/*
    * Licensed to the Apache Software Foundation (ASF) under one or more
    * contributor license agreements.  See the NOTICE file distributed with
    * this work for additional information regarding copyright ownership.
    * The ASF licenses this file to You under the Apache License, Version 2.0
    * (the "License"); you may not use this file except in compliance with
    * the License.  You may obtain a copy of the License at
    *
    *      http://www.apache.org/licenses/LICENSE-2.0
   *
   * Unless required by applicable law or agreed to in writing, software
   * distributed under the License is distributed on an "AS IS" BASIS,
   * WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
   * See the License for the specific language governing permissions and
   * limitations under the License.
   */
  package org.apache.commons.rng.core.source64;
  
  import java.math.BigInteger;
  import java.util.SplittableRandom;
  import java.util.concurrent.ThreadLocalRandom;
  import java.util.function.Function;
  import java.util.function.LongSupplier;
  import java.util.function.Supplier;
  import java.util.function.UnaryOperator;
  import java.util.stream.IntStream;
  import java.util.stream.LongStream;
  import java.util.stream.Stream;
  import org.apache.commons.rng.LongJumpableUniformRandomProvider;
  import org.apache.commons.rng.RestorableUniformRandomProvider;
  import org.apache.commons.rng.core.RandomAssert;
  import org.apache.commons.rng.core.util.NumberFactory;
  import org.junit.jupiter.api.Assertions;
  import org.junit.jupiter.api.RepeatedTest;
  import org.junit.jupiter.api.Test;
  import org.junit.jupiter.api.TestInstance;
  import org.junit.jupiter.api.TestInstance.Lifecycle;
  import org.junit.jupiter.params.ParameterizedTest;
  import org.junit.jupiter.params.provider.Arguments;
  import org.junit.jupiter.params.provider.MethodSource;
  
  /**
   * Base test for LXM generators. These generators all use the same basic steps:
   * <pre>
   * s = state of LCG
   * t = state of XBG
   *
   * generate():
   *    z <- mix(combine(w upper bits of s, w upper bits of t))
   *    s <- LCG state update
   *    t <- XBG state update
   * </pre>
   *
   * <p>This base class provides a composite generator of an LCG and XBG
   * both using w = 64-bits. Tests for a RNG implementation must define
   * a factory for constructing a reference composite LXM generator. Implementations
   * for the 64-bit and 128-bit LCG used in the LXM family are provided.
   * Implementations for the XBG are provided based on version in the Commons RNG core library.
   *
   * <p>It is assumed the XBG generator is a {@link LongJumpableUniformRandomProvider}.
   * The composite generator requires the sub-generators to provide a jump and long jump
   * equivalent operation. This is performed by advancing/rewinding the LCG and XBG the same number
   * of cycles. In practice this is performed using:
   * <ul>
   * <li>A large jump of the XBG that wraps the state of the LCG.
   * <li>Leaving the XBG state unchanged and advancing the LCG. This effectively
   * rewinds the state of the LXM by the period of the XBG multiplied by the number of
   * cycles advanced by the LCG.
   * </ul>
   *
   * <p>The paper by Steele and Vigna suggest advancing the LCG to take advantage of the fast
   * update step of the LCG. This is particularly true for the 64-bit LCG variants. If
   * the LCG and XBG sub-generators support jump/longJump then the composite can then be
   * used to test arbitrary combinations of calls to: generate the next long value; and jump
   * operations. This is not possible using the reference implementations of the LXM family
   * in JDK 17 which do not implement jumping (instead providing a split operation to create
   * new RNGs).
   *
   * <p>The test assumes the following conditions:
   * <ul>
   * <li>The seed length equals the state size of the LCG and XBG generators.
   * <li>The LXM generator seed is the seed for the LCG appended with the seed for the XBG.
   * <li>The LCG seed in order is [additive parameter, initial state]. The additive parameter
   * must be odd for a maximum period LCG and the test asserts the final bit of the add parameter
   * from the seed is effectively ignored as it is forced to be odd in the constructor.
   * <li>If the XBG seed is all zeros, the LXM generator is partially functional. It will output
   * non-zero values but the sequence may be statistically weak and the period is that of the LCG.
   * This cannot be practically tested but non-zero output is verified for an all zero seed.
   * </ul>
   *
   * <p>Note: The seed order prioritises the additive parameter first. This parameter can be used to
   * create independent streams of generators. It allows constructing a generator from a single long
   * value, where the rest of the state is filled with a procedure generating non-zero values,
   * which will be independent from a second generator constructed with a different single additive
   * parameter. The difference must be in the high 63-bits of the seed value for 64-bit LCG variants.
   * A suitable filling procedure from an initial seed value is provided in the Commons RNG Simple
   * module.
   *
   * <p>The class uses a per-class lifecycle. This allows abstract methods to be overridden
  * in implementing classes to control test behaviour.
  */
 @TestInstance(Lifecycle.PER_CLASS)
 abstract class AbstractLXMTest {
     /**
      * A function to mix two long values.
      * Implements the combine and mix functions of the LXM generator.
      */
     interface Mix {
         /**
          * Mix the values.
          *
          * @param a Value a
          * @param b Value b
          * @return the result
          */
         long apply(long a, long b);
     }
 
     /**
      * A jumpable sub-generator. This can be a linear congruential generator (LCG)
      * or xor-based generator (XBG) when used in the LXM family.
      *
      * <p>For simplicity the steps of obtaining the upper bits of the state
      * and updating the state are combined to a single operation.
      */
     interface SubGen {
         /**
          * Return the upper 64-bits of the current state and update the state.
          *
          * @return the upper 64-bits of the old state
          */
         long stateAndUpdate();
 
