Package com.github.tommyettinger.random

Class Xoshiro128PlusPlusRandom

java.lang.Object

java.util.Random

com.github.tommyettinger.random.EnhancedRandom

com.github.tommyettinger.random.Xoshiro128PlusPlusRandom

All Implemented Interfaces:

Externalizable, Serializable, RandomGenerator

public class Xoshiro128PlusPlusRandom
extends EnhancedRandom

A random number generator that is optimized for performance on 32-bit machines and with Google Web Toolkit, this uses no multiplication and is identical to the published xoshiro128++ algorithm when generating int values. When generating long values, it is a little different. The trick this uses for generating 64-bit values is to separately scramble states A and D to get the uppermost bits (this is what generating an int normally does), then to scramble states B and C differently to get the lowermost bits. This means a call to nextLong() advances the state exactly as much as nextInt(), which is an uncommon trait for mostly-32-bit-math generators.
The actual speed of this is going to vary wildly depending on the platform being benchmarked. On GWT, which is the main place where the performance of a random number generator might actually be a bottleneck in a game, this performs very well, especially when producing long values. On desktop platforms, it is faster at generating int values than long, which is to be expected for a 32-bit generator, but not as fast as some other generators, like ChopRandom.
Xoshiro128PlusPlusRandom has a guaranteed period of pow(2, 128) - 1. For int outputs only, it is 3-dimensionally equidistributed. For long outputs, equidistribution is unknown. It passes 64TB of PractRand testing without anomalies (generating 64-bit numbers), and passes 2 to the 57.32 bytes of ReMort testing without suspect results. ReMort is a very challenging test to pass for long sequences, so this result is encouraging, even if the p-values dipped low in the middle of testing (they got better). This generator can be seen as a "safer alternative" to ChopRandom, which is generally faster but has a lower minimum period and may have quality issues that haven't yet been discovered. The Xoshiro family of generators is generally well-researched and most flaws are already known and minor (with the PlusPlus scrambler, the only issue I know of is that this can't tolerate an all-zero state). The way this generates 64-bit longs from a 32-bit generator is new and hasn't been tested by anyone else, so it could have issues.
This implements all optional methods in EnhancedRandom except EnhancedRandom.skip(long).
Based on this public-domain code by Vigna and Blackman.

See Also:

• Serialized Form

Nested Class Summary

Nested classes/interfaces inherited from interface java.util.random.RandomGenerator

RandomGenerator.ArbitrarilyJumpableGenerator, RandomGenerator.JumpableGenerator, RandomGenerator.LeapableGenerator, RandomGenerator.SplittableGenerator, RandomGenerator.StreamableGenerator

Field Summary

Fields

Modifier and Type	Field	Description
protected int	stateA	The first state; can be any int.
protected int	stateB	The second state; can be any int.
protected int	stateC	The third state; can be any int.
protected int	stateD	The fourth state; can be any int.

Constructor Summary

Constructors

Constructor	Description
Xoshiro128PlusPlusRandom()	Creates a new Xoshiro128PlusPlusRandom with a random state.
Xoshiro128PlusPlusRandom(int stateA, int stateB, int stateC, int stateD)	Creates a new Xoshiro128PlusPlusRandom with the given four states; all int values are permitted.
Xoshiro128PlusPlusRandom(long seed)	Creates a new Xoshiro128PlusPlusRandom with the given seed; all long values are permitted.

