├── fast-rng ├── gradle.properties ├── src │ ├── test │ │ └── java │ │ │ └── biz │ │ │ └── k11i │ │ │ └── rng │ │ │ ├── GaussianRNGTest.java │ │ │ ├── UniformRNGUtilsTest.java │ │ │ ├── ExponentialRNGTest.java │ │ │ ├── GammaRNGTest.java │ │ │ └── BetaRNGTest.java │ └── main │ │ └── java │ │ └── biz │ │ └── k11i │ │ └── rng │ │ ├── UniformRNGUtils.java │ │ ├── ExponentialRNG.java │ │ ├── BetaRNG.java │ │ ├── GaussianRNG.java │ │ └── GammaRNG.java └── build.gradle ├── .travis.yml ├── .gitignore ├── gradle └── wrapper │ ├── gradle-wrapper.jar │ └── gradle-wrapper.properties ├── settings.gradle ├── Makefile ├── fast-rng-test ├── src │ ├── main │ │ ├── resources │ │ │ └── simplelogger.properties │ │ └── java │ │ │ └── biz │ │ │ └── k11i │ │ │ └── rng │ │ │ └── test │ │ │ ├── util │ │ │ ├── distribution │ │ │ │ ├── DiscreteDistribution.java │ │ │ │ ├── ContinuousDistribution.java │ │ │ │ ├── ContinuousDistributionBase.java │ │ │ │ └── ProbabilityDistributions.java │ │ │ ├── inference │ │ │ │ ├── MTest.java │ │ │ │ └── AndersonDarlingTest.java │ │ │ ├── SplittableRandomWrapper.java │ │ │ └── ComputationAndSorting.java │ │ │ ├── SecondLevelTest.java │ │ │ └── gof │ │ │ ├── GoodnessOfFitTest.java │ │ │ ├── ContinuousGofTest.java │ │ │ └── DiscreteGofTest.java │ ├── test │ │ └── java │ │ │ └── biz │ │ │ └── k11i │ │ │ └── rng │ │ │ └── test │ │ │ ├── SecondLevelTestTest.java │ │ │ └── util │ │ │ ├── inference │ │ │ ├── AndersonDarlingTestTest.java │ │ │ └── MTestTest.java │ │ │ └── distribution │ │ │ ├── ProbabilityDistributionTestBase.java │ │ │ ├── BetaTest.java │ │ │ ├── GammaTest.java │ │ │ └── GaussianTest.java │ └── jmh │ │ └── java │ │ └── biz │ │ └── k11i │ │ └── rng │ │ └── test │ │ └── util │ │ └── distribution │ │ └── BetaDistributionBenchmark.java └── build.gradle ├── NOTICE-commons-math3.txt ├── .github └── workflows │ └── test.yml ├── benchmark ├── build.gradle └── src │ └── jmh │ └── java │ └── biz │ └── k11i │ └── rng │ ├── util │ ├── ParameterPool.java │ ├── UniformRandomSupplier.java │ ├── MtRandom.java │ └── ThreadLocalRandomGenerator.java │ ├── ExponentialBenchmark.java │ ├── GaussianBenchmark.java │ ├── NextIntWithBoundBenchmark.java │ ├── GammaBenchmark.java │ └── BetaBenchmark.java ├── RELEASE-NOTES.md ├── .circleci └── config.yml ├── LICENSE ├── gradlew.bat ├── README.md └── gradlew /fast-rng/gradle.properties: -------------------------------------------------------------------------------- 1 | release.useAutomaticVersion = true 2 | version = 0.2.1-SNAPSHOT 3 | -------------------------------------------------------------------------------- /.travis.yml: -------------------------------------------------------------------------------- 1 | language: java 2 | script: travis_wait 60 ./gradlew clean check 3 | jdk: 4 | - oraclejdk7 5 | - openjdk7 6 | -------------------------------------------------------------------------------- /.gitignore: -------------------------------------------------------------------------------- 1 | # Gradle 2 | .gradle/ 3 | build/ 4 | 5 | # IntelliJ IDEA 6 | out/ 7 | .idea/ 8 | *.iml 9 | 10 | .envrc 11 | -------------------------------------------------------------------------------- /gradle/wrapper/gradle-wrapper.jar: -------------------------------------------------------------------------------- https://raw.githubusercontent.com/komiya-atsushi/fast-rng-java/HEAD/gradle/wrapper/gradle-wrapper.jar -------------------------------------------------------------------------------- /settings.gradle: -------------------------------------------------------------------------------- 1 | rootProject.name = 'fast-rng-java' 2 | include 'fast-rng' 3 | include 'benchmark' 4 | include 'fast-rng-test' 5 | -------------------------------------------------------------------------------- /Makefile: -------------------------------------------------------------------------------- 1 | GRADLE = ./gradlew 2 | 3 | 4 | .PHONY: test release 5 | 6 | test: 7 | $(GRADLE) test 8 | 9 | release: 10 | $(GRADLE) clean fast-rng:release --no-daemon -x test 11 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/resources/simplelogger.properties: -------------------------------------------------------------------------------- 1 | org.slf4j.simpleLogger.showDateTime=true 2 | org.slf4j.simpleLogger.logFile=System.out 3 | org.slf4j.simpleLogger.dateTimeFormat=yyyy-MM-dd HH:mm:ss:SSS Z 4 | org.slf4j.simpleLogger.showShortLogName=true 5 | -------------------------------------------------------------------------------- /gradle/wrapper/gradle-wrapper.properties: -------------------------------------------------------------------------------- 1 | #Thu Apr 18 00:17:42 JST 2019 2 | distributionBase=GRADLE_USER_HOME 3 | distributionPath=wrapper/dists 4 | zipStoreBase=GRADLE_USER_HOME 5 | zipStorePath=wrapper/dists 6 | distributionUrl=https\://services.gradle.org/distributions/gradle-5.4-all.zip 7 | -------------------------------------------------------------------------------- /NOTICE-commons-math3.txt: -------------------------------------------------------------------------------- 1 | Apache Commons Math 2 | Copyright 2001-2016 The Apache Software Foundation 3 | 4 | This product includes software developed at 5 | The Apache Software Foundation (http://www.apache.org/). 6 | 7 | This product includes software developed for Orekit by 8 | CS Systèmes d'Information (http://www.c-s.fr/) 9 | Copyright 2010-2012 CS Systèmes d'Information -------------------------------------------------------------------------------- /.github/workflows/test.yml: -------------------------------------------------------------------------------- 1 | name: test 2 | on: push 3 | 4 | jobs: 5 | test: 6 | runs-on: ubuntu-latest 7 | strategy: 8 | matrix: 9 | java: [ '1.8', '11' ] 10 | steps: 11 | - uses: actions/checkout@master 12 | - uses: actions/setup-java@master 13 | with: 14 | java-version: ${{ matrix.java }} 15 | - name: Run tests 16 | run: ./gradlew test 17 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/util/distribution/DiscreteDistribution.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | /** 4 | * Discrete probability distribution. 5 | */ 6 | public interface DiscreteDistribution { 7 | /** 8 | * Calculates cumulative distribution function. 9 | */ 10 | double cdf(int x); 11 | 12 | /** 13 | * Calculates inverse distribution function. 14 | */ 15 | int inverseCdf(double p); 16 | } 17 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/util/distribution/ContinuousDistribution.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | /** 4 | * Continuous probability distribution. 5 | */ 6 | public interface ContinuousDistribution { 7 | /** 8 | * Calculates cumulative distribution function. 9 | */ 10 | double cdf(double x); 11 | 12 | /** 13 | * Calculates inverse distribution function. 14 | */ 15 | double inverseCdf(double p); 16 | } 17 | -------------------------------------------------------------------------------- /benchmark/build.gradle: -------------------------------------------------------------------------------- 1 | plugins { 2 | id 'me.champeau.gradle.jmh' version '0.4.8' 3 | } 4 | 5 | dependencies { 6 | jmh group: 'org.apache.commons', name: 'commons-math3', version: '3.6' 7 | jmh project(':fast-rng') 8 | } 9 | 10 | jmh { 11 | fork = 3 12 | humanOutputFile = project.file("${project.buildDir}/reports/jmh/human.txt") 13 | resultsFile = project.file("${project.buildDir}/reports/jmh/results.txt") 14 | resultFormat = 'CSV' 15 | // threads = 100 16 | } 17 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/util/ParameterPool.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.util; 2 | 3 | import biz.k11i.rng.ExponentialRNG; 4 | import biz.k11i.rng.util.MtRandom; 5 | 6 | public class ParameterPool { 7 | private double[] parameters; 8 | private int index; 9 | 10 | public ParameterPool(int seed, int count, double theta) { 11 | parameters = new double[count]; 12 | MtRandom r = new MtRandom(seed); 13 | 14 | for (int i = 0; i < count; i++) { 15 | parameters[i] = Math.nextUp(ExponentialRNG.FAST_RNG.generate(r, theta)); 16 | } 17 | } 18 | 19 | public double next() { 20 | if (index >= parameters.length) { 21 | index = 0; 22 | } 23 | 24 | return parameters[index++]; 25 | } 26 | } 27 | -------------------------------------------------------------------------------- /RELEASE-NOTES.md: -------------------------------------------------------------------------------- 1 | # Release notes 2 | 3 | ## 0.2.0 4 | 5 | - Fast-rng now requires Java 8 or later. 6 | - Introduces a new class [`UniformRNGUtils`](fast-rng/src/main/java/biz/k11i/rng/UniformRNGUtils.java). 7 | - The method `UniformRNGUtils#nextInt(java.util.Random random, int bound)` is faster than [`Random#nextInt(int bound)`](https://docs.oracle.com/javase/8/docs/api/java/util/Random.html#nextInt-int-). 8 | 9 | ## 0.1.5 10 | 11 | - Support beta random number generator 12 | 13 | ## 0.1.4 14 | 15 | - Improve speed performance of `GammaRNG` 16 | 17 | ## 0.1.3 18 | 19 | - Support exponential random number generator 20 | 21 | ## 0.1.2 22 | 23 | - Provide two implementations of Ziggurat algorithm for Gaussian RNG 24 | - `GaussianRNG.FAST_RNG` and `GaussianRNG.GENERAL_RNG` 25 | 26 | ## 0.1.1 27 | 28 | - Support gamma random number generator 29 | 30 | 31 | ## 0.1.0 32 | 33 | - Initial release 34 | - Support gaussian random number generator 35 | -------------------------------------------------------------------------------- /.circleci/config.yml: -------------------------------------------------------------------------------- 1 | version: 2.1 2 | 3 | executors: 4 | builder: 5 | docker: 6 | - image: circleci/openjdk:8-jdk 7 | working_directory: 8 | /tmp/workspace 9 | 10 | jobs: 11 | test: 12 | executor: builder 13 | steps: 14 | - checkout 15 | - restore_cache: 16 | key: gradle-cache 17 | - run: 18 | name: Run tests 19 | command: ./gradlew fast-rng:test 20 | - run: 21 | name: Save test results 22 | command: | 23 | mkdir -p ~/test-results/junit/ 24 | find . -type f -regex ".*/build/test-results/.*xml" -exec cp {} ~/test-results/junit/ \; 25 | when: always 26 | - store_test_results: 27 | path: ~/test-results 28 | - store_artifacts: 29 | path: ~/test-results/junit 30 | - save_cache: 31 | paths: 32 | - ~/.gradle 33 | key: gradle-cache 34 | 35 | workflows: 36 | test: 37 | jobs: 38 | - test 39 | -------------------------------------------------------------------------------- /fast-rng-test/build.gradle: -------------------------------------------------------------------------------- 1 | plugins { 2 | id 'java-library' 3 | id 'me.champeau.gradle.jmh' version '0.4.8' 4 | } 5 | 6 | repositories { 7 | mavenCentral() 8 | } 9 | 10 | dependencies { 11 | api platform(group: 'org.junit', name: 'junit-bom', version: '5.5.2') 12 | api group: 'org.junit.jupiter', name: 'junit-jupiter-api' 13 | api group: 'org.junit.jupiter', name: 'junit-jupiter-params' 14 | api group: 'org.junit.jupiter', name: 'junit-jupiter-engine' 15 | api group: 'org.assertj', name: 'assertj-core', version: '3.11.1' 16 | api group: 'org.apache.commons', name: 'commons-math3', version: '3.6.1' 17 | api group: 'net.jafama', name: 'jafama', version: '2.3.1' 18 | api group: 'org.slf4j', name: 'slf4j-api', version: '1.7.28' 19 | api group: 'org.slf4j', name: 'slf4j-simple', version: '1.7.28' 20 | } 21 | 22 | test { 23 | useJUnitPlatform() 24 | } 25 | 26 | jmh { 27 | // fork = 1 28 | // warmup = '1s' 29 | // timeOnIteration = '1s' 30 | } 31 | -------------------------------------------------------------------------------- /fast-rng/src/test/java/biz/k11i/rng/GaussianRNGTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import biz.k11i.rng.test.gof.GoodnessOfFitTest; 4 | import biz.k11i.rng.test.SecondLevelTest; 5 | import biz.k11i.rng.test.util.distribution.ProbabilityDistributions; 6 | import org.junit.jupiter.api.Test; 7 | 8 | class GaussianRNGTest { 9 | @Test 10 | void testFast() { 11 | test(GaussianRNG.FAST_RNG); 12 | } 13 | 14 | @Test 15 | void testGeneral() { 16 | test(GaussianRNG.GENERAL_RNG); 17 | } 18 | 19 | private void test(GaussianRNG rng) { 20 | GoodnessOfFitTest gofTest = GoodnessOfFitTest.continuous() 21 | .probabilityDistribution(ProbabilityDistributions.gaussian(0.0, 1.0)) 22 | .randomNumberGenerator("Gaussian", rng::generate) 23 | .numRandomValues(2_000_000) 24 | .build(); 25 | 26 | SecondLevelTest.builder() 27 | .numIterations(20) 28 | .build() 29 | .testAndVerify(gofTest); 30 | } 31 | } 32 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/util/UniformRandomSupplier.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.util; 2 | 3 | import org.apache.commons.math3.random.MersenneTwister; 4 | import org.apache.commons.math3.random.RandomGenerator; 5 | 6 | import java.util.Random; 7 | import java.util.concurrent.ThreadLocalRandom; 8 | 9 | public enum UniformRandomSupplier { 10 | THREAD_LOCAL_RANDOM() { 11 | @Override 12 | Random newRandom() { 13 | return ThreadLocalRandom.current(); 14 | } 15 | 16 | @Override 17 | RandomGenerator newRandomGenerator() { 18 | return new ThreadLocalRandomGenerator(); 19 | } 20 | }, 21 | MERSENNE_TWISTER() { 22 | @Override 23 | Random newRandom() { 24 | return new MtRandom(); 25 | } 26 | 27 | @Override 28 | RandomGenerator newRandomGenerator() { 29 | return new MersenneTwister(); 30 | } 31 | } 32 | ; 33 | 34 | abstract Random newRandom(); 35 | 36 | abstract RandomGenerator newRandomGenerator(); 37 | } 38 | -------------------------------------------------------------------------------- /fast-rng-test/src/test/java/biz/k11i/rng/test/SecondLevelTestTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test; 2 | 3 | import biz.k11i.rng.test.gof.GoodnessOfFitTest; 4 | import biz.k11i.rng.test.util.distribution.ProbabilityDistributions; 5 | import org.junit.jupiter.api.Test; 6 | 7 | import java.util.Random; 8 | 9 | import static org.assertj.core.api.Assertions.assertThatThrownBy; 10 | 11 | class SecondLevelTestTest { 12 | @Test 13 | void test() { 14 | GoodnessOfFitTest gofTest = GoodnessOfFitTest.continuous() 15 | .probabilityDistribution(ProbabilityDistributions.gaussian(0.0, 1.002 /* not 1.0 */)) 16 | .numRandomValues(1_000_000) 17 | .randomNumberGenerator("buggy", Random::nextGaussian) 18 | .build(); 19 | 20 | SecondLevelTest secondLevelTest = SecondLevelTest.builder() 21 | .numIterations(20) 22 | .build(); 23 | 24 | assertThatThrownBy(() -> secondLevelTest.testAndVerify(gofTest)) 25 | .isInstanceOf(AssertionError.class); 26 | } 27 | } 28 | -------------------------------------------------------------------------------- /LICENSE: -------------------------------------------------------------------------------- 1 | The MIT License (MIT) 2 | 3 | Copyright (c) 2016 KOMIYA Atsushi 4 | 5 | Permission is hereby granted, free of charge, to any person obtaining a copy 6 | of this software and associated documentation files (the "Software"), to deal 7 | in the Software without restriction, including without limitation the rights 8 | to use, copy, modify, merge, publish, distribute, sublicense, and/or sell 9 | copies of the Software, and to permit persons to whom the Software is 10 | furnished to do so, subject to the following conditions: 11 | 12 | The above copyright notice and this permission notice shall be included in all 13 | copies or substantial portions of the Software. 14 | 15 | THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR 16 | IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, 17 | FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE 18 | AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER 19 | LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, 20 | OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE 21 | SOFTWARE. 22 | -------------------------------------------------------------------------------- /fast-rng/src/test/java/biz/k11i/rng/UniformRNGUtilsTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import biz.k11i.rng.test.SecondLevelTest; 4 | import biz.k11i.rng.test.gof.GoodnessOfFitTest; 5 | import org.apache.commons.math3.distribution.UniformIntegerDistribution; 6 | import org.junit.jupiter.params.ParameterizedTest; 7 | import org.junit.jupiter.params.provider.MethodSource; 8 | 9 | import java.util.stream.Stream; 10 | 11 | class UniformRNGUtilsTest { 12 | static Stream bounds() { 13 | return Stream.of(3, 7, 997, 100_000, (1 << 30) + (1 << 29), Integer.MAX_VALUE - 1); 14 | } 15 | 16 | @ParameterizedTest 17 | @MethodSource("bounds") 18 | void test(int bound) { 19 | GoodnessOfFitTest gofTest = GoodnessOfFitTest.discrete() 20 | .probabilityDistribution(new UniformIntegerDistribution(0, bound - 1)) 21 | .randomNumberGenerator(String.format("Nearly divisionless nextInt(%d)", bound), r -> UniformRNGUtils.nextInt(r, bound)) 22 | .numRandomValues(2_000_000) 23 | .maxFrequencyBins(1000) 24 | .build(); 25 | 26 | SecondLevelTest.builder() 27 | .numIterations(20) 28 | .build() 29 | .testAndVerify(gofTest); 30 | } 31 | } 32 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/ExponentialBenchmark.