         /**
          * Create a copy and then advance the state in a single jump; the copy is returned.
          *
          * @return the copy
          */
         SubGen copyAndJump();
 
         /**
          * Create a copy and then advance the state in a single long jump; the copy is returned.
          *
          * @return the copy
          */
         SubGen copyAndLongJump();
     }
 
     /**
      * Mix the sum using the star star function.
      *
      * @param a Value a
      * @param b Value b
      * @return the result
      */
     static long mixStarStar(long a, long b) {
         return Long.rotateLeft((a + b) * 5, 7) * 9;
     }
 
     /**
      * Mix the sum using the lea64 function.
      *
      * @param a Value a
      * @param b Value b
      * @return the result
      */
     static long mixLea64(long a, long b) {
         return LXMSupport.lea64(a + b);
     }
 
     /**
      * A 64-bit linear congruential generator.
      */
     static class LCG64 implements SubGen {
         /** Multiplier. */
         private static final long M = LXMSupport.M64;
         /** Additive parameter (must be odd). */
         private final long a;
         /** State. */
         private long s;
         /** Power of 2 for the jump. */
         private final int jumpPower;
         /** Power of 2 for the long jump. */
         private final int longJumpPower;
 
         /**
          * Create an instance with a jump of 1 cycle and long jump of 2^32 cycles.
          *
          * @param a Additive parameter (set to odd)
          * @param s State
          */
         LCG64(long a, long s) {
             this(a, s, 0, 32);
         }
 
         /**
          * @param a Additive parameter (set to odd)
          * @param s State
          * @param jumpPower Jump size as a power of 2
          * @param longJumpPower Long jump size as a power of 2
          */
         LCG64(long a, long s, int jumpPower, int longJumpPower) {
             this.a = a | 1;
             this.s = s;
             this.jumpPower = jumpPower;
             this.longJumpPower = longJumpPower;
         }
 
         @Override
         public long stateAndUpdate() {
             final long s0 = s;
             s = M * s + a;
             return s0;
         }
 
         @Override
         public SubGen copyAndJump() {
             final SubGen copy = new LCG64(a, s, jumpPower, longJumpPower);
             s = LXMSupportTest.lcgAdvancePow2(s, M, a, jumpPower);
             return copy;
         }
 
         @Override
         public SubGen copyAndLongJump() {
             final SubGen copy = new LCG64(a, s, jumpPower, longJumpPower);
             s = LXMSupportTest.lcgAdvancePow2(s, M, a, longJumpPower);
             return copy;
         }
     }
 
     /**
      * A 128-bit linear congruential generator.
      */
     static class LCG128 implements SubGen {
         /** Low half of 128-bit multiplier. The upper half is 1. */
         private static final long ML = LXMSupport.M128L;
         /** High bits of additive parameter. */
         private final long ah;
         /** Low bits of additive parameter (must be odd). */
         private final long al;
         /** High bits of state. */
         private long sh;
         /** Low bits of state. */
         private long sl;
         /** Power of 2 for the jump. */
         private final int jumpPower;
         /** Power of 2 for the long jump. */
         private final int longJumpPower;
 
         /**
          * Create an instance with a jump of 1 cycle and long jump of 2^64 cycles.
          *
          * @param ah High bits of additive parameter
          * @param al Low bits of additive parameter (set to odd)
          * @param sh High bits of the 128-bit state
          * @param sl Low bits of the 128-bit state
          */
         LCG128(long ah, long al, long sh, long sl) {
             this(ah, al, sh, sl, 0, 64);
         }
 
         /**
          * @param ah High bits of additive parameter
          * @param al Low bits of additive parameter (set to odd)
          * @param sh High bits of the 128-bit state
          * @param sl Low bits of the 128-bit state
          * @param jumpPower Jump size as a power of 2
          * @param longJumpPower Long jump size as a power of 2
          */
         LCG128(long ah, long al, long sh, long sl, int jumpPower, int longJumpPower) {
             this.ah = ah;
             this.al = al | 1;
             this.sh = sh;
             this.sl = sl;
             this.jumpPower = jumpPower;
             this.longJumpPower = longJumpPower;
         }
 
         @Override
         public long stateAndUpdate() {
             final long s0 = sh;
             // The LCG is, in effect, "s = m * s + a" where m = ((1LL << 64) + ML)
             final long u = ML * sl;
             // High half
             sh = (ML * sh) + LXMSupport.unsignedMultiplyHigh(ML, sl) + sl + ah;
             // Low half
             sl = u + al;
             // Carry propagation
             if (Long.compareUnsigned(sl, u) < 0) {
                 ++sh;
             }
             return s0;
         }
 
         @Override
         public SubGen copyAndJump() {
             final SubGen copy = new LCG128(ah, al, sh, sl, jumpPower, longJumpPower);
             final long nsl = LXMSupportTest.lcgAdvancePow2(sl, ML, al, jumpPower);
             sh = LXMSupportTest.lcgAdvancePow2High(sh, sl, 1, ML, ah, al, jumpPower);
             sl = nsl;
             return copy;
         }
 
         @Override
         public SubGen copyAndLongJump() {
             final SubGen copy = new LCG128(ah, al, sh, sl, jumpPower, longJumpPower);
             final long nsl = LXMSupportTest.lcgAdvancePow2(sl, ML, al, longJumpPower);
             sh = LXMSupportTest.lcgAdvancePow2High(sh, sl, 1, ML, ah, al, longJumpPower);
             sl = nsl;
             return copy;
         }
     }
 
