fix: KS test
This commit is contained in:
randogoth
parent
249a16536a
commit
bd56c1ec33
4 changed files with 95 additions and 161 deletions
95
Cargo.lock
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95
Cargo.lock
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@ -60,12 +60,6 @@ dependencies = [
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"miniz_oxide",
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"miniz_oxide",
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]
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]
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[[package]]
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name = "fuchsia-cprng"
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version = "0.1.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "a06f77d526c1a601b7c4cdd98f54b5eaabffc14d5f2f0296febdc7f357c6d3ba"
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[[package]]
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[[package]]
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name = "getrandom"
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name = "getrandom"
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version = "0.2.15"
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version = "0.2.15"
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@ -89,15 +83,6 @@ version = "2.0.5"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "b248f5224d1d606005e02c97f5aa4e88eeb230488bcc03bc9ca4d7991399f2b5"
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checksum = "b248f5224d1d606005e02c97f5aa4e88eeb230488bcc03bc9ca4d7991399f2b5"
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[[package]]
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name = "kolmogorov_smirnov"
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version = "1.1.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "96ceadb630ffd3ceb5c4d739232d8a9d51d23c383b14f3b64ffc67368cbc59b5"
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dependencies = [
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"rand 0.3.23",
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]
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[[package]]
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[[package]]
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name = "libc"
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name = "libc"
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version = "0.2.169"
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version = "0.2.169"
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@ -149,7 +134,7 @@ dependencies = [
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"num-complex",
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"num-complex",
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"num-rational",
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"num-rational",
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"num-traits",
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"num-traits",
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"rand 0.8.5",
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"rand",
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"rand_distr",
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"rand_distr",
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"simba",
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"simba",
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"typenum",
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"typenum",
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@ -215,7 +200,6 @@ name = "onod3000"
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version = "0.1.0"
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version = "0.1.0"
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dependencies = [
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dependencies = [
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"flate2",
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"flate2",
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"kolmogorov_smirnov",
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"pyo3",
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"pyo3",
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"statrs",
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"statrs",
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]
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]
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@ -322,29 +306,6 @@ dependencies = [
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"proc-macro2",
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"proc-macro2",
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]
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]
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[[package]]
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name = "rand"
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version = "0.3.23"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "64ac302d8f83c0c1974bf758f6b041c6c8ada916fbb44a609158ca8b064cc76c"
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dependencies = [
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"libc",
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"rand 0.4.6",
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]
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[[package]]
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name = "rand"
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version = "0.4.6"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "552840b97013b1a26992c11eac34bdd778e464601a4c2054b5f0bff7c6761293"
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dependencies = [
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"fuchsia-cprng",
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"libc",
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"rand_core 0.3.1",
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"rdrand",
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"winapi",
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]
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[[package]]
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[[package]]
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name = "rand"
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name = "rand"
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version = "0.8.5"
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version = "0.8.5"
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@ -353,7 +314,7 @@ checksum = "34af8d1a0e25924bc5b7c43c079c942339d8f0a8b57c39049bef581b46327404"
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dependencies = [
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dependencies = [
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"libc",
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"libc",
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"rand_chacha",
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"rand_chacha",
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"rand_core 0.6.4",
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"rand_core",
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]
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]
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[[package]]
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[[package]]
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@ -363,24 +324,9 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
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checksum = "e6c10a63a0fa32252be49d21e7709d4d4baf8d231c2dbce1eaa8141b9b127d88"
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dependencies = [
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dependencies = [
