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phase5: kernel lane (SPEC §13) — FP-tolerance equivalence gate + reference-diff testing
The parser/service targets only ever needed byte-identical golden replay.
The kernel lane is the case that breaks it: a matmul optimization
(transpose-B for cache locality + eight-accumulator ILP) that REORDERS the
floating-point reduction, so its low bits differ by construction —
byte-identical is the wrong gate.
Adds:
- EquivalencePolicy::compare + Divergence (diff-test): byte-identical is
exact; fp-tolerance tokenizes and compares numeric tokens within
abs + rel*|baseline|, with explicit NaN handling. Non-numeric tokens and
token-count mismatches still fail exactly.
- fp-compare bin: applies a target's equivalence.toml to two output files.
- targets/matmul/kernel.c: matmul_ref (single-accumulator oracle) vs
matmul_opt (reordered, faster), with emit/check/run/bench modes.
- targets/matmul/equivalence.toml: fp-tolerance abs 1e-4 + rel 1e-3.
- scripts/kernel-lane-demo.sh + results/phase5/kernel-lane.txt: byte-identical
FAILs, fp-tolerance is EQUIVALENT, a +0.5 perturbation is still REJECTED,
speedup 3.23× measured with the same interleaved A/B + bootstrap CI.
Ledger row phase5-matmul-opt = needs-human-review: using the FP-tolerance
tier at all is a human-review signal (SPEC §8), same posture as mimalloc.
The trust machinery is unchanged; only the timer and the gate differ, which
is exactly the shape a future GPU kernel would slot into.
Co-Authored-By: Claude Fable 5 <noreply@anthropic.com>
Claude-Session: https://claude.ai/code/session_01EcKPWQ3MQD4NdEHwar96u2
This commit is contained in:
Claude
@@ -0,0 +1,39 @@
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//! Apply a target's equivalence policy to two output files (SPEC §13
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//! kernel lane). Loads `targets/<target>/equivalence.toml` (byte-identical
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//! by default, or fp-tolerance) and reports whether the candidate output
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//! is equivalent to the baseline under it.
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//!
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//! fp-compare <target-dir> <baseline-file> <candidate-file>
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use anyhow::{Context, Result};
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use diff_test::policy::EquivalencePolicy;
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use std::path::PathBuf;
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fn main() -> Result<()> {
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let mut args = std::env::args().skip(1);
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let target_dir = PathBuf::from(
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args.next()
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.context("usage: fp-compare <target-dir> <baseline> <candidate>")?,
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);
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let baseline_path = args.next().context("missing baseline file")?;
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let candidate_path = args.next().context("missing candidate file")?;
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let policy = EquivalencePolicy::load(&target_dir)?;
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let baseline = std::fs::read_to_string(&baseline_path)?;
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let candidate = std::fs::read_to_string(&candidate_path)?;
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println!("policy: {policy:?}");
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match policy.compare(&baseline, &candidate) {
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Ok(()) => {
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println!("EQUIVALENT under policy");
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Ok(())
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}
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Err(d) => {
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println!(
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"DIVERGENT at token/offset {}: baseline={:?} candidate={:?} — {}",
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d.token, d.baseline, d.candidate, d.reason
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);
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std::process::exit(1);
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}
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}
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}
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@@ -40,6 +40,96 @@ impl EquivalencePolicy {
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}
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Ok(policy)
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}
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/// Compare two outputs under this policy. `ByteIdentical` requires an
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/// exact match. `FpTolerance` tokenizes on whitespace and compares
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/// numeric tokens within `abs + rel*|baseline|`; non-numeric tokens
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/// (and mismatched token counts) must still match exactly. This is the
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/// gate the kernel lane (SPEC §13) needs: an optimization that reorders
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/// floating-point accumulation changes the last ULPs, so it fails
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/// byte-identical but passes a declared tolerance — while a genuine
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/// correctness bug (a wrong result) still exceeds it.