     /**
      * A xor-based generator using XoRoShiRo128.
      *
      * <p>The generator can be configured to perform jumps or simply return a copy.
      * The LXM generator would jump by advancing only the LCG state.
      */
     static class XBGXoRoShiRo128 extends AbstractXoRoShiRo128 implements SubGen {
         /** Jump flag. */
         private final boolean jump;
 
         /**
          * Create an instance with jumping enabled.
          *
          * @param seed seed
          */
         XBGXoRoShiRo128(long[] seed) {
             super(seed);
             jump = true;
         }
 
         /**
          * @param seed0 seed element 0
          * @param seed1 seed element 1
          * @param jump Set to true to perform jumping, otherwise a jump returns a copy
          */
         XBGXoRoShiRo128(long seed0, long seed1, boolean jump) {
             super(seed0, seed1);
             this.jump = jump;
         }
 
         /**
          * Copy constructor.
          *
          * @param source the source to copy
          */
         XBGXoRoShiRo128(XBGXoRoShiRo128 source) {
             // There is no super-class copy constructor so just construct
             // from the RNG state.
             // Warning:
             // This will not copy the cached state from 'source'
             // which matters if tests use nextInt or nextBoolean.
             // Currently tests only target the long output.
             this(source.state0, source.state1, source.jump);
         }
 
         @Override
         public long stateAndUpdate() {
             final long s0 = state0;
             next();
             return s0;
         }
 
         @Override
         public SubGen copyAndJump() {
             return (SubGen) (jump ? super.jump() : copy());
         }
 
         @Override
         public SubGen copyAndLongJump() {
             return (SubGen) (jump ? super.longJump() : copy());
         }
 
         @Override
         protected long nextOutput() {
             // Not used
             return 0;
         }
 
         @Override
         protected XBGXoRoShiRo128 copy() {
             return new XBGXoRoShiRo128(this);
         }
     }
 
     /**
      * A xor-based generator using XoShiRo256.
      *
      * <p>The generator can be configured to perform jumps or simply return a copy.
      * The LXM generator would jump by advancing only the LCG state.
      */
     static class XBGXoShiRo256 extends AbstractXoShiRo256 implements SubGen {
         /** Jump flag. */
         private final boolean jump;
 
         /**
          * Create an instance with jumping enabled.
          *
          * @param seed seed
          */
         XBGXoShiRo256(long[] seed) {
             super(seed);
             jump = true;
         }
 
         /**
          * @param seed0 seed element 0
          * @param seed1 seed element 1
          * @param seed2 seed element 2
          * @param seed3 seed element 3
          * @param jump Set to true to perform jumping, otherwise a jump returns a copy
          */
         XBGXoShiRo256(long seed0, long seed1, long seed2, long seed3, boolean jump) {
             super(seed0, seed1, seed2, seed3);
             this.jump = jump;
         }
 
         /**
          * Copy constructor.
          *
          * @param source the source to copy
          */
         XBGXoShiRo256(XBGXoShiRo256 source) {
             super(source);
             jump = source.jump;
         }
 
         @Override
         public long stateAndUpdate() {
             final long s0 = state0;
             next();
             return s0;
         }
 
         @Override
         public SubGen copyAndJump() {
             return (SubGen) (jump ? super.jump() : copy());
         }
 
         @Override
         public SubGen copyAndLongJump() {
             return (SubGen) (jump ? super.longJump() : copy());
         }
 
         @Override
         protected long nextOutput() {
             // Not used
             return 0;
         }
 
         @Override
         protected XBGXoShiRo256 copy() {
             return new XBGXoShiRo256(this);
         }
     }
 
     /**
      * A xor-based generator using XoRoShiRo1024.
      *
      * <p>The generator can be configured to perform jumps or simply return a copy.
      * The LXM generator would jump by advancing only the LCG state.
      *
      * <p>Note: To avoid changes to the parent class this test class uses the save/restore
      * function to initialise the index. The rng state update can be managed by the
      * super-class and this class holds a reference to the most recent s0 value.
      */
     static class XBGXoRoShiRo1024 extends AbstractXoRoShiRo1024 implements SubGen {
         /** Jump flag. */
         private final boolean jump;
         /** The most recent s0 variable passed to {@link #transform(long, long)}. */
         private long state0;
 
         /**
          * Create an instance with jumping enabled.
          *
          * @param seed 16-element seed
          */
         XBGXoRoShiRo1024(long[] seed) {
             this(seed, true);
         }
 
         /**
          * @param seed 16-element seed
          * @param jump Set to true to perform jumping, otherwise a jump returns a copy
          */
         XBGXoRoShiRo1024(long[] seed, boolean jump) {
             super(seed);
             this.jump = jump;
             // Ensure the first state returned corresponds to state[0].
             // This requires setting:
             // index = state.length - 1
             // To avoid changing the private visibility of super-class state variables
             // this is done using the save/restore function. It avoids any issues
             // with using reflection on the 'index' field but must be maintained
             // inline with the save/restore logic of the super-class.
             final byte[] s = super.getStateInternal();
             final byte[][] c = splitStateInternal(s, 17 * Long.BYTES);
             final long[] tmp = NumberFactory.makeLongArray(c[0]);
             // Here: index = state.length - 1
             tmp[16] = 15;
             c[0] = NumberFactory.makeByteArray(tmp);
             super.setStateInternal(composeStateInternal(c[0], c[1]));
         }
 
         /**
          * Copy constructor.
          *
          * @param source the source to copy
          */
         XBGXoRoShiRo1024(XBGXoRoShiRo1024 source) {
             super(source);
             jump = source.jump;
         }
 
         @Override
         public long stateAndUpdate() {
             next();
             return state0;
         }
 
