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572 lines
23 KiB
Go
572 lines
23 KiB
Go
// Copyright 2021 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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// Histogram encodes a sparse, high-resolution histogram. See the design
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// document for full details:
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// https://docs.google.com/document/d/1cLNv3aufPZb3fNfaJgdaRBZsInZKKIHo9E6HinJVbpM/edit#
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//
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// The most tricky bit is how bucket indices represent real bucket boundaries.
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// An example for schema 0 (by which each bucket is twice as wide as the
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// previous bucket):
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//
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// Bucket boundaries → [-2,-1) [-1,-0.5) [-0.5,-0.25) ... [-0.001,0.001] ... (0.25,0.5] (0.5,1] (1,2] ....
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// ↑ ↑ ↑ ↑ ↑ ↑ ↑
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// Zero bucket (width e.g. 0.001) → | | | ZB | | |
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// Positive bucket indices → | | | ... -1 0 1 2 3
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// Negative bucket indices → 3 2 1 0 -1 ...
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//
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// Which bucket indices are actually used is determined by the spans.
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type Histogram struct {
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// Currently valid schema numbers are -4 <= n <= 8. They are all for
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// base-2 bucket schemas, where 1 is a bucket boundary in each case, and
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// then each power of two is divided into 2^n logarithmic buckets. Or
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// in other words, each bucket boundary is the previous boundary times
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// 2^(2^-n).
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Schema int32
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// Width of the zero bucket.
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ZeroThreshold float64
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// Observations falling into the zero bucket.
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ZeroCount uint64
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// Total number of observations.
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Count uint64
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// Sum of observations. This is also used as the stale marker.
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Sum float64
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// Spans for positive and negative buckets (see Span below).
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PositiveSpans, NegativeSpans []Span
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// Observation counts in buckets. The first element is an absolute
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// count. All following ones are deltas relative to the previous
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// element.
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PositiveBuckets, NegativeBuckets []int64
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}
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// A Span defines a continuous sequence of buckets.
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type Span struct {
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// Gap to previous span (always positive), or starting index for the 1st
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// span (which can be negative).
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Offset int32
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// Length of the span.
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Length uint32
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}
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// Copy returns a deep copy of the Histogram.
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func (h *Histogram) Copy() *Histogram {
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c := *h
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if len(h.PositiveSpans) != 0 {
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c.PositiveSpans = make([]Span, len(h.PositiveSpans))
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copy(c.PositiveSpans, h.PositiveSpans)
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}
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if len(h.NegativeSpans) != 0 {
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c.NegativeSpans = make([]Span, len(h.NegativeSpans))
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copy(c.NegativeSpans, h.NegativeSpans)
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}
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if len(h.PositiveBuckets) != 0 {
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c.PositiveBuckets = make([]int64, len(h.PositiveBuckets))
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copy(c.PositiveBuckets, h.PositiveBuckets)
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}
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if len(h.NegativeBuckets) != 0 {
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c.NegativeBuckets = make([]int64, len(h.NegativeBuckets))
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copy(c.NegativeBuckets, h.NegativeBuckets)
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}
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return &c
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}
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// String returns a string representation of the Histogram.
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func (h *Histogram) String() string {
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var sb strings.Builder
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fmt.Fprintf(&sb, "{count:%d, sum:%g", h.Count, h.Sum)
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var nBuckets []Bucket
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for it := h.NegativeBucketIterator(); it.Next(); {
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bucket := it.At()
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if bucket.Count != 0 {
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nBuckets = append(nBuckets, it.At())
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}
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}
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for i := len(nBuckets) - 1; i >= 0; i-- {
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fmt.Fprintf(&sb, ", %s", nBuckets[i].String())
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}
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if h.ZeroCount != 0 {
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fmt.Fprintf(&sb, ", %s", h.ZeroBucket().String())
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}
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for it := h.PositiveBucketIterator(); it.Next(); {
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bucket := it.At()
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if bucket.Count != 0 {
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fmt.Fprintf(&sb, ", %s", bucket.String())
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}
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}
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sb.WriteRune('}')
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return sb.String()
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}
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// ZeroBucket returns the zero bucket.