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"ppv-lite86",
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"ppv-lite86",
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"rand_core 0.6.4",
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"rand_core",
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]
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]
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[[package]]
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name = "rand_core"
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version = "0.3.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "7a6fdeb83b075e8266dcc8762c22776f6877a63111121f5f8c7411e5be7eed4b"
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dependencies = [
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"rand_core 0.4.2",
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]
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[[package]]
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name = "rand_core"
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version = "0.4.2"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "9c33a3c44ca05fa6f1807d8e6743f3824e8509beca625669633be0acbdf509dc"
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[[package]]
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[[package]]
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name = "rand_core"
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name = "rand_core"
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version = "0.6.4"
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version = "0.6.4"
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@ -397,7 +343,7 @@ source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "32cb0b9bc82b0a0876c2dd994a7e7a2683d3e7390ca40e6886785ef0c7e3ee31"
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checksum = "32cb0b9bc82b0a0876c2dd994a7e7a2683d3e7390ca40e6886785ef0c7e3ee31"
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dependencies = [
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dependencies = [
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"num-traits",
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"num-traits",
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"rand 0.8.5",
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"rand",
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]
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]
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[[package]]
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[[package]]
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@ -406,15 +352,6 @@ version = "0.2.1"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "60a357793950651c4ed0f3f52338f53b2f809f32d83a07f72909fa13e4c6c1e3"
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checksum = "60a357793950651c4ed0f3f52338f53b2f809f32d83a07f72909fa13e4c6c1e3"
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[[package]]
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name = "rdrand"
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version = "0.4.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "678054eb77286b51581ba43620cc911abf02758c91f93f479767aed0f90458b2"
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dependencies = [
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"rand_core 0.3.1",
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]
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[[package]]
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[[package]]
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name = "safe_arch"
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name = "safe_arch"
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version = "0.7.4"
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version = "0.7.4"
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@ -446,7 +383,7 @@ dependencies = [
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"approx",
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"approx",
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"nalgebra",
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"nalgebra",
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"num-traits",
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"num-traits",
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"rand 0.8.5",
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"rand",
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]
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]
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[[package]]
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[[package]]
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@ -500,28 +437,6 @@ dependencies = [
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"safe_arch",
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"safe_arch",
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]
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]
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[[package]]
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name = "winapi"
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version = "0.3.9"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "5c839a674fcd7a98952e593242ea400abe93992746761e38641405d28b00f419"
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dependencies = [
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"winapi-i686-pc-windows-gnu",
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"winapi-x86_64-pc-windows-gnu",
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]
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[[package]]
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name = "winapi-i686-pc-windows-gnu"
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version = "0.4.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "ac3b87c63620426dd9b991e5ce0329eff545bccbbb34f3be09ff6fb6ab51b7b6"
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[[package]]
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name = "winapi-x86_64-pc-windows-gnu"
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version = "0.4.0"
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source = "registry+https://github.com/rust-lang/crates.io-index"
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checksum = "712e227841d057c1ee1cd2fb22fa7e5a5461ae8e48fa2ca79ec42cfc1931183f"
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[[package]]
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[[package]]
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name = "zerocopy"
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name = "zerocopy"
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version = "0.7.35"
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version = "0.7.35"
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@ -9,7 +9,6 @@ crate-type = ["cdylib", "staticlib", "lib"]
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[dependencies]
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[dependencies]
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flate2 = "1.0.35"
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flate2 = "1.0.35"
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kolmogorov_smirnov = "1.1.0"
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pyo3 = {version = "0.23.4", optional = true}
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pyo3 = {version = "0.23.4", optional = true}
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statrs = "0.18.0"
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statrs = "0.18.0"
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15
readme.md
15
readme.md
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@ -103,7 +103,7 @@ ChiBit | 0.9299 | 0.9299 | |
