Improving Random
Simon Peyton Jones
simonpj at microsoft.com
Mon Jun 1 10:52:23 UTC 2020
Friends
Random number generation lies far outside my expertise, but I know it to be an area where it's easy to mess up, either in performance or in generating genuinely random numbers. So I'm delighted that Dominic and his colleagues have been working so hard on this. We all owe them a debt of thanks. Good RNGs are at the beating heart of many other algorithms, but are rather un-loved as an object of study in their own right.
So thank you Dominic, @curiousleo @lehins -- and indeed Guy Steele and colleagues, on whose work this is based. We don't often get perf boosts of 1000x!
I hope that that, after suitable scrutiny and refinement if necessary, this ends up being accepted.
Simon
From: Libraries <libraries-bounces at haskell.org> On Behalf Of dominic at steinitz.org
Sent: 26 May 2020 11:00
To: libraries <libraries at haskell.org>
Cc: Alexey Kuleshevich <alexey at kuleshevi.ch>
Subject: Improving Random
Hello Libraries,
You may recall that following the blog post<https://alexey.kuleshevi.ch/blog/2019/12/21/random-benchmarks/> by @lehins, a group of us (@curiousleo, @lehins and me) invited participation in February<https://mail.haskell.org/pipermail/libraries/2020-February/030261.html> to take this work and apply it to improving the current random library.
Our proximate goals were to fix #25<https://github.com/haskell/random/issues/25> (filed in 2015) and #51<https://github.com/haskell/random/issues/51> (filed in 2018). After a lot of discussion and experimentation, we have a proposal that addresses both these issues and also: #26<https://github.com/haskell/random/issues/26>, #44<https://github.com/haskell/random/issues/44>, #53<https://github.com/haskell/random/issues/53>, #55<https://github.com/haskell/random/issues/55>, #58<https://github.com/haskell/random/issues/58> and #59<https://github.com/haskell/random/issues/59>.
For backwards compatibility, the proposal retains the old style classes and enhances them. Thus in 1.1 we have
class RandomGen g where
next :: g -> (Int, g)
genRange :: g -> (Int, Int)
split :: g -> (g, g)
{-# MINIMAL next, split #-}
and in 1.2 we have
class RandomGen g where
next :: g -> (Int, g)
genWord8 :: g -> (Word8, g)
genWord16 :: g -> (Word16, g)
genWord32 :: g -> (Word32, g)
genWord64 :: g -> (Word64, g)
genWord32R :: Word32 -> g -> (Word32, g)
genWord64R :: Word64 -> g -> (Word64, g)
genShortByteString :: Int
-> g -> (Data.ByteString.Short.Internal.ShortByteString, g)
genRange :: g -> (Int, Int)
split :: g -> (g, g)
{-# MINIMAL split, (genWord32 | genWord64 | next, genRange) #-}
and next and genRange are deprecated. This interface is what allows the significantly faster performance as no longer is everything forced to go via Integer.
Several new interfaces are introduced and it is recommended that new applications use these and, where feasible, existing applications migrate to using them.
The major API addition in this PR is the definition of a new class MonadRandom:
-- | 'MonadRandom' is an interface to monadic pseudo-random number generators.
class Monad m => MonadRandom g s m | g m -> s where
{-# MINIMAL freezeGen,thawGen,(uniformWord32|uniformWord64) #-}
type Frozen g = (f :: Type) | f -> g
freezeGen :: g s -> m (Frozen g)
thawGen :: Frozen g -> m (g s)
uniformWord32 :: g s -> m Word32 -- default implementation in terms of uniformWord64
uniformWord64 :: g s -> m Word64 -- default implementation in terms of uniformWord32
-- plus methods for other word sizes and for byte strings
-- all have default implementations so the MINIMAL pragma holds
Conceptually, in MonadRandom g s m, g s is the type of the generator, s is the state type, and m the underlying monad. Via the functional dependency g m -> s, the state type is determined by the generator and monad.
Frozen is the type of the generator's state "at rest". It is defined as an injective type family via f -> g, so there is no ambiguity as to which g any Frozen g belongs to.
