From 99e525bab4ea7170166613ee27e21fb0ea0f00db Mon Sep 17 00:00:00 2001 From: Dennis Zhuang Date: Sat, 17 Oct 2026 20:29:07 +0800 Subject: [PATCH 1/6] feat(promql): evaluate classic histogram_quantile and histogram_fraction over grid series Group bucket series by their labels other than le and evaluate each point as Prometheus BucketQuantile and BucketFraction do, including bucket coalescing, the small-delta tolerance and forced monotonicity. Signed-off-by: Dennis Zhuang --- src/promql/src/classic_histogram.rs | 328 ++ .../classic_histogram/prometheus_cases.txt | 3863 +++++++++++++++++ src/promql/src/classic_histogram/tests.rs | 85 + src/promql/src/grid_series.rs | 4 +- src/promql/src/lib.rs | 1 + 5 files changed, 4279 insertions(+), 2 deletions(-) create mode 100644 src/promql/src/classic_histogram.rs create mode 100644 src/promql/src/classic_histogram/prometheus_cases.txt create mode 100644 src/promql/src/classic_histogram/tests.rs diff --git a/src/promql/src/classic_histogram.rs b/src/promql/src/classic_histogram.rs new file mode 100644 index 00000000000..37a2393b9d3 --- /dev/null +++ b/src/promql/src/classic_histogram.rs @@ -0,0 +1,328 @@ +// Copyright 2023 Greptime Team +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +//! `histogram_quantile` and `histogram_fraction` over classic histograms, following Prometheus +//! `resetHistograms`, `BucketQuantile` and `BucketFraction`. + +use std::collections::HashMap; +use std::sync::Arc; + +use datafusion::error::{DataFusionError, Result}; +use datatypes::series::MetricName; +use datatypes::series::samples::{SampleRef, Series, SeriesSchema}; +use datatypes::series::time::TimeAxis; + +use crate::grid_series::{GridSeriesBuilder, LabelSet, label_set, merge_same_labelset}; + +#[cfg(test)] +mod tests; + +const BUCKET_LABEL: &str = "le"; +/// Relative difference under which neighbouring bucket counts are taken as equal. +const SMALL_DELTA_TOLERANCE: f64 = 1e-12; + +/// A classic histogram function with its constant arguments. +#[derive(Debug, Clone, Copy, PartialEq)] +pub enum ClassicHistogramFunction { + /// `histogram_quantile(q, v)`. + Quantile(f64), + /// `histogram_fraction(lower, upper, v)`. + Fraction { lower: f64, upper: f64 }, +} + +/// Evaluates `function` over the classic histograms in `series`. +/// +/// Series form a histogram when their labels other than `le` are equal; series whose `le` does +/// not parse as a float are ignored. At every point, each field is evaluated over the buckets +/// present there. Results drop `le` and `__name__`; histograms that then share a label set are +/// merged as [`merge_same_labelset`] does. +pub fn classic_histogram( + function: ClassicHistogramFunction, + schema: &Arc, + series: &[Series], +) -> Result> { + let mut histograms: HashMap> = HashMap::new(); + for series in series { + let Some(upper_bound) = series.metric.get(BUCKET_LABEL).and_then(parse_bound) else { + continue; + }; + let mut metric = series.metric.clone(); + metric.remove(BUCKET_LABEL); + histograms + .entry(label_set(&metric)) + .or_insert_with(|| Histogram { + metric, + members: Vec::new(), + }) + .members + .push((upper_bound, series)); + } + + let mut output = Vec::with_capacity(histograms.len()); + let mut builder = GridSeriesBuilder::try_new(schema.clone())?; + let mut buckets = Vec::new(); + let mut values = vec![None; schema.fields.len()]; + for Histogram { + mut metric, + mut members, + } in histograms.into_values() + { + // Pre-sorting by bound keeps the buckets of every point sorted. + members.sort_by(|a, b| a.0.total_cmp(&b.0)); + let mut ranges = Vec::with_capacity(members.len()); + for (_, series) in &members { + let TimeAxis::Grid(range) = &series.time else { + return Err(DataFusionError::Execution( + "histogram functions require evaluated series".into(), + )); + }; + ranges.push((range.start(), range.start() + range.len())); + } + let start = ranges.iter().map(|range| range.0).min().unwrap_or(0); + let end = ranges.iter().map(|range| range.1).max().unwrap_or(0); + for point in start..end { + for (field, value) in values.iter_mut().enumerate() { + buckets.clear(); + for ((upper_bound, series), &(series_start, series_end)) in + members.iter().zip(&ranges) + { + if !(series_start..series_end).contains(&point) { + continue; + } + match series.fields.as_slice()[field].sample(point - series_start) { + SampleRef::Missing => {} + SampleRef::Float(count) => buckets.push(Bucket { + upper_bound: *upper_bound, + count, + }), + SampleRef::Histogram(_) => { + return Err(DataFusionError::NotImplemented( + "histogram functions over native histogram samples".into(), + )); + } + } + } + *value = (!buckets.is_empty()).then(|| match function { + ClassicHistogramFunction::Quantile(q) => bucket_quantile(q, &mut buckets), + ClassicHistogramFunction::Fraction { lower, upper } => { + bucket_fraction(lower, upper, &mut buckets) + } + }); + } + builder.push(point, &values)?; + } + metric.remove("__name__"); + output.extend(builder.finish(metric)?); + } + merge_same_labelset(schema, output) +} + +/// Go's `strconv.ParseFloat`, which rejects finite literals out of the f64 range. +fn parse_bound(text: &str) -> Option { + let value: f64 = text.parse().ok()?; + if value.is_infinite() { + let unsigned = text.trim_start_matches(['+', '-']); + if !unsigned.eq_ignore_ascii_case("inf") && !unsigned.eq_ignore_ascii_case("infinity") { + return None; + } + } + Some(value) +} + +/// The bucket series of one histogram, with their upper bounds. +struct Histogram<'a> { + metric: MetricName, + members: Vec<(f64, &'a Series)>, +} + +#[derive(Debug, Clone, Copy)] +struct Bucket { + upper_bound: f64, + count: f64, +} + +/// Prometheus `BucketQuantile` over buckets sorted by upper bound. +fn bucket_quantile(q: f64, buckets: &mut Vec) -> f64 { + if q.is_nan() { + return f64::NAN; + } + if q < 0.0 { + return f64::NEG_INFINITY; + } + if q > 1.0 { + return f64::INFINITY; + } + if buckets.last().unwrap().upper_bound != f64::INFINITY { + return f64::NAN; + } + coalesce(buckets); + ensure_monotonic(buckets); + if buckets.len() < 2 { + return f64::NAN; + } + let observations = buckets.last().unwrap().count; + if observations == 0.0 { + return f64::NAN; + } + let mut rank = q * observations; + let b = go_search(buckets.len() - 1, |i| buckets[i].count >= rank); + if b == buckets.len() - 1 { + return buckets[buckets.len() - 2].upper_bound; + } + if b == 0 && buckets[0].upper_bound <= 0.0 { + return buckets[0].upper_bound; + } + let mut bucket_start = 0.0; + let bucket_end = buckets[b].upper_bound; + let mut count = buckets[b].count; + if b > 0 { + bucket_start = buckets[b - 1].upper_bound; + count -= buckets[b - 1].count; + rank -= buckets[b - 1].count; + } + bucket_start + (bucket_end - bucket_start) * (rank / count) +} + +/// Prometheus `BucketFraction` over buckets sorted by upper bound. +fn bucket_fraction(lower: f64, upper: f64, buckets: &mut Vec) -> f64 { + if buckets.last().unwrap().upper_bound != f64::INFINITY { + return f64::NAN; + } + coalesce(buckets); + let count = buckets.last().unwrap().count; + if count == 0.0 || lower.is_nan() || upper.is_nan() { + return f64::NAN; + } + if lower >= upper { + return 0.0; + } + + let (mut rank, mut lower_rank, mut upper_rank) = (0.0, 0.0, 0.0); + let (mut lower_set, mut upper_set) = (false, false); + let mut lower_bound = if buckets[0].upper_bound <= 0.0 { + f64::NEG_INFINITY + } else { + 0.0 + }; + for (i, bucket) in buckets.iter().enumerate() { + if i > 0 { + lower_bound = buckets[i - 1].upper_bound; + } + let upper_bound = bucket.upper_bound; + // An infinite-width bucket contributes nothing to the interpolation. + let interpolate = |value: f64| { + if lower_bound == f64::NEG_INFINITY { + bucket.count + } else { + rank + (bucket.count - rank) * (value - lower_bound) / (upper_bound - lower_bound) + } + }; + if !lower_set && lower_bound >= lower { + lower_rank = rank; + lower_set = true; + } + if !upper_set && lower_bound >= upper { + upper_rank = rank; + upper_set = true; + } + if lower_set && upper_set { + break; + } + if !lower_set && lower_bound < lower && upper_bound > lower { + lower_rank = interpolate(lower); + lower_set = true; + } + if !upper_set && lower_bound < upper && upper_bound > upper { + upper_rank = interpolate(upper); + upper_set = true; + } + if lower_set && upper_set { + break; + } + rank = bucket.count; + } + if !lower_set || lower_rank > count { + lower_rank = count; + } + if !upper_set || upper_rank > count { + upper_rank = count; + } + (upper_rank - lower_rank) / count +} + +/// Merges buckets with the same upper bound. +fn coalesce(buckets: &mut Vec) { + let mut last = buckets[0]; + let mut i = 0; + for j in 1..buckets.len() { + let bucket = buckets[j]; + if bucket.upper_bound == last.upper_bound { + last.count += bucket.count; + } else { + buckets[i] = last; + last = bucket; + i += 1; + } + } + buckets[i] = last; + buckets.truncate(i + 1); +} + +/// Prometheus `ensureMonotonicAndIgnoreSmallDeltas`: counts that differ from the previous one by +/// a negligible relative amount, or are lower, are raised to it. +fn ensure_monotonic(buckets: &mut [Bucket]) { + let mut prev = buckets[0].count; + for bucket in &mut buckets[1..] { + let curr = bucket.count; + if curr == prev { + continue; + } + if almost_equal(prev, curr, SMALL_DELTA_TOLERANCE) || curr < prev { + bucket.count = prev; + continue; + } + prev = curr; + } +} + +/// Prometheus `almost.Equal`. +fn almost_equal(a: f64, b: f64, epsilon: f64) -> bool { + if a.is_nan() && b.is_nan() { + return true; + } + if a == b { + return true; + } + let abs_sum = a.abs() + b.abs(); + let diff = (a - b).abs(); + if a == 0.0 || b == 0.0 || abs_sum < f64::MIN_POSITIVE { + return diff < epsilon * f64::MIN_POSITIVE; + } + diff / abs_sum.min(f64::MAX) < epsilon +} + +/// Go's `sort.Search`: the smallest index in `[0, n)` where `f` holds, or `n`, found by the same +/// bisection, so a predicate that is not monotonic (NaN counts) picks the same index. +fn go_search(n: usize, f: impl Fn(usize) -> bool) -> usize { + let (mut i, mut j) = (0, n); + while i < j { + let h = (i + j) / 2; + if !f(h) { + i = h + 1; + } else { + j = h; + } + } + i +} diff --git a/src/promql/src/classic_histogram/prometheus_cases.txt b/src/promql/src/classic_histogram/prometheus_cases.txt new file mode 100644 index 00000000000..65fed767a05 --- /dev/null +++ b/src/promql/src/classic_histogram/prometheus_cases.txt @@ -0,0 +1,3863 @@ +# Generated by promql-compat cmd/narthex-golden-histogram built for amd64 (Prometheus +# v3.15.0 engine, seed 1, 150 cases per function). Each case lists its operation and +# tab-separated arguments, the grid, the input series and either the result series or +# the error. Points are `grid index:hex bits`. +case quantile 3fefae147ae147ae +grid 100000 10000 2 +series __name__=a_bucket|job=x ; 0:4026000000000000 1:4018000000000000 +series __name__=a_bucket|job=x|le=abc ; 0:404f000000000000 1:4057c00000000000 +series __name__=a_bucket|job=x|le=+Inf ; 0:403c000000000000 1:403c000000000000 +series __name__=a_bucket|job=y|le=0.1 ; 0:4051500000000000 1:4053b00000000000 +series __name__=a_bucket|job=y|le=0.5 ; 0:4058e00000000000 +series __name__=a_bucket|job=y|le=1 ; 0:405d300000000000 1:4069600000000000 +series __name__=a_bucket|job=y|le=5 ; 0:4065580000000000 +series __name__=a_bucket|job=y|le=+Inf ; 0:406c280000000000 1:4074240000000000 +series __name__=b_bucket|job=z|le=0.25 ; 0:404ba00000000000 1:4040200000000000 +series __name__=b_bucket|job=z|le=2.5 ; 0:4060580000000000 1:405a100000000000 +series __name__=b_bucket|job=z|le=inf ; 0:4065680000000000 1:4065180000000000 +result job=x ; 0:7ff8000000000001 1:7ff8000000000001 +result job=y ; 0:4014000000000000 1:3ff0000000000000 +result job=z ; 0:4004000000000000 1:4004000000000000 +end +case quantile 3fe0000000000000 +grid 100000 10000 3 +series __name__=a_bucket|job=x|le=1 ; 0:404c800000000000 1:404a800000000000 2:4057800000000000 +series __name__=a_bucket|job=x|le=1.0 ; 0:4055c00000000000 1:4056c00000000000 2:403a000000000000 +series __name__=a_bucket|job=x|le=2 ; 1:4054800000000000 2:4000000000000000 +series __name__=a_bucket|job=x|le=+Inf ; 0:4024000000000000 1:4055000000000000 2:4054400000000000 +result job=x ; 0:3fe0000000000000 1:3fe0000000000000 2:3fe0000000000000 +end +case quantile bfe0000000000000 +grid 100000 10000 4 +series __name__=b_bucket|job=z|le=0.1 ; 0:403e000000000000 1:4018000000000000 2:4008000000000000 +series __name__=b_bucket|job=z|le=0.5 ; 0:403e000000000000 1:4036000000000000 2:4008000000000000 3:4047000000000287 +series __name__=b_bucket|job=z|le=1 ; 0:4049000000000000 1:403600000000f1e4 2:4024000000000000 3:4047000000000287 +series __name__=b_bucket|job=z|le=5 ; 2:4028000000000000 3:404c000000000287 +series __name__=b_bucket|job=z|le=+Inf ; 1:403600000002d5ae 2:4045800000000000 3:404c00000000059b +result job=z ; 0:fff0000000000000 1:fff0000000000000 2:fff0000000000000 3:fff0000000000000 +end +case quantile 3ff8000000000000 +grid 100000 10000 1 +series __name__=a_bucket|job=x|le=1 ; 0:402c000000000000 +series __name__=a_bucket|job=x|le=2 ; +series __name__=a_bucket|job=x|le=5 ; 0:404f000000000000 +result job=x ; 0:7ff0000000000000 +end +case quantile 3ff0000000000000 +grid 100000 10000 7 +series __name__=a_bucket|job=x|le=-1 ; 0:404b800000000000 1:4020000000000000 2:4042800000000000 3:4038000000000000 4:403c000000000000 5:404f000000000000 6:404e800000000000 +series __name__=a_bucket|job=x|le=0 ; 0:4026000000000000 1:403c000000000000 2:4055800000000000 3:4055c00000000000 4:4030000000000000 5:4056400000000000 6:4000000000000000 +series __name__=a_bucket|job=x|le=1 ; 0:4045800000000000 1:404a800000000000 2:4050c00000000000 3:404c800000000000 4:403a000000000000 +series __name__=a_bucket|job=x|le=+Inf ; 1:4052800000000000 2:402c000000000000 3:4052800000000000 4:4053400000000000 5:4055c00000000000 +series __name__=b_bucket|job=y|le=0.25 ; 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0:3ff0000000000000 1:402a000000000000 3:4028000000000000 4:4010000000000000 +series __name__=a_bucket|job=x|le=abc ; 0:4040000000000000 1:404a000000000000 2:40280000000002a3 3:4047000000000000 +series __name__=a_bucket|job=x ; 0:40400000000001c2 1:4055c00000000000 2:4027fffffffefac1 3:404700000000fce3 4:401000000000afec +series __name__=a_bucket|job=x|le=+Inf ; 0:403fffffffffffff 1:4055c00000000264 2:40427fffffffbeb0 3:4054800000007e72 4:403c000000002bfb +series __name__=b_bucket|job=y|le=0.25 ; 0:4012000000000000 2:4051e00000000000 3:401e000000000000 +series __name__=b_bucket|job=y|le=2.5 ; 0:4051400000000000 1:4044c00000000000 2:4065400000000000 4:4060b80000000000 +series __name__=b_bucket|job=y|le=inf ; 0:4064f00000000000 1:4055e00000000000 2:4065680000000000 +series __name__=b_bucket|job=z|le=-1 ; 0:4036800000000000 1:400e000000000000 2:404ac00000000000 3:4045c00000000000 4:4032c00000000000 +series __name__=b_bucket|job=z|le=0 ; 0:405cf00000000000 1:4043200000000000 2:4053400000000000 3:404b400000000000 4:4047800000000000 +series __name__=b_bucket|job=z|le=1 ; 0:4062080000000000 1:4060c80000000000 3:404ba00000000000 4:4052300000000000 +series __name__=b_bucket|job=z|le=+Inf ; 0:406ae80000000000 1:4068080000000000 2:405ea00000000000 3:4061e00000000000 4:4058400000000000 +result job=x ; 0:0 1:0 2:0 3:0 4:0 +result job=y ; 0:0 1:0 2:0 3:7ff8000000000001 4:7ff8000000000001 +result job=z ; 0:0 1:0 2:0 3:0 4:0 +end diff --git a/src/promql/src/classic_histogram/tests.rs b/src/promql/src/classic_histogram/tests.rs new file mode 100644 index 00000000000..27ee9a397ea --- /dev/null +++ b/src/promql/src/classic_histogram/tests.rs @@ -0,0 +1,85 @@ +// Copyright 2023 Greptime Team +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +use std::collections::BTreeMap; +use std::sync::Arc; + +use datatypes::series::samples::{FieldSpec, SeriesSchema}; + +use super::{ClassicHistogramFunction, classic_histogram}; +use crate::grid_series::reference::{ + canonical_bits, golden_cases, labels_of, points_of, series_of, +}; + +#[test] +fn classic_histograms_match_prometheus() { + let cases = golden_cases(include_str!("prometheus_cases.txt")); + assert_eq!(cases.len(), 300); + let (mut matched, mut failed) = (0, 0); + for case in cases { + let schema = Arc::new(SeriesSchema { + fields: vec![FieldSpec { + name: Arc::from("value"), + }] + .into(), + eval_grid: Some(case.grid.clone()), + }); + // The fixture lists buckets by bound; the kernel must not rely on input order. + let input: Vec<_> = case + .inputs + .iter() + .rev() + .filter_map(|(labels, points)| series_of(&schema, labels, points)) + .collect(); + let argument = + |index: usize| f64::from_bits(u64::from_str_radix(&case.spec[index], 16).unwrap()); + let function = match case.spec[0].as_str() { + "quantile" => ClassicHistogramFunction::Quantile(argument(1)), + "fraction" => ClassicHistogramFunction::Fraction { + lower: argument(1), + upper: argument(2), + }, + other => panic!("unknown case {other}"), + }; + match (classic_histogram(function, &schema, &input), case.outcome) { + (Ok(actual), Ok(expected)) => { + let actual: BTreeMap<_, _> = actual + .iter() + .map(|series| (labels_of(&series.metric), points_of(series))) + .collect(); + let expected: BTreeMap<_, _> = expected + .into_iter() + .map(|(labels, points)| { + let points = points + .into_iter() + .map(|(index, bits)| (index, canonical_bits(f64::from_bits(bits)))) + .collect(); + (labels, points) + }) + .collect(); + assert_eq!(actual, expected, "case {:?}", case.spec); + matched += 1; + } + (Err(actual), Err(expected)) => { + assert!(actual.to_string().contains(&expected), "{actual}"); + failed += 1; + } + (actual, expected) => panic!("case {:?}: {actual:?} is not {expected:?}", case.spec), + } + } + assert!