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fix(metrics): keep the spread of values too small to square in f64 - #1151
A numeric column of very small values keeps its coefficient of variation, skewness and kurtosis. For values near 1e-200 the squared deviations underflowed to zero: the variance read 0.0, and the coefficient of variation and kurtosis described a constant column (0.0 and 0.0, where the same values at unit scale give 51.64 and -1.2). At 1e-160 the kurtosis already drifted, to -1.1973.
NumericAccumulator (crates/dataprof-metrics/src/stats/accumulator.rs) now holds Welford's M2 at one of three scales instead of two: raised by 2^1000 while it is small, at its true scale, and reduced by 2^-64 once it would overflow, as before (#805). M2 starts raised and moves to the next scale whenever an addition overflows; M2 never decreases, so it never moves back. Each squared deviation is formed at the scale M2 is held at, (delta * 2^500) * (deviation * 2^500) while raised, so it stays a normal f64 for deviations down to about 2^-1011 (1e-304). Below that it rounds in the subnormal range, and for subnormal values it can vanish. Scaling by a power of two is exact, so a spread that fits reports the same bits as before.
The standard deviation is taken at the scale M2 is held at, so it is finite where the variance underflows. Where the variance overflows it stays absent, as before.
A variance that underflows to zero while M2 is not zero is reported as null, like a variance that overflows. A true constant column still reports 0.0.
A varying column whose held M2 is below count times 2^-1034 is reported with no variance and no standard deviation, so no coefficient of variation, skewness or kurtosis either. Each squared deviation rounded in the subnormal range is off by at most 2^-1075, so above that line they cannot reach 2^-41 of M2; below it, as for values near 1e-313 or 5e-324, the spread came out with almost none of its digits or as zero, on master and before this round.
The SIMD path builds lane M2 at true scale. It now falls back to the scalar pass when a varying lane's M2 is below 2^-968, where a subnormal product's rounding could reach its last bit, and from_lane_state holds a lane's M2 raised where it fits, because values that cycle every four rows leave each lane constant and put the whole spread in the merge of the lanes.
Every input path takes its spread from NumericAccumulator, so the CSV engines, JSON, JSONL, Parquet, Arrow, pandas, polars, Python columns and analyze_column all change together. docs/schema/README.md says when the variance is null at the small end, what is still reported, and that values below about 1e-306 report no std_dev either.
Accumulate on scaled values, as the mean already does, so representable spread survives; or, where it cannot, report the derived statistics as absent rather than zero: M2 is held raised while small, the standard deviation, coefficient of variation, skewness and kurtosis survive, and the variance, which no f64 holds below about 1e-308, is null.
A test over scales from 1e-300 to 1e300 requiring scale-invariant statistics to agree, or to be absent: tests/small_spread_variance.rs and python/tests/test_small_spread_variance.py profile two shapes at 1, 1e-160, 1e-200, 1e-300, 1e-313, 5e-324, 1e100, 1e160 and 1e300. From 1e-300 to 1e100 the coefficient of variation, skewness and kurtosis must equal the unit-scale ones (and the standard deviation the unit-scale one times the scale, in Rust); from 1e160, where the spread itself overflows, and at 1e-313 and 5e-324, where subnormal rounding took it, all of them must be absent. The Rust test covers the standard CSV reader, the three engines, JSON, JSONL, Parquet and analyze_column; the Python test covers the three engines, Python columns, pyarrow, pandas, polars, Parquet and JSONL.
Per-part reverts, each written from snapshotted bytes, with a_tiny_spread_keeps_its_standard_deviation (unit) and small_spread_variance (integration) run by name:
Reverted part
unit
integration
M2 starts at true scale
fails
fails
standard deviation from the variance
fails
fails
underflowed variance kept as 0.0
fails
fails
no SIMD fallback on a tiny lane M2
fails
fails
lanes held at true scale
fails
fails
Both pass on the fixed tree. The unit test compares the standard deviation at 2^-530, 2^-665 and 2^-997 with the unit-scale one times the scale: bit for bit on the single and merged paths, within 1e-14 on SIMD, which falls back to the scalar pass at those scales and so rounds in another order. a_spread_that_fits_reports_the_same_bits_at_every_scale checks that the standard deviation of an ordinary spread is still the square root of its variance.
$ cargo test --workspace --all-features116 test suites, every one `test result: ok`
$ cargo clippy --all --all-targets -- -D warningsFinished
$ cargo fmt --all
$ uv run pytest python/tests -q2849 passed, 19 skipped
$ uv run ruff format / ruff check / ty checkAll checks passed
Timing, in-process over 5,000,000 values, best of 15 in release: scalar accumulation 28 to 31 ms on this branch and 29 to 30 ms on master, the SIMD path 10 to 15 ms against 11 to 12 ms. No measurable difference.