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ChiByte | 0.9819 | 0.9819 | |
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ChiByte | 0.9819 | 0.9819 | |
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MeanByte | 0.7964 | 0.7964 | |
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MeanByte | 0.7964 | 0.7964 | |
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Compression | N/A | 0.0146 | |
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Compression | N/A | 0.0146 | |
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KS | 0.5313 | 0.2476 | Mismatch |
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KS | 0.5313 | 0.9998 | Different method |
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Pi | 0.3784 | 0.3784 | |
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Pi | 0.3784 | 0.3784 | |
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Shells | 0.7559 | 0.7559 | |
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Shells | 0.7559 | 0.7559 | |
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Gaps | 0.0000 | 0.0000 | |
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Gaps | 0.0000 | 0.0000 | |
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@ -125,7 +125,7 @@ ChiBit | 0.5590 | 0.5590 | |
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ChiByte | 0.3748 | 0.3748 | |
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ChiByte | 0.3748 | 0.3748 | |
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MeanByte | 0.0183 | 0.0183 | |
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MeanByte | 0.0183 | 0.0183 | |
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Compression | N/A | 0.9308 | |
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Compression | N/A | 0.9308 | |
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KS | 0.2900 | 0.0178 | Mismatch |
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KS | 0.2900 | 0.1158 | Different method |
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Pi | 0.9765 | 0.9765 | |
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Pi | 0.9765 | 0.9765 | |
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Shells | 0.7235 | 0.7235 | |
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Shells | 0.7235 | 0.7235 | |
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Gaps | 0.6425 | 0.6425 | |
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Gaps | 0.6425 | 0.6425 | |
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@ -145,7 +145,7 @@ ChiBit | 0.8428 | 0.8428 | |
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ChiByte | 0.5785 | 0.5785 | |
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ChiByte | 0.5785 | 0.5785 | |
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MeanByte | 0.9601 | 0.9601 | |
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MeanByte | 0.9601 | 0.9601 | |
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Compression | N/A | 0.9308 | |
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Compression | N/A | 0.9308 | |
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KS | 0.7395 | 0.0441 | Mismatch |
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KS | 0.7395 | 0.7777 | Different method |
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Pi | 0.2806 | 0.2806 | |
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Pi | 0.2806 | 0.2806 | |
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Shells | 0.7711 | 0.7711 | |
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Shells | 0.7711 | 0.7711 | |
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Gaps | 0.1937 | 0.1937 | |
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Gaps | 0.1937 | 0.1937 | |
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@ -157,14 +157,9 @@ UnCorrelation | 0.4674 | 0.4674 | |
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### Conclusions
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### Conclusions
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Although the implementation of the randomness tests closely follows the original Java logic, differences in the results arise in the Kolmogorov-Smirnov test. The external libraries used for running the test probably differ in their implementation. Also the uniform distribution to test against is provided by the Apache Commons Math library. Since it would be way beyond the scope of this porting project to try to fully match the functionality of the dependencies used we just accept the minor difference. Another issue might be that Java emphasizes predictability and portability, enforcing strict IEEE 754 behavior across platforms. Rust on the other hand prioritizes performance and flexibility, allowing platform-specific optimizations that may deviate slightly from strict IEEE semantics.
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Although the implementation of the randomness tests closely follows the original Java logic, the Kolmogorov-Smirnov test deliberately differs. The Java version compares the data against a pseudo-random uniform sample, which makes the p-value change from run to run for the same input. This port instead runs a one-sample KS test of the byte values against the exact discrete uniform distribution over 0..255, with p-values from the asymptotic Kolmogorov distribution (Stephens' small-sample correction). The result is deterministic and calibrated: on `/dev/urandom` it fails about 1% of the time at alpha = 0.01, slightly less on small inputs because the discrete null makes the test a little conservative.
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These differences are generally negligible for practical purposes and do not affect the overall functionality or
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All other differences are generally negligible for practical purposes and do not affect the overall functionality or statistical significance of the tests.
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statistical significance of the test.
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### Bonus
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We implemented a Well Equidistributed Long-period Linear pseudo-random number generator that is used with a random seed derived from an epoch timestamp that is being used as uniform distribution for the KS test.
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## License
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## License
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@ -23,79 +23,104 @@
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// SOFTWARE.
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// SOFTWARE.
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use kolmogorov_smirnov::test_f64;
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use std::time::{SystemTime, UNIX_EPOCH};
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use statrs::distribution::ContinuousCDF;
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use crate::Onod;
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use crate::Onod;
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use crate::well19937c::Well19937c;
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impl Onod {
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impl Onod {
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/// KS randomness test
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/// KS randomness test
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/// Performs the Kolmogorov-Smirnov test to evaluate the uniformity of data distribution
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/// Performs a one-sample Kolmogorov-Smirnov test of the byte values against the
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/// and returns the test statistic (D-statistic), z-score, and p-value.