( + matched > 250 && failed > 20, + "{matched} matched, {failed} failed" + ); +} diff --git a/src/promql/src/grid_series.rs b/src/promql/src/grid_series.rs index e5e9bd53532..950fadd63e3 100644 --- a/src/promql/src/grid_series.rs +++ b/src/promql/src/grid_series.rs @@ -142,10 +142,10 @@ impl GridSeriesBuilder { } } -type LabelSet = Vec<(Arc, Arc)>; +pub(crate) type LabelSet = Vec<(Arc, Arc)>; /// The label set Prometheus compares, which has no empty values. -fn label_set(metric: &MetricName) -> LabelSet { +pub(crate) fn label_set(metric: &MetricName) -> LabelSet { let name = metric .name() .filter(|name| !name.is_empty()) diff --git a/src/promql/src/lib.rs b/src/promql/src/lib.rs index dac3eb899a1..9f8051f83e1 100644 --- a/src/promql/src/lib.rs +++ b/src/promql/src/lib.rs @@ -12,6 +12,7 @@ // See the License for the specific language governing permissions and // limitations under the License. +pub mod classic_histogram; pub mod error; pub mod extension_plan; pub mod functions; From 0b478fb4997961560dad1d1d5fb3625c48c78334 Mon Sep 17 00:00:00 2001 From: Dennis Zhuang Date: Sat, 17 Oct 2026 20:52:58 +0800 Subject: [PATCH 2/6] feat(promql): evaluate native histogram functions over grid series Add histogram_count/sum/avg/stddev/stdvar and native histogram_quantile and histogram_fraction, ported from Prometheus HistogramQuantile, HistogramFraction and histogramVariance with Go's bucket iteration, exponential bound table and math.Log2/Exp2. histogram_quantile and histogram_fraction now evaluate classic and native histograms in one vector and skip both where they conflict, as resetHistograms does. Signed-off-by: Dennis Zhuang --- src/promql/src/classic_histogram/tests.rs | 85 - src/promql/src/grid_series/reference.rs | 35 +- src/promql/src/histogram_eval.rs | 240 ++ src/promql/src/histogram_eval/bounds.rs | 167 + .../classic.rs} | 132 +- .../classic_cases.txt} | 0 .../src/histogram_eval/go_math_cases.txt | 404 +++ src/promql/src/histogram_eval/native.rs | 523 +++ .../src/histogram_eval/native_cases.txt | 2964 +++++++++++++++++ src/promql/src/histogram_eval/tests.rs | 270 ++ src/promql/src/lib.rs | 2 +- 11 files changed, 4600 insertions(+), 222 deletions(-) delete mode 100644 src/promql/src/classic_histogram/tests.rs create mode 100644 src/promql/src/histogram_eval.rs create mode 100644 src/promql/src/histogram_eval/bounds.rs rename src/promql/src/{classic_histogram.rs => histogram_eval/classic.rs} (55%) rename src/promql/src/{classic_histogram/prometheus_cases.txt => histogram_eval/classic_cases.txt} (100%) create mode 100644 src/promql/src/histogram_eval/go_math_cases.txt create mode 100644 src/promql/src/histogram_eval/native.rs create mode 100644 src/promql/src/histogram_eval/native_cases.txt create mode 100644 src/promql/src/histogram_eval/tests.rs diff --git a/src/promql/src/classic_histogram/tests.rs b/src/promql/src/classic_histogram/tests.rs deleted file mode 100644 index 27ee9a397ea..00000000000 --- a/src/promql/src/classic_histogram/tests.rs +++ /dev/null @@ -1,85 +0,0 @@ -// Copyright 2023 Greptime Team -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -use std::collections::BTreeMap; -use std::sync::Arc; - -use datatypes::series::samples::{FieldSpec, SeriesSchema}; - -use super::{ClassicHistogramFunction, classic_histogram}; -use crate::grid_series::reference::{ - canonical_bits, golden_cases, labels_of, points_of, series_of, -}; - -#[test] -fn classic_histograms_match_prometheus() { - let cases = golden_cases(include_str!("prometheus_cases.txt")); - assert_eq!(cases.len(), 300); - let (mut matched, mut failed) = (0, 0); - for case in cases { - let schema = Arc::new(SeriesSchema { - fields: vec![FieldSpec { - name: Arc::from("value"), - }] - .into(), - eval_grid: Some(case.grid.clone()), - }); - // The fixture lists buckets by bound; the kernel must not rely on input order. - let input: Vec<_> = case - .inputs - .iter() - .rev() - .filter_map(|(labels, points)| series_of(&schema, labels, points)) - .collect(); - let argument = - |index: usize| f64::from_bits(u64::from_str_radix(&case.spec[index], 16).unwrap()); - let function = match case.spec[0].as_str() { - "quantile" => ClassicHistogramFunction::Quantile(argument(1)), - "fraction" => ClassicHistogramFunction::Fraction { - lower: argument(1), - upper: argument(2), - }, - other => panic!("unknown case {other}"), - }; - match (classic_histogram(function, &schema, &input), case.outcome) { - (Ok(actual), Ok(expected)) => { - let actual: BTreeMap<_, _> = actual - .iter() - .map(|series| (labels_of(&series.metric), points_of(series))) - .collect(); - let expected: BTreeMap<_, _> = expected - .into_iter() - .map(|(labels, points)| { - let points = points - .into_iter() - .map(|(index, bits)| (index, canonical_bits(f64::from_bits(bits)))) - .collect(); - (labels, points) - }) - .collect(); - assert_eq!(actual, expected, "case {:?}", case.spec); - matched += 1; - } - (Err(actual), Err(expected)) => { - assert!(actual.to_string().contains(&expected), "{actual}"); - failed += 1; - } - (actual, expected) => panic!("case {:?}: {actual:?} is not {expected:?}", case.spec), - } - } - assert!( - matched > 250 && failed > 20, - "{matched} matched, {failed} failed" - ); -} diff --git a/src/promql/src/grid_series/reference.rs b/src/promql/src/grid_series/reference.rs index 047b1f65126..ae6c55a3ca9 100644 --- a/src/promql/src/grid_series/reference.rs +++ b/src/promql/src/grid_series/reference.rs @@ -127,6 +127,8 @@ pub(crate) struct GoldenCase { pub(crate) spec: Vec, pub(crate) grid: Arc, pub(crate) inputs: Vec<(Labels, Points)>, + /// Native histogram points of each input, as written by the generator. + pub(crate) histograms: Vec>, /// Result series by label set, or the error message. pub(crate) outcome: Result, String>, } @@ -142,16 +144,19 @@ pub(crate) fn golden_cases(text: &str) -> Vec { }) .collect() }; - let points = |text: &str| -> Points { - text.split_whitespace() - .map(|point| { - let (index, bits) = point.split_once(':').unwrap(); - ( - index.parse().unwrap(), - u64::from_str_radix(bits, 16).unwrap(), - ) - }) - .collect() + let points = |text: &str| -> (Points, BTreeMap) { + let mut floats = Points::new(); + let mut histograms = BTreeMap::new(); + for point in text.split_whitespace() { + let (index, value) = point.split_once(':').unwrap(); + let index = index.parse().unwrap(); + if let Some(histogram) = value.strip_prefix('H') { + histograms.insert(index, histogram.to_string()); + } else { + floats.insert(index, u64::from_str_radix(value, 16).unwrap()); + } + } + (floats, histograms) }; let mut cases = Vec::new(); for case in text.split("end\n").filter(|case| case.contains("case ")) { @@ -164,6 +169,7 @@ pub(crate) fn golden_cases(text: &str) -> Vec { .collect(); let grid = GridSpec::try_new(grid[0], grid[1], grid[2] as u64).unwrap(); let mut inputs = Vec::new(); + let mut histograms = Vec::new(); let mut outcome = Ok(BTreeMap::new()); for line in &lines[2..] { if let Some(message) = line.strip_prefix("error ") { @@ -172,9 +178,13 @@ pub(crate) fn golden_cases(text: &str) -> Vec { } let (kind, rest) = line.split_once(' ').unwrap(); let (series_labels, series_points) = rest.split_once(" ;").unwrap(); - let entry = (labels(series_labels), points(series_points)); + let (floats, histogram_points) = points(series_points); + let entry = (labels(series_labels), floats); match kind { - "series" => inputs.push(entry), + "series" => { + inputs.push(entry); + histograms.push(histogram_points); + } "result" => { outcome.as_mut().unwrap().insert(entry.0, entry.1); } @@ -185,6 +195,7 @@ pub(crate) fn golden_cases(text: &str) -> Vec { spec: spec.split('\t').map(str::to_string).collect(), grid: Arc::new(EvalGrid::try_new(grid).unwrap()), inputs, + histograms, outcome, }); } diff --git a/src/promql/src/histogram_eval.rs b/src/promql/src/histogram_eval.rs new file mode 100644 index 00000000000..dfdce804a24 --- /dev/null +++ b/src/promql/src/histogram_eval.rs @@ -0,0 +1,240 @@ +// Copyright 2023 Greptime Team +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +//! Histogram functions over evaluated series: `histogram_quantile` and `histogram_fraction` over +//! classic and native histograms (Prometheus `funcHistogramQuantile`, `funcHistogramFraction` +//! and `resetHistograms`), and `histogram_count`, `histogram_sum`, `histogram_avg`, +//! `histogram_stddev` and `histogram_stdvar` over native histograms. + +mod bounds; +mod classic; +mod native; +#[cfg(test)] +mod tests; + +use std::collections::HashMap; +use std::sync::Arc; + +use datafusion::error::{DataFusionError, Result}; +use datatypes::series::MetricName; +use datatypes::series::histogram::HistogramView; +use datatypes::series::samples::{DenseSamplesRef, SampleRef, Series, SeriesSchema}; +use datatypes::series::time::TimeAxis; + +use crate::grid_series::{GridSeriesBuilder, LabelSet, label_set, merge_same_labelset}; + +const BUCKET_LABEL: &str = "le"; + +/// `histogram_quantile` or `histogram_fraction` with its constant arguments. +#[derive(Debug, Clone, Copy, PartialEq)] +pub enum HistogramFunction { + /// `histogram_quantile(q, v)`. + Quantile(f64), + /// `histogram_fraction(lower, upper, v)`. + Fraction { lower: f64, upper: f64 }, +} + +/// Evaluates `function` over the classic and native histograms in `series`. +/// +/// Float series with the same labels other than `le` form a classic histogram; a float series +/// whose `le` does not parse is ignored. Native histogram samples are evaluated one by one. At a +/// point where a native histogram and classic buckets with the same labels (`le` aside) are both +/// present, neither is evaluated. Each field is evaluated on its own. Results drop `le` and +/// `__name__`, and series that then share a label set are merged as [`merge_same_labelset`] +/// does. +pub fn evaluate_histograms( + function: HistogramFunction, + schema: &Arc, + series: &[Series], +) -> Result> { + let mut groups: HashMap> = HashMap::new(); + for series in series { + let range = grid_range(series)?; + if let Some(upper_bound) = series + .metric + .get(BUCKET_LABEL) + .and_then(classic::parse_bound) + { + let mut metric = series.metric.clone(); + metric.remove(BUCKET_LABEL); + groups + .entry(label_set(&metric)) + .or_insert_with(|| Group::new(metric)) + .classic + .push((upper_bound, series, range)); + } + if has_histograms(series) { + let metric = series.metric.clone(); + groups + .entry(label_set(&metric)) + .or_insert_with(|| Group::new(metric)) + .native = Some((series, range)); + } + } + + let mut output = Vec::with_capacity(groups.len()); + let mut builder = GridSeriesBuilder::try_new(schema.clone())?; + let mut classic_buckets = Vec::new(); + let mut native_buckets = Vec::new(); + let mut values = vec![None; schema.fields.len()]; + for mut group in groups.into_values() { + // Pre-sorting by bound keeps the buckets of every point sorted. + group.classic.sort_by(|a, b| a.0.total_cmp(&b.0)); + let ranges = group + .classic + .iter() + .map(|member| member.2) + .chain(group.native.map(|native| native.1)); + let start = ranges.clone().map(|range| range.0).min().unwrap_or(0); + let end = ranges.map(|range| range.1).max().unwrap_or(0); + for point in start..end { + for (field, value) in values.iter_mut().enumerate() { + classic_buckets.clear(); + for &(upper_bound, series, range) in &group.classic { + if let Some(SampleRef::Float(count)) = sample(series, range, field, point) { + classic_buckets.push(classic::Bucket { upper_bound, count }); + } + } + let native = group.native.and_then(|(series, range)| { + match sample(series, range, field, point) { + Some(SampleRef::Histogram(h)) => Some(h), + _ => None, + } + }); + // A native histogram and classic buckets of one label set conflict. + *value = match (native, classic_buckets.is_empty()) { + (Some(_), false) | (None, true) => None, + (Some(h), true) => Some(match function { + HistogramFunction::Quantile(q) => { + native::quantile(q, &h, &mut native_buckets)? + } + HistogramFunction::Fraction { lower, upper } => { + native::fraction(lower, upper, &h, &mut native_buckets)? + } + }), + (None, false) => Some(match function { + HistogramFunction::Quantile(q) => { + classic::bucket_quantile(q, &mut classic_buckets) + } + HistogramFunction::Fraction { lower, upper } => { + classic::bucket_fraction(lower, upper, &mut classic_buckets) + } + }), + }; + } + builder.push(point, &values)?; + } + group.metric.remove("__name__"); + output.extend(builder.finish(group.metric)?); + } + merge_same_labelset(schema, output) +} + +/// The series of one label set (`le` aside): classic buckets, and the series of exactly that +/// label set when it holds native histograms. +struct Group<'a> { + metric: MetricName, + classic: Vec<(f64, &'a Series, (usize, usize))>, + native: Option<(&'a Series, (usize, usize))>, +} + +impl Group<'_> { + fn new(metric: MetricName) -> Self { + Self { + metric, + classic: Vec::new(), + native: None, + } + } +} + +/// The absolute grid range `[start, end)` of `series`. +fn grid_range(series: &Series) -> Result<(usize, usize)> { + let TimeAxis::Grid(range) = &series.time else { + return Err(DataFusionError::Execution( + "histogram functions require evaluated series".into(), + )); + }; + Ok((range.start(), range.start() + range.len())) +} + +fn sample( + series: &Series, + (start, end): (usize, usize), + field: usize, + point: usize, +) -> Option> { + (start..end) + .contains(&point) + .then(|| series.fields.as_slice()[field].sample(point - start)) +} + +fn has_histograms(series: &Series) -> bool { + series.fields.iter().any(|samples| { + samples + .segments() + .iter() + .any(|segment| !matches!(segment.dense(), Some(DenseSamplesRef::Float(_)))) + }) +} + +/// A function of one native histogram. +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +pub enum NativeHistogramFunction { + Count, + Sum, + Avg, + StdDev, + StdVar, +} + +/// Applies `function` to the native histogram samples of `series`; float samples are dropped and +/// so is `__name__`. The result is `None` when the series has no histogram sample. +/// +/// Series that share a label set once their names are dropped must then go through +/// [`merge_same_labelset`]. +pub fn map_native_histogram( + function: NativeHistogramFunction, + schema: &Arc, + series: &Series, +) -> Result> { + let range = grid_range(series)?; + let mut builder = GridSeriesBuilder::try_new(schema.clone())?; + let mut buckets = Vec::new(); + let mut values = vec![None; schema.fields.len()]; + for point in range.0..range.1 { + for (field, value) in values.iter_mut().enumerate() { + *value = match sample(series, range, field, point) { + Some(SampleRef::Histogram(h)) => Some(function.apply(&h, &mut buckets)?), + _ => None, + }; + } + builder.push(point, &values)?; + } + let mut metric = series.metric.clone(); + metric.remove("__name__"); + builder.finish(metric) +} + +impl NativeHistogramFunction { + fn apply(self, h: &HistogramView<'_>, buckets: &mut Vec) -> Result { + Ok(match self { + Self::Count => h.count, + Self::Sum => h.sum, + Self::Avg => h.sum / h.count, + Self::StdDev => native::variance(h, buckets)?.sqrt(), + Self::StdVar => native::variance(h, buckets)?, + }) + } +} diff --git a/src/promql/src/histogram_eval/bounds.rs b/src/promql/src/histogram_eval/bounds.rs new file mode 100644 index 00000000000..ddc3a69290d --- /dev/null +++ b/src/promql/src/histogram_eval/bounds.rs @@ -0,0 +1,167 @@ +// Copyright 2023 Greptime Team +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +//! Prometheus `exponentialBounds` (`model/histogram/generic.go`): the bucket bounds in [0.5, 1) +//! of exponential schemas 0 to 8, which `getBoundExponential` scales by a power of two. + +#[rustfmt::skip] +pub(super) const EXPONENTIAL_BOUNDS: [&[f64]; 9] = [ + &[ + 0.5, + ], + &[ + 0.5, 0.7071067811865475, + ], + &[ + 0.5, 0.5946035575013605, 0.7071067811865475, 0.8408964152537144, + ], + &[ + 0.5, 0.5452538663326288, 0.5946035575013605, 0.6484197773255048, + 0.7071067811865475, 0.7711054127039704, 0.8408964152537144, 0.9170040432046711, + ], + &[ + 0.5, 0.5221368912137069, 0.5452538663326288, 0.5693943173783458, + 0.5946035575013605, 0.620928906036742, 0.6484197773255048, 0.6771277734684463, + 0.7071067811865475, 0.7384130729697496, 0.7711054127039704, 0.805245165974627, + 0.8408964152537144, 0.8781260801866495, 0.9170040432046711, 0.9576032806985735, + ], + &[ + 0.5, 0.5109485743270583, 0.5221368912137069, 0.5335702003384117, + 0.5452538663326288, 0.5571933712979462, 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0.5221368912137069, 0.5249720429003435, 0.5278225891802786, 0.5306886136446309, + 0.5335702003384117, 0.5364674337629877, 0.5393803988785598, 0.5423091811066545, + 0.5452538663326288, 0.5482145409081883, 0.5511912916539204, 0.5541842058618393, + 0.5571933712979462, 0.5602188762048033, 0.5632608093041209, 0.5663192597993595, + 0.5693943173783458, 0.572486072215902, 0.5755946149764913, 0.5787200368168754, + 0.5818624293887887, 0.585021884841625, 0.5881984958251406, 0.5913923554921704, + 0.5946035575013605, 0.5978321960199137, 0.6010783657263515, 0.6043421618132907, + 0.6076236799902344, 0.6109230164863786, 0.6142402680534349, 0.6175755319684665, + 0.620928906036742, 0.6243004885946023, 0.6276903785123455, 0.6310986751971253, + 0.6345254785958666, 0.637970889198196, 0.6414350080393891, 0.6449179367033329, + 0.6484197773255048, 0.6519406325959679, 0.6554806057623822, 0.659039800633032, + 0.6626183215798706, 0.6662162735415805, 0.6698337620266515, 0.6734708931164728, + 0.6771277734684463, 0.6808045103191123, 0.6845012114872953, 0.688217985377265, + 0.6919549409819159, 0.6957121878859629, 0.6994898362691555, 0.7032879969095076, + 0.7071067811865475, 0.7109463010845827, 0.7148066691959849, 0.718687998724491, + 0.7225904034885232, 0.7265139979245261, 0.7304588970903234, 0.7344252166684908, + 0.7384130729697496, 0.7424225829363761, 0.7464538641456323, 0.7505070348132126, + 0.7545822137967112, 0.7586795205991071, 0.762799075372269, 0.7669409989204777, + 0.7711054127039704, 0.7752924388424999, 0.7795022001189185, 0.7837348199827764, + 0.7879904225539431, 0.7922691326262467, 0.7965710756711334, 0.8008963778413465, + 0.805245165974627, 0.8096175675974316, 0.8140137109286738, 0.8184337248834821, + 0.8228777390769823, 0.8273458838280969, 0.8318382901633681, 0.8363550898207981, + 0.8408964152537144, 0.8454623996346523, 0.8500531768592616, 0.8546688815502312, + 0.8593096490612387, 0.8639756154809185, 0.8686669176368529, 0.8733836930995842, + 0.8781260801866495, 0.8828942179666361, 0.8876882462632604, 0.8925083056594671, + 0.8973545375015533, 0.9022270839033115, 0.9071260877501991, 0.9120516927035263, + 0.9170040432046711, 0.9219832844793128, 0.9269895625416926, 0.9320230241988943, + 0.9370838170551498, 0.9421720895161669, 0.9472879907934827, 0.9524316709088368, + 0.9576032806985735, 0.9628029718180622, 0.9680308967461471, 0.9732872087896164, + 0.9785720620876999, 0.9838856116165875, 0.9892280131939752, 0.9945994234836328, + ], + &[ + 0.5, 0.5013556375251013, 0.5027149505564014, 0.5040779490592088, + 0.5054446430258502, 0.5068150424757447, 0.5081891574554764, 0.509566998038869, + 0.5109485743270583, 0.5123338964485679, 0.5137229745593818, 0.5151158188430205, + 0.5165124395106142, 0.5179128468009786, 0.5193170509806894, 0.520725062344158, + 0.5221368912137069, 0.5235525479396449, 0.5249720429003435, 0.526395386502313, + 0.5278225891802786, 0.5292536613972564, 0.5306886136446309, 0.5321274564422321, + 0.5335702003384117, 0.5350168559101208, 0.5364674337629877, 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0.9120516927035263, 0.9145245157024483, + 0.9170040432046711, 0.9194902933879467, 0.9219832844793128, 0.9244830347552253, + 0.9269895625416926, 0.92950288621441, 0.9320230241988943, 0.9345499949706191, + 0.9370838170551498, 0.93962450902828, 0.9421720895161669, 0.9447265771954693, + 0.9472879907934827, 0.9498563490882775, 0.9524316709088368, 0.9550139751351947, + 0.9576032806985735, 0.9601996065815236, 0.9628029718180622, 0.9654133954938133, + 0.9680308967461471, 0.9706554947643201, 0.9732872087896164, 0.9759260581154889, + 0.9785720620876999, 0.9812252401044634, 0.9838856116165875, 0.9865531961276168, + 0.9892280131939752, 0.9919100824251095, 0.9945994234836328, 0.9972960560854698, + ], +]; diff --git