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histogram: Modify getBound to deal properly with infinity
The bucket receiving math.MaxFloat64 observations now has math.MaxFloat64 as upper bound, while the bucket after it (the last possible bucket) has +Inf. This also adds a test for getBound and moves the getBound code to generic.go (where it should have been in the first place). Signed-off-by: beorn7 <beorn@grafana.com>
This commit is contained in:
beorn7
parent
dccfb9db4e
commit
bf0847073d
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@ -15,6 +15,7 @@ package histogram
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import (
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import (
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"fmt"
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"fmt"
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"math"
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"strings"
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"strings"
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)
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)
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@ -325,3 +326,211 @@ func compactBuckets[IBC internalBucketCount](buckets []IBC, spans []Span, maxEmp
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return buckets, spans
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return buckets, spans
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}
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}
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func getBound(idx, schema int32) float64 {
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// Here a bit of context about the behavior for the last bucket counting
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// regular numbers (called simply "last bucket" below) and the bucket
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// counting observations of ±Inf (called "inf bucket" below, with an idx
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// one higher than that of the "last bucket"):
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//
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// If we apply the usual formula to the last bucket, its upper bound
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// would be calculated as +Inf. The reason is that the max possible
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// regular float64 number (math.MaxFloat64) doesn't coincide with one of
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// the calculated bucket boundaries. So the calculated boundary has to
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// be larger than math.MaxFloat64, and the only float64 larger than
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// math.MaxFloat64 is +Inf. However, we want to count actual
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// observations of ±Inf in the inf bucket. Therefore, we have to treat
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// the upper bound of the last bucket specially and set it to
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// math.MaxFloat64. (The upper bound of the inf bucket, with its idx
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// being one higher than that of the last bucket, naturally comes out as
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// +Inf by the usual formula. So that's fine.)
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//
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// math.MaxFloat64 has a frac of 0.9999999999999999 and an exp of
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// 1024. If there were a float64 number following math.MaxFloat64, it
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// would have a frac of 1.0 and an exp of 1024, or equivalently a frac
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// of 0.5 and an exp of 1025. However, since frac must be smaller than
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// 1, and exp must be smaller than 1025, either representation overflows
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// a float64. (Which, in turn, is the reason that math.MaxFloat64 is the
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// largest possible float64. Q.E.D.) However, the formula for
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// calculating the upper bound from the idx and schema of the last
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// bucket results in precisely that. It is either frac=1.0 & exp=1024
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// (for schema < 0) or frac=0.5 & exp=1025 (for schema >=0). (This is,
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// by the way, a power of two where the exponent itself is a power of
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// two, 2¹⁰ in fact, which coinicides with a bucket boundary in all
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// schemas.) So these are the special cases we have to catch below.
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if schema < 0 {
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exp := int(idx) << -schema
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if exp == 1024 {
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// This is the last bucket before the overflow bucket
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// (for ±Inf observations). Return math.MaxFloat64 as
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// explained above.
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return math.MaxFloat64
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}
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return math.Ldexp(1, exp)
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}
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fracIdx := idx & ((1 << schema) - 1)
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frac := exponentialBounds[schema][fracIdx]
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exp := (int(idx) >> schema) + 1
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if frac == 0.5 && exp == 1025 {
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// This is the last bucket before the overflow bucket (for ±Inf
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// observations). Return math.MaxFloat64 as explained above.
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return math.MaxFloat64
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}
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return math.Ldexp(frac, exp)
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}
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// exponentialBounds is a precalculated table of bucket bounds in the interval
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// [0.5,1) in schema 0 to 8.