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import biz.k11i.rng.util.ThreadLocalRandomGenerator; 4 | import org.apache.commons.math3.distribution.ExponentialDistribution; 5 | import org.openjdk.jmh.annotations.Benchmark; 6 | import org.openjdk.jmh.annotations.Scope; 7 | import org.openjdk.jmh.annotations.Setup; 8 | import org.openjdk.jmh.annotations.State; 9 | 10 | import java.util.concurrent.ThreadLocalRandom; 11 | 12 | @State(Scope.Benchmark) 13 | public class ExponentialBenchmark { 14 | private ExponentialDistribution exponentialDistribution; 15 | 16 | @Setup 17 | public void setUp() { 18 | exponentialDistribution = new ExponentialDistribution( 19 | new ThreadLocalRandomGenerator(), 20 | 1.0, 21 | ExponentialDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY); 22 | } 23 | 24 | @Benchmark 25 | public double commonsMath3_algorithmSA() { 26 | return exponentialDistribution.sample(); 27 | } 28 | 29 | @Benchmark 30 | public double fastRng_fast() { 31 | return ExponentialRNG.FAST_RNG.generate(ThreadLocalRandom.current(), 1.0); 32 | } 33 | 34 | @Benchmark 35 | public double fastRng_general() { 36 | return ExponentialRNG.GENERAL_RNG.generate(ThreadLocalRandom.current(), 1.0); 37 | } 38 | } 39 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/GaussianBenchmark.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import org.openjdk.jmh.annotations.Benchmark; 4 | import org.openjdk.jmh.annotations.Scope; 5 | import org.openjdk.jmh.annotations.State; 6 | 7 | import java.util.Random; 8 | import java.util.concurrent.ThreadLocalRandom; 9 | 10 | @State(Scope.Thread) 11 | public class GaussianBenchmark { 12 | private static Random javaUtilRandom = new Random(); 13 | 14 | @Benchmark 15 | public double javaUtilRandom() { 16 | return javaUtilRandom.nextGaussian(); 17 | } 18 | 19 | @Benchmark 20 | public double threadLocalRandom() { 21 | return ThreadLocalRandom.current().nextGaussian(); 22 | } 23 | 24 | @Benchmark 25 | public double fastRngWithThreadLocalRandom() { 26 | return GaussianRNG.FAST_RNG.generate(ThreadLocalRandom.current()); 27 | } 28 | 29 | @Benchmark 30 | public double fastRngWithJavaUtilRandom() { 31 | return GaussianRNG.FAST_RNG.generate(javaUtilRandom); 32 | } 33 | 34 | @Benchmark 35 | public double generalRngWithThreadLocalRandom() { 36 | return GaussianRNG.GENERAL_RNG.generate(ThreadLocalRandom.current()); 37 | } 38 | 39 | @Benchmark 40 | public double generalRngWithJavaUtilRandom() { 41 | return GaussianRNG.GENERAL_RNG.generate(javaUtilRandom); 42 | } 43 | } 44 | -------------------------------------------------------------------------------- /fast-rng/src/test/java/biz/k11i/rng/ExponentialRNGTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import biz.k11i.rng.test.SecondLevelTest; 4 | import biz.k11i.rng.test.gof.GoodnessOfFitTest; 5 | import org.apache.commons.math3.distribution.ExponentialDistribution; 6 | import org.junit.jupiter.params.ParameterizedTest; 7 | import org.junit.jupiter.params.provider.MethodSource; 8 | 9 | import java.util.stream.Stream; 10 | 11 | class ExponentialRNGTest { 12 | static Stream parameter() { 13 | return Stream.of(0.01, 1.0, 100.0); 14 | } 15 | 16 | @ParameterizedTest 17 | @MethodSource("parameter") 18 | void testFast(double theta) { 19 | test(ExponentialRNG.FAST_RNG, theta); 20 | } 21 | 22 | @ParameterizedTest 23 | @MethodSource("parameter") 24 | void testGeneral(double theta) { 25 | test(ExponentialRNG.GENERAL_RNG, theta); 26 | } 27 | 28 | private void test(ExponentialRNG rng, double theta) { 29 | GoodnessOfFitTest gofTest = GoodnessOfFitTest.continuous() 30 | .probabilityDistribution(new ExponentialDistribution(theta)) 31 | .randomNumberGenerator(String.format("Exp(%f)", theta), r -> rng.generate(r, theta)) 32 | .numRandomValues(2_000_000) 33 | .build(); 34 | 35 | SecondLevelTest.builder() 36 | .numIterations(20) 37 | .build() 38 | .testAndVerify(gofTest); 39 | } 40 | } 41 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/util/MtRandom.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.util; 2 | 3 | import org.apache.commons.math3.random.MersenneTwister; 4 | 5 | import java.util.Random; 6 | 7 | public class MtRandom extends Random { 8 | private final MersenneTwister mersenneTwister; 9 | 10 | public MtRandom() { 11 | mersenneTwister = new MersenneTwister(); 12 | } 13 | 14 | public MtRandom(int seed) { 15 | mersenneTwister = new MersenneTwister(seed); 16 | } 17 | 18 | @Override 19 | public boolean nextBoolean() { 20 | return mersenneTwister.nextBoolean(); 21 | } 22 | 23 | @Override 24 | public void nextBytes(byte[] bytes) { 25 | mersenneTwister.nextBytes(bytes); 26 | } 27 | 28 | @Override 29 | public double nextDouble() { 30 | return mersenneTwister.nextDouble(); 31 | } 32 | 33 | @Override 34 | public float nextFloat() { 35 | return mersenneTwister.nextFloat(); 36 | } 37 | 38 | @Override 39 | public double nextGaussian() { 40 | return mersenneTwister.nextGaussian(); 41 | } 42 | 43 | @Override 44 | public int nextInt() { 45 | return mersenneTwister.nextInt(); 46 | } 47 | 48 | @Override 49 | public int nextInt(int n) throws IllegalArgumentException { 50 | return mersenneTwister.nextInt(n); 51 | } 52 | 53 | @Override 54 | public long nextLong() { 55 | return mersenneTwister.nextLong(); 56 | } 57 | } 58 | -------------------------------------------------------------------------------- /fast-rng/src/test/java/biz/k11i/rng/GammaRNGTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import biz.k11i.rng.test.SecondLevelTest; 4 | import biz.k11i.rng.test.gof.GoodnessOfFitTest; 5 | import biz.k11i.rng.test.util.distribution.ProbabilityDistributions; 6 | import org.junit.jupiter.params.ParameterizedTest; 7 | import org.junit.jupiter.params.provider.MethodSource; 8 | 9 | import java.util.stream.Stream; 10 | 11 | class GammaRNGTest { 12 | private static final double SCALE = 0.01; 13 | 14 | static Stream parameter() { 15 | return Stream.of(0.05, 0.1, 0.5, 0.9, 1.0, 1.1, 50.0, 10000.0); 16 | } 17 | 18 | @ParameterizedTest 19 | @MethodSource("parameter") 20 | void testFast(double shape) { 21 | test(GammaRNG.FAST_RNG, shape); 22 | } 23 | 24 | @ParameterizedTest 25 | @MethodSource("parameter") 26 | void testGeneral(double shape) { 27 | test(GammaRNG.GENERAL_RNG, shape); 28 | } 29 | 30 | private void test(GammaRNG rng, double shape) { 31 | GoodnessOfFitTest gofTest = GoodnessOfFitTest.continuous() 32 | .probabilityDistribution(ProbabilityDistributions.gamma(shape, SCALE)) 33 | .randomNumberGenerator(String.format("Gamma(%f, %f)", shape, SCALE), r -> rng.generate(r, shape, SCALE)) 34 | .numRandomValues(2_000_000) 35 | .build(); 36 | 37 | SecondLevelTest.builder() 38 | .numIterations(20) 39 | .build() 40 | .testAndVerify(gofTest); 41 | } 42 | } 43 | -------------------------------------------------------------------------------- /fast-rng-test/src/test/java/biz/k11i/rng/test/util/inference/AndersonDarlingTestTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.inference; 2 | 3 | import org.junit.jupiter.api.Test; 4 | 5 | import java.util.SplittableRandom; 6 | import java.util.stream.IntStream; 7 | 8 | import static org.assertj.core.api.Assertions.assertThat; 9 | 10 | class AndersonDarlingTestTest { 11 | @Test 12 | void testNonuniformityDetectin() { 13 | double[] x = new double[1000]; 14 | 15 | assertThat(AndersonDarlingTest.andersonDarlingTest(x)) 16 | .isGreaterThanOrEqualTo(0.0) 17 | .isLessThan(1e-5); 18 | } 19 | 20 | @Test 21 | void testUniformityDetection() { 22 | double[] x = new double[1000]; 23 | for (int i = 0; i < x.length; i++) { 24 | x[i] = (i) / (double) (x.length); 25 | } 26 | 27 | assertThat(AndersonDarlingTest.andersonDarlingTest(x)) 28 | .isGreaterThan(1.0 - 1e-5) 29 | .isLessThanOrEqualTo(1.0); 30 | } 31 | 32 | @Test 33 | void testRandom() { 34 | SplittableRandom r = new SplittableRandom(1); 35 | double[] pValues = IntStream.range(0, 100) 36 | .mapToDouble(ignore -> AndersonDarlingTest.andersonDarlingTest(r.doubles(100).sorted().toArray())) 37 | .peek(System.out::println) 38 | .sorted() 39 | .toArray(); 40 | 41 | assertThat(AndersonDarlingTest.andersonDarlingTest(pValues)) 42 | .isGreaterThan(1e-5) 43 | .isLessThan(1.0 - 1e-5); 44 | } 45 | } -------------------------------------------------------------------------------- /fast-rng-test/src/test/java/biz/k11i/rng/test/util/distribution/ProbabilityDistributionTestBase.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | import org.apache.commons.math3.distribution.RealDistribution; 4 | 5 | import java.util.function.DoubleFunction; 6 | import java.util.function.IntToDoubleFunction; 7 | 8 | import static org.junit.jupiter.api.Assertions.assertEquals; 9 | 10 | class ProbabilityDistributionTestBase { 11 | void testCdf( 12 | ContinuousDistribution sut, 13 | RealDistribution referenceImpl, 14 | int n, 15 | IntToDoubleFunction f, 16 | String description, 17 | DoubleFunction descriptionArgsGenerator) { 18 | 19 | for (int i = 0; i <= n; i++) { 20 | double x = f.applyAsDouble(i); 21 | assertEquals( 22 | referenceImpl.cumulativeProbability(x), 23 | sut.cdf(x), 24 | () -> String.format(description, descriptionArgsGenerator.apply(x))); 25 | } 26 | } 27 | 28 | void testInverseCdf( 29 | ContinuousDistribution sut, 30 | RealDistribution referenceImpl, 31 | int n, 32 | String description, 33 | DoubleFunction descriptionArgsGenerator) { 34 | 35 | for (int i = 0; i <= n; i++) { 36 | double p = i / (double) n; 37 | assertEquals( 38 | referenceImpl.inverseCumulativeProbability(p), 39 | sut.inverseCdf(p), 40 | () -> String.format(description, descriptionArgsGenerator.apply(p))); 41 | } 42 | } 43 | } 44 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/util/ThreadLocalRandomGenerator.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.util; 2 | 3 | import org.apache.commons.math3.random.RandomGenerator; 4 | 5 | import java.util.concurrent.ThreadLocalRandom; 6 | 7 | public class ThreadLocalRandomGenerator implements RandomGenerator { 8 | @Override 9 | public void setSeed(int seed) { 10 | ThreadLocalRandom.current().setSeed(seed); 11 | } 12 | 13 | @Override 14 | public void setSeed(int[] seed) { 15 | throw new UnsupportedOperationException(); 16 | } 17 | 18 | @Override 19 | public void setSeed(long seed) { 20 | ThreadLocalRandom.current().setSeed(seed); 21 | } 22 | 23 | @Override 24 | public void nextBytes(byte[] bytes) { 25 | ThreadLocalRandom.current().nextBytes(bytes); 26 | } 27 | 28 | @Override 29 | public int nextInt() { 30 | return ThreadLocalRandom.current().nextInt(); 31 | } 32 | 33 | @Override 34 | public int nextInt(int n) { 35 | return ThreadLocalRandom.current().nextInt(n); 36 | } 37 | 38 | @Override 39 | public long nextLong() { 40 | return ThreadLocalRandom.current().nextLong(); 41 | } 42 | 43 | @Override 44 | public boolean nextBoolean() { 45 | return ThreadLocalRandom.current().nextBoolean(); 46 | } 47 | 48 | @Override 49 | public float nextFloat() { 50 | return ThreadLocalRandom.current().nextFloat(); 51 | } 52 | 53 | @Override 54 | public double nextDouble() { 55 | return ThreadLocalRandom.current().nextDouble(); 56 | } 57 | 58 | @Override 59 | public double nextGaussian() { 60 | return ThreadLocalRandom.current().nextGaussian(); 61 | } 62 | } 63 | -------------------------------------------------------------------------------- /fast-rng-test/src/test/java/biz/k11i/rng/test/util/inference/MTestTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.inference; 2 | 3 | import org.junit.jupiter.api.Test; 4 | 5 | import java.util.Arrays; 6 | import java.util.SplittableRandom; 7 | import java.util.stream.IntStream; 8 | 9 | import static org.assertj.core.api.Assertions.assertThat; 10 | 11 | class MTestTest { 12 | @Test 13 | void testOutlierDetection() { 14 | final int N = 100; 15 | 16 | double[] probs = new double[N]; 17 | Arrays.fill(probs, 1.0 / N); 18 | 19 | long[] freqs = new long[N]; 20 | Arrays.fill(freqs, 100); 21 | freqs[0] = 40; 22 | 23 | assertThat(MTest.mTest(probs, freqs)) 24 | .isGreaterThanOrEqualTo(0.0) 25 | .isLessThan(1e-5); 26 | } 27 | 28 | @Test 29 | void testRandom() { 30 | final int N = 100; 31 | 32 | double[] probs = new double[N]; 33 | Arrays.fill(probs, 1.0 / N); 34 | 35 | SplittableRandom r = new SplittableRandom(1); 36 | double[] pValues = IntStream.range(0, 100) 37 | .mapToDouble(ignore -> { 38 | long[] freqs = new long[N]; 39 | r.ints(1000, 0, N).forEach(x -> { 40 | freqs[x]++; 41 | }); 42 | return MTest.mTest(probs, freqs); 43 | }) 44 | .peek(System.out::println) 45 | .sorted() 46 | .toArray(); 47 | 48 | // Test uniformity of p-values by Anderson-Darling test 49 | assertThat(AndersonDarlingTest.andersonDarlingTest(pValues)) 50 | .isGreaterThan(1e-5) 51 | .isLessThan(1.0 - 1e-5); 52 | } 53 | } -------------------------------------------------------------------------------- /fast-rng-test/src/test/java/biz/k11i/rng/test/util/distribution/BetaTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | import org.apache.commons.math3.distribution.BetaDistribution; 4 | import org.junit.jupiter.params.ParameterizedTest; 5 | import org.junit.jupiter.params.provider.Arguments; 6 | import org.junit.jupiter.params.provider.MethodSource; 7 | 8 | import java.util.Arrays; 9 | import java.util.stream.Stream; 10 | 11 | class BetaTest extends ProbabilityDistributionTestBase { 12 | private static final int N = 10000; 13 | 14 | private static Stream distributionParameters() { 15 | double[] values = {0.001, 0.1, 0.5, 0.999, 1.0, 1.1, 5.5, 16.0, 256.0, 1024.0}; 16 | 17 | return Arrays.stream(values) 18 | .boxed() 19 | .flatMap(alpha -> Arrays.stream(values).mapToObj(beta -> Arguments.of(alpha, beta))); 20 | } 21 | 22 | @ParameterizedTest 23 | @MethodSource("distributionParameters") 24 | void testCdf(double alpha, double beta) { 25 | testCdf( 26 | ProbabilityDistributions.beta(alpha, beta), 27 | new BetaDistribution(alpha, beta), 28 | N, 29 | i -> i / (double) N, 30 | "Beta(%f, %f).cdf(%f)", 31 | x -> new Object[]{alpha, beta, x}); 32 | } 33 | 34 | @ParameterizedTest 35 | @MethodSource("distributionParameters") 36 | void testInverseCdf(double alpha, double beta) { 37 | testInverseCdf( 38 | ProbabilityDistributions.beta(alpha, beta), 39 | new BetaDistribution(alpha, beta), 40 | N, 41 | "Beta(%f, %f).inverseCDF(%f)", 42 | p -> new Object[]{alpha, beta, p}); 43 | } 44 | } 45 | -------------------------------------------------------------------------------- /fast-rng-test/src/test/java/biz/k11i/rng/test/util/distribution/GammaTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | import org.apache.commons.math3.distribution.GammaDistribution; 4 | import org.apache.commons.math3.util.FastMath; 5 | import org.junit.jupiter.params.ParameterizedTest; 6 | import org.junit.jupiter.params.provider.Arguments; 7 | import org.junit.jupiter.params.provider.MethodSource; 8 | 9 | import java.util.Arrays; 10 | import java.util.function.IntToDoubleFunction; 11 | import java.util.stream.Stream; 12 | 13 | class GammaTest extends ProbabilityDistributionTestBase { 14 | private static final int N = 10000; 15 | 16 | private static Stream distributionParameters() { 17 | double[] values = {0.001, 0.1, 0.5, 0.999, 1.0, 1.1, 5.5, 16.0, 256.0, 1024.0}; 18 | 19 | return Arrays.stream(values) 20 | .boxed() 21 | .flatMap(shape -> Arrays.stream(values).mapToObj(scale -> Arguments.of(shape, scale))); 22 | } 23 | 24 | @ParameterizedTest 25 | @MethodSource("distributionParameters") 26 | void testCdf(double shape, double scale) { 27 | IntToDoubleFunction f = i -> (i == 0 ? 0.0 : FastMath.pow(10, (double) (i - 5000) / 100)); 28 | testCdf( 29 | ProbabilityDistributions.gamma(shape, scale), 30 | new GammaDistribution(shape, scale), 31 | N, 32 | f, 33 | "Gamma(%f, %f).cdf(%f)", 34 | x -> new Object[]{shape, scale, x}); 35 | } 36 | 37 | @ParameterizedTest 38 | @MethodSource("distributionParameters") 39 | void testInverseCdf(double shape, double scale) { 40 | testInverseCdf( 41 | ProbabilityDistributions.gamma(shape, scale), 42 | new GammaDistribution(shape, scale), 43 | N, 44 | "Gamma(%f, %f).inverseCdf(%f)", 45 | p -> new Object[]{shape, scale, p}); 46 | } 47 | } 48 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/util/inference/MTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.inference; 2 | 3 | import biz.k11i.rng.test.util.distribution.ContinuousDistribution; 4 | import biz.k11i.rng.test.util.distribution.ProbabilityDistributions; 5 | import org.apache.commons.math3.exception.DimensionMismatchException; 6 | 7 | /** 8 | * Implements M-test to detect outliers in contingency table. 9 | * 10 | *

