From 6e177ce868003ef6bde3d0586f49d671bbab201a Mon Sep 17 00:00:00 2001 From: randogoth Date: Sun, 25 Oct 2026 17:30:41 +0200 Subject: [PATCH] feat: add calibrated health score and survival depth --- examples/calibrate.rs | 425 +++++++++++++++++++++++++++++++++++ include/onod3000.h | 20 ++ src/bin/onod3000.rs | 103 +++++---- src/calibration/mod.rs | 280 +++++++++++++++++++++++ src/calibration/table.rs | 472 +++++++++++++++++++++++++++++++++++++++ src/ffi.rs | 67 +++++- src/lib.rs | 23 ++ src/python.rs | 27 +++ src/score.rs | 273 ++++++++++++++++++++++ 9 files changed, 1645 insertions(+), 45 deletions(-) create mode 100644 examples/calibrate.rs create mode 100644 src/calibration/mod.rs create mode 100644 src/calibration/table.rs create mode 100644 src/score.rs diff --git a/examples/calibrate.rs b/examples/calibrate.rs new file mode 100644 index 0000000..2b1f2d3 --- /dev/null +++ b/examples/calibrate.rs @@ -0,0 +1,425 @@ +// MIT License + +// Copyright (c) 2025 Tobias Raayoni Last (@randogoth) + +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions: + +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. + +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. + +//! Builds the null calibration tables in `src/calibration/table.rs`, or checks them. +//! +//! cargo run --release --example calibrate -- [--reps N] [--seed S] [--urandom] [--out PATH] [--dump PATH] +//! cargo run --release --example calibrate -- --from-dump PATH [--out PATH] +//! cargo run --release --example calibrate -- --check N [--sizes A,B,..] [--seed S] [--urandom] +//! +//! Generation runs every test on N random samples at each calibrated size and stores the +//! quantiles of the z-scores, then the quantiles of the Cauchy combination statistic. The +//! raw z-scores are dumped so the tables can be rebuilt with `--from-dump` without +//! simulating again. `--check` scores N fresh samples per size with the compiled-in +//! tables and reports how often the calibrated p-values fall below 0.05 ... 0.0001. + +use std::fs::File; +use std::io::{self, Read, Write}; +use std::sync::atomic::{AtomicUsize, Ordering}; +use std::sync::Mutex; + +use onod3000::calibration::{self, LEVELS, MAX_LOG2, MIN_LOG2, SIZES, TWO_SIDED}; +use onod3000::score::acat; +use onod3000::{Onod, TESTS}; + +const DEFAULT_REPS: usize = 20_000; +const DEFAULT_SEED: u64 = 0x0d3000; + +/// xoshiro256** seeded through SplitMix64. +struct Xoshiro([u64; 4]); + +impl Xoshiro { + fn new(seed: u64) -> Self { + let mut x = seed; + Xoshiro(std::array::from_fn(|_| { + x = x.wrapping_add(0x9e3779b97f4a7c15); + let mut z = x; + z = (z ^ (z >> 30)).wrapping_mul(0xbf58476d1ce4e5b9); + z = (z ^ (z >> 27)).wrapping_mul(0x94d049bb133111eb); + z ^ (z >> 31) + })) + } + + fn next(&mut self) -> u64 { + let s = &mut self.0; + let result = s[1].wrapping_mul(5).rotate_left(7).wrapping_mul(9); + let t = s[1] << 17; + s[2] ^= s[0]; + s[3] ^= s[1]; + s[1] ^= s[2]; + s[0] ^= s[3]; + s[2] ^= t; + s[3] = s[3].rotate_left(45); + result + } + + fn fill(&mut self, buf: &mut [u8]) { + for chunk in buf.chunks_mut(8) { + let bytes = self.next().to_le_bytes(); + chunk.copy_from_slice(&bytes[..chunk.len()]); + } + } +} + +struct Args { + reps: usize, + seed: u64, + out: String, + dump: String, + from_dump: Option, + urandom: bool, + check: Option, + sizes: Option>, +} + +fn parse_args() -> Args { + let mut args = Args { + reps: DEFAULT_REPS, + seed: DEFAULT_SEED, + out: String::from("src/calibration/table.rs"), + dump: String::from("target/calibration-runs.bin"), + from_dump: None, + urandom: false, + check: None, + sizes: None, + }; + let mut it = std::env::args().skip(1); + while let Some(arg) = it.next() { + let mut value = || it.next().unwrap_or_else(|| usage()); + match arg.as_str() { + "--reps" => args.reps = value().parse().unwrap_or_else(|_| usage()), + "--seed" => args.seed = value().parse().unwrap_or_else(|_| usage()), + "--out" => args.out = value(), + "--dump" => args.dump = value(), + "--from-dump" => args.from_dump = Some(value()), + "--check" => args.check = Some(value().parse().unwrap_or_else(|_| usage())), + "--sizes" => { + args.sizes = Some(value().split(',').map(|n| n.parse().unwrap_or_else(|_| usage())).collect()) + } + "--urandom" => args.urandom = true, + _ => usage(), + } + } + args +} + +fn usage() -> ! { + eprintln!("Usage: calibrate [--reps N] [--seed S] [--urandom] [--out PATH] [--dump PATH]"); + eprintln!(" calibrate --from-dump PATH [--out PATH]"); + eprintln!(" calibrate --check N [--sizes A,B,..] [--seed S] [--urandom]"); + std::process::exit(1); +} + +/// Fills `buf` with the random sample for repetition `rep` at size index `size`. +fn sample(buf: &mut [u8], urandom: &Option>, seed: u64, size: usize, rep: usize) { + match urandom { + Some(file) => file.lock().unwrap().read_exact(buf).expect("reading /dev/urandom"), + None => Xoshiro::new(seed ^ ((size as u64) << 40) ^ rep as u64).fill(buf), + } +} + +/// Runs `job(rep, buf)` for every repetition on all cores, collecting the results in order. +fn parallel(reps: usize, n: usize, job: impl Fn(usize, &mut [u8]) -> T + Sync) -> Vec { + let next = AtomicUsize::new(0); + let results: Mutex>> = Mutex::new((0..reps).map(|_| None).collect()); + let threads = std::thread::available_parallelism().map_or(4, |n| n.get()); + std::thread::scope(|scope| { + for _ in 0..threads { + scope.spawn(|| { + let mut buf = vec![0u8; n]; + loop { + let rep = next.fetch_add(1, Ordering::Relaxed); + if rep >= reps { + break; + } + let result = job(rep, &mut buf); + results.lock().unwrap()[rep] = Some(result); + } + }); + } + }); + results.into_inner().unwrap().into_iter().map(Option::unwrap).collect() +} + +/// Quantiles of `values` at the calibration levels (linear between order statistics). +fn quantiles(values: &mut [f64]) -> [f64; LEVELS] { + values.sort_by(f64::total_cmp); + let last = (values.len() - 1) as f64; + calibration::levels().map(|p| { + let h = p * last; + let (i, w) = (h.floor() as usize, h.fract()); + let next = values[(i + 1).min(values.len() - 1)]; + if w == 0.0 || next == values[i] { values[i] } else { values[i] + w * (next - values[i]) } + }) +} + +/// z-score and raw p of every test per repetition and size, NaN where the test skipped. +type Runs = Vec>; + +fn simulate(args: &Args, urandom: &Option>) -> Runs { + (0..SIZES) + .map(|s| { + let n = 1usize << (MIN_LOG2 as usize + s); + let started = std::time::Instant::now(); + let runs = parallel(args.reps, n, |rep, buf| { + sample(buf, urandom, args.seed, s, rep); + std::array::from_fn(|t| { + let (stat, z, p) = Onod::run(TESTS[t].1, buf); + calibration::calibration_z(t, stat, z, n).map_or((f64::NAN, f64::NAN), |z| (z, p)) + }) + }); + eprintln!("{:>8} B {} reps in {:.1} s", n, args.reps, started.elapsed().as_secs_f64()); + runs + }) + .collect() +} + +/// Dump format: header line "\n", then per size a u64 count followed by +/// count * 15 * (z, p) little-endian f64 values. +fn save_runs(path: &str, source: &str, runs: &Runs) -> io::Result<()> { + let mut out = io::BufWriter::new(File::create(path)?); + writeln!(out, "{}", source)?; + for size in runs { + out.write_all(&(size.len() as u64).to_le_bytes())?; + for run in size { + for &(z, p) in run { + out.write_all(&z.to_le_bytes())?; + out.write_all(&p.to_le_bytes())?; + } + } + } + eprintln!