Whole-report diff against the 0.13.0 wheel (report_diff.py, 105 files, 487 file/path runs, with a CSV of the two shapes at 1, 1e-160, 1e-200 and 1e-300 added to the corpus, and its derived Parquet copy): every other file differs only in generator.commit and in the changes #1144, #1145 and #1147 made, so no spread that fits changed a serialized value. In the new file the unit-scale columns are unchanged; cycled_1e-200 goes from variance, CV, skewness and kurtosis 0.0 to null, 77.43, 0.7797 and -0.9898, the unit-scale values; blocked_1e-160 from CV 80.19 and kurtosis -0.7821 to 80.18 and -0.782; the 1e-300 columns as at 1e-200. Parity: 0 disagreements introduced.
Anything reviewers should know
The raw variance of values near 1e-160 is a subnormal number with a few digits, as before; it serializes as 0.0 at four decimals, as std_dev and mean of such values do. The serialized statistics that change are the scale-free ones, and variance where it becomes null.
sample_variance() and population_variance() return NaN for an underflowed variance, as they return infinity for an overflowed one; every report path keeps only finite values, so both become null.
Improved statistical results for datasets with very small or very large numeric spreads. Variance is now reported as unavailable when it cannot be represented, while standard deviation and related statistics remain available when representable.
Improved consistency of coefficient of variation, skewness, and kurtosis across supported analysis methods and data formats.
Documentation
Clarified when variance, standard deviation, and derived statistics may be unavailable.
Review round 1
CodeRabbit (minor): the comment on UNDERFLOW_SCALE claimed squared deviations down to 2^-2074 stay normal at the raised scale; they stay normal only down to 2^-2022, and for subnormal values the raised increment can still round or vanish. Comment corrected, and so is the same claim in this description. Beyond the comment: at 2^-1040 the column reported CV and skewness 0.0 and at 5e-324 everything 0.0, as on master. A larger factor is not available (f64 holds no power of two above 2^1023), so a varying column whose held M2 is below count times 2^-1034 now reports its spread as absent, which is the issue's fallback. Guards: a_spread_lost_to_subnormal_rounding_is_not_reported and the 1e-313 and 5e-324 columns of both twins; with the rule reverted, the unit test and small_spread_variance fail, and both pass restored.
Review round 2
Codex reviewed c5ec038 with no findings; CodeRabbit accepted round 1 and resolved its thread.
Self-review: docs/schema/README.md described the 1e-200 case but not the lost-spread rule added in round 1. It now says values below about 1e-306 report no std_dev; for the four-value pattern of the tests, 1e-306 keeps its statistics and 1e-307 reports them absent.
The accumulator now tracks M2 across raised, unit, and reduced scales. Standard deviation is computed from the held scale, while variance is reported as unavailable when it underflows. SIMD processing falls back to scalar accumulation for tiny nonconstant spreads. Rust and Python tests cover input paths, and schema documentation describes the output contract.
NumericAccumulator tracks M2 at raised, unit, and reduced scales for scalar updates and merges. Variance and standard deviation use scale-aware reporting.
SIMD processing falls back when a nonconstant lane has M2 below the safe threshold. Lane-state construction raises incoming M2 when the conversion remains finite.
Statistics contract and regression coverage tests/small_spread_variance.rs, python/tests/test_small_spread_variance.py, crates/dataprof-metrics/src/stats/accumulator.rs, docs/schema/README.md
Rust and Python tests compare statistics across scales and input paths. The schema documentation states that variance may be unavailable even when standard deviation and derived statistics remain reportable.
1150: The accumulator’s scale transitions also cover M2 overflow, but the supplied context identifies remaining overflow behavior; it does not establish that this change resolves that follow-up.
1149: The supplied description says this change cannot recover decimal digits lost before accumulation, so that issue’s objective is not addressed.
Correct the misleading range description before merging. The remaining extreme-subnormal limitation predates this change.
Pre-merge checks: 4 · 1
Failed checks: 1 warning
Check name
Status
Explanation
Resolution
Docstring Coverage
Docstring coverage is 65.38% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff with cyclomatic complexity of at least 2. Documenta…
Write docstrings for the functions missing them to satisfy the coverage threshold.
Passed checks: 4 passed
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Status
Explanation
Title check
The title is concise, specific, and accurately describes the main change: preserving value spread when squared deviations are too small to represent in f64.
