Exponential Bucket Histogram - part 1

src/OpenTelemetry/Metrics/ExponentialBucketHistogram.cs

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+// <copyright file="ExponentialBucketHistogram.cs" company="OpenTelemetry Authors">
+// 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.
+// </copyright>
+
+#if NET6_0_OR_GREATER
+
+using System;
+using System.Diagnostics;
+
+using OpenTelemetry.Internal;
+
+namespace OpenTelemetry.Metrics
+{
+    /// <summary>
+    /// Represents an exponential bucket histogram with base = 2 ^ (2 ^ (-scale)).
+    /// An exponential bucket histogram has infinite number of buckets, which are
+    /// identified by <c>Bucket[i] = ( base ^ i, base ^ (i + 1) ]</c>, where <c>i</c>
+    /// is an integer.
+    /// </summary>
+    internal class ExponentialBucketHistogram
+    {
+        private static readonly double Log2E = Math.Log2(Math.E); // 1 / Math.Log(2)
+
+        private int scale;
+        private double scalingFactor; // 2 ^ scale / log(2)
+
+        public ExponentialBucketHistogram(int scale, int maxBuckets = 160)
+        {
+            Guard.ThrowIfOutOfRange(scale, min: -20, max: 20); // TODO: calculate the actual range
+
+            this.Scale = scale;
+        }
+
+        internal int Scale
+        {
+            get
+            {
+                return this.scale;
+            }
+
+            private set
+            {
+                this.scale = value;
+                this.scalingFactor = Math.ScaleB(Log2E, value);
+            }
+        }
+
+        internal long ZeroCount { get; private set; }
+
+        /// <inheritdoc/>
+        public override string ToString()
+        {
+            return nameof(ExponentialBucketHistogram)
+                + "{"
+                + nameof(this.Scale) + "=" + this.Scale
+                + "}";
+        }
+
+        public int MapToIndex(double value)
+        {
+            Debug.Assert(value != 0, "IEEE-754 zero values should be handled by ZeroCount.");
+
+            // TODO: handle +Inf, -Inf, NaN
+
+            value = Math.Abs(value);
+
+            if (this.Scale > 0)
+            {
+                // TODO: due to precision issue, the values that are close to the bucket
+                // boundaries should be closely examined to avoid off-by-one.
+                return (int)Math.Ceiling(Math.Log(value) * this.scalingFactor) - 1;
+            }
+            else
+            {
+                var bits = BitConverter.DoubleToInt64Bits(value);
+                var exp = (int)((bits & IEEE754Double.EXPONENT_MASK) >> IEEE754Double.FRACTION_BITS);
+                var fraction = bits & IEEE754Double.FRACTION_MASK;
+
+                if (exp == 0)
+                {
+                    // TODO: benchmark and see if this should be changed to a lookup table.
+                    fraction--;
+
+                    for (int i = IEEE754Double.FRACTION_BITS - 1; i >= 0; i--)
+                    {
+                        if ((fraction >> i) != 0)
+                        {
+                            break;
+                        }
+
+                        exp--;
+                    }
+                }
+                else if (fraction == 0)
+                {
+                    exp--;
+                }
+
+                return (exp - IEEE754Double.EXPONENT_BIAS) >> -this.Scale;
+            }
+        }
+
+        public sealed class IEEE754Double
+        {
+#pragma warning disable SA1310 // Field name should not contain an underscore
+            internal const int EXPONENT_BIAS = 1023;
+            internal const long EXPONENT_MASK = 0x7FF0000000000000L;
+            internal const int FRACTION_BITS = 52;
+            internal const long FRACTION_MASK = 0xFFFFFFFFFFFFFL;
+#pragma warning restore SA1310 // Field name should not contain an underscore
+
+            public static string ToString(double value)
+            {
+                var repr = Convert.ToString(BitConverter.DoubleToInt64Bits(value), 2);
+                return new string('0', 64 - repr.Length) + repr + ":" + "(" + value + ")";
+            }
+        }
+    }
+}
+
+#endif

src/OpenTelemetry/Metrics/ExponentialBucketHistogramConfiguration.cs

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+// <copyright file="ExponentialBucketHistogramConfiguration.cs" company="OpenTelemetry Authors">
+// 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.
+// </copyright>
+
+namespace OpenTelemetry.Metrics
+{
+    /// <summary>
+    /// Stores configuration for a histogram metric stream with exponential bucket boundaries.
+    /// </summary>
+    internal class ExponentialBucketHistogramConfiguration : MetricStreamConfiguration
+    {
+        /// <summary>
+        /// Gets or sets the maximum number of buckets in each of the positive and negative ranges, not counting the special zero bucket.
+        /// </summary>
+        /// <remarks>
+        /// The default value is 160.
+        /// </remarks>
+        public int MaxSize { get; set; } = 160;
+    }
+}