a/src/promql/src/classic_histogram.rs b/src/promql/src/histogram_eval/classic.rs similarity index 55% rename from src/promql/src/classic_histogram.rs rename to src/promql/src/histogram_eval/classic.rs index 37a2393b9d3..9a3752cbec6 100644 --- a/src/promql/src/classic_histogram.rs +++ b/src/promql/src/histogram_eval/classic.rs @@ -12,124 +12,14 @@ // See the License for the specific language governing permissions and // limitations under the License. -//! `histogram_quantile` and `histogram_fraction` over classic histograms, following Prometheus -//! `resetHistograms`, `BucketQuantile` and `BucketFraction`. +//! Prometheus `BucketQuantile` and `BucketFraction` over the buckets of a classic histogram at +//! one point. -use std::collections::HashMap; -use std::sync::Arc; - -use datafusion::error::{DataFusionError, Result}; -use datatypes::series::MetricName; -use datatypes::series::samples::{SampleRef, Series, SeriesSchema}; -use datatypes::series::time::TimeAxis; - -use crate::grid_series::{GridSeriesBuilder, LabelSet, label_set, merge_same_labelset}; - -#[cfg(test)] -mod tests; - -const BUCKET_LABEL: &str = "le"; /// Relative difference under which neighbouring bucket counts are taken as equal. const SMALL_DELTA_TOLERANCE: f64 = 1e-12; -/// A classic histogram function with its constant arguments. -#[derive(Debug, Clone, Copy, PartialEq)] -pub enum ClassicHistogramFunction { - /// `histogram_quantile(q, v)`. - Quantile(f64), - /// `histogram_fraction(lower, upper, v)`. - Fraction { lower: f64, upper: f64 }, -} - -/// Evaluates `function` over the classic histograms in `series`. -/// -/// Series form a histogram when their labels other than `le` are equal; series whose `le` does -/// not parse as a float are ignored. At every point, each field is evaluated over the buckets -/// present there. Results drop `le` and `__name__`; histograms that then share a label set are -/// merged as [`merge_same_labelset`] does. -pub fn classic_histogram( - function: ClassicHistogramFunction, - schema: &Arc, - series: &[Series], -) -> Result> { - let mut histograms: HashMap> = HashMap::new(); - for series in series { - let Some(upper_bound) = series.metric.get(BUCKET_LABEL).and_then(parse_bound) else { - continue; - }; - let mut metric = series.metric.clone(); - metric.remove(BUCKET_LABEL); - histograms - .entry(label_set(&metric)) - .or_insert_with(|| Histogram { - metric, - members: Vec::new(), - }) - .members - .push((upper_bound, series)); - } - - let mut output = Vec::with_capacity(histograms.len()); - let mut builder = GridSeriesBuilder::try_new(schema.clone())?; - let mut buckets = Vec::new(); - let mut values = vec![None; schema.fields.len()]; - for Histogram { - mut metric, - mut members, - } in histograms.into_values() - { - // Pre-sorting by bound keeps the buckets of every point sorted. - members.sort_by(|a, b| a.0.total_cmp(&b.0)); - let mut ranges = Vec::with_capacity(members.len()); - for (_, series) in &members { - let TimeAxis::Grid(range) = &series.time else { - return Err(DataFusionError::Execution( - "histogram functions require evaluated series".into(), - )); - }; - ranges.push((range.start(), range.start() + range.len())); - } - let start = ranges.iter().map(|range| range.0).min().unwrap_or(0); - let end = ranges.iter().map(|range| range.1).max().unwrap_or(0); - for point in start..end { - for (field, value) in values.iter_mut().enumerate() { - buckets.clear(); - for ((upper_bound, series), &(series_start, series_end)) in - members.iter().zip(&ranges) - { - if !(series_start..series_end).contains(&point) { - continue; - } - match series.fields.as_slice()[field].sample(point - series_start) { - SampleRef::Missing => {} - SampleRef::Float(count) => buckets.push(Bucket { - upper_bound: *upper_bound, - count, - }), - SampleRef::Histogram(_) => { - return Err(DataFusionError::NotImplemented( - "histogram functions over native histogram samples".into(), - )); - } - } - } - *value = (!buckets.is_empty()).then(|| match function { - ClassicHistogramFunction::Quantile(q) => bucket_quantile(q, &mut buckets), - ClassicHistogramFunction::Fraction { lower, upper } => { - bucket_fraction(lower, upper, &mut buckets) - } - }); - } - builder.push(point, &values)?; - } - metric.remove("__name__"); - output.extend(builder.finish(metric)?); - } - merge_same_labelset(schema, output) -} - /// Go's `strconv.ParseFloat`, which rejects finite literals out of the f64 range. -fn parse_bound(text: &str) -> Option { +pub(super) fn parse_bound(text: &str) -> Option { let value: f64 = text.parse().ok()?; if value.is_infinite() { let unsigned = text.trim_start_matches(['+', '-']); @@ -140,20 +30,14 @@ fn parse_bound(text: &str) -> Option { Some(value) } -/// The bucket series of one histogram, with their upper bounds. -struct Histogram<'a> { - metric: MetricName, - members: Vec<(f64, &'a Series)>, -} - #[derive(Debug, Clone, Copy)] -struct Bucket { - upper_bound: f64, - count: f64, +pub(super) struct Bucket { + pub(super) upper_bound: f64, + pub(super) count: f64, } /// Prometheus `BucketQuantile` over buckets sorted by upper bound. -fn bucket_quantile(q: f64, buckets: &mut Vec) -> f64 { +pub(super) fn bucket_quantile(q: f64, buckets: &mut Vec) -> f64 { if q.is_nan() { return f64::NAN; } @@ -195,7 +79,7 @@ fn bucket_quantile(q: f64, buckets: &mut Vec) -> f64 { } /// Prometheus `BucketFraction` over buckets sorted by upper bound. -fn bucket_fraction(lower: f64, upper: f64, buckets: &mut Vec) -> f64 { +pub(super) fn bucket_fraction(lower: f64, upper: f64, buckets: &mut Vec) -> f64 { if buckets.last().unwrap().upper_bound != f64::INFINITY { return f64::NAN; } diff --git a/src/promql/src/classic_histogram/prometheus_cases.txt b/src/promql/src/histogram_eval/classic_cases.txt similarity index 100% rename from src/promql/src/classic_histogram/prometheus_cases.txt rename to src/promql/src/histogram_eval/classic_cases.txt diff --git a/src/promql/src/histogram_eval/go_math_cases.txt b/src/promql/src/histogram_eval/go_math_cases.txt new file mode 100644 index 00000000000..f225d51aa8d --- /dev/null +++ b/src/promql/src/histogram_eval/go_math_cases.txt @@ -0,0 +1,404 @@ +# Generated by promql-compat cmd/narthex-golden-log2exp2 built for amd64: Go math.Log2 and +# math.Exp2, which Prometheus uses for native histogram bucket interpolation, as +# ` `. 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c046dc1e552045b0 3d136e75dd02c0bc +exp2 4053f91334fee51e 44edb012573b1061 diff --git a/src/promql/src/histogram_eval/native.rs b/src/promql/src/histogram_eval/native.rs new file mode 100644 index 00000000000..e3fd468267a --- /dev/null +++ b/src/promql/src/histogram_eval/native.rs @@ -0,0 +1,523 @@ +// Copyright 2023 Greptime Team +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +//! Prometheus `HistogramQuantile`, `HistogramFraction` and the `histogramVariance` estimate over +//! one native histogram, with the bucket iteration of `model/histogram` and the Go `math` +//! functions they call, so results match Prometheus on amd64 bit for bit. + +use datafusion::error::{DataFusionError, Result}; +use datatypes::series::histogram::{BucketSideView, HistogramView}; + +use super::bounds::EXPONENTIAL_BOUNDS; + +const CUSTOM_BUCKETS_SCHEMA: i32 = -53; + +#[derive(Debug, Clone, Copy)] +pub(super) struct NativeBucket { + lower: f64, + upper: f64, + count: f64, +} + +/// The buckets of `h` from the lowest to the highest, or the reverse: negative buckets, the zero +/// bucket when it has observations, then positive buckets (Go `AllBucketIterator` and +/// `AllReverseBucketIterator`). Buckets overlapping the zero bucket are clipped to it. +pub(super) fn all_buckets( + h: &HistogramView<'_>, + reverse: bool, + out: &mut Vec, +) -> Result<()> { + out.clear(); + let (low, high) = if reverse { + (h.positive, h.negative) + } else { + (h.negative, h.positive) + }; + // The first side runs from its highest index down, the second from its lowest index up. + side(h, low, reverse, out)?; + out.reverse(); + if h.zero_count > 0.0 { + if h.schema == CUSTOM_BUCKETS_SCHEMA { + return Err(DataFusionError::Execution( + "histograms with custom buckets have no zero bucket".into(), + )); + } + out.push(NativeBucket { + lower: -h.zero_threshold, + upper: h.zero_threshold, + count: h.zero_count, + }); + } + side(h, high, !reverse, out)?; + for bucket in out.iter_mut() { + if bucket.upper < 0.0 && bucket.upper > -h.zero_threshold { + bucket.upper = -h.zero_threshold; + } else if bucket.lower > 0.0 && bucket.lower < h.zero_threshold { + bucket.lower = h.zero_threshold; + } + } + Ok(()) +} + +/// Appends the buckets of one side by increasing index. +fn side( + h: &HistogramView<'_>, + side: BucketSideView<'_>, + positive: bool, + out: &mut Vec, +) -> Result<()> { + if side.span_offsets.len() != side.span_lengths.len() { + return Err(invalid_layout()); + } + let mut counts = side.buckets.iter(); + let mut index = 0i64; + for (&offset, &length) in side.span_offsets.iter().zip(side.span_lengths) { + if length < 0 { + return Err(invalid_layout()); + } + index += i64::from(offset); + for _ in 0..length { + let count = *counts.next().ok_or_else(invalid_layout)?; + let idx = i32::try_from(index).map_err(|_| invalid_layout())?; + out.push(bucket(h, idx, count, positive)?); + index += 1; + } + } + if counts.next().is_some() { + return Err(invalid_layout()); + } + Ok(()) +} + +fn bucket(h: &HistogramView<'_>, idx: i32, count: f64, positive: bool) -> Result { + let bound = |idx: i32| bound(idx, h.schema, h.custom_values); + Ok(if positive { + NativeBucket { + lower: bound(idx - 1)?, + upper: bound(idx)?, + count, + } + } else { + NativeBucket { + lower: -bound(idx)?, + upper: -bound(idx - 1)?, + count, + } + }) +} + +/// Go `getBound`. +fn bound(idx: i32, schema: i32, custom_values: &[f64]) -> Result { + if schema == CUSTOM_BUCKETS_SCHEMA { + let len = custom_values.len() as i64; + return match i64::from(idx) { + -1 => Ok(f64::NEG_INFINITY), + i if i == len => Ok(f64::INFINITY), + i if (0..len).contains(&i) => Ok(custom_values[i as usize]), + _ => Err(invalid_layout()), + }; + } + if schema < 0 { + if schema < -4 { + return Err(invalid_layout()); + } + let exp = i64::from(idx) << -schema; + if exp == 1024 { + return Ok(f64::MAX); + } + return Ok(ldexp(1.0, exp)); + } + let bounds = EXPONENTIAL_BOUNDS + .get(schema as usize) + .ok_or_else(invalid_layout)?; + let frac = bounds[(idx & ((1 << schema) - 1)) as usize]; + let exp = i64::from(idx >> schema) + 1; + if frac == 0.5 && exp == 1025 { + return Ok(f64::MAX); + } + Ok(ldexp(frac, exp)) +} + +fn invalid_layout() -> DataFusionError { + DataFusionError::Execution("native histogram has an invalid bucket layout".into()) +} + +/// Prometheus `HistogramQuantile`. +pub(super) fn quantile( + q: f64, + h: &HistogramView<'_>, + buckets: &mut Vec, +) -> Result { + if q < 0.0 { + return Ok(f64::NEG_INFINITY); + } + if q > 1.0 { + return Ok(f64::INFINITY); + } + if h.count == 0.0 || q.is_nan() { + return Ok(f64::NAN); + } + let custom = h.schema == CUSTOM_BUCKETS_SCHEMA; + let forward = h.sum.is_nan() || q < 0.5; + all_buckets(h, !forward, buckets)?; + let mut rank = if forward { + q * h.count + } else { + (1.0 - q) * h.count + }; + // Go keeps the last bucket visited, empty or not, and a zero bucket when there is none. + let mut bucket = NativeBucket { + lower: 0.0, + upper: 0.0, + count: 0.0, + }; + let mut count = 0.0; + let mut visited = 0; + for &next in buckets.iter() { + visited += 1; + bucket = next; + if bucket.count == 0.0 { + continue; + } + count += bucket.count; + if count >= rank { + break; + } + } + if !custom && bucket.lower < 0.0 && bucket.upper > 0.0 { + if h.negative.buckets.is_empty() && !h.positive.buckets.is_empty() { + bucket.lower = 0.0; + } else if h.positive.buckets.is_empty() && !h.negative.buckets.is_empty() { + bucket.upper = 0.0; + } + } else if custom { + if bucket.lower == f64::NEG_INFINITY { + if bucket.upper <= 0.0 { + return Ok(bucket.upper); + } + bucket.lower = 0.0; + } else if bucket.upper == f64::INFINITY { + return Ok(bucket.lower); + } + } + if count > h.count { + count = h.count; + } + if count < rank { + return Ok(if h.sum.is_nan() { + f64::NAN + } else { + bucket.upper + }); + } + if forward { + rank -= count - bucket.count; + } else { + rank = count - rank; + } + if h.sum.is_nan() { + // Prometheus walks the remaining buckets to annotate NaN observations and leaves the last + // one in `bucket`, which the interpolation below then uses. + for &next in &buckets[visited..] { + bucket = next; + } + } + let fraction = rank / bucket.count; + if custom || (bucket.lower <= 0.0 && bucket.upper >= 0.0) { + return Ok(bucket.lower + (bucket.upper - bucket.lower) * fraction); + } + let log_lower = log2(bucket.lower.abs()); + let log_upper = log2(bucket.upper.abs()); + if bucket.lower > 0.0 { + return Ok(exp2(log_lower + (log_upper - log_lower) * fraction)); + } + Ok(-exp2( + log_upper + (log_lower - log_upper) * (1.0 - fraction), + )) +} + +/// Prometheus `HistogramFraction`. +pub(super) fn fraction( + lower: f64, + upper: f64, + h: &HistogramView<'_>, + buckets: &mut Vec, +) -> Result { + if h.count == 0.0 || lower.is_nan() || upper.is_nan() { + return Ok(f64::NAN); + } + if lower >= upper { + return Ok(0.0); + } + let custom = h.schema == CUSTOM_BUCKETS_SCHEMA; + all_buckets(h, false, buckets)?; + let (mut count, mut rank, mut lower_rank, mut upper_rank) = (0.0, 0.0, 0.0, 0.0); + let (mut lower_set, mut upper_set) = (false, false); + let mut visited = 0; + for b in buckets.iter() { + visited += 1; + let mut b = *b; + count += b.count; + let mut zero_bucket = false; + if b.lower <= 0.0 && b.upper >= 0.0 { + zero_bucket = true; + if h.negative.buckets.is_empty() && !h.positive.buckets.is_empty() { + b.lower = 0.0; + } else if h.positive.buckets.is_empty() && !h.negative.buckets.is_empty() { + b.upper = 0.0; + } + } + let interpolate = |v: f64| { + if custom || zero_bucket { + if b.lower == f64::NEG_INFINITY { + b.count + } else { + rank + b.count * ((v - b.lower) / (b.upper - b.lower)) + } + } else { + rank + b.count * fraction_below_exponential(b, v) + } + }; + if !lower_set && b.lower >= lower { + lower_rank = rank; + lower_set = true; + } + if !upper_set && b.lower >= upper { + upper_rank = rank; + upper_set = true; + } + if lower_set && upper_set { + break; + } + if !lower_set && b.lower < lower && b.upper > lower { + lower_rank = interpolate(lower); + lower_set = true; + } + if !upper_set && b.lower < upper && b.upper > upper { + upper_rank = interpolate(upper); + upper_set = true; + } + if lower_set && upper_set { + break; + } + rank += b.count; + } + if h.sum.is_nan() { + for b in &buckets[visited..] { + count += b.count; + } + } else { + count = h.count; + } + if !lower_set || lower_rank > count { + lower_rank = count; + } + if !upper_set || upper_rank > count { + upper_rank = count; + } + Ok((upper_rank - lower_rank) / h.count) +} + +/// Go `Bucket.FractionBelow` with exponential interpolation. +fn fraction_below_exponential(b: NativeBucket, v: f64) -> f64 { + let log_lower = log2(b.lower.abs()); + let log_upper = log2(b.upper.abs()); + let log_v = log2(v.abs()); + if v > 0.0 { + (log_v - log_lower) / (log_upper - log_lower) + } else { + 1.0 - ((log_v - log_upper) / (log_lower - log_upper)) + } +} + +/// Prometheus `histogramVariance`: bucket midpoints weighted by count around the mean. +pub(super) fn variance(h: &HistogramView<'_>, buckets: &mut Vec) -> Result { + let mean = h.sum / h.count; + let custom = h.schema == CUSTOM_BUCKETS_SCHEMA; + all_buckets(h, false, buckets)?; + let (mut variance, mut compensation) = (0.0, 0.0); + for bucket in buckets.iter().filter(|bucket| bucket.count != 0.0) { + let value = if custom { + (bucket.upper + bucket.lower) / 2.0 + } else if bucket.lower <= 0.0 && bucket.upper >= 0.0 { + 0.0 + } else { + let value = (bucket.upper * bucket.lower).sqrt(); + if bucket.upper < 0.0 { -value } else { value } + }; + let delta = value - mean; + (variance, compensation) = kahan_inc(bucket.count * delta * delta, variance, compensation); + } + Ok((variance + compensation) / h.count) +} + +/// Prometheus `kahansum.Inc`. +fn kahan_inc(inc: f64, sum: f64, c: f64) -> (f64, f64) { + let t = sum + inc; + if t.is_infinite() { + return (t, 0.0); + } + let c = if sum.abs() >= inc.abs() { + c + ((sum - t) + inc) + } else { + c + ((inc - t) + sum) + }; + (t, c) +} + +/// Go `math.Ldexp` for a positive normal `frac`. +fn ldexp(frac: f64, exp: i64) -> f64 { + let bits = frac.to_bits(); + let exp = exp + ((bits >> 52) & 0x7FF) as i64 - 1023; + if exp < -1075 { + return 0.0; + } + if exp > 1023 { + return f64::INFINITY; + } + let (exp, scale) = if exp < -1022 { + (exp + 53, 1.0 / (1u64 << 53) as f64) + } else { + (exp, 1.0) + }; + scale * f64::from_bits((bits & !(0x7FF << 52)) | (((exp + 1023) as u64) << 52)) +} + +/// Go `math.Frexp`. +fn frexp(x: f64) -> (f64, i64) { + if x == 0.0 || x.is_infinite() || x.is_nan() { + return (x, 0); + } + let (x, mut exp) = if x.abs() < f64::MIN_POSITIVE { + (x * (1u64 << 52) as f64, -52) + } else { + (x, 0) + }; + let bits = x.to_bits(); + exp += ((bits >> 52) & 0x7FF) as i64 - 1023 + 1; + (f64::from_bits((bits & !(0x7FF << 52)) | (1022 << 52)), exp) +} + +/// Go `math.Log`, whose amd64 assembly performs the same operations for normal inputs. +// Constants are copied verbatim from Go's `math` package. +#[allow(clippy::excessive_precision)] +fn log(x: f64) -> f64 { + const LN2_HI: f64 = 6.93147180369123816490e-01; + const LN2_LO: f64 = 1.90821492927058770002e-10; + const L1: f64 = 6.666666666666735130e-01; + const L2: f64 = 3.999999999940941908e-01; + const L3: f64 = 2.857142874366239149e-01; + const L4: f64 = 2.222219843214978396e-01; + const L5: f64 = 1.818357216161805012e-01; + const L6: f64 = 1.531383769920937332e-01; + const L7: f64 = 1.479819860511658591e-01; + if x.is_nan() || x == f64::INFINITY { + return x; + } + if x < 0.0 { + return f64::NAN; + } + if x == 0.0 { + return f64::NEG_INFINITY; + } + let (mut f1, mut ki) = frexp(x); + if f1 < std::f64::consts::SQRT_2 / 2.0 { + f1 *= 2.0; + ki -= 1; + } + let f = f1 - 1.0; + let k = ki as f64; + let s = f / (2.0 + f); + let s2 = s * s; + let s4 = s2 * s2; + let t1 = s2 * (L1 + s4 * (L3 + s4 * (L5 + s4 * L7))); + let t2 = s4 * (L2 + s4 * (L4 + s4 * L6)); + let r = t1 + t2; + let hfsq = 0.5 * f * f; + k * LN2_HI - ((hfsq - (s * (hfsq + r) + k * LN2_LO)) - f) +} + +/// Go `math.Log2`. +fn log2(x: f64) -> f64 { + let (frac, exp) = frexp(x); + if frac == 0.5 { + return (exp - 1) as f64; + } + log(frac) * std::f64::consts::LOG2_E + exp as f64 +} + +/// Go `math.Exp2`, which is not assembly on amd64. +// Constants are copied verbatim from Go's `math` package. +#[allow(clippy::excessive_precision)] +fn exp2(x: f64) -> f64 { + const LN2_HI: f64 = 6.93147180369123816490e-01; + const LN2_LO: f64 = 1.90821492927058770002e-10; + const OVERFLOW: f64 = 1.0239999999999999e+03; + const UNDERFLOW: f64 = -1.0740e+03; + const P1: f64 = 1.66666666666666657415e-01; + const P2: f64 = -2.77777777770155933842e-03; + const P3: f64 = 6.61375632143793436117e-05; + const P4: f64 = -1.65339022054652515390e-06; + const P5: f64 = 4.13813679705723846039e-08; + if x.is_nan() || x == f64::INFINITY { + return x; + } + if x == f64::NEG_INFINITY || x < UNDERFLOW { + return 0.0; + } + if x > OVERFLOW { + return f64::INFINITY; + } + let k = if x > 0.0 { + (x + 0.5) as i64 + } else if x < 0.0 { + (x - 0.5) as i64 + } else { + 0 + }; + let t = x - k as f64; + let hi = t * LN2_HI; + let lo = -t * LN2_LO; + let r = hi - lo; + let t = r * r; + let c = r - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); + let y = 1.0 - ((lo - (r * c) / (2.0 - c)) - hi); + ldexp(y, k) +} + +#[cfg(test)] +mod tests { + /// The bucket interpolation goes through Go's `math.Log2` and `math.Exp2`, which differ from + /// the platform functions in the last bit on some arguments. + #[test] + fn log2_and_exp2_match_go() { + let mut checked = 0; + for line in include_str!