This definition is generic enough to accommodate, for example, the Gen type from mwc-random, which itself abstracts over the underlying primitive monad and state token. This is the full instance declaration (provided here as an example - this instance is not part of random as random does not depend on mwc-random):
instance (s ~ PrimState m, PrimMonad m) => MonadRandom MWC.Gen s m where
type Frozen MWC.Gen = MWC.Seed
freezeGen = MWC.save
thawGen = MWC.restore
uniformWord8 = MWC.uniform
uniformWord16 = MWC.uniform
uniformWord32 = MWC.uniform
uniformWord64 = MWC.uniform
uniformShortByteString n g = unsafeSTToPrim (genShortByteStringST n (MWC.uniform g))
Pure random number generators can also be made instances of this class providing a uniform interface to both pure and stateful random number generators. An instance for the standard number generator StdGen is provided.
The Random typeclass has conceptually been split into Uniform and UniformRange. The Random typeclass is still included for backwards compatibility. Uniform is for types where it is possible to sample from the type's entire domain; UniformRange is for types where one can sample from a specified range:
class Uniform a where
uniformM :: MonadRandom g s m => g s -> m a
class UniformRange a where
uniformRM :: MonadRandom g s m => (a, a) -> g s -> m a
The proposal is a breaking change but the changes are not very intrusive and we have PRs ready for the affected downstream libraries:
* requires base >= 4.10 (GHC-8.2)
* StdGen is no longer an instance of Read
* randomIO and randomRIO were extracted from the Random class into separate functions
In addition, there may be import clashes with new functions, e.g. uniform and uniformR.
Further explanatory details may be found here<https://github.com/idontgetoutmuch/random/blob/v1.2-release-notes/RELEASE-NOTES-v1.2.md#api-changes> and the PR for the proposed new version is here<https://github.com/haskell/random/pull/61>.
Here are some benchmarks run on a 3.1 GHz Intel Core i7. The full benchmarks can be run using e.g. stack bench. The benchmarks are measured in milliseconds per 100,000 generations. In some cases, the performance is over x1000(!) times better; the minimum performance increase for the types listed below is more than x35.
| Name | Mean (1.1) | Mean (1.2) | Improvement|
| ----------------------- | ---------- | ---------- | ---------- |
| pure/random/Float | 30 | 0.03 | 1038|
| pure/random/Double | 52 | 0.03 | 1672|
| pure/random/Integer | 43 | 0.33 | 131|
| pure/uniform/Word8 | 14 | 0.03 | 422|
| pure/uniform/Word16 | 13 | 0.03 | 375|
| pure/uniform/Word32 | 21 | 0.03 | 594|
| pure/uniform/Word64 | 42 | 0.03 | 1283|
| pure/uniform/Word | 44 | 0.03 | 1491|
| pure/uniform/Int8 | 15 | 0.03 | 511|
| pure/uniform/Int16 | 15 | 0.03 | 507|
| pure/uniform/Int32 | 22 | 0.03 | 749|
| pure/uniform/Int64 | 44 | 0.03 | 1405|
| pure/uniform/Int | 43 | 0.03 | 1512|
| pure/uniform/Char | 17 | 0.49 | 35|
| pure/uniform/Bool | 18 | 0.03 | 618|
| pure/uniform/CChar | 14 | 0.03 | 485|
| pure/uniform/CSChar | 14 | 0.03 | 455|
| pure/uniform/CUChar | 13 | 0.03 | 448|
| pure/uniform/CShort | 14 | 0.03 | 473|
| pure/uniform/CUShort | 13 | 0.03 | 457|
| pure/uniform/CInt | 21 | 0.03 | 737|
| pure/uniform/CUInt | 21 | 0.03 | 742|
| pure/uniform/CLong | 43 | 0.03 | 1544|
| pure/uniform/CULong | 42 | 0.03 | 1460|
| pure/uniform/CPtrdiff | 43 | 0.03 | 1494|
| pure/uniform/CSize | 43 | 0.03 | 1475|
| pure/uniform/CWchar | 22 | 0.03 | 785|
| pure/uniform/CSigAtomic | 21 | 0.03 | 749|
| pure/uniform/CLLong | 43 | 0.03 | 1554|
| pure/uniform/CULLong | 42 | 0.03 | 1505|
| pure/uniform/CIntPtr | 43 | 0.03 | 1476|
| pure/uniform/CUIntPtr | 42 | 0.03 | 1463|
| pure/uniform/CIntMax | 43 | 0.03 | 1535|
| pure/uniform/CUIntMax | 42 | 0.03 | 1493|
Dominic Steinitz
dominic at steinitz.org<mailto:dominic at steinitz.org>
http://idontgetoutmuch.org
Twitter: @idontgetoutmuch
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