11 | * Fuchs, Camil, and Ron Kenett. 12 | * "A test for detecting outlying cells in the multinomial distribution and two-way contingency tables." 13 | * Journal of the American Statistical Association 75.370 (1980): 395-398. 14 | *

15 | */ 16 | public class MTest { 17 | private static final ContinuousDistribution GAUSSIAN = ProbabilityDistributions.gaussian(0, 1); 18 | 19 | /** 20 | * Tests for detecting outliers in array. 21 | * 22 | * @param probs array of expected probabilities or expected frequency counts 23 | * @param freqs array of observed frequency counts 24 | * @return p-value 25 | */ 26 | public static double mTest(final double[] probs, final long[] freqs) { 27 | if (probs.length != freqs.length) { 28 | throw new DimensionMismatchException(probs.length, freqs.length); 29 | } 30 | 31 | int k = probs.length; 32 | double pSum = 0; 33 | long fSum = 0; 34 | 35 | for (int i = 0; i < k; i++) { 36 | pSum += probs[i]; 37 | fSum += freqs[i]; 38 | } 39 | 40 | double maxZ = Double.NEGATIVE_INFINITY; 41 | for (int i = 0; i < k; i++) { 42 | double mean = fSum * (probs[i] / pSum); 43 | double var = mean * (1 - probs[i] / pSum); 44 | 45 | double z = Math.abs((freqs[i] - mean) / Math.sqrt(var)); 46 | if (z > maxZ) { 47 | maxZ = z; 48 | } 49 | } 50 | 51 | return 1 - Math.pow((2 * GAUSSIAN.cdf(maxZ) - 1), k); 52 | } 53 | } 54 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/NextIntWithBoundBenchmark.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import org.openjdk.jmh.annotations.Benchmark; 4 | import org.openjdk.jmh.annotations.Param; 5 | import org.openjdk.jmh.annotations.Scope; 6 | import org.openjdk.jmh.annotations.Setup; 7 | import org.openjdk.jmh.annotations.State; 8 | 9 | import java.util.SplittableRandom; 10 | import java.util.concurrent.ThreadLocalRandom; 11 | import java.util.stream.IntStream; 12 | 13 | public class NextIntWithBoundBenchmark { 14 | @State(Scope.Benchmark) 15 | public static class FixedBound { 16 | @Param({"1025", // 2^10 + 1 17 | "1048577", // 2^20 + 1 18 | "1073741828", // 2^30 + 4 19 | }) 20 | private int bound; 21 | 22 | @Benchmark 23 | public int jdk() { 24 | return ThreadLocalRandom.current().nextInt(bound); 25 | } 26 | 27 | @Benchmark 28 | public int nearlyDivisionless() { 29 | return UniformRNGUtils.nextInt(ThreadLocalRandom.current(), bound); 30 | } 31 | } 32 | 33 | @State(Scope.Benchmark) 34 | public static class ArbitraryBounds { 35 | private static final int NUM_BOUNDS = 1 << 10; 36 | private int[] bounds; 37 | private int index; 38 | 39 | @Setup 40 | public void setUp() { 41 | SplittableRandom r = new SplittableRandom(12345); 42 | bounds = IntStream 43 | .generate(() -> r.nextInt(Integer.MAX_VALUE - 1) + 1) 44 | .limit(NUM_BOUNDS) 45 | .toArray(); 46 | } 47 | 48 | @Benchmark 49 | public int jdk() { 50 | index = (index + 1) & (NUM_BOUNDS - 1); 51 | return ThreadLocalRandom.current().nextInt(bounds[index]); 52 | } 53 | 54 | @Benchmark 55 | public int nearlyDivisionless() { 56 | index = (index + 1) & (NUM_BOUNDS - 1); 57 | return UniformRNGUtils.nextInt(ThreadLocalRandom.current(), bounds[index]); 58 | } 59 | } 60 | } 61 | -------------------------------------------------------------------------------- /fast-rng-test/src/test/java/biz/k11i/rng/test/util/distribution/GaussianTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | import org.apache.commons.math3.distribution.NormalDistribution; 4 | import org.apache.commons.math3.util.FastMath; 5 | import org.junit.jupiter.params.ParameterizedTest; 6 | import org.junit.jupiter.params.provider.Arguments; 7 | import org.junit.jupiter.params.provider.MethodSource; 8 | 9 | import java.util.Arrays; 10 | import java.util.function.IntToDoubleFunction; 11 | import java.util.stream.Stream; 12 | 13 | class GaussianTest extends ProbabilityDistributionTestBase { 14 | private static final int N = 10000; 15 | 16 | private static Stream distributionParameters() { 17 | double[] means = {0.0, -1.5, 2.5, -1e10, 1e-10}; 18 | double[] stdDevs = {1e-10, 0.3, 1.0, 3.4, 1e10}; 19 | 20 | return Arrays.stream(means) 21 | .boxed() 22 | .flatMap(mean -> Arrays.stream(stdDevs).mapToObj(sd -> Arguments.of(mean, sd))); 23 | } 24 | 25 | @ParameterizedTest 26 | @MethodSource("distributionParameters") 27 | void testCdf(double mean, double sd) { 28 | IntToDoubleFunction f = value -> { 29 | double hi = (value / 100.0) - 50; 30 | double lo = (value % 100) - 50; 31 | 32 | return hi * FastMath.pow(10, lo / 2); 33 | }; 34 | 35 | testCdf( 36 | ProbabilityDistributions.gaussian(mean, sd), 37 | new NormalDistribution(mean, sd), 38 | N, 39 | f, 40 | "Gaussian(%f, %f).cdf(%f)", 41 | x -> new Object[]{mean, sd, x}); 42 | } 43 | 44 | @ParameterizedTest 45 | @MethodSource("distributionParameters") 46 | void testInverseCdf(double mean, double sd) { 47 | testInverseCdf( 48 | ProbabilityDistributions.gaussian(mean, sd), 49 | new NormalDistribution(mean, sd), 50 | N, 51 | "Gaussian(%f, %f).inverseCDF(%f)", 52 | p -> new Object[]{mean, sd, p}); 53 | } 54 | } 55 | -------------------------------------------------------------------------------- /fast-rng-test/src/jmh/java/biz/k11i/rng/test/util/distribution/BetaDistributionBenchmark.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | import org.apache.commons.math3.distribution.BetaDistribution; 4 | import org.openjdk.jmh.annotations.Benchmark; 5 | import org.openjdk.jmh.annotations.Level; 6 | import org.openjdk.jmh.annotations.OutputTimeUnit; 7 | import org.openjdk.jmh.annotations.Param; 8 | import org.openjdk.jmh.annotations.Scope; 9 | import org.openjdk.jmh.annotations.Setup; 10 | import org.openjdk.jmh.annotations.State; 11 | 12 | import java.util.concurrent.TimeUnit; 13 | import java.util.stream.IntStream; 14 | 15 | @State(Scope.Benchmark) 16 | @OutputTimeUnit(TimeUnit.MILLISECONDS) 17 | public class BetaDistributionBenchmark { 18 | @Param({"0.1", "1.0", "100.0"}) 19 | private double alpha; 20 | 21 | @Param({"0.1", "1.0", "100.0"}) 22 | private double beta; 23 | 24 | private ContinuousDistribution probDist; 25 | private BetaDistribution commonsMath3; 26 | 27 | @State(Scope.Benchmark) 28 | public static class X { 29 | private final double[] values; 30 | private int index; 31 | private double next; 32 | 33 | public X() { 34 | final int N = 100000; 35 | values = IntStream.rangeClosed(0, N) 36 | .mapToDouble(i -> i / (double) N) 37 | .toArray(); 38 | } 39 | 40 | @Setup(Level.Iteration) 41 | public void init() { 42 | index = 0; 43 | } 44 | 45 | @Setup(Level.Invocation) 46 | public void next() { 47 | next = values[index]; 48 | 49 | if (++index >= values.length) { 50 | index = 0; 51 | } 52 | } 53 | } 54 | 55 | @Setup(Level.Trial) 56 | public void setUp() { 57 | probDist = ProbabilityDistributions.beta(alpha, beta); 58 | commonsMath3 = new BetaDistribution(alpha, beta); 59 | } 60 | 61 | @Benchmark 62 | public double commonsMath3Cdf(X x) { 63 | return commonsMath3.cumulativeProbability(x.next); 64 | } 65 | 66 | @Benchmark 67 | public double commonsMath3InverseCdf(X x) { 68 | return commonsMath3.inverseCumulativeProbability(x.next); 69 | } 70 | 71 | @Benchmark 72 | public double cdf(X x) { 73 | return probDist.cdf(x.next); 74 | } 75 | 76 | @Benchmark 77 | public double inverseCdf(X x) { 78 | return probDist.inverseCdf(x.next); 79 | } 80 | } 81 | -------------------------------------------------------------------------------- /fast-rng/build.gradle: -------------------------------------------------------------------------------- 1 | plugins { 2 | id 'maven-publish' 3 | id 'net.researchgate.release' version '2.8.0' 4 | id 'com.jfrog.bintray' version '1.8.4' 5 | } 6 | 7 | repositories { 8 | maven { 9 | url 'http://simulation.tudelft.nl/maven/' 10 | } 11 | } 12 | 13 | dependencies { 14 | testImplementation project(':fast-rng-test') 15 | } 16 | 17 | test { 18 | useJUnitPlatform() 19 | 20 | testLogging { 21 | events 'PASSED', 'FAILED', 'SKIPPED' 22 | } 23 | afterSuite { desc, result -> 24 | if (!desc.parent) { 25 | println "\nTest result: ${result.resultType}" 26 | println "Test summary: ${result.testCount} tests, " + 27 | "${result.successfulTestCount} succeeded, " + 28 | "${result.failedTestCount} failed, " + 29 | "${result.skippedTestCount} skipped" 30 | } 31 | } 32 | } 33 | 34 | javadoc { 35 | options.locale = 'en_US' 36 | } 37 | 38 | task sourcesJar(type: Jar, dependsOn: classes) { 39 | archiveClassifier = 'sources' 40 | from sourceSets.main.allSource 41 | } 42 | 43 | task javadocJar(type: Jar, dependsOn: javadoc) { 44 | archiveClassifier = 'javadoc' 45 | from javadoc.destinationDir 46 | } 47 | 48 | artifacts { 49 | archives jar 50 | archives sourcesJar 51 | archives javadocJar 52 | } 53 | 54 | publishing { 55 | publications { 56 | mavenJava(MavenPublication) { 57 | from components.java 58 | artifact sourcesJar 59 | artifact javadocJar 60 | } 61 | } 62 | } 63 | 64 | bintray { 65 | user = project.hasProperty('bintrayUser') ? bintrayUser : '' 66 | key = project.hasProperty('bintrayKey') ? bintrayKey : '' 67 | publications = ['mavenJava'] 68 | 69 | pkg { 70 | repo = 'maven' 71 | name = 'fast-rng' 72 | userOrg = 'komiya-atsushi' 73 | licenses = ['MIT'] 74 | 75 | websiteUrl = 'https://github.com/komiya-atsushi/fast-rng-java' 76 | issueTrackerUrl = 'https://github.com/komiya-atsushi/fast-rng-java/issues' 77 | vcsUrl = 'https://github.com/komiya-atsushi/fast-rng-java.git' 78 | 79 | version { 80 | name = project.version 81 | desc = 'fast-rng: Fast random number generator for various distributions' 82 | } 83 | } 84 | } 85 | 86 | release { 87 | preTagCommitMessage = '[skip ci] [Gradle Release Plugin] - pre tag commit: ' 88 | newVersionCommitMessage = '[skip ci] [Gradle Release Plugin] - new version commit: ' 89 | } 90 | 91 | afterReleaseBuild.dependsOn bintrayUpload 92 | -------------------------------------------------------------------------------- /benchmark/src/jmh/java/biz/k11i/rng/GammaBenchmark.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import biz.k11i.rng.util.MtRandom; 4 | import biz.k11i.rng.util.ParameterPool; 5 | import org.apache.commons.math3.distribution.GammaDistribution; 6 | import org.apache.commons.math3.random.MersenneTwister; 7 | import org.openjdk.jmh.annotations.Benchmark; 8 | import org.openjdk.jmh.annotations.Param; 9 | import org.openjdk.jmh.annotations.Scope; 10 | import org.openjdk.jmh.annotations.Setup; 11 | import org.openjdk.jmh.annotations.State; 12 | 13 | import java.util.Random; 14 | 15 | public class GammaBenchmark { 16 | @State(Scope.Benchmark) 17 | public static class FixedParameters { 18 | @Param({"0.05", "0.1", "0.2", "0.5", "0.9", "1.0", "1.1", "40.0", "10000.0"}) 19 | public double shape; 20 | public double scale = 1.0; 21 | 22 | private Random random = new MtRandom(); 23 | private GammaDistribution gammaDistribution; 24 | 25 | @Setup 26 | public void setUp() { 27 | gammaDistribution = new GammaDistribution( 28 | new MersenneTwister(), 29 | shape, 30 | scale, 31 | GammaDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY); 32 | } 33 | 34 | @Benchmark 35 | public double commonsMath3() { 36 | return gammaDistribution.sample(); 37 | } 38 | 39 | @Benchmark 40 | public double fastRng() { 41 | return GammaRNG.FAST_RNG.generate(random, shape, scale); 42 | } 43 | 44 | @Benchmark 45 | public double generalRng() { 46 | return GammaRNG.GENERAL_RNG.generate(random, shape, scale); 47 | } 48 | } 49 | 50 | @State(Scope.Benchmark) 51 | public static class ArbitraryParameters { 52 | private double scale = 1.0; 53 | private Random random = new MtRandom(); 54 | private MersenneTwister mersenneTwister = new MersenneTwister(); 55 | private ParameterPool parameters = new ParameterPool(12345, 10000, 10.0); 56 | 57 | @Benchmark 58 | public double commonsMath3() { 59 | return new GammaDistribution(mersenneTwister, parameters.next(), scale, GammaDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY).sample(); 60 | } 61 | 62 | @Benchmark 63 | public double fastRng() { 64 | return GammaRNG.FAST_RNG.generate(random, parameters.next(), scale); 65 | } 66 | 67 | @Benchmark 68 | public double generalRng() { 69 | return GammaRNG.GENERAL_RNG.generate(random, parameters.next(), scale); 70 | } 71 | } 72 | } 73 | -------------------------------------------------------------------------------- /gradlew.bat: -------------------------------------------------------------------------------- 1 | @if "%DEBUG%" == "" @echo off 2 | @rem ########################################################################## 3 | @rem 4 | @rem Gradle startup script for Windows 5 | @rem 6 | @rem ########################################################################## 7 | 8 | @rem Set local scope for the variables with windows NT shell 9 | if "%OS%"=="Windows_NT" setlocal 10 | 11 | @rem Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script. 12 | set DEFAULT_JVM_OPTS= 13 | 14 | set DIRNAME=%~dp0 15 | if "%DIRNAME%" == "" set DIRNAME=. 16 | set APP_BASE_NAME=%~n0 17 | set APP_HOME=%DIRNAME% 18 | 19 | @rem Find java.exe 20 | if defined JAVA_HOME goto findJavaFromJavaHome 21 | 22 | set JAVA_EXE=java.exe 23 | %JAVA_EXE% -version >NUL 2>&1 24 | if "%ERRORLEVEL%" == "0" goto init 25 | 26 | echo. 27 | echo ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH. 28 | echo. 29 | echo Please set the JAVA_HOME variable in your environment to match the 30 | echo location of your Java installation. 31 | 32 | goto fail 33 | 34 | :findJavaFromJavaHome 35 | set JAVA_HOME=%JAVA_HOME:"=% 36 | set JAVA_EXE=%JAVA_HOME%/bin/java.exe 37 | 38 | if exist "%JAVA_EXE%" goto init 39 | 40 | echo. 41 | echo ERROR: JAVA_HOME is set to an invalid directory: %JAVA_HOME% 42 | echo. 43 | echo Please set the JAVA_HOME variable in your environment to match the 44 | echo location of your Java installation. 45 | 46 | goto fail 47 | 48 | :init 49 | @rem Get command-line arguments, handling Windowz variants 50 | 51 | if not "%OS%" == "Windows_NT" goto win9xME_args 52 | if "%@eval[2+2]" == "4" goto 4NT_args 53 | 54 | :win9xME_args 55 | @rem Slurp the command line arguments. 56 | set CMD_LINE_ARGS= 57 | set _SKIP=2 58 | 59 | :win9xME_args_slurp 60 | if "x%~1" == "x" goto execute 61 | 62 | set CMD_LINE_ARGS=%* 63 | goto execute 64 | 65 | :4NT_args 66 | @rem Get arguments from the 4NT Shell from JP Software 67 | set CMD_LINE_ARGS=%$ 68 | 69 | :execute 70 | @rem Setup the command line 71 | 72 | set CLASSPATH=%APP_HOME%\gradle\wrapper\gradle-wrapper.jar 73 | 74 | @rem Execute Gradle 75 | "%JAVA_EXE%" %DEFAULT_JVM_OPTS% %JAVA_OPTS% %GRADLE_OPTS% "-Dorg.gradle.appname=%APP_BASE_NAME%" -classpath "%CLASSPATH%" org.gradle.wrapper.GradleWrapperMain %CMD_LINE_ARGS% 76 | 77 | :end 78 | @rem End local scope for the variables with windows NT shell 79 | if "%ERRORLEVEL%"=="0" goto mainEnd 80 | 81 | :fail 82 | rem Set variable GRADLE_EXIT_CONSOLE if you need the _script_ return code instead of 83 | rem the _cmd.exe /c_ return code! 84 | if not "" == "%GRADLE_EXIT_CONSOLE%" exit 1 85 | exit /b 1 86 | 87 | :mainEnd 88 | if "%OS%"=="Windows_NT" endlocal 89 | 90 | :omega 91 | -------------------------------------------------------------------------------- /fast-rng/src/main/java/biz/k11i/rng/UniformRNGUtils.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import java.util.Random; 4 | import java.util.SplittableRandom; 5 | 6 | @SuppressWarnings("Duplicates") 7 | public class UniformRNGUtils { 8 | /** 9 | * Returns a random integer sampled from discrete uniform distribution {@code unif{0, bound - 1}}. 10 | * 11 | *

12 | * This implementation uses "nearly divisionless" algorithm by Lemire. 13 | *

14 | *

15 | * Lemire, Daniel. 16 | * "Fast random integer generation in an interval." 17 | * ACM Transactions on Modeling and Computer Simulation (TOMACS) 29.1 (2019): 3. 18 | *

19 | * 20 | * @param random random number generator ({@link Random} object) 21 | * @param bound the upper bound (exclusive) 22 | * @return sampled random integer between 0 (inclusive) and {@code bound} (exclusive) 23 | */ 24 | public static int nextInt(Random random, int bound) { 25 | if (bound <= 0) { 26 | throw new IllegalArgumentException("bound must be positive"); 27 | } 28 | 29 | long x = ((long) random.nextInt()) & 0xffff_ffffL; 30 | long m = x * bound; 31 | long l = m & 0xffff_ffffL; 32 | 33 | if (l < bound) { 34 | for (long t = 0x1_0000_0000L % bound; l < t; ) { 35 | x = ((long) random.nextInt()) & 0xffff_ffffL; 36 | m = x * bound; 37 | l = m & 0xffff_ffffL; 38 | } 39 | } 40 | 41 | return (int) (m >>> 32); 42 | } 43 | 44 | /** 45 | * Returns a random integer sampled from discrete uniform distribution {@code unif{0, bound - 1}}. 46 | * 47 | *

48 | * This implementation uses "nearly divisionless" algorithm by Lemire. 49 | *

50 | *

51 | * Lemire, Daniel. 52 | * "Fast random integer generation in an interval." 53 | * ACM Transactions on Modeling and Computer Simulation (TOMACS) 29.1 (2019): 3. 54 | *

55 | * 56 | * @param random random number generator ({@link SplittableRandom} object) 57 | * @param bound the upper bound (exclusive) 58 | * @return sampled random integer between 0 (inclusive) and {@code bound} (exclusive) 59 | */ 60 | public static int nextInt(SplittableRandom random, int bound) { 61 | if (bound <= 0) { 62 | throw new IllegalArgumentException("bound must be positive"); 63 | } 64 | 65 | long x = ((long) random.nextInt()) & 0xffff_ffffL; 66 | long m = x * bound; 67 | long l = m & 0xffff_ffffL; 68 | 69 | if (l < bound) { 70 | for (long t = 0x1_0000_0000L % bound; l < t; ) { 71 | x = ((long) random.nextInt()) & 0xffff_ffffL; 72 | m = x * bound; 73 | l = m & 0xffff_ffffL; 74 | } 75 | } 76 | 77 | return (int) (m >>> 32); 78 | } 79 | } 80 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/util/inference/AndersonDarlingTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.inference; 2 | 3 | import static org.apache.commons.math3.util.FastMath.*; 4 | 5 | /** 6 | * Implements Anderson–Darling test 7 | * for uniformity. 8 | *

9 | * Marsaglia, George, and John Marsaglia. 10 | * "Evaluating the anderson-darling distribution." 11 | * Journal of Statistical Software 9.2 (2004): 1-5. 12 | *