("go_math_cases.txt").lines() { + if line.starts_with('#') { + continue; + } + let fields: Vec<&str> = line.split(' ').collect(); + let bits = |field: &str| u64::from_str_radix(field, 16).unwrap(); + let argument = f64::from_bits(bits(fields[1])); + let actual = match fields[0] { + "log2" => super::log2(argument), + "exp2" => super::exp2(argument), + function => panic!("unknown function {function}"), + }; + assert_eq!(actual.to_bits(), bits(fields[2]), "{line}"); + checked += 1; + } + assert_eq!(checked, 400); + } +} diff --git a/src/promql/src/histogram_eval/native_cases.txt b/src/promql/src/histogram_eval/native_cases.txt new file mode 100644 index 00000000000..dd5f8b1f981 --- /dev/null +++ b/src/promql/src/histogram_eval/native_cases.txt @@ -0,0 +1,2964 @@ +# Generated by promql-compat cmd/narthex-golden-native built for amd64 (Prometheus +# v3.15.0 engine, seed 1, 60 cases per function). Each case lists its operation and +# tab-separated arguments, the grid, the input series and either the result series or +# the error. Float points are `grid index:hex bits`; histogram points are +# `grid index:H` followed by `/`-separated schema, zero threshold, zero count, count, +# sum, reset hint, positive spans, positive buckets, negative spans, negative buckets and +# custom values; spans are `offset_length` lists and floats are hex bits, lists joined +# by `,`. +case histogram_count +grid 100000 10000 2 +series __name__=a|job=y ; 0:H-4/255bba08cf8c979d/4042d00000000000/404b000000000000/40bca3aee49e3f05/3/4_1,1_2,0_1/4018000000000000,0,4051d80000000000,4047800000000000/// 1:H-4/3fe0000000000000/0/4008000000000000/7ff8000000000001/3///// +series __name__=a|job=z ; 0:H1/3f50624dd2f1a9fc/404a800000000000/4056c00000000000/7ff8000000000001/0/7_3/0,0,4043000000000000/// 1:H-53/0/0/0/8000000000000000/0/////3fd0000000000000 +result job=y ; 0:404b000000000000 1:4008000000000000 +result job=z ; 0:4056c00000000000 1:0 +end +case histogram_count +grid 100000 10000 1 +series __name__=a|job=x ; 0:3ff0000000000000 +series __name__=a|job=z ; 0:H3/255bba08cf8c979d/4058800000000000/4081f00000000000/40d2606d34762ab9/0/3_0,1_3,1_3/403a000000000000,4054400000000000,4050800000000000,0,4055800000000000,4054400000000000/5_3/403c000000000000,4055000000000000,4038000000000000/ +result job=z ; 0:4081f00000000000 +end +case histogram_count +grid 100000 10000 5 +series __name__=a|job=x ; 0:H0/0/0/4000000000000000/7ff8000000000001/0///// 1:H3/3f50624dd2f1a9fc/4045000000000000/4066d40000000000/7ff8000000000001/0/-2_2,0_3,0_0/404c800000000000,0,4053e80000000000,0,0/// 2:H0/255bba08cf8c979d/404c000000000000/404c000000000000/40a22497d7e41cf7/0/5_0,0_0//// 3:H-4/0/0/4061d00000000000/40b7ccf9d47d7792/0///6_1,0_3,1_1/0,4057400000000000,0,403d800000000000,4034000000000000/ 4:H-53/0/0/0/8000000000000000/0/////3fd0000000000000 +series __name__=a|job=z ; 0:H-1/255bba08cf8c979d/0/4060c00000000000/7ff8000000000001/0/-1_2,0_2,1_0/4052400000000000,0,4035000000000000,0/-1_2,1_0/0,4042800000000000/ 1:H-1/255bba08cf8c979d/0/4044800000000000/40ab519348da4b73/0/-5_0,1_3/4040600000000000,403ae00000000000,4050800000000000/// 3:H3/3fe0000000000000/405e480000000000/4073300000000000/c075ccdcb0528633/0/-4_2,0_2,0_0/404c800000000000,4043800000000000,404ef00000000000,403c000000000000/-4_0// 4:H-4/255bba08cf8c979d/404e800000000000/4065400000000000/c0cc9f58a1ee9ac1/0/-8_3,1_0/0,4040600000000000,4047300000000000/6_2,2_3,0_3/4054000000000000,403f000000000000,0,4055000000000000,4037000000000000,4052400000000000,404a800000000000,403b000000000000/ +result job=x ; 0:4000000000000000 1:4066d40000000000 2:404c000000000000 3:4061d00000000000 4:0 +result job=z ; 0:4060c00000000000 1:4044800000000000 3:4073300000000000 4:4065400000000000 +end +case histogram_count +grid 100000 10000 2 +series __name__=a|job=y ; 0:H-4/255bba08cf8c979d/4054c00000000000/407dd40000000000/c0c452c0eb92a2d3/0/0_2,1_1/4058800000000000,405ed00000000000,4046800000000000/-4_0,1_3,1_0/404a800000000000,4052c00000000000,0/ 1:H-1/255bba08cf8c979d/0/4061c00000000000/7ff8000000000001/0/-7_0,0_1,0_1/404d800000000000,4054000000000000/// +result job=y ; 0:407dd40000000000 1:4061c00000000000 +end +case histogram_count +grid 100000 10000 4 +series __name__=a|job=x ; 0:H8/3f50624dd2f1a9fc/0/4063480000000000/40bec09d2c1231dc/0/0_1/4050100000000000/4_1,2_2,0_1/3ff0000000000000,4056000000000000,0,3ff0000000000000/ 1:H-4/255bba08cf8c979d/4039000000000000/405da00000000000/40bef49f83cde895/3/-4_3/4051a00000000000,4037000000000000,0/// 2:H1/3f50624dd2f1a9fc/0/401c000000000000/404dfd47b4837d39/3/-5_3/4035000000000000,3ff0000000000000,0/// +series __name__=a|job=y ; 0:H-53/0/0/0/0/3/0_0////3fd0000000000000 1:H3/0/0/4042700000000000/c07997ab8ad6be0a/0/-3_2/4010000000000000,4040700000000000/// 2:H8/0/0/0/8000000000000000/0/-9_0//// 3:H3/0/4056d80000000000/4062a00000000000/40c58987c6f44fab/0/-9_3,0_0,1_3/4044000000000000,4058800000000000,0,4054800000000000,4051800000000000,4051000000000000/// +result job=x ; 0:4063480000000000 1:405da00000000000 2:401c000000000000 +result job=y ; 0:0 1:4042700000000000 2:0 3:4062a00000000000 +end +case histogram_count +grid 100000 10000 2 +series __name__=a|job=x ; 0:4022000000000000 1:H8/3f50624dd2f1a9fc/0/4064040000000000/409a9e3ad6d08d5b/0/0_1,2_2/4041800000000000,0,4059480000000000/7_1,2_1/0,4038000000000000/ +series __name__=a|job=y ; 0:H-53/0/0/405dc00000000000/c0586a52738aa638/0/0_0,2_2/4036400000000000,4058300000000000///bff0000000000000,0,3fe0000000000000,4024000000000000 1:H1/0/0/0/0/0/8_0//// +result job=x ; 1:4064040000000000 +result job=y ; 0:405dc00000000000 1:0 +end +case histogram_count +grid 100000 10000 1 +series __name__=a|job=x ; 0:H1/0/404f000000000000/4070400000000000/40c8a27ef4200055/3/2_3,2_1,0_1/0,0,0,4058c00000000000,4058c00000000000/// +series __name__=a|job=y ; 0:3ff0000000000000 +series __name__=a|job=z ; 0:H3/3fe0000000000000/0/4049400000000000/40a29def9af030fc/0/-5_2,2_0,2_0/4036800000000000,403c000000000000/// +result job=x ; 0:4070400000000000 +result job=z ; 0:4049400000000000 +end +case histogram_count +grid 100000 10000 3 +series __name__=a|job=y ; 0:H-4/255bba08cf8c979d/0/4082900000000000/40c30aa7238dc94d/0/-9_3,0_2,0_0/4056000000000000,0,4043000000000000,0,4046000000000000/-2_2,1_3,1_2/4056000000000000,0,4054f80000000000,4057c80000000000,4042000000000000,4055000000000000,4042800000000000/ 1:H8/3fe0000000000000/4057c00000000000/4064400000000000/409a25233d7fdae1/0/6_0,0_3/4050000000000000,0,4008000000000000/// 2:H8/255bba08cf8c979d/0/4014000000000000/c07e64fbbcca6b14/0///2_2,0_0/4030000000000000,3ff0000000000000/ +result job=y ; 0:4082900000000000 1:4064400000000000 2:4014000000000000 +end +case histogram_count +grid 100000 10000 2 +end +case histogram_count +grid 100000 10000 5 +series __name__=a|job=z ; 0:H-4/3fe0000000000000/0/0/0/0///// 1:H3/0/0/0/0/0///// 2:H-1/3fe0000000000000/4041200000000000/4067280000000000/c098e6abecebd599/0/-7_3/4049000000000000,4056c00000000000,4024000000000000/// 3:H-1/0/4053580000000000/4076200000000000/7ff8000000000001/0/-5_3/4044700000000000,4033000000000000,4054c00000000000/0_3,0_0,0_2/3fe8000000000000,4052000000000000,403d000000000000,402c000000000000,4032000000000000/ 4:4014000000000000 +result job=z ; 0:0 1:0 2:4067280000000000 3:4076200000000000 +end +case histogram_count +grid 100000 10000 4 +series __name__=a|job=x ; 0:H0/3fe0000000000000/4053000000000000/40696c0000000000/c0b627d2cac6d483/0///8_3/404d300000000000,4035000000000000,4048000000000000/ 2:H3/255bba08cf8c979d/0/40701e0000000000/40becb99412570a4/0/9_3,0_2,1_1/4036000000000000,4034e00000000000,4054800000000000,0,4055400000000000,4048000000000000/// 3:4010000000000000 +series __name__=a|job=y ; 0:H-53/0/0/403a000000000000/40931d4b46bf84a4/0/0_2/403a000000000000,0///3fd0000000000000 1:H1/255bba08cf8c979d/404a000000000000/4067c00000000000/40c35e03e185bf3a/0/4_1/0/-1_0,2_0,2_2/4057400000000000,4046800000000000/ 2:H-1/3f50624dd2f1a9fc/0/4068c00000000000/7ff8000000000001/0/6_2,0_3,0_1/403d000000000000,0,0,4054800000000000,4044000000000000,4046800000000000/// 3:H8/3f50624dd2f1a9fc/4028400000000000/4059c80000000000/408639ae8840e7b9/0/-3_2/4048800000000000,4045000000000000/// +series __name__=a|job=z ; 0:H-4/0/0/4054c00000000000/4085f28ca4d6cd2a/0///8_1/4054c00000000000/ 1:H8/3f50624dd2f1a9fc/0/403c600000000000/40957a7da06300f0/0/1_3/4022000000000000,4033600000000000,0/// 2:H-53/0/0/4036000000000000/c05a958b91aad932/0/0_1,1_2/0,0,4036000000000000///3ff0000000000000,4000000000000000,4014000000000000 3:H0/255bba08cf8c979d/4036200000000000/401c000000000000/408ec1266c78900d/0///// +result job=x ; 0:40696c0000000000 2:40701e0000000000 +result job=y ; 0:403a000000000000 1:4067c00000000000 2:4068c00000000000 3:4059c80000000000 +result job=z ; 0:4054c00000000000 1:403c600000000000 2:4036000000000000 3:401c000000000000 +end +case histogram_count +grid 100000 10000 2 +series __name__=a|job=x ; 0:H-4/3f50624dd2f1a9fc/405da80000000000/405fe80000000000/40b2994e32204cec/0/9_1/4022000000000000/// 1:H0/3fe0000000000000/0/404b800000000000/40a125d73e51f626/0/5_2,0_0/4048000000000000,405db80000000000/// +series __name__=a|job=z ; 0:4018000000000000 1:H-1/0/4056400000000000/4067600000000000/40c1b7352254b66e/0/4_2,1_0,2_0/4018000000000000,4057000000000000/// +result job=x ; 0:405fe80000000000 1:404b800000000000 +result job=z ; 1:4067600000000000 +end +case histogram_count +grid 100000 10000 4 +series __name__=a|job=z ; 0:H-4/0/404a000000000000/4076b00000000000/40d740838ccec50c/0/-10_1,1_3,0_2/4054800000000000,404a000000000000,404e000000000000,4053000000000000,4044800000000000,0/// 1:H-53/0/0/4054400000000000/7ff8000000000001/0/1_2/4054400000000000,0///bff0000000000000,0,3fe0000000000000,4024000000000000 2:4022000000000000 3:H-53/0/0/4065600000000000/7ff8000000000001/0/0_1,0_1/4052c00000000000,4057c00000000000///3ff0000000000000,4000000000000000,4014000000000000 +result job=z ; 0:4076b00000000000 1:4054400000000000 3:4065600000000000 +end +case histogram_count +grid 100000 10000 3 +series __name__=a|job=x ; 0:H-53/0/0/4064280000000000/c0a23289f49c5cfe/0/0_2,0_1/402b000000000000,405d300000000000,403f000000000000///bff0000000000000,0,3fe0000000000000,4024000000000000 1:H-53/0/0/0/0/3/////3ff0000000000000,4000000000000000,4014000000000000 2:H-1/3f50624dd2f1a9fc/0/4062a00000000000/40b101b22ff4a545/0/-3_1,1_1/404e000000000000,4056400000000000/// +series __name__=a|job=z ; 0:H-1/255bba08cf8c979d/4036000000000000/406b9c0000000000/40b2498cf961625a/0/-10_2,0_2,1_2/0,0,4055800000000000,403fa00000000000,4054500000000000,0/// 1:4010000000000000 2:H1/255bba08cf8c979d/0/4030a00000000000/7ff8000000000001/0/3_1,0_0/4010000000000000/9_0,2_0,0_1/4023400000000000/ +result job=x ; 0:4064280000000000 1:0 2:4062a00000000000 +result job=z ; 0:406b9c0000000000 2:4030a00000000000 +end +case histogram_count +grid 100000 10000 2 +series __name__=a|job=x ; 1:H-1/0/0/4070000000000000/40b700c4627eb2c2/3/0_3/404a800000000000,4055c00000000000,0/-10_1,1_0,1_2/404b000000000000,4049000000000000,4028000000000000/ +series __name__=a|job=y ; 1:H-4/0/0/4065bc0000000000/c0b168ae06880a18/3/9_2,1_1/4048800000000000,4055f80000000000,0/-4_2/4026000000000000,403a000000000000/ +result job=x ; 1:4070000000000000 +result job=y ; 1:4065bc0000000000 +end +case histogram_count +grid 100000 10000 4 +series __name__=a|job=x ; 0:H1/3fe0000000000000/0/4062c40000000000/40a7c4a4eced0680/0///1_3,2_0,2_2/404d900000000000,0,4052800000000000,0,4031000000000000/ 1:H-1/3f50624dd2f1a9fc/0/4069140000000000/c098492a776b073f/3/8_3/405f280000000000,0,4053000000000000/// 2:H0/0/0/4066480000000000/40c8374ab972950c/0/4_0,2_3/4043200000000000,4047000000000000,4057800000000000/// 3:H0/255bba08cf8c979d/0/4056b80000000000/4049329591b48916/0///9_3,2_2/4031e00000000000,0,404a000000000000,0,4035000000000000/ +series __name__=a|job=y ; 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0:4046a1f08981695f 2:fff8000000000000 3:4032b4ec02b451b6 4:4040d445abe08e19 +result job=z ; 0:40280ee3e3a1ec44 1:4046b23194ee3ebb 3:4055dc2848bf5a54 4:401069a2fc421057 +end +case histogram_stddev +grid 100000 10000 4 +series __name__=a|job=x ; 0:H-1/3fe0000000000000/4053b00000000000/4066fc0000000000/c09754d5efcd1d5b/0/1_3,2_2/0,4034e00000000000,403e000000000000,4046200000000000,4024000000000000/// 1:H3/0/4051800000000000/404e000000000000/40bafe8041412e8d/0/3_1,1_0,1_3/4046800000000000,0,4040800000000000,4040000000000000/// 2:H8/255bba08cf8c979d/4053400000000000/4071100000000000/40d1f3d04fe5c055/0///-2_2,0_3/0,404a800000000000,4049000000000000,403b000000000000,4050800000000000/ 3:H-1/3f50624dd2f1a9fc/4051d80000000000/4075060000000000/40b4ebd7af1d3cc9/0/-2_2,2_3,1_1/4047800000000000,403d000000000000,403e000000000000,403c000000000000,404b000000000000,4053400000000000/// +result job=x ; 0:40a0e43032b07c24 1:4068b9e1b7771e36 2:405103ad42b48727 3:408e6ac8c1aae2a2 +end +case histogram_stddev +grid 100000 10000 1 +series __name__=a|job=x ; 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0:H0/255bba08cf8c979d/403b000000000000/403f000000000000/7ff8000000000001/0/-2_0,2_0//// 1:H-53/0/0/0/0/0/////3fd0000000000000 2:H8/255bba08cf8c979d/404a000000000000/404a000000000000/40a3f088dc204200/0///// 3:H1/3fe0000000000000/0/0/0/0///// +result job=x ; 0:0 1:7ff8000000000001 3:0 +result job=y ; 0:0 1:7ff8000000000001 2:0 3:7ff8000000000001 +end diff --git a/src/promql/src/histogram_eval/tests.rs b/src/promql/src/histogram_eval/tests.rs new file mode 100644 index 00000000000..6556b738c77 --- /dev/null +++ b/src/promql/src/histogram_eval/tests.rs @@ -0,0 +1,270 @@ +// Copyright 2023 Greptime Team +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +use std::collections::BTreeMap; +use std::sync::Arc; + +use datafusion::arrow::array::{Float64Array, UInt32Array}; +use datafusion::error::DataFusionError; +use datatypes::series::histogram::{ + BucketSideView, CounterResetHint, HistogramBatchBuilder, HistogramView, +}; +use datatypes::series::samples::{ + FieldSpec, HistogramSamples, Samples, Series, SeriesFields, SeriesSchema, +}; +use datatypes::series::time::{GridRange, TimeAxis}; + +use super::{ + HistogramFunction, NativeHistogramFunction, evaluate_histograms, map_native_histogram, +}; +use crate::grid_series::merge_same_labelset; +use crate::grid_series::reference::{ + GoldenCase, Labels, Points, canonical_bits, golden_cases, labels_of, metric_of, points_of, +}; + +fn schema(case: &GoldenCase) -> Arc { + Arc::new(SeriesSchema { + fields: vec![FieldSpec { + name: Arc::from("value"), + }] + .into(), + eval_grid: Some(case.grid.clone()), + }) +} + +fn bits_argument(case: &GoldenCase, index: usize) -> f64 { + f64::from_bits(u64::from_str_radix(&case.spec[index], 16).unwrap()) +} + +/// A native histogram written by the generator as `/`-separated fields. +struct OwnedHistogram { + schema: i32, + zero_threshold: f64, + zero_count: f64, + count: f64, + sum: f64, + reset_hint: i32, + positive: (Vec, Vec, Vec), + negative: (Vec, Vec, Vec), + custom_values: Vec, +} + +impl OwnedHistogram { + fn parse(text: &str) -> Self { + let fields: Vec<&str> = text.split('/').collect(); + let float = |text: &str| f64::from_bits(u64::from_str_radix(text, 16).unwrap()); + let floats = |text: &str| -> Vec { + text.split(',') + .filter(|v| !v.is_empty()) + .map(float) + .collect() + }; + let spans = |text: &str| -> (Vec, Vec) { + text.split(',') + .filter(|v| !v.is_empty()) + .map(|span| { + let (offset, length) = span.split_once('_').unwrap(); + ( + offset.parse::().unwrap(), + length.parse::().unwrap(), + ) + }) + .unzip() + }; + let (positive_offsets, positive_lengths) = spans(fields[6]); + let (negative_offsets, negative_lengths) = spans(fields[8]); + Self { + schema: fields[0].parse().unwrap(), + zero_threshold: float(fields[1]), + zero_count: float(fields[2]), + count: float(fields[3]), + sum: float(fields[4]), + reset_hint: fields[5].parse().unwrap(), + positive: (positive_offsets, positive_lengths, floats(fields[7])), + negative: (negative_offsets, negative_lengths, floats(fields[9])), + custom_values: floats(fields[10]), + } + } + + fn view(&self) -> HistogramView<'_> { + fn side( + (offsets, lengths, buckets): &(Vec, Vec, Vec), + ) -> BucketSideView<'_> { + BucketSideView { + span_offsets: offsets, + span_lengths: lengths, + buckets, + } + } + HistogramView { + schema: self.schema, + zero_threshold: self.zero_threshold, + sum: self.sum, + count: self.count, + zero_count: self.zero_count, + reset_hint: CounterResetHint::from(self.reset_hint), + start_timestamp: None, + custom_values: &self.custom_values, + positive: side(&self.positive), + negative: side(&self.negative), + } + } +} + +/// A single-field series holding float and native histogram points. +fn mixed_series( + schema: &Arc, + labels: &Labels, + floats: &Points, + histograms: &BTreeMap, +) -> Option { + let points = floats.keys().chain(histograms.keys()); + let start = *points.clone().min()?; + let end = *points.max()? + 1; + let float_values: Float64Array = (start..end) + .map(|point| floats.get(&point).map(|bits| f64::from_bits(*bits))) + .collect(); + let samples = if histograms.is_empty() { + Samples::from_float(float_values) + } else { + let mut builder = HistogramBatchBuilder::new(); + let indices: Vec<_> = (start..end) + .map(|point| { + let text = histograms.get(&point)?; + Some(builder.push(OwnedHistogram::parse(text).view()).unwrap()) + }) + .collect(); + let histograms = + HistogramSamples::try_new(UInt32Array::from(indices), builder.finish().unwrap()) + .unwrap(); + Samples::try_from_mixed(float_values, histograms).unwrap() + }; + let range = GridRange::try_new(schema.eval_grid.clone().unwrap(), start, end - start).unwrap(); + Some( + Series::try_new( + schema, + metric_of(labels), + TimeAxis::Grid(range), + SeriesFields::one(samples), + ) + .unwrap(), + ) +} + +/// Compares a kernel outcome with a fixture outcome; returns whether it was an error. +fn assert_outcome( + case: &GoldenCase, + actual: Result, DataFusionError>, + expected: &Result, String>, +) -> bool { + match (actual, expected) { + (Ok(actual), Ok(expected)) => { + let actual: BTreeMap<_, _> = actual + .iter() + .map(|series| (labels_of(&series.metric), points_of(series))) + .collect(); + let expected: BTreeMap<_, _> = expected + .iter() + .map(|(labels, points)| { + let points = points + .iter() + .map(|(&index, &bits)| (index, canonical_bits(f64::from_bits(bits)))) + .collect::(); + (labels.clone(), points) + }) + .collect(); + assert_eq!