("Saved raw runs to {}", path); + Ok(()) +} + +fn load_runs(path: &str) -> io::Result<(String, Runs)> { + let mut data = Vec::new(); + File::open(path)?.read_to_end(&mut data)?; + let newline = data.iter().position(|&b| b == b'\n').expect("dump header"); + let source = String::from_utf8_lossy(&data[..newline]).into_owned(); + let mut pos = newline + 1; + let mut next = || { + let v = u64::from_le_bytes(data[pos..pos + 8].try_into().unwrap()); + pos += 8; + v + }; + let runs = (0..SIZES) + .map(|_| { + let count = next() as usize; + (0..count) + .map(|_| std::array::from_fn(|_| (f64::from_bits(next()), f64::from_bits(next())))) + .collect() + }) + .collect(); + Ok((source, runs)) +} + +fn generate(args: &Args, urandom: &Option>) -> io::Result<()> { + let (source, runs) = match &args.from_dump { + Some(path) => load_runs(path)?, + None => { + let source = if args.urandom { + String::from("/dev/urandom") + } else { + format!("xoshiro256** seed {:#x}", args.seed) + }; + let runs = simulate(args, urandom); + save_runs(&args.dump, &source, &runs)?; + (source, runs) + } + }; + let reps = runs[0].len(); + + let mut z_rows = vec![[[f64::NAN; LEVELS]; 15]; SIZES]; + let mut t_rows = vec![[f64::NAN; LEVELS]; SIZES]; + let mut raw_fail = vec![[f64::NAN; 15]; SIZES]; + let mut notes = Vec::new(); + + for (s, runs) in runs.iter().enumerate() { + let n = 1usize << (MIN_LOG2 as usize + s); + for t in 0..15 { + let mut zs: Vec = runs.iter().map(|r| r[t].0).filter(|z| !z.is_nan()).collect(); + let skipped = 1.0 - zs.len() as f64 / runs.len() as f64; + if skipped > 0.5 { + notes.push(format!("{:>8} B {:<14} skipped in {:.0}% of runs, not calibrated", n, TESTS[t].0, 100.0 * skipped)); + continue; + } + raw_fail[s][t] = runs.iter().filter(|r| r[t].1 < 0.01).count() as f64 / zs.len() as f64; + z_rows[s][t] = quantiles(&mut zs); + if z_rows[s][t][LEVELS - 1] - z_rows[s][t][0] <= 1e-9 * (1.0 + z_rows[s][t][0].abs()) { + notes.push(format!("{:>8} B {:<14} constant on random data (z = {})", n, TESTS[t].0, z_rows[s][t][0])); + } + } + + // Null distribution of the combination statistic, with the same lookup as at runtime. + // Cross-fitted: each run is scored against tables built from the other half of the + // runs, since runs look less extreme against tables that include themselves. + let halves: [Vec<[f64; LEVELS]>; 2] = std::array::from_fn(|h| { + (0..15) + .map(|t| { + let mut zs: Vec = + runs.iter().skip(h).step_by(2).map(|r| r[t].0).filter(|z| !z.is_nan()).collect(); + if zs.is_empty() { [f64::NAN; LEVELS] } else { quantiles(&mut zs) } + }) + .collect() + }); + let mut ts: Vec = runs + .iter() + .enumerate() + .map(|(rep, r)| { + let other = &halves[1 - rep % 2]; + let ps: Vec = (0..15) + .filter(|&t| !r[t].0.is_nan() && !z_rows[s][t][0].is_nan() && !other[t][0].is_nan()) + .map(|t| calibration::tail_p(&other[t], r[t].0, TWO_SIDED[t])) + .collect(); + acat(&ps) + }) + .filter(|t| !t.is_nan()) + .collect(); + t_rows[s] = quantiles(&mut ts); + } + + report(&raw_fail); + for note in ¬es { + println!("{}", note); + } + write_table(&args.out, &source, reps, &z_rows, &t_rows) +} + +/// Prints how often each raw p-value falls below 0.01 on random data (should be 1%). +fn report(raw_fail: &[[f64; 15]]) { + println!("\nRaw p < 0.01 on random data, in % (1.0 if the raw p-value were right):"); + print!("{:<14}", "bytes"); + for s in 0..SIZES { + print!("{:>7}", format!("2^{}", MIN_LOG2 as usize + s)); + } + println!(); + for t in 0..15 { + print!("{:<14}", TESTS[t].0); + for row in raw_fail { + if row[t].is_nan() { print!("{:>7}", "-") } else { print!("{:>7.1}", 100.0 * row[t]) } + } + println!(); + } + println!(); +} + +fn write_table(path: &str, source: &str, reps: usize, z_rows: &[[[f64; LEVELS]; 15]], t_rows: &[[f64; LEVELS]]) -> io::Result<()> { + let row = |q: &[f64; LEVELS]| -> String { + if q[0].is_nan() { + return format!("[f64::NAN; {}]", LEVELS); + } + let values: Vec = q.iter().map(|v| format!("{:?}", v)).collect(); + format!("[{}]", values.join(", ")) + }; + + let mut out = String::new(); + out.push_str("// Generated by `cargo run --release --example calibrate`. Do not edit.\n"); + out.push_str(&format!("// Null source: {}, {} samples per size, 2^{}..2^{} bytes.\n\n", source, reps, MIN_LOG2, MAX_LOG2)); + out.push_str("use super::{LEVELS, SIZES};\n\n"); + out.push_str(&format!("pub const REPS: usize = {};\n", reps)); + out.push_str(&format!("pub const SOURCE: &str = {:?};\n\n", source)); + out.push_str("/// Quantiles of each test's z-score on random data, per size and test.\n"); + out.push_str("#[rustfmt::skip]\npub static Z: [[[f64; LEVELS]; 15]; SIZES] = [\n"); + for (s, tests) in z_rows.iter().enumerate() { + out.push_str(&format!(" // 2^{} bytes\n [\n", MIN_LOG2 as usize + s)); + for (t, q) in tests.iter().enumerate() { + out.push_str(&format!(" // {}\n {},\n", TESTS[t].0, row(q))); + } + out.push_str(" ],\n"); + } + out.push_str("];\n\n/// Quantiles of the Cauchy combination statistic on random data, per size.\n"); + out.push_str("#[rustfmt::skip]\npub static T: [[f64; LEVELS]; SIZES] = [\n"); + for (s, q) in t_rows.iter().enumerate() { + out.push_str(&format!(" // 2^{} bytes\n {},\n", MIN_LOG2 as usize + s, row(q))); + } + out.push_str("];\n"); + + File::create(path)?.write_all(out.as_bytes())?; + println!("Wrote {}", path); + Ok(()) +} + +fn check(reps: usize, args: &Args, urandom: &Option>) { + if calibration::REPS == 0 { + eprintln!("No calibration table compiled in. Generate one first."); + std::process::exit(1); + } + // Calibrated sizes plus some in between and beyond, to exercise interpolation and extrapolation. + let default_sizes = vec![256, 1000, 1024, 4096, 10_000, 65_536, 100_000, 259_200, 1 << 20, 1_500_000, 4_000_000]; + let sizes = args.sizes.clone().unwrap_or(default_sizes); + const ALPHAS: [f64; 4] = [0.05, 0.01, 1e-3, 1e-4]; + const BATCH: usize = 100_000; + + println!("Calibrated p below 0.05 / 0.01 / 0.001 / 0.0001 on fresh random data, in % of samples."); + for (i, &n) in sizes.iter().enumerate() { + // Counts per test (and combined, last) per alpha, plus the number of non-skipped runs. + let mut below = [[0usize; 4]; 16]; + let mut total = [0usize; 16]; + for start in (0..reps).step_by(BATCH) { + let batch = BATCH.min(reps - start); + // Seeds offset from generation, so these samples were not used to build the table. + let scores = parallel(batch, n, |rep, buf| { + sample(buf, urandom, args.seed.wrapping_add(0x5eed), 100 + i, start + rep); + let score = Onod::score(buf, false); + let mut ps = [f64::NAN; 16]; + for (p, r) in ps.iter_mut().zip(&score.tests) { + *p = r.p_cal.unwrap_or(f64::NAN); + } + ps[15] = score.p_combined; + ps + }); + for ps in &scores { + for k in 0..16 { + if ps[k].is_nan() { + continue; + } + total[k] += 1; + for (a, &alpha) in ALPHAS.iter().enumerate() { + below[k][a] += (ps[k] < alpha) as usize; + } + } + } + } + + println!("\n{} bytes, {} samples (expected {:.2} / {:.2} / {:.3} / {:.4}):", n, reps, 5.0, 1.0, 0.1, 0.01); + for k in 0..16 { + let name = if k < 15 { TESTS[k].0 } else { "Combined" }; + if total[k] == 0 { + println!(" {:<14} -", name); + continue; + } + let rate = |a: usize| 100.0 * below[k][a] as f64 / total[k] as f64; + println!