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pub fn compare(&self, baseline: &str, candidate: &str) -> Result<(), Divergence> {
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match self {
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Self::ByteIdentical => {
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if baseline == candidate {
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Ok(())
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} else {
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let pos = baseline
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.bytes()
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.zip(candidate.bytes())
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.position(|(a, b)| a != b)
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.unwrap_or(baseline.len().min(candidate.len()));
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Err(Divergence {
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token: pos,
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baseline: snippet(baseline, pos),
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candidate: snippet(candidate, pos),
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reason: "byte-identical mismatch".into(),
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})
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}
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}
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Self::FpTolerance { abs, rel } => {
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let bt: Vec<&str> = baseline.split_whitespace().collect();
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let ct: Vec<&str> = candidate.split_whitespace().collect();
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if bt.len() != ct.len() {
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return Err(Divergence {
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token: bt.len().min(ct.len()),
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baseline: format!("{} tokens", bt.len()),
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candidate: format!("{} tokens", ct.len()),
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reason: "token-count mismatch".into(),
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});
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}
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for (i, (b, c)) in bt.iter().zip(&ct).enumerate() {
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match (b.parse::<f64>(), c.parse::<f64>()) {
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(Ok(bn), Ok(cn)) => {
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if bn.is_nan() && cn.is_nan() {
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continue;
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}
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let d = (bn - cn).abs();
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let tol = abs + rel * bn.abs();
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// Explicit NaN handling: a lone NaN (the other
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// side finite) is a divergence, not a pass.
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if d.is_nan() || d > tol {
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return Err(Divergence {
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token: i,
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baseline: (*b).to_string(),
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candidate: (*c).to_string(),
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reason: format!("|Δ|={d:.3e} exceeds tolerance {tol:.3e}"),
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});
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}
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}
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_ => {
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if b != c {
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return Err(Divergence {
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token: i,
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baseline: (*b).to_string(),
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candidate: (*c).to_string(),
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reason: "non-numeric token mismatch".into(),
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});
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}
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}
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}
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}
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Ok(())
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}
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}
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}
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}
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/// The first place two outputs diverge under a policy.
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#[derive(Debug, Clone, PartialEq)]
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pub struct Divergence {
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/// Token index (FpTolerance) or byte offset (ByteIdentical).
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pub token: usize,
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pub baseline: String,
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pub candidate: String,
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pub reason: String,
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}
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fn snippet(s: &str, pos: usize) -> String {
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let start = pos.saturating_sub(8);
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let end = (pos + 8).min(s.len());
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s.get(start..end).unwrap_or("").replace('\n', "\\n")
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}
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#[cfg(test)]
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@@ -73,4 +163,28 @@ mod tests {
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}
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);
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}
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#[test]
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fn byte_identical_rejects_reordered_fp() {
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// The blocked kernel's low-bit difference: byte-identical says no.
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let p = EquivalencePolicy::ByteIdentical;
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assert!(p.compare("1.0000000 2.0", "1.0000001 2.0").is_err());
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}
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#[test]
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fn fp_tolerance_accepts_low_bits_rejects_real_error() {
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let p = EquivalencePolicy::FpTolerance {
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abs: 1e-6,
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rel: 1e-5,
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};
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// Last-ULP reordering: within tolerance.
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assert!(p.compare("1.0000000 42.0", "1.0000001 42.0").is_ok());
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// A genuine wrong result: exceeds tolerance, caught.
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let d = p.compare("1.0 42.0", "1.0 42.5").unwrap_err();
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assert_eq!(d.token, 1);
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// Non-numeric tokens still must match exactly.
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assert!(p.compare("ok 1.0", "bad 1.0").is_err());
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// Token-count mismatch is a divergence.
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assert!(p.compare("1.0 2.0", "1.0").is_err());
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}
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}
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Binary file not shown.
@@ -0,0 +1,32 @@
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# Kernel-lane demonstration — matmul (n=512, f32)
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## 1. Equivalence: byte-identical is the wrong gate
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byte-identical: FAIL — 244901 of 262144 result values differ (accumulation reordered)
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diff-test FP-tolerance policy (targets/matmul/equivalence.toml):
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policy: FpTolerance { abs: 0.0001, rel: 0.001 }
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EQUIVALENT under policy
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in-process reference differential test:
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kernel differential test (opt vs reference):
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max_abs_err = 3.815e-05
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max_rel_err = 2.173e-02 (dominated by near-zero elements; see abs floor)
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tolerance = abs 1.000e-04 + rel 1.000e-03 * |ref|
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byte_identical = NO (accumulation reordered by design)
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within_tolerance = YES
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verdict = EQUIVALENT
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control — a genuine wrong result IS caught by the tolerance:
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tolerance correctly REJECTS a +0.5 perturbation of one element
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## 2. Speedup: interleaved A/B, bootstrap 95% CI
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speedup (baseline/candidate): median 3.2301, 95% CI [3.1600, 3.2594]
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verdict: accepted
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## What it demonstrates
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A real matmul speedup (transpose for cache locality + eight-accumulator
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ILP) that reorders the reduction. Byte-identical rejects it; the
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FP-tolerance gate accepts it (abs 1e-4 + rel 1e-3) while still catching
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a wrong result; the bench measures it with the same CI machinery as
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every other target. The GPU extension (Triton/CUDA vs a reference
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kernel) is the same shape — only the timer and the hardware change.
