mirror of
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bf0847073d
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>
537 lines
22 KiB
Go
537 lines
22 KiB
Go
// Copyright 2022 The Prometheus Authors
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// Licensed under the Apache License, Version 2.0 (the "License");
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// you may not use this file except in compliance with the License.
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// You may obtain a copy of the License at
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//
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// http://www.apache.org/licenses/LICENSE-2.0
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//
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// Unless required by applicable law or agreed to in writing, software
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// distributed under the License is distributed on an "AS IS" BASIS,
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// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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// See the License for the specific language governing permissions and
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// limitations under the License.
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package histogram
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import (
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"fmt"
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"math"
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"strings"
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)
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// BucketCount is a type constraint for the count in a bucket, which can be
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// float64 (for type FloatHistogram) or uint64 (for type Histogram).
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type BucketCount interface {
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float64 | uint64
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}
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// internalBucketCount is used internally by Histogram and FloatHistogram. The
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// difference to the BucketCount above is that Histogram internally uses deltas
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// between buckets rather than absolute counts (while FloatHistogram uses
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// absolute counts directly). Go type parameters don't allow type
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// specialization. Therefore, where special treatment of deltas between buckets
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// vs. absolute counts is important, this information has to be provided as a
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// separate boolean parameter "deltaBuckets"
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type internalBucketCount interface {
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float64 | int64
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}
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// Bucket represents a bucket with lower and upper limit and the absolute count
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// of samples in the bucket. It also specifies if each limit is inclusive or
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// not. (Mathematically, inclusive limits create a closed interval, and
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// non-inclusive limits an open interval.)
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//
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// To represent cumulative buckets, Lower is set to -Inf, and the Count is then
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// cumulative (including the counts of all buckets for smaller values).
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type Bucket[BC BucketCount] struct {
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Lower, Upper float64
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LowerInclusive, UpperInclusive bool
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Count BC
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// Index within schema. To easily compare buckets that share the same
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// schema and sign (positive or negative). Irrelevant for the zero bucket.
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Index int32
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}
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// String returns a string representation of a Bucket, using the usual
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// mathematical notation of '['/']' for inclusive bounds and '('/')' for
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// non-inclusive bounds.
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func (b Bucket[BC]) String() string {
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var sb strings.Builder
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if b.LowerInclusive {
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sb.WriteRune('[')
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} else {
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sb.WriteRune('(')
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}
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fmt.Fprintf(&sb, "%g,%g", b.Lower, b.Upper)
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if b.UpperInclusive {
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sb.WriteRune(']')
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} else {
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sb.WriteRune(')')
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}
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fmt.Fprintf(&sb, ":%v", b.Count)
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return sb.String()
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}
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// BucketIterator iterates over the buckets of a Histogram, returning decoded
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// buckets.
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type BucketIterator[BC BucketCount] interface {
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// Next advances the iterator by one.
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Next() bool
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// At returns the current bucket.
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At() Bucket[BC]
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}
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// baseBucketIterator provides a struct that is shared by most BucketIterator
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// implementations, together with an implementation of the At method. This
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// iterator can be embedded in full implementations of BucketIterator to save on
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// code replication.
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type baseBucketIterator[BC BucketCount, IBC internalBucketCount] struct {
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schema int32
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spans []Span
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buckets []IBC
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positive bool // Whether this is for positive buckets.
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spansIdx int // Current span within spans slice.
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idxInSpan uint32 // Index in the current span. 0 <= idxInSpan < span.Length.
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bucketsIdx int // Current bucket within buckets slice.
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currCount IBC // Count in the current bucket.
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currIdx int32 // The actual bucket index.
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}
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func (b baseBucketIterator[BC, IBC]) At() Bucket[BC] {
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bucket := Bucket[BC]{
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Count: BC(b.currCount),
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Index: b.currIdx,
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}
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if b.positive {
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bucket.Upper = getBound(b.currIdx, b.schema)
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bucket.Lower = getBound(b.currIdx-1, b.schema)
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} else {
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bucket.Lower = -getBound(b.currIdx, b.schema)
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bucket.Upper = -getBound(b.currIdx-1, b.schema)
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}
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bucket.LowerInclusive = bucket.Lower < 0
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bucket.UpperInclusive = bucket.Upper > 0
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return bucket
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}
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// compactBuckets is a generic function used by both Histogram.Compact and
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// FloatHistogram.Compact. Set deltaBuckets to true if the provided buckets are
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// deltas. Set it to false if the buckets contain absolute counts.
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func compactBuckets[IBC internalBucketCount](buckets []IBC, spans []Span, maxEmptyBuckets int, deltaBuckets bool) ([]IBC, []Span) {
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// Fast path: If there are no empty buckets AND no offset in any span is
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// <= maxEmptyBuckets AND no span has length 0, there is nothing to do and we can return
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// immediately. We check that first because it's cheap and presumably
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// common.
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nothingToDo := true
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var currentBucketAbsolute IBC
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for _, bucket := range buckets {
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if deltaBuckets {
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currentBucketAbsolute += bucket
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} else {
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currentBucketAbsolute = bucket
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}
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if currentBucketAbsolute == 0 {
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nothingToDo = false
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break
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}
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}
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if nothingToDo {
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for _, span := range spans {
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if int(span.Offset) <= maxEmptyBuckets || span.Length == 0 {
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nothingToDo = false
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break
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}
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}
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if nothingToDo {
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return buckets, spans
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}
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}
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var iBucket, iSpan int
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var posInSpan uint32
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currentBucketAbsolute = 0
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// Helper function.