(actual, expected, "case {:?}", case.spec); + false + } + (Err(actual), Err(expected)) => { + assert!(actual.to_string().contains(expected), "{actual}"); + true + } + (actual, expected) => panic!("case {:?}: {actual:?} is not {expected:?}", case.spec), + } +} + +#[test] +fn classic_histograms_match_prometheus() { + let cases = golden_cases(include_str!("classic_cases.txt")); + assert_eq!(cases.len(), 300); + let mut failed = 0; + for case in &cases { + let schema = schema(case); + // The fixture lists buckets by bound; the kernel must not rely on input order. + let input: Vec<_> = case + .inputs + .iter() + .rev() + .filter_map(|(labels, points)| mixed_series(&schema, labels, points, &BTreeMap::new())) + .collect(); + let function = match case.spec[0].as_str() { + "quantile" => HistogramFunction::Quantile(bits_argument(case, 1)), + "fraction" => HistogramFunction::Fraction { + lower: bits_argument(case, 1), + upper: bits_argument(case, 2), + }, + other => panic!("unknown case {other}"), + }; + let actual = evaluate_histograms(function, &schema, &input); + failed += usize::from(assert_outcome(case, actual, &case.outcome)); + } + assert!(failed > 20, "{failed} failed"); +} + +#[test] +fn native_histograms_match_prometheus() { + let cases = golden_cases(include_str!("native_cases.txt")); + assert_eq!(cases.len(), 420); + for case in &cases { + let schema = schema(case); + let input: Vec<_> = case + .inputs + .iter() + .zip(&case.histograms) + .filter_map(|((labels, floats), histograms)| { + mixed_series(&schema, labels, floats, histograms) + }) + .collect(); + let map = |function| -> Result, DataFusionError> { + let mapped = input + .iter() + .filter_map(|series| map_native_histogram(function, &schema, series).transpose()) + .collect::, _>>()?; + merge_same_labelset(&schema, mapped) + }; + let actual = match case.spec[0].as_str() { + "histogram_count" => map(NativeHistogramFunction::Count), + "histogram_sum" => map(NativeHistogramFunction::Sum), + "histogram_avg" => map(NativeHistogramFunction::Avg), + "histogram_stddev" => map(NativeHistogramFunction::StdDev), + "histogram_stdvar" => map(NativeHistogramFunction::StdVar), + "histogram_quantile" => evaluate_histograms( + HistogramFunction::Quantile(bits_argument(case, 1)), + &schema, + &input, + ), + "histogram_fraction" => evaluate_histograms( + HistogramFunction::Fraction { + lower: bits_argument(case, 1), + upper: bits_argument(case, 2), + }, + &schema, + &input, + ), + other => panic!("unknown case {other}"), + }; + assert_outcome(case, actual, &case.outcome); + } +} diff --git a/src/promql/src/lib.rs b/src/promql/src/lib.rs index 9f8051f83e1..bbcddfcdfcd 100644 --- a/src/promql/src/lib.rs +++ b/src/promql/src/lib.rs @@ -12,11 +12,11 @@ // See the License for the specific language governing permissions and // limitations under the License. -pub mod classic_histogram; pub mod error; pub mod extension_plan; pub mod functions; pub mod grid_series; +pub mod histogram_eval; pub mod map_label; pub mod map_time; mod metrics; From 53f5f698415b051912c1ba256fe9d59d11d9566f Mon Sep 17 00:00:00 2001 From: Dennis Zhuang Date: Sat, 17 Oct 2026 22:42:42 +0800 Subject: [PATCH 3/6] fix(promql): drop metadata labels from histogram_quantile and histogram_fraction Prometheus drops __type__ and __unit__ with __name__ for these functions, but only __name__ for the single-histogram functions. Signed-off-by: Dennis Zhuang --- src/promql/src/histogram_eval.rs | 5 ++- src/promql/src/histogram_eval/tests.rs | 59 ++++++++++++++++++++++++++ 2 files changed, 63 insertions(+), 1 deletion(-) diff --git a/src/promql/src/histogram_eval.rs b/src/promql/src/histogram_eval.rs index dfdce804a24..c429d052b03 100644 --- a/src/promql/src/histogram_eval.rs +++ b/src/promql/src/histogram_eval.rs @@ -35,6 +35,8 @@ use datatypes::series::time::TimeAxis; use crate::grid_series::{GridSeriesBuilder, LabelSet, label_set, merge_same_labelset}; const BUCKET_LABEL: &str = "le"; +/// Prometheus `schema.IsMetadataLabel`: the labels removed with the metric name. +const METADATA_LABELS: [&str; 3] = ["__name__", "__type__", "__unit__"]; /// `histogram_quantile` or `histogram_fraction` with its constant arguments. #[derive(Debug, Clone, Copy, PartialEq)] @@ -135,7 +137,7 @@ pub fn evaluate_histograms( } builder.push(point, &values)?; } - group.metric.remove("__name__"); + group.metric.remove_all(&METADATA_LABELS); output.extend(builder.finish(group.metric)?); } merge_same_labelset(schema, output) @@ -223,6 +225,7 @@ pub fn map_native_histogram( builder.push(point, &values)?; } let mut metric = series.metric.clone(); + // Prometheus `simpleHistogramFunc` drops only `__name__`, unlike `histogram_quantile`. metric.remove("__name__"); builder.finish(metric) } diff --git a/src/promql/src/histogram_eval/tests.rs b/src/promql/src/histogram_eval/tests.rs index 6556b738c77..3f27cc2bba3 100644 --- a/src/promql/src/histogram_eval/tests.rs +++ b/src/promql/src/histogram_eval/tests.rs @@ -268,3 +268,62 @@ fn native_histograms_match_prometheus() { assert_outcome(case, actual, &case.outcome); } } + +/// `histogram_quantile` drops all metadata labels; the single-histogram functions drop only +/// `__name__`, as Prometheus does. +#[test] +fn histogram_functions_drop_metadata_labels() { + let grid = Arc::new( + datatypes::series::time::EvalGrid::try_new( + datatypes::series::time::GridSpec::try_new(0, 1_000, 1).unwrap(), + ) + .unwrap(), + ); + let schema = Arc::new(SeriesSchema { + fields: vec![FieldSpec { + name: Arc::from("value"), + }] + .into(), + eval_grid: Some(grid), + }); + let labels = |extra: &[(&str, &str)]| -> Labels { + [ + ("__name__", "m"), + ("__type__", "histogram"), + ("__unit__", "seconds"), + ("job", "x"), + ] + .iter() + .chain(extra) + .map(|(name, value)| (name.to_string(), value.to_string())) + .collect() + }; + let one = BTreeMap::from([(0, 1f64.to_bits())]); + let buckets = vec![ + mixed_series(&schema, &labels(&[("le", "1")]), &one, &BTreeMap::new()).unwrap(), + mixed_series(&schema, &labels(&[("le", "+Inf")]), &one, &BTreeMap::new()).unwrap(), + ]; + let quantile = + evaluate_histograms(HistogramFunction::Quantile(0.5), &schema, &buckets).unwrap(); + assert_eq!( + labels_of(&quantile[0].metric), + Labels::from([("job".to_string(), "x".to_string())]) + ); + + let native = mixed_series( + &schema, + &labels(&[]), + &BTreeMap::new(), + &BTreeMap::from([( + 0, + "0/0/0/3ff0000000000000/3ff0000000000000/0/0_1/3ff0000000000000///".to_string(), + )]), + ) + .unwrap(); + let count = map_native_histogram(NativeHistogramFunction::Count, &schema, &native) + .unwrap() + .unwrap(); + let mut expected = labels(&[]); + expected.remove("__name__"); + assert_eq!(labels_of(&count.metric), expected); +} From 423c1fee28ded83b9097294e4a1de16b72537981 Mon Sep 17 00:00:00 2001 From: Dennis Zhuang Date: Sat, 17 Oct 2026 22:58:03 +0800 Subject: [PATCH 4/6] refactor(promql): use standard math for native histogram bounds and interpolation Results only need to agree with Prometheus within the relative tolerance promql-compat uses, so Go's bound table and the ports of math.Log2, Exp2, Ldexp and Frexp go; the fixtures are compared within that tolerance. Signed-off-by: Dennis Zhuang --- src/promql/src/histogram_eval.rs | 1 - src/promql/src/histogram_eval/bounds.rs | 167 -------- .../src/histogram_eval/go_math_cases.txt | 404 ------------------ src/promql/src/histogram_eval/native.rs | 191 +-------- src/promql/src/histogram_eval/tests.rs | 43 +- 5 files changed, 65 insertions(+), 741 deletions(-) delete mode 100644 src/promql/src/histogram_eval/bounds.rs delete mode 100644 src/promql/src/histogram_eval/go_math_cases.txt diff --git a/src/promql/src/histogram_eval.rs b/src/promql/src/histogram_eval.rs index c429d052b03..5aa9843774e 100644 --- a/src/promql/src/histogram_eval.rs +++ b/src/promql/src/histogram_eval.rs @@ -17,7 +17,6 @@ //! and `resetHistograms`), and `histogram_count`, `histogram_sum`, `histogram_avg`, //! `histogram_stddev` and `histogram_stdvar` over native histograms. -mod bounds; mod classic; mod native; #[cfg(test)] diff --git a/src/promql/src/histogram_eval/bounds.rs b/src/promql/src/histogram_eval/bounds.rs deleted file mode 100644 index ddc3a69290d..00000000000 --- a/src/promql/src/histogram_eval/bounds.rs +++ /dev/null @@ -1,167 +0,0 @@ -// Copyright 2023 Greptime Team -// -// Licensed under the Apache License, Version 2.0 (the "License"); -// you may not use this file except in compliance with the License. -// You may obtain a copy of the License at -// -// http://www.apache.org/licenses/LICENSE-2.0 -// -// Unless required by applicable law or agreed to in writing, software -// distributed under the License is distributed on an "AS IS" BASIS, -// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. -// See the License for the specific language governing permissions and -// limitations under the License. - -//! Prometheus `exponentialBounds` (`model/histogram/generic.go`): the bucket bounds in [0.5, 1) -//! of exponential schemas 0 to 8, which `getBoundExponential` scales by a power of two. - -#[rustfmt::skip] -pub(super) const EXPONENTIAL_BOUNDS: [&[f64]; 9] = [ - &[ - 0.5, - ], - &[ - 0.5, 0.7071067811865475, - ], - &[ - 0.5, 0.5946035575013605, 0.7071067811865475, 0.8408964152537144, - ], - &[ - 0.5, 0.5452538663326288, 0.5946035575013605, 0.6484197773255048, - 0.7071067811865475, 0.7711054127039704, 0.8408964152537144, 0.9170040432046711, - ], - &[ - 0.5, 0.5221368912137069, 0.5452538663326288, 0.5693943173783458, - 0.5946035575013605, 0.620928906036742, 0.6484197773255048, 0.6771277734684463, - 0.7071067811865475, 0.7384130729697496, 0.7711054127039704, 0.805245165974627, - 0.8408964152537144, 0.8781260801866495, 0.9170040432046711, 0.9576032806985735, - ], - &[ - 0.5, 0.5109485743270583, 0.5221368912137069, 0.5335702003384117, - 0.5452538663326288, 0.5571933712979462, 0.5693943173783458, 0.5818624293887887, - 0.5946035575013605, 0.6076236799902344, 0.620928906036742, 0.6345254785958666, - 0.6484197773255048, 0.6626183215798706, 0.6771277734684463, 0.6919549409819159, - 0.7071067811865475, 0.7225904034885232, 0.7384130729697496, 0.7545822137967112, - 0.7711054127039704, 0.7879904225539431, 0.805245165974627, 0.8228777390769823, - 0.8408964152537144, 0.8593096490612387, 0.8781260801866495, 0.8973545375015533, - 0.9170040432046711, 0.9370838170551498, 0.9576032806985735, 0.9785720620876999, - ], - &[ - 0.5, 0.5054446430258502, 0.5109485743270583, 0.5165124395106142, - 0.5221368912137069, 0.5278225891802786, 0.5335702003384117, 0.5393803988785598, - 0.5452538663326288, 0.5511912916539204, 0.5571933712979462, 0.5632608093041209, - 0.5693943173783458, 0.5755946149764913, 0.5818624293887887, 0.5881984958251406, - 0.5946035575013605, 0.6010783657263515, 0.6076236799902344, 0.6142402680534349, - 0.620928906036742, 0.6276903785123455, 0.6345254785958666, 0.6414350080393891, - 0.6484197773255048, 0.6554806057623822, 0.6626183215798706, 0.6698337620266515, - 0.6771277734684463, 0.6845012114872953, 0.6919549409819159, 0.6994898362691555, - 0.7071067811865475, 0.7148066691959849, 0.7225904034885232, 0.7304588970903234, - 0.7384130729697496, 0.7464538641456323, 0.7545822137967112, 0.762799075372269, - 0.7711054127039704, 0.7795022001189185, 0.7879904225539431, 0.7965710756711334, - 0.805245165974627, 0.8140137109286738, 0.8228777390769823, 0.8318382901633681, - 0.8408964152537144, 0.8500531768592616, 0.8593096490612387, 0.8686669176368529, - 0.8781260801866495, 0.8876882462632604, 0.8973545375015533, 0.9071260877501991, - 0.9170040432046711, 0.9269895625416926, 0.9370838170551498, 0.9472879907934827, - 0.9576032806985735, 0.9680308967461471, 0.9785720620876999, 0.9892280131939752, - ], - &[ - 0.5, 0.5027149505564014, 0.5054446430258502, 0.5081891574554764, - 0.5109485743270583, 0.5137229745593818, 0.5165124395106142, 0.5193170509806894, - 0.5221368912137069, 0.5249720429003435, 0.5278225891802786, 0.5306886136446309, - 0.5335702003384117, 0.5364674337629877, 0.5393803988785598, 0.5423091811066545, - 0.5452538663326288, 0.5482145409081883, 0.5511912916539204, 0.5541842058618393, - 0.5571933712979462, 0.5602188762048033, 0.5632608093041209, 0.5663192597993595, - 0.5693943173783458, 0.572486072215902, 0.5755946149764913, 0.5787200368168754, - 0.5818624293887887, 0.585021884841625, 0.5881984958251406, 0.5913923554921704, - 0.5946035575013605, 0.5978321960199137, 0.6010783657263515, 0.6043421618132907, - 0.6076236799902344, 0.6109230164863786, 0.6142402680534349, 0.6175755319684665, - 0.620928906036742, 0.6243004885946023, 0.6276903785123455, 0.6310986751971253, - 0.6345254785958666, 0.637970889198196, 0.6414350080393891, 0.6449179367033329, - 0.6484197773255048, 0.6519406325959679, 0.6554806057623822, 0.659039800633032, - 0.6626183215798706, 0.6662162735415805, 0.6698337620266515, 0.6734708931164728, - 0.6771277734684463, 0.6808045103191123, 0.6845012114872953, 0.688217985377265, - 0.6919549409819159, 0.6957121878859629, 0.6994898362691555, 0.7032879969095076, - 0.7071067811865475, 0.7109463010845827, 0.7148066691959849, 0.718687998724491, - 0.7225904034885232, 0.7265139979245261, 0.7304588970903234, 0.7344252166684908, - 0.7384130729697496, 0.7424225829363761, 0.7464538641456323, 0.7505070348132126, - 0.7545822137967112, 0.7586795205991071, 0.762799075372269, 0.7669409989204777, - 0.7711054127039704, 0.7752924388424999, 0.7795022001189185, 0.7837348199827764, - 0.7879904225539431, 0.7922691326262467, 0.7965710756711334, 0.8008963778413465, - 0.805245165974627, 0.8096175675974316, 0.8140137109286738, 0.8184337248834821, - 0.8228777390769823, 0.8273458838280969, 0.8318382901633681, 0.8363550898207981, - 0.8408964152537144, 0.8454623996346523, 0.8500531768592616, 0.8546688815502312, - 0.8593096490612387, 0.8639756154809185, 0.8686669176368529, 0.8733836930995842, - 0.8781260801866495, 0.8828942179666361, 0.8876882462632604, 0.8925083056594671, - 0.8973545375015533, 0.9022270839033115, 0.9071260877501991, 0.9120516927035263, - 0.9170040432046711, 0.9219832844793128, 0.9269895625416926, 0.9320230241988943, - 0.9370838170551498, 0.9421720895161669, 0.9472879907934827, 0.9524316709088368, - 0.9576032806985735, 0.9628029718180622, 0.9680308967461471, 0.9732872087896164, - 0.9785720620876999, 0.9838856116165875, 0.9892280131939752, 0.9945994234836328, - ], - &[ - 0.5, 0.5013556375251013, 0.5027149505564014, 0.5040779490592088, - 0.5054446430258502, 0.5068150424757447, 0.5081891574554764, 0.509566998038869, - 0.5109485743270583, 0.5123338964485679, 0.5137229745593818, 0.5151158188430205, - 0.5165124395106142, 0.5179128468009786, 0.5193170509806894, 0.520725062344158, - 0.5221368912137069, 0.5235525479396449, 0.5249720429003435, 0.526395386502313, - 0.5278225891802786, 0.5292536613972564, 0.5306886136446309, 0.5321274564422321, - 0.5335702003384117, 0.5350168559101208, 0.5364674337629877, 0.5379219445313954, - 0.5393803988785598, 0.5408428074966075, 0.5423091811066545, 0.5437795304588847, - 0.5452538663326288, 0.5467321995364429, 0.5482145409081883, 0.549700901315111, - 0.5511912916539204, 0.5526857228508706, 0.5541842058618393, 0.5556867516724088, - 0.5571933712979462, 0.5587040757836845, 0.5602188762048033, 0.5617377836665098, - 0.5632608093041209, 0.564787964283144, 0.5663192597993595, 0.5678547070789026, - 0.5693943173783458, 0.5709381019847808, 0.572486072215902, 0.5740382394200894, - 0.5755946149764913, 0.5771552102951081, 0.5787200368168754, 0.5802891060137493, - 0.5818624293887887, 0.5834400184762408, 0.585021884841625, 0.5866080400818185, - 0.5881984958251406, 0.5897932637314379, 0.5913923554921704, 0.5929957828304968, - 0.5946035575013605, 0.5962156912915756, 0.5978321960199137, 0.5994530835371903, - 0.6010783657263515, 0.6027080545025619, 0.6043421618132907, 0.6059806996384005, - 0.6076236799902344, 0.6092711149137041, 0.6109230164863786, 0.6125793968185725, - 0.6142402680534349, 0.6159056423670379, 0.6175755319684665, 0.6192499490999082, - 0.620928906036742, 0.622612415087629, 0.6243004885946023, 0.6259931389331581, - 0.6276903785123455, 0.6293922197748583, 0.6310986751971253, 0.6328097572894031, - 0.6345254785958666, 0.6362458516947014, 0.637970889198196, 0.6397006037528346, - 0.6414350080393891, 0.6431741147730128, 0.6449179367033329, 0.6466664866145447, - 0.6484197773255048, 0.6501778216898253, 0.6519406325959679, 0.6537082229673385, - 0.6554806057623822, 0.6572577939746774, 0.659039800633032, 0.6608266388015788, - 0.6626183215798706, 0.6644148621029772, 0.6662162735415805, 0.6680225691020727, - 0.6698337620266515, 0.6716498655934177, 0.6734708931164728, 0.6752968579460171, - 0.6771277734684463, 0.6789636531064505, 0.6808045103191123, 0.6826503586020058, - 0.6845012114872953, 0.6863570825438342, 0.688217985377265, 0.690083933630119, - 0.6919549409819159, 0.6938310211492645, 0.6957121878859629, 0.6975984549830999, - 0.6994898362691555, 0.7013863456101023, 0.7032879969095076, 0.7051948041086352, - 0.7071067811865475, 0.7090239421602076, 0.7109463010845827, 0.7128738720527471, - 0.7148066691959849, 0.7167447066838943, 0.718687998724491, 0.7206365595643126, - 0.7225904034885232, 0.7245495448210174, 0.7265139979245261, 0.7284837772007218, - 0.7304588970903234, 0.7324393720732029, 0.7344252166684908, 0.7364164454346837, - 0.7384130729697496, 0.7404151139112358, 0.7424225829363761, 0.7444354947621984, - 0.7464538641456323, 0.7484777058836176, 0.7505070348132126, 0.7525418658117031, - 0.7545822137967112, 0.7566280937263048, 0.7586795205991071, 0.7607365094544071, - 0.762799075372269, 0.7648672334736434, 0.7669409989204777, 0.7690203869158282, - 0.7711054127039704, 0.7731960915705107, 0.7752924388424999, 0.7773944698885442, - 0.7795022001189185, 0.7816156449856788, 0.7837348199827764, 0.7858597406461707, - 0.7879904225539431, 0.7901268813264122, 0.7922691326262467, 0.7944171921585818, - 0.7965710756711334, 0.7987307989543135, 0.8008963778413465, 0.8030678282083853, - 0.805245165974627, 0.8074284071024302, 0.8096175675974316, 0.8118126635086642, - 0.8140137109286738, 0.8162207259936375, 0.8184337248834821, 0.820652723822003, - 0.8228777390769823, 0.8251087869603088, 0.8273458838280969, 0.8295890460808079, - 0.8318382901633681, 0.8340936325652911, 0.8363550898207981, 0.8386226785089391, - 0.8408964152537144, 0.8431763167241966, 0.8454623996346523, 0.8477546807446661, - 0.8500531768592616, 0.8523579048290255, 0.8546688815502312, 0.8569861239649629, - 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0.9892280131939752, 0.9919100824251095, 0.9945994234836328, 0.9972960560854698, - ], -]; diff --git a/src/promql/src/histogram_eval/go_math_cases.txt b/src/promql/src/histogram_eval/go_math_cases.txt deleted file mode 100644 index f225d51aa8d..00000000000 --- a/src/promql/src/histogram_eval/go_math_cases.txt +++ /dev/null @@ -1,404 +0,0 @@ -# Generated by promql-compat cmd/narthex-golden-log2exp2 built for amd64: Go math.Log2 and -# math.Exp2, which Prometheus uses for native histogram bucket interpolation, as -# ` `. 