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@@ -0,0 +1,60 @@
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#!/bin/sh
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# Kernel-lane demonstration (SPEC §13 research fork). Shows the one thing
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# the parser/service targets never needed: an optimization that reorders
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# floating-point accumulation, so byte-identical golden replay is the WRONG
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# gate and a floating-point TOLERANCE gate is required — while a genuine
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# wrong result is still caught. Measured with the same interleaved A/B +
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# bootstrap CI as every other target.
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#
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# sh scripts/kernel-lane-demo.sh [n]
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set -eu
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ROOT=$(cd "$(dirname "$0")/.." && pwd)
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N=${1:-512}
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OUT="$ROOT/results/phase5"
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mkdir -p "$OUT" /tmp/kl
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cd "$ROOT"
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clang -O2 -o /tmp/kl/kernel targets/matmul/kernel.c -lm
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cargo build -q -p diff-test -p bench-runner
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{
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echo "# Kernel-lane demonstration — matmul (n=$N, f32)"
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echo
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echo "## 1. Equivalence: byte-identical is the wrong gate"
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/tmp/kl/kernel "$N" emit ref > /tmp/kl/ref.txt
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/tmp/kl/kernel "$N" emit opt > /tmp/kl/opt.txt
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if diff -q /tmp/kl/ref.txt /tmp/kl/opt.txt >/dev/null; then
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echo "byte-identical: MATCH (unexpected — no reorder)"
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else
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d=$(diff /tmp/kl/ref.txt /tmp/kl/opt.txt | grep -c '^<' || true)
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echo "byte-identical: FAIL — $d of $((N*N)) result values differ (accumulation reordered)"
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fi
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echo
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echo "diff-test FP-tolerance policy (targets/matmul/equivalence.toml):"
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"$ROOT/target/debug/fp-compare" targets/matmul /tmp/kl/ref.txt /tmp/kl/opt.txt | sed 's/^/ /'
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echo
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echo "in-process reference differential test:"
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/tmp/kl/kernel "$N" check 1e-4 1e-3 | sed 's/^/ /'
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echo
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echo "control — a genuine wrong result IS caught by the tolerance:"
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awk 'NR==1{$1=$1+0.5} {print}' /tmp/kl/opt.txt > /tmp/kl/wrong.txt
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if "$ROOT/target/debug/fp-compare" targets/matmul /tmp/kl/ref.txt /tmp/kl/wrong.txt >/dev/null 2>&1; then
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echo " !! tolerance accepted a wrong result (bug)"
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else
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echo " tolerance correctly REJECTS a +0.5 perturbation of one element"
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fi
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echo
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echo "## 2. Speedup: interleaved A/B, bootstrap 95% CI"
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cargo run -q -p bench-runner -- --config config/accept.toml compare \
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--baseline "taskset -c 2 /tmp/kl/kernel $N run ref" \
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--candidate "taskset -c 2 /tmp/kl/kernel $N run opt" 2>/dev/null \
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| grep -E "speedup|verdict" | sed 's/^/ /'
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echo
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echo "## What it demonstrates"
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echo "A real matmul speedup (transpose for cache locality + eight-accumulator"
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echo "ILP) that reorders the reduction. Byte-identical rejects it; the"
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echo "FP-tolerance gate accepts it (abs 1e-4 + rel 1e-3) while still catching"
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echo "a wrong result; the bench measures it with the same CI machinery as"
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echo "every other target. The GPU extension (Triton/CUDA vs a reference"
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echo "kernel) is the same shape — only the timer and the hardware change."
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} | tee "$OUT/kernel-lane.txt"
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@@ -0,0 +1,14 @@
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# Kernel-lane equivalence policy (SPEC §13, §3.2). The blocked matmul
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# reorders floating-point accumulation, so byte-identical golden replay is
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# the WRONG gate — it would reject a correct optimization for differing in
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# the last ULPs. Instead, numeric outputs must agree within tolerance;
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# anything non-numeric still matches exactly, and a genuine wrong result
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# (beyond the tolerance) is still caught.
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#
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# rel = 1e-3 is generous for f32 accumulation over 512 terms in a different
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# order (observed max relative error ~1e-4); a real bug moves it far past
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# this. Using this tier at all is itself a needs-human-review signal per
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# SPEC §8 — a human confirms the tolerance is defensible for the workload.
