Combine multiple commits.

.circleci/config.yml

@@ -0,0 +1,16 @@
+version: 2
+
+jobs:
+  test:
+    working_directory: ~/go/src/github.com/lightstep/varopt
+    docker:
+      - image: circleci/golang:1.15
+    steps:
+      - checkout
+      - run: go test -v ./...
+
+workflows:
+  version: 2
+  test:
+    jobs:
+      - test

LICENSE

@@ -0,0 +1,201 @@
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README.md

@@ -1,3 +1,58 @@
+[![Docs](https://godoc.org/github.com/lightstep/varopt?status.svg)](https://godoc.org/github.com/lightstep/varopt)
+
+# VarOpt Sampling Algorithm
+
 This is an implementation of VarOpt, an unbiased weighted sampling
 algorithm described in the paper [Stream sampling for variance-optimal
-estimation of subset sums](https://arxiv.org/pdf/0803.0473.pdf).
+estimation of subset sums](https://arxiv.org/pdf/0803.0473.pdf) (2008)
+by Edith Cohen, Nick Duffield, Haim Kaplan, Carsten Lund, and Mikkel
+Thorup.
+
+VarOpt is a reservoir-type sampler that maintains a fixed-size sample
+and provides a mechanism for merging unequal-weight samples.
+
+This repository also includes a simple reservoir sampling algorithm,
+often useful in conjunction with weighed reservoir sampling, that
+implements Algorithm R from [Random sampling with a
+reservoir](https://en.wikipedia.org/wiki/Reservoir_sampling#Algorithm_R)
+(1985) by Jeffrey Vitter.
+
+## Usage: Natural Weights
+
+A typical use of VarOpt sampling is to estimate network flows using
+sample packets.  In this use-case, the weight applied to each sample
+is the size of the packet.  Because VarOpt computes an unbiased
+sample, sample data points can be summarized along secondary
+dimensions.  For example, we can select a subset of sampled packets
+according to a secondary attribute, sum the sample weights, and the
+result is expected to equal the size of packets corresponding to the
+secondary attribute from the original population.
+
+See [weighted_test.go](https://github.com/lightstep/varopt/blob/master/weighted_test.go) for an example.
+
+## Usage: Inverse-probability Weights
+
+Another use for VarOpt sampling uses inverse-probability weights to
+estimate frequencies while simultaneously controlling sample
+diversity.  Suppose a sequence of observations can be naturally
+categorized into N different buckets.  The goal in this case is to
+compute a sample where each bucket is well represented, while
+maintaining frequency estimates.
+
+In this use-case, the weight assigned to each observation is the
+inverse probability of the bucket it belongs to.  The result of
+weighted sampling with inverse-probability weights is a uniform
+expectated value; in this example we expect an equal number of
+observations falling into each bucket.  Each observation represents a
+frequency of its sample weight (computed by VarOpt) divided by its
+original weight (the inverse-probability).
+
+See [frequency_test.go](https://github.com/lightstep/varopt/blob/master/frequency_test.go) for an example.
+
+## Usage: Merging Samples
+
+VarOpt supports merging independently collected samples one
+observation at a time.  This is useful for building distributed
+sampling schemes.  In this use-case, each node in a distributed system
+computes a weighted sample.  To combine samples, simply input all the
+observations and their corresponding weights into a new VarOpt sample.

benchmark_test.go

@@ -0,0 +1,72 @@
+// Copyright 2019, LightStep Inc.
+//
+// The benchmark results point to a performance drop when the
+// largeHeap starts to be used because of interface conversions in and
+// out of the heap, primarily due to the heap interface.  This
+// suggests room for improvement by avoiding the built-in heap.
+
+/*
+BenchmarkAdd_Norm_100-8       	37540165	        32.1 ns/op	       8 B/op	       0 allocs/op
+BenchmarkAdd_Norm_10000-8     	39850280	        30.6 ns/op	       8 B/op	       0 allocs/op
+BenchmarkAdd_Norm_1000000-8   	 7958835	       183 ns/op	      52 B/op	       0 allocs/op
+BenchmarkAdd_Exp_100-8        	41565934	        28.5 ns/op	       8 B/op	       0 allocs/op
+BenchmarkAdd_Exp_10000-8      	43622184	        29.2 ns/op	       8 B/op	       0 allocs/op
+BenchmarkAdd_Exp_1000000-8    	 8103663	       220 ns/op	      55 B/op	       0 allocs/op
+*/
+
+package varopt_test
+
+import (
+	"math"
+	"math/rand"
+	"testing"
+
+	"github.com/lightstep/varopt"
+)
+
+func normValue(rnd *rand.Rand) float64 {
+	return 1 + math.Abs(rnd.NormFloat64())
+}
+
+func expValue(rnd *rand.Rand) float64 {
+	return rnd.ExpFloat64()
+}
+
+func BenchmarkAdd_Norm_100(b *testing.B) {
+	benchmarkAdd(b, 100, normValue)
+}
+
+func BenchmarkAdd_Norm_10000(b *testing.B) {
+	benchmarkAdd(b, 10000, normValue)
+}
+
+func BenchmarkAdd_Norm_1000000(b *testing.B) {
+	benchmarkAdd(b, 1000000, normValue)
+}
+
+func BenchmarkAdd_Exp_100(b *testing.B) {
+	benchmarkAdd(b, 100, expValue)
+}
+
+func BenchmarkAdd_Exp_10000(b *testing.B) {
+	benchmarkAdd(b, 10000, expValue)
+}
+
+func BenchmarkAdd_Exp_1000000(b *testing.B) {
+	benchmarkAdd(b, 1000000, expValue)
+}
+
+func benchmarkAdd(b *testing.B, size int, f func(rnd *rand.Rand) float64) {
+	b.ReportAllocs()
+	rnd := rand.New(rand.NewSource(3331))
+	v := varopt.New(size, rnd)
+	weights := make([]float64, b.N)
+	for i := 0; i < b.N; i++ {
+		weights[i] = f(rnd)
+	}
+
+	b.StartTimer()
+	for i := 0; i < b.N; i++ {
+		v.Add(nil, weights[i])
+	}
+}

doc.go

@@ -0,0 +1,22 @@
+// Copyright 2019, LightStep Inc.
+
+/*
+Package varopt contains an implementation of VarOpt, an unbiased weighted
+sampling algorithm described in the paper "Stream sampling for
+variance-optimal estimation of subset sums"
+https://arxiv.org/pdf/0803.0473.pdf (2008), by Edith Cohen, Nick
+Duffield, Haim Kaplan, Carsten Lund, and Mikkel Thorup.
+
+VarOpt is a reservoir-type sampler that maintains a fixed-size sample
+and provides a mechanism for merging unequal-weight samples.
+
+This package also includes a simple reservoir sampling algorithm,
+often useful in conjunction with weighed reservoir sampling, using
+Algorithm R from "Random sampling with a
+reservoir", https://en.wikipedia.org/wiki/Reservoir_sampling#Algorithm_R
+(1985), by Jeffrey Vitter.
+
+See https://github.com/lightstep/varopt/blob/master/README.md for
+more detail.
+*/
+package varopt