t-digest

A Rust implementation of the t-digest data structure for accurate online accumulation of rank-based statistics such as quantiles and trimmed means, using a variant of 1-dimensional k-means clustering.

This implementation follows Facebook's folly TDigest.

Features

• Approximate quantiles with finer resolution at the tails (p99, p99.9)
• Mergeable -- combine digests computed on different machines or threads
• Compact -- retained state scales with the compression factor, rather than the number of samples
• No dependencies by default (optional serde support behind a feature flag)
• no_std + alloc support, including serde without its std feature

Installation

Add this to your Cargo.toml:

[dependencies]
tdigest = "1.0"

Optional features

Feature	Description
std	Enabled by default; disable it for no_std builds
serde	Enables Serialize/Deserialize for TDigest and Centroid
use_serde	Deprecated compatibility alias for serde

[dependencies]
tdigest = { version = "1.0", features = ["serde"] }

Quick start

use tdigest::TDigest;

// Create a digest with a compression factor of 100
let t = TDigest::new_with_size(100);

// Feed it one million values
let values: Vec<f64> = (1..=1_000_000).map(f64::from).collect();
let t = t.merge_sorted(values);

// Estimate quantiles
let p99 = t.estimate_quantile(0.99).unwrap();
let expected = 990_000.0;
assert!((expected - p99).abs() / expected < 0.01);

Usage

Creating a digest

use tdigest::TDigest;

// With explicit compression factor (controls accuracy vs. memory)
let t = TDigest::new_with_size(100);

// With default settings (max_size = 100)
let t = TDigest::default();

Adding data

use tdigest::TDigest;

let t = TDigest::new_with_size(100);

// Pre-sorted data (fastest)
let sorted = vec![1.0, 2.0, 3.0, 4.0, 5.0];
let t = t.merge_sorted(sorted);

// Unsorted data (sorts internally)
let unsorted = vec![5.0, 3.0, 1.0, 4.0, 2.0];
let t = t.merge_unsorted(unsorted);

merge_sorted requires ascending input. Use merge_unsorted when the order is unknown. Both methods borrow the existing digest and return a new one; keep the returned value to retain the inserted data.

For streaming ingestion, use the buffered mutable API and flush before a centroid-based query:

use tdigest::TDigest;

let mut t = TDigest::new_with_size(100);
for value in [5.0, 3.0, 1.0, 4.0, 2.0] {
    t.push(value);
}
t.flush();
assert_eq!(t.estimate_quantile(0.5), Some(3.0));

push, extend_values, and the standard Extend<f64> implementation update count, sum, mean, min, max, and is_empty immediately. Call flush before estimate_quantile, quantiles, estimate_rank, trimmed_mean, centroids, immutable merges, or serialization. Automatic compression happens when the buffer fills, so a partially filled buffer still needs an explicit flush.

Collecting an iterator creates a digest with the default compression factor and flushes it before returning:

use tdigest::TDigest;

let t: TDigest = [5.0, 1.0, 3.0].into_iter().collect();
assert_eq!(t.estimate_quantile(0.5), Some(3.0));

Querying

use tdigest::TDigest;

let t = TDigest::new_with_size(100);
let t = t.merge_sorted(vec![1.0, 2.0, 3.0, 4.0, 5.0]);

// Returns None for empty digests, Some(value) otherwise
let median = t.estimate_quantile(0.5);  // ~3.0
let min    = t.min();                    // Some(1.0)
let max    = t.max();                    // Some(5.0)
let mean   = t.mean();                   // Some(3.0)
let count  = t.count();                  // 5.0
let sum    = t.sum();                    // 15.0

// Estimate several quantiles in one call; input order is preserved
let percentiles = t.quantiles(&[0.5, 0.9, 0.99]);

// Approximate CDF and the mean of the middle 80% of the distribution
let rank = t.estimate_rank(3.0);
let middle_mean = t.trimmed_mean(0.1, 0.9);

Quantiles at or below 0 return the minimum; quantiles at or above 1 return the maximum. trimmed_mean clamps its bounds to [0, 1] and returns None for an empty interval or NaN bound. Rank and trimmed-mean queries also return None for empty digests. These queries interpolate compressed data and need not match an exact sample percentile or empirical CDF.