Method Summary

Modifier and Type	Method	Description
Xoshiro128PlusPlusRandom	copy()	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.
boolean	equals(Object o)
long	getSelectedState(int selection)	Gets the state determined by selection, as-is.
long	getStateA()
long	getStateB()
long	getStateC()
int	getStateCount()	This generator has 4 int states, so this returns 4.
long	getStateD()
String	getTag()	Gets the tag used to identify this type of EnhancedRandom, as a String.
long	leap()	Jumps extremely far in the generator's sequence, such that it requires Math.pow(2, 64) calls to leap() to complete a cycle through the generator's entire sequence.
int	next(int bits)	Generates the next pseudorandom number with a specific maximum size in bits (not a max number).
boolean	nextBoolean()	Returns the next pseudorandom, uniformly distributed boolean value from this random number generator's sequence.
void	nextBytes(byte[] bytes)	Generates random bytes and places them into a user-supplied byte array.
float	nextFloat()	Returns the next pseudorandom, uniformly distributed float value between 0.0 (inclusive) and 1.0 (exclusive) from this random number generator's sequence.
float	nextInclusiveFloat()	This is just like EnhancedRandom.nextFloat(), returning a float between 0 and 1, except that it is inclusive on both 0.0 and 1.0.
int	nextInt()	Returns the next pseudorandom, uniformly distributed int value from this random number generator's sequence.
int	nextInt(int bound)	Returns a pseudorandom, uniformly distributed int value between 0 (inclusive) and the specified value (exclusive), drawn from this random number generator's sequence.
long	nextLong()	Returns the next pseudorandom, uniformly distributed long value from this random number generator's sequence.
long	nextLong(long inner, long outer)	Returns a pseudorandom, uniformly distributed long value between the specified innerBound (inclusive) and the specified outerBound (exclusive).
int	nextSignedInt(int outerBound)	Returns a pseudorandom, uniformly distributed int value between an inner bound of 0 (inclusive) and the specified outerBound (exclusive).
long	nextSignedLong(long inner, long outer)	Returns a pseudorandom, uniformly distributed long value between the specified innerBound (inclusive) and the specified outerBound (exclusive).
int	previousInt()	Optional; moves the state to its previous value and returns the previous int that would have been produced by EnhancedRandom.nextInt().
long	previousLong()	Optional; moves the state to its previous value and returns the previous long that would have been produced by EnhancedRandom.nextLong().
void	setSeed(long seed)	This initializes all 4 states of the generator to random values based on the given seed.
void	setSelectedState(int selection, long value)	Sets one of the states, determined by selection, to the lower 32 bits of value, as-is.
void	setState(long stateA, long stateB, long stateC, long stateD)	Sets the state completely to the given four state variables, casting each to an int.
void	setStateA(long stateA)	Sets the first part of the state by casting the parameter to an int.
void	setStateB(long stateB)	Sets the second part of the state by casting the parameter to an int.
void	setStateC(long stateC)	Sets the third part of the state by casting the parameter to an int.
void	setStateD(long stateD)	Sets the fourth part of the state by casting the parameter to an int.
String	toString()

Methods inherited from class com.github.tommyettinger.random.EnhancedRandom

areEqual, fixGamma, maxDoubleOf, maxFloatOf, maxIntOf, maxLongOf, minDoubleOf, minFloatOf, minIntOf, minLongOf, nextBoolean, nextDouble, nextDouble, nextDouble, nextExclusiveDouble, nextExclusiveDouble, nextExclusiveDouble, nextExclusiveDoubleEquidistant, nextExclusiveFloat, nextExclusiveFloat, nextExclusiveFloat, nextExclusiveFloatEquidistant, nextExclusiveSignedDouble, nextExclusiveSignedFloat, nextFloat, nextFloat, nextGaussian, nextGaussian, nextInclusiveDouble, nextInclusiveDouble, nextInclusiveDouble, nextInclusiveFloat, nextInclusiveFloat, nextInt, nextLong, nextSign, nextSignedInt, nextSignedLong, nextTriangular, nextTriangular, nextTriangular, nextTriangular, nextUnsignedInt, probit, randomElement, randomElement, readExternal, seedFromMath, setState, setState, setState, setState, setState, setWith, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, shuffle, skip, stringDeserialize, stringDeserialize, stringSerialize, stringSerialize, writeExternal

Methods inherited from class java.util.Random

doubles, doubles, doubles, doubles, ints, ints, ints, ints, longs, longs, longs, longs

Methods inherited from class java.lang.Object

clone, finalize, getClass, hashCode, notify, notifyAll, wait, wait, wait

Methods inherited from interface java.util.random.RandomGenerator

isDeprecated, nextExponential

Field Details

stateA

protected int stateA

The first state; can be any int.

stateB

protected int stateB

The second state; can be any int.

stateC

protected int stateC

The third state; can be any int.

stateD

protected int stateD

The fourth state; can be any int.

Constructor Details

Xoshiro128PlusPlusRandom

public Xoshiro128PlusPlusRandom()

Creates a new Xoshiro128PlusPlusRandom with a random state.

