PCGRandom¶

Permuted Linear Congurential Random Number Generator

This module provides PCG random number generation routines. See http://www.pcg-random.org/ and the paper, PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation by M.E. O'Neill.

It also includes some Chapel-specific features, such as generating real, imag, and complex numbers; and generating numbers in a range in parallel. These features are not available in the reference implementations of PCG.

The related module PCGRandomLib provides a lower-level interface to many PCG functions.

class RandomStream¶

Models a stream of pseudorandom numbers generated by the PCG random number generator. See http://www.pcg-random.org/ and the paper, PCG: A Family of Simple Fast Space-Efficient Statistically Good Algorithms for Random Number Generation by M.E. O'Neill.

This class builds upon the pcg_setseq_64_xsh_rr_32_rng PCG RNG which has 64 bits of state and 32 bits of output.

While the PCG RNG used here is believed to have good statistical properties, it is not suitable for generating key material for encryption since the output of this RNG may be predictable. Additionally, if statistical properties of the random numbers are very important, another strategy may be required.

We have good confidence that the random numbers generated by this class match the C PCG reference implementation and have specifically verified equal output given the same seed. However, this implementation differs from the C PCG reference implementation in how it produces random integers within particular bounds (with RandomStream.getNext using min and max arguments). In addition, this implementation directly supports the generation of random real values, unlike the C PCG implementation.

Smaller numbers, such as uint(8) or uint(16), are generated from the high-order bits of the 32-bit output.

To generate larger numbers, several 32-bit-output RNGs are ganged together. This strategy is recommended by the author of PCG (and demonstrated in the file pcg32x2-demo.c. Each of these 32-bit RNGs has a different sequence constant and so will be independent and uncorrelated. For example, to generate 128-bit complex numbers, this RNG will use 4 ganged 32-bit PCG RNGs with different sequence constants. One impact of this approach is that this implementation will only generate 2**64 different complex numbers with a given seed (for example).

This class also supports generating integers within particular bounds. When that is required, this class uses a strategy different from the PCG reference implementation in order to work better in a parallel setting. In particular, when more than 1 random value is required as part of generating a value in a range, conceptually it uses more ganged-together RNGs (as with the 32x2 strategy). Each new value beyond the first that is computed will be computed with a different ganged-together RNG. This strategy is meant to avoid statistical bias. While we have tested this strategy to our satisfaction, it has not been subject to rigorous analysis and may have undesireable statistical properties.

When generating a real, imaginary, or complex number, this implementation uses the strategy of generating a 64-bit unsigned integer and then multiplying it by 2.0**-64 in order to convert it to a floating point number. While this does construct a uniform distribution on rounded floating point values, it leaves out many possible real values (for example, 2**-128). We believe that this strategy has reasonable statistical properties. One side effect of this strategy is that the real number 1.0 can be generated because of rounding. The real number 0.0 can be generated because PCG can produce the value 0 as a random integer.

We have tested this implementation with TestU01 (available at http://simul.iro.umontreal.ca/testu01/tu01.html ). We measured our implementation with TestU01 1.2.3 and the Crush suite, which consists of 144 statistical tests. The results were:

• no failures for generating uniform reals
• 1 failure for generating 32-bit values (which is also true for the reference version of PCG with the same configuration)
• 0 failures for generating 64-bit values (which we provided to TestU01 as 2 different 32-bit values since it only accepts 32 bits at a time)
• 0 failures for generating bounded integers (which we provided to TestU01 by requesting values in [0..,2**31+2**30+1) until we had two values < 2**31, removing the top 0 bit, and then combining the top 16 bits into the value provided to TestU01).

Note

This class is currently called RandomStream, but at some point we expect to rename it PCGRandomStream. At that point, RandomStream will represent the default RNG and will initially refer to PCGRandomStream.

type eltType¶

Specifies the type of value generated by the PCGRandomStream. All numeric types are supported: int, uint, real, imag, complex, and bool types of all sizes.

param parSafe: bool = true¶

Indicates whether or not the PCGRandomStream needs to be parallel-safe by default. If multiple tasks interact with it in an uncoordinated fashion, this must be set to true. If it will only be called from a single task, or if only one task will call into it at a time, setting to false will reduce overhead related to ensuring mutual exclusion.

const seed: int(64)¶

The seed value for the PRNG.

proc RandomStream(seed: int(64) = SeedGenerator.currentTime, param parSafe: bool = true, type eltType = real(64))¶

Constructs a new stream of random numbers using the specified seed and parallel safety.

Arguments:	seed : int(64) -- The seed to use for the PRNG. Defaults to currentTime from RandomSupport.SeedGenerator. Can be any int(64) value. parSafe : bool -- The parallel safety setting. Defaults to true. eltType : type -- The element type to be generated. Defaults to real(64).

proc getNext(type resultType = eltType): resultType¶

Returns the next value in the random stream.

Generated reals are in [0,1] - both 0.0 and 1.0 are possible values. Imaginary numbers are analagously in [0i, 1i]. Complex numbers will consist of a generated real and imaginary part, so 0.0+0.0i and 1.0+1.0i are possible.

Generated integers cover the full value range of the integer.

Arguments:	resultType -- the type of the result. Defaults to eltType. resultType must be the same or a smaller size number.
Returns:	The next value in the random stream as type resultType.

proc getNext(min: eltType, max: eltType): eltType

Return the next random value but within a particular range. Returns a number in [min, max] (inclusive).

Note

For integers, this class uses a strategy for generating a value in a particular range that has not been subject to rigorous study and may have statistical problems.

For real numbers, this class generates a random value in [max, min] by computing a random value in [0,1] and scaling and shifting that value. Note that not all possible floating point values in the interval [min, max] can be constructed in this way.

proc skipToNth(n: integral)¶

Advances/rewinds the stream to the n-th value in the sequence. The first corresponds to n=1. It is an error to call this routine with n <= 0.

Arguments:	n : integral -- The position in the stream to skip to. Must be > 0.

proc getNth(n: integral): eltType¶

Advance/rewind the stream to the n-th value and return it (advancing the stream by one). This is equivalent to skipToNth() followed by getNext().

Arguments:	n : integral -- The position in the stream to skip to. Must be > 0.
Returns:	The n-th value in the random stream as type eltType.

proc fillRandom(arr: [] eltType)¶

Fill the argument array with pseudorandom values. This method is identical to the standalone fillRandom procedure, except that it consumes random values from the RandomStream object on which it's invoked rather than creating a new stream for the purpose of the call.

Arguments:	arr : [] eltType -- The array to be filled

proc shuffle(arr: [] eltType)¶

Randomly shuffle a 1-D non-strided array.

proc permutation(arr: [] eltType)¶

Produce a random permutation, storing it in a 1-D array. The resulting array will include each value from low..high exactly once, where low and high refer to the array's domain.

proc iterate(D: domain, type resultType = eltType)¶

Returns an iterable expression for generating D.numIndices random numbers. The RNG state will be immediately advanced by D.numIndices before the iterable expression yields any values.

The returned iterable expression is useful in parallel contexts, including standalone and zippered iteration. The domain will determine the parallelization strategy.

Arguments:	D -- a domain resultType -- the type of number to yield
Returns:	an iterable expression yielding random resultType values