(" {:<14} {:>6.2} {:>6.2} {:>7.3} {:>8.4}", name, rate(0), rate(1), rate(2), rate(3)); + } + } +} + +fn main() -> io::Result<()> { + let args = parse_args(); + let urandom = if args.urandom { Some(Mutex::new(File::open("/dev/urandom")?)) } else { None }; + match args.check { + Some(reps) => check(reps, &args, &urandom), + None => generate(&args, &urandom)?, + } + Ok(()) +} diff --git a/include/onod3000.h b/include/onod3000.h index cfd07c1..e9fe5ea 100644 --- a/include/onod3000.h +++ b/include/onod3000.h @@ -13,6 +13,26 @@ bool onod_run(const char* test, size_t len, double* result /* length >= 3 */); +// Health score of a sample. NaN marks values that are not available. +typedef struct { + double p_combined; // calibrated p-value of all tests combined + double score; // -log10(p_combined), capped at 12; < 2 pass, < 4 suspect + int verdict; // 0 pass, 1 suspect, 2 fail, 3 insufficient data (< 256 bytes) + int weakest; // index of the test with the lowest calibrated p, -1 if none + double depth_bits; // log2 of the bits in the longest passing prefix + bool depth_complete;// true if every prefix up to the whole sample passed + double p_cal[15]; // calibrated p-value per test, NaN if skipped +} OnodScore; + +// Returns true on success. With depth, also computes the survival depth (up to 2x slower). +bool onod_score(const uint8_t* samples, + size_t len, + bool depth, + OnodScore* result); + +// Name of test index 0..14 as used in OnodScore.p_cal, NULL past the last one. +const char* onod_test_name(size_t index); + #ifdef __cplusplus } #endif diff --git a/src/bin/onod3000.rs b/src/bin/onod3000.rs index 1ea1098..c49e8ae 100644 --- a/src/bin/onod3000.rs +++ b/src/bin/onod3000.rs @@ -30,7 +30,8 @@ use std::fs::File; use std::io::{self, Read}; use std::path::Path; -use onod3000::Onod; +use onod3000::calibration::MIN_BYTES; +use onod3000::{Onod, TestResult, Verdict, TESTS}; fn main() -> io::Result<()> { let mut args = std::env::args(); @@ -38,22 +39,30 @@ fn main() -> io::Result<()> { let mut input_data = Vec::new(); let mut source = String::from("stdin"); + let mut file_path = None; + let mut depth = true; - if let Some(arg) = args.next() { + while let Some(arg) = args.next() { if arg == "-f" { - if let Some(file_path) = args.next() { - source = file_path.clone(); - let path = Path::new(&file_path); - let mut file = File::open(path)?; - file.read_to_end(&mut input_data)?; + if let Some(path) = args.next() { + file_path = Some(path); } else { eprintln!("Error: No file path provided after -f."); std::process::exit(1); } + } else if arg == "--depth-off" { + depth = false; } else { - eprintln!("Usage: {} [-f ]", std::env::args().next().unwrap()); + eprintln!("Usage: {} [-f ] [--depth-off]", std::env::args().next().unwrap()); std::process::exit(1); } + } + + if let Some(file_path) = file_path { + source = file_path.clone(); + let path = Path::new(&file_path); + let mut file = File::open(path)?; + file.read_to_end(&mut input_data)?; } else { io::stdin().read_to_end(&mut input_data)?; } @@ -64,60 +73,68 @@ fn main() -> io::Result<()> { } println!("\nTesting {} bytes from {}.", input_data.len(), source); - println!("--------------------------------------------------------"); - println!("Randomness Test Value Z-Score P-Value Pass"); - println!("--------------------------------------------------------"); + println!("----------------------------------------------------------------"); + println!("Randomness Test Value Z-Score P-Value Cal-P Pass"); + println!("----------------------------------------------------------------"); let mut passed_tests = 0; let alpha = 0.01; - // Create vectors to store results - let (mut observations, mut z_scores, mut p_values) = (Vec::new(), Vec::new(), Vec::new()); + let score = Onod::score(&input_data, depth); - // Run each test with the appropriate handling - let tests = [ - ("Shannon", Onod::shannon(&input_data)), - ("Monobit", Onod::monobit(&input_data)), - ("ChiBit", Onod::chi_bit(&input_data)), - ("ChiByte", Onod::chi_byte(&input_data)), - ("MeanByte", Onod::mean_byte(&input_data)), - ("Compression", Onod::compression(&input_data)), - ("Kolm.-Smirnov", Onod::ks(&input_data)), - ("Pi", Onod::pi(&input_data)), - ("Shells", Onod::shells(&input_data)), - ("Gaps", Onod::gaps(&input_data)), - ("Avalanche", Onod::avalanche(&input_data)), - ("Runs", Onod::runs(&input_data)), - ("RunUps", Onod::run_ups(&input_data)), - ("Prediction", Onod::prediction(&input_data)), - ("UnCorrelation", Onod::uncorrelation(&input_data)), - ]; + // Below the calibrated size the score has no test results, so run them raw. + let tests: Vec = if score.tests.is_empty() { + TESTS + .iter() + .map(|&(name, key)| { + let (stat, z, p_raw) = Onod::run(key, &input_data); + TestResult { name, stat, z, p_raw, p_cal: None } + }) + .collect() + } else { + score.tests.clone() + }; - for (test_name, (observation, z_score, p_value)) in &tests { - let result = if *p_value >= alpha && *observation != -1.0 { + for test in &tests { + // Pass on the calibrated p-value where there is one. + let p_value = test.p_cal.unwrap_or(test.p_raw); + let result = if p_value >= alpha && test.stat != -1.0 { passed_tests += 1; "✅" } else { - if *observation == -1.0 { + if test.stat == -1.0 { "SKIP" } else { "❌" - } + } }; + let p_cal = test.p_cal.map_or(String::from("-"), |p| format!("{:.4}", p)); println!( - "{:<15} {:>15.3} {:>8.4} {:>7.4} {:>2}", - test_name, observation, z_score, p_value, result + "{:<15} {:>15.3} {:>8.4} {:>7.4} {:>7} {:>2}", + test.name, test.stat, test.z, test.p_raw, p_cal, result ); - - observations.push(*observation); - z_scores.push(*z_score); - p_values.push(*p_value); } - println!("--------------------------------------------------------"); + println!("----------------------------------------------------------------"); println!("{}/{} tests passed.", passed_tests, tests.len()); - println!("--------------------------------------------------------"); + println!("----------------------------------------------------------------"); + if score.verdict == Verdict::Insufficient && score.tests.is_empty() { + println!("Score needs at least {} bytes.", MIN_BYTES); + } else if score.verdict == Verdict::Insufficient { + println!("Score unavailable: no calibration table compiled in."); + } else { + let weakest = score.weakest.map_or(String::new(), |i| { + format!(" · weakest: {} p={:.3}", tests[i].name, tests[i].p_cal.unwrap_or(f64::NAN)) + }); + let depth = if depth { + format!(" · Depth {:.1}{} bits", score.depth_bits, if score.depth_complete { "+" } else { "" }) + } else { + String::new() + }; + println!("Score {:.2} ({}){}{}", score.score, score.verdict.as_str(), weakest, depth); + } + println!("----------------------------------------------------------------"); Ok(()) } \ No newline at end of file diff --git a/src/calibration/mod.rs b/src/calibration/mod.rs new file mode 100644 index 0000000..4e45233 --- /dev/null +++ b/src/calibration/mod.rs @@ -0,0 +1,280 @@ +// MIT License + +// Copyright (c) 2025 Tobias Raayoni Last (@randogoth) + +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions: + +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. + +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. + +//! Empirical null calibration of the test z-scores. +//! +//! The raw p-values of some tests rest on asymptotics that do not hold at small sample +//! sizes (Shannon, Gaps) or on made-up constants (Compression). `examples/calibrate.rs` +//! measures the distribution of every test's z-score on random data at the sample sizes +//! 2^8..2^20 bytes and stores its quantiles in `table.rs`. A z-score is turned into a +//! p-value by locating it in that null distribution. + +mod table; + +pub use table::{REPS, SOURCE}; + +/// Smallest and largest calibrated sample size, as log2 of the byte count. +pub const MIN_LOG2: u32 = 8; +pub const MAX_LOG2: u32 = 20; +pub const SIZES: usize = (MAX_LOG2 - MIN_LOG2 + 1) as usize; +/// Smallest sample size in bytes that can be calibrated. +pub const MIN_BYTES: usize = 1 << MIN_LOG2; + +/// Number of quantiles stored per null distribution. +pub const LEVELS: usize = 199; +/// Outermost probability level of the quantile tables. +pub const TAIL: f64 = 5e-4; + +/// p-value given to a test whose statistic is constant on random data but not on the input. +pub const DEGENERATE_P: f64 = 1e-12; + +/// Whether each test in `TESTS` order is two-sided (z-type) or upper-tailed (chi^2 and KS). +pub const TWO_SIDED: [bool; 15] = [ + true, // Shannon + true, // Monobit + false, // ChiBit + false, // ChiByte + true, // MeanByte + true, // Compression + false, // Kolm.