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func (h *Histogram) ZeroBucket() Bucket {
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return Bucket{
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Lower: -h.ZeroThreshold,
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Upper: h.ZeroThreshold,
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LowerInclusive: true,
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UpperInclusive: true,
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Count: h.ZeroCount,
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}
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}
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// PositiveBucketIterator returns a BucketIterator to iterate over all positive
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// buckets in ascending order (starting next to the zero bucket and going up).
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func (h *Histogram) PositiveBucketIterator() BucketIterator {
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return newRegularBucketIterator(h, true)
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}
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// NegativeBucketIterator returns a BucketIterator to iterate over all negative
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// buckets in descending order (starting next to the zero bucket and going down).
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func (h *Histogram) NegativeBucketIterator() BucketIterator {
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return newRegularBucketIterator(h, false)
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}
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// CumulativeBucketIterator returns a BucketIterator to iterate over a
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// cumulative view of the buckets. This method currently only supports
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// Histograms without negative buckets and panics if the Histogram has negative
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// buckets. It is currently only used for testing.
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func (h *Histogram) CumulativeBucketIterator() BucketIterator {
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if len(h.NegativeBuckets) > 0 {
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panic("CumulativeBucketIterator called on Histogram with negative buckets")
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}
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return &cumulativeBucketIterator{h: h, posSpansIdx: -1}
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}
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// ToFloat returns a FloatHistogram representation of the Histogram. It is a
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// deep copy (e.g. spans are not shared).
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func (h *Histogram) ToFloat() *FloatHistogram {
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var (
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positiveSpans, negativeSpans []Span
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positiveBuckets, negativeBuckets []float64
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)
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if len(h.PositiveSpans) != 0 {
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positiveSpans = make([]Span, len(h.PositiveSpans))
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copy(positiveSpans, h.PositiveSpans)
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}
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if len(h.NegativeSpans) != 0 {
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negativeSpans = make([]Span, len(h.NegativeSpans))
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copy(negativeSpans, h.NegativeSpans)
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}
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if len(h.PositiveBuckets) != 0 {
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positiveBuckets = make([]float64, len(h.PositiveBuckets))
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var current float64
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for i, b := range h.PositiveBuckets {
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current += float64(b)
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positiveBuckets[i] = current
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}
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}
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if len(h.NegativeBuckets) != 0 {
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negativeBuckets = make([]float64, len(h.NegativeBuckets))
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var current float64
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for i, b := range h.NegativeBuckets {
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current += float64(b)
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negativeBuckets[i] = current
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}
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}
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return &FloatHistogram{
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Schema: h.Schema,
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ZeroThreshold: h.ZeroThreshold,
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ZeroCount: float64(h.ZeroCount),
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Count: float64(h.Count),
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Sum: h.Sum,
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PositiveSpans: positiveSpans,
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NegativeSpans: negativeSpans,
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PositiveBuckets: positiveBuckets,
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NegativeBuckets: negativeBuckets,
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}
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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 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
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}
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// Bucket represents a bucket with lower and upper limit and the count of
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// 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 struct {
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Lower, Upper float64
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LowerInclusive, UpperInclusive bool
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Count uint64
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Index int32 // Index within schema. To easily compare buckets that share the same schema.
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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) 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, ":%d", b.Count)
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return sb.String()
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}
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type regularBucketIterator struct {
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schema int32
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spans []Span
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buckets []int64
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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 int64 // Count in the current bucket.
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currIdx int32 // The actual bucket index.
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currLower, currUpper float64 // Limits of the current bucket.
