Extract HDR histogram implementation into a shared package (#4611)

Author: joanlopez

internal/ds/histogram/doc.go

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+// Package histogram provides histogram implementations that are used to track the distribution of metrics.
+package histogram

internal/ds/histogram/hdr.go

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+package histogram
+
+import (
+	"math"
+	"math/bits"
+)
+
+const (
+	// defaultMinimumResolution is the default resolution used by Hdr.
+	// It allows to have a higher granularity compared to the basic 1.0 value,
+	// supporting floating points up to 3 digits.
+	defaultMinimumResolution = .001
+
+	// lowestTrackable represents the minimum value that the Hdr tracks.
+	// Essentially, it excludes negative numbers.
+	// Most of the metrics tracked by histograms are durations
+	// where we don't expect negative numbers.
+	lowestTrackable = 0
+)
+
+// Hdr represents a distribution of metrics samples' values as histogram.
+//
+// A Hdr is the representation of base-2 exponential histogram with two layers.
+// The first layer has primary buckets in the form of a power of two, and a second layer of buckets
+// for each primary bucket with an equally distributed amount of buckets inside.
+//
+// Hdr has a series of (N * 2^m) buckets, where:
+// N = a power of 2 that defines the number of primary buckets
+// m = a power of 2 that defines the number of the secondary buckets
+// The current version is: f(N = 25, m = 7) = 3200.
+type Hdr struct {
+	// Buckets stores the counters for each bin of the histogram.
+	// It does not include counters for the untrackable values,
+	// because they contain exception cases and require to be tracked in a dedicated way.
+	Buckets map[uint32]uint32
+
+	// ExtraLowBucket counts occurrences of observed values smaller
+	// than the minimum trackable value.
+	ExtraLowBucket uint32
+
+	// ExtraHighBucket counts occurrences of observed values bigger
+	// than the maximum trackable value.
+	ExtraHighBucket uint32
+
+	// Max is the absolute observed maximum value.
+	Max float64
+
+	// Min is the absolute observed minimum value.
+	Min float64
+
+	// Sum is the sum of all observed values.
+	Sum float64
+
+	// Count is counts the amount of observed values.
+	Count uint32
+
+	// MinimumResolution represents resolution used by Hdr.
+	// In principle, it is a multiplier factor for the tracked values.
+	MinimumResolution float64
+}
+
+// NewHdr creates a new Hdr histogram with default settings.
+func NewHdr() *Hdr {
+	return &Hdr{
+		MinimumResolution: defaultMinimumResolution,
+		Buckets:           make(map[uint32]uint32),
+		Max:               -math.MaxFloat64,
+		Min:               math.MaxFloat64,
+	}
+}
+
+// Add adds a value to the Hdr histogram.
+func (h *Hdr) Add(v float64) {
+	h.addToBucket(v)
+}
+
+// addToBucket increments the counter of the bucket of the provided value.
+// If the value is lower or higher than the trackable limits
+// then it is counted into specific buckets. All the stats are also updated accordingly.
+func (h *Hdr) addToBucket(v float64) {
+	if v > h.Max {
+		h.Max = v
+	}
+	if v < h.Min {
+		h.Min = v
+	}
+
+	h.Count++
+	h.Sum += v
+
+	v /= h.MinimumResolution
+
+	if v < lowestTrackable {
+		h.ExtraLowBucket++
+		return
+	}
+	if v > math.MaxInt64 {
+		h.ExtraHighBucket++
+		return
+	}
+
+	h.Buckets[resolveBucketIndex(v)]++
+}
+
+// resolveBucketIndex returns the index
+// of the bucket in the histogram for the provided value.
+func resolveBucketIndex(val float64) uint32 {
+	if val < lowestTrackable {
+		return 0
+	}
+
+	// We upscale to the next integer to ensure that each sample falls
+	// within a specific bucket, even when the value is fractional.
+	// This avoids under-representing the distribution in the Hdr histogram.
+	upscaled := uint64(math.Ceil(val))
+
+	// In Hdr histograms, bucket boundaries are usually defined as multiples of powers of 2,
+	// allowing for efficient computation of bucket indexes.
+	//
+	// We define k=7 in our case, because it allows for sufficient granularity in the
+	// distribution (2^7=128 primary buckets of which each can be further
+	// subdivided if needed).
+	//
+	// k is the constant balancing factor between granularity and
+	// computational efficiency.
+	//
+	// In our case:
+	// i.e 2^7  = 128  ~  100 = 10^2
+	//     2^10 = 1024 ~ 1000 = 10^3
+	// f(x) = 3*x + 1 - empiric formula that works for us
+	// since f(2)=7 and f(3)=10
+	const k = uint64(7)
+
+	// 256 = 1 << (k+1)
+	if upscaled < 256 {
+		return uint32(upscaled)
+	}
+
+	// `nkdiff` helps us find the right bucket for `upscaled`. It does so by determining the
+	// index for the "major" bucket (a set of values within a power of two range) and then
+	// the "sub" bucket within that major bucket. This system provides us with a fine level
+	// of granularity within a computationally efficient bucketing system. The result is a
+	// histogram that provides a detailed representation of the distribution of values.
+	//
+	// Here we use some math to get simple formula
+	// derivation:
+	// let u = upscaled
+	// let n = msb(u) - most significant digit position
+	// i.e. n = floor(log(u, 2))
+	//   major_bucket_index = n - k + 1
+	//   sub_bucket_index = u>>(n - k) - (1<<k)
+	//   bucket = major_bucket_index << k + sub_bucket_index =
+	//          = (n-k+1)<<k + u>>(n-k) - (1<<k) =
+	//          = (n-k)<<k + u>>(n-k)
+	//
+	nkdiff := uint64(bits.Len64(upscaled>>k)) - 1 //nolint:gosec // msb index
+
+	// We cast safely downscaling because we don't expect we may hit the uint32 limit
+	// with the bucket index. The bucket represented from the index as MaxUint32
+	// would be a very huge number bigger than the trackable limits.
+	return uint32((nkdiff << k) + (upscaled >> nkdiff)) //nolint:gosec
+}