-Smirnov + true, // Pi + false, // Shells + false, // Gaps + true, // Avalanche + true, // Runs + false, // RunUps + false, // Prediction + true, // UnCorrelation +]; + +/// Probability levels of the quantile tables, logit-spaced so the tails are dense. +pub fn levels() -> [f64; LEVELS] { + let l = ((1.0 - TAIL) / TAIL).ln(); + std::array::from_fn(|i| { + let x = -l + 2.0 * l * i as f64 / (LEVELS - 1) as f64; + 1.0 / (1.0 + (-x).exp()) + }) +} + +/// Tests whose z-score on random data is a fixed but irregular function of the sample +/// size, so it is measured against a reference sample instead of interpolated. For +/// Compression this is deflate's stored-block overhead. +const CENTERED: [bool; 15] = { + let mut centered = [false; 15]; + centered[5] = true; // Compression + centered +}; + +/// The z-score of test `t` as it is calibrated, from the test's (observation, z-score) +/// output on `n` bytes. None if the test skipped. +pub fn calibration_z(t: usize, observation: f64, z: f64, n: usize) -> Option { + if observation == -1.0 || z.is_nan() { + return None; + } + if CENTERED[t] { + let (_, reference, _) = crate::Onod::run(crate::TESTS[t].1, &reference_sample(n)); + return Some(z - reference); + } + Some(z) +} + +/// Calibrated p-value of test `t` (index into `TESTS`) for a sample of `n` bytes, from +/// the test's (observation, z-score) output. None if the test skipped or `n` is too small. +pub fn test_p(t: usize, observation: f64, z: f64, n: usize) -> Option { + let q = interpolate(n, |s| &table::Z[s][t])?; + let z = calibration_z(t, observation, z, n)?; + Some(tail_p(&q, z, TWO_SIDED[t])) +} + +/// Fixed pseudo-random bytes (SplitMix64) of length `n`. +fn reference_sample(n: usize) -> Vec { + let mut x: u64 = 0x0d3000; + let mut bytes = Vec::with_capacity(n + 8); + while bytes.len() < n { + x = x.wrapping_add(0x9e3779b97f4a7c15); + let mut z = x; + z = (z ^ (z >> 30)).wrapping_mul(0xbf58476d1ce4e5b9); + z = (z ^ (z >> 27)).wrapping_mul(0x94d049bb133111eb); + bytes.extend_from_slice(&(z ^ (z >> 31)).to_le_bytes()); + } + bytes.truncate(n); + bytes +} + +/// Combined p-value of the Cauchy combination statistic `t` for a sample of `n` bytes. +pub fn combined_p(t: f64, n: usize) -> f64 { + let Some(q) = interpolate(n, |s| &table::T[s]) else { + return f64::NAN; + }; + if t.is_nan() { + return f64::NAN; + } + // Beyond the simulated range follow the Cauchy tail, which holds under dependence. + let top = q[LEVELS - 1]; + if t > top { + return TAIL * cauchy_sf(t) / cauchy_sf(top); + } + tail_p(&q, t, false) +} + +fn cauchy_sf(t: f64) -> f64 { + 0.5 - t.atan() / std::f64::consts::PI +} + +/// Null quantiles at `n` bytes, interpolated linearly in 1/sqrt(n) between the calibrated +/// sizes and extrapolated the same way beyond the largest one. That is exact for tests +/// whose z-score drifts like 1/sqrt(n) (Shannon's finite-sample bias, Avalanche's scale) +/// and leaves tests with a size-independent null unchanged. None below `MIN_BYTES` or +/// where the test mostly skipped during calibration (stored as NaN). +fn interpolate(n: usize, row: impl Fn(usize) -> &'static [f64; LEVELS]) -> Option<[f64; LEVELS]> { + if n < MIN_BYTES { + return None; + } + if n.is_power_of_two() && n <= 1 << MAX_LOG2 { + // Exact grid sizes use the table as is, so ties of discrete statistics stay exact. + let a = row(n.trailing_zeros() as usize - MIN_LOG2 as usize); + return if a[0].is_nan() { None } else { Some(*a) }; + } + let s = ((n as f64).log2().floor() as usize - MIN_LOG2 as usize).min(SIZES - 2); + let u = |n: f64| 1.0 / n.sqrt(); + let (n_a, n_b) = ((1usize << (MIN_LOG2 as usize + s)) as f64, (1usize << (MIN_LOG2 as usize + s + 1)) as f64); + let w = (u(n as f64) - u(n_a)) / (u(n_b) - u(n_a)); + let (a, b) = (row(s), row(s + 1)); + if a[0].is_nan() || b[0].is_nan() { + return None; + } + // Extrapolation can amplify Monte-Carlo noise enough to swap neighbouring quantiles. + let mut q: [f64; LEVELS] = std::array::from_fn(|k| a[k] + w * (b[k] - a[k])); + for k in 1..LEVELS { + q[k] = q[k].max(q[k - 1]); + } + Some(q) +} + +/// p-value of `z` against the null quantiles `q`, upper-tailed or two-sided. +/// +/// Inside the table the null CDF is linear between quantiles, and a value hit by tied +/// quantiles (discrete statistics) counts at the middle of the tie. Beyond the outermost +/// quantiles the tail is extrapolated with a power law, see `extrapolate`. +pub fn tail_p(q: &[f64; LEVELS], z: f64, two_sided: bool) -> f64 { + let p = levels(); + let last = LEVELS - 1; + + let tolerance = 1e-9 * (1.0 + q[0].abs()); + if q[last] - q[0] <= tolerance { + // Degenerate null: the statistic is constant on random data. + return if (z - q[0]).abs() <= tolerance { 1.0 } else { DEGENERATE_P }; + } + + // Lower and upper tail probabilities, each computed directly to keep precision. + let (lower, upper) = if z < q[0] { + let lower = extrapolate(&p, q[LEVELS / 2] - z, |k| q[LEVELS / 2] - q[k]); + (lower, 1.0 - lower) + } else if z > q[last] { + let upper = extrapolate(&p, z - q[LEVELS / 2], |k| q[last - k] - q[LEVELS / 2]); + (1.0 - upper, upper) + } else { + let lo = q.partition_point(|&v| v < z); + let hi = q.partition_point(|&v| v <= z); + let cdf = if lo < hi { + (p[lo] + p[hi - 1]) / 2.0 + } else { + p[lo - 1] + (p[lo] - p[lo - 1]) * (z - q[lo - 1]) / (q[lo] - q[lo - 1]) + }; + (cdf, 1.0 - cdf) + }; + + if two_sided { + (2.0 * lower.min(upper)).min(1.0) + } else { + upper + } +} + +/// Tail probability at distance `d` from the median, beyond the table. `dist(k)` is the +/// distance from the median of the quantile with tail probability `p[k]`. +/// +/// The tail follows a power law in the distance, fitted to the table's outermost decade +/// (tail probability 10 * TAIL down to TAIL, or further in where a discrete statistic is +/// tied there). A power law decays more slowly than the normal, chi^2 or lumpy small-sample +/// tails of the tests, so extrapolated p-values err on the large side. +fn extrapolate(p: &[f64; LEVELS], d: f64, dist: impl Fn(usize) -> f64) -> f64 { + let edge = dist(0); + let start = p.iter().position(|&v| v >= 10.0 * TAIL).unwrap(); + match (start..LEVELS / 2).find(|&k| dist(k) > 0.0 && dist(k) < edge) { + Some(k) => { + let exponent = (p[k] / TAIL).ln() / (edge / dist(k)).ln(); + TAIL * (edge / d).powf(exponent) + } + // No shape to fit, e.g. half the mass tied at the median: rarer than the table. + None => TAIL, + } +} + +#[cfg(test)] +mod tests { + use super::*; + + fn normal_quantiles() -> [f64; LEVELS] { + use statrs::distribution::{ContinuousCDF, Normal}; + let normal = Normal::new(0.0, 1.0).unwrap(); + levels().map(|p| normal.inverse_cdf(p)) + } + + #[test] + fn levels_are_symmetric() { + let p = levels(); + assert!((p[0] - TAIL).abs() < 1e-15); + assert!((p[LEVELS / 2] - 0.5).abs() < 1e-15); + for i in 0..LEVELS { + assert!((p[i] + p[LEVELS - 1 - i] - 1.0).abs() < 1e-12); + } + } + + #[test] + fn standard_normal_null() { + let q = normal_quantiles(); + assert!((tail_p(&q, 0.0, true) - 1.0).abs() < 1e-9); + assert!((tail_p(&q, 1.959964, true) - 0.05).abs() < 1e-3); + assert!((tail_p(&q, 2.326348, false) - 0.01).abs() < 1e-4); + // The power-law extrapolation stays conservative in the far tail. + let p5 = tail_p(&q, 5.0, false); + assert!(p5 > 2.9e-7 && p5 < 1e-4); + assert!(tail_p(&q, -5.0, true) > 5.7e-7); + assert!