From b555c05f8554b235442a2a0a223e721326d6338f Mon Sep 17 00:00:00 2001 From: Brian Dillmann Date: Thu, 6 Aug 2026 16:18:33 -0400 Subject: [PATCH] goodhistogram: spell out the native histogram bounds table nativeHistogramBounds was computed at init time with math.Pow. math.Pow is not bit-portable: it has architecture-specific implementations, so the table came out one ULP different on arm64 than on amd64, and matched Prometheus's published table on neither. The boundaries are not an internal detail. getLe derives the classic Prometheus bucket upper bounds from them, and those are exported as `le` label values, so a boundary that varies by architecture splits a single bucket into two time series across a mixed-architecture deployment, and makes any golden-file test of the exported format architecture-dependent. Transcribe the table from client_golang instead, which spells the values out as literals for exactly this reason. Boundaries are now bit-identical everywhere and identical to Prometheus's own, so the classic buckets we export line up with what Prometheus computes for the same native bucket. Co-Authored-By: roachdev-claude --- histogram.go | 183 +++++++++++++++++++++++++++++++++++++++++----- histogram_test.go | 32 ++++++++ 2 files changed, 195 insertions(+), 20 deletions(-) diff --git a/histogram.go b/histogram.go index 3a11051..e8be760 100644 --- a/histogram.go +++ b/histogram.go @@ -38,27 +38,170 @@ const maxSchema = 8 // bound of a bucket in [0.5, 1.0), matching the range of math.Frexp's // fractional part. // -// The boundary for bucket j in schema s is: 2^(j / 2^s) / 2, which -// equals the fractional part of the Prometheus bucket boundary when -// decomposed via math.Frexp. +// The boundary for bucket j in schema s is 2^(j / 2^s) / 2, which equals the +// fractional part of the Prometheus bucket boundary when decomposed via +// math.Frexp. // -// These are computed at init time and are identical to the -// nativeHistogramBounds table in the Prometheus client_golang library. -var nativeHistogramBounds [maxSchema + 1][]float64 - -func init() { - for s := int32(0); s <= maxSchema; s++ { - bucketsPerGroup := 1 << s - bounds := make([]float64, bucketsPerGroup) - for j := 0; j < bucketsPerGroup; j++ { - // The Prometheus bucket boundary for bucket j in schema s - // within a power-of-2 group is 2^(j / 2^s). When decomposed via - // math.Frexp, the fractional part is 2^(j / 2^s) / 2 (since - // Frexp returns frac in [0.5, 1.0) with value = frac * 2^exp). - bounds[j] = math.Ldexp(math.Pow(2, float64(j)/float64(bucketsPerGroup)), -1) - } - nativeHistogramBounds[s] = bounds - } +// The values are transcribed from the table of the same name in +// github.com/prometheus/client_golang, and are spelled out as literals rather +// than computed from math.Pow for the same reason client_golang spells them +// out: math.Pow has architecture-specific implementations and is not +// bit-portable, so a table computed at init time differs by an ULP between +// (say) arm64 and amd64. Bucket boundaries are exported as Prometheus label +// values, so a boundary that varies by architecture splits one bucket into +// two time series across a mixed-architecture deployment, and makes any +// golden-file test of the exported format architecture-dependent. +var nativeHistogramBounds = [maxSchema + 1][]float64{ + // Schema "0": + {0.5}, + // Schema 1: + {0.5, 0.7071067811865475}, + // Schema 2: + {0.5, 0.5946035575013605, 0.7071067811865475, 0.8408964152537144}, + // Schema 3: + { + 0.5, 0.5452538663326288, 0.5946035575013605, 0.6484197773255048, + 0.7071067811865475, 0.7711054127039704, 0.8408964152537144, 0.9170040432046711, + }, + // Schema 4: + { + 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, + }, + // Schema 5: + { + 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, + }, + // Schema 6: + { + 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, + }, + // Schema 7: + { + 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, + }, + // Schema 8: + { + 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, + 0.8593096490612387, 0.8616394738731368, 0.8639756154809185, 0.8663180910111553, + 0.8686669176368529, 0.871022112577578, 0.8733836930995842, 0.8757516765159389, + 0.8781260801866495, 0.8805069215187917, 0.8828942179666361, 0.8852879870317771, + 0.8876882462632604, 0.890095013257712, 0.8925083056594671, 0.8949281411607002, + 0.8973545375015533, 0.8997875124702672, 0.9022270839033115, 0.9046732696855155, + 0.9071260877501991, 0.909585556079304, 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, + }, } // schemaRelativeError returns the relative error for a given schema. diff --git a/histogram_test.go b/histogram_test.go index 3e4e87d..e5fa885 100644 --- a/histogram_test.go +++ b/histogram_test.go @@ -947,3 +947,35 @@ func TestPrometheusExport(t *testing.T) { require.Equal(t, uint64(1001), total) }) } + +// TestNativeHistogramBounds guards the transcribed boundary table against both +// transcription errors and any temptation to recompute it at init time. The +// exact-value assertions are the ones that matter: they are the entries where +// math.Pow disagrees with the canonical table (and, on some entries, with +// itself across architectures). +func TestNativeHistogramBounds(t *testing.T) { + for s := 0; s <= maxSchema; s++ { + bounds := nativeHistogramBounds[s] + require.Len(t, bounds, 1< 0 { + require.Greater(t, b, bounds[j-1]) + } + // Approximately 2^(j / 2^s) / 2. Deliberately not an equality + // check: math.Pow is not bit-portable, which is the whole reason + // the table is spelled out rather than computed. A few ULP of + // slack is still tight enough to catch a transcription error. + want := math.Ldexp(math.Pow(2, float64(j)/float64(int(1)<