         @Override
         public SubGen copyAndJump() {
             return (SubGen) (jump ? super.jump() : copy());
         }
 
         @Override
         public SubGen copyAndLongJump() {
             return (SubGen) (jump ? super.longJump() : copy());
         }
 
         @Override
         protected long transform(long s0, long s15) {
             this.state0 = s0;
             // No transformation required.
             return 0;
         }
 
         @Override
         protected XBGXoRoShiRo1024 copy() {
             return new XBGXoRoShiRo1024(this);
         }
     }
 
     /**
      * A composite LXM generator. Implements:
      * <pre>
      * s = state of LCG
      * t = state of XBG
      *
      * generate():
      *    z <- mix(combine(w upper bits of s, w upper bits of t))
      *    s <- LCG state update
      *    t <- XBG state update
      * </pre>
      * <p>w is assumed to be 64-bits.
      */
     static class LXMGenerator extends LongProvider implements LongJumpableUniformRandomProvider {
         /** Mix implementation. */
         private final Mix mix;
         /** LCG implementation. */
         private final SubGen lcg;
         /** XBG implementation. */
         private final SubGen xbg;
 
         /**
          * Create a new instance.
          * The jump and long jump of the LCG are assumed to appropriately match those of the XBG.
          * This can be achieved by an XBG jump that wraps the period of the LCG; or advancing
          * the LCG and leaving the XBG state unchanged, effectively rewinding the LXM generator.
          *
          * @param mix Mix implementation
          * @param lcg LCG implementation
          * @param xbg XBG implementation
          */
         LXMGenerator(Mix mix, SubGen lcg, SubGen xbg) {
             this.lcg = lcg;
             this.xbg = xbg;
             this.mix = mix;
         }
 
         @Override
         public long next() {
             return mix.apply(lcg.stateAndUpdate(), xbg.stateAndUpdate());
         }
 
         @Override
         public LXMGenerator jump() {
             return new LXMGenerator(mix, lcg.copyAndJump(), xbg.copyAndJump());
         }
 
         @Override
         public LXMGenerator longJump() {
             return new LXMGenerator(mix, lcg.copyAndLongJump(), xbg.copyAndLongJump());
         }
     }
 
     /**
      * A factory for creating LXMGenerator objects.
      */
     interface LXMGeneratorFactory {
         /**
          * Return the size of the LCG long seed array.
          *
          * @return the LCG seed size
          */
         int lcgSeedSize();
 
         /**
          * Return the size of the XBG long seed array.
          *
          * @return the XBG seed size
          */
         int xbgSeedSize();
 
         /**
          * Return the size of the long seed array.
          * The default implementation adds the size of the LCG and XBG seed.
          *
          * @return the seed size
          */
         default int seedSize() {
             return lcgSeedSize() + xbgSeedSize();
         }
 
         /**
          * Creates a new LXMGenerator.
          *
          * <p>Tests using the LXMGenerator assume the seed is a composite containing the
          * LCG seed and then the XBG seed.
          *
          * @param seed the seed
          * @return the generator
          */
         LXMGenerator create(long[] seed);
 
         /**
          * Gets the mix implementation. This is used to test initial output of the generator.
          * The default implementation is {@link AbstractLXMTest#mixLea64(long, long)}.
          *
          * @return the mix
          */
         default Mix getMix() {
             return AbstractLXMTest::mixLea64;
         }
     }
 
     /**
      * Test the LCG implementations. These tests should execute only once, and not
      * for each instance of the abstract outer class (i.e. the test is not {@code @Nested}).
      *
      * <p>Note: The LCG implementations are not present in the main RNG core package and
      * this test ensures an LCG update of:
      * <pre>
      * s = m * s + a
      *
      * s = state
      * m = multiplier
      * a = addition
      * </pre>
      *
      * <p>A test is made to ensure the LCG can perform jump and long jump operations using
      * small jumps that can be verified by an equal number of single state updates.
      */
     static class LCGTest {
         /** 65-bit multiplier for the 128-bit LCG. */
         private static final BigInteger M = BigInteger.ONE.shiftLeft(64).add(toUnsignedBigInteger(LXMSupport.M128L));
         /** 2^128. Used as the modulus for the 128-bit LCG. */
         private static final BigInteger MOD = BigInteger.ONE.shiftLeft(128);
 
         /** A count {@code k} where a jump of {@code 2^k} will wrap the LCG state. */
         private static final int NO_JUMP = -1;
         /** A count {@code k=2} for a jump of {@code 2^k}, or 4 cycles. */
         private static final int JUMP = 2;
         /** A count {@code k=4} for a long jump of {@code 2^k}, or 16 cycles. */
         private static final int LONG_JUMP = 4;
 
         @RepeatedTest(value = 10)
         void testLCG64DefaultJump() {
             final SplittableRandom rng = new SplittableRandom();
             final long state = rng.nextLong();
             final long add = rng.nextLong();
             final SubGen lcg1 = new LCG64(add, state);
             final SubGen lcg2 = new LCG64(add, state, 0, 32);
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(lcg1.stateAndUpdate(), lcg2.stateAndUpdate(),
                     () -> String.format("seed %d,%d", state, add));
             }
             lcg1.copyAndJump();
             lcg2.copyAndJump();
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(lcg1.stateAndUpdate(), lcg2.stateAndUpdate(),
                     () -> String.format("seed %d,%d", state, add));
             }
             lcg1.copyAndLongJump();
             lcg2.copyAndLongJump();
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(lcg1.stateAndUpdate(), lcg2.stateAndUpdate(),
                     () -> String.format("seed %d,%d", state, add));
             }
         }
 