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c00cecbbcf39910a 3fb4e29ae791e13c -exp2 404da18e398ac9e1 43a3303290444a8a -exp2 c02ca61738979e54 3f098e6635467cf6 -exp2 40264e6dc3547f6c 40a1cad438f1e7c6 -exp2 c02adf93e41f42a2 3f17a48a09c309bc -exp2 3fdedd87f3b46910 3ff659dee69e00f2 -exp2 4053a29735facb89 44d74573272b946e -exp2 4055611d55ba0022 4546e6f7cc7c4158 -exp2 c040ade4f26b09eb 3dd8f5565b062df6 -exp2 403c863f8b3780c5 41b703734457c16c -exp2 c04bcd8f21bbf206 3c7506885f4efab8 -exp2 c047d969c426d4b4 3cf3b7df5fbba402 -exp2 4053051248694848 44b0e744b6e51652 -exp2 4042513f5aed801d 4238d7b6876d690e -exp2 405232297c19f7be 447b8bd48a9d48d4 -exp2 404031ce3a0782ce 41f4f40be9eec12e -exp2 4043b1ceade5a557 4264f4190f9c4a72 -exp2 c04eb96d64d5a3d6 3c1772815d244300 -exp2 40472bd0374ad3d2 42d448c802925a4a -exp2 c03a6165874c4b9e 3e48950dc1fca25c -exp2 c029d8e56cfa38f2 3f20deae03bd48e8 -exp2 c04848972e06dd07 3ce59951ed2cb5f2 -exp2 4056f121b15b42e8 45ab3d919d0d553c -exp2 40157178c16459a9 40448bdf72ba47a0 -exp2 c04c8df8efb89a1b 3c5dab08827e2694 -exp2 404b64c0c7674dc7 435b9c3ab93414ea -exp2 40552f7d068fcca4 453ac28f0dc5231a -exp2 c0439c33023463e6 3d7b77df8a1e3068 -exp2 c045e79cbb10379b 3d32424885d1eb92 -exp2 c0471f70e6a143c3 3d0afd81c374d1e5 -exp2 4056c3d7bd0b8bc1 45a0ae10e0e2f2bd -exp2 4044ab79e9385126 42843f4f53bc3b98 -exp2 c04b4b44f62dce09 3c8549b029d8664e -exp2 4056869fc9e3e333 459130a7cf7495a1 -exp2 404ad116020be133 4348d2272ffd5006 -exp2 4045f62afe91f763 42ae573e7b79848d -exp2 bfe488227547f64c 3fe4830526318d5e -exp2 c002672edd8548f2 3fc9fc3557502b86 -exp2 c056d0961c564780 3a3abd03d1b54c40 -exp2 c05566233300c8b8 3a952c178996313a -exp2 c02856333e594df1 3f2c79aec1b28c03 -exp2 403f4eb05197864f 41e3cc9f46980448 -exp2 404d150254ac13e8 4391ed8a0fe9a2f4 -exp2 404824fcd702e8cd 42f38c58c90566ed -exp2 c041fb6ed54f43d8 3db066904a46659d -exp2 4047830b5101c8b1 42e044150e5a32a8 -exp2 c038b3662aecdec2 3e63b00cc49aafd3 -exp2 c04b6fb7d74431f0 3c81798af8822cd6 -exp2 c050d7bf9ca2150d 3bb8be205b7974d4 -exp2 405516591a8eed13 453461aa1b9db25c -exp2 4048ceadd9eee528 43087fdf5d78bd1a -exp2 405098c551e440f3 4414ec6216e1f4cf -exp2 c05485a1cf7d4736 3ace1b3dceeeed37 -exp2 c035ace0aa188f9c 3e9409d5edc75e68 -exp2 403383ca0deb9b92 4126dc5b2d263172 -exp2 c052d7a71739ccc2 3b38c4b36918aec3 -exp2 c0227aee989ac54c 3f5b180c94ff9863 -exp2 40481720b353229b 42f2227f60bf2009 -exp2 c052fb83030bc63a 3b30cc05e4b7a448 -exp2 404dac009273df89 43a44e187ad2135d -exp2 c0492d64dc58abcc 3cc906ac1956d283 -exp2 c0234c0c53a9d0c6 3f5469eab68074e5 -exp2 403bff3ef2b78dd4 41afef4a573add59 -exp2 405783e785d81ffc 45d0b0eb18a0c5e6 -exp2 40506b73a3fc44d9 44099d836fa45256 -exp2 c051ba3ec8242190 3b810769aca80765 -exp2 c0036d0eff778dad 3fc7c7fbc7c72c05 -exp2 401b4093f45420d9 405c1c6c7344b277 -exp2 403f6d0fbc1c6ea4 41e57f124a5a114f -exp2 c052984d0cabc324 3b489856867e5ad2 -exp2 c031ddd5175bc871 3ed18d0319c52d65 -exp2 c047cd5f79ae85c2 3cf50bf62456785d -exp2 c03d0814f8846e79 3e1f4eaf3a69f2cd -exp2 c04f93cf727b4d6c 3bfcbeaea4658b32 -exp2 40103e2c8ddc0da4 4030b00fd8a398a8 -exp2 c046dc1e552045b0 3d136e75dd02c0bc -exp2 4053f91334fee51e 44edb012573b1061 diff --git a/src/promql/src/histogram_eval/native.rs b/src/promql/src/histogram_eval/native.rs index e3fd468267a..3b2cc222660 100644 --- a/src/promql/src/histogram_eval/native.rs +++ b/src/promql/src/histogram_eval/native.rs @@ -13,14 +13,11 @@ // limitations under the License. //! Prometheus `HistogramQuantile`, `HistogramFraction` and the `histogramVariance` estimate over -//! one native histogram, with the bucket iteration of `model/histogram` and the Go `math` -//! functions they call, so results match Prometheus on amd64 bit for bit. +//! one native histogram, with the bucket iteration of `model/histogram`. use datafusion::error::{DataFusionError, Result}; use datatypes::series::histogram::{BucketSideView, HistogramView}; -use super::bounds::EXPONENTIAL_BOUNDS; - const CUSTOM_BUCKETS_SCHEMA: i32 = -53; #[derive(Debug, Clone, Copy)] @@ -128,25 +125,17 @@ fn bound(idx: i32, schema: i32, custom_values: &[f64]) -> Result { _ => Err(invalid_layout()), }; } - if schema < 0 { - if schema < -4 { - return Err(invalid_layout()); - } - let exp = i64::from(idx) << -schema; - if exp == 1024 { - return Ok(f64::MAX); - } - return Ok(ldexp(1.0, exp)); + if !(-4..=8).contains(&schema) { + return Err(invalid_layout()); } - let bounds = EXPONENTIAL_BOUNDS - .get(schema as usize) - .ok_or_else(invalid_layout)?; - let frac = bounds[(idx & ((1 << schema) - 1)) as usize]; - let exp = i64::from(idx >> schema) + 1; - if frac == 0.5 && exp == 1025 { + // The upper bound of bucket `idx` is 2^(idx / 2^schema). + let exponent = f64::from(idx) * 2f64.powi(-schema); + if exponent == 1024.0 { + // The last bucket of finite values; its computed bound would overflow to +Inf, which + // Go reserves for the bucket of infinite observations. return Ok(f64::MAX); } - Ok(ldexp(frac, exp)) + Ok(exponent.exp2()) } fn invalid_layout() -> DataFusionError { @@ -237,14 +226,12 @@ pub(super) fn quantile( if custom || (bucket.lower <= 0.0 && bucket.upper >= 0.0) { return Ok(bucket.lower + (bucket.upper - bucket.lower) * fraction); } - let log_lower = log2(bucket.lower.abs()); - let log_upper = log2(bucket.upper.abs()); + let log_lower = bucket.lower.abs().log2(); + let log_upper = bucket.upper.abs().log2(); if bucket.lower > 0.0 { - return Ok(exp2(log_lower + (log_upper - log_lower) * fraction)); + return Ok((log_lower + (log_upper - log_lower) * fraction).exp2()); } - Ok(-exp2( - log_upper + (log_lower - log_upper) * (1.0 - fraction), - )) + Ok(-(log_upper + (log_lower - log_upper) * (1.0 - fraction)).exp2()) } /// Prometheus `HistogramFraction`. @@ -331,9 +318,9 @@ pub(super) fn fraction( /// Go `Bucket.FractionBelow` with exponential interpolation. fn fraction_below_exponential(b: NativeBucket, v: f64) -> f64 { - let log_lower = log2(b.lower.abs()); - let log_upper = log2(b.upper.abs()); - let log_v = log2(v.abs()); + let log_lower = b.lower.abs().log2(); + let log_upper = b.upper.abs().log2(); + let log_v = v.abs().log2(); if v > 0.0 { (log_v - log_lower) / (log_upper - log_lower) } else { @@ -376,148 +363,16 @@ fn kahan_inc(inc: f64, sum: f64, c: f64) -> (f64, f64) { (t, c) } -/// Go `math.Ldexp` for a positive normal `frac`. -fn ldexp(frac: f64, exp: i64) -> f64 { - let bits = frac.to_bits(); - let exp = exp + ((bits >> 52) & 0x7FF) as i64 - 1023; - if exp < -1075 { - return 0.0; - } - if exp > 1023 { - return f64::INFINITY; - } - let (exp, scale) = if exp < -1022 { - (exp + 53, 1.0 / (1u64 << 53) as f64) - } else { - (exp, 1.0) - }; - scale * f64::from_bits((bits & !(0x7FF << 52)) | (((exp + 1023) as u64) << 52)) -} - -/// Go `math.Frexp`. -fn frexp(x: f64) -> (f64, i64) { - if x == 0.0 || x.is_infinite() || x.is_nan() { - return (x, 0); - } - let (x, mut exp) = if x.abs() < f64::MIN_POSITIVE { - (x * (1u64 << 52) as f64, -52) - } else { - (x, 0) - }; - let bits = x.to_bits(); - exp += ((bits >> 52) & 0x7FF) as i64 - 1023 + 1; - (f64::from_bits((bits & !(0x7FF << 52)) | (1022 << 52)), exp) -} - -/// Go `math.Log`, whose amd64 assembly performs the same operations for normal inputs. -// Constants are copied verbatim from Go's `math` package. -#[allow(clippy::excessive_precision)] -fn log(x: f64) -> f64 { - const LN2_HI: f64 = 6.93147180369123816490e-01; - const LN2_LO: f64 = 1.90821492927058770002e-10; - const L1: f64 = 6.666666666666735130e-01; - const L2: f64 = 3.999999999940941908e-01; - const L3: f64 = 2.857142874366239149e-01; - const L4: f64 = 2.222219843214978396e-01; - const L5: f64 = 1.818357216161805012e-01; - const L6: f64 = 1.531383769920937332e-01; - const L7: f64 = 1.479819860511658591e-01; - if x.is_nan() || x == f64::INFINITY { - return x; - } - if x < 0.0 { - return f64::NAN; - } - if x == 0.0 { - return f64::NEG_INFINITY; - } - let (mut f1, mut ki) = frexp(x); - if f1 < std::f64::consts::SQRT_2 / 2.0 { - f1 *= 2.0; - ki -= 1; - } - let f = f1 - 1.0; - let k = ki as f64; - let s = f / (2.0 + f); - let s2 = s * s; - let s4 = s2 * s2; - let t1 = s2 * (L1 + s4 * (L3 + s4 * (L5 + s4 * L7))); - let t2 = s4 * (L2 + s4 * (L4 + s4 * L6)); - let r = t1 + t2; - let hfsq = 0.5 * f * f; - k * LN2_HI - ((hfsq - (s * (hfsq + r) + k * LN2_LO)) - f) -} - -/// Go `math.Log2`. -fn log2(x: f64) -> f64 { - let (frac, exp) = frexp(x); - if frac == 0.5 { - return (exp - 1) as f64; - } - log(frac) * std::f64::consts::LOG2_E + exp as f64 -} - -/// Go `math.Exp2`, which is not assembly on amd64. -// Constants are copied verbatim from Go's `math` package. -#[allow(clippy::excessive_precision)] -fn exp2(x: f64) -> f64 { - const LN2_HI: f64 = 6.93147180369123816490e-01; - const LN2_LO: f64 = 1.90821492927058770002e-10; - const OVERFLOW: f64 = 1.0239999999999999e+03; - const UNDERFLOW: f64 = -1.0740e+03; - const P1: f64 = 1.66666666666666657415e-01; - const P2: f64 = -2.77777777770155933842e-03; - const P3: f64 = 6.61375632143793436117e-05; - const P4: f64 = -1.65339022054652515390e-06; - const P5: f64 = 4.13813679705723846039e-08; - if x.is_nan() || x == f64::INFINITY { - return x; - } - if x == f64::NEG_INFINITY || x < UNDERFLOW { - return 0.0; - } - if x > OVERFLOW { - return f64::INFINITY; - } - let k = if x > 0.0 { - (x + 0.5) as i64 - } else if x < 0.0 { - (x - 0.5) as i64 - } else { - 0 - }; - let t = x - k as f64; - let hi = t * LN2_HI; - let lo = -t * LN2_LO; - let r = hi - lo; - let t = r * r; - let c = r - t * (P1 + t * (P2 + t * (P3 + t * (P4 + t * P5)))); - let y = 1.0 - ((lo - (r * c) / (2.0 - c)) - hi); - ldexp(y, k) -} - #[cfg(test)] mod tests { - /// The bucket interpolation goes through Go's `math.Log2` and `math.Exp2`, which differ from - /// the platform functions in the last bit on some arguments. + /// The last bucket of finite values ends at `f64::MAX`; only the next one, which counts + /// infinite observations, ends at +Inf. #[test] - fn log2_and_exp2_match_go() { - let mut checked = 0; - for line in include_str!("go_math_cases.txt").lines() { - if line.starts_with('#') { - continue; - } - let fields: Vec<&str> = line.split(' ').collect(); - let bits = |field: &str| u64::from_str_radix(field, 16).unwrap(); - let argument = f64::from_bits(bits(fields[1])); - let actual = match fields[0] { - "log2" => super::log2(argument), - "exp2" => super::exp2(argument), - function => panic!("unknown function {function}"), - }; - assert_eq!(actual.to_bits(), bits(fields[2]), "{line}"); - checked += 1; + fn last_finite_bucket_ends_at_max() { + for schema in [-4, 0, 3, 8] { + let last = 1024i32 << schema.max(0) >> (-schema).max(0); + assert_eq!(super::bound(last, schema, &[]).unwrap(), f64::MAX); + assert_eq!(super::bound(last + 1, schema, &[]).unwrap(), f64::INFINITY); } - assert_eq!(checked, 400); } } diff --git a/src/promql/src/histogram_eval/tests.rs b/src/promql/src/histogram_eval/tests.rs index 3f27cc2bba3..8755a81fd04 100644 --- a/src/promql/src/histogram_eval/tests.rs +++ b/src/promql/src/histogram_eval/tests.rs @@ -184,7 +184,30 @@ fn assert_outcome( (labels.clone(), points) }) .collect(); - assert_eq!(actual, expected, "case {:?}", case.spec); + let keys = |series: &BTreeMap| { + series + .iter() + .map(|(labels, points)| (labels.clone(), points.keys().copied().collect())) + .collect::)>>() + }; + assert_eq!(keys(&actual), keys(&expected), "case {:?}", case.spec); + // promql-compat's tolerance for ill-conditioned evaluation covers the variance. + let epsilon = if case.spec[0].contains("stddev") || case.spec[0].contains("stdvar") { + 1e-6 + } else { + 1e-10 + }; + for (labels, points) in &actual { + for (point, &bits) in points { + let got = f64::from_bits(bits); + let want = f64::from_bits(expected[labels][point]); + assert!( + close(got, want, epsilon), + "case {:?}: {labels:?} at {point}: {got} vs {want}", + case.spec + ); + } + } false } (Err(actual), Err(expected)) => { @@ -327,3 +350,21 @@ fn histogram_functions_drop_metadata_labels() { expected.remove("__name__"); assert_eq!(labels_of(&count.metric), expected); } + +/// Prometheus `almost.Equal`, treating results below 1e-10 as equal and any NaN as equal to NaN, +/// as promql-compat compares engines. +fn close(a: f64, b: f64, epsilon: f64) -> bool { + if a.is_nan() || b.is_nan() { + return a.is_nan() && b.is_nan(); + } + if a == b { + return true; + } + let (diff, sum) = ((a - b).abs(), a.abs() + b.abs()); + let equal = if a == 0.0 || b == 0.0 || sum < f64::MIN_POSITIVE { + diff < epsilon * f64::MIN_POSITIVE + } else { + diff / sum.min(f64::MAX) < epsilon + }; + equal || (a.abs() < 1e-10 && b.abs() < 1e-10) +} From 329fed910baa28840b8fb86905bccbcb43f4d40a Mon Sep 17 00:00:00 2001 From: Dennis Zhuang Date: Sat, 17 Oct 2026 23:21:36 +0800 Subject: [PATCH 5/6] fix(promql): keep the first of equal classic bucket bounds like Prometheus Prometheus compares bounds with < and >, so +0 and -0 are equal, keep input order, and coalescing keeps the first; ordering -0 first returned the other zero and flipped the sign of an infinite reciprocal. Signed-off-by: Dennis Zhuang --- src/promql/src/histogram_eval.rs | 10 ++++++-- src/promql/src/histogram_eval/tests.rs | 33 ++++++++++++++++++++++++++ 2 files changed, 41 insertions(+), 2 deletions(-) diff --git a/src/promql/src/histogram_eval.rs b/src/promql/src/histogram_eval.rs index 5aa9843774e..c6d9a44e8a3 100644 --- a/src/promql/src/histogram_eval.rs +++ b/src/promql/src/histogram_eval.rs @@ -90,8 +90,14 @@ pub fn evaluate_histograms( let mut native_buckets = Vec::new(); let mut values = vec![None; schema.fields.len()]; for mut group in groups.into_values() { - // Pre-sorting by bound keeps the buckets of every point sorted. - group.classic.sort_by(|a, b| a.0.total_cmp(&b.0)); + // Pre-sorting by bound keeps the buckets of every point sorted. Like Go's comparison, + // +0 and -0 are equal and keep input order, and coalescing keeps the first bound. + group + .classic + .sort_by(|a, b| match (a.0.is_nan(), b.0.is_nan()) { + (false, false) => a.0.partial_cmp(&b.0).expect("neither is NaN"), + (nan_a, nan_b) => nan_a.cmp(&nan_b), + }); let ranges = group .classic .iter() diff --git a/src/promql/src/histogram_eval/tests.rs b/src/promql/src/histogram_eval/tests.rs index 8755a81fd04..4cda9c71bbf 100644 --- a/src/promql/src/histogram_eval/tests.rs +++ b/src/promql/src/histogram_eval/tests.rs @@ -368,3 +368,36 @@ fn close(a: f64, b: f64, epsilon: f64) -> bool { }; equal || (a.abs() < 1e-10 && b.abs() < 1e-10) } + +/// Bounds +0 and -0 compare equal and keep input order, so coalescing keeps the first one: +/// `1 / histogram_quantile(0, sort_desc(h))` over `le` "+Inf", "0", "-0" is +Inf. +#[test] +fn classic_bounds_keep_the_first_signed_zero() { + let grid = Arc::new( + datatypes::series::time::EvalGrid::try_new( + datatypes::series::time::GridSpec::try_new(0, 1_000, 1).unwrap(), + ) + .unwrap(), + ); + let schema = Arc::new(SeriesSchema { + fields: vec![FieldSpec { + name: Arc::from("value"), + }] + .into(), + eval_grid: Some(grid), + }); + let buckets: Vec<_> = [("+Inf", 3.0), ("0", 2.0), ("-0", 1.0)] + .iter() + .map(|(le, count)| { + let labels = Labels::from([ + ("__name__".to_string(), "h".to_string()), + ("le".to_string(), le.to_string()), + ]); + let points = BTreeMap::from([(0, f64::to_bits(*count))]); + mixed_series(&schema, &labels, &points, &BTreeMap::new()).unwrap() + }) + .collect(); + let result = evaluate_histograms(HistogramFunction::Quantile(0.0), &schema, &buckets).unwrap(); + let points = points_of(&result[0]); + assert_eq!(1.0 / f64::from_bits(points[&0]), f64::INFINITY); +} From e57cd6301437a837cf576c6dac0c8bcbca64add5 Mon Sep 17 00:00:00 2001 From: Dennis Zhuang Date: Sun, 18 Oct 2026 00:40:17 +0800 Subject: [PATCH 6/6] fix(promql): sort classic buckets per point like Go and parse le like strconv Signed-off-by: Dennis Zhuang --- src/promql/src/go_sort.rs | 342 +++++++++++++++++++++++ src/promql/src/go_sort_cases.txt | 208 ++++++++++++++ src/promql/src/histogram_eval.rs | 19 +- src/promql/src/histogram_eval/classic.rs | 27 +- src/promql/src/histogram_eval/tests.rs | 64 +++++ src/promql/src/lib.rs | 1 + 6 files changed, 648 insertions(+), 13 deletions(-) create mode 100644 src/promql/src/go_sort.rs create mode 100644 src/promql/src/go_sort_cases.txt diff --git a/src/promql/src/go_sort.rs b/src/promql/src/go_sort.rs new file mode 100644 index 00000000000..6e49fc83924 --- /dev/null +++ b/src/promql/src/go_sort.rs @@ -0,0 +1,342 @@ +// Copyright 2023 Greptime Team +// +// Licensed under the Apache License, Version 2.0 (the "License"); +// you may not use this file except in compliance with the License. +// You may obtain a copy of the License at +// +// http://www.apache.org/licenses/LICENSE-2.0 +// +// Unless required by applicable law or agreed to in writing, software +// distributed under the License is distributed on an "AS IS" BASIS, +// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. +// See the License for the specific language governing permissions and +// limitations under the License. + +//! A port of Go's `sort.Sort` / `slices.SortFunc` (pattern-defeating quicksort, Go 1.19+). +//! +//! Prometheus orders results with these, and with comparators that are not total orders +//! (NaN ranks first in `Less` against everything, `natsort.Compare` holds both ways for "1" +//! and "01"). The order of such elements is part of the result, and Rust's sorts may panic on +//! such comparators, so the exact algorithm is reproduced. + +/// Sorts `v` the way Go's `sort.Sort` does with `less` as `Less`. +pub(crate) fn sort_by(v: &mut [T], mut less: impl FnMut(&T, &T) -> bool) { + let n = v.len(); + if n <= 1 { + return; + } + let limit = bit_len(n); + let mut sorter = Sorter { v, less: &mut less }; + sorter.pdqsort(0, n, limit); +} + +fn bit_len(n: usize) -> usize { + (usize::BITS - n.leading_zeros()) as usize +} + +#[derive(PartialEq, Eq)] +enum Hint { + Unknown, + Increasing, + Decreasing, +} + +struct Sorter<'a, T, F> { + v: &'a mut [T], + less: &'a mut F, +} + +impl bool> Sorter<'_, T, F> { + fn less(&mut self, i: usize, j: usize) -> bool { + (self.less)(&self.v[i], &self.v[j]) + } + + fn swap(&mut self, i: usize, j: usize) { + self.v.swap(i, j); + } + + fn insertion_sort(&mut self, a: usize, b: usize) { + for i in a + 1..b { + let mut j = i; + while j > a && self.less(j, j - 1) { + self.swap(j, j - 1); + j -= 1; + } + } + } + + fn sift_down(&mut self, lo: usize, hi: usize, first: usize) { + let mut root = lo; + loop { + let mut child = 2 * root + 1; + if child >= hi { + break; + } + if child + 1 < hi && self.less(first + child, first + child + 1) { + child += 1; + } + if !self.less(first + root, first + child) { + return; + } + self.swap(first + root, first + child); + root = child; + } + } + + fn heap_sort(&mut self, a: usize, b: usize) { + let first = a; + let hi = b - a; + for i in (0..