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}
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func newRegularBucketIterator(h *Histogram, positive bool) *regularBucketIterator {
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r := ®ularBucketIterator{schema: h.Schema, positive: positive}
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if positive {
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r.spans = h.PositiveSpans
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r.buckets = h.PositiveBuckets
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} else {
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r.spans = h.NegativeSpans
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r.buckets = h.NegativeBuckets
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}
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return r
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}
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func (r *regularBucketIterator) Next() bool {
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if r.spansIdx >= len(r.spans) {
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return false
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}
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span := r.spans[r.spansIdx]
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// Seed currIdx for the first bucket.
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if r.bucketsIdx == 0 {
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r.currIdx = span.Offset
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} else {
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r.currIdx++
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}
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for r.idxInSpan >= span.Length {
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// We have exhausted the current span and have to find a new
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// one. We'll even handle pathologic spans of length 0.
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r.idxInSpan = 0
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r.spansIdx++
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if r.spansIdx >= len(r.spans) {
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return false
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}
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span = r.spans[r.spansIdx]
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r.currIdx += span.Offset
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}
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r.currCount += r.buckets[r.bucketsIdx]
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if r.positive {
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r.currUpper = getBound(r.currIdx, r.schema)
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r.currLower = getBound(r.currIdx-1, r.schema)
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} else {
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r.currLower = -getBound(r.currIdx, r.schema)
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r.currUpper = -getBound(r.currIdx-1, r.schema)
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}
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r.idxInSpan++
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r.bucketsIdx++
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return true
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}
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func (r *regularBucketIterator) At() Bucket {
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return Bucket{
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Count: uint64(r.currCount),
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Lower: r.currLower,
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Upper: r.currUpper,
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LowerInclusive: r.currLower < 0,
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UpperInclusive: r.currUpper > 0,
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Index: r.currIdx,
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}
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}
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type cumulativeBucketIterator struct {
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h *Histogram
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posSpansIdx int // Index in h.PositiveSpans we are in. -1 means 0 bucket.
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posBucketsIdx int // Index in h.PositiveBuckets.
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idxInSpan uint32 // Index in the current span. 0 <= idxInSpan < span.Length.
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initialized bool
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currIdx int32 // The actual bucket index after decoding from spans.
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currUpper float64 // The upper boundary of the current bucket.
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currCount int64 // Current non-cumulative count for the current bucket. Does not apply for empty bucket.
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currCumulativeCount uint64 // Current "cumulative" count for the current bucket.
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// Between 2 spans there could be some empty buckets which
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// still needs to be counted for cumulative buckets.
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// When we hit the end of a span, we use this to iterate
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// through the empty buckets.
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emptyBucketCount int32
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}
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func (c *cumulativeBucketIterator) Next() bool {
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if c.posSpansIdx == -1 {
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// Zero bucket.
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c.posSpansIdx++
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if c.h.ZeroCount == 0 {
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return c.Next()
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}
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c.currUpper = c.h.ZeroThreshold
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c.currCount = int64(c.h.ZeroCount)
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c.currCumulativeCount = uint64(c.currCount)
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return true
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}
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if c.posSpansIdx >= len(c.h.PositiveSpans) {
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return false
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}
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if c.emptyBucketCount > 0 {
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// We are traversing through empty buckets at the moment.
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c.currUpper = getBound(c.currIdx, c.h.Schema)
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c.currIdx++
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c.emptyBucketCount--
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return true
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}
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span := c.h.PositiveSpans[c.posSpansIdx]
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if c.posSpansIdx == 0 && !c.initialized {
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// Initializing.
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c.currIdx = span.Offset
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// The first bucket is an absolute value and not a delta with Zero bucket.
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c.currCount = 0
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c.initialized = true
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}
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c.currCount += c.h.PositiveBuckets[c.posBucketsIdx]
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c.currCumulativeCount += uint64(c.currCount)
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c.currUpper = getBound(c.currIdx, c.h.Schema)
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c.posBucketsIdx++
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c.idxInSpan++
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c.currIdx++
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if c.idxInSpan >= span.Length {
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// Move to the next span. This one is done.