         @RepeatedTest(value = 10)
         void testLCG64() {
             final SplittableRandom rng = new SplittableRandom();
             final long state = rng.nextLong();
             final long add = rng.nextLong();
             long s = state;
             final long a = add | 1;
             final SubGen lcg = new LCG64(add, state, NO_JUMP, NO_JUMP);
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(s, lcg.stateAndUpdate(),
                     () -> String.format("seed %d,%d", state, add));
                 s = LXMSupport.M64 * s + a;
             }
         }
 
         @RepeatedTest(value = 10)
         void testLCG64Jump() {
             final SplittableRandom rng = new SplittableRandom();
             final long state = rng.nextLong();
             final long add = rng.nextLong();
             final Supplier<String> msg = () -> String.format("seed %d,%d", state, add);
             long s = state;
             final long a = add | 1;
             final SubGen lcg = new LCG64(add, state, JUMP, LONG_JUMP);
 
             final SubGen copy1 = lcg.copyAndJump();
             for (int j = 1 << JUMP; j-- != 0;) {
                 Assertions.assertEquals(s, copy1.stateAndUpdate(), msg);
                 s = LXMSupport.M64 * s + a;
             }
             Assertions.assertEquals(s, lcg.stateAndUpdate(), msg);
             s = LXMSupport.M64 * s + a;
 
             final SubGen copy2 = lcg.copyAndLongJump();
             for (int j = 1 << LONG_JUMP; j-- != 0;) {
                 Assertions.assertEquals(s, copy2.stateAndUpdate(), msg);
                 s = LXMSupport.M64 * s + a;
             }
             Assertions.assertEquals(s, lcg.stateAndUpdate(), msg);
         }
 
         @RepeatedTest(value = 10)
         void testLCG128DefaultJump() {
             final SplittableRandom rng = new SplittableRandom();
             final long stateh = rng.nextLong();
             final long statel = rng.nextLong();
             final long addh = rng.nextLong();
             final long addl = rng.nextLong();
             final SubGen lcg1 = new LCG128(addh, addl, stateh, statel);
             final SubGen lcg2 = new LCG128(addh, addl, stateh, statel, 0, 64);
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(lcg1.stateAndUpdate(), lcg2.stateAndUpdate(),
                     () -> String.format("seed %d,%d,%d,%d", stateh, statel, addh, addl));
             }
             lcg1.copyAndJump();
             lcg2.copyAndJump();
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(lcg1.stateAndUpdate(), lcg2.stateAndUpdate(),
                     () -> String.format("seed %d,%d,%d,%d", stateh, statel, addh, addl));
             }
             lcg1.copyAndLongJump();
             lcg2.copyAndLongJump();
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(lcg1.stateAndUpdate(), lcg2.stateAndUpdate(),
                     () -> String.format("seed %d,%d,%d,%d", stateh, statel, addh, addl));
             }
         }
 
         @RepeatedTest(value = 10)
         void testLCG128() {
             final SplittableRandom rng = new SplittableRandom();
             final long stateh = rng.nextLong();
             final long statel = rng.nextLong();
             final long addh = rng.nextLong();
             final long addl = rng.nextLong();
             BigInteger s = toUnsignedBigInteger(stateh).shiftLeft(64).add(toUnsignedBigInteger(statel));
             final BigInteger a = toUnsignedBigInteger(addh).shiftLeft(64).add(toUnsignedBigInteger(addl | 1));
             final SubGen lcg = new LCG128(addh, addl, stateh, statel, NO_JUMP, NO_JUMP);
             for (int j = 0; j < 10; j++) {
                 Assertions.assertEquals(s.shiftRight(64).longValue(), lcg.stateAndUpdate(),
                         () -> String.format("seed %d,%d,%d,%d", stateh, statel, addh, addl));
                 s = M.multiply(s).add(a).mod(MOD);
             }
         }
 
         @RepeatedTest(value = 10)
         void testLCG128Jump() {
             final SplittableRandom rng = new SplittableRandom();
             final long stateh = rng.nextLong();
             final long statel = rng.nextLong();
             final long addh = rng.nextLong();
             final long addl = rng.nextLong();
             final Supplier<String> msg = () -> String.format("seed %d,%d,%d,%d", stateh, statel, addh, addl);
             BigInteger s = toUnsignedBigInteger(stateh).shiftLeft(64).add(toUnsignedBigInteger(statel));
             final BigInteger a = toUnsignedBigInteger(addh).shiftLeft(64).add(toUnsignedBigInteger(addl | 1));
             final SubGen lcg = new LCG128(addh, addl, stateh, statel, JUMP, LONG_JUMP);
 
             final SubGen copy1 = lcg.copyAndJump();
             for (int j = 1 << JUMP; j-- != 0;) {
                 Assertions.assertEquals(s.shiftRight(64).longValue(), copy1.stateAndUpdate(), msg);
                 s = M.multiply(s).add(a).mod(MOD);
             }
             Assertions.assertEquals(s.shiftRight(64).longValue(), lcg.stateAndUpdate(), msg);
             s = M.multiply(s).add(a).mod(MOD);
 
             final SubGen copy2 = lcg.copyAndLongJump();
             for (int j = 1 << LONG_JUMP; j-- != 0;) {
                 Assertions.assertEquals(s.shiftRight(64).longValue(), copy2.stateAndUpdate(), msg);
                 s = M.multiply(s).add(a).mod(MOD);
             }
             Assertions.assertEquals(s.shiftRight(64).longValue(), lcg.stateAndUpdate(), msg);
         }
 
