elapsed().as_secs_f64();
+
+        let flop = n as f64 * n as f64 / 2.0 * EMBEDDING_DIM as f64 * 2.0;
+        println!(
+            "{n:>8}  {secs:>8.2}s  {:>10}  {:>9.1}",
+            pairs.len(),
+            flop / secs / 1e9
+        );
+    }
+}
+
+/// `n` L2-normalised embeddings in a handful of loose clusters.
+///
+/// Clustered rather than uniform so the scan finds a plausible number of pairs
+/// to keep — a population where nothing survives the threshold would time the
+/// rejection path alone, which is not the path that matters. Hashed from an
+/// index rather than drawn from an RNG, so a number is reproducible from the
+/// command that produced it.
+fn population(n: usize) -> (Vec<f32>, Vec<f32>, Vec<u64>) {
+    let identities = (n / 12).max(1);
+    let mut embeddings = Vec::with_capacity(n * EMBEDDING_DIM);
+    for i in 0..n {
+        let mut v = unit(i % identities);
+        let noise = unit(i + 1_000_000);
+        for (x, e) in v.iter_mut().zip(&noise) {
+            *x = 0.75 * *x + 0.25 * e;
+        }
+        embeddings.extend(normalise(v));
+    }
+    // Every face in its own photograph: the co-occurrence rule skips pairs
+    // rather than scoring them, and skipped pairs are not what is being timed.
+    ((embeddings), vec![150.0; n], (0..n as u64).collect())
+}
+
+fn unit(seed: usize) -> Vec<f32> {
+    let mut s = (seed as u64).wrapping_mul(0x9E37_79B9_7F4A_7C15) | 1;
+    let mut v = Vec::with_capacity(EMBEDDING_DIM);
+    for _ in 0..EMBEDDING_DIM {
+        s ^= s << 13;
+        s ^= s >> 7;
+        s ^= s << 17;
+        v.push(((s >> 11) as f64 / (1u64 << 53) as f64) as f32 - 0.5);
+    }
+    normalise(v)
+}
+
+fn normalise(mut v: Vec<f32>) -> Vec<f32> {
+    let len = v.iter().map(|x| x * x).sum::<f32>().sqrt();
+    for x in &mut v {
+        *x /= len;
+    }
+    v
+}