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goodhistogram: spell out the native histogram bounds table #10

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183 changes: 163 additions & 20 deletions histogram.go
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Original file line number Diff line number Diff line change
Expand Up @@ -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.
Expand Down
32 changes: 32 additions & 0 deletions histogram_test.go
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Original file line number Diff line number Diff line change
Expand Up @@ -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<<s)
require.Equal(t, 0.5, bounds[0])
for j, b := range bounds {
require.GreaterOrEqual(t, b, 0.5)
require.Less(t, b, 1.0)
if j > 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)<<s)), -1)
require.InEpsilon(t, want, b, 1e-15)
}
}

// Exact bit-for-bit values, as published by Prometheus.
require.Equal(t, 0.7071067811865475, nativeHistogramBounds[1][1])
require.Equal(t, 0.8408964152537144, nativeHistogramBounds[2][3])
require.Equal(t, 0.5946035575013605, nativeHistogramBounds[2][1])
require.Equal(t, 0.9972960560854698, nativeHistogramBounds[8][255])
}