Package com.github.tommyettinger.random

Class HornRandom

java.lang.Object
java.util.Random
com.github.tommyettinger.random.EnhancedRandom
com.github.tommyettinger.random.HornRandom
All Implemented Interfaces:
Externalizable, Serializable, RandomGenerator
public class HornRandom extends EnhancedRandom
A tiny hash-on-counter generator that has been designed specifically to use only constants that a human can remember. Uses two bijective Xor-Square-Or operations along with a bitwise rotation and a xor-shift. Allows all states, and will eventually produce every 64-bit output from nextLong() (it is 1D-equidistributed exactly). This generator passes 64TB of PractRand testing with no anomalies. It also passes Initial Correlation Evaluator (ICE) tests, including Immediate Initial Correlation Evaluator (IICE) tests, which mostly means the unary hash function used is high-quality when given sufficiently-different inputs. The large odd-number counter used here guarantees all inputs to the hash will be quite different when used as a PRNG.
The constants used here are 5555555555555555555L for the counter increment (nineteen decimal digits, all of them 5; if you try using twenty repetitions of 5, that won't fit in a long), bitwise OR with 7, and bitwise unsigned right shifts by 27 (with a left shift by -27 to make one a bitwise rotation).
The most complicated operation here is xor-square-or, which unlike most math involving multiplying a number by itself, is possible to invert (it is bijective), which is a critical property to ensure equidistribution. The inverse can be found here along with the thread that discovered the pattern is bijective in the first place. Xor-square-or, or XQO, looks like x ^= (x * x) | 1;, with some variations possible; any odd number can be used instead of 1. In the most extreme case, 1 can be replaced with -1, which makes the entire step equivalent to `x ^= -1;` or `x = ~x;`, which is also a bijection (every input x corresponds to exactly one different output ~x). The reason squaring is preferable to a multiplication by a constant is simply performance; according to Godbolt Compiler Explorer, squaring a 64-bit variable requires only two expensive vpmuludq operations, while multiplying a 64-bit variable by a 64-bit constant requires three. This is also the reason why a bitwise rotation is used directly instead of a more-typical xor-shift in the third line; xor-shift requires two operations (a XOR and an unsigned right shift), while in theory a bitwise rotation can be only one operation. It isn't a single operation in Compiler Explorer's output (for whatever reason, Clang performs a left and a right shift and bitwise ORs them, which may be faster for AVX vectors), but it might be in the JVM's output.
This generator is strongly inspired by the design (and memorability) of the Squares generator, but unlike Squares, this generator is 1D-equidistributed and does not use a "key". You can swap out 5555555555555555555L for any odd constant of your choice, which has similar results to changing the key in Squares. Some constants are not good choices, such as 1L or 5L, and you can run any odd long through EnhancedRandom.fixGamma(long, int) with a threshold as low as 1 to find a "better" increment/key/gamma/stream constant. 5555555555555555555L works if the threshold is 3 or higher, and won't be changed in that case.
You can use a very similar algorithm as a stateless hash function with Hasher.randomizeH(long). There are sometimes advantages to using a stateless function, such as in massively-parallel contexts, that individual random number generator objects can't beat.
The name comes from how a horn fits on a ram, and this generator should fit in a person's random-access memory.
See Also:

  • Field Details

    • state

      public long state
      The only state variable; can be any long.

  • Constructor Details

    • HornRandom

      public HornRandom()
      Creates a new HornRandom with a random state.

    • HornRandom

      public HornRandom(long state)
      Creates a new HornRandom with the given state; all long values are permitted.
      Parameters:
      state - any long value

  • Method Details

    • getTag

      public String getTag()
      Description copied from class: EnhancedRandom
      Gets the tag used to identify this type of EnhancedRandom, as a String. This tag should be unique, and for uniformity purposes, all tags used in this library are 4 characters long. User-defined tags should have a different length.
      Specified by:
      getTag in class EnhancedRandom
      Returns:
      a unique String identifier for this type of EnhancedRandom; usually 4 chars long.

    • getMinimumPeriod

      public BigInteger getMinimumPeriod()
      2 to the 64.
      Overrides:
      getMinimumPeriod in class EnhancedRandom
      Returns:
      2 to the 64

    • getStateCount

      public int getStateCount()
      This has one long state.
      Overrides:
      getStateCount in class EnhancedRandom
      Returns:
      1 (one)

    • getSelectedState

      public long getSelectedState(int selection)
      Gets the only state, which can be any long value.
      Overrides:
      getSelectedState in class EnhancedRandom
      Parameters:
      selection - ignored; this always returns the same, only state
      Returns:
      the only state's exact value

    • setSelectedState

      public void setSelectedState(int selection, long value)
      Sets the only state, which can be given any long value. The selection can be anything and is ignored.
      Overrides:
      setSelectedState in class EnhancedRandom
      Parameters:
      selection - ignored; this always sets the same, only state
      value - the exact value to use for the state; all longs are valid

    • setSeed

      public void setSeed(long seed)
      Sets the only state, which can be given any long value; this seed value will not be altered. Equivalent to setSelectedState(int, long) with any selection and seed passed as the value.
      Specified by:
      setSeed in class EnhancedRandom
      Parameters:
      seed - the exact value to use for the state; all longs are valid