Linked Issues check
Issue #1088 requires scaled accumulation or absent derived statistics when variance cannot represent the spread, plus tests from 1e-300 to 1e300. NumericAccumulator starts M2 at UNDERFLOW_SCALE, f…
Out of Scope Changes check
The changed accumulator, SIMD fallback, schema documentation, and Rust and Python tests all support issue #1088. The tests validate the implementation across input paths and are directly connected to …
Description check
The pull request description follows the required template. It explains the behavior change, links the issue, maps acceptance criteria to files and tests, documents verification commands and results, …
Full details: Linked Issues check
Explanation
Issue #1088 requires scaled accumulation or absent derived statistics when variance cannot represent the spread, plus tests from 1e-300 to 1e300. NumericAccumulator starts M2 at UNDERFLOW_SCALE, forms raised squared deviations, changes scale on overflow, reports underflowed variance as NaN for serialization as null, and computes standard deviation at the held scale. The Rust and Python regression tests cover the required scales, both lane layouts, and the listed input paths. The tests require scale-free statistics to match unit scale when the spread fits and to be absent when the spread overflows. The true constant-column behavior remains separate. The decimal limitation and overflow-side follow-up are outside issue #1088's required coding scope.
Full details: Out of Scope Changes check
Explanation
The changed accumulator, SIMD fallback, schema documentation, and Rust and Python tests all support issue #1088. The tests validate the implementation across input paths and are directly connected to the issue requirement. No unrelated change is established by the reviewed change summary or the inspected files.
Full details: Description check
Explanation
The pull request description follows the required template. It explains the behavior change, links the issue, maps acceptance criteria to files and tests, documents verification commands and results, and records reviewer-relevant limitations and follow-up issues.
Full details: Docstring Coverage
Explanation
Docstring coverage is 65.38% which is insufficient. The required threshold is 80.00%. Docstring coverage is scoped to functions touched by this diff with cyclomatic complexity of at least 2. Documentation-only edits and deletions within surviving functions are included; unchanged diff context and fully deleted functions are excluded. Analyzed 26 functions across 4 files. (1 skipped: 1 unsupported.)
Resolution
Write docstrings for the functions missing them to satisfy the coverage threshold.
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Actionable comments posted: 1
🪄 Fix comments: Fix CodeRabbit comments on this PR
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Inline comments:
Review comments at @crates/dataprof-metrics/src/stats/accumulator.rs:
- Around line 93-98: Correct the `UNDERFLOW_SCALE` documentation: clarify that
squared deviations remain normal down to 2^-2022 and may remain nonzero as
subnormals down to 2^-2074, and note that the raised Welford increment can still
underflow for smaller input differences. Preserve the existing M2 range
statement and do not change behavior.
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Files selected for processing: 5
crates/dataprof-metrics/src/acceleration/simd.rs
crates/dataprof-metrics/src/stats/accumulator.rs
docs/schema/README.md
python/tests/test_small_spread_variance.py
tests/small_spread_variance.rs
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What changed
A numeric column of very small values keeps its coefficient of variation, skewness and kurtosis. For values near 1e-200 the squared deviations underflowed to zero: the variance read 0.0, and the coefficient of variation and kurtosis described a constant column (0.0 and 0.0, where the same values at unit scale give 51.64 and -1.2). At 1e-160 the kurtosis already drifted, to -1.1973.
