OTel Exponential Histogram implementation

CHANGELOG.md

@@ -12,6 +12,7 @@ This project adheres to [Semantic Versioning](https://semver.org/spec/v2.0.0.htm
 
 - Support Go 1.19.
   Include compatibility testing and document support. (#3077)
+- OpenTelemetry Exponential histogram data structure for public use. (#3022)
 
 ## [1.9.0/0.0.3] - 2022-08-01
 

sdk/metric/aggregator/exponential/README.md

@@ -2,15 +2,48 @@
 
 ## Design
 
-This document is a placeholder for future Aggregator, once seen in [PR
-2393](https://github.com/open-telemetry/opentelemetry-go/pull/2393).
+This is a fixed-size data structure for aggregating the OpenTelemetry
+base-2 exponential histogram introduced in [OTEP
+149](https://github.com/open-telemetry/oteps/blob/main/text/0149-exponential-histogram.md)
+and [described in the metrics data
+model](https://github.com/open-telemetry/opentelemetry-specification/blob/main/specification/metrics/datamodel.md#exponentialhistogram).
+The exponential histogram data point is characterized by a `scale`
+factor that determines resolution.  Positive scales correspond with
+more resolution, and negatives scales correspond with less resolution.
 
-Only the mapping functions have been made available at this time.  The
-equations tested here are specified in the [data model for Exponential
-Histogram data points](https://github.com/open-telemetry/opentelemetry-specification/blob/main/specification/metrics/data-model.md#exponentialhistogram).
+Given a maximum size, in terms of the number of buckets, the
+implementation determines the best scale possible given the set of
+measurements received.  The size of the histogram is configured using
+the `WithMaxSize()` option, which defaults to 160.
+
+The implementation here maintains the best resolution possible.  Since
+the scale parameter is shared by the positive and negative ranges, the
+best value of the scale parameter is determined by the range with the
+greater difference between minimum and maximum bucket index:
+
+```golang
+func bucketsNeeded(minValue, maxValue float64, scale int32) int32 {
+	return bucketIndex(maxValue, scale) - bucketIndex(minValue, scale) + 1
+}
+
+func bucketIndex(value float64, scale int32) int32 {
+	return math.Log(value) * math.Ldexp(math.Log2E, scale)
+}
+```
+
+The best scale is uniquely determined when `maxSize/2 <
+bucketsNeeded(minValue, maxValue, scale) <= maxSize`.  This
+implementation maintains the best scale by rescaling as needed to stay
+within the maximum size.
+
+## Layout
 