test/OpenTelemetry.Tests/Metrics/ExponentialBucketHistogramTest.cs

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+// <copyright file="ExponentialBucketHistogramTest.cs" company="OpenTelemetry Authors">
+// 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.
+// </copyright>
+
+#if NET6_0_OR_GREATER
+
+using System;
+using Xunit;
+
+namespace OpenTelemetry.Metrics.Tests
+{
+    public class ExponentialBucketHistogramTest
+    {
+        [Fact]
+        public void IndexLookup()
+        {
+            // An exponential bucket histogram with scale = 0.
+            // The base is 2 ^ (2 ^ -0) = 2.
+            // The buckets are:
+            //
+            // ...
+            // bucket[-3]: (1/8, 1/4]
+            // bucket[-2]: (1/4, 1/2]
+            // bucket[-1]: (1/2, 1]
+            // bucket[0]:  (1, 2]
+            // bucket[1]:  (2, 4]
+            // bucket[2]:  (4, 8]
+            // bucket[3]:  (8, 16]
+            // ...
+
+            var histogram_scale0 = new ExponentialBucketHistogram(0);
+
+            Assert.Equal(-1075, histogram_scale0.MapToIndex(double.Epsilon));
+
+            Assert.Equal(-1074, histogram_scale0.MapToIndex(double.Epsilon * 2));
+
+            Assert.Equal(-1073, histogram_scale0.MapToIndex(double.Epsilon * 3));
+            Assert.Equal(-1073, histogram_scale0.MapToIndex(double.Epsilon * 4));
+
+            Assert.Equal(-1072, histogram_scale0.MapToIndex(double.Epsilon * 5));
+            Assert.Equal(-1072, histogram_scale0.MapToIndex(double.Epsilon * 6));
+            Assert.Equal(-1072, histogram_scale0.MapToIndex(double.Epsilon * 7));
+            Assert.Equal(-1072, histogram_scale0.MapToIndex(double.Epsilon * 8));
+
+            Assert.Equal(-1023, histogram_scale0.MapToIndex(2.2250738585072009E-308));
+            Assert.Equal(-1023, histogram_scale0.MapToIndex(2.2250738585072014E-308));
+
+            Assert.Equal(-3, histogram_scale0.MapToIndex(0.25));
+
+            Assert.Equal(-2, histogram_scale0.MapToIndex(0.375));
+            Assert.Equal(-2, histogram_scale0.MapToIndex(0.5));
+
+            Assert.Equal(-1, histogram_scale0.MapToIndex(0.75));
+            Assert.Equal(-1, histogram_scale0.MapToIndex(1));
+
+            Assert.Equal(0, histogram_scale0.MapToIndex(1.5));
+            Assert.Equal(0, histogram_scale0.MapToIndex(2));
+
+            Assert.Equal(1, histogram_scale0.MapToIndex(3));
+            Assert.Equal(1, histogram_scale0.MapToIndex(4));
+
+            Assert.Equal(2, histogram_scale0.MapToIndex(5));
+            Assert.Equal(2, histogram_scale0.MapToIndex(6));
+            Assert.Equal(2, histogram_scale0.MapToIndex(7));
+            Assert.Equal(2, histogram_scale0.MapToIndex(8));
+
+            Assert.Equal(3, histogram_scale0.MapToIndex(9));
+            Assert.Equal(3, histogram_scale0.MapToIndex(16));
+
+            Assert.Equal(4, histogram_scale0.MapToIndex(17));
+            Assert.Equal(4, histogram_scale0.MapToIndex(32));
+
+            // An exponential bucket histogram with scale = 1.
+            // The base is 2 ^ (2 ^ -1) = sqrt(2) = 1.41421356237.
+            // The buckets are:
+            //
+            // ...
+            // bucket[-3]: (0.35355339059, 1/2]
+            // bucket[-2]: (1/2, 0.70710678118]
+            // bucket[-1]: (0.70710678118, 1]
+            // bucket[0]:  (1, 1.41421356237]
+            // bucket[1]:  (1.41421356237, 2]
+            // bucket[2]:  (2, 2.82842712474]
+            // bucket[3]:  (2.82842712474, 4]
+            // ...
+
+            var histogram_scale1 = new ExponentialBucketHistogram(1);
+
+            Assert.Equal(-3, histogram_scale1.MapToIndex(0.5));
+
+            Assert.Equal(-2, histogram_scale1.MapToIndex(0.6));
+
+            Assert.Equal(-1, histogram_scale1.MapToIndex(1));
+
+            Assert.Equal(1, histogram_scale1.MapToIndex(2));
+
+            Assert.Equal(3, histogram_scale1.MapToIndex(4));
+        }
+    }
+}
+
+#endif