Haskell: System.Random.MWC: High Quality Fixed Seeds

2013-04-23*
haskell, rng

I use Bryan O’Sullivan’s mwc-random package for my PRNG (pseudorandom number generator) needs in my Haskell projects. mwc-random is very fast and generates high quality random numbers. It has a pretty simple API, and gives you several options of initializing the RNG state. One way is to use the initialize function, which simply takes a list of Word32 elements and takes the first 256 of them to seed the generator (if less than 256, it fills the rest from a hard-coded list). I’ve discovered that using a simple list of 3 small numbers representing the year, month, and day (e.g., [2013, 4, 11]) is not very good as an argument to initialize, as the generator behaves somewhat similarly to, say, one with slightly different date (e.g., [2013, 4, 12]).

The Problem

I have a program that needs to be seeded on a day-by-day basis, and it must use the current date (year, month, and day only) as the seed; however, I need the seed to be random enough to make the MWC state spit out substantially different random numbers on different, yet similar days. In essence, I need to change

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import qualified Data.Vector as V
import System.Random.MWC

	...
	gen <- initialize $ V.fromList [year, month, day]
	...

to something that has a much higher quality in terms of randomness.

Enter the SHA-1 Hash Function

Ah, the venerable SHA-1 function. It’s a real gem because you can use it to generate an extremely high-quality 160-bit (20-byte) random number from a given set of bytes; and, even if you change the input by a single byte, it will generate a totally different number. You can think of the SHA-1 hash function as a function that takes a seed and generates a random number — where the seed can be 0 bytes or 123 bytes or whatever size. Thankfully, there is a SHA-1 package available, so I don’t need to write my own correct implementation of SHA-1 (not to mention that only a handful of programmers can even write such code).

The Solution

To solve my problem, I just take the current date, then feed it to the SHA-1 function to get sha1Hash; I then then repeatedly call SHA-1 against sha1Hash recursively. Meanwhile, each time I get a SHA-1 hash of 20 bytes, I append it to an empty string of bytes, acc. When acc is large enough to be split up into 256 Word32 elements, I feed it to initialize. The result is that I get much better seed-vs-similar-seed randomness with MWC.

Here is the code:

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import Data.Bits
import qualified Data.ByteString.Lazy as B
import Data.Digest.Pure.SHA
import Data.List (foldl')
import qualified Data.Vector as V
import Data.Word
import System.Random.MWC

--	...
--	gen <- initialize' $ year' + month' + day'
--	...

-- | Given a Word32 'num' generate a growing ByteString 'x' by repeatedly
-- generating a SHA1 digest, as a ByteString 'y', and appending it back to
-- 'x'. When 'x' is sufficiently large (at least 256 * 4 elements, as each
-- element is Word8 and we need 4 of these to get 1 Word32, and ultimately we
-- need 256 Word32s), convert it back down to [Word32] and call
-- System.Random.MWC's 'initialize' function on it.
initialize' :: PrimMonad m => Word32 -> m (Gen (PrimState m))
initialize' num = initialize . V.fromList . loop B.empty . B.pack $ octetsLE num
	where
	loop :: B.ByteString -> B.ByteString -> [Word32]
	loop acc bs
		| B.length acc >= (256 * 4) = take 256 $ toW32s acc
		| otherwise = loop (B.append acc $ sha1Bytes bs) (sha1Bytes bs)
	sha1Bytes :: B.ByteString -> B.ByteString
	sha1Bytes = bytestringDigest . sha1
	toW32s :: B.ByteString -> [Word32]
	toW32s = map fromOctetsLE . chop 4 . B.unpack
	chop :: Int -> [a] -> [[a]]
	chop _ [] = []
	chop n xs = take n xs : chop n (drop n xs)

-- For little-endian conversion.
octetsLE :: Word32 -> [Word8]
octetsLE w =
	[ fromIntegral w
	, fromIntegral (w `shiftR` 8)
	, fromIntegral (w `shiftR` 16)
	, fromIntegral (w `shiftR` 24)
	]

-- For big-endian conversion.
octetsBE :: Word32 -> [Word8]
octetsBE = reverse . octetsLE

fromOctetsBE :: [Word8] -> Word32
fromOctetsBE = foldl' accum 0
	where
	accum a o = (a `shiftL` 8) .|. fromIntegral o

fromOctetsLE :: [Word8] -> Word32
fromOctetsLE = fromOctetsBE . reverse

The neat chop function is by Dan Burton. The octet conversion functions between Word8 and Word32 types are from this message.1


  1. The distinction between big-endianness and little-endianness does not matter at all for purposes of my solution, but I still distinguished them anyway as a reference.