 ### Mapping function
 
+The `mapping` sub-package contains the equations specified in the [data
+model for Exponential Histogram data
+points](https://github.com/open-telemetry/opentelemetry-specification/blob/main/specification/metrics/data-model.md#exponentialhistogram).
+
 There are two mapping functions used, depending on the sign of the
 scale.  Negative and zero scales use the `mapping/exponent` mapping
 function, which computes the bucket index directly from the bits of
@@ -25,3 +58,158 @@ function is used with `0 < scale <= 20`.  The maximum scale is
 selected because at scale 21, simply, it becomes difficult to test
 correctness--at this point `math.MaxFloat64` maps to index
 `math.MaxInt32` and the `math/big` logic used in testing breaks down.
+
+### Data structure
+
+The `structure` sub-package contains a Histogram aggregator for use by
+the OpenTelemetry-Go Metrics SDK as well as OpenTelemetry Collector
+receivers, processors, and exporters.
+
+## Implementation
+
+The implementation maintains a slice of buckets and grows the array in
+size only as necessary given the actual range of values, up to the
+maximum size.  The structure of a single range of buckets is:
+
+```golang
+type buckets struct {
+	backing    bucketsVarwidth[T]  // for T = uint8 | uint16 | uint32 | uint64
+	indexBase  int32
+	indexStart int32
+	indexEnd   int32
+}
+```
+
+The `backing` field is a generic slice of `[]uint8`, `[]uint16`,
+`[]uint32`, or `[]uint64`.
+
+The positive and negative backing arrays are independent, so the
+maximum space used for `buckets` by one `Aggregator` is twice the
+configured maximum size.
+
+### Backing array
+
+The backing array is circular.  The first observation is counted in
+the 0th index of the backing array and the initial bucket number is
+stored in `indexBase`.  After the initial observation, the backing
+array grows in either direction (i.e., larger or smaller bucket
+numbers), until rescaling is necessary.  This mechanism allows the
+histogram to maintain the ideal scale without shifting values inside
+the array.
+
+The `indexStart` and `indexEnd` fields store the current minimum and
+maximum bucket number.  The initial conditition is `indexBase ==
+indexStart == indexEnd`, representing a single bucket.
+
+Following the first observation, new observations may fall into a
+bucket up to `size-1` in either direction.  Growth is possible by
+adjusting either `indexEnd` or `indexStart` as long as the constraint
+`indexEnd-indexStart < size` remains true.
+
+Bucket numbers in the range `[indexBase, indexEnd]` are stored in the
+interval `[0, indexEnd-indexBase+1]` of the backing array.  Buckets in
+the range `[indexStart, indexBase-1]` are stored in the interval
+`[size+indexStart-indexBase, size-1]` of the backing array.
+
+Considering the `aggregation.Buckets` interface, `Offset()` returns
+`indexStart`, `Len()` returns `indexEnd-indexStart+1`, and `At()`
+locates the correct bucket in the circular array.
+
+### Determining change of scale
+
+The algorithm used to determine the (best) change of scale when a new
+value arrives is:
+
+```golang
+func newScale(minIndex, maxIndex, scale, maxSize int32) int32 {
+    return scale - changeScale(minIndex, maxIndex, scale, maxSize)
+}
+
+func changeScale(minIndex, maxIndex, scale, maxSize int32) int32 {
+    var change int32
+    for maxIndex - minIndex >= maxSize {
+	   maxIndex >>= 1
+	   minIndex >>= 1
+	   change++
+    }
+	return change
+}
+```
+
+The `changeScale` function is also used to determine how many bits to
+shift during `Merge`.
+
+### Downscale function
+
+The downscale function rotates the circular backing array so that
+`indexStart == indexBase`, using the "3 reversals" method, before
+combining the buckets in place.
+
+### Merge function
+
+`Merge` first calculates the correct final scale by comparing the
+combined positive and negative ranges.  The destination aggregator is
+then downscaled, if necessary, and the `UpdateByIncr` code path to add
+the source buckets to the destination buckets.
+
+### Scale function
+
+The `Scale` function returns the current scale of the histogram.
+
+If the scale is variable and there are no non-zero values in the
+histogram, the scale is zero by definition; when there is only a
+single value in this case, its scale is MinScale (20) by definition.
+
+If the scale is fixed because of range limits, the fixed scale will be
+returned even for any size histogram.
+
+### Handling subnormal values
+
+Subnormal values are those in the range [0x1p-1074, 0x1p-1022), these
+being numbers that "gradually underflow" and use less than 52 bits of
+precision in the significand at the smallest representable exponent
+(i.e., -1022).  Subnormal numbers present special challenges for both
+the exponent- and logarithm-based mapping function, and to avoid
+additional complexity induced by corner cases, subnormal numbers are
+rounded up to 0x1p-1022 in this implementation.
+
+Handling subnormal numbers is difficult for the logarithm mapping
+function because Golang's `math.Log()` function rounds subnormal
+numbers up to 0x1p-1022.  Handling subnormal numbers is difficult for
+the exponent mapping function because Golang's `math.Frexp()`, the
+natural API for extracting a value's base-2 exponent, also rounds
+subnormal numbers up to 0x1p-1022.
+
+While the additional complexity needed to correctly map subnormal
+numbers is small in both cases, there are few real benefits in doing
+so because of the inherent loss of precision.  As secondary
+motivation, clamping values to the range [0x1p-1022, math.MaxFloat64]
+increases symmetry. This limit means that minimum bucket index and the
+maximum bucket index have similar magnitude, which helps support
+greater maximum scale.  Supporting numbers smaller than 0x1p-1022
+would mean changing the valid scale interval to [-11,19] compared with
+[-10,20].
+
+### UpdateByIncr interface
+
+The OpenTelemetry metrics SDK `Aggregator` type supports an `Update()`
+interface which implies updating the histogram by a count of 1.  This
+implementation also supports `UpdateByIncr()`, which makes it possible
+to support counting multiple observations in a single API call.  This
+extension is useful in applying `Histogram` aggregation to _sampled_
+metric events (e.g. in the [OpenTelemetry statsd
+receiver](https://github.com/open-telemetry/opentelemetry-collector-contrib/tree/main/receiver/statsdreceiver)).
+
+Another use for `UpdateByIncr` is in a Span-to-metrics pipeline
+following [probability sampling in OpenTelemetry tracing
+(WIP)](https://github.com/open-telemetry/opentelemetry-specification/pull/2047).
+
+## Acknowledgements
+
+This implementation is based on work by [Yuke
+Zhuge](https://github.com/yzhuge) and [Otmar
+Ertl](https://github.com/oertl).  See
+[NrSketch](https://github.com/newrelic-experimental/newrelic-sketch-java/blob/1ce245713603d61ba3a4510f6df930a5479cd3f6/src/main/java/com/newrelic/nrsketch/indexer/LogIndexer.java)
+and
+[DynaHist](https://github.com/dynatrace-oss/dynahist/blob/9a6003fd0f661a9ef9dfcced0b428a01e303805e/src/main/java/com/dynatrace/dynahist/layout/OpenTelemetryExponentialBucketsLayout.java)
+repositories for more detail.