Merging digests (distributed / parallel use)

use tdigest::TDigest;

// Build digests independently (e.g. on different threads)
let data: Vec<f64> = (1..=10_000).map(f64::from).collect();
let mut digests = Vec::new();
for chunk in data.chunks(1000) {
    let t = TDigest::new_with_size(100);
    let t = t.merge_unsorted(chunk.to_vec());
    digests.push(t);
}

// Merge into a single digest
let combined = TDigest::merge_digests(digests);
let p99 = combined.estimate_quantile(0.99);

Flush any digests built with mutable ingestion before merging. The result uses the largest input max_size; an empty input vector produces an empty digest with the default size of 100. Repeated merging can change estimates, so measure accuracy with the merge pattern used by your application.

Serialization (serde)

Enable the serde feature, then use any serde-compatible format. The deprecated use_serde alias remains available for existing users.

use tdigest::TDigest;

let t = TDigest::new_with_size(100);
let t = t.merge_sorted(vec![1.0, 2.0, 3.0]);

let json = serde_json::to_string(&t).unwrap();
let restored: TDigest = serde_json::from_str(&json).unwrap();

To run this JSON example with exact finite-float round trips, add serde_json = { version = "1.0", features = ["float_roundtrip"] } to your dependencies. Without that feature, JSON parsing can introduce small rounding differences in centroid values.

The pending ingestion buffer is omitted from serialization. Always call flush after mutable ingestion: serializing without it succeeds but loses pending samples while retaining their summary statistics. Deserialization validates centroid ordering, weights, extrema, and count consistency, and rejects inconsistent payloads such as an omitted buffer that leaves a count mismatch. The 1.0 format uses Option<f64> for min and max; data written by older versions may need migration, depending on the serialization format.

Compression factor

The positive max_size parameter controls the trade-off between accuracy and memory; zero is rejected. The default is 100.

max_size	Centroid payload (approx.)	Full ingestion buffer
50	0.8 KB	2 KB
100	1.6 KB	4 KB
200	3.2 KB	8 KB
500	8 KB	20 KB

Each centroid holds two f64 values (16 bytes); the streaming buffer holds up to 5 * max_size values (8 bytes each), allocated on the first mutable insertion and reused after flushing. Batch-only digests do not allocate this buffer. These are payload estimates in decimal KB, excluding the digest struct, spare vector capacity, allocator overhead, input vectors, and temporary storage during merges. max_size is a compression target, not an exact byte budget.

Larger values generally improve accuracy at the cost of more memory and merge work. Start with the default of 100, then measure on your own distribution.

Input and numeric limits

Inserted values must be finite. NaN and positive or negative infinity violate the ingestion contract: debug builds reject them, while release-build estimates are unspecified. NaN also violates the contract for estimate_quantile, quantiles, and estimate_rank; trimmed_mean instead returns None for a NaN bound.

Counts and sums use f64. Integer counts are exact only through 2^53, and a sum of finite values can overflow to infinity or NaN. mean normally computes sum / count; when the sum is non-finite, it falls back to an approximate weighted mean of the centroids and pending values. This fallback takes linear time in the retained state. sum remains non-finite: formats such as JSON cannot round-trip that value. Scale inputs when you need a finite sum or JSON storage.

Minimum Supported Rust Version (MSRV)

Rust 1.62 -- verified in CI.

no_std

Disable default features to use the crate with alloc but without std:

[dependencies]
tdigest = { version = "1.0", default-features = false }

Serde also works in this configuration by adding features = ["serde"].

Accuracy

Run cargo run --release --example accuracy to compare estimated and exact quantiles across deterministic uniform, normal, lognormal, exponential, bimodal, and adversarial distributions. See architecture and internals for a summary of the measured error profile.

The crate does not provide a distribution-independent error bound. Tail resolution improves with compression size, but skew, repeated values, gaps in the distribution, batch boundaries, and merge order can affect estimates.

Benchmarks

Run cargo bench to measure sorted and unsorted batch ingestion, incremental ingestion, digest merging, quantile queries, and compression-size sensitivity. The benchmark inputs use fixed random seeds so results can be compared across changes. Run cargo run --release --example accuracy for the accuracy harness.

Documentation

• API docs on docs.rs
• Architecture and internals

License

Apache-2.0 -- see LICENSE for details.