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mode = "fp-tolerance"
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abs = 1e-4
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rel = 1e-3
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@@ -0,0 +1,180 @@
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/* hotpath kernel-lane demonstration (SPEC §13).
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*
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* A single-precision matrix multiply in two implementations that are
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* mathematically identical but numerically different because they sum the
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* inner products in a different ORDER:
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*
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* matmul_ref — naive i,j,k with a single sequential accumulator. The
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* reference oracle.
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* matmul_opt — eight independent accumulators over the k-reduction,
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* tree-combined at the end. This breaks the float-add
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* dependency chain (hiding ~4-cycle add latency behind
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* instruction-level parallelism, so it is faster) AND sums
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* the inner product in a different ORDER, so results differ
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* in the last few ULPs — bit-identical is impossible by
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* construction.
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*
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* This is the crux of the kernel lane: a real optimization here CANNOT be
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* gated by byte-identical golden replay (the low bits differ by design);
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* it needs a floating-point *tolerance* gate that accepts last-ULP
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* reordering while still catching a genuine wrong result. The reference
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* implementation is the oracle; the candidate is differential-tested
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* against it within a declared tolerance. On a GPU this same shape holds
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* (a Triton/CUDA kernel vs a reference kernel) — only the timer and the
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* hardware change.
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*
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* kernel <n> emit ref|opt # print the result matrix
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* kernel <n> check <abs-tol> <rel-tol> # in-process differential test
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* kernel <n> run ref|opt # one matmul, no output (for A/B)
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* kernel <n> bench ref|opt <reps> # time one implementation
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*/
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#include <stdio.h>
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#include <stdlib.h>
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#include <string.h>
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#include <math.h>
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#include <time.h>
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#define BS 64 /* block size */
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/* Deterministic f32 fill — xorshift, identical on every machine. */
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static void fill(float *m, long n, unsigned seed) {
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unsigned s = seed ? seed : 1;
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for (long i = 0; i < n * n; i++) {
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s ^= s << 13; s ^= s >> 17; s ^= s << 5;
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/* in [-1, 1) */
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m[i] = (float)((double)s / 2147483648.0 - 1.0);
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}
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}
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static void matmul_ref(const float *A, const float *B, float *C, long n) {
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for (long i = 0; i < n; i++)
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for (long j = 0; j < n; j++) {
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float acc = 0.0f;
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for (long k = 0; k < n; k++)
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acc += A[i * n + k] * B[k * n + j];
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C[i * n + j] = acc;
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}
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}
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static void matmul_opt(const float *A, const float *B, float *C, long n) {
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/* Transpose B so the inner reduction walks BT[j] contiguously instead
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* of striding B by n (the cache win), and use eight independent
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* accumulators (the ILP win, which also REORDERS the reduction). Both
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* levers together are a robust speedup AND make bit-identical output
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* impossible — the kernel lane in one function. */
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float *BT = malloc((size_t)n * n * sizeof(float));
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if (!BT) {
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matmul_ref(A, B, C, n);
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return;
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}
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for (long i = 0; i < n; i++)