sdk/metric/aggregator/exponential/structure/config.go

@@ -0,0 +1,97 @@
+// Copyright The OpenTelemetry Authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package structure // import "go.opentelemetry.io/otel/sdk/metric/aggregator/exponential/structure"
+
+import "fmt"
+
+// DefaultMaxSize is the default maximum number of buckets per
+// positive or negative number range.  The value 160 is specified by
+// OpenTelemetry--yields a maximum relative error of less than 5% for
+// data with contrast 10**5 (e.g., latencies in the range 1ms to 100s).
+// See the derivation here:
+// https://github.com/open-telemetry/opentelemetry-specification/blob/main/specification/metrics/sdk.md#exponential-bucket-histogram-aggregation
+const DefaultMaxSize int32 = 160
+
+// MinSize is the smallest reasonable configuration, which is small
+// enough to contain the entire normal floating point range at
+// MinScale.
+const MinSize = 2
+
+// MaximumMaxSize is an arbitrary limit meant to limit accidental use
+// of giant histograms.
+const MaximumMaxSize = 16384
+
+// Config contains configuration for exponential histogram creation.
+type Config struct {
+	maxSize int32
+}
+
+// Option is the interface that applies a configuration option.
+type Option interface {
+	// apply sets the Option value of a config.
+	apply(Config) Config
+}
+
+// WithMaxSize sets
+func WithMaxSize(size int32) Option {
+	return maxSize(size)
+}
+
+// maxSize is an option to set the maximum histogram size.
+type maxSize int32
+
+// apply implements Option.
+func (ms maxSize) apply(cfg Config) Config {
+	cfg.maxSize = int32(ms)
+	return cfg
+}
+
+// NewConfig returns an exponential histogram configuration with
+// defaults and limits applied.
+func NewConfig(opts ...Option) Config {
+	var cfg Config
+	for _, opt := range opts {
+		cfg = opt.apply(cfg)
+	}
+	return cfg
+}
+
+// Validate returns true for valid configurations.
+func (c Config) Valid() bool {
+	_, err := c.Validate()
+	return err == nil
+}
+
+// Validate returns the nearest valid Config object to th einput and a
+// boolean indicating whether the the input was a valid
+// configurations.
+func (c Config) Validate() (Config, error) {
+	if c.maxSize >= MinSize && c.maxSize <= MaximumMaxSize {
+		return c, nil
+	}
+	if c.maxSize == 0 {
+		c.maxSize = DefaultMaxSize
+		return c, nil
+	}
+	err := fmt.Errorf("invalid histogram size: %d", c.maxSize)
+	if c.maxSize < 0 {
+		c.maxSize = DefaultMaxSize
+	} else if c.maxSize < MinSize {
+		c.maxSize = MinSize
+	} else if c.maxSize > MaximumMaxSize {
+		c.maxSize = MaximumMaxSize
+	}
+	return c, err
+}

sdk/metric/aggregator/exponential/structure/config_test.go

@@ -0,0 +1,33 @@
+// Copyright The OpenTelemetry Authors
+//
+// Licensed under the Apache License, Version 2.0 (the "License");
+// you may not use this file except in compliance with the License.
+// You may obtain a copy of the License at
+//
+//     http://www.apache.org/licenses/LICENSE-2.0
+//
+// Unless required by applicable law or agreed to in writing, software
+// distributed under the License is distributed on an "AS IS" BASIS,
+// WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
+// See the License for the specific language governing permissions and
+// limitations under the License.
+
+package structure // import "go.opentelemetry.io/otel/sdk/metric/aggregator/exponential/structure"
+
+import (
+	"testing"
+
+	"github.com/stretchr/testify/require"
+)
+
+func TestConfigValid(t *testing.T) {
+	require.True(t, Config{}.Valid())
+	require.True(t, NewConfig().Valid())
+	require.True(t, NewConfig(WithMaxSize(MinSize)).Valid())
+	require.True(t, NewConfig(WithMaxSize(MaximumMaxSize)).Valid())
+	require.True(t, NewConfig(WithMaxSize((MinSize+MaximumMaxSize)/2)).Valid())
+
+	require.False(t, NewConfig(WithMaxSize(-1)).Valid())
+	require.False(t, NewConfig(WithMaxSize(1<<20)).Valid())
+	require.False(t, NewConfig(WithMaxSize(1)).Valid())
+}