    • getState

      public long getState()
      Gets the current state; it's already public, but I guess this could still be useful. The state can be any long.
      Returns:
      the current state, as a long

    • setState

      public void setState(long state)
      Sets each state variable to the given state. This implementation simply sets the one state variable to state.
      Overrides:
      setState in class EnhancedRandom
      Parameters:
      state - the long value to use for the state variable

    • nextLong

      public long nextLong()
      Description copied from class: EnhancedRandom
      Returns the next pseudorandom, uniformly distributed long value from this random number generator's sequence. The general contract of nextLong is that one long value is pseudorandomly generated and returned.
      The only methods that need to be implemented by this interface are this and EnhancedRandom.copy(), though other methods can be implemented as appropriate for generators that, for instance, natively produce ints rather than longs.
      Specified by:
      nextLong in interface RandomGenerator
      Specified by:
      nextLong in class EnhancedRandom
      Returns:
      the next pseudorandom, uniformly distributed long value from this random number generator's sequence

    • skip

      public long skip(long advance)
      Skips the state forward or backwards by the given advance, then returns the result of nextLong() at the same point in the sequence. If advance is 1, this is equivalent to nextLong(). If advance is 0, this returns the same long as the previous call to the generator (if it called nextLong()), and doesn't change the state. If advance is -1, this moves the state backwards and produces the long before the last one generated by nextLong(). More positive numbers move the state further ahead, and more negative numbers move the state further behind; all of these take constant time.
      Overrides:
      skip in class EnhancedRandom
      Parameters:
      advance - how many steps to advance the state before generating a long
      Returns:
      a random long by the same algorithm as nextLong(), using the appropriately-advanced state

    • previousLong

      public long previousLong()
      Description copied from class: EnhancedRandom
      Optional; moves the state to its previous value and returns the previous long that would have been produced by EnhancedRandom.nextLong(). This can be equivalent to calling EnhancedRandom.skip(long) with -1L, but not always; many generators can't efficiently skip long distances, but can step back by one value.
      Generators that natively generate int results typically produce long values by generating an int for the high 32 bits and an int for the low 32 bits. When producing the previous long, the order the high and low bits are generated, such as by EnhancedRandom.previousInt(), should be reversed. Generators that natively produce long values usually don't need to implement EnhancedRandom.previousInt(), but those that produce int usually should implement it, and may optionally call previousInt() twice in this method.
      If you know how to implement the reverse of a particular random number generator, it is recommended you do so here, rather than rely on skip(). This isn't always easy, but should always be possible for any decent PRNG (some historical PRNGs, such as the Middle-Square PRNG, cannot be reversed at all). If a generator cannot be reversed because multiple initial states can transition to the same subsequent state, it is known to have statistical problems that are not necessarily present in a generator that matches one initial state to one subsequent state.
      The public implementation calls EnhancedRandom.skip(long) with -1L, and if skip() has not been implemented differently, then it will throw an UnsupportedOperationException.
      Overrides:
      previousLong in class EnhancedRandom
      Returns:
      the previous number this would have produced with EnhancedRandom.nextLong()

    • next

      public int next(int bits)
      Description copied from class: EnhancedRandom
      Generates the next pseudorandom number with a specific maximum size in bits (not a max number). If you want to get a random number in a range, you should usually use EnhancedRandom.nextInt(int) instead. For some specific cases, this method is more efficient and less biased than EnhancedRandom.nextInt(int). For bits values between 1 and 30, this should be similar in effect to nextInt(1 << bits); though it won't typically produce the same values, they will have the correct range. If bits is 31, this can return any non-negative int; note that nextInt(1 << 31) won't behave this way because 1 << 31 is negative. If bits is 32 (or 0), this can return any int.

      The general contract of next is that it returns an int value and if the argument bits is between 1 and 32 (inclusive), then that many low-order bits of the returned value will be (approximately) independently chosen bit values, each of which is (approximately) equally likely to be 0 or 1.

      Note that you can give this values for bits that are outside its expected range of 1 to 32, but the value used, as long as bits is positive, will effectively be bits % 32. As stated before, a value of 0 for bits is the same as a value of 32.

      Overrides:
      next in class EnhancedRandom
      Parameters:
      bits - the amount of random bits to request, from 1 to 32
      Returns:
      the next pseudorandom value from this random number generator's sequence

    • copy

      public HornRandom copy()
      Description copied from class: EnhancedRandom
      Creates a new EnhancedRandom with identical states to this one, so if the same EnhancedRandom methods are called on this object and its copy (in the same order), the same outputs will be produced. This is not guaranteed to copy the inherited state of any parent class, so if you call methods that are only implemented by a superclass (like Random) and not this one, the results may differ.
      Specified by:
      copy in class EnhancedRandom
      Returns:
      a deep copy of this EnhancedRandom.

    • equals

      public boolean equals(Object o)
      Overrides:
      equals in class Object

    • toString

      public String toString()
      Overrides:
      toString in class Object