(tail_p(&q, 8.0, false) < tail_p(&q, 5.0, false)); + } + + #[test] + fn ties_count_at_their_middle() { + // Half the mass at 0, the rest spread over (0, 1]. + let p = levels(); + let q = p.map(|p| if p <= 0.5 { 0.0 } else { 2.0 * p - 1.0 }); + assert!((tail_p(&q, 0.0, false) - 0.75).abs() < 0.01); + } + + #[test] + fn degenerate_null() { + let q = [3.0; LEVELS]; + assert_eq!(tail_p(&q, 3.0, true), 1.0); + assert_eq!(tail_p(&q, 3.1, true), DEGENERATE_P); + } +} diff --git a/src/calibration/table.rs b/src/calibration/table.rs new file mode 100644 index 0000000..d4e9e1f --- /dev/null +++ b/src/calibration/table.rs @@ -0,0 +1,472 @@ +// Generated by `cargo run --release --example calibrate`. Do not edit. +// Null source: xoshiro256** seed 0xd3000, 20000 samples per size, 2^8..2^20 bytes. + +use super::{LEVELS, SIZES}; + +pub const REPS: usize = 20000; +pub const SOURCE: &str = "xoshiro256** seed 0xd3000"; + +/// Quantiles of each test's z-score on random data, per size and test. +#[rustfmt::skip] +pub static Z: [[[f64; LEVELS]; 15]; SIZES] = [ + // 2^8 bytes + [ + // Shannon + [-17.74960560631695, -17.744147549928925, -17.734169173585148, -17.694265393598773, -17.665358698594492, -17.64525586230901, -17.61263889313526, -17.582846173655597, -17.56689840951768, -17.542145425675514, -17.51498659332963, -17.48981671337745, -17.455075639942404, -17.440928767441697, -17.38181012770055, -17.37505680949622, -17.33618271197194, -17.32330943652073, -17.31647868780796, -17.288125298737757, -17.278422219722362, -17.244607960679765, -17.208604437488734, -17.176996176663202, -17.15816112301072, -17.123383811249717, -17.08196912484242, -17.05762530813025, -17.02046610578519, -17.002176974321163, -16.964133199069504, -16.93121157586097, -16.901118244298697, -16.874529877521685, -16.850902141037402, -16.81374840478077, -16.77276781886446, -16.757321521364407, -16.729730617037525, -16.689188750302023, -16.660772302597763, -16.625599822894365, -16.59855528584098, -16.567021355017665, -16.54193125585749, -16.510136890451964, -16.483405453918934, -16.454887012533206, -16.416607590098238, -16.393694924363796, -16.35328610940772, -16.32148490274013, -16.28614585791859, -16.250687016024298, -16.223166764896497, -16.194527563995482, -16.157795432484352, -16.131063995951305, -16.09926278928373, -16.072531352750683, -16.038961227006133, -16.000944651440104, -15.962304755560986, -15.928734629816422, -15.8993256625389, -15.863986617717345, -15.832185411049773, -15.798615285305193, -15.755528939604623, -15.717512364038594, -15.677103549082501, -15.643533423337937, -15.603124608381842, -15.56687695189279, -15.52469921785972, -15.488451561370665, -15.44758911262619, -15.410026170848543, -15.367409149642224, -15.324762091114888, -15.290751289090906, -15.243944461202698, -15.201789299937776, -15.161072620859095, -15.120663805903016, -15.075303800387681, -15.02856103695783, -14.985474691257245, -14.940619426479687, -14.898441692446601, -14.848516657534502, -14.803661392756942, -14.761483658723865, -14.711558623811756, -14.673542048245729, -14.630455702545143, -14.58430471391021, -14.541030464344448, -14.496175199566888, -14.455766384610794, -14.410911119833232, -14.37050230487714, -14.332485729311111, -14.282560694398995, -14.237705429621435, -14.19729661466534, -14.161957569843787, -14.112032534931688, -14.067177270154128, -14.026768455198033, -13.981913190420473, -13.941504375464378, -13.896649110686804, -13.856240295730725, -13.81999263924167, -13.784653594420117, -13.741567248719548, -13.701158433763453, -13.667588308018889, -13.629571732452845, -13.591174715942415, -13.552915261007712, -13.515183976796108, -13.478936320307055, -13.442688663818, -13.409118538073436, -13.375548412328873, -13.337976615811376, -13.29712302180675, -13.263552896062187, -13.229982770317623, -13.193735113828568, -13.168772596372511, -13.135202470627947, -13.101632344883383, -13.06806221913882, -13.0396638620284, -13.005083126116718, -12.978351689583684, -12.946550482916113, -12.912980357171548, -12.8862489206385, -12.861286403182458, -12.841419366782013, -12.809592449193367, -12.779811434005595, -12.74245219770424, -12.724328369459712, -12.69075824371515, -12.672634415470622, -12.64590297893759, -12.620940461481531, -12.602960912601331, -12.56924650749244, -12.553800209992405, -12.52023008424784, -12.502106256003314, -12.466485964182494, -12.434966004514187, -12.41684217626966, -12.385360286924188, -12.353003981037109, -12.331578096536006, -12.313454268291478, -12.295330440046952, -12.279884142546916, -12.250896341025127, -12.210066360313297, -12.19462006281326, -12.176496234568734, -12.129504848385551, -12.124802280579644, -12.096845570085373, -12.09123215483508, -12.064500718302048, -12.05582881551115, -12.039538200845989, -12.021658505899493, -12.005968075101425, -11.987844246856898, -11.987844246856898, -11.961112810323867, -11.954274121112336, -11.919622245027112, -11.877889379022413, -11.852785975716987, -11.818927482187453, -11.803746786069642, -11.783579061156761, -11.764626984252795, -11.747498305155974, -11.747498305155974, -11.738169764474522, -11.687196742878376, -11.66959464950744, -11.643381086923162, -11.63766428630885, -11.62637304803179, -11.617375541300165], + // Monobit + [-3.1377863415153042, -3.1025642445424078, -3.093592167691145, -3.093592167691145, -3.093592167691145, -3.093592167691145, -3.0562347512049826, -3.0445982783725842, -3.005203820042827, -3.005203820042827, -3.005203820042827, -2.9610096462186677, -2.9610096462186677, -2.9610096462186677, -2.9168154723945086, -2.9168154723945086, -2.9118255434340194, -2.872621298570349, -2.82842712474619, -2.82842712474619, -2.7842329509220307, -2.7842329509220307, -2.7834576938380695, -2.7400387770978716, -2.697877891482766, -2.6958446032737124, -2.651650429449553, -2.6074562556253937, -2.6074562556253937, -2.5632620818012346, -2.5632620818012346, -2.5190679079770755, -2.5190679079770755, -2.4748737341529163, -2.4748737341529163, -2.4306795603287568, -2.4306795603287568, -2.3864853865045976, -2.3864853865045976, -2.3422912126804385, -2.3422912126804385, -2.2980970388562794, -2.2539028650321202, -2.2539028650321202, -2.2097086912079607, -2.1655145173838015, -2.1655145173838015, -2.1213203435596424, -2.1213203435596424, -2.0771261697354833, -2.032931995911324, -1.9887378220871648, -1.9887378220871648, -1.9445436482630056, -1.9003494744388463, -1.9003494744388463, -1.8561553006146871, -1.811961126790528, -1.7677669529663687, -1.7235727791422095, -1.6793786053180502, -1.6793786053180502, -1.635184431493891, -1.590990257669732, -1.5467960838455725, -1.5026019100214134, -1.4584077361972543, -1.414213562373095, -1.3700193885489358, 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7.416962364075524, 7.464747302655869, 7.509205152167559, 7.560017333981428, 7.636386355098099], + // Prediction + [-0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7071067811865475, -0.7069334707009626, -0.7069334707009626, -0.7069334707009626, -0.7069334707009626, -0.7069334707009626, -0.7069334707009626, -0.7069334707009626, -0.7069334707009626, -0.7069334707009626, 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2.0008695560781105, 2.088218040812919, 2.176953009432408, 2.2670744619365752, 2.312655119645414, 2.4048562979766013, 2.4984439601924677, 2.545757722757156, 2.6897787362782393, 2.738478982727607, 2.8369193385398517, 2.9367461782367763, 3.0379595018183796, 3.1405593092846633, 3.2445456006356266, 3.3499183758712685, 3.4031246949458445, 3.564823377996592, 3.619416180955847, 3.729641649787868, 3.7852743156606334, 3.897579510319673, 3.9369467290121967, 4.011271188863392, 4.068636959592007, 4.184408363962746, 4.24281399760487, 4.360665127802628, 4.477671276921134, 4.540041480383039, 