Xoshiro128PlusPlusRandom

public Xoshiro128PlusPlusRandom(long seed)

Creates a new Xoshiro128PlusPlusRandom with the given seed; all long values are permitted. The seed will be passed to setSeed(long) to attempt to adequately distribute the seed randomly.

Parameters:

seed - any long value

Xoshiro128PlusPlusRandom

public Xoshiro128PlusPlusRandom(int stateA,
 int stateB,
 int stateC,
 int stateD)

Creates a new Xoshiro128PlusPlusRandom with the given four states; all int values are permitted. These states will be used verbatim, unless all are 0 -- if they are all 0, then stateD is replaced with 1.

Parameters:

stateA - any int value

stateB - any int value

stateC - any int value

stateD - any int 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.

getStateCount

public int getStateCount()

This generator has 4 int states, so this returns 4.

Overrides:

getStateCount in class EnhancedRandom

Returns:

4 (four)

getSelectedState

public long getSelectedState(int selection)

Gets the state determined by selection, as-is. The value for selection should be between 0 and 3, inclusive; if it is any other value this gets state D as if 3 was given.

Overrides:

getSelectedState in class EnhancedRandom

Parameters:

selection - used to select which state variable to get; generally 0, 1, 2, or 3

Returns:

the value of the selected state, which is an int that will be promoted to long

setSelectedState

public void setSelectedState(int selection,
 long value)

Sets one of the states, determined by selection, to the lower 32 bits of value, as-is. Selections 0, 1, 2, and 3 refer to states A, B, C, and D, and if the selection is anything else, this treats it as 3 and sets stateD. This always casts value to an int before using it. If all four states would be 0 as a result of this call, it instead sets the fourth part of the state to 1.

Overrides:

setSelectedState in class EnhancedRandom

Parameters:

selection - used to select which state variable to set; generally 0, 1, 2, or 3

value - the exact value to use for the selected state, if valid

setSeed

public void setSeed(long seed)

This initializes all 4 states of the generator to random values based on the given seed. (2 to the 64) possible initial generator states can be produced here. This is not capable of setting the full state to the only invalid value (all zeros).

Specified by:

setSeed in class EnhancedRandom

Parameters:

seed - the initial seed; may be any long

getStateA

public long getStateA()

setStateA

public void setStateA(long stateA)

Sets the first part of the state by casting the parameter to an int.

Parameters:

stateA - can be any long, but will be cast to an int before use

getStateB

public long getStateB()

setStateB

public void setStateB(long stateB)

Sets the second part of the state by casting the parameter to an int.

Parameters:

stateB - can be any long, but will be cast to an int before use

getStateC

public long getStateC()

setStateC

public void setStateC(long stateC)

Sets the third part of the state by casting the parameter to an int.

Parameters:

stateC - can be any long, but will be cast to an int before use

getStateD

public long getStateD()

setStateD

public void setStateD(long stateD)

Sets the fourth part of the state by casting the parameter to an int. If all four states would be 0 as a result of this call, it instead sets the fourth part of the state to 1.

Parameters:

stateD - can be any long, but will be cast to an int before use

setState

public void setState(long stateA,
 long stateB,
 long stateC,
 long stateD)

Sets the state completely to the given four state variables, casting each to an int. This is the same as calling setStateA(long), setStateB(long), setStateC(long), and setStateD(long) as a group. If all four states would be 0 as a result of this call, it instead sets the fourth part of the state to 1.

Overrides:

setState in class EnhancedRandom

Parameters:

stateA - the first state; can be any long, but will be cast to an int before use

stateB - the second state; can be any long, but will be cast to an int before use

stateC - the third state; can be any long, but will be cast to an int before use

stateD - the fourth state; can be any long, but will be cast to an int before use

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

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()

previousInt

public int previousInt()

Description copied from class: EnhancedRandom

Optional; moves the state to its previous value and returns the previous int that would have been produced by EnhancedRandom.nextInt(). This can be equivalent to calling EnhancedRandom.previousLong() and casting to int, but not always; generators that natively generate int results typically move the state once in nextInt() and twice in nextLong(), and should move the state back once here.
If EnhancedRandom.nextInt() is implemented using a call to EnhancedRandom.nextLong(), the implementation in this class is almost always sufficient and correct. If nextInt() changes state differently from nextLong(), then this should be implemented, if feasible, and EnhancedRandom.previousLong() can be implemented using 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.previousLong() and casts it to int, and if previousLong() and skip() have not been implemented differently, then it will throw an UnsupportedOperationException.