=(hi - 1) / 2).rev() { + self.sift_down(i, hi, first); + } + for i in (0..hi).rev() { + self.swap(first, first + i); + self.sift_down(0, i, first); + } + } + + fn pdqsort(&mut self, mut a: usize, mut b: usize, mut limit: usize) { + const MAX_INSERTION: usize = 12; + let mut was_balanced = true; + let mut was_partitioned = true; + loop { + let length = b - a; + if length <= MAX_INSERTION { + self.insertion_sort(a, b); + return; + } + if limit == 0 { + self.heap_sort(a, b); + return; + } + if !was_balanced { + self.break_patterns(a, b); + limit -= 1; + } + + let (mut pivot, mut hint) = self.choose_pivot(a, b); + if hint == Hint::Decreasing { + self.reverse_range(a, b); + pivot = (b - 1) - (pivot - a); + hint = Hint::Increasing; + } + if was_balanced + && was_partitioned + && hint == Hint::Increasing + && self.partial_insertion_sort(a, b) + { + return; + } + if a > 0 && !self.less(a - 1, pivot) { + a = self.partition_equal(a, b, pivot); + continue; + } + + let (mid, already_partitioned) = self.partition(a, b, pivot); + was_partitioned = already_partitioned; + let (left_len, right_len) = (mid - a, b - mid); + let balance_threshold = length / 8; + if left_len < right_len { + was_balanced = left_len >= balance_threshold; + self.pdqsort(a, mid, limit); + a = mid + 1; + } else { + was_balanced = right_len >= balance_threshold; + self.pdqsort(mid + 1, b, limit); + b = mid; + } + } + } + + // Indices stay signed here: `j` can step to `a` - 1 when nothing is below the pivot. + fn partition(&mut self, a: usize, b: usize, pivot: usize) -> (usize, bool) { + self.swap(a, pivot); + let (mut i, mut j) = (a as isize + 1, b as isize - 1); + let at = |k: isize| k as usize; + while i <= j && self.less(at(i), a) { + i += 1; + } + while i <= j && !self.less(at(j), a) { + j -= 1; + } + if i > j { + self.swap(at(j), a); + return (at(j), true); + } + self.swap(at(i), at(j)); + i += 1; + j -= 1; + loop { + while i <= j && self.less(at(i), a) { + i += 1; + } + while i <= j && !self.less(at(j), a) { + j -= 1; + } + if i > j { + break; + } + self.swap(at(i), at(j)); + i += 1; + j -= 1; + } + self.swap(at(j), a); + (at(j), false) + } + + fn partition_equal(&mut self, a: usize, b: usize, pivot: usize) -> usize { + self.swap(a, pivot); + let (mut i, mut j) = (a as isize + 1, b as isize - 1); + let at = |k: isize| k as usize; + loop { + while i <= j && !self.less(a, at(i)) { + i += 1; + } + while i <= j && self.less(a, at(j)) { + j -= 1; + } + if i > j { + break; + } + self.swap(at(i), at(j)); + i += 1; + j -= 1; + } + at(i) + } + + fn partial_insertion_sort(&mut self, a: usize, b: usize) -> bool { + const MAX_STEPS: usize = 5; + const SHORTEST_SHIFTING: usize = 50; + let mut i = a + 1; + for _ in 0..MAX_STEPS { + while i < b && !self.less(i, i - 1) { + i += 1; + } + if i == b { + return true; + } + if b - a < SHORTEST_SHIFTING { + return false; + } + self.swap(i, i - 1); + if i - a >= 2 { + let mut j = i - 1; + while j >= 1 { + if !self.less(j, j - 1) { + break; + } + self.swap(j, j - 1); + j -= 1; + } + } + if b - i >= 2 { + for j in i + 1..b { + if !self.less(j, j - 1) { + break; + } + self.swap(j, j - 1); + } + } + } + false + } + + fn break_patterns(&mut self, a: usize, b: usize) { + let length = b - a; + if length >= 8 { + let mut random = length as u64; + let modulus = 1usize << bit_len(length); + for idx in a + (length / 4) * 2 - 1..=a + (length / 4) * 2 + 1 { + random ^= random << 13; + random ^= random >> 7; + random ^= random << 17; + let mut other = (random as usize) & (modulus - 1); + if other >= length { + other -= length; + } + self.swap(idx, a + other); + } + } + } + + fn choose_pivot(&mut self, a: usize, b: usize) -> (usize, Hint) { + const SHORTEST_NINTHER: usize = 50; + const MAX_SWAPS: usize = 4 * 3; + let l = b - a; + let mut swaps = 0; + let mut i = a + l / 4; + let mut j = a + l / 4 * 2; + let mut k = a + l / 4 * 3; + if l >= 8 { + if l >= SHORTEST_NINTHER { + i = self.median(i - 1, i, i + 1, &mut swaps); + j = self.median(j - 1, j, j + 1, &mut swaps); + k = self.median(k - 1, k, k + 1, &mut swaps); + } + j = self.median(i, j, k, &mut swaps); + } + match swaps { + 0 => (j, Hint::Increasing), + MAX_SWAPS => (j, Hint::Decreasing), + _ => (j, Hint::Unknown), + } + } + + fn order2(&mut self, a: usize, b: usize, swaps: &mut usize) -> (usize, usize) { + if self.less(b, a) { + *swaps += 1; + return (b, a); + } + (a, b) + } + + fn median(&mut self, a: usize, b: usize, c: usize, swaps: &mut usize) -> usize { + let (a, b) = self.order2(a, b, swaps); + let (b, _) = self.order2(b, c, swaps); + let (_, b) = self.order2(a, b, swaps); + b + } + + fn reverse_range(&mut self, a: usize, b: usize) { + let (mut i, mut j) = (a, b - 1); + while i < j { + self.swap(i, j); + i += 1; + j -= 1; + } + } +} + +#[cfg(test)] +mod tests { + /// Orders produced by Go's `sort.Sort` (and identically `slices.SortFunc`), generated by + /// promql-compat `cmd/narthex-golden-gosort`; line format: `kind keys | ids`. + #[test] + fn matches_go_sort_on_comparators_that_are_not_total_orders() { + let text = include_str!("go_sort_cases.txt"); + let mut cases = 0; + for line in text.lines() { + let (head, expected) = line.split_once(" | ").unwrap(); + let (kind, keys) = head.split_once(' ').unwrap(); + let kind: u8 = kind.parse().unwrap(); + let parse = |list: &str| -> Vec { + list.split(',') + .filter(|item| !item.is_empty()) + .map(|item| item.trim().parse().unwrap()) + .collect() + }; + let mut items: Vec<(usize, usize)> = parse(keys).into_iter().zip(0..).collect(); + super::sort_by(&mut items, |&(a, a_id), &(b, b_id)| match kind { + 0 => a < b, + 1 => a == 0 || a < b, + 2 => a % 3 < b % 3, + _ => (a_id * 31 + b_id * 17) % 5 < 2, + }); + let actual: Vec = items.iter().map(|&(_, id)| id).collect(); + assert_eq!(actual, parse(expected), "{line}"); + cases += 1; + } + assert!(cases >= 200); + } +} diff --git a/src/promql/src/go_sort_cases.txt b/src/promql/src/go_sort_cases.txt new file mode 100644 index 00000000000..1f16b1e793a --- /dev/null +++ b/src/promql/src/go_sort_cases.txt @@ -0,0 +1,208 @@ +0 | +0 | +0 | +0 | +1 | +1 | +1 | +1 | +2 | +2 | +2 | +2 | +3 | +3 | +3 | +3 | +0 0 | 0 +0 0 | 0 +0 1 | 0 +0 0 | 0 +1 0 | 0 +1 0 | 0 +1 1 | 0 +1 0 | 0 +2 0 | 0 +2 0 | 0 +2 1 | 0 +2 0 | 0 +3 0 | 0 +3 0 | 0 +3 1 | 0 +3 0 | 0 +0 1,0 | 1,0 +0 0,1 | 0,1 +0 2,1 | 1,0 +0 0,1 | 0,1 +1 1,0 | 1,0 +1 0,1 | 0,1 +1 2,1 | 1,0 +1 0,1 | 0,1 +2 0,0 | 0,1 +2 0,1 | 0,1 +2 2,1 | 1,0 +2 0,1 | 0,1 +3 0,1 | 1,0 +3 0,1 | 1,0 +3 2,1 | 1,0 +3 0,1 | 1,0 +0 0,2,1,2,0 | 0,4,2,1,3 +0 0,1,2,3,4 | 0,1,2,3,4 +0 5,4,3,2,1 | 4,3,2,1,0 +0 0,1,2,3,4 | 0,1,2,3,4 +1 2,2,2,2,0 | 4,0,1,2,3 +1 0,1,2,3,4 | 0,1,2,3,4 +1 5,4,3,2,1 | 4,3,2,1,0 +1 0,1,2,3,4 | 0,1,2,3,4 +2 2,1,0,1,1 | 2,1,3,4,0 +2 0,1,2,3,4 | 0,3,1,4,2 +2 5,4,3,2,1 | 2,1,4,0,3 +2 0,1,2,3,4 | 0,3,1,4,2 +3 1,0,0,1,0 | 1,0,2,4,3 +3 0,1,2,3,4 | 1,0,2,4,3 +3 5,4,3,2,1 | 1,0,2,4,3 +3 0,1,2,3,4 | 1,0,2,4,3 +0 6,4,3,6,0,0,5,4,6,3,6,0 | 4,5,11,2,9,1,7,6,0,3,8,10 +0 0,1,2,3,4,5,6,7,8,9,10,11 | 0,1,2,3,4,5,6,7,8,9,10,11 +0 12,11,10,9,8,7,6,5,4,3,2,1 | 11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4 | 0,7,1,8,2,9,3,10,4,11,5,6 +1 6,1,1,4,6,4,6,0,5,0,1,4 | 9,7,1,2,10,3,5,11,8,0,4,6 +1 0,1,2,3,4,5,6,7,8,9,10,11 | 0,1,2,3,4,5,6,7,8,9,10,11 +1 12,11,10,9,8,7,6,5,4,3,2,1 | 11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4 | 7,0,1,8,2,9,3,10,4,11,5,6 +2 2,3,5,6,5,0,1,3,5,4,0,1 | 1,3,5,7,10,6,9,11,0,2,4,8 +2 0,1,2,3,4,5,6,7,8,9,10,11 | 0,3,6,9,1,4,7,10,2,5,8,11 +2 12,11,10,9,8,7,6,5,4,3,2,1 | 0,3,6,9,2,5,8,11,1,4,7,10 +2 0,1,2,3,4,5,6,0,1,2,3,4 | 0,3,6,7,10,1,4,8,11,2,5,9 +3 5,2,1,0,1,2,3,4,0,0,6,5 | 1,0,2,4,5,3,6,7,9,10,8,11 +3 0,1,2,3,4,5,6,7,8,9,10,11 | 1,0,2,4,5,3,6,7,9,10,8,11 +3 12,11,10,9,8,7,6,5,4,3,2,1 | 1,0,2,4,5,3,6,7,9,10,8,11 +3 0,1,2,3,4,5,6,0,1,2,3,4 | 1,0,2,4,5,3,6,7,9,10,8,11 +0 0,1,0,3,5,3,4,6,1,5,6,3,6 | 2,0,8,1,3,11,5,6,9,4,7,10,12 +0 0,1,2,3,4,5,6,7,8,9,10,11,12 | 0,1,2,3,4,5,6,7,8,9,10,11,12 +0 13,12,11,10,9,8,7,6,5,4,3,2,1 | 12,11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4,5 | 7,0,1,8,2,9,3,10,4,11,5,12,6 +1 5,3,4,6,6,6,2,6,3,5,3,5,3 | 6,1,12,10,8,2,9,0,11,7,5,4,3 +1 0,1,2,3,4,5,6,7,8,9,10,11,12 | 0,1,2,3,4,5,6,7,8,9,10,11,12 +1 13,12,11,10,9,8,7,6,5,4,3,2,1 | 12,11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4,5 | 0,7,1,8,2,9,3,10,4,11,5,12,6 +2 0,1,0,5,4,0,6,1,5,5,6,2,0 | 10,2,0,5,6,12,1,4,7,3,9,11,8 +2 0,1,2,3,4,5,6,7,8,9,10,11,12 | 6,3,0,9,12,1,4,7,10,2,5,8,11 +2 13,12,11,10,9,8,7,6,5,4,3,2,1 | 4,1,10,7,6,0,3,9,12,5,8,2,11 +2 0,1,2,3,4,5,6,0,1,2,3,4,5 | 6,3,0,7,10,1,4,8,11,2,5,9,12 +3 3,2,6,4,6,5,6,6,4,0,4,3,4 | 10,5,9,0,4,3,6,7,8,1,11,12,2 +3 0,1,2,3,4,5,6,7,8,9,10,11,12 | 10,5,9,0,4,3,6,7,8,1,11,12,2 +3 13,12,11,10,9,8,7,6,5,4,3,2,1 | 10,5,9,0,4,3,6,7,8,1,11,12,2 +3 0,1,2,3,4,5,6,0,1,2,3,4,5 | 10,5,9,0,4,3,6,7,8,1,11,12,2 +0 9,8,10,6,6,4,0,9,2,3,3,1,6,7,4,4,6,7,6,0 | 6,19,11,8,10,9,5,14,15,16,3,12,4,18,13,17,1,0,7,2 +0 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 +0 20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5 | 14,0,7,1,15,8,9,2,16,10,3,17,11,4,18,12,5,19,6,13 +1 4,9,1,1,3,5,7,2,8,3,6,4,0,6,9,2,7,2,2,4 | 12,2,3,18,7,17,15,4,9,19,0,11,5,13,10,16,6,8,14,1 +1 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 +1 20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5 | 7,0,14,1,15,8,9,2,16,10,3,17,11,4,18,12,5,19,6,13 +2 8,9,7,5,10,4,2,2,2,8,6,6,4,9,0,5,8,2,9,5 | 10,1,18,14,13,11,5,12,2,4,6,0,7,9,3,15,16,17,8,19 +2 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 | 9,18,15,3,12,0,6,10,7,4,13,16,1,19,8,5,11,14,2,17 +2 20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 8,17,2,14,11,5,10,16,19,1,7,4,13,12,3,15,0,9,18,6 +2 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5 | 10,17,0,3,14,13,6,7,15,8,11,4,1,18,9,12,5,2,16,19 +3 9,1,5,6,6,10,10,8,10,7,1,5,4,1,5,4,8,2,7,3 | 1,16,11,6,5,15,0,10,9,8,12,7,13,3,17,2,18,4,14,19 +3 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19 | 1,16,11,6,5,15,0,10,9,8,12,7,13,3,17,2,18,4,14,19 +3 20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 1,16,11,6,5,15,0,10,9,8,12,7,13,3,17,2,18,4,14,19 +3 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5 | 1,16,11,6,5,15,0,10,9,8,12,7,13,3,17,2,18,4,14,19 +0 3,13,18,6,19,7,7,2,0,6,3,20,17,18,20,21,11,7,20,10,22,4,11,10,20,4,4,14,10,1,6,7,16,0,14,12,8,11,4,10,9,15,19,14,15,12,15,0,9 | 33,47,8,29,7,0,10,21,26,25,38,9,30,3,17,5,31,6,36,48,40,23,19,39,28,22,16,37,35,45,1,27,34,43,41,44,46,32,12,13,2,42,4,24,18,14,11,15,20 +0 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48 +0 49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6 | 7,0,28,14,35,42,21,36,8,22,1,43,15,29,44,30,16,2,37,23,9,24,31,10,38,17,45,3,25,4,39,11,32,18,46,40,5,47,33,12,19,26,34,13,27,41,20,6,48 +1 23,10,18,21,15,24,19,20,11,13,22,19,20,24,12,24,18,6,23,2,20,22,21,17,1,15,7,4,17,4,6,21,5,11,18,3,16,9,17,8,8,3,3,24,9,0,24,6,12 | 45,24,19,35,41,42,29,27,32,30,47,17,26,39,40,37,44,1,33,8,14,48,9,25,4,36,38,28,23,16,2,34,6,11,7,20,12,3,31,22,10,21,0,18,13,43,15,5,46 +1 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48 +1 49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6 | 21,42,35,14,28,0,7,36,8,22,1,43,15,29,44,30,16,2,37,23,9,24,31,10,38,17,45,3,25,4,39,11,32,18,46,40,5,47,33,12,19,26,34,13,27,41,20,6,48 +2 11,17,14,8,9,21,23,24,12,7,24,14,6,21,8,3,16,1,2,12,11,1,5,12,14,23,12,5,9,3,9,11,2,18,20,21,3,15,20,6,5,1,9,16,6,20,5,9,2 | 36,37,47,44,4,5,42,7,8,39,10,26,12,13,35,15,33,30,29,19,28,23,17,21,43,9,41,16,3,14,20,31,32,22,27,24,0,11,38,18,40,25,6,1,34,45,46,2,48 +2 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48 | 24,18,48,3,45,42,6,39,36,9,33,30,12,27,0,15,21,37,10,19,46,16,22,4,1,43,25,13,28,40,7,31,34,41,29,35,8,26,38,11,32,14,5,17,44,23,20,47,2 +2 49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 16,1,46,43,4,40,37,7,34,31,10,28,25,13,22,19,24,33,18,15,48,21,45,3,0,12,42,27,39,6,30,9,36,41,26,35,32,29,38,8,11,17,5,23,44,14,2,47,20 +2 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6 | 21,48,45,3,42,41,6,7,38,0,10,35,34,13,14,31,28,17,27,24,20,36,11,1,46,25,43,18,4,29,39,15,32,8,22,12,16,37,33,30,40,5,9,26,44,2,19,47,23 +3 17,3,0,18,5,8,6,15,8,9,17,23,12,23,22,3,8,2,21,23,13,6,24,6,15,6,7,2,2,4,8,5,11,12,12,4,21,18,23,6,15,22,20,19,6,24,24,20,19 | 12,7,42,32,47,27,2,17,22,37,38,33,8,13,43,28,3,48,18,23,24,35,1,19,4,46,26,16,44,29,6,31,14,11,34,21,36,41,9,39,20,0,25,45,15,5,30,10,40 +3 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48 | 12,7,42,32,47,27,2,17,22,37,38,33,8,13,43,28,3,48,18,23,24,35,1,19,4,46,26,16,44,29,6,31,14,11,34,21,36,41,9,39,20,0,25,45,15,5,30,10,40 +3 49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 12,7,42,32,47,27,2,17,22,37,38,33,8,13,43,28,3,48,18,23,24,35,1,19,4,46,26,16,44,29,6,31,14,11,34,21,36,41,9,39,20,0,25,45,15,5,30,10,40 +3 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6 | 12,7,42,32,47,27,2,17,22,37,38,33,8,13,43,28,3,48,18,23,24,35,1,19,4,46,26,16,44,29,6,31,14,11,34,21,36,41,9,39,20,0,25,45,15,5,30,10,40 +0 23,25,24,5,17,14,17,14,3,12,1,13,3,17,25,13,15,13,17,22,2,9,15,12,7,3,19,9,12,7,0,24,14,17,18,20,5,20,12,0,15,18,21,6,25,7,1,11,12,24 | 30,39,46,10,20,12,25,8,3,36,43,45,29,24,27,21,47,38,9,23,28,48,11,17,15,5,32,7,16,22,40,13,18,4,6,33,41,34,26,37,35,42,19,0,31,2,49,14,44,1 +0 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 +0 50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 35,21,0,49,28,14,42,7,15,22,1,36,8,29,43,9,16,30,44,2,23,37,24,17,3,10,38,45,31,46,4,18,32,39,11,25,12,5,19,33,40,47,26,20,13,27,6,41,48,34 +1 24,19,4,9,21,6,22,5,5,1,1,6,6,2,13,16,1,0,4,17,4,20,13,20,25,9,16,23,12,25,14,19,0,17,11,20,19,12,24,6,12,18,21,24,1,0,3,3,21,14 | 17,32,45,9,44,10,16,13,47,46,20,18,2,8,7,39,12,11,5,25,3,34,28,37,40,22,14,49,30,26,15,19,33,41,36,1,31,21,35,23,48,4,42,6,27,38,43,0,24,29 +1 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 +1 50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 7,42,14,28,49,0,21,35,15,22,1,36,8,29,43,9,16,30,44,2,23,37,24,17,3,10,38,45,31,46,4,18,32,39,11,25,12,5,19,33,40,47,26,20,13,27,6,41,48,34 +2 23,8,5,18,5,6,15,24,2,10,12,23,8,20,1,4,24,19,13,3,19,9,0,24,17,17,3,4,3,12,8,24,11,15,17,20,2,9,8,14,6,9,7,24,4,21,22,1,19,2 | 16,22,31,3,37,5,6,7,33,29,10,28,43,26,40,41,45,23,21,19,20,18,14,15,17,48,42,27,44,9,46,47,24,32,34,35,36,30,38,39,25,0,13,12,11,8,4,2,1,49 +2 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 | 18,48,45,3,42,39,6,36,33,9,30,27,12,0,24,15,21,25,4,19,49,16,22,1,46,13,43,40,28,37,10,31,7,34,17,26,32,29,38,5,35,11,8,41,44,2,14,47,23,20 +2 50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 17,47,2,44,41,5,38,35,8,32,29,11,26,23,14,20,25,34,49,19,1,46,22,13,43,16,4,40,28,10,37,31,7,0,42,9,36,30,6,39,27,12,33,24,3,45,21,15,48,18 +2 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 24,49,48,3,45,42,6,7,41,38,10,35,34,13,14,31,28,17,27,0,20,21,25,11,22,1,46,18,4,29,43,15,32,8,39,36,5,2,9,12,40,33,44,23,37,16,26,47,30,19 +3 12,11,5,17,3,6,23,16,22,15,25,22,21,6,16,12,25,2,11,21,2,23,0,18,9,11,3,18,24,4,14,5,10,10,4,24,4,16,10,10,7,16,6,1,15,13,1,15,1,6 | 36,1,46,26,41,31,16,6,11,21,15,0,20,5,25,40,30,45,10,35,34,49,22,47,24,17,14,27,2,29,44,12,32,42,19,9,4,37,7,39,38,8,33,43,13,3,28,23,48,18 +3 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49 | 36,1,46,26,41,31,16,6,11,21,15,0,20,5,25,40,30,45,10,35,34,49,22,47,24,17,14,27,2,29,44,12,32,42,19,9,4,37,7,39,38,8,33,43,13,3,28,23,48,18 +3 50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 36,1,46,26,41,31,16,6,11,21,15,0,20,5,25,40,30,45,10,35,34,49,22,47,24,17,14,27,2,29,44,12,32,42,19,9,4,37,7,39,38,8,33,43,13,3,28,23,48,18 +3 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 36,1,46,26,41,31,16,6,11,21,15,0,20,5,25,40,30,45,10,35,34,49,22,47,24,17,14,27,2,29,44,12,32,42,19,9,4,37,7,39,38,8,33,43,13,3,28,23,48,18 +0 7,12,11,20,8,3,9,20,12,12,15,1,7,2,18,9,12,9,9,23,25,20,0,8,8,18,13,1,0,10,16,18,22,16,15,14,16,6,13,2,25,6,0,2,25,0,8,13,11,16,11 | 28,45,22,42,27,11,39,43,13,5,37,41,0,12,24,23,4,46,15,17,18,6,29,2,48,50,1,9,8,16,26,47,38,35,10,34,33,30,36,49,14,31,25,3,7,21,32,19,40,44,20 +0 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50 +0 51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1 | 42,21,0,28,49,14,35,7,15,29,8,22,36,43,1,50,16,30,9,23,2,44,37,24,10,3,45,38,31,17,11,25,32,4,46,18,39,26,47,12,40,19,33,5,6,13,34,27,48,20,41 +1 8,1,0,0,19,11,24,7,3,0,14,15,14,21,5,14,10,16,8,4,23,18,5,25,23,25,17,11,2,25,19,23,2,3,9,9,5,20,24,25,7,17,2,14,21,6,15,21,21,11,6 | 9,2,3,1,28,32,42,33,8,19,36,22,14,50,45,7,40,0,18,34,35,16,49,27,5,12,15,43,10,11,46,17,26,41,21,4,30,37,13,44,47,48,20,24,31,38,6,39,23,25,29 +1 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50 +1 51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1 | 7,35,14,49,28,0,21,42,15,29,8,22,36,43,1,50,16,30,9,23,2,44,37,24,10,3,45,38,31,17,11,25,32,4,46,18,39,26,47,12,40,19,33,5,6,13,34,27,48,20,41 +2 18,23,0,11,6,16,0,17,12,13,4,1,25,1,5,4,11,7,23,10,25,25,5,13,0,21,19,0,24,24,16,22,25,10,16,16,5,1,20,2,16,13,9,24,22,17,13,2,6,10,10 | 24,48,2,43,4,42,6,29,8,28,27,25,0,12,32,15,50,17,49,19,20,21,46,23,13,11,26,10,9,44,30,31,5,33,34,35,41,37,40,39,38,36,14,3,7,45,22,47,1,18,16 +2 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50 | 18,48,45,3,42,39,6,36,33,9,30,27,12,0,24,15,21,25,4,19,49,16,22,1,46,13,43,40,28,37,10,31,7,34,17,26,32,29,38,5,11,41,35,44,8,2,14,47,23,20,50 +2 51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 18,48,45,3,42,39,6,36,33,9,30,27,12,24,0,15,21,23,17,50,20,47,2,14,44,41,26,11,5,29,38,35,32,8,34,43,7,37,10,28,40,25,4,31,13,22,46,16,1,49,19 +2 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1 | 24,49,48,3,45,42,6,7,41,38,10,35,34,13,14,31,28,17,27,0,20,21,25,29,22,50,1,18,46,39,4,15,32,43,8,11,36,37,9,23,40,12,5,33,44,30,16,47,2,26,19 +3 11,3,19,10,13,24,14,2,18,5,10,5,14,7,18,21,21,23,18,0,25,22,4,23,4,9,7,0,16,20,23,3,0,0,0,25,11,17,7,14,13,23,21,15,0,24,14,18,18,16,2 | 41,31,21,46,16,36,6,1,26,11,45,15,30,50,40,5,25,20,0,10,35,42,48,23,3,18,43,8,28,38,33,13,27,17,47,37,32,12,22,2,7,9,19,39,44,4,24,29,34,49,14 +3 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50 | 41,31,21,46,16,36,6,1,26,11,45,15,30,50,40,5,25,20,0,10,35,42,48,23,3,18,43,8,28,38,33,13,27,17,47,37,32,12,22,2,7,9,19,39,44,4,24,29,34,49,14 +3 51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 41,31,21,46,16,36,6,1,26,11,45,15,30,50,40,5,25,20,0,10,35,42,48,23,3,18,43,8,28,38,33,13,27,17,47,37,32,12,22,2,7,9,19,39,44,4,24,29,34,49,14 +3 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1 | 41,31,21,46,16,36,6,1,26,11,45,15,30,50,40,5,25,20,0,10,35,42,48,23,3,18,43,8,28,38,33,13,27,17,47,37,32,12,22,2,7,9,19,39,44,4,24,29,34,49,14 +0 0,5,13,1,12,30,1,25,26,18,15,21,15,0,4,21,3,16,3,5,9,24,4,21,14,18,11,0,1,5,2,13,28,6,1,22,12,23,21,29,4,15,1,5,10,9,31,17,11,14,16,0,5,6,19,23,18,26,29,2,27,17,26,10 | 