4.600526839852182, 4.722537421703978, 4.845934487440455, 5.021405421365437, 5.096888070567445, 5.099408652532307, 5.22444458795796, 5.28874277810997, 5.353387589233153, 5.4813845814417475, 5.549401748429718, 5.554084770412031, 5.681810959416611, 5.8156066542881835, 5.875412345472271, 5.883024433180724, 5.883024433180724, 6.011760370591633, 6.148983932766186, 6.2253126422109775, 6.2901193242044515, 6.368508329323582, 6.434845019283166, 6.624401883482097, 6.65856985090234, 6.7659067130429325, 6.952692283521564, 7.082159682942911, 7.107347822154609, 7.155816639316509, 7.155890816204084], + // UnCorrelation + [-3.3507536805128253, -3.2535871381952544, -3.2178674181255835, -3.2019734258858654, -3.187207670472044, -3.157074475983954, -3.144023206269211, -3.140942017283327, -3.1188262768723765, -3.07724097932446, -3.0275251194492245, -3.000949341711265, -2.9849674606539622, -2.9751114060792796, -2.963336603074859, -2.9563414610592544, -2.9277152948412213, -2.919760760273433, -2.8819884922427685, -2.852039819838016, -2.8343457707428774, -2.8004164562727527, -2.7865773718987947, -2.7789629325593586, -2.7691828891603985, -2.74564017173922, -2.732445631107755, -2.7062929115517056, -2.6809370587735257, -2.651976937149214, -2.6275974566769147, -2.6101376814839594, -2.584090723849909, -2.570721959049419, -2.540328234511604, -2.5216170874354207, -2.48546073129935, -2.443540210256253, -2.4223977997215327, -2.3834822561632802, -2.349388326629394, -2.330608848535928, -2.3016797864736835, -2.2773028289083608, -2.2413581510367684, -2.1948692459347257, -2.166978040634922, -2.1369384768690143, -2.100570326485854, -2.0717985577405944, -2.031097726724808, -2.003698454605061, -1.9757438485045826, -1.9420322690073473, -1.9110509783264173, -1.878637289035413, -1.8296225462205793, -1.7922782618563495, -1.7551948359131053, -1.7167539308546622, -1.6814576339938951, -1.6478058304002083, -1.6102574198955517, -1.580403550786917, -1.5463886469108483, -1.5085990882160185, -1.4719080261820376, -1.434583128606695, -1.3991663115509294, -1.3563818090511306, -1.3167929263618605, -1.2688984436060717, -1.2221368661612646, -1.1784946550292321, -1.140062416731075, -1.1001028237865529, -1.0641443881973782, -1.0226870205473584, -0.9783213370769746, -0.9356014828998737, -0.8981498494848466, -0.8532197665673398, -0.8039876777694089, -0.7614312243307387, -0.7167409378776702, -0.6754958469540782, 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1.5566563635144774, 1.5918734670362622, 1.6297479091258742, 1.6602998174617873, 1.689982114768864, 1.7208351683720164, 1.7557658839544443, 1.7926694013874125, 1.8188596636424523, 1.857070956180237, 1.8880767594937844, 1.925246566279939, 1.9590864553685452, 1.9930697948260336, 2.0250738342499957, 2.0569974052767037, 2.086057115177219, 2.1197942130654672, 2.161352993547967, 2.18859747444927, 2.2307570367756795, 2.275317915176214, 2.2990305341558908, 2.340253248213421, 2.3742418531137193, 2.409054726648522, 2.4384871315963372, 2.467020636204804, 2.495996248522723, 2.51578284022919, 2.540264337958774, 2.5669858665497705, 2.5926765864793007, 2.626194216484569, 2.6413876981369273, 2.6565213366587668, 2.678631302526178, 2.717696687407809, 2.741064630686069, 2.779061036415656, 2.810955569191211, 2.8233906523465215, 2.8522100821131353, 2.867532775773336, 2.8935910992667537, 2.9168739327240614, 2.9463625608201585, 2.972827523128633, 2.9797375421074705, 2.9953650243580667, 3.0207879595678113, 3.037920621670474, 3.051473677527509, 3.060082993477984, 3.0821139069487087, 3.1185110533917557, 3.169097099890466, 3.1912333561252884, 3.2149451677221466, 3.222372093780014, 3.245718812502081, 3.2751250522115307, 3.2959556591768364, 3.3171769529091173], + ], +]; + +/// Quantiles of the Cauchy combination statistic on random data, per size. +#[rustfmt::skip] +pub static T: [[f64; LEVELS]; SIZES] = [ + // 2^8 bytes + [-8.945737537707952, -8.875216362635754, -8.856121021537849, -8.833050421360436, -8.802226078177002, -8.713283193846475, -8.62274935481616, -8.537709723678265, -8.423797745926997, -8.382845889049237, -8.171667573503502, -8.116752318339909, -8.02869352550088, -7.985518688795375, -7.812328977077734, -7.7855140633707975, -7.616224218188398, -7.50318046782861, -7.441637568226524, -7.381479349617942, -7.292705335000488, -7.14668494047215, -7.106016608375838, -7.04949219842881, -6.989750335720596, -6.937484675752055, -6.91032784889346, -6.857291325849058, -6.803045094717967, -6.722551820392861, -6.660856385214953, -6.578757380491104, -6.527505816315909, -6.427947140850192, -6.388309730929417, -6.34605523672522, -6.314624612973699, -6.25961270326348, -6.185733452855678, -6.141426779162132, -6.053736078291123, -5.950275679421013, -5.8788704472117885, -5.8142982232518845, -5.74165296195836, -5.685134640090149, -5.6259845641844555, -5.568271296811969, -5.489467539356751, -5.424821359245265, -5.380577482304103, -5.318967889584988, -5.2620854634873115, -5.20723928910974, -5.155810138456734, -5.089530946248081, -5.0300907629146305, -4.976375645364415, -4.903938783059701, -4.848275890305197, -4.7828864056183225, -4.719818945267024, -4.657549661692447, -4.592662583584859, -4.521186477806122, -4.458011821328746, -4.384820541957455, -4.308984481250466, -4.236137669057515, -4.164219234693915, -4.071853442718775, -3.9941504724900736, -3.9110219530074923, -3.8304824852285124, -3.7468349159396372, -3.663149231381471, -3.588974016940762, -3.509589813663576, -3.4402663728581317, -3.363763124853936, -3.290913210669507, -3.22354539917287, -3.1558351013645316, -3.083845633273052, -3.0139576505721255, -2.948593606055651, -2.8842536067760163, -2.8270474551123654, -2.76719079966252, -2.7132630925051933, -2.656431103796812, -2.601780922590888, -2.5438093840344367, -2.4877098961046817, -2.4309385311157468, -2.381829625928473, -2.3279937727358475, -2.2760784985393934, -2.2177738562722706, -2.1708414325629617, -2.116039994407561, -2.0601552967753336, -2.006166267638079, -1.9471393963779395, -1.8886184787187585, -1.8274328954506174, -1.7605531909835177, -1.701823202007114, -1.6344506746933778, -1.5667364374216164, -1.4987739282711683, -1.414081900413507, -1.3226711122806862, -1.2293746371511376, -1.1438996951469576, -1.0330091072139698, -0.922499003903544, -0.7986005419070505, -0.6770280278178314, -0.5693894437755396, -0.436530902283127, -0.29769034974488556, -0.1564958721056179, 0.01000052733996461, 0.17820251453566394, 0.3657009218675739, 0.5555598239458146, 0.7632675819673904, 0.9780559214099026, 1.2206325413071253, 1.5028974686624756, 1.8028184506960476, 2.1304217586880774, 2.5355201467172566, 2.9073227335748673, 3.310134013776124, 3.76742078892085, 4.15300485147174, 4.7743767931360575, 5.3296824329877, 6.085004941739744, 6.821237319361155, 7.51895025763551, 8.120930821844926, 8.705750601558082, 9.446865360191197, 10.338079189189408, 11.131263673298609, 11.995279931185323, 13.053714113303792, 14.207822929713998, 16.140482088966394, 18.047457918619138, 19.219119477214623, 20.83191534621028, 23.55804168286622, 26.07514120883979, 27.806036584806346, 30.64973032622092, 32.45504880085961, 34.83160283588673, 36.80682985830366, 38.314423232244096, 39.63265374529591, 42.87843665316157, 48.20533828927555, 50.44343917088267, 53.899500392635154, 56.56244975605118, 59.33252565295149, 64.18135361571176, 72.89554348414472, 79.60257118224926, 83.9498319898505, 93.59597056769704, 98.84988959050553, 101.03890811741144, 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37.052379254581, 40.14792254431242, 43.49418073029144, 46.91991345347286, 49.95150188874705, 53.81968921734731, 56.930044628345236, 61.9657271228186, 65.23971646779184, 74.06895730962914, 