NPBRandom

Usage

use NPBRandom;

or

import NPBRandom;

Warning

The ‘NPBRandom’ module is unstable and subject to change

NAS Parallel Benchmark Random Number Generator.

The pseudorandom number generator (PRNG) implemented by this module uses the algorithm from the NAS Parallel Benchmarks (NPB, available at: https://www.nas.nasa.gov/publications/npb.html which can be used to generate random values of type real(64), imag(64), and complex(128).

Paraphrasing the comments from the NPB reference implementation:

This generator returns uniform pseudorandom real values in the range (0, 1) by using the linear congruential generator

x_{k+1} = a x_k (mod 2**46)

where 0 < x_k < 2**46 and 0 < a < 2**46. This scheme generates 2**44 numbers before repeating. The generated values are normalized to be between 0 and 1, i.e., 2**(-46) * x_k.

This generator should produce the same results on any computer with at least 48 mantissa bits for real(64) data.

To generate complex elements, consecutive pairs of random numbers are assigned to the real and imaginary components, respectively.

The values generated by this NPB RNG do not include 0.0 and 1.0.

We have tested this implementation with TestU01 (available at http://simul.iro.umontreal.ca/testu01/tu01.html ). In our experiments with TestU01 1.2.3 and the Crush suite (which consists of 144 statistical tests), this NPB RNG failed 41/144 tests. As a linear congruential generator, this RNG has known statistical problems that TestU01 was able to detect.

Note

This module is currently restricted to generating real(64), imag(64), and complex(128) complex values.

proc oddTimeSeed() : int(64)

Generate an odd integer seed value based on the current time.

proc fillRandom(ref arr: [] ?t, seed: int)  where isRealOrComplexType(t) && arr.isRectangular()

Fill a rectangular array of numeric values with pseudorandom values in parallel using a new NPBRandomStream. The first arr.size values from the stream will be assigned to the array’s elements in row-major order. The parallelization strategy is determined by the array.

Arguments:

  • arr – An array of numeric values

  • seed – The seed to use to create the NPBRandomStream

proc fillRandom(ref arr: [] ?t)  where isRealOrComplexType(t) && arr.isRectangular()

Fill a rectangular array of numeric values with pseudorandom values in parallel using a new NPBRandomStream. The first arr.size values from the stream will be assigned to the array’s elements in row-major order. The parallelization strategy is determined by the array.

Note

a seed will be generated in an implementation specific manner that depends on the current time.

Arguments:

arr – An array of numeric values

class NPBRandomStream : writeSerializable

Models a stream of pseudorandom numbers. See the module-level notes for NPBRandom for details on the PRNG used.

type eltType = real(64)

Specifies the type of value generated by the NPBRandomStream. Currently, only real(64), imag(64), and complex(128) are supported.

const seed : int(64)

The seed value for the PRNG. It must be an odd integer in the interval [1, 2**46).

param parSafe : bool = true

Indicates whether or not the NPBRandomStream 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.

proc init(type eltType = real(64), seed: int(64) = oddTimeSeed(), param parSafe: bool = true)

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

Note

The NPB generator requires an odd seed value. Constructing an NPBRandomStream with an even seed value will cause a call to halt(). Only the lower 46 bits of the seed will be used.

Arguments:

  • eltType : type – The element type to be generated.

  • seed : int(64) – The seed to use for the RNG. Defaults to a value based on the current time.

  • parSafe : bool – The parallel safety setting. Defaults to true.

proc getNext() : eltType

Returns the next value in the random stream.

Real numbers generated by the NPB RNG are in (0,1). It is not possible for this particular RNG to generate 0.0 or 1.0.

Returns:

The next value in the random stream as type eltType.

proc skipToNth(n: integral) throws

Advances/rewinds the stream to the n-th value in the sequence. The first value corresponds to n=0. n must be >= 0, otherwise an IllegalArgumentError is thrown.

Arguments:

n : integral – The position in the stream to skip to. Must be >= 0.

Throws:

IllegalArgumentError – When called with negative n value.

proc getNth(n: integral) : eltType throws

Advance/rewind the stream to the n-th value and return it (advancing the stream by one). n must be >= 0, otherwise an IllegalArgumentError is thrown. 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.

Throws:

IllegalArgumentError – When called with negative n value.

proc fillRandom(ref 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 NPBRandomStream 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 iterate(D: domain, type resultType = real)

Returns an iterable expression for generating D.size random numbers. The RNG state will be immediately advanced by D.size 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