27,0,51,13,6,28,3,42,34,59,30,18,16,40,14,22,52,29,1,19,43,53,33,20,45,63,44,26,48,36,4,2,31,49,24,12,41,10,50,17,61,47,56,9,25,54,23,15,11,38,35,55,37,21,7,8,57,62,60,32,58,39,5,46 +0 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63 +0 64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 56,28,49,21,63,42,0,7,14,35,8,57,50,43,1,15,22,29,36,9,37,2,16,23,51,58,44,30,24,10,52,31,45,59,38,3,17,32,46,39,4,60,11,53,18,25,19,5,40,61,47,26,33,12,54,55,27,13,6,34,41,20,62,48 +1 14,24,10,27,16,19,18,1,21,5,21,3,22,3,20,2,1,14,10,5,1,22,22,13,0,0,21,12,9,7,21,24,1,4,8,26,19,3,15,21,24,7,20,8,24,20,32,3,6,11,1,14,21,14,30,12,14,14,17,11,11,29,26,26 | 24,25,50,32,7,20,16,15,13,47,37,11,33,9,19,48,41,29,43,34,28,2,18,49,59,60,55,27,23,51,57,0,17,56,53,38,4,58,6,5,36,45,14,42,8,30,39,10,26,52,21,12,22,31,1,44,40,62,35,63,3,61,54,46 +1 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63 +1 64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 56,7,0,42,14,35,21,49,28,63,29,57,8,43,50,15,22,36,1,9,37,2,16,23,51,58,44,30,24,10,52,31,45,59,38,3,17,32,46,39,4,60,11,53,18,25,19,5,40,61,47,26,33,12,54,55,27,13,6,34,41,20,62,48 +2 27,13,32,1,15,10,27,9,22,21,16,3,32,6,15,15,21,24,2,31,4,26,10,24,10,17,1,17,27,26,11,12,31,14,11,28,18,2,12,16,2,12,26,5,19,22,1,27,17,17,13,13,2,6,4,3,14,5,29,8,2,19,14,32 | 23,4,6,7,9,55,53,47,41,38,11,36,0,13,14,15,16,17,31,28,32,51,22,20,24,61,26,1,19,54,3,50,5,46,45,35,44,8,10,39,52,33,42,43,2,34,21,12,48,49,37,18,56,30,29,27,40,57,58,59,60,25,62,63 +2 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63 | 24,63,60,3,57,54,6,51,48,9,45,42,12,39,36,15,33,0,18,30,27,21,31,43,22,25,1,61,28,58,19,4,55,16,34,52,7,37,49,13,40,46,10,53,5,11,41,47,8,38,50,14,35,44,32,23,56,17,29,59,2,20,62,26 +2 64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 22,1,61,58,4,55,52,7,49,46,10,43,40,13,37,34,16,31,28,19,25,33,6,63,24,60,3,27,18,57,30,54,21,0,15,51,36,48,9,39,12,45,42,53,17,41,38,47,14,8,50,35,32,44,5,11,56,29,26,59,20,2,62,23 +2 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 28,63,62,3,59,56,6,7,55,52,10,49,48,13,14,0,45,17,42,41,20,21,38,35,24,34,31,27,15,46,1,60,32,4,25,57,36,29,22,39,8,53,18,43,50,11,37,40,12,16,44,51,9,19,54,47,5,23,58,33,26,61,2,30 +3 6,3,27,8,19,1,0,31,30,21,21,12,10,25,24,23,27,26,24,23,25,19,17,7,27,13,25,24,6,13,22,6,10,13,22,31,30,15,24,2,19,29,17,2,28,9,9,15,16,20,0,27,26,12,4,0,4,30,32,30,5,13,2,25 | 41,6,31,36,61,46,11,26,56,1,21,51,16,2,22,47,62,57,7,17,52,42,12,27,37,32,53,63,28,3,30,23,0,33,60,35,20,58,38,5,40,18,15,43,8,45,55,13,48,25,50,10,9,49,54,14,44,39,19,59,34,4,29,24 +3 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63 | 41,6,31,36,61,46,11,26,56,1,21,51,16,2,22,47,62,57,7,17,52,42,12,27,37,32,53,63,28,3,30,23,0,33,60,35,20,58,38,5,40,18,15,43,8,45,55,13,48,25,50,10,9,49,54,14,44,39,19,59,34,4,29,24 +3 64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 41,6,31,36,61,46,11,26,56,1,21,51,16,2,22,47,62,57,7,17,52,42,12,27,37,32,53,63,28,3,30,23,0,33,60,35,20,58,38,5,40,18,15,43,8,45,55,13,48,25,50,10,9,49,54,14,44,39,19,59,34,4,29,24 +3 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0 | 41,6,31,36,61,46,11,26,56,1,21,51,16,2,22,47,62,57,7,17,52,42,12,27,37,32,53,63,28,3,30,23,0,33,60,35,20,58,38,5,40,18,15,43,8,45,55,13,48,25,50,10,9,49,54,14,44,39,19,59,34,4,29,24 +0 19,7,7,31,49,38,37,49,50,48,20,6,43,43,13,41,27,45,2,16,31,30,5,31,31,42,47,29,43,34,21,50,36,14,45,14,22,44,11,11,26,9,31,35,24,42,1,3,22,39,41,2,3,21,9,25,0,30,50,26,30,45,20,17,19,4,44,39,16,30,17,19,35,47,37,22,11,37,6,46,13,24,23,15,46,42,24,41,31,8,15,48,8,26,45,31,8,34,11,34 | 56,46,18,51,47,52,65,22,78,11,1,2,96,92,89,54,41,38,76,98,39,14,80,33,35,90,83,19,68,70,63,71,0,64,62,10,53,30,36,75,48,82,81,44,86,55,40,93,59,16,27,60,57,69,21,42,95,24,3,20,88,23,97,29,99,43,72,32,6,74,77,5,49,67,87,50,15,45,85,25,12,13,28,37,66,34,94,61,17,79,84,26,73,91,9,7,4,31,58,8 +0 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99 +0 100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +0 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1 | 21,56,63,49,70,98,42,7,35,77,28,84,0,91,14,29,99,57,1,64,85,15,22,50,43,92,71,36,8,78,44,86,79,58,30,2,51,37,23,65,72,93,16,9,24,87,31,66,73,94,52,80,45,38,10,59,3,17,25,39,60,4,95,11,53,88,18,67,81,32,46,74,89,19,61,75,5,96,33,54,12,68,82,47,26,40,20,69,48,55,90,13,27,83,6,62,34,97,76,41 +1 35,27,50,10,46,32,25,24,16,24,36,50,16,38,19,19,47,37,32,1,12,38,30,39,14,15,44,45,11,50,29,8,48,40,49,31,21,36,47,24,26,40,48,15,27,14,33,41,18,28,11,30,28,19,18,20,46,28,11,48,47,4,8,26,5,14,42,17,23,20,38,0,30,45,2,0,30,38,50,31,9,49,42,11,9,36,39,45,41,49,3,36,35,45,1,7,5,14,46,27 | 75,71,94,19,74,90,61,96,64,95,62,31,80,84,3,28,83,58,50,20,65,45,97,24,25,43,12,8,67,48,54,14,15,53,69,55,36,68,39,9,7,6,40,63,99,1,44,52,49,57,30,22,51,72,76,79,35,5,18,46,92,0,91,37,85,10,17,77,13,21,70,23,86,41,33,88,47,66,82,26,87,93,73,27,4,98,56,38,16,60,42,32,59,89,81,34,29,2,78,11 +1 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99 | 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99 +1 100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1,0 +1 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1 | 84,28,77,35,7,91,98,70,49,63,56,0,14,21,42,29,99,57,1,64,85,15,22,50,43,92,71,36,8,78,44,86,79,58,30,2,51,37,23,65,72,93,16,9,24,87,31,66,73,94,52,80,45,38,10,59,3,17,25,39,60,4,95,11,53,88,18,67,81,32,46,74,89,19,61,75,5,96,33,54,12,68,82,47,26,40,20,69,48,55,90,13,27,83,6,62,34,97,76,41 +2 7,34,22,28,34,45,37,8,37,33,46,7,29,0,17,37,43,15,19,41,27,48,7,48,6,45,20,50,30,32,1,17,10,5,12,3,31,19,17,31,35,34,19,11,16,22,16,0,34,4,12,18,7,44,44,36,35,44,5,8,0,35,19,5,47,20,0,12,15,40,28,27,13,39,18,2,27,11,27,34,39,2,34,12,50,37,49,25,12,22,35,33,50,15,32,14,43,25,49,10 | 51,74,93,50,91,5,88,83,80,9,78,76,73,13,71,68,67,17,66,60,20,21,55,23,24,25,47,35,28,34,10,6,32,99,98,97,96,37,2,18,3,41,42,4,44,45,46,89,36,72,87,0,52,86,85,22,82,8,79,11,49,1,62,30,48,70,39,16,15,69,26,14,63,12,64,75,59,77,65,58,57,81,56,7,84,54,53,92,19,31,90,43,40,38,94,95,61,27,29,33 +2 0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26,27,28,29,30,31,32,33,34,35,36,37,38,39,40,41,42,43,44,45,46,47,48,49,50,51,52,53,54,55,56,57,58,59,60,61,62,63,64,65,66,67,68,69,70,71,72,73,74,75,76,77,78,79,80,81,82,83,84,85,86,87,88,89,90,91,92,93,94,95,96,97,98,99 | 36,99,96,3,93,90,6,87,84,9,81,78,12,75,72,15,69,66,18,63,60,21,57,54,24,51,0,27,48,45,30,42,39,33,49,67,34,37,1,97,40,94,31,43,4,91,46,88,28,7,85,25,52,82,10,55,79,22,58,76,13,61,73,19,64,70,16,17,8,35,65,71,14,62,74,20,59,77,11,56,80,23,53,83,68,50,86,26,47,89,5,29,92,44,41,95,2,32,98,38 +2 100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 34,1,97,94,4,91,88,7,85,82,10,79,76,13,73,70,16,67,64,19,61,58,22,55,52,25,49,46,28,43,40,31,37,51,84,99,36,96,3,39,30,93,42,90,6,45,27,87,48,33,69,0,24,9,54,81,78,57,21,12,60,75,72,63,18,15,66,26,68,17,65,71,62,14,74,20,59,77,56,11,80,23,53,83,50,8,86,47,44,89,29,5,92,41,38,95,32,2,98,35 +2 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1 | 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51,1,106,256,111,251,6,96,116,91,121,11,126,241,86,236,16,131,81,231,136,21,141,226,76,221,26,146,71,216,151,31,246,211,156,206,36,66,181,201,161,41,61,196,191,166,46,171,186,56,101,176,242,97,62,237,22,212,102,182,202,122,17,227,207,12,2,142,217,72,177,197,147,152,57,137,157,132,232,67,127,167,222,32,82,172,52,7,27,247,87,47,252,187,112,107,37,162,42,92,117,77,192,180,104,254,4,99,249,109,9,244,239,14,114,234,94,19,229,119,224,24,89,219,124,29,214,209,34,129,204,84,39,199,134,194,44,79,189,139,184,49,179,54,144,174,74,169,59,149,164,64,69,159,154,205,100,155,190,60,145,230,255,220,200,5,110,55,50,150,210,70,235,215,140,120,75,30,195,240,45,245,10,185,250,25,165,20,170,40,95,15,125,135,130,0,35,115,65,85,225,90,80,160,105,175,103,93,208,203,38,33,83,213,88,133,198,28,218,123,43,193,138,223,188,48,23,183,228,118,78,128,18,233,68,178,53,113,238,143,173,13,58,243,98,73,168,8,248,108,148,163,63,253,153,158,3 +3 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51,1,106,256,111,251,6,96,116,91,121,11,126,241,86,236,16,131,81,231,136,21,141,226,76,221,26,146,71,216,151,31,246,211,156,206,36,66,181,201,161,41,61,196,191,166,46,171,186,56,101,176,242,97,62,237,22,212,102,182,202,122,17,227,207,12,2,142,217,72,177,197,147,152,57,137,157,132,232,67,127,167,222,32,82,172,52,7,27,247,87,47,252,187,112,107,37,162,42,92,117,77,192,180,104,254,4,99,249,109,9,244,239,14,114,234,94,19,229,119,224,24,89,219,124,29,214,209,34,129,204,84,39,199,134,194,44,79,189,139,184,49,179,54,144,174,74,169,59,149,164,64,69,159,154,205,100,155,190,60,145,230,255,220,200,5,110,55,50,150,210,70,235,215,140,120,75,30,195,240,45,245,10,185,250,25,165,20,170,40,95,15,125,135,130,0,35,115,65,85,225,90,80,160,105,175,103,93,208,203,38,33,83,213,88,133,198,28,218,123,43,193,138,223,188,48,23,183,228,118,78,128,18,233,68,178,53,113,238,143,173,13,58,243,98,73,168,8,248,108,148,163,63,253,153,158,3 +3 257,256,255,254,253,252,251,250,249,248,247,246,245,244,243,242,241,240,239,238,237,236,235,234,233,232,231,230,229,228,227,226,225,224,223,222,221,220,219,218,217,216,215,214,213,212,211,210,209,208,207,206,205,204,203,202,201,200,199,198,197,196,195,194,193,192,191,190,189,188,187,186,185,184,183,182,181,180,179,178,177,176,175,174,173,172,171,170,169,168,167,166,165,164,163,162,161,160,159,158,157,156,155,154,153,152,151,150,149,148,147,146,145,144,143,142,141,140,139,138,137,136,135,134,133,132,131,130,129,128,127,126,125,124,123,122,121,120,119,118,117,116,115,114,113,112,111,110,109,108,107,106,105,104,103,102,101,100,99,98,97,96,95,94,93,92,91,90,89,88,87,86,85,84,83,82,81,80,79,78,77,76,75,74,73,72,71,70,69,68,67,66,65,64,63,62,61,60,59,58,57,56,55,54,53,52,51,50,49,48,47,46,45,44,43,42,41,40,39,38,37,36,35,34,33,32,31,30,29,28,27,26,25,24,23,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1 | 51,1,106,256,111,251,6,96,116,91,121,11,126,241,86,236,16,131,81,231,136,21,141,226,76,221,26,146,71,216,151,31,246,211,156,206,36,66,181,201,161,41,61,196,191,166,46,171,186,56,101,176,242,97,62,237,22,212,102,182,202,122,17,227,207,12,2,142,217,72,177,197,147,152,57,137,157,132,232,67,127,167,222,32,82,172,52,7,27,247,87,47,252,187,112,107,37,162,42,92,117,77,192,180,104,254,4,99,249,109,9,244,239,14,114,234,94,19,229,119,224,24,89,219,124,29,214,209,34,129,204,84,39,199,134,194,44,79,189,139,184,49,179,54,144,174,74,169,59,149,164,64,69,159,154,205,100,155,190,60,145,230,255,220,200,5,110,55,50,150,210,70,235,215,140,120,75,30,195,240,45,245,10,185,250,25,165,20,170,40,95,15,125,135,130,0,35,115,65,85,225,90,80,160,105,175,103,93,208,203,38,33,83,213,88,133,198,28,218,123,43,193,138,223,188,48,23,183,228,118,78,128,18,233,68,178,53,113,238,143,173,13,58,243,98,73,168,8,248,108,148,163,63,253,153,158,3 +3 0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4,5,6,0,1,2,3,4 | 51,1,106,256,111,251,6,96,116,91,121,11,126,241,86,236,16,131,81,231,136,21,141,226,76,221,26,146,71,216,151,31,246,211,156,206,36,66,181,201,161,41,61,196,191,166,46,171,186,56,101,176,242,97,62,237,22,212,102,182,202,122,17,227,207,12,2,142,217,72,177,197,147,152,57,137,157,132,232,67,127,167,222,32,82,172,52,7,27,247,87,47,252,187,112,107,37,162,42,92,117,77,192,180,104,254,4,99,249,109,9,244,239,14,114,234,94,19,229,119,224,24,89,219,124,29,214,209,34,129,204,84,39,199,134,194,44,79,189,139,184,49,179,54,144,174,74,169,59,149,164,64,69,159,154,205,100,155,190,60,145,230,255,220,200,5,110,55,50,150,210,70,235,215,140,120,75,30,195,240,45,245,10,185,250,25,165,20,170,40,95,15,125,135,130,0,35,115,65,85,225,90,80,160,105,175,103,93,208,203,38,33,83,213,88,133,198,28,218,123,43,193,138,223,188,48,23,183,228,118,78,128,18,233,68,178,53,113,238,143,173,13,58,243,98,73,168,8,248,108,148,163,63,253,153,158,3 diff --git a/src/promql/src/histogram_eval.rs b/src/promql/src/histogram_eval.rs index c6d9a44e8a3..9a02221e849 100644 --- a/src/promql/src/histogram_eval.rs +++ b/src/promql/src/histogram_eval.rs @@ -31,6 +31,7 @@ use datatypes::series::histogram::HistogramView; use datatypes::series::samples::{DenseSamplesRef, SampleRef, Series, SeriesSchema}; use datatypes::series::time::TimeAxis; +use crate::go_sort; use crate::grid_series::{GridSeriesBuilder, LabelSet, label_set, merge_same_labelset}; const BUCKET_LABEL: &str = "le"; @@ -51,9 +52,9 @@ pub enum HistogramFunction { /// Float series with the same labels other than `le` form a classic histogram; a float series /// whose `le` does not parse is ignored. Native histogram samples are evaluated one by one. At a /// point where a native histogram and classic buckets with the same labels (`le` aside) are both -/// present, neither is evaluated. Each field is evaluated on its own. Results drop `le` and -/// `__name__`, and series that then share a label set are merged as [`merge_same_labelset`] -/// does. +/// present, neither is evaluated. Each field is evaluated on its own. Classic results drop +/// `le`; all results drop `__name__`, `__type__` and `__unit__`. Series that then share a label +/// set are merged as [`merge_same_labelset`] does. pub fn evaluate_histograms( function: HistogramFunction, schema: &Arc, @@ -90,14 +91,6 @@ pub fn evaluate_histograms( let mut native_buckets = Vec::new(); let mut values = vec![None; schema.fields.len()]; for mut group in groups.into_values() { - // Pre-sorting by bound keeps the buckets of every point sorted. Like Go's comparison, - // +0 and -0 are equal and keep input order, and coalescing keeps the first bound. - group - .classic - .sort_by(|a, b| match (a.0.is_nan(), b.0.is_nan()) { - (false, false) => a.0.partial_cmp(&b.0).expect("neither is NaN"), - (nan_a, nan_b) => nan_a.cmp(&nan_b), - }); let ranges = group .classic .iter() @@ -113,6 +106,10 @@ pub fn evaluate_histograms( classic_buckets.push(classic::Bucket { upper_bound, count }); } } + // Go sorts the buckets present at each point by `<`: +0 and -0 tie and NaN + // ties with everything, so which of them coalescing keeps and where a NaN + // bound lands follow its sort algorithm. + go_sort::sort_by(&mut classic_buckets, |a, b| a.upper_bound < b.upper_bound); let native = group.native.and_then(|(series, range)| { match sample(series, range, field, point) { Some(SampleRef::Histogram(h)) => Some(h), diff --git a/src/promql/src/histogram_eval/classic.rs b/src/promql/src/histogram_eval/classic.rs index 9a3752cbec6..ee326ac0c9a 100644 --- a/src/promql/src/histogram_eval/classic.rs +++ b/src/promql/src/histogram_eval/classic.rs @@ -18,9 +18,21 @@ /// Relative difference under which neighbouring bucket counts are taken as equal. const SMALL_DELTA_TOLERANCE: f64 = 1e-12; -/// Go's `strconv.ParseFloat`, which rejects finite literals out of the f64 range. +/// Go's `strconv.ParseFloat`, which rejects finite literals out of the f64 range and a signed +/// NaN, and accepts `_` between digits. Hexadecimal literals are not supported. pub(super) fn parse_bound(text: &str) -> Option { - let value: f64 = text.parse().ok()?; + let unsigned = text.trim_start_matches(['+', '-']); + if unsigned.len() != text.len() && unsigned.eq_ignore_ascii_case("nan") { + return None; + } + let value: f64 = if text.contains('_') { + if !underscores_ok(text) { + return None; + } + text.replace('_', "").parse().ok()? + } else { + text.parse().ok()? + }; if value.is_infinite() { let unsigned = text.trim_start_matches(['+', '-']); if !unsigned.eq_ignore_ascii_case("inf") && !unsigned.eq_ignore_ascii_case("infinity") { @@ -30,6 +42,17 @@ pub(super) fn parse_bound(text: &str) -> Option { Some(value) } +/// Go's `strconv.underscoreOK` for a decimal literal: every `_` sits between two digits. +fn underscores_ok(text: &str) -> bool { + let digits = text.strip_prefix(['+', '-']).unwrap_or(text).as_bytes(); + digits.iter().enumerate().all(|(i, &byte)| { + byte != b'_' + || (i > 0 + && digits[i - 1].is_ascii_digit() + && digits.get(i + 1).is_some_and(u8::is_ascii_digit)) + }) +} + #[derive(Debug, Clone, Copy)] pub(super) struct Bucket { pub(super) upper_bound: f64, diff --git a/src/promql/src/histogram_eval/tests.rs b/src/promql/src/histogram_eval/tests.rs index 4cda9c71bbf..0da3af7e710 100644 --- a/src/promql/src/histogram_eval/tests.rs +++ b/src/promql/src/histogram_eval/tests.rs @@ -401,3 +401,67 @@ fn classic_bounds_keep_the_first_signed_zero() { let points = points_of(&result[0]); assert_eq!(1.0 / f64::from_bits(points[&0]), f64::INFINITY); } + +/// Classic histograms over `le` values in input order, at one point. +fn classic_result(function: HistogramFunction, buckets: &[(&str, f64)]) -> f64 { + let grid = Arc::new( + datatypes::series::time::EvalGrid::try_new( + datatypes::series::time::GridSpec::try_new(0, 1_000, 1).unwrap(), + ) + .unwrap(), + ); + let schema = Arc::new(SeriesSchema { + fields: vec![FieldSpec { + name: Arc::from("value"), + }] + .into(), + eval_grid: Some(grid), + }); + let series: Vec<_> = buckets + .iter() + .map(|(le, count)| { + let labels = Labels::from([ + ("__name__".to_string(), "h".to_string()), + ("le".to_string(), le.to_string()), + ]); + let points = BTreeMap::from([(0, f64::to_bits(*count))]); + mixed_series(&schema, &labels, &points, &BTreeMap::new()).unwrap() + }) + .collect(); + let result = evaluate_histograms(function, &schema, &series).unwrap(); + f64::from_bits(points_of(&result[0])[&0]) +} + +/// Go's insertion sort cannot move a bucket across a NaN bound, so a NaN bucket stays where it +/// is and `+Inf` can still end the list. Values are from Prometheus v3.15.0. +#[test] +fn nan_bounds_stay_in_place() { + let buckets = [("1", 10.0), ("NaN", 20.0), ("inf", 30.0)]; + let quantile = classic_result(HistogramFunction::Quantile(0.1), &buckets); + assert!((quantile - 0.3).abs() < 1e-12, "{quantile}"); + let fraction = classic_result( + HistogramFunction::Fraction { + lower: 0.0, + upper: 0.5, + }, + &buckets, + ); + assert!((fraction - 1.0 / 6.0).abs() < 1e-12, "{fraction}"); +} + +/// `le` parses like Go's `strconv.ParseFloat`: a signed NaN is not a bound, and `_` may separate +/// digits. Values are from Prometheus v3.15.0. +#[test] +fn bounds_parse_like_go() { + let signed_nan = [("1", 10.0), ("+nan", 20.0), ("+Inf", 30.0)]; + for (q, expected) in [(0.1, 0.3), (0.5, 1.0)] { + let quantile = classic_result(HistogramFunction::Quantile(q), &signed_nan); + assert!((quantile - expected).abs() < 1e-12, "{q}: {quantile}"); + } + let underscore = [("1", 10.0), ("1_000", 20.0), ("+Inf", 30.0)]; + let quantile = classic_result(HistogramFunction::Quantile(0.5), &underscore); + assert!((quantile - 500.5).abs() < 1e-9, "{quantile}"); + for rejected in ["-nan", "_1", "1__0", "1_", "1_.5", "1e_5"] { + assert_eq!(super::classic::parse_bound(rejected), None, "{rejected}"); + } +} diff --git a/src/promql/src/lib.rs b/src/promql/src/lib.rs index bbcddfcdfcd..74b40da149f 100644 --- a/src/promql/src/lib.rs +++ b/src/promql/src/lib.rs @@ -15,6 +15,7 @@ pub mod error; pub mod extension_plan; pub mod functions; +mod go_sort; pub mod grid_series; pub mod histogram_eval; pub mod map_label;