13 | */ 14 | public class AndersonDarlingTest { 15 | private static final double EPSILON = Math.ulp(1.0) / 2.0; 16 | 17 | /** 18 | * Tests uniformity of double values. 19 | * 20 | * @param x array of double values that must be sorted in ascending order. 21 | * @return p-value 22 | */ 23 | public static double andersonDarlingTest(double[] x) { 24 | final int n = x.length; 25 | double z = 0; 26 | double prev = Double.NEGATIVE_INFINITY; 27 | 28 | for (int i = 0; i < n; i++) { 29 | if (prev > x[i]) { 30 | throw new IllegalArgumentException("Array of double values 'x' must be sorted in ascending order"); 31 | } 32 | 33 | double u = x[i], v = x[n - 1 - i]; 34 | if (u <= EPSILON) { 35 | u = EPSILON; 36 | } else if (v >= 1.0 - EPSILON) { 37 | v = 1.0 - EPSILON; 38 | } 39 | 40 | double t = u * (1.0 - v); 41 | z = z - (i + i + 1) * log(t); 42 | 43 | prev = x[i]; 44 | } 45 | 46 | return 1 - Math.max(AD(n, -n + z / n), 0.0); 47 | } 48 | 49 | private static double AD(int n, double z) { 50 | double c, v, x; 51 | x = adinf(z); 52 | /* now x=adinf(z). Next, get v=errfix(n,x) and return x+v; */ 53 | if (x > .8) { 54 | v = (-130.2137 + (745.2337 - (1705.091 - (1950.646 - (1116.360 - 255.7844 * x) * x) * x) * x) * x) / n; 55 | return x + v; 56 | } 57 | c = .01265 + .1757 / n; 58 | if (x < c) { 59 | v = x / c; 60 | v = sqrt(v) * (1. - v) * (49 * v - 102); 61 | return x + v * (.0037 / (n * n) + .00078 / n + .00006) / n; 62 | } 63 | v = (x - c) / (.8 - c); 64 | v = -.00022633 + (6.54034 - (14.6538 - (14.458 - (8.259 - 1.91864 * v) * v) * v) * v) * v; 65 | return x + v * (.04213 + .01365 / n) / n; 66 | } 67 | 68 | private static double adinf(double z) { 69 | if (z < 2.) 70 | return exp(-1.2337141 / z) / sqrt(z) * (2.00012 + (.247105 - (.0649821 - (.0347962 - (.011672 - .00168691 * z) * z) * z) * z) * z); 71 | /* max |error| < .000002 for z<2, (p=.90816...) */ 72 | return exp(-exp(1.0776 - (2.30695 - (.43424 - (.082433 - (.008056 - .0003146 * z) * z) * z) * z) * z)); 73 | /* max |error|<.0000008 for 4 { 10 | private final SplittableRandom splittableRandom; 11 | 12 | @Override 13 | public SplittableRandomWrapper split() { 14 | return new SplittableRandomWrapper(splittableRandom.split()); 15 | } 16 | 17 | private SplittableRandomWrapper(SplittableRandom splittableRandom) { 18 | this.splittableRandom = splittableRandom; 19 | } 20 | 21 | public SplittableRandomWrapper(long seed) { 22 | this.splittableRandom = new SplittableRandom(seed); 23 | } 24 | 25 | @Override 26 | public int nextInt() { 27 | return splittableRandom.nextInt(); 28 | } 29 | 30 | @Override 31 | public int nextInt(int bound) { 32 | return splittableRandom.nextInt(bound); 33 | } 34 | 35 | @Override 36 | public long nextLong() { 37 | return splittableRandom.nextLong(); 38 | } 39 | 40 | @Override 41 | public double nextDouble() { 42 | return splittableRandom.nextDouble(); 43 | } 44 | 45 | @Override 46 | public boolean nextBoolean() { 47 | return splittableRandom.nextBoolean(); 48 | } 49 | 50 | @Override 51 | public IntStream ints(long streamSize) { 52 | return splittableRandom.ints(streamSize); 53 | } 54 | 55 | @Override 56 | public IntStream ints() { 57 | return splittableRandom.ints(); 58 | } 59 | 60 | @Override 61 | public IntStream ints(long streamSize, int randomNumberOrigin, int randomNumberBound) { 62 | return splittableRandom.ints(streamSize, randomNumberOrigin, randomNumberBound); 63 | } 64 | 65 | @Override 66 | public IntStream ints(int randomNumberOrigin, int randomNumberBound) { 67 | return splittableRandom.ints(randomNumberOrigin, randomNumberBound); 68 | } 69 | 70 | @Override 71 | public LongStream longs(long streamSize) { 72 | return splittableRandom.longs(streamSize); 73 | } 74 | 75 | @Override 76 | public LongStream longs() { 77 | return splittableRandom.longs(); 78 | } 79 | 80 | @Override 81 | public LongStream longs(long streamSize, long randomNumberOrigin, long randomNumberBound) { 82 | return splittableRandom.longs(streamSize, randomNumberOrigin, randomNumberBound); 83 | } 84 | 85 | @Override 86 | public LongStream longs(long randomNumberOrigin, long randomNumberBound) { 87 | return splittableRandom.longs(randomNumberOrigin, randomNumberBound); 88 | } 89 | 90 | @Override 91 | public DoubleStream doubles(long streamSize) { 92 | return splittableRandom.doubles(streamSize); 93 | } 94 | 95 | @Override 96 | public DoubleStream doubles() { 97 | return splittableRandom.doubles(); 98 | } 99 | 100 | @Override 101 | public DoubleStream doubles(long streamSize, double randomNumberOrigin, double randomNumberBound) { 102 | return splittableRandom.doubles(streamSize, randomNumberOrigin, randomNumberBound); 103 | } 104 | 105 | @Override 106 | public DoubleStream doubles(double randomNumberOrigin, double randomNumberBound) { 107 | return splittableRandom.doubles(randomNumberOrigin, randomNumberBound); 108 | } 109 | } 110 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # fast-rng: Fast random number generator for various distributions 2 | 3 | [![Download](https://api.bintray.com/packages/komiya-atsushi/maven/fast-rng/images/download.svg) ](https://bintray.com/komiya-atsushi/maven/fast-rng/_latestVersion) 4 | 5 | # Getting started 6 | 7 | ## Resolving artifacts using Maven 8 | 9 | ```xml 10 | 11 | 12 | bintray-komiya-atsushi-maven 13 | http://dl.bintray.com/komiya-atsushi/maven 14 | 15 | 16 | 17 | 18 | 19 | biz.k11i 20 | fast-rng 21 | 0.2.0 22 | 23 | 24 | ``` 25 | 26 | ## Resolving artifacts using Gradle 27 | 28 | ```groovy 29 | repositories { 30 | maven { 31 | url "http://dl.bintray.com/komiya-atsushi/maven" 32 | } 33 | } 34 | 35 | dependencies { 36 | compile group: 'biz.k11i', name: 'fast-rng', version: '0.2.0' 37 | } 38 | ``` 39 | 40 | ## Generating random values 41 | 42 | ```java 43 | package biz.k11i.rng.demo; 44 | 45 | import java.util.Random; 46 | 47 | public class FastRngDemo { 48 | public static void main(String[] args) { 49 | // Fast-rng requires a java.util.Random instance to generate 50 | // uniformly distributed random values. 51 | Random random = new Random(); 52 | 53 | System.out.println( 54 | // Generate a gaussian random value. 55 | GaussianRNG.FAST_RNG.generate(random) 56 | ); 57 | } 58 | } 59 | ``` 60 | 61 | 62 | # Supported distributions 63 | 64 | - [Gaussian distribution (Normal distribution)](https://en.wikipedia.org/wiki/Normal_distribution) 65 | - [Exponential distribution](https://en.wikipedia.org/wiki/Exponential_distribution) 66 | - [Gamma distribution](https://en.wikipedia.org/wiki/Gamma_distribution) 67 | - [Beta distribution](https://en.wikipedia.org/wiki/Beta_distribution) 68 | 69 | 70 | # License 71 | 72 | This software is licensed under the terms of the MIT license. See LICENSE. 73 | 74 | 75 | # Acknowledgments 76 | 77 | ## commons-math3 78 | 79 | This product includes software developed at 80 | The Apache Software Foundation (http://www.apache.org/). 81 | https://github.com/apache/commons-math 82 | 83 | ## Jafama 84 | 85 | This product includes software developed by Jeff Hain. 86 | https://github.com/jeffhain/jafama 87 | 88 | 89 | # References 90 | 91 | - Tesuaki Yotsuji. 92 | *計算機シミュレーションのための確率分布乱数生成法.* 93 | Pleiades Publishing Co.,Ltd. (2010) 94 | - Marsaglia, George, and Wai Wan Tsang. 95 | *The ziggurat method for generating random variables.* 96 | Journal of statistical software 5.8 (2000): 1-7. 97 | - Ahrens, Joachim H., and Ulrich Dieter. 98 | *Computer methods for sampling from gamma, beta, poisson and bionomial distributions.* 99 | Computing 12.3 (1974): 223-246. 100 | - Marsaglia, George, and Wai Wan Tsang. 101 | *A simple method for generating gamma variables.* 102 | ACM Transactions on Mathematical Software (TOMS) 26.3 (2000): 363-372. 103 | - Best, D. J. 104 | *A note on gamma variate generators with shape parameter less than unity.* 105 | Computing 30.2 (1983): 185-188. 106 | - Wilson, Edwin B., and Margaret M. Hilferty. 107 | *The distribution of chi-square.* 108 | Proceedings of the National Academy of Sciences 17.12 (1931): 684-688. 109 | - Jöhnk, M. D. 110 | *Erzeugung von betaverteilten und gammaverteilten Zufallszahlen.* 111 | Metrika 8.1 (1964): 5-15. 112 | - Sakasegawa, H. 113 | *Stratified rejection and squeeze method for generating beta random numbers.* 114 | Annals of the Institute of Statistical Mathematics 35.1 (1983): 291-302. 115 | - Lemire, Daniel. 116 | *Fast random integer generation in an interval.* 117 | ACM Transactions on Modeling and Computer Simulation (TOMACS) 29.1 (2019): 3. 118 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/SecondLevelTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test; 2 | 3 | import biz.k11i.rng.test.gof.GoodnessOfFitTest; 4 | import biz.k11i.rng.test.util.inference.AndersonDarlingTest; 5 | import org.slf4j.Logger; 6 | import org.slf4j.LoggerFactory; 7 | 8 | import java.util.LinkedHashMap; 9 | import java.util.Map; 10 | import java.util.concurrent.ForkJoinPool; 11 | import java.util.concurrent.TimeUnit; 12 | import java.util.stream.Collector; 13 | import java.util.stream.IntStream; 14 | 15 | import static java.util.stream.Collectors.collectingAndThen; 16 | import static java.util.stream.Collectors.groupingBy; 17 | import static java.util.stream.Collectors.mapping; 18 | import static java.util.stream.Collectors.toList; 19 | import static org.assertj.core.api.Assertions.assertThat; 20 | 21 | public class SecondLevelTest { 22 | public static class Builder { 23 | private int numIterations; 24 | 25 | public Builder numIterations(int numIterations) { 26 | this.numIterations = numIterations; 27 | return this; 28 | } 29 | 30 | public SecondLevelTest build() { 31 | return new SecondLevelTest(numIterations); 32 | } 33 | } 34 | 35 | private static final Logger LOGGER = LoggerFactory.getLogger(SecondLevelTest.class); 36 | 37 | private final int numIterations; 38 | 39 | private SecondLevelTest(int numIterations) { 40 | this.numIterations = numIterations; 41 | } 42 | 43 | public void testAndVerify(GoodnessOfFitTest gofTest) { 44 | boolean parallel = Runtime.getRuntime().availableProcessors() > 1; 45 | 46 | Map results = test(gofTest, parallel); 47 | assertThat(results).isNotEmpty(); 48 | 49 | results.forEach((t, p) -> 50 | assertThat(p) 51 | .describedAs("At a significance level of %e, the second level Goodness-of-Fit test of [%s] should fail to reject null hypothesis.\n" + 52 | "This means that the random sequence generated by the random number generator [%s] fit the theoretical probability distribution.", 53 | gofTest.significanceLevel, t, gofTest.rngName) 54 | .isGreaterThanOrEqualTo(0.001)); 55 | } 56 | 57 | private Map test(GoodnessOfFitTest gofTest, boolean parallel) { 58 | ForkJoinPool pool = parallel ? new ForkJoinPool() : null; 59 | 60 | try { 61 | Map result = IntStream.range(0, numIterations) 62 | .peek(i -> LOGGER.info("First level #{}", i + 1)) 63 | .mapToObj(ignore -> parallel ? gofTest.testInParallel(pool) : gofTest.test()) 64 | .flatMap(r -> r.entrySet().stream()) 65 | .collect(groupingBy( 66 | Map.Entry::getKey, 67 | LinkedHashMap::new, 68 | mapping(Map.Entry::getValue, computeAndersonDarlingP()))); 69 | 70 | result.forEach((key, value) -> LOGGER.info("[{}] Second level p-value: {}", key, value)); 71 | 72 | return result; 73 | 74 | } finally { 75 | if (pool != null) { 76 | pool.shutdown(); 77 | try { 78 | pool.awaitTermination(2, TimeUnit.SECONDS); 79 | } catch (InterruptedException ignore) { 80 | } 81 | } 82 | } 83 | } 84 | 85 | private static Collector toDoubleArray() { 86 | return collectingAndThen(toList(), l -> l.stream().mapToDouble(v -> v).sorted().toArray()); 87 | } 88 | 89 | private static Collector computeAndersonDarlingP() { 90 | return collectingAndThen( 91 | toDoubleArray(), 92 | AndersonDarlingTest::andersonDarlingTest); 93 | } 94 | 95 | public static Builder builder() { 96 | return new Builder(); 97 | } 98 | } 99 | -------------------------------------------------------------------------------- /fast-rng/src/test/java/biz/k11i/rng/BetaRNGTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import biz.k11i.rng.test.SecondLevelTest; 4 | import biz.k11i.rng.test.gof.GoodnessOfFitTest; 5 | import biz.k11i.rng.test.util.distribution.ProbabilityDistributions; 6 | import org.junit.jupiter.params.ParameterizedTest; 7 | import org.junit.jupiter.params.provider.Arguments; 8 | import org.junit.jupiter.params.provider.MethodSource; 9 | 10 | import java.util.stream.Stream; 11 | 12 | class BetaRNGTest { 13 | static Stream parameterCase1() { 14 | return Stream.of( 15 | Arguments.of(0.1, 0.5), 16 | Arguments.of(0.1, 0.9), 17 | Arguments.of(0.45, 0.46), 18 | Arguments.of(0.46, 0.45), 19 | Arguments.of(0.5, 0.5), 20 | Arguments.of(0.5, 0.9), 21 | Arguments.of(0.9, 0.5), 22 | Arguments.of(0.99998, 0.99999), 23 | Arguments.of(0.99999, 0.99998)); 24 | } 25 | 26 | @ParameterizedTest 27 | @MethodSource("parameterCase1") 28 | void testCase1_fast(double alpha, double beta) { 29 | test(BetaRNG.FAST_RNG, alpha, beta); 30 | } 31 | 32 | @ParameterizedTest 33 | @MethodSource("parameterCase1") 34 | void testCase1_general(double alpha, double beta) { 35 | test(BetaRNG.GENERAL_RNG, alpha, beta); 36 | } 37 | 38 | static Stream parameterCase2() { 39 | return Stream.of( 40 | Arguments.of(0.099, 10.0), 41 | Arguments.of(0.6, 1.2), 42 | Arguments.of(1.2, 0.6), 43 | Arguments.of(0.7, 5.0), 44 | Arguments.of(0.8, 20.0), 45 | Arguments.of(20.0, 0.8), 46 | Arguments.of(0.9, 80.0)); 47 | } 48 | 49 | @ParameterizedTest 50 | @MethodSource("parameterCase2") 51 | void testCase2_fast(double alpha, double beta) { 52 | test(BetaRNG.FAST_RNG, alpha, beta); 53 | } 54 | 55 | @ParameterizedTest 56 | @MethodSource("parameterCase2") 57 | void testCase2_general(double alpha, double beta) { 58 | test(BetaRNG.GENERAL_RNG, alpha, beta); 59 | } 60 | 61 | static Stream parameterCase3() { 62 | return Stream.of( 63 | Arguments.of(1.5, 1.5), 64 | Arguments.of(1.5, 4.0), 65 | Arguments.of(4.0, 1.5), 66 | Arguments.of(4.0, 100.0), 67 | Arguments.of(100.0, 4.0)); 68 | } 69 | 70 | @ParameterizedTest 71 | @MethodSource("parameterCase3") 72 | void testCase3_fast(double alpha, double beta) { 73 | test(BetaRNG.FAST_RNG, alpha, beta); 74 | } 75 | 76 | @ParameterizedTest 77 | @MethodSource("parameterCase3") 78 | void testCase3_general(double alpha, double beta) { 79 | test(BetaRNG.GENERAL_RNG, alpha, beta); 80 | } 81 | 82 | static Stream parameterSpecialCase() { 83 | return Stream.of( 84 | Arguments.of(1.0, 1.01), 85 | Arguments.of(1.0, 0.99), 86 | Arguments.of(1.0, 10.0), 87 | Arguments.of(1.01, 1.0), 88 | Arguments.of(0.99, 1.0), 89 | Arguments.of(10.0, 1.0), 90 | Arguments.of(1.0, 1.0)); 91 | } 92 | 93 | @ParameterizedTest 94 | @MethodSource("parameterSpecialCase") 95 | void testSpecialCase_fast(double alpha, double beta) { 96 | test(BetaRNG.FAST_RNG, alpha, beta); 97 | } 98 | 99 | @ParameterizedTest 100 | @MethodSource("parameterSpecialCase") 101 | void testSpecialCase_general(double alpha, double beta) { 102 | test(BetaRNG.GENERAL_RNG, alpha, beta); 103 | } 104 | 105 | private void test(BetaRNG rng, double alpha, double beta) { 106 | GoodnessOfFitTest gofTest = GoodnessOfFitTest.continuous() 107 | .probabilityDistribution(ProbabilityDistributions.beta(alpha, beta)) 108 | .randomNumberGenerator(String.format("Beta(%f, %f)", alpha, beta), r -> rng.generate(r, alpha, beta)) 109 | .numRandomValues(1_000_000) 110 | .build(); 111 | 112 | SecondLevelTest.builder() 113 | .numIterations(20) 114 | .build() 115 | .testAndVerify(gofTest); 116 | } 117 | } 118 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/util/distribution/ContinuousDistributionBase.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | import org.apache.commons.math3.analysis.UnivariateFunction; 4 | import org.apache.commons.math3.analysis.solvers.UnivariateSolverUtils; 5 | import org.apache.commons.math3.distribution.RealDistribution; 6 | import org.apache.commons.math3.exception.OutOfRangeException; 7 | import org.apache.commons.math3.util.FastMath; 8 | 9 | /** 10 | * Base class of {@link ContinuousDistribution}. 11 | * 12 | *

13 | * This implementation includes a part of Apache Commons Math 14 | * that is licensed under the Apache License 2.0. 15 | *

