Restore the exponential mapping functions

sdk/metric/metricdata/exponential/README.md

@@ -0,0 +1,32 @@
+# Base-2 Exponential Histogram
+
+## Design
+
+This document is a placeholder for the future when this directory
+contains both the mapping and data structure of the OpenTelemetry
+Exponential Histogram.  The complete prototype for this data structure
+and the SDK integration has been seen in draft PRs
+[2393](https://github.com/open-telemetry/opentelemetry-go/pull/2393),
+[3022](https://github.com/open-telemetry/opentelemetry-go/pull/3022),
+and [3174](https://github.com/open-telemetry/opentelemetry-go/pull/3174).
+
+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).
+
+### 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/metricdata/exponential/mapping/exponent/exponent.go

@@ -0,0 +1,127 @@
+// 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/metricdata/exponential/mapping/exponent"
+
+import (
+	"fmt"
+	"math"
+
+	"go.opentelemetry.io/otel/sdk/metric/metricdata/exponential/mapping"
+	"go.opentelemetry.io/otel/sdk/metric/metricdata/exponential/mapping/internal"
+)
+
+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
+}
+
+// minNormalLowerBoundaryIndex is the largest index such that
+// base**index is <= MinValue.  A histogram bucket with this index
+// covers the range (base**index, base**(index+1)], including
+// MinValue.
+func (e *exponentMapping) minNormalLowerBoundaryIndex() int32 {
+	idx := int32(internal.MinNormalExponent) >> e.shift
+	if e.shift < 2 {
+		// For scales -1 and 0 the minimum value 2**-1022
+		// is a power-of-two multiple, meaning it belongs
+		// to the index one less.
+		idx--
+	}
+	return idx
+}
+
+// maxNormalLowerBoundaryIndex is the index such that base**index
+// equals the largest representable boundary.  A histogram bucket with this
+// index covers the range (0x1p+1024/base, 0x1p+1024], which includes
+// MaxValue; note that this bucket is incomplete, since the upper
+// boundary cannot be represented.  One greater than this index
+// corresponds with the bucket containing values > 0x1p1024.
+func (e *exponentMapping) maxNormalLowerBoundaryIndex() int32 {
+	return int32(internal.MaxNormalExponent) >> e.shift
+}
+
+// MapToIndex implements mapping.Mapping.
+func (e *exponentMapping) MapToIndex(value float64) int32 {
+	// Note: we can assume not a 0, Inf, or NaN; positive sign bit.
+	if value < internal.MinValue {
+		return e.minNormalLowerBoundaryIndex()
+	}
+
+	// Extract the raw exponent.
+	rawExp := internal.GetNormalBase2(value)
+
+	// In case the value is an exact power of two, compute a
+	// correction of -1:
+	correction := int32((internal.GetSignificand(value) - 1) >> internal.SignificandWidth)
+
+	// Note: bit-shifting does the right thing for negative
+	// exponents, e.g., -1 >> 1 == -1.
+	return (rawExp + correction) >> e.shift
+}
+
+// LowerBoundary implements mapping.Mapping.
+func (e *exponentMapping) LowerBoundary(index int32) (float64, error) {
+	if min := e.minNormalLowerBoundaryIndex(); index < min {
+		return 0, mapping.ErrUnderflow
+	}
+
+	if max := e.maxNormalLowerBoundaryIndex(); index > max {
+		return 0, mapping.ErrOverflow
+	}
+
+	return math.Ldexp(1, int(index<<e.shift)), nil
+}
+
+// Scale implements mapping.Mapping.
+func (e *exponentMapping) Scale() int32 {
+	return -int32(e.shift)
+}