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c.posSpansIdx++
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c.idxInSpan = 0
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if c.posSpansIdx < len(c.h.PositiveSpans) {
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c.emptyBucketCount = c.h.PositiveSpans[c.posSpansIdx].Offset
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}
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}
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return true
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}
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func (c *cumulativeBucketIterator) At() Bucket {
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return Bucket{
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Upper: c.currUpper,
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Lower: math.Inf(-1),
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UpperInclusive: true,
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LowerInclusive: true,
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Count: c.currCumulativeCount,
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Index: c.currIdx - 1,
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}
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}
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func getBound(idx, schema int32) float64 {
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if schema < 0 {
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return math.Ldexp(1, int(idx)<<(-schema))
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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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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,
|
|
0.9576032806985735, 0.9680308967461471, 0.9785720620876999, 0.9892280131939752,
|
|
},
|
|
// Schema 7:
|
|
{
|
|
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,
|
|
0.9785720620876999, 0.9838856116165875, 0.9892280131939752, 0.9945994234836328,
|
|
},
|
|
// Schema 8:
|
|
{
|
|
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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0.7148066691959849, 0.7167447066838943, 0.718687998724491, 0.7206365595643126,
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0.7225904034885232, 0.7245495448210174, 0.7265139979245261, 0.7284837772007218,
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0.7304588970903234, 0.7324393720732029, 0.7344252166684908, 0.7364164454346837,
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0.7384130729697496, 0.7404151139112358, 0.7424225829363761, 0.7444354947621984,
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0.7464538641456323, 0.7484777058836176, 0.7505070348132126, 0.7525418658117031,
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0.7545822137967112, 0.7566280937263048, 0.7586795205991071, 0.7607365094544071,
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0.762799075372269, 0.7648672334736434, 0.7669409989204777, 0.7690203869158282,
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0.7711054127039704, 0.7731960915705107, 0.7752924388424999, 0.7773944698885442,
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0.7795022001189185, 0.7816156449856788, 0.7837348199827764, 0.7858597406461707,
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0.7879904225539431, 0.7901268813264122, 0.7922691326262467, 0.7944171921585818,
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0.7965710756711334, 0.7987307989543135, 0.8008963778413465, 0.8030678282083853,
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0.805245165974627, 0.8074284071024302, 0.8096175675974316, 0.8118126635086642,
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0.8140137109286738, 0.8162207259936375, 0.8184337248834821, 0.820652723822003,
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0.8228777390769823, 0.8251087869603088, 0.8273458838280969, 0.8295890460808079,
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0.8318382901633681, 0.8340936325652911, 0.8363550898207981, 0.8386226785089391,
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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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0.8593096490612387, 0.8616394738731368, 0.8639756154809185, 0.8663180910111553,
|
|
0.8686669176368529, 0.871022112577578, 0.8733836930995842, 0.8757516765159389,
|
|
0.8781260801866495, 0.8805069215187917, 0.8828942179666361, 0.8852879870317771,
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0.8876882462632604, 0.890095013257712, 0.8925083056594671, 0.8949281411607002,
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|
0.8973545375015533, 0.8997875124702672, 0.9022270839033115, 0.9046732696855155,
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|
0.9071260877501991, 0.909585556079304, 0.9120516927035263, 0.9145245157024483,
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0.9170040432046711, 0.9194902933879467, 0.9219832844793128, 0.9244830347552253,
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|
0.9269895625416926, 0.92950288621441, 0.9320230241988943, 0.9345499949706191,
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0.9370838170551498, 0.93962450902828, 0.9421720895161669, 0.9447265771954693,
|
|
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|
0.9576032806985735, 0.9601996065815236, 0.9628029718180622, 0.9654133954938133,
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|
0.9680308967461471, 0.9706554947643201, 0.9732872087896164, 0.9759260581154889,
|
|
0.9785720620876999, 0.9812252401044634, 0.9838856116165875, 0.9865531961276168,
|
|
0.9892280131939752, 0.9919100824251095, 0.9945994234836328, 0.9972960560854698,
|
|
},
|
|
}
|