16 | * 
 17 |  * Licensed to the Apache Software Foundation (ASF) under one or more
 18 |  * contributor license agreements.  See the NOTICE file distributed with
 19 |  * this work for additional information regarding copyright ownership.
 20 |  * The ASF licenses this file to You under the Apache License, Version 2.0
 21 |  * (the "License"); you may not use this file except in compliance with
 22 |  * the License.  You may obtain a copy of the License at
 23 |  *
 24 |  *      http://www.apache.org/licenses/LICENSE-2.0
 25 |  *
 26 |  * Unless required by applicable law or agreed to in writing, software
 27 |  * distributed under the License is distributed on an "AS IS" BASIS,
 28 |  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 29 |  * See the License for the specific language governing permissions and
 30 |  * limitations under the License.
 31 |  *
32 | */ 33 | abstract class ContinuousDistributionBase implements ContinuousDistribution { 34 | private final double supportLowerBound; 35 | private final double supportUpperBound; 36 | private final double mu; 37 | private final double sig; 38 | private final boolean chebyshevApplies; 39 | private final boolean isSupportConnected; 40 | private final double solverAbsoluteAccuracy; 41 | 42 | ContinuousDistributionBase(RealDistribution distribution, double solverAbsoluteAccuracy) { 43 | this.supportLowerBound = distribution.getSupportLowerBound(); 44 | this.supportUpperBound = distribution.getSupportUpperBound(); 45 | this.mu = distribution.getNumericalMean(); 46 | this.sig = FastMath.sqrt(distribution.getNumericalVariance()); 47 | this.chebyshevApplies = !(Double.isInfinite(mu) || Double.isNaN(mu) || 48 | Double.isInfinite(sig) || Double.isNaN(sig)); 49 | this.isSupportConnected = distribution.isSupportConnected(); 50 | this.solverAbsoluteAccuracy = solverAbsoluteAccuracy; 51 | } 52 | 53 | @Override 54 | public double inverseCdf(double p) { 55 | if (p < 0.0 || p > 1.0) { 56 | throw new OutOfRangeException(p, 0, 1); 57 | } 58 | 59 | if (p == 0.0) { 60 | return supportLowerBound; 61 | } 62 | 63 | if (p == 1.0) { 64 | return supportUpperBound; 65 | } 66 | 67 | double lowerBound = supportLowerBound; 68 | if (supportLowerBound == Double.NEGATIVE_INFINITY) { 69 | if (chebyshevApplies) { 70 | lowerBound = mu - sig * FastMath.sqrt((1. - p) / p); 71 | } else { 72 | lowerBound = -1.0; 73 | while (cdf(lowerBound) >= p) { 74 | lowerBound *= 2.0; 75 | } 76 | } 77 | } 78 | 79 | double upperBound = supportUpperBound; 80 | if (upperBound == Double.POSITIVE_INFINITY) { 81 | if (chebyshevApplies) { 82 | upperBound = mu + sig * FastMath.sqrt(p / (1. - p)); 83 | } else { 84 | upperBound = 1.0; 85 | while (cdf(upperBound) < p) { 86 | upperBound *= 2.0; 87 | } 88 | } 89 | } 90 | 91 | final UnivariateFunction toSolve = new UnivariateFunction() { 92 | /** {@inheritDoc} */ 93 | public double value(final double x) { 94 | return cdf(x) - p; 95 | } 96 | }; 97 | 98 | double x = UnivariateSolverUtils.solve(toSolve, 99 | lowerBound, 100 | upperBound, 101 | solverAbsoluteAccuracy); 102 | 103 | if (!isSupportConnected) { 104 | /* Test for plateau. */ 105 | if (x - solverAbsoluteAccuracy >= supportLowerBound) { 106 | double px = cdf(x); 107 | if (cdf(x - solverAbsoluteAccuracy) == px) { 108 | upperBound = x; 109 | while (upperBound - lowerBound > solverAbsoluteAccuracy) { 110 | final double midPoint = 0.5 * (lowerBound + upperBound); 111 | if (cdf(midPoint) < px) { 112 | lowerBound = midPoint; 113 | } else { 114 | upperBound = midPoint; 115 | } 116 | } 117 | return upperBound; 118 | } 119 | } 120 | } 121 | return x; 122 | } 123 | } 124 | -------------------------------------------------------------------------------- /gradlew: -------------------------------------------------------------------------------- 1 | #!/usr/bin/env bash 2 | 3 | ############################################################################## 4 | ## 5 | ## Gradle start up script for UN*X 6 | ## 7 | ############################################################################## 8 | 9 | # Add default JVM options here. You can also use JAVA_OPTS and GRADLE_OPTS to pass JVM options to this script. 10 | DEFAULT_JVM_OPTS="" 11 | 12 | APP_NAME="Gradle" 13 | APP_BASE_NAME=`basename "$0"` 14 | 15 | # Use the maximum available, or set MAX_FD != -1 to use that value. 16 | MAX_FD="maximum" 17 | 18 | warn ( ) { 19 | echo "$*" 20 | } 21 | 22 | die ( ) { 23 | echo 24 | echo "$*" 25 | echo 26 | exit 1 27 | } 28 | 29 | # OS specific support (must be 'true' or 'false'). 30 | cygwin=false 31 | msys=false 32 | darwin=false 33 | case "`uname`" in 34 | CYGWIN* ) 35 | cygwin=true 36 | ;; 37 | Darwin* ) 38 | darwin=true 39 | ;; 40 | MINGW* ) 41 | msys=true 42 | ;; 43 | esac 44 | 45 | # Attempt to set APP_HOME 46 | # Resolve links: $0 may be a link 47 | PRG="$0" 48 | # Need this for relative symlinks. 49 | while [ -h "$PRG" ] ; do 50 | ls=`ls -ld "$PRG"` 51 | link=`expr "$ls" : '.*-> \(.*\)$'` 52 | if expr "$link" : '/.*' > /dev/null; then 53 | PRG="$link" 54 | else 55 | PRG=`dirname "$PRG"`"/$link" 56 | fi 57 | done 58 | SAVED="`pwd`" 59 | cd "`dirname \"$PRG\"`/" >/dev/null 60 | APP_HOME="`pwd -P`" 61 | cd "$SAVED" >/dev/null 62 | 63 | CLASSPATH=$APP_HOME/gradle/wrapper/gradle-wrapper.jar 64 | 65 | # Determine the Java command to use to start the JVM. 66 | if [ -n "$JAVA_HOME" ] ; then 67 | if [ -x "$JAVA_HOME/jre/sh/java" ] ; then 68 | # IBM's JDK on AIX uses strange locations for the executables 69 | JAVACMD="$JAVA_HOME/jre/sh/java" 70 | else 71 | JAVACMD="$JAVA_HOME/bin/java" 72 | fi 73 | if [ ! -x "$JAVACMD" ] ; then 74 | die "ERROR: JAVA_HOME is set to an invalid directory: $JAVA_HOME 75 | 76 | Please set the JAVA_HOME variable in your environment to match the 77 | location of your Java installation." 78 | fi 79 | else 80 | JAVACMD="java" 81 | which java >/dev/null 2>&1 || die "ERROR: JAVA_HOME is not set and no 'java' command could be found in your PATH. 82 | 83 | Please set the JAVA_HOME variable in your environment to match the 84 | location of your Java installation." 85 | fi 86 | 87 | # Increase the maximum file descriptors if we can. 88 | if [ "$cygwin" = "false" -a "$darwin" = "false" ] ; then 89 | MAX_FD_LIMIT=`ulimit -H -n` 90 | if [ $? -eq 0 ] ; then 91 | if [ "$MAX_FD" = "maximum" -o "$MAX_FD" = "max" ] ; then 92 | MAX_FD="$MAX_FD_LIMIT" 93 | fi 94 | ulimit -n $MAX_FD 95 | if [ $? -ne 0 ] ; then 96 | warn "Could not set maximum file descriptor limit: $MAX_FD" 97 | fi 98 | else 99 | warn "Could not query maximum file descriptor limit: $MAX_FD_LIMIT" 100 | fi 101 | fi 102 | 103 | # For Darwin, add options to specify how the application appears in the dock 104 | if $darwin; then 105 | GRADLE_OPTS="$GRADLE_OPTS \"-Xdock:name=$APP_NAME\" \"-Xdock:icon=$APP_HOME/media/gradle.icns\"" 106 | fi 107 | 108 | # For Cygwin, switch paths to Windows format before running java 109 | if $cygwin ; then 110 | APP_HOME=`cygpath --path --mixed "$APP_HOME"` 111 | CLASSPATH=`cygpath --path --mixed "$CLASSPATH"` 112 | JAVACMD=`cygpath --unix "$JAVACMD"` 113 | 114 | # We build the pattern for arguments to be converted via cygpath 115 | ROOTDIRSRAW=`find -L / -maxdepth 1 -mindepth 1 -type d 2>/dev/null` 116 | SEP="" 117 | for dir in $ROOTDIRSRAW ; do 118 | ROOTDIRS="$ROOTDIRS$SEP$dir" 119 | SEP="|" 120 | done 121 | OURCYGPATTERN="(^($ROOTDIRS))" 122 | # Add a user-defined pattern to the cygpath arguments 123 | if [ "$GRADLE_CYGPATTERN" != "" ] ; then 124 | OURCYGPATTERN="$OURCYGPATTERN|($GRADLE_CYGPATTERN)" 125 | fi 126 | # Now convert the arguments - kludge to limit ourselves to /bin/sh 127 | i=0 128 | for arg in "$@" ; do 129 | CHECK=`echo "$arg"|egrep -c "$OURCYGPATTERN" -` 130 | CHECK2=`echo "$arg"|egrep -c "^-"` ### Determine if an option 131 | 132 | if [ $CHECK -ne 0 ] && [ $CHECK2 -eq 0 ] ; then ### Added a condition 133 | eval `echo args$i`=`cygpath --path --ignore --mixed "$arg"` 134 | else 135 | eval `echo args$i`="\"$arg\"" 136 | fi 137 | i=$((i+1)) 138 | done 139 | case $i in 140 | (0) set -- ;; 141 | (1) set -- "$args0" ;; 142 | (2) set -- "$args0" "$args1" ;; 143 | (3) set -- "$args0" "$args1" "$args2" ;; 144 | (4) set -- "$args0" "$args1" "$args2" "$args3" ;; 145 | (5) set -- "$args0" "$args1" "$args2" "$args3" "$args4" ;; 146 | (6) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" ;; 147 | (7) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" ;; 148 | (8) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" ;; 149 | (9) set -- "$args0" "$args1" "$args2" "$args3" "$args4" "$args5" "$args6" "$args7" "$args8" ;; 150 | esac 151 | fi 152 | 153 | # Split up the JVM_OPTS And GRADLE_OPTS values into an array, following the shell quoting and substitution rules 154 | function splitJvmOpts() { 155 | JVM_OPTS=("$@") 156 | } 157 | eval splitJvmOpts $DEFAULT_JVM_OPTS $JAVA_OPTS $GRADLE_OPTS 158 | JVM_OPTS[${#JVM_OPTS[*]}]="-Dorg.gradle.appname=$APP_BASE_NAME" 159 | 160 | exec "$JAVACMD" "${JVM_OPTS[@]}" -classpath "$CLASSPATH" org.gradle.wrapper.GradleWrapperMain "$@" 161 | -------------------------------------------------------------------------------- /fast-rng/src/main/java/biz/k11i/rng/ExponentialRNG.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import java.util.Random; 4 | 5 | import static biz.k11i.util.MathFunctions.exp; 6 | import static biz.k11i.util.MathFunctions.log; 7 | import static biz.k11i.util.MathFunctions.log1p; 8 | 9 | /** 10 | * Exponential random number generator. 11 | */ 12 | public interface ExponentialRNG { 13 | ExponentialRNG FAST_RNG = ZigguratFast.Z_256; 14 | ExponentialRNG GENERAL_RNG = ZigguratGeneral.Z_256; 15 | 16 | /** 17 | * Generates a random value sampled from exponential distribution. 18 | * 19 | * @param random random number generator 20 | * @param theta mean of the distribution 21 | * @return a random value 22 | */ 23 | double generate(Random random, double theta); 24 | 25 | abstract class ZigguratBase implements ExponentialRNG { 26 | final int N; 27 | final double R; 28 | final double V; 29 | final int INDEX_BIT_MASK; 30 | final int TAIL_INDEX; 31 | 32 | ZigguratBase(int nBits, double r, double v) { 33 | N = 1 << nBits; 34 | R = r; 35 | V = v; 36 | 37 | INDEX_BIT_MASK = (1 << nBits) - 1; 38 | TAIL_INDEX = (1 << nBits) - 1; 39 | } 40 | 41 | static double finv(double x, double v) { 42 | return -log(exp(-x) + v / x); 43 | } 44 | 45 | @Override 46 | public double generate(Random random, double theta) { 47 | return theta * generate(random, 0); 48 | } 49 | 50 | abstract double generate(Random random, int recursionCount); 51 | } 52 | 53 | /** 54 | * Implementation of Exponential random number generator using Ziggurat algorithm. 55 | *

56 | * Tesuaki Yotsuji. 計算機シミュレーションのための確率分布乱数生成法. 57 | * Pleiades PUBLISHING Co.,Ltd. (2010) 58 | *

59 | *

60 | * This implementation assumes that the values returned from {@link Random#nextLong()} 61 | * have the independence of each bit. 62 | *

63 | */ 64 | class ZigguratFast extends ZigguratBase implements ExponentialRNG { 65 | private static final ZigguratFast Z_256 = new ZigguratFast(8, 7.697117470131, 0.00394965982258); 66 | 67 | private final int INDEX_BITS; 68 | 69 | private final long[] k; 70 | private final double[] w; 71 | private final double[] f; 72 | 73 | ZigguratFast(int nBits, double r, double v) { 74 | super(nBits, r, v); 75 | 76 | INDEX_BITS = nBits; 77 | 78 | w = new double[N]; 79 | k = new long[N]; 80 | f = new double[N]; 81 | 82 | long b = 1L << (64 - nBits); 83 | w[N - 1] = v * exp(r) / b; 84 | w[N - 2] = r / b; 85 | k[N - 1] = (long) Math.floor(r / w[N - 1]); 86 | f[N - 1] = exp(-r); 87 | 88 | double x = r; 89 | for (int i = N - 2; i >= 1; i--) { 90 | x = finv(x, v); 91 | w[i - 1] = x / b; 92 | k[i] = (long) Math.floor(x / w[i]); 93 | f[i] = exp(-x); 94 | } 95 | 96 | k[0] = 0; 97 | f[0] = 1; 98 | } 99 | 100 | @Override 101 | double generate(Random random, int recursiveCount) { 102 | while (true) { 103 | long u = random.nextLong(); 104 | int i = (int) (u & INDEX_BIT_MASK); 105 | u >>>= INDEX_BITS; 106 | 107 | if (u < k[i]) { 108 | return u * w[i]; 109 | } 110 | 111 | if (i == TAIL_INDEX) { 112 | if (recursiveCount < 2) { 113 | return R + generate(random, recursiveCount + 1); 114 | } 115 | return R - log1p(-random.nextDouble()); 116 | } 117 | 118 | double x = u * w[i]; 119 | double fx = exp(-x); 120 | if (random.nextDouble() * (f[i] - f[i + 1]) <= fx - f[i + 1]) { 121 | return x; 122 | } 123 | } 124 | } 125 | } 126 | 127 | /** 128 | * Implementation of Exponential random number generator using Ziggurat algorithm. 129 | *

130 | * Tesuaki Yotsuji. 計算機シミュレーションのための確率分布乱数生成法. 131 | * Pleiades PUBLISHING Co.,Ltd. (2010) 132 | *

133 | *

134 | * This implementation is a bit slower than {@link ZigguratFast} 135 | * but it does not require the independence of each bit to the values returned from {@link Random#nextLong()}. 136 | *

137 | */ 138 | class ZigguratGeneral extends ZigguratBase implements ExponentialRNG { 139 | private static final ZigguratGeneral Z_256 = new ZigguratGeneral(8, 7.697117470131, 0.00394965982258); 140 | 141 | private final double[] x; 142 | private final double[] t; 143 | 144 | ZigguratGeneral(int nBits, double r, double v) { 145 | super(nBits, r, v); 146 | 147 | x = new double[N + 1]; 148 | t = new double[N]; 149 | 150 | x[N] = v * exp(r); 151 | x[N - 1] = r; 152 | for (int i = N - 2; i >= 1; i--) { 153 | x[i] = finv(x[i + 1], v); 154 | } 155 | x[0] = 0; 156 | 157 | for (int i = 0; i < N; i++) { 158 | t[i] = x[i] / x[i + 1]; 159 | } 160 | } 161 | 162 | @Override 163 | double generate(Random random, int recursiveCount) { 164 | while (true) { 165 | int i = (int) (random.nextLong() & INDEX_BIT_MASK); 166 | double u1 = random.nextDouble(); 167 | 168 | if (u1 < t[i]) { 169 | return u1 * x[i + 1]; 170 | } 171 | 172 | if (i == TAIL_INDEX) { 173 | if (recursiveCount < 2) { 174 | return R + generate(random, recursiveCount + 1); 175 | } 176 | return R - log1p(-random.nextDouble()); 177 | } 178 | 179 | double y = u1 * x[i + 1]; 180 | double gu = exp(-(x[i] - y)); 181 | double gl = exp(-(x[i + 1] - y)); 182 | if (random.nextDouble() * (gu - gl) <= 1 - gl) { 183 | return y; 184 | } 185 | } 186 | } 187 | } 188 | } 189 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/util/ComputationAndSorting.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util; 2 | 3 | import java.util.Arrays; 4 | import java.util.concurrent.ForkJoinTask; 5 | import java.util.concurrent.RecursiveAction; 6 | 7 | public class ComputationAndSorting> { 8 | @FunctionalInterface 9 | public interface Computation> { 10 | double compute(S splittable, int index); 11 | } 12 | 13 | @FunctionalInterface 14 | public interface Splittable> { 15 | S split(); 16 | } 17 | 18 | public static class NullSplittable implements Splittable { 19 | public static final NullSplittable INSTANCE = new NullSplittable(); 20 | 21 | @Override 22 | public NullSplittable split() { 23 | return this; 24 | } 25 | } 26 | 27 | private final Computation computation; 28 | private final int splitThreshold; 29 | private final int parallelMergeThreshold; 30 | 31 | public ComputationAndSorting(int n, int numParallels, Computation computation) { 32 | this.computation = computation; 33 | int g = n / numParallels; 34 | this.splitThreshold = g; 35 | this.parallelMergeThreshold = g; 36 | } 37 | 38 | public ForkJoinTask newForkJoinTask(S splittable, double[] result, double[] work) { 39 | return new ComputationAction(0, result.length, result, work, splittable); 40 | } 41 | 42 | class ComputationAction extends RecursiveAction { 43 | private final int startInclusive; 44 | private final int endExclusive; 45 | private final double[] output; 46 | private final double[] work; 47 | private final S splittable; 48 | 49 | ComputationAction(int startInclusive, int endExclusive, double[] output, double[] work, S splittable) { 50 | this.startInclusive = startInclusive; 51 | this.endExclusive = endExclusive; 52 | this.output = output; 53 | this.work = work; 54 | this.splittable = splittable; 55 | } 56 | 57 | @Override 58 | protected void compute() { 59 | split(startInclusive, endExclusive, output, work); 60 | } 61 | 62 | private void split(int startInclusive, int endExclusive, double[] output, double[] work) { 63 | int n = endExclusive - startInclusive; 64 | if (n > splitThreshold) { 65 | int mid = startInclusive + (n >>> 1); 66 | 67 | ForkJoinTask h2 = new ComputationAction(mid, endExclusive, work, output, splittable.split()).fork(); 68 | split(startInclusive, mid, work, output); 69 | h2.join(); 70 | 71 | if (n > parallelMergeThreshold) { 72 | mergeInParallel(startInclusive, mid, endExclusive, output, work); 73 | } else { 74 | mergeSequentially(startInclusive, mid, endExclusive, output, work); 75 | } 76 | 77 | } else { 78 | computeSequentially(startInclusive, endExclusive, output); 79 | } 80 | } 81 | 82 | private void mergeInParallel(int startInclusive, int mid, int endExclusive, double[] output, double[] work) { 83 | int q1 = (startInclusive + mid) >>> 1; 84 | double split = work[q1]; 85 | 86 | int left = mid; 87 | int right = endExclusive; 88 | 89 | while (left < right) { 90 | int searchMid = (left + right) >>> 1; 91 | if (work[searchMid] < split) { 92 | left = searchMid + 1; 93 | } else { 94 | right = searchMid; 95 | } 96 | } 97 | 98 | int s = (q1 + 1) + (right - mid); 99 | ForkJoinTask m2 = new MergeAction(work, 100 | q1 + 1, mid, 101 | right, endExclusive, 102 | output, s).fork(); 103 | MergeAction.mergeSequentially(work, 104 | startInclusive, q1 + 1, 105 | mid, right, 106 | output, startInclusive); 107 | m2.join(); 108 | } 109 | 110 | private void mergeSequentially(int startInclusive, int mid, int endExclusive, double[] output, double[] work) { 111 | MergeAction.mergeSequentially(work, startInclusive, mid, mid, endExclusive, output, startInclusive); 112 | } 113 | 114 | private void computeSequentially(int startInclusive, int endExclusive, double[] result) { 115 | for (int i = startInclusive; i < endExclusive; i++) { 116 | result[i] = computation.compute(splittable, i); 117 | } 118 | 119 | Arrays.sort(result, startInclusive, endExclusive); 120 | } 121 | } 122 | 123 | static class MergeAction extends RecursiveAction { 124 | private final double[] src; 125 | private final int src1Start; 126 | private final int src1End; 127 | private final int src2Start; 128 | private final int src2End; 129 | private final double[] dst; 130 | private final int dstStart; 131 | 132 | MergeAction(double[] src, int src1Start, int src1End, int src2Start, int src2End, double[] dst, int dstStart) { 133 | this.src = src; 134 | this.src1Start = src1Start; 135 | this.src1End = src1End; 136 | this.src2Start = src2Start; 137 | this.src2End = src2End; 138 | this.dst = dst; 139 | this.dstStart = dstStart; 140 | } 141 | 142 | @Override 143 | protected void compute() { 144 | mergeSequentially(src, src1Start, src1End, src2Start, src2End, dst, dstStart); 145 | } 146 | 147 | static void mergeSequentially(double[] src, int left, int leftEnd, int right, int rightEnd, double[] dst, int dstStart) { 148 | for (int i = dstStart; ; i++) { 149 | if (left >= leftEnd) { 150 | System.arraycopy(src, right, dst, i, rightEnd - right); 151 | return; 152 | } 153 | if (right >= rightEnd) { 154 | System.arraycopy(src, left, dst, i, leftEnd - left); 155 | return; 156 | } 157 | 158 | if (src[left] <= src[right]) { 159 | dst[i] = src[left++]; 160 | } else { 161 | dst[i] = src[right++]; 162 | } 163 | } 164 | } 165 | } 166 | } 167 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/gof/GoodnessOfFitTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.gof; 2 | 3 | import org.slf4j.Logger; 4 | 5 | import java.util.ArrayList; 6 | import java.util.Arrays; 7 | import java.util.Comparator; 8 | import java.util.List; 9 | import java.util.Map; 10 | import java.util.concurrent.ForkJoinPool; 11 | import java.util.concurrent.TimeUnit; 12 | import java.util.function.Consumer; 13 | import java.util.function.Function; 14 | 15 | import static org.assertj.core.api.Assertions.assertThat; 16 | 17 | /** 18 | * Provides functionalities for Goodness-of-Fit test to test randomness of the given random number generator. 19 | */ 20 | @SuppressWarnings("unused") 21 | public abstract class GoodnessOfFitTest { 22 | static class BuilderBase> { 23 | @SuppressWarnings("unchecked") 24 | private final SELF self = (SELF) this; 25 | 26 | int numRandomValues; 27 | double significanceLevel = DEFAULT_SIGNIFICANCE_LEVEL; 28 | 29 | public SELF numRandomValues(int numRandomValues) { 30 | this.numRandomValues = numRandomValues; 31 | return self; 32 | } 33 | 34 | public SELF significanceLevel(double significanceLevel) { 35 | this.significanceLevel = significanceLevel; 36 | return self; 37 | } 38 | } 39 | 40 | /** Default significance level (0.1%) */ 41 | private static final double DEFAULT_SIGNIFICANCE_LEVEL = 0.001; 42 | 43 | /** Name of the random number generator to be tested */ 44 | public final String rngName; 45 | 46 | /** Significance level to reject the null hypothesis */ 47 | public final double significanceLevel; 48 | 49 | GoodnessOfFitTest(String rngName, double significanceLevel) { 50 | this.rngName = rngName; 51 | this.significanceLevel = significanceLevel; 52 | } 53 | 54 | /** 55 | * Returns {@link ContinuousGofTest} builder object. 56 | * 57 | * @return builder object. 58 | */ 59 | public static ContinuousGofTest.Builder continuous() { 60 | return new ContinuousGofTest.Builder(); 61 | } 62 | 63 | /** 64 | * Returns {@link DiscreteGofTest} builder object. 65 | * 66 | * @return builder obbject. 67 | */ 68 | public static DiscreteGofTest.Builder discrete() { 69 | return new DiscreteGofTest.Builder(); 70 | } 71 | 72 | /** 73 | * Calculate p-values of Goodness-of-Fit test. 74 | * 75 | * @return test result. 76 | */ 77 | public abstract Map test(); 78 | 79 | /** 80 | * Calculate p-values of Goodness-of-Fit test in parallel. 81 | * 82 | * @return test result. 83 | */ 84 | public Map testInParallel() { 85 | ForkJoinPool pool = new ForkJoinPool(); 86 | try { 87 | return testInParallel(pool); 88 | 89 | } finally { 90 | pool.shutdown(); 91 | try { 92 | pool.awaitTermination(1, TimeUnit.SECONDS); 93 | } catch (InterruptedException ignore) { 94 | } 95 | } 96 | } 97 | 98 | /** 99 | * Calculate p-values of Goodness-of-Fit test in parallel using given {@link ForkJoinPool} instance. 100 | * 101 | * @param pool Fork/Join pool to execute tasks in paralle. 102 | * @return test result. 103 | */ 104 | public abstract Map testInParallel(ForkJoinPool pool); 105 | 106 | /** 107 | * Runs Goodness-of-Fit tests and verifis whether the test failed to reject the null hypothesis 108 | * (which means the random sequence that was generated by random number generator can be described as random) or not. 109 | */ 110 | public void testAndVerify() { 111 | Map result = test(); 112 | 113 | result.forEach((t, p) -> 114 | assertThat(p) 115 | .describedAs("At a significance level of %e, the Goodness-of-Fit test of [%s] should fail to reject null hypothesis (The p-value %f should be greater than or equal to %e).\n" + 116 | "This means that the random sequence generated by the random number generator [%s] fit the theoretical probability distribution.", 117 | significanceLevel, t, p, significanceLevel, 118 | rngName) 119 | .isGreaterThanOrEqualTo(significanceLevel)); 120 | } 121 | } 122 | 123 | @SuppressWarnings("unused") 124 | class PerformanceMeasure { 125 | static class LogRecord { 126 | private final String message; 127 | private Object[] args; 128 | private final long beginMillis = System.currentTimeMillis(); 129 | private long endMillis; 130 | 131 | LogRecord(String message) { 132 | this.message = message; 133 | } 134 | 135 | void updateArgs(Object... args) { 136 | this.args = args; 137 | } 138 | 139 | long elapsedMillis() { 140 | return endMillis - beginMillis; 141 | } 142 | } 143 | 144 | private final List bufferedLogs = new ArrayList<>(); 145 | 146 | static T run(Logger logger, Function process) { 147 | PerformanceMeasure m = new PerformanceMeasure(); 148 | try { 149 | return process.apply(m); 150 | } finally { 151 | m.flushLogs(logger); 152 | } 153 | } 154 | 155 | void measure(String logMessageTemplate, Consumer processToMeasure) { 156 | measure(logMessageTemplate, args(), processToMeasure); 157 | } 158 | 159 | void measure(String logMessageTemplate, Object arg1, Consumer processToMeasure) { 160 | measure(logMessageTemplate, args(arg1), processToMeasure); 161 | } 162 | 163 | void measure(String logMessageTemplate, Object arg1, Object arg2, Consumer processToMeasure) { 164 | measure(logMessageTemplate, args(arg1, arg2), processToMeasure); 165 | } 166 | 167 | void measure(String logMessageTemplate, Object[] args, Consumer processToMeasure) { 168 | long begin = System.currentTimeMillis(); 169 | 170 | LogRecord logRecord = new LogRecord(logMessageTemplate); 171 | logRecord.args = args; 172 | bufferedLogs.add(logRecord); 173 | 174 | processToMeasure.accept(logRecord); 175 | logRecord.endMillis = System.currentTimeMillis(); 176 | } 177 | 178 | Object[] args(Object... args) { 179 | return args; 180 | } 181 | 182 | private void flushLogs(Logger logger) { 183 | bufferedLogs.sort(Comparator.comparingLong(o -> o.beginMillis)); 184 | 185 | for (LogRecord log : bufferedLogs) { 186 | Object[] args = Arrays.copyOf(log.args, log.args.length + 1); 187 | args[log.args.length] = log.elapsedMillis(); 188 | logger.info(log.message + " ({} ms)", args); 189 | } 190 | } 191 | } 192 | -------------------------------------------------------------------------------- /fast-rng/src/main/java/biz/k11i/rng/BetaRNG.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import java.util.Random; 4 | 5 | import static biz.k11i.util.MathFunctions.exp; 6 | import static biz.k11i.util.MathFunctions.log; 7 | import static biz.k11i.util.MathFunctions.pow; 8 | 9 | /** 10 | * Beta random number generator. 11 | */ 12 | public interface BetaRNG { 13 | BetaRNG FAST_RNG = new BetaRNGImpl(GammaRNG.FAST_RNG); 14 | BetaRNG GENERAL_RNG = new BetaRNGImpl(GammaRNG.GENERAL_RNG); 15 | 16 | /** 17 | * Generates a random value sampled from beta distribution. 18 | * 19 | * @param random random number generator 20 | * @param alpha shape parameter (alpha) 21 | * @param beta shape parameter (beta) 22 | * @return a random value 23 | */ 24 | double generate(Random random, double alpha, double beta); 25 | 26 | class BetaRNGImpl implements BetaRNG { 27 | private static final double[] CASE2_MAX_THRESHOLDS; 28 | 29 | static { 30 | CASE2_MAX_THRESHOLDS = new double[11]; 31 | CASE2_MAX_THRESHOLDS[0] = 90.0; 32 | CASE2_MAX_THRESHOLDS[1 /* 0.01 */] = 70.0; 33 | CASE2_MAX_THRESHOLDS[2 /* 0.02 */] = 50.0; 34 | CASE2_MAX_THRESHOLDS[3 /* 0.03 */] = 12.0; 35 | CASE2_MAX_THRESHOLDS[4 /* 0.04 */] = 6.0; 36 | CASE2_MAX_THRESHOLDS[5 /* 0.05 */] = 3.0; 37 | CASE2_MAX_THRESHOLDS[6 /* 0.06 */] = 2.5; 38 | CASE2_MAX_THRESHOLDS[7 /* 0.07 */] = 2.0; 39 | CASE2_MAX_THRESHOLDS[8 /* 0.08 */] = 1.6; 40 | CASE2_MAX_THRESHOLDS[9 /* 0.09 */] = 1.3; 41 | CASE2_MAX_THRESHOLDS[10 /* 0.10 */] = 1.0; 42 | } 43 | 44 | private final BetaRNG twoGammaVariates; 45 | 46 | BetaRNGImpl(GammaRNG gammaRNG) { 47 | this.twoGammaVariates = new BetaRNGAlgorithms.TwoGammaVariates(gammaRNG); 48 | } 49 | 50 | @Override 51 | public double generate(Random random, double alpha, double beta) { 52 | return (alpha <= beta ? selectAlgorithm(alpha, beta) : selectAlgorithm(beta, alpha)) 53 | .generate(random, alpha, beta); 54 | } 55 | 56 | BetaRNG selectAlgorithm(double min, double max) { 57 | if (min > 1.0) { // case 3: max >= min > 1 58 | return twoGammaVariates; 59 | } 60 | 61 | if (max < 1.0) { // case 1: min <= max < 1 62 | return max + min <= 1.5 ? BetaRNGAlgorithms.Johnk.INSTANCE : BetaRNGAlgorithms.B00.INSTANCE; 63 | } 64 | 65 | // case 2 + special case 66 | // min <= 1, max >= 1 67 | 68 | if (min < 0.1 && max <= CASE2_MAX_THRESHOLDS[(int) (min * 100)]) { 69 | return BetaRNGAlgorithms.Johnk.INSTANCE; 70 | } 71 | 72 | if (max > 1.0) { 73 | return twoGammaVariates; 74 | } 75 | 76 | // min <= 1, max = 1 77 | 78 | if (min == 1.0) { 79 | // max = 1, min = 1 80 | return BetaRNGAlgorithms.Unif.INSTANCE; 81 | } 82 | 83 | return BetaRNGAlgorithms.CdfInversion.INSTANCE; 84 | } 85 | } 86 | 87 | 88 | } 89 | 90 | class BetaRNGAlgorithms { 91 | /** 92 | * Implementation of Beta random number generator using Jöhnk's algorithm. 93 | *