Overrides:

previousInt in class EnhancedRandom

Returns:

the previous number this would have produced with EnhancedRandom.nextInt()

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

nextInt

public int nextInt()

Description copied from class: EnhancedRandom

Returns the next pseudorandom, uniformly distributed int value from this random number generator's sequence. The general contract of nextInt is that one int value is pseudorandomly generated and returned. All 2³² possible int values are produced with (approximately) equal probability.

Specified by:

nextInt in interface RandomGenerator

Overrides:

nextInt in class EnhancedRandom

Returns:

the next pseudorandom, uniformly distributed int value from this random number generator's sequence

nextInt

public int nextInt(int bound)

Description copied from class: EnhancedRandom

Returns a pseudorandom, uniformly distributed int value between 0 (inclusive) and the specified value (exclusive), drawn from this random number generator's sequence. The general contract of nextInt is that one int value in the specified range is pseudorandomly generated and returned. All bound possible int values are produced with (approximately) equal probability.
This method clamps bound to be at least 0; it never returns a negative int.
It should be mentioned that the technique this uses has some bias, depending on bound, but it typically isn't measurable without specifically looking for it. Using the method this does allows this method to always advance the state by one step, instead of a varying and unpredictable amount with the more typical ways of rejection-sampling random numbers and only using numbers that can produce an int within the bound without bias. See M.E. O'Neill's blog about random numbers for discussion of alternative, unbiased methods.

Specified by:

nextInt in interface RandomGenerator

Overrides:

nextInt in class EnhancedRandom

Parameters:

bound - the upper bound (exclusive). If negative or 0, this always returns 0.

Returns:

the next pseudorandom, uniformly distributed int value between zero (inclusive) and bound (exclusive) from this random number generator's sequence

nextSignedInt

public int nextSignedInt(int outerBound)

Description copied from class: EnhancedRandom

Returns a pseudorandom, uniformly distributed int value between an inner bound of 0 (inclusive) and the specified outerBound (exclusive). This is meant for cases where the outer bound may be negative, especially if the bound is unknown or may be user-specified. A negative outer bound is used as the lower bound; a positive outer bound is used as the upper bound. An outer bound of -1, 0, or 1 will always return 0, keeping the bound exclusive (except for outer bound 0). This method is slightly slower than EnhancedRandom.nextInt(int).

Overrides:

nextSignedInt in class EnhancedRandom

Parameters:

outerBound - the outer exclusive bound; may be any int value, allowing negative

Returns:

a pseudorandom int between 0 (inclusive) and outerBound (exclusive)

See Also:

• Here's a note about the bias present in the bounded generation.

nextBytes

public void nextBytes(byte[] bytes)

Description copied from class: EnhancedRandom

Generates random bytes and places them into a user-supplied byte array. The number of random bytes produced is equal to the length of the byte array.

Specified by:

nextBytes in interface RandomGenerator

Overrides:

nextBytes in class EnhancedRandom

Parameters:

bytes - the byte array to fill with random bytes

nextLong

public long nextLong(long inner,
 long outer)

Description copied from class: EnhancedRandom

Returns a pseudorandom, uniformly distributed long value between the specified innerBound (inclusive) and the specified outerBound (exclusive). If outerBound is less than or equal to innerBound, this always returns innerBound.
For any case where outerBound might be valid but less than innerBound, you can use EnhancedRandom.nextSignedLong(long, long).

Specified by:

nextLong in interface RandomGenerator

Overrides:

nextLong in class EnhancedRandom

Parameters:

inner - the inclusive inner bound; may be any long, allowing negative

outer - the exclusive outer bound; must be greater than innerBound (otherwise this returns innerBound)

Returns:

a pseudorandom long between innerBound (inclusive) and outerBound (exclusive)

See Also:

• Here's a note about the bias present in the bounded generation.

nextSignedLong

public long nextSignedLong(long inner,
 long outer)

Description copied from class: EnhancedRandom

Returns a pseudorandom, uniformly distributed long value between the specified innerBound (inclusive) and the specified outerBound (exclusive). This is meant for cases where either bound may be negative, especially if the bounds are unknown or may be user-specified.