         /**
          * Create a big integer treating the value as unsigned.
          *
          * @param v Value
          * @return the big integer
          */
         private static BigInteger toUnsignedBigInteger(long v) {
             // Delegate
             return LXMSupportTest.toUnsignedBigInteger(v);
         }
     }
 
     /**
      * Test the XBG implementations. These tests should execute only once, and not
      * for each instance of the abstract outer class (i.e. the test is not {@code @Nested}).
      *
      * <p>Note: The XBG implementation are extensions of RNGs already verified against
      * reference implementations. These tests ensure that the upper bits of the state is
      * identical after {@code n} cycles then a jump; or a jump then {@code n} cycles.
      * This is the functionality required for a jumpable XBG generator.
      */
     static class XBGTest {
 
         @RepeatedTest(value = 5)
         void testXBGXoRoShiRo128NoJump() {
             final SplittableRandom r = new SplittableRandom();
             assertNoJump(new XBGXoRoShiRo128(r.nextLong(), r.nextLong(), false));
         }
 
         @RepeatedTest(value = 5)
         void testXBGXoShiRo256NoJump() {
             final SplittableRandom r = new SplittableRandom();
             assertNoJump(new XBGXoShiRo256(r.nextLong(), r.nextLong(), r.nextLong(), r.nextLong(), false));
         }
 
         @RepeatedTest(value = 5)
         void testXBGXoRoShiRo1024NoJump() {
             final SplittableRandom r = new SplittableRandom();
             assertNoJump(new XBGXoRoShiRo1024(r.longs(16).toArray(), false));
         }
 
         void assertNoJump(SubGen g) {
             final SubGen g1 = g.copyAndJump();
             Assertions.assertNotSame(g, g1);
             for (int i = 0; i < 10; i++) {
                 Assertions.assertEquals(g.stateAndUpdate(), g1.stateAndUpdate());
             }
             final SubGen g2 = g.copyAndLongJump();
             Assertions.assertNotSame(g, g2);
             for (int i = 0; i < 10; i++) {
                 Assertions.assertEquals(g.stateAndUpdate(), g2.stateAndUpdate());
             }
         }
 
         @RepeatedTest(value = 5)
         void testXBGXoRoShiRo128Jump() {
             assertJumpAndCycle(ThreadLocalRandom.current().nextLong(), 2, XBGXoRoShiRo128::new, SubGen::copyAndJump);
         }
 
         @RepeatedTest(value = 5)
         void testXBGXoRoShiRo128LongJump() {
             assertJumpAndCycle(ThreadLocalRandom.current().nextLong(), 2, XBGXoRoShiRo128::new, SubGen::copyAndLongJump);
         }
 
         @RepeatedTest(value = 5)
         void testXBGXoShiRo256Jump() {
             assertJumpAndCycle(ThreadLocalRandom.current().nextLong(), 4, XBGXoShiRo256::new, SubGen::copyAndJump);
         }
 
         @RepeatedTest(value = 5)
         void testXBGXShiRo256LongJump() {
             assertJumpAndCycle(ThreadLocalRandom.current().nextLong(), 4, XBGXoShiRo256::new, SubGen::copyAndLongJump);
         }
 
         @RepeatedTest(value = 5)
         void testXBGXoRoShiRo1024Jump() {
             assertJumpAndCycle(ThreadLocalRandom.current().nextLong(), 16, XBGXoRoShiRo1024::new, SubGen::copyAndJump);
         }
 
         @RepeatedTest(value = 5)
         void testXBGXoRoShiRo1024LongJump() {
             assertJumpAndCycle(ThreadLocalRandom.current().nextLong(), 16, XBGXoRoShiRo1024::new, SubGen::copyAndLongJump);
         }
 
         /**
          * Assert alternating jump and cycle of the XBG.
          *
          * <p>This test verifies one generator can jump and advance {@code n} steps
          * while the other generator advances {@code n} steps then jumps. The two should
          * be in the same state. The copy left behind by the first jump should match the
          * state of the other generator as it cycles.
          *
          * @param testSeed A seed for the test
          * @param seedSize The seed size
          * @param factory Factory to create the XBG
          * @param jump XBG jump function
          */
         private static void assertJumpAndCycle(long testSeed, int seedSize,
                 Function<long[], SubGen> factory, UnaryOperator<SubGen> jump) {
             final SplittableRandom r = new SplittableRandom(testSeed);
             final long[] seed = r.longs(seedSize).toArray();
             final int[] steps = createSteps(r, seedSize);
             final int cycles = 2 * seedSize;
 
             final SubGen rng1 = factory.apply(seed);
             final SubGen rng2 = factory.apply(seed);
 
             // Try jumping and stepping with a number of steps up to the seed size
             for (int i = 0; i < steps.length; i++) {
                 final int step = steps[i];
                 final int index = i;
                 // Jump 1
                 final SubGen copy = jump.apply(rng1);
                 // Advance 2; it should match the copy
                 for (int j = 0; j < step; j++) {
                     Assertions.assertEquals(rng2.stateAndUpdate(), copy.stateAndUpdate(),
                         () -> String.format("[%d] Incorrect trailing copy, seed=%d", index, testSeed));
                     // Advance in parallel
                     rng1.stateAndUpdate();
                 }
                 // Catch up 2; it should match 1
                 jump.apply(rng2);
                 for (int j = 0; j < cycles; j++) {
                     Assertions.assertEquals(rng1.stateAndUpdate(), rng2.stateAndUpdate(),
                         () -> String.format("[%d] Incorrect after catch up jump, seed=%d", index, testSeed));
                 }
             }
         }
     }
 
     /////////////////////////////////////
     // Tests for the LXM implementation
     /////////////////////////////////////
 
