Fast approximate quantiles in Go
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This is a Go implementation of Ted Dunning's t-digest, which is a clever data structure/algorithm for computing approximate quantiles of a stream of data.

You should use this if you want to efficiently compute extreme rank statistics of a large stream of data, like the 99.9th percentile.


An example is available in the Godoc which shows the API:

func ExampleTDigest() {
	values := make(chan float64)

	// Generate 100k uniform random data between 0 and 100
	var (
		n        int     = 100000
		min, max float64 = 0, 100
	go func() {
		for i := 0; i < n; i++ {
			values <- min + rand.Float64()*(max-min)

	// Pass the values through a TDigest.
	td := New()

	for val := range values {
		// Add the value with weight 1
		td.Add(val, 1)

	// Print the 50th, 90th, 99th, 99.9th, and 99.99th percentiles
	fmt.Printf("50th: %.5f\n", td.Quantile(0.5))
	fmt.Printf("90th: %.5f\n", td.Quantile(0.9))
	fmt.Printf("99th: %.5f\n", td.Quantile(0.99))
	fmt.Printf("99.9th: %.5f\n", td.Quantile(0.999))
	fmt.Printf("99.99th: %.5f\n", td.Quantile(0.9999))
	// Output:
	// 50th: 48.74854
	// 90th: 89.79825
	// 99th: 98.92954
	// 99.9th: 99.90189
	// 99.99th: 99.98740


For example, in the Real World, the stream of data might be service timings, measuring how long a server takes to respond to clients. You can feed this stream of data through a t-digest and get out approximations of any quantile you like: the 50th percentile or 95th percentile or 99th or 99.99th or 28.31th are all computable.

Exact quantiles would require that you hold all the data in memory, but the t-digest can hold a small fraction - often just a few kilobytes to represent many millions of datapoints. Measurements of the compression ratio show that compression improves super-linearly as more datapoints are fed into the t-digest.

How good are the approximations? Well, it depends, but they tend to be quite good, especially out towards extreme percentiles like the 99th or 99.9th; Ted Dunning found errors of just a few parts per million at the 99.9th and 0.1th percentiles.

Error will be largest in the middle - the median is the least accurate point in the t-digest.

The actual precision can be controlled with the compression parameter passed to the constructor function NewWithCompression in this package. Lower compression parameters will result in poorer compression, but will improve performance in estimating quantiles. If you care deeply about tuning such things, experiment with the compression ratio.


Data compresses well, with compression ratios of around 20 for small datasets (1k datapoints) and 500 for largeish ones (1M datapoints). The precise compression ratio depends a bit on your data's distribution - exponential data does well, while ordered data does poorly:

compression benchmark

In general, adding a datapoint takes about 1 to 4 microseconds on my 2014 Macbook Pro. This is fast enough for many purposes, but if you have any concern, you should just run the benchmarks on your targeted syste. You can do that with go test -bench . ./....

Quantiles are very, very quick to calculate, and typically take tens of nanoseconds. They might take up to a few hundred nanoseconds for large, poorly compressed (read: ordered) datasets, but in general, you don't have to worry about the speed of calls to Quantile.