78.23257719881488, 86.20208762845175, 99.15263172812557, 105.93176392432649, 115.94063634128713, 128.22626600793782, 134.6446964822469, 139.65499776373542, 145.0573398425592, 151.71889899894697, 157.68015049289085, 183.27584902013382, 206.83858305153709, 227.3524988949901, 276.2021339648136, 288.18931468753215, 299.9250307006911, 310.59017799098154, 318.81257375548415, 328.18221065019503, 335.04435338159465, 407.16223433237394, 455.7982390731328, 551.3454700530654, 603.0275728568, 634.2200030715255, 667.7154098878634, 670.6915645697662], + // 2^20 bytes + [-8.396591125075993, -8.383541469941044, -8.297355938605047, -8.208489726569848, -8.14789536498161, -8.117080283332452, -8.07417651610047, -7.995918023194527, -7.968310956343969, -7.909335867556764, -7.89530703016894, -7.772949457433727, 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36.393641840863, 38.99980450245989, 41.91006460267012, 46.75513889713547, 51.92585113615457, 55.4365915393194, 58.208909969901356, 60.660826724182975, 63.925114821830086, 67.52439808647114, 69.55887622834217, 71.20495198197129, 77.28173152218001, 80.96993647951261, 85.69922734540887, 92.33101698005608, 96.85055356937163, 100.513110783684, 105.37615229419704, 119.38277977371743, 135.04724332680914, 142.43486396507885, 151.21854279086523, 158.36234755616434, 167.55193872582575, 177.07484841030228, 179.86068609072709, 182.72095517890145, 196.6668196583697, 205.438468302692, 210.15404597986313, 217.20652177672454, 237.81825528531365, 247.18247277811392, 253.23604431840275, 264.8526785436929, 283.5622652876917, 300.6129053160348, 301.2650770681399], +]; diff --git a/src/ffi.rs b/src/ffi.rs index 0b3b513..12e4e12 100644 --- a/src/ffi.rs +++ b/src/ffi.rs @@ -26,9 +26,72 @@ // Original work is licensed under the terms specified in the respective file header. -use std::ffi::{c_char, c_double, CStr}; +use std::ffi::{c_char, c_double, c_int, CStr}; -use crate::Onod; +use crate::{Onod, TESTS}; + +/// Health score of a sample, see `Score`. NaN marks values that are not available. +#[repr(C)] +pub struct OnodScore { + pub p_combined: c_double, + pub score: c_double, + /// 0 pass, 1 suspect, 2 fail, 3 insufficient data + pub verdict: c_int, + /// Index of the weakest test, -1 if none + pub weakest: c_int, + pub depth_bits: c_double, + pub depth_complete: bool, + /// Calibrated p-value per test in `onod_test_name` order, NaN if skipped + pub p_cal: [c_double; 15], +} + +/// Display name of test `index`, or null past the last one. +#[no_mangle] +pub extern "C" fn onod_test_name(index: usize) -> *const c_char { + const NAMES: [&str; 15] = [ + "Shannon\0", "Monobit\0", "ChiBit\0", "ChiByte\0", "MeanByte\0", + "Compression\0", "Kolm.-Smirnov\0", "Pi\0", "Shells\0", "Gaps\0", + "Avalanche\0", "Runs\0", "RunUps\0", "Prediction\0", "UnCorrelation\0", + ]; + debug_assert!(NAMES.iter().zip(TESTS.iter()).all(|(c, t)| c.trim_end_matches('\0') == t.0)); + NAMES.get(index).map_or(std::ptr::null(), |name| name.as_ptr() as *const c_char) +} + +/// Scores a sample. With `depth` also computes the survival depth (up to 2x slower). +#[no_mangle] +pub extern "C" fn onod_score( + samples: *const u8, + len: usize, + depth: bool, + result: *mut OnodScore, +) -> bool { + if samples.is_null() || result.is_null() { + eprintln!("Error: Null pointer passed to onod_score."); + return false; + } + + let samples = unsafe { std::slice::from_raw_parts(samples, len) }; + let score = Onod::score(samples, depth); + + let mut p_cal = [f64::NAN; 15]; + for (p, test) in p_cal.iter_mut().zip(&score.tests) { + *p = test.p_cal.unwrap_or(f64::NAN); + } + + unsafe { + *result = OnodScore { + p_combined: score.p_combined, + score: score.score, + verdict: score.verdict as c_int, + weakest: score.weakest.map_or(-1, |i| i as c_int), + depth_bits: score.depth_bits, + depth_complete: score.depth_complete, + p_cal, + }; + } + + true +} #[no_mangle] pub extern "C" fn onod_run( diff --git a/src/lib.rs b/src/lib.rs index a670d98..2d6abd4 100644 --- a/src/lib.rs +++ b/src/lib.rs @@ -29,12 +29,35 @@ pub struct Onod; mod uniformity; +pub mod calibration; pub mod chisquaretest; +pub mod score; pub mod well19937c; pub mod ffi; #[cfg(feature = "python")] pub mod python; +pub use score::{Score, TestResult, Verdict}; + +/// All tests as (display name, `Onod::run` key), in report order. +pub const TESTS: [(&str, &str); 15] = [ + ("Shannon", "shannon"), + ("Monobit", "monobit"), + ("ChiBit", "chi_bit"), + ("ChiByte", "chi_byte"), + ("MeanByte", "mean_byte"), + ("Compression", "compression"), + ("Kolm.-Smirnov", "ks"), + ("Pi", "pi"), + ("Shells", "shells"), + ("Gaps", "gaps"), + ("Avalanche", "avalanche"), + ("Runs", "runs"), + ("RunUps", "run_ups"), + ("Prediction", "prediction"), + ("UnCorrelation", "uncorrelation"), +]; + impl Onod { pub fn run(test: &str, samples: &[u8]) -> (f64, f64, f64) { diff --git a/src/python.rs b/src/python.rs index 699263c..7148bd2 100644 --- a/src/python.rs +++ b/src/python.rs @@ -27,6 +27,7 @@ use pyo3::prelude::*; +use pyo3::types::{PyDict, PyList}; use super::Onod as O; #[pyclass] @@ -38,6 +39,32 @@ impl Onod { pub fn run(test: &str, samples: Vec) -> (f64, f64, f64) { O::run(test, &samples) } + + /// Health score of a sample as a dict, see `Score`. + #[staticmethod] + #[pyo3(signature = (samples, depth=true))] + pub fn score<'py>(py: Python<'py>, samples: Vec, depth: bool) -> PyResult> { + let score = O::score(&samples, depth); + let tests = PyList::empty(py); + for test in &score.tests { + let entry = PyDict::new(py); + entry.set_item("name", test.name)?; + entry.set_item("stat", test.stat)?; + entry.set_item("z", test.z)?; + entry.set_item("p_raw", test.p_raw)?; + entry.set_item("p_cal", test.p_cal)?; + tests.append(entry)?; + } + let dict = PyDict::new(py); + dict.set_item("tests", tests)?; + dict.set_item("p_combined", score.p_combined)?; + dict.set_item("score", score.score)?; + dict.set_item("verdict", score.verdict.as_str())?; + dict.set_item("weakest", score.weakest.map(|i| score.tests[i].name))?; + dict.set_item("depth_bits", score.depth_bits)?; + dict.set_item("depth_complete", score.depth_complete)?; + Ok(dict) + } } #[pymodule] diff --git a/src/score.rs b/src/score.rs new file mode 100644 index 0000000..407e710 --- /dev/null +++ b/src/score.rs @@ -0,0 +1,273 @@ +// MIT License + +// Copyright (c) 2025 Tobias Raayoni Last (@randogoth) + +// Permission is hereby granted, free of charge, to any person obtaining a copy +// of this software and associated documentation files (the "Software"), to deal +// in the Software without restriction, including without limitation the rights +// to use, copy, modify, merge, publish, distribute, sublicense, and/or sell +// copies of the Software, and to permit persons to whom the Software is +// furnished to do so, subject to the following conditions: + +// The above copyright notice and this permission notice shall be included in all +// copies or substantial portions of the Software. + +// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR +// IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, +// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE +// AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER +// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, +// OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE +// SOFTWARE. + +//! Health score of a sample: all calibrated p-values combined into one number, plus a +//! QNGmeter-style survival depth. + +use std::f64::consts::PI; + +use crate::calibration::{self, MIN_BYTES}; +use crate::{Onod, TESTS}; + +/// Score at or above which a sample is suspect, and at or above which it fails. +pub