94 | * Jöhnk, M. D. 95 | * "Erzeugung von betaverteilten und gammaverteilten Zufallszahlen." 96 | * Metrika 8.1 (1964): 5-15. 97 | *

98 | */ 99 | static class Johnk implements BetaRNG { 100 | static final BetaRNG INSTANCE = new Johnk(); 101 | 102 | @Override 103 | public double generate(Random random, double alpha, double beta) { 104 | while (true) { 105 | double u = log(random.nextDouble()) / alpha; 106 | double v = log(random.nextDouble()) / beta; 107 | 108 | double uu = exp(u); 109 | double vv = exp(v); 110 | 111 | double w = uu + vv; 112 | if (w <= 1) { 113 | if (w > 0) { 114 | return uu / w; 115 | } 116 | 117 | double logM = u > v ? u : v; 118 | u -= logM; 119 | v -= logM; 120 | 121 | return exp(u - log(exp(u) + exp(v))); 122 | } 123 | } 124 | } 125 | } 126 | 127 | /** 128 | * Implementation of Beta random number generator using Sakasegawa's B00 algorithm. 129 | *

130 | * Sakasegawa, H. 131 | * "Stratified rejection and squeeze method for generating beta random numbers." 132 | * Annals of the Institute of Statistical Mathematics 35.1 (1983): 291-302. 133 | *

134 | */ 135 | static class B00 implements BetaRNG { 136 | static final BetaRNG INSTANCE = new B00(); 137 | 138 | @Override 139 | public double generate(Random random, double alpha, double beta) { 140 | double t = (1 - alpha) / (2 - alpha - beta); 141 | double s = (beta - alpha) * (1 - alpha - beta); 142 | double r = alpha * (1 - alpha); 143 | t -= ((s * t + 2 * r) * t - r) / 2 * (s * t + r); 144 | double p = t / alpha; 145 | double q = (1 - t) / beta; 146 | s = pow((1 - t), beta - 1); 147 | double c = pow(t, alpha - 1); 148 | r = (c - 1) / (t - 1); 149 | 150 | while (true) { 151 | // step 1 152 | double u = random.nextDouble() * (p + q); 153 | double v = random.nextDouble(); 154 | 155 | if (u <= p) { 156 | // step 2 157 | double x = t * pow(u / p, 1 / alpha); 158 | v *= s; 159 | 160 | if (v < (1 - beta) * x + 1) { 161 | return x; 162 | } 163 | if (v < (s - 1) * x / t + 1 && v <= pow(1 - x, beta - 1)) { 164 | return x; 165 | } 166 | 167 | } else { 168 | // step 3 169 | double x = 1 - (1 - t) * pow((u - p) / q, 1 / beta); 170 | v *= c; 171 | 172 | if (v < (alpha - 1) * (x - 1) + 1) { 173 | return x; 174 | } 175 | if (v <= r * (x - 1) + 1 && v <= pow(x, alpha - 1)) { 176 | return x; 177 | } 178 | } 179 | } 180 | } 181 | } 182 | 183 | /** 184 | * Generates Beta variates using two Gamma variates. 185 | */ 186 | static class TwoGammaVariates implements BetaRNG { 187 | private final GammaRNG gammaRNG; 188 | 189 | TwoGammaVariates(GammaRNG gammaRNG) { 190 | this.gammaRNG = gammaRNG; 191 | } 192 | 193 | @Override 194 | public double generate(Random random, double alpha, double beta) { 195 | double a = gammaRNG.generate(random, alpha, 1); 196 | if (a == 0.0) { 197 | return 0.0; 198 | } 199 | 200 | return a / (a + gammaRNG.generate(random, beta, 1)); 201 | } 202 | } 203 | 204 | /** 205 | * Generates Beta variates using inversion method. 206 | */ 207 | static class CdfInversion implements BetaRNG { 208 | static final BetaRNG INSTANCE = new CdfInversion(); 209 | 210 | @Override 211 | public double generate(Random random, double alpha, double beta) { 212 | return alpha == 1.0 213 | ? 1 - pow(random.nextDouble(), 1.0 / beta) 214 | : pow(random.nextDouble(), 1.0 / alpha); 215 | } 216 | } 217 | 218 | static class Unif implements BetaRNG { 219 | static final BetaRNG INSTANCE = new Unif(); 220 | 221 | @Override 222 | public double generate(Random random, double ignore1, double ignore2) { 223 | return random.nextDouble(); 224 | } 225 | } 226 | } -------------------------------------------------------------------------------- /fast-rng/src/main/java/biz/k11i/rng/GaussianRNG.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import java.util.Random; 4 | 5 | import static biz.k11i.util.MathFunctions.exp; 6 | import static biz.k11i.util.MathFunctions.log; 7 | 8 | /** 9 | * Gaussian random number generator. 10 | */ 11 | public interface GaussianRNG { 12 | GaussianRNG FAST_RNG = ZigguratFast.Z_256; 13 | GaussianRNG GENERAL_RNG = ZigguratGeneral.Z_256; 14 | 15 | /** 16 | * Generates a random value sampled from gaussian distribution (normal distribution). 17 | * 18 | * @param random random number generator 19 | * @return a random value 20 | */ 21 | double generate(Random random); 22 | 23 | abstract class ZigguratBase { 24 | static double f(double x) { 25 | // f(x) = e^{-x^2 / 2} 26 | return exp(-0.5 * x * x); 27 | } 28 | 29 | static double tail(Random random, double r) { 30 | double _x, _y; 31 | do { 32 | _x = -log(random.nextDouble()) / r; 33 | _y = -log(random.nextDouble()); 34 | 35 | } while (_y + _y < _x * _x); 36 | return r + _x; 37 | } 38 | } 39 | 40 | /** 41 | * Implementation of Gaussian random number generator using Ziggurat algorithm. 42 | *

43 | * Marsaglia, George, and Wai Wan Tsang. 44 | * "The ziggurat method for generating random variables." 45 | * Journal of statistical software 5.8 (2000): 1-7. 46 | *

47 | *

48 | * Tesuaki Yotsuji. 計算機シミュレーションのための確率分布乱数生成法. 49 | * Pleiades PUBLISHING Co.,Ltd. (2010) 50 | *

51 | *

52 | * This implementation assumes that the values returned from {@link Random#nextLong()} 53 | * have the independence of each bit. 54 | *

55 | */ 56 | class ZigguratFast extends ZigguratBase implements GaussianRNG { 57 | private static final ZigguratFast Z_256 = new ZigguratFast(8, 3.6541528853610088, 0.00492867323399); 58 | 59 | private final int N; 60 | private final double R; 61 | private final double V; 62 | private final int INDEX_RIGHT_SHIFT_BITS; 63 | private final long SIGN_BIT_MASK; 64 | private final long U_BIT_MASK; 65 | private final int TAIL_INDEX; 66 | 67 | private final long[] k; 68 | private final double[] w; 69 | private final double[] f; 70 | 71 | /** 72 | * Constructs {@link ZigguratFast} with parameters. 73 | * 74 | * @param nBits number of rectangles (2^nBits) 75 | * @param r rightmost x_i 76 | * @param v area of the rectangle 77 | */ 78 | ZigguratFast(int nBits, double r, double v) { 79 | N = 1 << nBits; 80 | R = r; 81 | V = v; 82 | INDEX_RIGHT_SHIFT_BITS = 64 - nBits; 83 | SIGN_BIT_MASK = 1L << (64 - nBits - 1); 84 | U_BIT_MASK = (1L << (64 - nBits - 1)) - 1; 85 | TAIL_INDEX = N - 1; 86 | 87 | k = new long[N]; 88 | w = new double[N]; 89 | f = new double[N]; 90 | 91 | double fr = f(r); 92 | long b = 1L << (64 - 8 - 1); 93 | 94 | w[N - 1] = v * exp(0.5 * r * r) / b; 95 | w[N - 2] = r / b; 96 | k[N - 1] = (long) Math.floor(r / w[N - 1]); 97 | f[N - 1] = fr; 98 | 99 | double x = r; 100 | 101 | for (int i = N - 2; i >= 1; i--) { 102 | x = Math.sqrt(-2.0 * log(f(x) + v / x)); 103 | w[i - 1] = x / b; 104 | k[i] = (long) Math.floor(x / w[i]); 105 | f[i] = f(x); 106 | } 107 | 108 | k[0] = 0; 109 | f[0] = 1; 110 | } 111 | 112 | public double generate(Random random) { 113 | while (true) { 114 | long u = random.nextLong(); 115 | int i = (int) (u >>> INDEX_RIGHT_SHIFT_BITS); 116 | int sign = (u & SIGN_BIT_MASK) == 0 ? 1 : -1; 117 | u &= U_BIT_MASK; 118 | 119 | if (u < k[i]) { 120 | return sign * u * w[i]; 121 | } 122 | 123 | if (i == TAIL_INDEX) { 124 | return sign * tail(random, R); 125 | } 126 | 127 | double x = u * w[i]; 128 | if (random.nextDouble() * (f[i] - f[i + 1]) <= f(x) - f[i + 1]) { 129 | return sign * x; 130 | } 131 | } 132 | } 133 | 134 | @Override 135 | public String toString() { 136 | return String.format("ZigguratFast(N = %d, R = %f, V = %f)", N, R, V); 137 | } 138 | } 139 | 140 | /** 141 | * Implementation of Gaussian random number generator using Ziggurat algorithm. 142 | *

143 | * Marsaglia, George, and Wai Wan Tsang. 144 | * "The ziggurat method for generating random variables." 145 | * Journal of statistical software 5.8 (2000): 1-7. 146 | *

147 | *

148 | * Tesuaki Yotsuji. 計算機シミュレーションのための確率分布乱数生成法. 149 | * Pleiades PUBLISHING Co.,Ltd. (2010) 150 | *

151 | *

152 | * This implementation is a bit slower than {@link ZigguratFast} 153 | * but it does not require the independence of each bit to the values returned from {@link Random#nextLong()}. 154 | *

155 | */ 156 | class ZigguratGeneral extends ZigguratBase implements GaussianRNG { 157 | private static final ZigguratGeneral Z_256 = new ZigguratGeneral(8, 3.6541528853610088, 0.00492867323399); 158 | 159 | private final int N; 160 | private final double R; 161 | private final double V; 162 | private final int INDEX_BIT_MASK; 163 | private final int TAIL_INDEX; 164 | 165 | private final double[] x; 166 | private final double[] xx; 167 | private final double[] t; 168 | 169 | /** 170 | * Constructs {@link ZigguratGeneral} with parameters. 171 | * 172 | * @param nBits number of rectangles (2^nBits) 173 | * @param r rightmost x_i 174 | * @param v area of the rectangle 175 | */ 176 | ZigguratGeneral(int nBits, double r, double v) { 177 | N = 1 << nBits; 178 | R = r; 179 | V = v; 180 | INDEX_BIT_MASK = N - 1; 181 | TAIL_INDEX = N - 1; 182 | 183 | x = new double[N + 1]; 184 | xx = new double[N + 1]; 185 | t = new double[N]; 186 | 187 | x[N] = v * exp(0.5 * r * r); 188 | x[N - 1] = r; 189 | 190 | for (int i = N - 2; i >= 1; i--) { 191 | x[i] = Math.sqrt(-2.0 * log(f(x[i + 1]) + v / x[i + 1])); 192 | } 193 | x[0] = 0; 194 | 195 | for (int i = 0; i < t.length; i++) { 196 | t[i] = x[i] / x[i + 1]; 197 | } 198 | 199 | for (int i = 0; i < x.length; i++) { 200 | xx[i] = x[i] * x[i]; 201 | } 202 | } 203 | 204 | @Override 205 | public double generate(Random random) { 206 | while (true) { 207 | int i = random.nextInt() & INDEX_BIT_MASK; 208 | 209 | double u1 = 2 * random.nextDouble() - 1; 210 | if (Math.abs(u1) < t[i]) { 211 | return u1 * x[i + 1]; 212 | } 213 | 214 | if (i == TAIL_INDEX) { 215 | return Math.signum(u1) * tail(random, R); 216 | } 217 | 218 | double y = u1 * x[i + 1]; 219 | double yy = y * y; 220 | double gU = exp(-0.5 * (xx[i] - yy)); 221 | double gL = exp(-0.5 * (xx[i + 1] - yy)); 222 | 223 | if (random.nextDouble() * (gU - gL) <= 1 - gL) { 224 | return y; 225 | } 226 | } 227 | } 228 | 229 | @Override 230 | public String toString() { 231 | return String.format("ZigguratGeneral(N = %d, R = %f, V = %f)", N, R, V); 232 | } 233 | } 234 | } 235 | -------------------------------------------------------------------------------- /fast-rng/src/main/java/biz/k11i/rng/GammaRNG.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng; 2 | 3 | import java.util.Random; 4 | 5 | import static biz.k11i.util.MathFunctions.*; 6 | import static java.lang.Math.sqrt; 7 | 8 | /** 9 | * Gamma random number generator. 10 | */ 11 | public interface GammaRNG { 12 | GammaRNG FAST_RNG = new FastRNG(); 13 | GammaRNG GENERAL_RNG = new GeneralRNG(); 14 | 15 | /** 16 | * Generates a random value sampled from gamma distribution. 17 | * 18 | * @param random random number generator 19 | * @param shape shape parameter (alpha) 20 | * @param scale scale parameter (beta) 21 | * @return a random value 22 | */ 23 | double generate(Random random, double shape, double scale); 24 | 25 | class FastRNG implements GammaRNG { 26 | private final GammaRNG mt = new GammaRNGAlgorithms.MarsagliaTsang(GaussianRNG.FAST_RNG); 27 | private final GammaRNG exponential = new GammaRNGAlgorithms.Exponential(ExponentialRNG.FAST_RNG); 28 | private final GammaRNG wh = new GammaRNGAlgorithms.WilsonHilfertyApproximation(GaussianRNG.FAST_RNG); 29 | 30 | @Override 31 | public double generate(Random random, double shape, double scale) { 32 | if (shape >= 50) { 33 | return wh.generate(random, shape, scale); 34 | } 35 | if (shape != 1.0) { 36 | return mt.generate(random, shape, scale); 37 | } 38 | 39 | // shape == 1.0 40 | return exponential.generate(random, shape, scale); 41 | } 42 | } 43 | 44 | class GeneralRNG implements GammaRNG { 45 | private final GammaRNG best = new GammaRNGAlgorithms.Best(); 46 | private final GammaRNG mt = new GammaRNGAlgorithms.MarsagliaTsang(GaussianRNG.GENERAL_RNG); 47 | private final GammaRNG exponential = new GammaRNGAlgorithms.Exponential(ExponentialRNG.GENERAL_RNG); 48 | private final GammaRNG wh = new GammaRNGAlgorithms.WilsonHilfertyApproximation(GaussianRNG.GENERAL_RNG); 49 | 50 | @Override 51 | public double generate(Random random, double shape, double scale) { 52 | if (shape >= 50) { 53 | return wh.generate(random, shape, scale); 54 | } 55 | if (shape < 0.1) { 56 | return best.generate(random, shape, scale); 57 | } 58 | if (shape != 1.0) { 59 | return mt.generate(random, shape, scale); 60 | } 61 | 62 | // shape == 1.0 63 | return exponential.generate(random, shape, scale); 64 | } 65 | } 66 | } 67 | 68 | class GammaRNGAlgorithms { 69 | abstract static class BaseGammaRNG implements GammaRNG { 70 | @Override 71 | public double generate(Random random, double shape, double scale) { 72 | return generate(random, shape) * scale; 73 | } 74 | 75 | abstract double generate(Random random, double shape); 76 | 77 | @Override 78 | public String toString() { 79 | return String.format("%s", this.getClass().getSimpleName()); 80 | } 81 | } 82 | 83 | /** 84 | * Implementation of Gamma random number generator using Best's algorithm (1983). 85 | *