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/// exact discrete uniform distribution over 0..=255 and returns the test statistic
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/// (D-statistic), the scaled statistic sqrt(n)*D, and the p-value.
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pub fn ks(samples: &[u8]) -> (f64, f64, f64) {
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pub fn ks(samples: &[u8]) -> (f64, f64, f64) {
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if samples.is_empty() {
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if samples.is_empty() {
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return (-1.0, 0.0, 1.0); // Invalid input
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return (-1.0, 0.0, 1.0); // Invalid input
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}
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}
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// Normalize the input samples to [0, 1) range
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let mut counts = [0u64; 256];
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let mut normalized_samples: Vec<f64> = samples.iter().map(|&x| x as f64 / 255.0).collect();
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for &b in samples {
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counts[b as usize] += 1;
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// Generate a uniform distribution for comparison
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let mut uniform_distribution: Vec<f64> = Self::generate_uniform_distribution(normalized_samples.len(), Self::get_timestamp_seed());
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// Sort both distributions
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normalized_samples.sort_by(|a, b| a.partial_cmp(b).unwrap());
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uniform_distribution.sort_by(|a, b| a.partial_cmp(b).unwrap());
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let debug = false;
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// Debugging: Optional print sorted values
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if debug {
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println!("Sorted Normalized Samples: {:?}", normalized_samples);
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println!("Sorted Uniform Distribution: {:?}", uniform_distribution);
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}
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}
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// Perform the Kolmogorov-Smirnov test
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// Both CDFs are step functions that jump only at the byte values, so the
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let confidence = 0.05; // Significance level
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// supremum of their difference is reached at one of those 256 points.
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let result = test_f64(&normalized_samples, &uniform_distribution, confidence);
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let n = samples.len() as f64;
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let mut cumulative = 0u64;
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// Extract the KS statistic (D-statistic)
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let mut ks_statistic: f64 = 0.0;
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let ks_statistic = result.statistic;
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for (k, &count) in counts.iter().enumerate() {
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cumulative += count;
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// Debugging: Print ECDF differences and max difference (D-statistic)
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let empirical = cumulative as f64 / n;
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if debug {
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let expected = (k + 1) as f64 / 256.0;
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for (i, (&sample, &uniform)) in normalized_samples.iter().zip(&uniform_distribution).enumerate() {
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ks_statistic = ks_statistic.max((empirical - expected).abs());
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let diff = (sample - uniform).abs();
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println!(
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"Index: {}, Sample: {:.6}, Uniform: {:.6}, Difference: {:.6}",
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i, sample, uniform, diff
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);
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}
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println!("D-Statistic: {:.6}", ks_statistic);
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}
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}
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// Calculate the z-score
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let sqrt_n = n.sqrt();
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let sample_size = normalized_samples.len() as f64;
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let z_score = ks_statistic * sqrt_n;
|
||||||
let z_score = ks_statistic * sample_size.sqrt();
|
|
||||||
|
// Asymptotic Kolmogorov distribution with Stephens' small-sample correction.
|
||||||
// Calculate the p-value
|
// For a discrete null this is slightly conservative.
|
||||||
let p_value = 2.0 * (1.0 - statrs::distribution::Normal::new(0.0, 1.0).unwrap().cdf(z_score.abs()));
|
let p_value = Self::kolmogorov_survival((sqrt_n + 0.12 + 0.11 / sqrt_n) * ks_statistic);
|
||||||
|
|
||||||
(ks_statistic, z_score, p_value)
|
(ks_statistic, z_score, p_value)
|
||||||
}
|
}
|
||||||
|
|
||||||
/// Generates a uniform distribution of the same length as the input data.
|
/// P(K > lambda) for the Kolmogorov distribution.