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emptyBucketsHere := func() int {
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i := 0
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abs := currentBucketAbsolute
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for uint32(i)+posInSpan < spans[iSpan].Length && abs == 0 {
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i++
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if i+iBucket >= len(buckets) {
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break
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}
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abs = buckets[i+iBucket]
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}
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return i
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}
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// Merge spans with zero-offset to avoid special cases later.
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if len(spans) > 1 {
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for i, span := range spans[1:] {
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if span.Offset == 0 {
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spans[iSpan].Length += span.Length
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continue
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}
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iSpan++
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if i+1 != iSpan {
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spans[iSpan] = span
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}
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}
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spans = spans[:iSpan+1]
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iSpan = 0
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}
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// Merge spans with zero-length to avoid special cases later.
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for i, span := range spans {
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if span.Length == 0 {
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if i+1 < len(spans) {
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spans[i+1].Offset += span.Offset
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}
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continue
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}
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if i != iSpan {
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spans[iSpan] = span
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}
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iSpan++
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}
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spans = spans[:iSpan]
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iSpan = 0
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// Cut out empty buckets from start and end of spans, no matter
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// what. Also cut out empty buckets from the middle of a span but only
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// if there are more than maxEmptyBuckets consecutive empty buckets.
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for iBucket < len(buckets) {
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if deltaBuckets {
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currentBucketAbsolute += buckets[iBucket]
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} else {
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currentBucketAbsolute = buckets[iBucket]
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}
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if nEmpty := emptyBucketsHere(); nEmpty > 0 {
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if posInSpan > 0 &&
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nEmpty < int(spans[iSpan].Length-posInSpan) &&
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nEmpty <= maxEmptyBuckets {
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// The empty buckets are in the middle of a
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// span, and there are few enough to not bother.
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// Just fast-forward.
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iBucket += nEmpty
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if deltaBuckets {
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currentBucketAbsolute = 0
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}
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posInSpan += uint32(nEmpty)
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continue
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}
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// In all other cases, we cut out the empty buckets.
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if deltaBuckets && iBucket+nEmpty < len(buckets) {
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currentBucketAbsolute = -buckets[iBucket]
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buckets[iBucket+nEmpty] += buckets[iBucket]
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}
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buckets = append(buckets[:iBucket], buckets[iBucket+nEmpty:]...)
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if posInSpan == 0 {
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// Start of span.
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if nEmpty == int(spans[iSpan].Length) {
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// The whole span is empty.
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offset := spans[iSpan].Offset
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spans = append(spans[:iSpan], spans[iSpan+1:]...)
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if len(spans) > iSpan {
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spans[iSpan].Offset += offset + int32(nEmpty)
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}
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continue
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}
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spans[iSpan].Length -= uint32(nEmpty)
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spans[iSpan].Offset += int32(nEmpty)
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continue
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}
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// It's in the middle or in the end of the span.
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// Split the current span.
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newSpan := Span{
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Offset: int32(nEmpty),
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Length: spans[iSpan].Length - posInSpan - uint32(nEmpty),
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}
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spans[iSpan].Length = posInSpan
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// In any case, we have to split to the next span.
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iSpan++
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posInSpan = 0
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if newSpan.Length == 0 {
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// The span is empty, so we were already at the end of a span.
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// We don't have to insert the new span, just adjust the next
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// span's offset, if there is one.
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if iSpan < len(spans) {
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spans[iSpan].Offset += int32(nEmpty)
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}
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continue
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}
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// Insert the new span.
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spans = append(spans, Span{})
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if iSpan+1 < len(spans) {
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copy(spans[iSpan+1:], spans[iSpan:])
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}
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spans[iSpan] = newSpan
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continue
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}
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iBucket++
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posInSpan++
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if posInSpan >= spans[iSpan].Length {
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posInSpan = 0
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iSpan++
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}
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}
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if maxEmptyBuckets == 0 || len(buckets) == 0 {
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return buckets, spans
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}
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// Finally, check if any offsets between spans are small enough to merge
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// the spans.
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iBucket = int(spans[0].Length)
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if deltaBuckets {
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currentBucketAbsolute = 0
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for _, bucket := range buckets[:iBucket] {
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currentBucketAbsolute += bucket
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}
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}
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iSpan = 1
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for iSpan < len(spans) {
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if int(spans[iSpan].Offset) > maxEmptyBuckets {
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l := int(spans[iSpan].Length)
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if deltaBuckets {
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for _, bucket := range buckets[iBucket : iBucket+l] {
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currentBucketAbsolute += bucket
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}
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}
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iBucket += l
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iSpan++
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continue
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}
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// Merge span with previous one and insert empty buckets.
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offset := int(spans[iSpan].Offset)
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spans[iSpan-1].Length += uint32(offset) + spans[iSpan].Length
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spans = append(spans[:iSpan], spans[iSpan+1:]...)
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newBuckets := make([]IBC, len(buckets)+offset)
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copy(newBuckets, buckets[:iBucket])
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copy(newBuckets[iBucket+offset:], buckets[iBucket:])
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if deltaBuckets {
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newBuckets[iBucket] = -currentBucketAbsolute
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newBuckets[iBucket+offset] += currentBucketAbsolute
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}
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iBucket += offset
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buckets = newBuckets
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currentBucketAbsolute = buckets[iBucket]
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// Note that with many merges, it would be more efficient to
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// first record all the chunks of empty buckets to insert and
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// then do it in one go through all the buckets.
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}
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return buckets, spans
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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,
|
|
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,
|
|
},
|
|
}
|