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var exponentialBounds = [][]float64{
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// Schema "0":
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{0.5},
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// Schema 1:
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{0.5, 0.7071067811865475},
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// Schema 2:
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{0.5, 0.5946035575013605, 0.7071067811865475, 0.8408964152537144},
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// Schema 3:
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{
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0.5, 0.5452538663326288, 0.5946035575013605, 0.6484197773255048,
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0.7071067811865475, 0.7711054127039704, 0.8408964152537144, 0.9170040432046711,
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},
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// Schema 4:
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{
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0.5, 0.5221368912137069, 0.5452538663326288, 0.5693943173783458,
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0.5946035575013605, 0.620928906036742, 0.6484197773255048, 0.6771277734684463,
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0.7071067811865475, 0.7384130729697496, 0.7711054127039704, 0.805245165974627,
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0.8408964152537144, 0.8781260801866495, 0.9170040432046711, 0.9576032806985735,
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},
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// Schema 5:
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{
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0.5, 0.5109485743270583, 0.5221368912137069, 0.5335702003384117,
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0.5452538663326288, 0.5571933712979462, 0.5693943173783458, 0.5818624293887887,
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0.5946035575013605, 0.6076236799902344, 0.620928906036742, 0.6345254785958666,
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0.6484197773255048, 0.6626183215798706, 0.6771277734684463, 0.6919549409819159,
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0.7071067811865475, 0.7225904034885232, 0.7384130729697496, 0.7545822137967112,
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0.7711054127039704, 0.7879904225539431, 0.805245165974627, 0.8228777390769823,
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0.8408964152537144, 0.8593096490612387, 0.8781260801866495, 0.8973545375015533,
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0.9170040432046711, 0.9370838170551498, 0.9576032806985735, 0.9785720620876999,
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},
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// Schema 6:
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{
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0.5, 0.5054446430258502, 0.5109485743270583, 0.5165124395106142,
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0.5221368912137069, 0.5278225891802786, 0.5335702003384117, 0.5393803988785598,
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0.5452538663326288, 0.5511912916539204, 0.5571933712979462, 0.5632608093041209,
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0.5693943173783458, 0.5755946149764913, 0.5818624293887887, 0.5881984958251406,
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0.5946035575013605, 0.6010783657263515, 0.6076236799902344, 0.6142402680534349,
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0.620928906036742, 0.6276903785123455, 0.6345254785958666, 0.6414350080393891,
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0.6484197773255048, 0.6554806057623822, 0.6626183215798706, 0.6698337620266515,
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0.6771277734684463, 0.6845012114872953, 0.6919549409819159, 0.6994898362691555,
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0.7071067811865475, 0.7148066691959849, 0.7225904034885232, 0.7304588970903234,
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0.7384130729697496, 0.7464538641456323, 0.7545822137967112, 0.762799075372269,
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0.7711054127039704, 0.7795022001189185, 0.7879904225539431, 0.7965710756711334,
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0.805245165974627, 0.8140137109286738, 0.8228777390769823, 0.8318382901633681,
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0.8408964152537144, 0.8500531768592616, 0.8593096490612387, 0.8686669176368529,
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0.8781260801866495, 0.8876882462632604, 0.8973545375015533, 0.9071260877501991,
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0.9170040432046711, 0.9269895625416926, 0.9370838170551498, 0.9472879907934827,
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0.9576032806985735, 0.9680308967461471, 0.9785720620876999, 0.9892280131939752,
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},
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// Schema 7:
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{
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0.5, 0.5027149505564014, 0.5054446430258502, 0.5081891574554764,
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0.5109485743270583, 0.5137229745593818, 0.5165124395106142, 0.5193170509806894,
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0.5221368912137069, 0.5249720429003435, 0.5278225891802786, 0.5306886136446309,
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0.5335702003384117, 0.5364674337629877, 0.5393803988785598, 0.5423091811066545,
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0.5452538663326288, 0.5482145409081883, 0.5511912916539204, 0.5541842058618393,