|
||||||
fn generate_uniform_distribution(len: usize, seed: u32) -> Vec<f64> {
|
fn kolmogorov_survival(lambda: f64) -> f64 {
|
||||||
let mut rng = Well19937c::new(seed);
|
if lambda <= 0.0 {
|
||||||
(0..len).map(|_| rng.next_f64()).collect()
|
return 1.0;
|
||||||
|
}
|
||||||
|
if lambda < 1.18 {
|
||||||
|
// P(K <= lambda) = sqrt(2*pi)/lambda * sum_k exp(-(2k-1)^2 * pi^2 / (8*lambda^2))
|
||||||
|
let w = -std::f64::consts::PI.powi(2) / (8.0 * lambda * lambda);
|
||||||
|
let cdf: f64 = (1..=8)
|
||||||
|
.map(|k| (((2 * k - 1) as f64).powi(2) * w).exp())
|
||||||
|
.sum::<f64>()
|
||||||
|
* (2.0 * std::f64::consts::PI).sqrt()
|
||||||
|
/ lambda;
|
||||||
|
(1.0 - cdf).clamp(0.0, 1.0)
|
||||||
|
} else {
|
||||||
|
// P(K > lambda) = 2 * sum_k (-1)^(k-1) * exp(-2 * k^2 * lambda^2)
|
||||||
|
let survival: f64 = (1..=100)
|
||||||
|
.map(|k| {
|
||||||
|
let sign = if k % 2 == 1 { 1.0 } else { -1.0 };
|
||||||
|
sign * (-2.0 * (k * k) as f64 * lambda * lambda).exp()
|
||||||
|
})
|
||||||
|
.sum::<f64>()
|
||||||
|
* 2.0;
|
||||||
|
survival.clamp(0.0, 1.0)
|
||||||
|
}
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
||||||
|
#[cfg(test)]
|
||||||
|
mod tests {
|
||||||
|
use crate::Onod;
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn perfectly_uniform_bytes_pass() {
|
||||||
|
let samples: Vec<u8> = (0..1024).map(|i| i as u8).collect();
|
||||||
|
let (d, _, p) = Onod::ks(&samples);
|
||||||
|
assert_eq!(d, 0.0);
|
||||||
|
assert_eq!(p, 1.0);
|
||||||
}
|
}
|
||||||
|
|
||||||
fn get_timestamp_seed() -> u32 {
|
#[test]
|
||||||
let duration = SystemTime::now()
|
fn skewed_bytes_fail() {
|
||||||
.duration_since(UNIX_EPOCH)
|
let samples: Vec<u8> = (0..4096).map(|i| (i % 128) as u8).collect();
|
||||||
.expect("Time went backwards");
|
let (_, _, p) = Onod::ks(&samples);
|
||||||
// Use seconds or nanoseconds as the seed
|
assert!(p < 1e-6);
|
||||||
(duration.as_secs() as u32) ^ (duration.subsec_nanos())
|
|
||||||
}
|
}
|
||||||
}
|
|
||||||
|
#[test]
|
||||||
|
fn deterministic() {
|
||||||
|
let samples: Vec<u8> = (0..10_000u32).map(|i| (i.wrapping_mul(2654435761) >> 24) as u8).collect();
|
||||||
|
assert_eq!(Onod::ks(&samples), Onod::ks(&samples));
|
||||||
|
}
|
||||||
|
|
||||||
|
#[test]
|
||||||
|
fn kolmogorov_reference_values() {
|
||||||
|
// Critical values of the Kolmogorov distribution.
|
||||||
|
assert!((Onod::kolmogorov_survival(1.3581) - 0.05).abs() < 1e-4);
|
||||||
|
assert!((Onod::kolmogorov_survival(1.6276) - 0.01).abs() < 1e-4);
|
||||||
|
// Both series agree at the switch point.
|
||||||
|
assert!((Onod::kolmogorov_survival(1.18 - 1e-12) - Onod::kolmogorov_survival(1.18)).abs() < 1e-9);
|
||||||
|
}
|
||||||
|
}
|
||||||
|
|
|
||||||
Loading…
Add table
Add a link
Reference in a new issue