     /**
      * Gets the factory to create a composite LXM generator.
      * The generator is used to provide reference output for the generator under test.
      *
      * @return the factory
      */
     abstract LXMGeneratorFactory getFactory();
 
     /**
      * Creates a new instance of the RNG under test.
      *
      * @param seed the seed
      * @return the RNG
      */
     abstract LongJumpableUniformRandomProvider create(long[] seed);
 
     /**
      * Gets a stream of reference data. Each Argument consist of the long array seed and
      * the long array of the expected output from the LXM generator.
      * <pre>
      * long[] seed;
      * long[] expected;
      * return Stream.of(Arguments.of(seed, expected));
      * </pre>
      *
      * @return the reference data
      */
     abstract Stream<Arguments> getReferenceData();
 
     /**
      * Test the reference data with the LXM generator.
      * The reference data should be created with a reference implementation of the
      * LXM algorithm, for example the implementations in JDK 17.
      */
     @ParameterizedTest
     @MethodSource(value = "getReferenceData")
     final void testReferenceData(long[] seed, long[] expected) {
         RandomAssert.assertEquals(expected, create(seed));
     }
 
     /**
      * Test the reference data with the composite LXM generator. This ensures the composite
      * correctly implements the LXM algorithm.
      */
     @ParameterizedTest
     @MethodSource(value = "getReferenceData")
     final void testReferenceDataWithComposite(long[] seed, long[] expected) {
         RandomAssert.assertEquals(expected, getFactory().create(seed));
     }
 
     /**
      * Test initial output is the mix of the most significant bits of the LCG and XBG state.
      * This test ensures the LXM algorithm applies the mix function to the current state
      * before state update. Thus the initial output should be a direct mix of the seed state.
      */
     @RepeatedTest(value = 5)
     final void testInitialOutput() {
         final long[] seed = createRandomSeed();
         // Upper 64 bits of LCG state
         final long s = seed[getFactory().lcgSeedSize() / 2];
         // Upper 64 bits of XBG state
         final long t = seed[getFactory().lcgSeedSize()];
         Assertions.assertEquals(getFactory().getMix().apply(s, t), create(seed).nextLong());
     }
 
     @Test
     final void testConstructorWithZeroSeedIsPartiallyFunctional() {
         // Note: It is impractical to demonstrate the RNG is partially functional:
         // output quality may be statistically poor and the period is that of the LCG.
         // The test demonstrates the RNG is not totally non-functional with a zero seed
         // which is not the case for a standard XBG.
         final int seedSize = getFactory().seedSize();
         RandomAssert.assertNextLongNonZeroOutput(create(new long[seedSize]), 0, seedSize);
     }
 
     @ParameterizedTest
     @MethodSource(value = "getReferenceData")
     final void testConstructorWithoutFullLengthSeed(long[] seed) {
         // Hit the case when the input seed is self-seeded when not full length
         final int seedSize = getFactory().seedSize();
         RandomAssert.assertNextLongNonZeroOutput(create(new long[] {seed[0]}),
                 seedSize, seedSize);
     }
 
     @RepeatedTest(value = 5)
     final void testConstructorIgnoresFinalAddParameterSeedBit() {
         final long[] seed1 = createRandomSeed();
         final long[] seed2 = seed1.clone();
         final int seedSize = getFactory().seedSize();
         // seed1 unset final add parameter bit; seed2 set final bit
         final int index = getFactory().lcgSeedSize() / 2 - 1;
         seed1[index] &= -1L << 1;
         seed2[index] |= 1;
         Assertions.assertEquals(1, seed1[index] ^ seed2[index]);
         final LongJumpableUniformRandomProvider rng1 = create(seed1);
         final LongJumpableUniformRandomProvider rng2 = create(seed2);
         RandomAssert.assertNextLongEquals(seedSize * 2, rng1, rng2);
     }
 
     @ParameterizedTest
     @MethodSource(value = "getReferenceData")
     final void testJump(long[] seed, long[] expected) {
         final long[] expectedAfter = createExpectedSequence(seed, expected.length, false);
         RandomAssert.assertJumpEquals(expected, expectedAfter, create(seed));
     }
 
     @ParameterizedTest
     @MethodSource(value = "getReferenceData")
     final void testLongJump(long[] seed, long[] expected) {
         final long[] expectedAfter = createExpectedSequence(seed, expected.length, true);
         RandomAssert.assertLongJumpEquals(expected, expectedAfter, create(seed));
     }
 
     @RepeatedTest(value = 5)
     final void testJumpAndOutput() {
         assertJumpAndOutput(false, ThreadLocalRandom.current().nextLong());
     }
 
     @RepeatedTest(value = 5)
     final void testLongJumpAndOutput() {
         assertJumpAndOutput(true, ThreadLocalRandom.current().nextLong());
     }
 
     /**
      * Assert alternating jump and output from the LXM generator and the
      * reference composite LXM generator.
      *
      * <p>The composite generator uses an LCG that is tested to match
      * output after a jump (see {@link LCGTest} or a series of cycles.
      * The XBG generator is <em>assumed</em> to function similarly.
      * The {@link XBGTest} verifies that the generator is in the same
      * state when using {@code n} steps then a jump; or a jump then
      * {@code n} steps.
      *
      * <p>This test verifies one LXM generator can jump and advance
      * {@code n} steps while the other generator advances {@code n}
      * steps then jumps. The two should be in the same state. The copy
      * left behind by the first jump should match the output of the other
      * generator as it cycles.
      *
      * @param longJump If true use the long jump; otherwise the jump
      * @param testSeed A seed for the test
      */
     private void assertJumpAndOutput(boolean longJump, long testSeed) {
         final SplittableRandom r = new SplittableRandom(testSeed);
         final long[] seed = createRandomSeed(r::nextLong);
         final int[] steps = createSteps(r);
         final int cycles = getFactory().seedSize();
 