NumericAccumulator(crates/dataprof-metrics/src/stats/accumulator.rs) now holds Welford's M2 at one of three scales instead of two: raised by 2^1000 while it is small, at its true scale, and reduced by 2^-64 once it would overflow, as before (#805). M2 starts raised and moves to the next scale whenever an addition overflows; M2 never decreases, so it never moves back. Each squared deviation is formed at the scale M2 is held at,(delta * 2^500) * (deviation * 2^500)while raised, so it stays a normalf64for deviations down to about 2^-1011 (1e-304). Below that it rounds in the subnormal range, and for subnormal values it can vanish. Scaling by a power of two is exact, so a spread that fits reports the same bits as before.null, like a variance that overflows. A true constant column still reports 0.0.counttimes 2^-1034 is reported with no variance and no standard deviation, so no coefficient of variation, skewness or kurtosis either. Each squared deviation rounded in the subnormal range is off by at most 2^-1075, so above that line they cannot reach 2^-41 of M2; below it, as for values near 1e-313 or 5e-324, the spread came out with almost none of its digits or as zero, on master and before this round.from_lane_stateholds a lane's M2 raised where it fits, because values that cycle every four rows leave each lane constant and put the whole spread in the merge of the lanes.Every input path takes its spread from
NumericAccumulator, so the CSV engines, JSON, JSONL, Parquet, Arrow, pandas, polars, Python columns andanalyze_columnall change together.docs/schema/README.mdsays when the variance isnullat the small end, what is still reported, and that values below about 1e-306 report nostd_deveither.Related issue: Closes #1088
Acceptance criteria
f64holds below about 1e-308, isnull.tests/small_spread_variance.rsandpython/tests/test_small_spread_variance.pyprofile two shapes at 1, 1e-160, 1e-200, 1e-300, 1e-313, 5e-324, 1e100, 1e160 and 1e300. From 1e-300 to 1e100 the coefficient of variation, skewness and kurtosis must equal the unit-scale ones (and the standard deviation the unit-scale one times the scale, in Rust); from 1e160, where the spread itself overflows, and at 1e-313 and 5e-324, where subnormal rounding took it, all of them must be absent. The Rust test covers the standard CSV reader, the three engines, JSON, JSONL, Parquet andanalyze_column; the Python test covers the three engines, Python columns, pyarrow, pandas, polars, Parquet and JSONL.f64spacing). There the input loses its digits before it reaches the accumulator, so this change does not reach it; it needs a decimal or scaled-integer offset and is now Decimal columns: a spread below f64 spacing collapses before accumulation and reports variance and CV 0.0 #1149.How it was verified
Per-part reverts, each written from snapshotted bytes, with
a_tiny_spread_keeps_its_standard_deviation(unit) andsmall_spread_variance(integration) run by name:Both pass on the fixed tree. The unit test compares the standard deviation at 2^-530, 2^-665 and 2^-997 with the unit-scale one times the scale: bit for bit on the single and merged paths, within 1e-14 on SIMD, which falls back to the scalar pass at those scales and so rounds in another order.
a_spread_that_fits_reports_the_same_bits_at_every_scalechecks that the standard deviation of an ordinary spread is still the square root of its variance.Timing, in-process over 5,000,000 values, best of 15 in release: scalar accumulation 28 to 31 ms on this branch and 29 to 30 ms on master, the SIMD path 10 to 15 ms against 11 to 12 ms. No measurable difference.
Whole-report diff against the 0.13.0 wheel (
report_diff.py, 105 files, 487 file/path runs, with a CSV of the two shapes at 1, 1e-160, 1e-200 and 1e-300 added to the corpus, and its derived Parquet copy): every other file differs only ingenerator.commitand in the changes #1144, #1145 and #1147 made, so no spread that fits changed a serialized value. In the new file the unit-scale columns are unchanged;cycled_1e-200goes from variance, CV, skewness and kurtosis 0.0 tonull, 77.43, 0.7797 and -0.9898, the unit-scale values;blocked_1e-160from CV 80.19 and kurtosis -0.7821 to 80.18 and -0.782; the 1e-300 columns as at 1e-200. Parity: 0 disagreements introduced.Anything reviewers should know
varianceof values near 1e-160 is a subnormal number with a few digits, as before; it serializes as 0.0 at four decimals, asstd_devandmeanof such values do. The serialized statistics that change are the scale-free ones, andvariancewhere it becomesnull.sample_variance()andpopulation_variance()return NaN for an underflowed variance, as they return infinity for an overflowed one; every report path keeps only finite values, so both becomenull.Gaps noticed
Summary by CodeRabbit
Bug Fixes
Documentation
Review round 1
UNDERFLOW_SCALEclaimed squared deviations down to 2^-2074 stay normal at the raised scale; they stay normal only down to 2^-2022, and for subnormal values the raised increment can still round or vanish. Comment corrected, and so is the same claim in this description. Beyond the comment: at 2^-1040 the column reported CV and skewness 0.0 and at 5e-324 everything 0.0, as on master. A larger factor is not available (f64holds no power of two above 2^1023), so a varying column whose held M2 is belowcounttimes 2^-1034 now reports its spread as absent, which is the issue's fallback. Guards:a_spread_lost_to_subnormal_rounding_is_not_reportedand the 1e-313 and 5e-324 columns of both twins; with the rule reverted, the unit test andsmall_spread_variancefail, and both pass restored.Review round 2
docs/schema/README.mddescribed the 1e-200 case but not the lost-spread rule added in round 1. It now says values below about 1e-306 report nostd_dev; for the four-value pattern of the tests, 1e-306 keeps its statistics and 1e-307 reports them absent.