Exponential Histogram mapping functions for public use (#2502)

* Exponential Histogram mapping functions for public use

* pr num

* Apply suggestions from code review

:+1:

Co-authored-by: Anthony Mirabella <a9@aneurysm9.com>

* mapping interface comments

* missed add

* Update CHANGELOG.md

Co-authored-by: Anthony Mirabella <a9@aneurysm9.com>
Co-authored-by: Tyler Yahn <MrAlias@users.noreply.github.com>

CHANGELOG.md

@@ -15,6 +15,10 @@ Code instrumented with the `go.opentelemetry.io/otel/metric` will need to be mod
 
 ### Added
 
+- Log the Exporters configuration in the TracerProviders message. (#2578)
+- Metrics Exponential Histogram support: Mapping functions have been made available
+  in `sdk/metric/aggregator/exponential/mapping` for other OpenTelemetry projects to take
+  dependencies on. (#2502)
 - Add go 1.18 to our compatibility tests. (#2679)
 - Allow configuring the Sampler with the `OTEL_TRACES_SAMPLER` and `OTEL_TRACES_SAMPLER_ARG` environment variables. (#2305, #2517)
 - Add the `metric/global` for obtaining and setting the global `MeterProvider` (#2660)

sdk/metric/aggregator/exponential/README.md

@@ -0,0 +1,27 @@
+# Base-2 Exponential Histogram
+
+## Design
+
+This document is a placeholder for future Aggregator, once seen in [PR
+2393](https://github.com/open-telemetry/opentelemetry-go/pull/2393).
+
+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/datamodel.md#exponentialhistogram).
+
+### Mapping function
+
+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
+the `float64` exponent.  This mapping function is used with scale `-10
+<= scale <= 0`.  Scales smaller than -10 map the entire normal
+`float64` number range into a single bucket, thus are not considered
+useful.
+
+The `mapping/logarithm` mapping function uses `math.Log(value)` times
+the scaling factor `math.Ldexp(math.Log2E, scale)`.  This mapping
+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.

sdk/metric/aggregator/exponential/mapping/exponent/exponent.go

@@ -0,0 +1,117 @@
+// 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 exponent // import "go.opentelemetry.io/otel/sdk/metric/aggregator/exponential/mapping/exponent"
+
+import (
+	"fmt"
+	"math"
+
+	"go.opentelemetry.io/otel/sdk/metric/aggregator/exponential/mapping"
+)
+
+const (
+	// MinScale defines the point at which the exponential mapping
+	// function becomes useless for float64.  With scale -10, ignoring
+	// subnormal values, bucket indices range from -1 to 1.
+	MinScale int32 = -10
+
+	// MaxScale is the largest scale supported in this code.  Use
+	// ../logarithm for larger scales.
+	MaxScale int32 = 0
+)
+
+type exponentMapping struct {
+	shift uint8 // equals negative scale
+}
+
+// exponentMapping is used for negative scales, effectively a
+// mapping of the base-2 logarithm of the exponent.
+var prebuiltMappings = [-MinScale + 1]exponentMapping{
+	{10},
+	{9},
+	{8},
+	{7},
+	{6},
+	{5},
+	{4},
+	{3},
+	{2},
+	{1},
+	{0},
+}
+
+// NewMapping constructs an exponential mapping function, used for scales <= 0.
+func NewMapping(scale int32) (mapping.Mapping, error) {
+	if scale > MaxScale {
+		return nil, fmt.Errorf("exponent mapping requires scale <= 0")
+	}
+	if scale < MinScale {
+		return nil, fmt.Errorf("scale too low")
+	}
+	return &prebuiltMappings[scale-MinScale], nil
+}
+
+// MapToIndex implements mapping.Mapping.
+func (e *exponentMapping) MapToIndex(value float64) int32 {
+	// Note: we can assume not a 0, Inf, or NaN; positive sign bit.
+
+	// Note: bit-shifting does the right thing for negative
+	// exponents, e.g., -1 >> 1 == -1.
+	return getBase2(value) >> e.shift
+}
+
+func (e *exponentMapping) minIndex() int32 {
+	return int32(MinNormalExponent) >> e.shift
+}
+
+func (e *exponentMapping) maxIndex() int32 {
+	return int32(MaxNormalExponent) >> e.shift
+}
+
+// LowerBoundary implements mapping.Mapping.
+func (e *exponentMapping) LowerBoundary(index int32) (float64, error) {
+	if min := e.minIndex(); index < min {
+		return 0, mapping.ErrUnderflow
+	}
+
+	if max := e.maxIndex(); index > max {
+		return 0, mapping.ErrOverflow
+	}
+
+	unbiased := int64(index << e.shift)
+
+	// Note: although the mapping function rounds subnormal values
+	// up to the smallest normal value, there are still buckets
+	// that may be filled that start at subnormal values.  The
+	// following code handles this correctly.  It's equivalent to and
+	// faster than math.Ldexp(1, int(unbiased)).
+	if unbiased < int64(MinNormalExponent) {
+		subnormal := uint64(1 << SignificandWidth)
+		for unbiased < int64(MinNormalExponent) {
+			unbiased++
+			subnormal >>= 1
+		}
+		return math.Float64frombits(subnormal), nil
+	}
+	exponent := unbiased + ExponentBias
+
+	bits := uint64(exponent << SignificandWidth)
+	return math.Float64frombits(bits), nil
+}
+
+// Scale implements mapping.Mapping.
+func (e *exponentMapping) Scale() int32 {
+	return -int32(e.shift)
+}