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for (long j = 0; j < n; j++)
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BT[j * n + i] = B[i * n + j];
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for (long i = 0; i < n; i++) {
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const float *a = &A[i * n];
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for (long j = 0; j < n; j++) {
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const float *b = &BT[j * n];
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float acc[8] = {0, 0, 0, 0, 0, 0, 0, 0};
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long k = 0;
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for (; k + 8 <= n; k += 8)
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for (int r = 0; r < 8; r++)
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acc[r] += a[k + r] * b[k + r];
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float s = ((acc[0] + acc[1]) + (acc[2] + acc[3]))
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+ ((acc[4] + acc[5]) + (acc[6] + acc[7]));
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for (; k < n; k++)
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s += a[k] * b[k];
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C[i * n + j] = s;
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}
|
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}
|
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free(BT);
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}
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|
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static double now_s(void) {
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struct timespec t;
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clock_gettime(CLOCK_MONOTONIC, &t);
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return (double)t.tv_sec + (double)t.tv_nsec / 1e9;
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}
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|
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int main(int argc, char **argv) {
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if (argc < 3) {
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fprintf(stderr, "usage: %s <n> emit ref|opt | check <abs-tol> <rel-tol> | run ref|opt | bench ref|opt <reps>\n", argv[0]);
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return 2;
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}
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long n = atol(argv[1]);
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if (n < 1) n = 512;
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const char *mode = argv[2];
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|
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float *A = malloc((size_t)n * n * sizeof(float));
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float *B = malloc((size_t)n * n * sizeof(float));
|
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float *C = malloc((size_t)n * n * sizeof(float));
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float *R = malloc((size_t)n * n * sizeof(float));
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if (!A || !B || !C || !R) return 2;
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fill(A, n, 0x9E3779B1u);
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fill(B, n, 0x85EBCA77u);
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||||
|
||||
if (strcmp(mode, "emit") == 0) {
|
||||
int blocked = (argc > 3 && strcmp(argv[3], "opt") == 0);
|
||||
if (blocked) matmul_opt(A, B, C, n);
|
||||
else matmul_ref(A, B, C, n);
|
||||
for (long i = 0; i < n * n; i++) printf("%.9g\n", C[i]);
|
||||
return 0;
|
||||
}
|
||||
|
||||
if (strcmp(mode, "check") == 0) {
|
||||
/* Combined abs+rel tolerance — the standard for FP comparison, and
|
||||
* what the diff-test policy uses. Rel-only is wrong here: result
|
||||
* elements near zero (catastrophic cancellation) have meaningless
|
||||
* relative error, so an abs floor is required. */
|
||||
double abs_tol = argc > 3 ? atof(argv[3]) : 1e-4;
|
||||
double rel_tol = argc > 4 ? atof(argv[4]) : 1e-3;
|
||||
matmul_ref(A, B, R, n);
|
||||
matmul_opt(A, B, C, n);
|
||||
double max_abs = 0.0, max_rel = 0.0, worst_excess = -1e30;
|
||||
for (long i = 0; i < n * n; i++) {
|
||||
double d = fabs((double)C[i] - (double)R[i]);
|
||||
double r = d / (fabs((double)R[i]) + 1e-30);
|
||||
double tol = abs_tol + rel_tol * fabs((double)R[i]);
|
||||
if (d > max_abs) max_abs = d;
|
||||
if (r > max_rel) max_rel = r;
|
||||
if (d - tol > worst_excess) worst_excess = d - tol;
|
||||
}
|
||||
int pass = worst_excess <= 0.0;
|
||||
printf("kernel differential test (opt vs reference):\n");
|
||||
printf(" max_abs_err = %.3e\n", max_abs);
|
||||
printf(" max_rel_err = %.3e (dominated by near-zero elements; see abs floor)\n", max_rel);
|
||||
printf(" tolerance = abs %.3e + rel %.3e * |ref|\n", abs_tol, rel_tol);
|
||||
printf(" byte_identical = NO (accumulation reordered by design)\n");
|
||||
printf(" within_tolerance = %s\n", pass ? "YES" : "NO");
|
||||
printf(" verdict = %s\n", pass ? "EQUIVALENT" : "DIVERGENT");
|
||||
return pass ? 0 : 1;
|
||||
}
|
||||
|
||||
/* One matmul, no output — for bench-runner's interleaved A/B (external
|
||||
* wall-clock timing with a bootstrap CI, like every other target). */
|
||||
if (strcmp(mode, "run") == 0) {
|
||||
if (strcmp(argv[3], "opt") == 0) matmul_opt(A, B, C, n);
|
||||
else matmul_ref(A, B, C, n);
|
||||
/* touch C so the compiler cannot elide the work */
|
||||
volatile float sink = C[n * n - 1];
|
||||
(void)sink;
|
||||
return 0;
|
||||
}
|
||||
|
||||
if (strcmp(mode, "bench") == 0) {
|
||||
int use_opt = strcmp(argv[3], "opt") == 0;
|
||||
long reps = argc > 4 ? atol(argv[4]) : 5;
|
||||
if (use_opt) matmul_opt(A, B, C, n); else matmul_ref(A, B, C, n);
|
||||
double best = 1e30;
|
||||
for (long r = 0; r < reps; r++) {
|
||||
double t0 = now_s();
|
||||
if (use_opt) matmul_opt(A, B, C, n); else matmul_ref(A, B, C, n);
|
||||
double dt = now_s() - t0;
|
||||
if (dt < best) best = dt;
|
||||
}
|
||||
printf("%.6f\n", best);
|
||||
return 0;
|
||||
}
|
||||
|
||||
fprintf(stderr, "unknown mode: %s\n", mode);
|
||||
return 2;
|
||||
}
|
||||
Reference in New Issue
Block a user