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0.5571933712979462, 0.5602188762048033, 0.5632608093041209, 0.5663192597993595,
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0.5693943173783458, 0.572486072215902, 0.5755946149764913, 0.5787200368168754,
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0.5818624293887887, 0.585021884841625, 0.5881984958251406, 0.5913923554921704,
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0.5946035575013605, 0.5978321960199137, 0.6010783657263515, 0.6043421618132907,
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0.6076236799902344, 0.6109230164863786, 0.6142402680534349, 0.6175755319684665,
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0.620928906036742, 0.6243004885946023, 0.6276903785123455, 0.6310986751971253,
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0.6345254785958666, 0.637970889198196, 0.6414350080393891, 0.6449179367033329,
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0.6484197773255048, 0.6519406325959679, 0.6554806057623822, 0.659039800633032,
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0.6626183215798706, 0.6662162735415805, 0.6698337620266515, 0.6734708931164728,
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0.6771277734684463, 0.6808045103191123, 0.6845012114872953, 0.688217985377265,
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0.6919549409819159, 0.6957121878859629, 0.6994898362691555, 0.7032879969095076,
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0.7071067811865475, 0.7109463010845827, 0.7148066691959849, 0.718687998724491,
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0.7225904034885232, 0.7265139979245261, 0.7304588970903234, 0.7344252166684908,
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0.7384130729697496, 0.7424225829363761, 0.7464538641456323, 0.7505070348132126,
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0.7545822137967112, 0.7586795205991071, 0.762799075372269, 0.7669409989204777,
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0.7711054127039704, 0.7752924388424999, 0.7795022001189185, 0.7837348199827764,
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0.7879904225539431, 0.7922691326262467, 0.7965710756711334, 0.8008963778413465,
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0.805245165974627, 0.8096175675974316, 0.8140137109286738, 0.8184337248834821,
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0.8228777390769823, 0.8273458838280969, 0.8318382901633681, 0.8363550898207981,
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0.8408964152537144, 0.8454623996346523, 0.8500531768592616, 0.8546688815502312,
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0.8593096490612387, 0.8639756154809185, 0.8686669176368529, 0.8733836930995842,
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0.8781260801866495, 0.8828942179666361, 0.8876882462632604, 0.8925083056594671,
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0.8973545375015533, 0.9022270839033115, 0.9071260877501991, 0.9120516927035263,
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0.9170040432046711, 0.9219832844793128, 0.9269895625416926, 0.9320230241988943,
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0.9370838170551498, 0.9421720895161669, 0.9472879907934827, 0.9524316709088368,
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0.9576032806985735, 0.9628029718180622, 0.9680308967461471, 0.9732872087896164,
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0.9785720620876999, 0.9838856116165875, 0.9892280131939752, 0.9945994234836328,
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},
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// Schema 8:
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{
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0.5, 0.5013556375251013, 0.5027149505564014, 0.5040779490592088,
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0.5054446430258502, 0.5068150424757447, 0.5081891574554764, 0.509566998038869,
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|
0.5109485743270583, 0.5123338964485679, 0.5137229745593818, 0.5151158188430205,
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0.5165124395106142, 0.5179128468009786, 0.5193170509806894, 0.520725062344158,
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0.5221368912137069, 0.5235525479396449, 0.5249720429003435, 0.526395386502313,
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0.5278225891802786, 0.5292536613972564, 0.5306886136446309, 0.5321274564422321,
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0.5335702003384117, 0.5350168559101208, 0.5364674337629877, 0.5379219445313954,
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0.5393803988785598, 0.5408428074966075, 0.5423091811066545, 0.5437795304588847,
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0.5452538663326288, 0.5467321995364429, 0.5482145409081883, 0.549700901315111,
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0.5511912916539204, 0.5526857228508706, 0.5541842058618393, 0.5556867516724088,
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0.5571933712979462, 0.5587040757836845, 0.5602188762048033, 0.5617377836665098,
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0.5632608093041209, 0.564787964283144, 0.5663192597993595, 0.5678547070789026,
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0.5693943173783458, 0.5709381019847808, 0.572486072215902, 0.5740382394200894,
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0.5755946149764913, 0.5771552102951081, 0.5787200368168754, 0.5802891060137493,
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0.5818624293887887, 0.5834400184762408, 0.585021884841625, 0.5866080400818185,
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0.5881984958251406, 0.5897932637314379, 0.5913923554921704, 0.5929957828304968,
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0.5946035575013605, 0.5962156912915756, 0.5978321960199137, 0.5994530835371903,
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|