86 | * Best, D. J. 87 | * “A note on gamma variate generators with shape parameter less than unity.” 88 | * Computing 30.2 (1983): 185-188. 89 | *

90 | */ 91 | static class Best extends BaseGammaRNG { 92 | @Override 93 | double generate(Random random, double shape) { 94 | double c1 = 0.07 + 0.75 * sqrt(1 - shape); 95 | double c2 = 1 + shape * exp(-c1) / c1; 96 | double c3 = 1.0 / shape; 97 | 98 | while (true) { 99 | double u1 = random.nextDouble(); 100 | double u2 = random.nextDouble(); 101 | double v = c2 * u1; 102 | 103 | if (v <= 1) { 104 | double x = c1 * pow(v, c3); 105 | if (u2 <= (2 - x) / (2 + x) || u2 <= exp(-x)) { 106 | return x; 107 | } 108 | } else { 109 | double x = -log(c1 * c3 * (c2 - v)); 110 | double y = x / c1; 111 | if (u2 * (shape + y - shape * y) <= 1 || u2 < pow(y, shape - 1)) { 112 | return x; 113 | } 114 | } 115 | } 116 | } 117 | } 118 | 119 | static class Exponential implements GammaRNG { 120 | private final ExponentialRNG exponentialRNG; 121 | 122 | Exponential(ExponentialRNG exponentialRNG) { 123 | this.exponentialRNG = exponentialRNG; 124 | } 125 | 126 | @Override 127 | public double generate(Random random, double shape, double scale) { 128 | return exponentialRNG.generate(random, 1.0) * scale; 129 | } 130 | 131 | @Override 132 | public String toString() { 133 | return String.format("Exponential[%s]", exponentialRNG.getClass().getSimpleName()); 134 | } 135 | } 136 | 137 | /** 138 | * Implementation of Gamma random number generator using Marsaglia and Tsang's algorithm (2000). 139 | *

140 | * Marsaglia, George, and Wai Wan Tsang. 141 | * "A simple method for generating gamma variables." 142 | * ACM Transactions on Mathematical Software (TOMS) 26.3 (2000): 363-372. 143 | *

144 | */ 145 | static class MarsagliaTsang extends BaseGammaRNG { 146 | private final GaussianRNG gaussianRNG; 147 | 148 | MarsagliaTsang(GaussianRNG gaussianRNG) { 149 | this.gaussianRNG = gaussianRNG; 150 | } 151 | 152 | @Override 153 | double generate(Random random, double shape) { 154 | if (shape >= 1) { 155 | return generateMT(random, shape); 156 | } 157 | 158 | double r = generateMT(random, shape + 1); 159 | double u = random.nextDouble(); 160 | 161 | if (shape != 0.5) { 162 | return r * pow(u, 1.0 / shape); 163 | } 164 | 165 | // shape == 0.5 166 | return r * u * u; 167 | } 168 | 169 | double generateMT(Random random, double shape) { 170 | double d = shape - 1.0 / 3; 171 | double c = 1 / sqrt(9 * d); 172 | 173 | while (true) { 174 | double x = gaussianRNG.generate(random); 175 | double v = 1 + c * x; 176 | if (v <= 0) { 177 | continue; 178 | } 179 | 180 | v = v * v * v; 181 | x = x * x; 182 | 183 | double u = random.nextDouble(); 184 | if (u < 1 - 0.0331 * x * x) { 185 | return d * v; 186 | } 187 | 188 | if (log(u) < 0.5 * x + d * (1 - v + log(v))) { 189 | return d * v; 190 | } 191 | } 192 | } 193 | 194 | @Override 195 | public String toString() { 196 | return String.format("%s[%s]", 197 | getClass().getSimpleName(), 198 | this.gaussianRNG.getClass().getSimpleName()); 199 | } 200 | } 201 | 202 | /** 203 | * Implementation of Gamma random number generator using Wilson-Hilferty approximation 204 | * for large shape parameter (>= 50). 205 | *

206 | * Wilson, Edwin B., and Margaret M. Hilferty. 207 | * “The distribution of chi-square.” 208 | * Proceedings of the National Academy of Sciences 17.12 (1931): 684-688. 209 | *

210 | */ 211 | static class WilsonHilfertyApproximation extends BaseGammaRNG { 212 | private final GaussianRNG gaussianRNG; 213 | 214 | WilsonHilfertyApproximation(GaussianRNG gaussianRNG) { 215 | this.gaussianRNG = gaussianRNG; 216 | } 217 | 218 | @Override 219 | double generate(Random random, double shape) { 220 | double t0 = 1.0 / (9.0 * shape); 221 | double t1 = 1.0 - t0; 222 | double t2 = sqrt(t0); 223 | 224 | while (true) { 225 | double t = t1 + t2 * gaussianRNG.generate(random); 226 | if (t <= 0) { 227 | continue; 228 | } 229 | 230 | return shape * t * t * t; 231 | } 232 | } 233 | 234 | @Override 235 | public String toString() { 236 | return String.format("WilsonHilfertyApproximation[%s]", gaussianRNG.getClass().getSimpleName()); 237 | } 238 | } 239 | } -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/gof/ContinuousGofTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.gof; 2 | 3 | import biz.k11i.rng.test.util.ComputationAndSorting; 4 | import biz.k11i.rng.test.util.SplittableRandomWrapper; 5 | import biz.k11i.rng.test.util.distribution.ContinuousDistribution; 6 | import biz.k11i.rng.test.util.distribution.ProbabilityDistributions; 7 | import biz.k11i.rng.test.util.inference.AndersonDarlingTest; 8 | import net.jafama.FastMath; 9 | import org.apache.commons.math3.distribution.RealDistribution; 10 | import org.slf4j.Logger; 11 | import org.slf4j.LoggerFactory; 12 | 13 | import java.util.Arrays; 14 | import java.util.HashMap; 15 | import java.util.LinkedHashMap; 16 | import java.util.Map; 17 | import java.util.Objects; 18 | import java.util.Random; 19 | import java.util.concurrent.ForkJoinPool; 20 | 21 | /** 22 | * Provides Goodness-of-Fit test for discrete random number generator. 23 | */ 24 | class ContinuousGofTest extends GoodnessOfFitTest { 25 | /** 26 | * Builds {@link ContinuousGofTest} object. 27 | */ 28 | public static class Builder extends BuilderBase { 29 | private ContinuousDistribution distribution; 30 | private String name; 31 | private RandomNumberGenerator generator; 32 | 33 | @SuppressWarnings("unused") 34 | public Builder probabilityDistribution(RealDistribution distribution) { 35 | this.distribution = ProbabilityDistributions.wrap(distribution); 36 | return this; 37 | } 38 | 39 | public Builder probabilityDistribution(ContinuousDistribution distribution) { 40 | this.distribution = Objects.requireNonNull(distribution); 41 | return this; 42 | } 43 | 44 | public Builder randomNumberGenerator(String name, RandomNumberGenerator generator) { 45 | this.name = name; 46 | this.generator = Objects.requireNonNull(generator); 47 | return this; 48 | } 49 | 50 | public GoodnessOfFitTest build() { 51 | return new ContinuousGofTest( 52 | name, 53 | significanceLevel, 54 | distribution, 55 | generator, 56 | numRandomValues); 57 | } 58 | } 59 | 60 | /** 61 | * Generates continuous random variates. 62 | */ 63 | @FunctionalInterface 64 | public interface RandomNumberGenerator { 65 | /** 66 | * Generates a continuous random variate. 67 | * 68 | * @param random uses to sample uniform random variates. 69 | * @return continuous random variate. 70 | */ 71 | double generate(Random random); 72 | } 73 | 74 | private static final Logger LOGGER = LoggerFactory.getLogger(ContinuousGofTest.class); 75 | 76 | private final ContinuousDistribution distribution; 77 | private final RandomNumberGenerator generator; 78 | private final int numRandomValues; 79 | private final double[] x; 80 | private final double[] work; 81 | private long seed; 82 | private final BufferRecycler bufferRecycler = new BufferRecycler(); 83 | private ComputationAndSorting computationAndSorting; 84 | 85 | private ContinuousGofTest( 86 | String name, 87 | double significanceLevel, 88 | ContinuousDistribution distribution, 89 | RandomNumberGenerator generator, 90 | int numRandomValues) { 91 | super(name, significanceLevel); 92 | this.distribution = distribution; 93 | this.generator = generator; 94 | this.numRandomValues = numRandomValues; 95 | this.x = new double[numRandomValues]; 96 | this.work = new double[numRandomValues]; 97 | } 98 | 99 | @Override 100 | public Map test() { 101 | return PerformanceMeasure.run(LOGGER, m -> { 102 | m.measure("Generate {} random numbers", numRandomValues, ignore -> { 103 | Random random = new SplittableRandomWrapper(seed++); 104 | for (int i = 0; i < numRandomValues; i++) { 105 | double rv = generator.generate(random); 106 | x[i] = distribution.cdf(rv); 107 | } 108 | }); 109 | 110 | m.measure("Sort {} random numbers", x.length, ignore -> Arrays.sort(x)); 111 | 112 | Map result = new LinkedHashMap<>(); 113 | 114 | m.measure("Transform sorted random numbers", ignore -> { 115 | for (Transformation t : Transformation.values()) { 116 | m.measure("Transform by [{}]: p-value = {}", r -> { 117 | double[] transformed = t.transform(x, bufferRecycler); 118 | double p = AndersonDarlingTest.andersonDarlingTest(transformed); 119 | result.put(t.toString(), p); 120 | 121 | r.updateArgs(t, p); 122 | }); 123 | } 124 | }); 125 | 126 | return result; 127 | }); 128 | } 129 | 130 | @Override 131 | public Map testInParallel(ForkJoinPool pool) { 132 | return PerformanceMeasure.run(LOGGER, m -> { 133 | if (computationAndSorting == null) { 134 | computationAndSorting = new ComputationAndSorting<>( 135 | numRandomValues, 136 | pool.getParallelism(), 137 | (r, index) -> distribution.cdf(generator.generate(r))); 138 | } 139 | 140 | m.measure("Generate & sort {} random numbers", numRandomValues, ignore -> { 141 | SplittableRandomWrapper random = new SplittableRandomWrapper(seed++); 142 | pool.invoke(computationAndSorting.newForkJoinTask(random, x, work)); 143 | }); 144 | 145 | Map result = new LinkedHashMap<>(); 146 | 147 | m.measure("Transform sorted random numbers", ignore -> { 148 | for (Transformation t : Transformation.values()) { 149 | m.measure("Transform by [{}]: p-value = {}", r -> { 150 | double[] transformed = t.transformInParallel(pool, x, bufferRecycler); 151 | double p = AndersonDarlingTest.andersonDarlingTest(transformed); 152 | result.put(t.toString(), p); 153 | 154 | r.updateArgs(t, p); 155 | }); 156 | } 157 | }); 158 | 159 | return result; 160 | }); 161 | } 162 | } 163 | 164 | enum Transformation { 165 | RAW { 166 | @Override 167 | public double[] transform(double[] x, BufferRecycler ignore) { 168 | return x; 169 | } 170 | }, 171 | 172 | SPACING { 173 | @Override 174 | public double[] transform(double[] x, BufferRecycler bufferRecycler) { 175 | int n = x.length; 176 | 177 | double[] s = bufferRecycler.allocate("SPACING_S", n + 1); 178 | initializeS(x, s); 179 | Arrays.sort(s); 180 | 181 | // Compute S 182 | for (int i = s.length - 1; i > 0; i--) { 183 | s[i] = (n - i + 1) * (s[i] - s[i - 1]); 184 | } 185 | s[0] = (n + 1) * s[0]; 186 | 187 | // Compute V 188 | double[] v = bufferRecycler.allocate("SPACING_V", n); 189 | double t = 0; 190 | 191 | for (int i = 0; i < n; i++) { 192 | v[i] = t + s[i]; 193 | t = v[i]; 194 | } 195 | 196 | return v; 197 | } 198 | 199 | private void initializeS(double[] values, double[] s) { 200 | // Initialize S 201 | double prevValue = 0.0; 202 | for (int i = 0; i < values.length; i++) { 203 | int si = i; 204 | int ui = i - 1; 205 | s[si] = values[ui + 1] - prevValue; 206 | prevValue = values[ui + 1]; 207 | } 208 | s[s.length - 1] = 1.0 - values[values.length - 1]; 209 | } 210 | 211 | @Override 212 | public double[] transformInParallel(ForkJoinPool pool, double[] x, BufferRecycler bufferRecycler) { 213 | int n = x.length; 214 | 215 | ComputationAndSorting spacingInitS = new ComputationAndSorting<>(n, pool.getParallelism(), (ignore, index) -> { 216 | if (index == 0) { 217 | return x[0]; 218 | } 219 | if (index < n) { 220 | return x[index] - x[index - 1]; 221 | } 222 | return 1.0 - x[n - 1]; 223 | }); 224 | 225 | double[] s = bufferRecycler.allocate("SPACING_S", n + 1); 226 | double[] work = bufferRecycler.allocate("SPACING_S_WORK", n + 1); 227 | pool.invoke(spacingInitS.newForkJoinTask(ComputationAndSorting.NullSplittable.INSTANCE, s, work)); 228 | 229 | // Compute S and V 230 | double[] v = bufferRecycler.allocate("SPACING_V", n); 231 | v[0] = (n + 1) * s[0]; 232 | 233 | for (int i = 1; i < n; i++) { 234 | v[i] = v[i - 1] + (n - i + 1) * (s[i] - s[i - 1]); 235 | } 236 | 237 | return v; 238 | } 239 | }, 240 | 241 | POWER_RATIO { 242 | @Override 243 | public double[] transform(double[] x, BufferRecycler bufferRecycler) { 244 | int n = x.length; 245 | double[] result = bufferRecycler.allocate("POWER_RATIO_RESULT", n); 246 | 247 | for (int i = 0; i < n - 1; i++) { 248 | if (x[i + 1] == 0) { 249 | result[i] = 1.0; 250 | } else { 251 | result[i] = FastMath.pow(x[i] / x[i + 1], i + 1); 252 | } 253 | } 254 | result[n - 1] = FastMath.pow(x[n - 1], n); 255 | 256 | Arrays.sort(result); 257 | 258 | return result; 259 | } 260 | 261 | @Override 262 | public double[] transformInParallel(ForkJoinPool pool, double[] x, BufferRecycler bufferRecycler) { 263 | int n = x.length; 264 | 265 | ComputationAndSorting powerRatio = new ComputationAndSorting<>(n, pool.getParallelism(), 266 | (ignore, index) -> { 267 | if (index < n - 1) { 268 | if (x[index + 1] == 0) { 269 | return 1.0; 270 | } 271 | return FastMath.pow(x[index] / x[index + 1], index + 1); 272 | } 273 | return FastMath.pow(x[n - 1], n); 274 | }); 275 | 276 | double[] result = bufferRecycler.allocate("POWER_RATIO_RESULT", n); 277 | double[] work = bufferRecycler.allocate("POWER_RATIO_WORK", n); 278 | pool.invoke(powerRatio.newForkJoinTask(ComputationAndSorting.NullSplittable.INSTANCE, result, work)); 279 | 280 | return result; 281 | } 282 | }; 283 | 284 | public abstract double[] transform(double[] x, BufferRecycler bufferRecycler); 285 | 286 | public double[] transformInParallel(ForkJoinPool pool, double[] x, BufferRecycler bufferRecycler) { 287 | return transform(x, bufferRecycler); 288 | } 289 | } 290 | 291 | class BufferRecycler { 292 | private Map buffers = new HashMap<>(10); 293 | 294 | double[] allocate(String name, int n) { 295 | return buffers.computeIfAbsent(name, ignore -> new double[n]); 296 | } 297 | } 298 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/gof/DiscreteGofTest.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.gof; 2 | 3 | import biz.k11i.rng.test.util.SplittableRandomWrapper; 4 | import biz.k11i.rng.test.util.distribution.DiscreteDistribution; 5 | import biz.k11i.rng.test.util.distribution.ProbabilityDistributions; 6 | import biz.k11i.rng.test.util.inference.MTest; 7 | import org.apache.commons.math3.distribution.IntegerDistribution; 8 | import org.apache.commons.math3.stat.inference.ChiSquareTest; 9 | import org.apache.commons.math3.stat.inference.GTest; 10 | import org.slf4j.Logger; 11 | import org.slf4j.LoggerFactory; 12 | 13 | import java.util.ArrayList; 14 | import java.util.Arrays; 15 | import java.util.LinkedHashMap; 16 | import java.util.List; 17 | import java.util.Map; 18 | import java.util.Random; 19 | import java.util.concurrent.Callable; 20 | import java.util.concurrent.ConcurrentHashMap; 21 | import java.util.concurrent.ForkJoinPool; 22 | 23 | /** 24 | * Provides Goodness-of-Fit test for discrete random number generator. 25 | */ 26 | class DiscreteGofTest extends GoodnessOfFitTest { 27 | /** 28 | * Builds {@link DiscreteGofTest} object. 29 | */ 30 | @SuppressWarnings("unused") 31 | public static class Builder extends BuilderBase { 32 | private DiscreteDistribution distribution; 33 | private int maxFrequencyBins; 34 | private String name; 35 | private RandomNumberGenerator generator; 36 | 37 | public Builder probabilityDistribution(IntegerDistribution distribution) { 38 | this.distribution = ProbabilityDistributions.wrap(distribution); 39 | return this; 40 | } 41 | 42 | public Builder probabilityDistribution(DiscreteDistribution distribution) { 43 | this.distribution = distribution; 44 | return this; 45 | } 46 | 47 | public Builder maxFrequencyBins(int maxFrequencyBins) { 48 | this.maxFrequencyBins = maxFrequencyBins; 49 | return this; 50 | } 51 | 52 | public Builder randomNumberGenerator(String name, RandomNumberGenerator generator) { 53 | this.name = name; 54 | this.generator = generator; 55 | return this; 56 | } 57 | 58 | public GoodnessOfFitTest build() { 59 | return new DiscreteGofTest( 60 | name, 61 | significanceLevel, 62 | distribution, 63 | generator, 64 | numRandomValues, 65 | maxFrequencyBins); 66 | } 67 | } 68 | 69 | /** 70 | * Generates discrete random variates. 71 | */ 72 | @FunctionalInterface 73 | public interface RandomNumberGenerator { 74 | /** 75 | * Generates a discrete random variate. 76 | * 77 | * @param random uses to sample uniform random variates. 78 | * @return discrete random variate. 79 | */ 80 | int generate(Random random); 81 | } 82 | 83 | private static final Logger LOGGER = LoggerFactory.getLogger(DiscreteGofTest.class); 84 | 85 | private final RandomNumberGenerator generator; 86 | private final int numRandomValues; 87 | private final FrequencyTable freqTable; 88 | private int seed; 89 | 90 | private DiscreteGofTest( 91 | String name, 92 | double significanceLevel, 93 | DiscreteDistribution distribution, 94 | RandomNumberGenerator generator, 95 | int numRandomValues, 96 | int maxFrequencyBins) { 97 | super(name, significanceLevel); 98 | this.generator = generator; 99 | this.numRandomValues = numRandomValues; 100 | this.freqTable = FrequencyTable.build(distribution, maxFrequencyBins); 101 | } 102 | 103 | @Override 104 | public Map test() { 105 | return PerformanceMeasure.run(LOGGER, m -> { 106 | m.measure("Generate {} random numbers and count frequencies", numRandomValues, ignore -> { 107 | Random random = new SplittableRandomWrapper(seed++); 108 | for (int i = 0; i < numRandomValues; i++) { 109 | int rv = generator.generate(random); 110 | freqTable.increment(rv); 111 | } 112 | }); 113 | 114 | return buildResult(m); 115 | }); 116 | } 117 | 118 | @Override 119 | public Map testInParallel(ForkJoinPool pool) { 120 | return PerformanceMeasure.run(LOGGER, m -> { 121 | m.measure("Generate {} random numbers and count frequencies", numRandomValues, ignore -> { 122 | SplittableRandomWrapper random = new SplittableRandomWrapper(seed++); 123 | 124 | int numTasks = pool.getParallelism(); 125 | List> tasks = new ArrayList<>(numTasks); 126 | 127 | for (int i = 0; i < numTasks; i++) { 128 | int start = i * numRandomValues / numTasks; 129 | int end = (i + 1) * numRandomValues / numTasks; 130 | 131 | tasks.add(new RandomValueGenerationTask(generator, end - start, freqTable, random.split())); 132 | } 133 | pool.invokeAll(tasks); 134 | }); 135 | 136 | return buildResult(m); 137 | }); 138 | } 139 | 140 | private Map buildResult(PerformanceMeasure m) { 141 | Map result = new LinkedHashMap<>(); 142 | 143 | m.measure("Test on contingency table", ignore -> { 144 | long[] freq = freqTable.sumUpAndReset(); 145 | for (TestMethod test : TestMethod.values()) { 146 | m.measure("Test by [{}]: p-value = {}", r -> { 147 | double p = test.test(freqTable.probs, freq); 148 | result.put(test.toString(), p); 149 | 150 | r.updateArgs(test, p); 151 | }); 152 | } 153 | 154 | long[] totalFreq = freqTable.totalFrequencies; 155 | for (TestMethod test : TestMethod.values()) { 156 | m.measure("Test total frequency by [{}]: p-value = {}", r -> { 157 | double p = test.test(freqTable.probs, totalFreq); 158 | r.updateArgs(test, p); 159 | }); 160 | } 161 | }); 162 | 163 | return result; 164 | } 165 | } 166 | 167 | /** 168 | * Statistical tests to test contingency tables. 169 | */ 170 | enum TestMethod { 171 | CHI_SQUARE_TEST { 172 | private final ChiSquareTest chiSquareTest = new ChiSquareTest(); 173 | 174 | @Override 175 | double test(double[] probabilities, long[] frequencies) { 176 | return chiSquareTest.chiSquareTest(probabilities, frequencies); 177 | } 178 | }, 179 | G_TEST { 180 | private final GTest gTest = new GTest(); 181 | 182 | @Override 183 | double test(double[] probabilities, long[] frequencies) { 184 | return gTest.gTest(probabilities, frequencies); 185 | } 186 | }, 187 | M_TEST { 188 | @Override 189 | double test(double[] probabilities, long[] frequencies) { 190 | return MTest.mTest(probabilities, frequencies); 191 | } 192 | }; 193 | 194 | abstract double test(double[] probabilities, long[] frequencies); 195 | } 196 | 197 | class FrequencyTable { 198 | private static final double EPSILON = Math.nextDown(1.0); 199 | private final boolean isParent; 200 | private final int numBins; 201 | final double[] probs; 202 | private final int[] bounds; 203 | final long[] totalFrequencies; 204 | private final long[] frequencies; 205 | private final ConcurrentHashMap children = new ConcurrentHashMap<>(); 206 | 207 | private FrequencyTable(double[] probs, int[] bounds) { 208 | this(true, probs, bounds); 209 | } 210 | 211 | private FrequencyTable(boolean isParent, double[] probs, int[] bounds) { 212 | this.isParent = isParent; 213 | this.numBins = probs.length; 214 | this.probs = probs; 215 | this.bounds = bounds; 216 | this.totalFrequencies = new long[numBins]; 217 | this.frequencies = new long[numBins]; 218 | } 219 | 220 | static FrequencyTable build(DiscreteDistribution distribution, int maxBins) { 221 | // Calculate boundaries 222 | int[] bounds = new int[maxBins - 1]; 223 | int boundaryCount = 0; 224 | 225 | for (int i = 1; i < maxBins; i++) { 226 | int bound = distribution.inverseCdf(i / (double) maxBins); 227 | if (boundaryCount > 0 && bound == bounds[boundaryCount - 1]) { 228 | continue; 229 | } 230 | double point = distribution.cdf(bound); 231 | if (point > EPSILON) { 232 | break; 233 | } 234 | bounds[boundaryCount++] = bound; 235 | } 236 | bounds = Arrays.copyOf(bounds, boundaryCount); 237 | 238 | // Calculate expected probabilities 239 | double[] probs = new double[boundaryCount + 1]; 240 | double prevPoint = 0; 241 | 242 | for (int i = 0; i < boundaryCount; i++) { 243 | double point = distribution.cdf(bounds[i]); 244 | probs[i] = point - prevPoint; 245 | prevPoint = point; 246 | } 247 | probs[boundaryCount] = 1.0 - prevPoint; 248 | 249 | return new FrequencyTable(probs, bounds); 250 | } 251 | 252 | void increment(int x) { 253 | int index = Arrays.binarySearch(bounds, x); 254 | if (index < 0) { 255 | index = ~index; 256 | } 257 | 258 | frequencies[index]++; 259 | } 260 | 261 | FrequencyTable child() { 262 | return children.computeIfAbsent( 263 | Thread.currentThread().getId(), 264 | ignore -> new FrequencyTable(false, this.probs, this.bounds)); 265 | } 266 | 267 | long[] sumUpAndReset() { 268 | if (!isParent) { 269 | throw new IllegalStateException("This object is not parent"); 270 | } 271 | 272 | for (FrequencyTable child : children.values()) { 273 | for (int i = 0; i < numBins; i++) { 274 | this.frequencies[i] += child.frequencies[i]; 275 | child.frequencies[i] = 0; 276 | } 277 | } 278 | 279 | long[] result = Arrays.copyOf(frequencies, numBins); 280 | for (int i = 0; i < numBins; i++) { 281 | totalFrequencies[i] += frequencies[i]; 282 | frequencies[i] = 0; 283 | } 284 | 285 | return result; 286 | } 287 | } 288 | 289 | class RandomValueGenerationTask implements Callable { 290 | private final DiscreteGofTest.RandomNumberGenerator generator; 291 | private final int numRandomValues; 292 | private final FrequencyTable parentFrequencyTable; 293 | private final SplittableRandomWrapper random; 294 | 295 | RandomValueGenerationTask( 296 | DiscreteGofTest.RandomNumberGenerator generator, 297 | int numRandomValues, 298 | FrequencyTable parentFrequencyTable, 299 | SplittableRandomWrapper random) { 300 | this.generator = generator; 301 | this.numRandomValues = numRandomValues; 302 | this.parentFrequencyTable = parentFrequencyTable; 303 | this.random = random; 304 | } 305 | 306 | @Override 307 | public Void call() { 308 | FrequencyTable table = parentFrequencyTable.child(); 309 | for (int i = 0; i < numRandomValues; i++) { 310 | int rv = generator.generate(random); 311 | table.increment(rv); 312 | } 313 | return null; 314 | } 315 | } 316 | -------------------------------------------------------------------------------- /fast-rng-test/src/main/java/biz/k11i/rng/test/util/distribution/ProbabilityDistributions.java: -------------------------------------------------------------------------------- 1 | package biz.k11i.rng.test.util.distribution; 2 | 3 | import org.apache.commons.math3.distribution.BetaDistribution; 4 | import org.apache.commons.math3.distribution.GammaDistribution; 5 | import org.apache.commons.math3.distribution.IntegerDistribution; 6 | import org.apache.commons.math3.distribution.RealDistribution; 7 | import org.apache.commons.math3.exception.MaxCountExceededException; 8 | import org.apache.commons.math3.exception.OutOfRangeException; 9 | import org.apache.commons.math3.special.Erf; 10 | import org.apache.commons.math3.util.ContinuedFraction; 11 | import org.apache.commons.math3.util.FastMath; 12 | 13 | /** 14 | * Provides probability distributions that can compute cumulative probability function and inverse distribution function. 15 | * 16 | *