Overrides:

nextSignedLong in class EnhancedRandom

Parameters:

inner - the inclusive inner bound; may be any long, allowing negative

outer - the exclusive outer bound; may be any long, allowing negative

Returns:

a pseudorandom long between innerBound (inclusive) and outerBound (exclusive)

See Also:

• Here's a note about the bias present in the bounded generation.

nextBoolean

public boolean nextBoolean()

Description copied from class: EnhancedRandom

Returns the next pseudorandom, uniformly distributed boolean value from this random number generator's sequence. The general contract of nextBoolean is that one boolean value is pseudorandomly generated and returned. The values true and false are produced with (approximately) equal probability.
The public implementation simply returns a sign check on EnhancedRandom.nextLong(), returning true if the generated long is negative. This is typically the safest way to implement this method; many types of generators have less statistical quality on their lowest bit, so just returning based on the lowest bit isn't always a good idea.

Specified by:

nextBoolean in interface RandomGenerator

Overrides:

nextBoolean in class EnhancedRandom

Returns:

the next pseudorandom, uniformly distributed boolean value from this random number generator's sequence

nextFloat

public float nextFloat()

Description copied from class: EnhancedRandom

Returns the next pseudorandom, uniformly distributed float value between 0.0 (inclusive) and 1.0 (exclusive) from this random number generator's sequence.

The general contract of nextFloat is that one float value, chosen (approximately) uniformly from the range 0.0f (inclusive) to 1.0f (exclusive), is pseudorandomly generated and returned. All 2²⁴ possible float values of the form m x 2^-24, where m is a positive integer less than 2²⁴, are produced with (approximately) equal probability.

The public implementation uses the upper 24 bits of EnhancedRandom.nextLong(), with an unsigned right shift and a multiply by a very small float (5.9604645E-8f or 0x1p-24f). It tends to be fast if nextLong() is fast, but alternative implementations could use 24 bits of EnhancedRandom.nextInt() (or just EnhancedRandom.next(int), giving it 24) if that generator doesn't efficiently generate 64-bit longs.

Specified by:

nextFloat in interface RandomGenerator

Overrides:

nextFloat in class EnhancedRandom

Returns:

the next pseudorandom, uniformly distributed float value between 0.0 and 1.0 from this random number generator's sequence

nextInclusiveFloat

public float nextInclusiveFloat()

Description copied from class: EnhancedRandom

This is just like EnhancedRandom.nextFloat(), returning a float between 0 and 1, except that it is inclusive on both 0.0 and 1.0. It returns 1.0 rarely, 0.00000596046412226771% of the time if there is no bias in the generator, but it can happen. This method does not return purely-equidistant floats, because there the resolution of possible floats it can generate is higher as it approaches 0.0 . The smallest non-zero float this can return is 5.421011E-20f (0x1p-64f in hex), and the largest non-one float this can return is 0.9999999f (0x1.fffffcp-1f in hex). This uses nearly identical code to EnhancedRandom.nextExclusiveFloat(), but carefully adds and subtracts a small number to force rounding at 0.0 and 1.0 . This retains the exclusive version's quality of having approximately uniform distributions for every mantissa bit, unlike most ways of generating random floating-point numbers.

Overrides:

nextInclusiveFloat in class EnhancedRandom

Returns:

a float between 0.0, inclusive, and 1.0, inclusive

copy

public Xoshiro128PlusPlusRandom 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.

leap

public long leap()

Jumps extremely far in the generator's sequence, such that it requires Math.pow(2, 64) calls to leap() to complete a cycle through the generator's entire sequence. This can be used to create over 18 quintillion substreams of this generator's sequence, each with a period of Math.pow(2, 64).

Returns:

the result of what nextLong() would return if it was called at the state this jumped to

equals

public boolean equals(Object o)

Overrides:

equals in class Object

toString

public String toString()

Overrides:

toString in class Object