0.6010783657263515, 0.6027080545025619, 0.6043421618132907, 0.6059806996384005,
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0.6076236799902344, 0.6092711149137041, 0.6109230164863786, 0.6125793968185725,
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|
0.6142402680534349, 0.6159056423670379, 0.6175755319684665, 0.6192499490999082,
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|
0.620928906036742, 0.622612415087629, 0.6243004885946023, 0.6259931389331581,
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|
0.6276903785123455, 0.6293922197748583, 0.6310986751971253, 0.6328097572894031,
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0.6345254785958666, 0.6362458516947014, 0.637970889198196, 0.6397006037528346,
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|
0.6414350080393891, 0.6431741147730128, 0.6449179367033329, 0.6466664866145447,
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|
0.6484197773255048, 0.6501778216898253, 0.6519406325959679, 0.6537082229673385,
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|
0.6554806057623822, 0.6572577939746774, 0.659039800633032, 0.6608266388015788,
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0.6626183215798706, 0.6644148621029772, 0.6662162735415805, 0.6680225691020727,
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0.6698337620266515, 0.6716498655934177, 0.6734708931164728, 0.6752968579460171,
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0.6771277734684463, 0.6789636531064505, 0.6808045103191123, 0.6826503586020058,
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0.6845012114872953, 0.6863570825438342, 0.688217985377265, 0.690083933630119,
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0.6919549409819159, 0.6938310211492645, 0.6957121878859629, 0.6975984549830999,
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0.6994898362691555, 0.7013863456101023, 0.7032879969095076, 0.7051948041086352,
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0.7071067811865475, 0.7090239421602076, 0.7109463010845827, 0.7128738720527471,
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||||||
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0.7148066691959849, 0.7167447066838943, 0.718687998724491, 0.7206365595643126,
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0.7225904034885232, 0.7245495448210174, 0.7265139979245261, 0.7284837772007218,
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||||||
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0.7304588970903234, 0.7324393720732029, 0.7344252166684908, 0.7364164454346837,
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||||||
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0.7384130729697496, 0.7404151139112358, 0.7424225829363761, 0.7444354947621984,
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||||||
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0.7464538641456323, 0.7484777058836176, 0.7505070348132126, 0.7525418658117031,
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||||||
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0.7545822137967112, 0.7566280937263048, 0.7586795205991071, 0.7607365094544071,
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||||||
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0.762799075372269, 0.7648672334736434, 0.7669409989204777, 0.7690203869158282,
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||||||
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0.7711054127039704, 0.7731960915705107, 0.7752924388424999, 0.7773944698885442,
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||||||
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0.7795022001189185, 0.7816156449856788, 0.7837348199827764, 0.7858597406461707,
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||||||
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0.7879904225539431, 0.7901268813264122, 0.7922691326262467, 0.7944171921585818,
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||||||
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0.7965710756711334, 0.7987307989543135, 0.8008963778413465, 0.8030678282083853,
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||||||
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0.805245165974627, 0.8074284071024302, 0.8096175675974316, 0.8118126635086642,
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||||||
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0.8140137109286738, 0.8162207259936375, 0.8184337248834821, 0.820652723822003,
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||||||
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0.8228777390769823, 0.8251087869603088, 0.8273458838280969, 0.8295890460808079,
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||||||
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0.8318382901633681, 0.8340936325652911, 0.8363550898207981, 0.8386226785089391,
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||||||
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0.8408964152537144, 0.8431763167241966, 0.8454623996346523, 0.8477546807446661,
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0.8500531768592616, 0.8523579048290255, 0.8546688815502312, 0.8569861239649629,
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||||||
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0.8593096490612387, 0.8616394738731368, 0.8639756154809185, 0.8663180910111553,
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0.8686669176368529, 0.871022112577578, 0.8733836930995842, 0.8757516765159389,
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||||||
|
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,
|
||||||
|
},
|
||||||
|
}
|
||||||
|
|
|
||||||
112
model/histogram/generic_test.go
Normal file
112
model/histogram/generic_test.go
Normal file
|
|
@ -0,0 +1,112 @@
|
||||||
|
// Copyright 2022 The Prometheus Authors
|
||||||
|
// 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.