         LongJumpableUniformRandomProvider rng1 = create(seed);
         LongJumpableUniformRandomProvider rng2 = getFactory().create(seed);
 
         final UnaryOperator<LongJumpableUniformRandomProvider> jump = longJump ?
             x -> (LongJumpableUniformRandomProvider) x.longJump() :
             x -> (LongJumpableUniformRandomProvider) x.jump();
 
         // Alternate jumping and stepping then stepping and jumping.
         for (int i = 0; i < steps.length; i++) {
             final int step = steps[i];
             final int index = i;
             // Jump 1
             LongJumpableUniformRandomProvider copy = jump.apply(rng1);
             // Advance 2; it should match the copy
             for (int j = 0; j < step; j++) {
                 Assertions.assertEquals(rng2.nextLong(), copy.nextLong(),
                     () -> String.format("[%d] Incorrect trailing copy, seed=%d", index, testSeed));
                 // Advance 1 in parallel
                 rng1.nextLong();
             }
             // Catch up 2; it should match 1
             jump.apply(rng2);
             for (int j = 0; j < cycles; j++) {
                 Assertions.assertEquals(rng1.nextLong(), rng2.nextLong(),
                     () -> String.format("[%d] Incorrect after catch up jump, seed=%d", index, testSeed));
             }
 
             // Swap
             copy = rng1;
             rng1 = rng2;
             rng2 = copy;
         }
     }
 
     @RepeatedTest(value = 5)
     final void testSaveRestoreAfterJump() {
         assertSaveRestoreAfterJump(false, ThreadLocalRandom.current().nextLong());
     }
 
     @RepeatedTest(value = 5)
     final void testSaveRestoreAfterLongJump() {
         assertSaveRestoreAfterJump(true, ThreadLocalRandom.current().nextLong());
     }
 
     /**
      * Assert that the precomputation of the jump coefficients functions
      * with saved/restore.
      *
      * @param longJump If true use the long jump; otherwise the jump
      * @param testSeed A seed for the test
      */
     private void assertSaveRestoreAfterJump(boolean longJump, long testSeed) {
         final SplittableRandom r = new SplittableRandom(testSeed);
         final int cycles = getFactory().seedSize();
 
         final UnaryOperator<LongJumpableUniformRandomProvider> jump = longJump ?
             x -> (LongJumpableUniformRandomProvider) x.longJump() :
             x -> (LongJumpableUniformRandomProvider) x.jump();
 
         // Create 2 generators and jump them
         final LongJumpableUniformRandomProvider rng1 = create(createRandomSeed(r::nextLong));
         final LongJumpableUniformRandomProvider rng2 = create(createRandomSeed(r::nextLong));
         jump.apply(rng1);
         jump.apply(rng2);
 
         // Restore the state from one to the other
         RestorableUniformRandomProvider g1 = (RestorableUniformRandomProvider) rng1;
         RestorableUniformRandomProvider g2 = (RestorableUniformRandomProvider) rng2;
         g2.restoreState(g1.saveState());
 
         // They should have the same output
         RandomAssert.assertNextLongEquals(cycles, rng1, rng2);
 
         // They should have the same output after a jump too
         jump.apply(rng1);
         jump.apply(rng2);
 
         RandomAssert.assertNextLongEquals(cycles, rng1, rng2);
     }
 
     /**
      * Create the expected sequence after a jump by advancing the XBG and LCG
      * sub-generators. This is done by creating and jumping the composite LXM
      * generator.
      *
      * @param seed the seed
      * @param length the length of the expected sequence
      * @param longJump If true use the long jump; otherwise the jump
      * @return the expected sequence
      */
     private long[] createExpectedSequence(long[] seed, int length, boolean longJump) {
         final LXMGenerator rng = getFactory().create(seed);
         if (longJump) {
             rng.longJump();
         } else {
             rng.jump();
         }
         return LongStream.generate(rng::nextLong).limit(length).toArray();
     }
 
     /**
      * Creates a random seed of the correct length. Used when the seed can be anything.
      *
      * @return the seed
      */
     private long[] createRandomSeed() {
         return createRandomSeed(new SplittableRandom()::nextLong);
     }
 
     /**
      * Creates a random seed of the correct length using the provided generator.
      * Used when the seed can be anything.
      *
      * @param gen the generator
      * @return the seed
      */
     private long[] createRandomSeed(LongSupplier gen) {
         return LongStream.generate(gen).limit(getFactory().seedSize()).toArray();
     }
 
     /**
      * Creates a random permutation of steps in [1, seed size].
      * The seed size is obtained from the LXM generator factory.
      *
      * @param rng Source of randomness
      * @return the steps
      */
     private int[] createSteps(SplittableRandom rng) {
         return createSteps(rng, getFactory().seedSize());
     }
 
     /**
      * Creates a random permutation of steps in [1, seed size].
      *
      * @param rng Source of randomness
      * @param seedSize Seed size
      * @return the steps
      */
     private static int[] createSteps(SplittableRandom rng, int seedSize) {
         final int[] steps = IntStream.rangeClosed(1, seedSize).toArray();
         // Fisher-Yates shuffle
         for (int i = steps.length; i > 1; i--) {
             final int j = rng.nextInt(i);
             final int tmp = steps[i - 1];
             steps[i - 1] = steps[j];
             steps[j] = tmp;
         }
         return steps;
     }
 }