17 | * Some implementations of the probability distribution came from the 18 | * Apache Commons Math that is licensed under the Apache License 2.0. 19 | *

20 | * 
 21 |  * Licensed to the Apache Software Foundation (ASF) under one or more
 22 |  * contributor license agreements.  See the NOTICE file distributed with
 23 |  * this work for additional information regarding copyright ownership.
 24 |  * The ASF licenses this file to You under the Apache License, Version 2.0
 25 |  * (the "License"); you may not use this file except in compliance with
 26 |  * the License.  You may obtain a copy of the License at
 27 |  *
 28 |  *      http://www.apache.org/licenses/LICENSE-2.0
 29 |  *
 30 |  * Unless required by applicable law or agreed to in writing, software
 31 |  * distributed under the License is distributed on an "AS IS" BASIS,
 32 |  * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
 33 |  * See the License for the specific language governing permissions and
 34 |  * limitations under the License.
 35 |  *
36 | *

37 | *

    38 | *
  • {@link Gaussian}
    • 39 | *
  • {@link Gamma}
    • 40 | *
  • {@link Beta}
    • 41 | *
42 | *

43 | */ 44 | public interface ProbabilityDistributions { 45 | static ContinuousDistribution gaussian(double mean, double sd) { 46 | return new Gaussian(mean, sd); 47 | } 48 | 49 | static ContinuousDistribution gamma(double shape, double scale) { 50 | return new Gamma(shape, scale); 51 | } 52 | 53 | static ContinuousDistribution beta(double alpha, double beta) { 54 | return new Beta(alpha, beta); 55 | } 56 | 57 | static ContinuousDistribution wrap(RealDistribution distribution) { 58 | return new CommonsMath3DistributionWrapper.Continuous(distribution); 59 | } 60 | 61 | static DiscreteDistribution wrap(IntegerDistribution distribution) { 62 | return new CommonsMath3DistributionWrapper.Discrete(distribution); 63 | } 64 | } 65 | 66 | /** 67 | * Implementation of Gaussian distrbution. 68 | *

69 | * This class includes the code came from {@link org.apache.commons.math3.distribution.NormalDistribution}, 70 | * {@link org.apache.commons.math3.special.Gamma} and {@link Erf}. 71 | *

72 | */ 73 | class Gaussian implements ContinuousDistribution { 74 | private static final double EPSILON = 1.0e-15; 75 | private static final int MAX_ITERATIONS = 10000; 76 | private static final double SQRT2 = FastMath.sqrt(2.0); 77 | private static final double A = 0.5; 78 | private static final double LOG_GAMMA_A = org.apache.commons.math3.special.Gamma.logGamma(A); 79 | private static final ContinuedFraction fraction = new ContinuedFraction() { 80 | /** {@inheritDoc} */ 81 | @Override 82 | protected double getA(int n, double x) { 83 | return ((2.0 * n) + 1.0) - A + x; 84 | } 85 | 86 | /** {@inheritDoc} */ 87 | @Override 88 | protected double getB(int n, double x) { 89 | return n * (A - n); 90 | } 91 | }; 92 | 93 | private final double mean; 94 | private final double sd; 95 | 96 | 97 | Gaussian(double mean, double sd) { 98 | this.mean = mean; 99 | this.sd = sd; 100 | } 101 | 102 | @Override 103 | public double cdf(double x) { 104 | final double dev = x - mean; 105 | if (FastMath.abs(dev) > 40 * sd) { 106 | return dev < 0 ? 0.0d : 1.0d; 107 | } 108 | return 0.5 * erfc(-dev / (sd * SQRT2)); 109 | } 110 | 111 | @Override 112 | public double inverseCdf(double p) { 113 | if (p < 0.0 || p > 1.0) { 114 | throw new OutOfRangeException(p, 0, 1); 115 | } 116 | return mean + sd * SQRT2 * Erf.erfInv(2 * p - 1); 117 | } 118 | 119 | private static double erfc(double x) { 120 | if (FastMath.abs(x) > 40) { 121 | return x > 0 ? 0 : 2; 122 | } 123 | final double ret = regularizedGammaQ(x * x); 124 | return x < 0 ? 2 - ret : ret; 125 | } 126 | 127 | private static double regularizedGammaP(double x) { 128 | double ret; 129 | 130 | // calculate series 131 | double n = 0.0; // current element index 132 | double an = 1.0 / A; // n-th element in the series 133 | double sum = an; // partial sum 134 | while (FastMath.abs(an / sum) > EPSILON && 135 | n < MAX_ITERATIONS && 136 | sum < Double.POSITIVE_INFINITY) { 137 | // compute next element in the series 138 | n += 1.0; 139 | an *= x / (A + n); 140 | 141 | // update partial sum 142 | sum += an; 143 | } 144 | if (n >= MAX_ITERATIONS) { 145 | throw new MaxCountExceededException(MAX_ITERATIONS); 146 | } else if (Double.isInfinite(sum)) { 147 | ret = 1.0; 148 | } else { 149 | ret = FastMath.exp(-x + (A * FastMath.log(x)) - LOG_GAMMA_A) * sum; 150 | } 151 | 152 | return ret; 153 | } 154 | 155 | private static double regularizedGammaQ(double x) { 156 | double ret; 157 | 158 | if (x == 0.0) { 159 | ret = 1.0; 160 | } else if (x < A + 1.0) { 161 | ret = 1.0 - regularizedGammaP(x); 162 | } else { 163 | ret = 1.0 / fraction.evaluate(x, EPSILON, MAX_ITERATIONS); 164 | ret = FastMath.exp(-x + (A * FastMath.log(x)) - LOG_GAMMA_A) * ret; 165 | } 166 | 167 | return ret; 168 | } 169 | } 170 | 171 | /** 172 | * Implementation of Gamma distrbution. 173 | *

174 | * This class includes the code came from {@link org.apache.commons.math3.distribution.GammaDistribution} and 175 | * {@link org.apache.commons.math3.special.Gamma}. 176 | *

177 | */ 178 | class Gamma extends ContinuousDistributionBase { 179 | private static final double DEFAULT_EPSILON = 10e-15; 180 | 181 | private final double a; 182 | private final double scale; 183 | private final double logGammaA; 184 | private final ContinuedFraction fraction; 185 | 186 | Gamma(double shape, double scale) { 187 | super(new GammaDistribution(shape, scale), GammaDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY); 188 | this.a = shape; 189 | this.scale = scale; 190 | this.logGammaA = org.apache.commons.math3.special.Gamma.logGamma(a); 191 | this.fraction = new ContinuedFraction() { 192 | /** {@inheritDoc} */ 193 | @Override 194 | protected double getA(int n, double x) { 195 | return ((2.0 * n) + 1.0) - a + x; 196 | } 197 | 198 | /** {@inheritDoc} */ 199 | @Override 200 | protected double getB(int n, double x) { 201 | return n * (a - n); 202 | } 203 | }; 204 | } 205 | 206 | @Override 207 | public double cdf(double x) { 208 | if (x <= 0) { 209 | return 0; 210 | } else { 211 | return regularizedGammaP(x / scale); 212 | } 213 | } 214 | 215 | private double regularizedGammaP(double x) { 216 | double ret; 217 | 218 | if (x >= a + 1) { 219 | // use regularizedGammaQ because it should converge faster in this 220 | // case. 221 | ret = 1.0 - regularizedGammaQ(x); 222 | } else { 223 | // calculate series 224 | double n = 0.0; // current element index 225 | double an = 1.0 / a; // n-th element in the series 226 | double sum = an; // partial sum 227 | while (FastMath.abs(an / sum) > DEFAULT_EPSILON && 228 | n < Integer.MAX_VALUE && 229 | sum < Double.POSITIVE_INFINITY) { 230 | // compute next element in the series 231 | n += 1.0; 232 | an *= x / (a + n); 233 | 234 | // update partial sum 235 | sum += an; 236 | } 237 | if (n >= Integer.MAX_VALUE) { 238 | throw new MaxCountExceededException(Integer.MAX_VALUE); 239 | } else if (Double.isInfinite(sum)) { 240 | ret = 1.0; 241 | } else { 242 | ret = FastMath.exp(-x + (a * FastMath.log(x)) - logGammaA) * sum; 243 | } 244 | } 245 | 246 | return ret; 247 | } 248 | 249 | private double regularizedGammaQ(double x) { 250 | double ret; 251 | 252 | ret = 1.0 / fraction.evaluate(x, DEFAULT_EPSILON, Integer.MAX_VALUE); 253 | ret = FastMath.exp(-x + (a * FastMath.log(x)) - logGammaA) * ret; 254 | 255 | return ret; 256 | } 257 | } 258 | 259 | /** 260 | * Implementation of Beta distrbution. 261 | *

262 | * This class includes the code came from {@link org.apache.commons.math3.distribution.BetaDistribution} and 263 | * {@link org.apache.commons.math3.special.Beta}. 264 | *

265 | */ 266 | class Beta extends ContinuousDistributionBase { 267 | private static final double DEFAULT_EPSILON = 1E-14; 268 | 269 | private final double a; 270 | private final double b; 271 | private final double t1; 272 | private final double t2; 273 | private final double logA; 274 | private final double logBeta; 275 | private final ContinuedFraction fraction; 276 | private final Beta sym; 277 | 278 | Beta(double alpha, double beta) { 279 | this(alpha, beta, null); 280 | } 281 | 282 | private Beta(double alpha, double beta, Beta sym) { 283 | super(new BetaDistribution(alpha, beta), BetaDistribution.DEFAULT_INVERSE_ABSOLUTE_ACCURACY); 284 | 285 | this.a = alpha; 286 | this.b = beta; 287 | this.t1 = (alpha + 1) / (2 + beta + alpha); 288 | this.t2 = (beta + 1) / (2 + beta + alpha); 289 | this.logA = FastMath.log(alpha); 290 | this.logBeta = org.apache.commons.math3.special.Beta.logBeta(alpha, beta); 291 | this.fraction = new ContinuedFraction() { 292 | /** {@inheritDoc} */ 293 | @Override 294 | protected double getB(int n, double x) { 295 | double ret; 296 | double m; 297 | if (n % 2 == 0) { // even 298 | m = n / 2.0; 299 | ret = (m * (b - m) * x) / 300 | ((a + (2 * m) - 1) * (a + (2 * m))); 301 | } else { 302 | m = (n - 1.0) / 2.0; 303 | ret = -((a + m) * (a + b + m) * x) / 304 | ((a + (2 * m)) * (a + (2 * m) + 1.0)); 305 | } 306 | return ret; 307 | } 308 | 309 | /** {@inheritDoc} */ 310 | @Override 311 | protected double getA(int n, double x) { 312 | return 1.0; 313 | } 314 | }; 315 | 316 | if (sym == null) { 317 | this.sym = new Beta(beta, alpha, this); 318 | } else { 319 | this.sym = sym; 320 | } 321 | } 322 | 323 | @Override 324 | public double cdf(double x) { 325 | if (x <= 0) { 326 | return 0; 327 | } else if (x >= 1) { 328 | return 1; 329 | } else { 330 | return regularizedBeta(x); 331 | } 332 | } 333 | 334 | private double regularizedBeta(double x) { 335 | double ret; 336 | 337 | if (x > t1 && 338 | 1 - x <= t2) { 339 | ret = 1 - sym.regularizedBeta(1 - x); 340 | } else { 341 | ret = FastMath.exp((a * FastMath.log(x)) + (b * FastMath.log1p(-x)) - 342 | logA - logBeta) * 343 | 1.0 / fraction.evaluate(x, DEFAULT_EPSILON, Integer.MAX_VALUE); 344 | } 345 | 346 | return ret; 347 | } 348 | } 349 | 350 | interface CommonsMath3DistributionWrapper { 351 | class Continuous implements ContinuousDistribution { 352 | private final RealDistribution distribution; 353 | 354 | Continuous(RealDistribution distribution) { 355 | this.distribution = distribution; 356 | } 357 | 358 | @Override 359 | public double cdf(double x) { 360 | return distribution.cumulativeProbability(x); 361 | } 362 | 363 | @Override 364 | public double inverseCdf(double p) { 365 | return distribution.inverseCumulativeProbability(p); 366 | } 367 | } 368 | 369 | class Discrete implements DiscreteDistribution { 370 | private final IntegerDistribution distribution; 371 | 372 | Discrete(IntegerDistribution distribution) { 373 | this.distribution = distribution; 374 | } 375 | 376 | @Override 377 | public double cdf(int x) { 378 | return distribution.cumulativeProbability(x); 379 | } 380 | 381 | @Override 382 | public int inverseCdf(double p) { 383 | return distribution.inverseCumulativeProbability(p); 384 | } 385 | } 386 | } 387 | --------------------------------------------------------------------------------