src/runtime/histogram.go

// Copyright 2020 The Go Authors. All rights reserved.
// Use of this source code is governed by a BSD-style
// license that can be found in the LICENSE file.

package runtime

import (
	"runtime/internal/atomic"
	"runtime/internal/sys"
	"unsafe"
)

const (
	// For the time histogram type, we use an HDR histogram.
	// Values are placed in super-buckets based solely on the most
	// significant set bit. Thus, super-buckets are power-of-2 sized.
	// Values are then placed into sub-buckets based on the value of
	// the next timeHistSubBucketBits most significant bits. Thus,
	// sub-buckets are linear within a super-bucket.
	//
	// Therefore, the number of sub-buckets (timeHistNumSubBuckets)
	// defines the error. This error may be computed as
	// 1/timeHistNumSubBuckets*100%. For example, for 16 sub-buckets
	// per super-bucket the error is approximately 6%.
	//
	// The number of super-buckets (timeHistNumSuperBuckets), on the
	// other hand, defines the range. To reserve room for sub-buckets,
	// bit timeHistSubBucketBits is the first bit considered for
	// super-buckets, so super-bucket indicies are adjusted accordingly.
	//
	// As an example, consider 45 super-buckets with 16 sub-buckets.
	//
	//    00110
	//    ^----
	//    │  ^
	//    │  └---- Lowest 4 bits -> sub-bucket 6
	//    └------- Bit 4 unset -> super-bucket 0
	//
	//    10110
	//    ^----
	//    │  ^
	//    │  └---- Next 4 bits -> sub-bucket 6
	//    └------- Bit 4 set -> super-bucket 1
	//    100010
	//    ^----^
	//    │  ^ └-- Lower bits ignored
	//    │  └---- Next 4 bits -> sub-bucket 1
	//    └------- Bit 5 set -> super-bucket 2
	//
	// Following this pattern, bucket 45 will have the bit 48 set. We don't
	// have any buckets for higher values, so the highest sub-bucket will
	// contain values of 2^48-1 nanoseconds or approx. 3 days. This range is
	// more than enough to handle durations produced by the runtime.
	timeHistSubBucketBits   = 4
	timeHistNumSubBuckets   = 1 << timeHistSubBucketBits
	timeHistNumSuperBuckets = 45
	timeHistTotalBuckets    = timeHistNumSuperBuckets*timeHistNumSubBuckets + 1
)

// timeHistogram represents a distribution of durations in
// nanoseconds.
//
// The accuracy and range of the histogram is defined by the
// timeHistSubBucketBits and timeHistNumSuperBuckets constants.
//
// It is an HDR histogram with exponentially-distributed
// buckets and linearly distributed sub-buckets.
//
// Counts in the histogram are updated atomically, so it is safe
// for concurrent use. It is also safe to read all the values
// atomically.
type timeHistogram struct {
	counts [timeHistNumSuperBuckets * timeHistNumSubBuckets]uint64

	// underflow counts all the times we got a negative duration
	// sample. Because of how time works on some platforms, it's
	// possible to measure negative durations. We could ignore them,
	// but we record them anyway because it's better to have some
	// signal that it's happening than just missing samples.
	underflow uint64
}

// record adds the given duration to the distribution.
func (h *timeHistogram) record(duration int64) {
	if duration < 0 {
		atomic.Xadd64(&h.underflow, 1)
		return
	}
	// The index of the exponential bucket is just the index
	// of the highest set bit adjusted for how many bits we
	// use for the subbucket. Note that it's timeHistSubBucketsBits-1
	// because we use the 0th bucket to hold values < timeHistNumSubBuckets.
	var superBucket, subBucket uint
	if duration >= timeHistNumSubBuckets {
		// At this point, we know the duration value will always be
		// at least timeHistSubBucketsBits long.
		superBucket = uint(sys.Len64(uint64(duration))) - timeHistSubBucketBits
		if superBucket*timeHistNumSubBuckets >= uint(len(h.counts)) {
			// The bucket index we got is larger than what we support, so
			// include this count in the highest bucket, which extends to
			// infinity.
			superBucket = timeHistNumSuperBuckets - 1
			subBucket = timeHistNumSubBuckets - 1
		} else {
			// The linear subbucket index is just the timeHistSubBucketsBits
			// bits after the top bit. To extract that value, shift down
			// the duration such that we leave the top bit and the next bits
			// intact, then extract the index.
			subBucket = uint((duration >> (superBucket - 1)) % timeHistNumSubBuckets)
		}
	} else {
		subBucket = uint(duration)
	}
	atomic.Xadd64(&h.counts[superBucket*timeHistNumSubBuckets+subBucket], 1)
}

const (
	fInf    = 0x7FF0000000000000
	fNegInf = 0xFFF0000000000000
)

func float64Inf() float64 {
	inf := uint64(fInf)
	return *(*float64)(unsafe.Pointer(&inf))
}

func float64NegInf() float64 {
	inf := uint64(fNegInf)
	return *(*float64)(unsafe.Pointer(&inf))
}

// timeHistogramMetricsBuckets generates a slice of boundaries for
// the timeHistogram. These boundaries are represented in seconds,
// not nanoseconds like the timeHistogram represents durations.
func timeHistogramMetricsBuckets() []float64 {
	b := make([]float64, timeHistTotalBuckets+1)
	b[0] = float64NegInf()
	for i := 0; i < timeHistNumSuperBuckets; i++ {
		superBucketMin := uint64(0)
		// The (inclusive) minimum for the first non-negative bucket is 0.
		if i > 0 {
			// The minimum for the second bucket will be
			// 1 << timeHistSubBucketBits, indicating that all
			// sub-buckets are represented by the next timeHistSubBucketBits
			// bits.
			// Thereafter, we shift up by 1 each time, so we can represent
			// this pattern as (i-1)+timeHistSubBucketBits.
			superBucketMin = uint64(1) << uint(i-1+timeHistSubBucketBits)
		}
		// subBucketShift is the amount that we need to shift the sub-bucket
		// index to combine it with the bucketMin.
		subBucketShift := uint(0)
		if i > 1 {
			// The first two super buckets are exact with respect to integers,
			// so we'll never have to shift the sub-bucket index. Thereafter,
			// we shift up by 1 with each subsequent bucket.
			subBucketShift = uint(i - 2)
		}
		for j := 0; j < timeHistNumSubBuckets; j++ {
			// j is the sub-bucket index. By shifting the index into position to
			// combine with the bucket minimum, we obtain the minimum value for that
			// sub-bucket.
			subBucketMin := superBucketMin + (uint64(j) << subBucketShift)

			// Convert the subBucketMin which is in nanoseconds to a float64 seconds value.
			// These values will all be exactly representable by a float64.
			b[i*timeHistNumSubBuckets+j+1] = float64(subBucketMin) / 1e9
		}
	}
	b[len(b)-1] = float64Inf()
	return b
}