|
||||||
|
|
||||||
|
package histogram
|
||||||
|
|
||||||
|
import (
|
||||||
|
"math"
|
||||||
|
"testing"
|
||||||
|
|
||||||
|
"github.com/stretchr/testify/require"
|
||||||
|
)
|
||||||
|
|
||||||
|
func TestGetBound(t *testing.T) {
|
||||||
|
scenarios := []struct {
|
||||||
|
idx int32
|
||||||
|
schema int32
|
||||||
|
want float64
|
||||||
|
}{
|
||||||
|
{
|
||||||
|
idx: -1,
|
||||||
|
schema: -1,
|
||||||
|
want: 0.25,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 0,
|
||||||
|
schema: -1,
|
||||||
|
want: 1,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 1,
|
||||||
|
schema: -1,
|
||||||
|
want: 4,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 512,
|
||||||
|
schema: -1,
|
||||||
|
want: math.MaxFloat64,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 513,
|
||||||
|
schema: -1,
|
||||||
|
want: math.Inf(+1),
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: -1,
|
||||||
|
schema: 0,
|
||||||
|
want: 0.5,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 0,
|
||||||
|
schema: 0,
|
||||||
|
want: 1,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 1,
|
||||||
|
schema: 0,
|
||||||
|
want: 2,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 1024,
|
||||||
|
schema: 0,
|
||||||
|
want: math.MaxFloat64,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 1025,
|
||||||
|
schema: 0,
|
||||||
|
want: math.Inf(+1),
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: -1,
|
||||||
|
schema: 2,
|
||||||
|
want: 0.8408964152537144,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 0,
|
||||||
|
schema: 2,
|
||||||
|
want: 1,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 1,
|
||||||
|
schema: 2,
|
||||||
|
want: 1.189207115002721,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 4096,
|
||||||
|
schema: 2,
|
||||||
|
want: math.MaxFloat64,
|
||||||
|
},
|
||||||
|
{
|
||||||
|
idx: 4097,
|
||||||
|
schema: 2,
|
||||||
|
want: math.Inf(+1),
|
||||||
|
},
|
||||||
|
}
|
||||||
|
|
||||||
|
for _, s := range scenarios {
|
||||||
|
got := getBound(s.idx, s.schema)
|
||||||
|
if s.want != got {
|
||||||
|
require.Equal(t, s.want, got, "idx %d, schema %d", s.idx, s.schema)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
@ -446,169 +446,3 @@ func (c *cumulativeBucketIterator) At() Bucket[uint64] {
|
||||||
Index: c.currIdx - 1,
|
Index: c.currIdx - 1,
|
||||||
}
|
}
|
||||||
}
|
}
|
||||||
|
|
||||||
func getBound(idx, schema int32) float64 {
|
|
||||||
if schema < 0 {
|
|
||||||
return math.Ldexp(1, int(idx)<<(-schema))
|
|
||||||
}
|
|
||||||
|
|
||||||
fracIdx := idx & ((1 << schema) - 1)
|
|
||||||
frac := exponentialBounds[schema][fracIdx]
|
|
||||||
exp := (int(idx) >> schema) + 1
|
|
||||||
return math.Ldexp(frac, exp)
|
|
||||||
}
|
|
||||||
|
|
||||||
// exponentialBounds is a precalculated table of bucket bounds in the interval
|
|
||||||
// [0.5,1) in schema 0 to 8.
|
|
||||||
var exponentialBounds = [][]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,
|
|
||||||
},
|
|
||||||
}
|
|
||||||
|
|
|
||||||
|
|
@ -185,9 +185,9 @@ func histogramQuantile(q float64, h *histogram.FloatHistogram) float64 {
|
||||||
count = h.Count
|
count = h.Count
|
||||||
}
|
}
|
||||||
// We could have hit the highest bucket without even reaching the rank
|
// We could have hit the highest bucket without even reaching the rank
|
||||||
// (observations not counted in any bucket are considered "overflow"
|
// (this should only happen if the histogram contains observations of
|
||||||
// observations above the highest bucket), in which case we simple
|
// the value NaN), in which case we simply return the upper limit of the
|
||||||
// return the upper limit of the highest explicit bucket.
|
// highest explicit bucket.
|
||||||
if count < rank {
|
if count < rank {
|
||||||
return bucket.Upper
|
return bucket.Upper
|
||||||
}
|
}
|
||||||
|
|
|
||||||
Loading…
Reference in a new issue