Tuesday, 09 February 2016
This post is part of a series of posts on implementing a minimal version of QuickCheck from scratch. The source code is available on GitHub.
I’ll be basing this minimal F# version of QuickCheck on QuickCheck 1.2.0.1, the last version of QuickCheck depending exclusively on base and Random 1.1^{1}.
Random is a basic random number generation library, including the ability to split random number generators. QuickCheck 1.2.0.1 uses
from the Random package, and so it’ll be easier to start by porting those in F#:
/// <summary>
/// This module deals with the common task of pseudo-random number generation.
/// It makes it possible to generate repeatable results, by starting with a
/// specified initial random number generator, or to get different results on
/// echch run by using the system-initialised generator or by supplying a seed
/// from some other source.
/// </summary>
/// <remarks>
/// This implementation uses the Portable Combined Generator of L'Ecuyer for
/// 32-bit computers, transliterated by Lennart Augustsson. It has a period of
/// roughly 2.30584e18.
/// </remarks>
[<AutoOpen>]
module internal LightCheck.Random
type StdGen =
private
| StdGen of int * int
/// <summary>
/// The next operation returns an Int that is uniformly distributed in the
/// rangge of at least 30 bits, and a new generator. The result of repeatedly
/// using next should be at least as statistically robust as the Minimal
/// Standard Random Number Generator. Until more is known about implementations
/// of split, all we require is that split deliver generators that are (a) not
/// identical and (b) independently robust in the sense just given.
/// </summary>
let private next (StdGen (s1, s2)) =
let k = s1 / 53668
let k' = s2 / 52774
let s1' = 40014 * (s1 - k * 53668) - k * 12211
let s2' = 40692 * (s2 - k' * 52774) - k' * 3791
let s1'' = if s1' < 0 then s1' + 2147483563 else s1'
let s2'' = if s2' < 0 then s2' + 2147483399 else s2'
let z = s1'' - s2''
let z' = if z < 1 then z + 2147483562 else z
(z', StdGen (s1'', s2''))
/// <summary>
/// The split operation allows one to obtain two distinct random number
/// generators. This is very useful in functional programs (for example, when
/// passing a random number generator down to recursive calls), but very little
/// work has been done on statistically robust implementations of split.
/// </summary>
let split (StdGen (s1, s2) as std) =
let s1' = if s1 = 2147483562 then 1 else s1 + 1
let s2' = if s2 = 1 then 2147483398 else s2 - 1
let (StdGen (t1, t2)) = next std |> snd
(StdGen (s1', t2), StdGen (t1, s2'))
/// <summary>
/// The range operation takes a range (lo,hi) and a random number generator g,
/// and returns a random value, uniformly distributed, in the closed interval
/// [lo,hi], together with a new generator.
/// </summary>
/// <remarks>
/// It is unspecified what happens if lo > hi. For continuous types there is no
/// requirement that the values lo and hi are ever produced, although they very
/// well may be, depending on the implementation and the interval.
/// </remarks>
let rec range (l, h) rng =
if l > h then range (h, l) rng
else
let (l', h') = (32767, 2147483647)
let b = h' - l' + 1
let q = 1000
let k = h - l + 1
let magnitude = k * q
let rec f c v g =
if c >= magnitude then (v, g)
else
let (x, g') = next g
let v' = (v * b + (x - l'))
f (c * b) v' g'
let (v, rng') = f 1 0 rng
(l + v % k), rng'
let private r = int System.DateTime.UtcNow.Ticks |> System.Random
/// <summary>
/// Provides a way of producing an initial generator using a random seed.
/// </summary>
let createNew() =
let s = r.Next() &&& 2147483647
let (q, s1) = (s / 2147483562, s % 2147483562)
let s2 = q % 2147483398
StdGen (s1 + 1, s2 + 1)
To port QuickCheck’s basic generators, and combinators for making custom ones, we need a type of Gen<'a>
:
/// <summary>
/// LightCheck exports some basic generators, and some combinators for making
/// new ones. Gen of 'a is the type for generators of 'a's and essentially is
/// a State Monad combining a pseudo-random generation seed, and a size value
/// for data structures (i.e. list length).
/// Using the type Gen of 'a, we can specify at the same time a set of values
/// that can be generated and a probability distribution on that set.
///
/// Read more about how it works here:
/// http://www.dcc.fc.up.pt/~pbv/aulas/tapf/slides/quickcheck.html#the-gen-monad
/// http://quviq.com/documentation/eqc/index.html
/// </summary>
module LightCheck.Gen
/// <summary>
/// A generator for values of type 'a.
/// </summary>
type Gen<'a> =
private
| Gen of (int -> StdGen -> 'a)
Finally, we also need a function^{2} that runs a generator; taking a Gen<'a>
and returning random test data of type 'a
:
/// <summary>
/// Runs a generator. The size passed to the generator is up to 30; if you want
/// another size then you should explicitly use 'resize'.
/// </summary>
let generate (Gen m) =
let (size, rand) = Random.createNew() |> Random.range (0, 30)
m size rand
val generate : Gen<'a> -> 'a
We’re all set! Let’s generate some random test data in the next post(s).
The other thing to notice about QuickCheck 1.2.0.1, is that it’s the last version before version 2 came out. In version 2 there’s added support for shrinking, which is a major advancement. The shrinking functions are going to be ported from QuickCheck 2.8.2. ↩
The implementation of the generate
function is based on both QuickCheck 1.2.0.1 and QuickCheck 2.8.2. ↩
This post has been filed under #f# #quickcheck
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