const SUSPECT_SCORE: f64 = 2.0; +pub const FAIL_SCORE: f64 = 4.0; +/// Highest reported score, i.e. p_combined is floored at 1e-12. +pub const MAX_SCORE: f64 = 12.0; +/// Combined p-value below which a prefix stops the survival depth (QNGmeter's freeze level). +pub const FREEZE_P: f64 = 1e-4; + +#[derive(Debug, Clone, Copy, PartialEq, Eq)] +#[repr(C)] +pub enum Verdict { + Pass = 0, + Suspect = 1, + Fail = 2, + /// Fewer than `MIN_BYTES` bytes, or no calibration table compiled in. + Insufficient = 3, +} + +impl Verdict { + pub fn as_str(self) -> &'static str { + match self { + Verdict::Pass => "pass", + Verdict::Suspect => "suspect", + Verdict::Fail => "fail", + Verdict::Insufficient => "insufficient data", + } + } +} + +#[derive(Debug, Clone)] +pub struct TestResult { + pub name: &'static str, + pub stat: f64, + pub z: f64, + /// The test's own p-value, as in the Java original. + pub p_raw: f64, + /// p-value from the calibrated null distribution. None if the test skipped. + pub p_cal: Option, +} + +#[derive(Debug, Clone)] +pub struct Score { + /// Per-test results in `TESTS` order. Empty below `MIN_BYTES`. + pub tests: Vec, + /// Calibrated p-value of all tests combined. NaN below `MIN_BYTES`. + pub p_combined: f64, + /// -log10(p_combined), capped at `MAX_SCORE`. 0 is the best possible, higher is worse. + pub score: f64, + pub verdict: Verdict, + /// Index into `tests` of the test with the lowest calibrated p-value. + pub weakest: Option, + /// log2 of the bits in the longest prefix (256 B, 512 B, ... then the whole sample) + /// that passed together with all shorter ones. 0 if none did or depth was not computed. + pub depth_bits: f64, + /// True if every prefix passed, i.e. the depth reached the whole sample. + pub depth_complete: bool, +} + +impl Onod { + /// Runs one test and adds its calibrated p-value: (observation, z, raw p, calibrated p). + pub fn calibrated(test: &str, samples: &[u8]) -> (f64, f64, f64, Option) { + let (stat, z, p) = Onod::run(test, samples); + let p_cal = TESTS + .iter() + .position(|&(_, key)| key == test) + .and_then(|t| calibration::test_p(t, stat, z, samples.len())); + (stat, z, p, p_cal) + } + + /// Scores a sample. With `depth` the tests are also run on every power-of-two prefix + /// to find the survival depth, which costs up to twice as long again. + pub fn score(samples: &[u8], depth: bool) -> Score { + let n = samples.len(); + if n < MIN_BYTES { + return Score { + tests: Vec::new(), + p_combined: f64::NAN, + score: f64::NAN, + verdict: Verdict::Insufficient, + weakest: None, + depth_bits: 0.0, + depth_complete: false, + }; + } + + let (tests, p_combined) = evaluate(samples); + // NaN only if nothing could be calibrated, then score stays NaN as well. + let score = if p_combined.is_nan() { f64::NAN } else { -(p_combined.max(10f64.powf(-MAX_SCORE))).log10() }; + let verdict = if score.is_nan() { + Verdict::Insufficient + } else if score >= FAIL_SCORE { + Verdict::Fail + } else if score >= SUSPECT_SCORE { + Verdict::Suspect + } else { + Verdict::Pass + }; + let weakest = tests + .iter() + .enumerate() + .filter_map(|(i, r)| r.p_cal.map(|p| (i, p))) + .min_by(|a, b| a.1.total_cmp(&b.1)) + .map(|(i, _)| i); + + let (mut depth_bits, mut depth_complete) = (0.0, false); + if depth && verdict != Verdict::Insufficient { + depth_complete = true; + let prefixes = std::iter::successors(Some(MIN_BYTES), |&len| Some(len * 2)) + .take_while(|&len| len < n) + .chain(std::iter::once(n)); + for len in prefixes { + let p = if len == n { p_combined } else { evaluate(&samples[..len]).1 }; + if !(p >= FREEZE_P) { + depth_complete = false; + break; + } + depth_bits = (8.0 * len as f64).log2(); + } + } + + Score { tests, p_combined, score, verdict, weakest, depth_bits, depth_complete } + } +} + +/// Runs all tests on a sample of at least `MIN_BYTES` and combines their calibrated p-values. +fn evaluate(samples: &[u8]) -> (Vec, f64) { + let n = samples.len(); + let tests: Vec = TESTS + .iter() + .enumerate() + .map(|(t, &(name, key))| { + let (stat, z, p_raw) = Onod::run(key, samples); + TestResult { name, stat, z, p_raw, p_cal: calibration::test_p(t, stat, z, n) } + }) + .collect(); + let ps: Vec = tests.iter().filter_map(|r| r.p_cal).collect(); + (tests, calibration::combined_p(acat(&ps), n)) +} + +/// Cauchy combination statistic of p-values (Liu & Xie 2020), the mean of +/// tan((0.5 - p) * pi). The p-values are clamped so a single 0 or 1 cannot dominate; +/// the null distribution of the result is calibrated empirically anyway. +pub fn acat(ps: &[f64]) -> f64 { + ps.iter().map(|&p| ((0.5 - p.clamp(1e-15, 0.99)) * PI).tan()).sum::() / ps.len() as f64 +} + +#[cfg(test)] +mod tests { + use super::*; + + /// SplitMix64 bytes, seeded apart from the calibration samples. + fn random_bytes(seed: u64, n: usize) -> Vec { + let mut x = seed.wrapping_mul(0x2545f4914f6cdd1d); + (0..n.div_ceil(8)) + .flat_map(|_| { + x = x.wrapping_add(0x9e3779b97f4a7c15); + let mut z = x; + z = (z ^ (z >> 30)).wrapping_mul(0xbf58476d1ce4e5b9); + z = (z ^ (z >> 27)).wrapping_mul(0x94d049bb133111eb); + (z ^ (z >> 31)).to_le_bytes() + }) + .take(n) + .collect() + } + + fn rejection_rates(n: usize, samples: u64) { + let scores: Vec = (0..samples).map(|seed| Onod::score(&random_bytes(seed, n), false)).collect(); + let below = |ps: &mut dyn Iterator, alpha: f64| { + let ps: Vec = ps.collect(); + ps.iter().filter(|&&p| p < alpha).count() as f64 / ps.len() as f64 + }; + let combined = below(&mut scores.iter().map(|s| s.p_combined), 0.05); + assert!(combined < 0.1, "{} B: combined p < 0.05 in {:.1}% of random samples", n, 100.0 * combined); + for (t, (name, _)) in TESTS.iter().enumerate() { + let rate = below(&mut scores.iter().filter_map(|s| s.tests[t].p_cal), 0.05); + assert!(rate < 0.12, "{} B: {} p < 0.05 in {:.1}% of random samples", n, name, 100.0 * rate); + } + } + + #[test] + fn random_data_is_calibrated_at_1k() { + rejection_rates(1024, 400); + } + + #[test] + fn random_data_is_calibrated_between_sizes() { + rejection_rates(3000, 200); + } + + #[test] + fn random_data_passes_with_full_depth() { + let samples = random_bytes(7, 65_536); + let score = Onod::score(&samples, true); + assert_eq!(score.verdict, Verdict::Pass); + assert!(score.depth_complete); + assert_eq!(score.depth_bits, 19.0); + } + + #[test] + fn biased_bits_fail() { + // Each bit set with probability 0.55. + let samples: Vec = random_bytes(1, 8 * 65_536) + .chunks(8) + .map(|c| c.iter().enumerate().fold(0u8, |b, (i, &r)| b | (((r < 141) as u8) << i))) + .collect(); + let score = Onod::score(&samples, true); + assert_eq!(score.verdict, Verdict::Fail); + assert!(!score.depth_complete); + assert!(score.depth_bits < 19.0); + } + + #[test] + fn counting_bytes_fail() { + let samples: Vec = (0..16_384).map(|i| i as u8).collect(); + let score = Onod::score(&samples, true); + assert_eq!(score.verdict, Verdict::Fail); + assert_eq!(score.depth_bits, 0.0); + } + + #[test] + fn repeated_block_fails() { + let block = random_bytes(3, 4096); + let samples: Vec = block.iter().cycle().take(65_536).copied().collect(); + let score = Onod::score(&samples, true); + assert_eq!(score.verdict, Verdict::Fail); + assert!(!score.depth_complete); + } + + #[test] + fn deterministic() { + let samples = random_bytes(11, 10_000); + let (a, b) = (Onod::score(&samples, true), Onod::score(&samples, true)); + assert_eq!(a.p_combined, b.p_combined); + assert_eq!(a.depth_bits, b.depth_bits); + } + + #[test] + fn too_short_is_insufficient() { + let score = Onod::score(&[0u8; 255], true); + assert_eq!(score.verdict, Verdict::Insufficient); + assert!(score.tests.is_empty()); + } +}