How to resolve the algorithm Pseudo-random numbers/PCG32 step by step in the Haskell programming language

Published on 7 June 2024 03:52 AM
#Haskell

How to resolve the algorithm Pseudo-random numbers/PCG32 step by step in the Haskell programming language

Table of Contents

Problem Statement

PCG32 has two unsigned 64-bit integers of internal state: Values of sequence allow 2**63 different sequences of random numbers from the same state. The algorithm is given 2 U64 inputs called seed_state, and seed_sequence. The algorithm proceeds in accordance with the following pseudocode:- Note that this an anamorphism – dual to catamorphism, and encoded in some languages as a general higher-order unfold function, dual to fold or reduce. numbers using the above. are: 2707161783 2068313097 3122475824 2211639955 3215226955

Let's start with the solution:

Step by Step solution about How to resolve the algorithm Pseudo-random numbers/PCG32 step by step in the Haskell programming language

The provided code defines a type PCGen and instances it as a random generator, providing the next function (which generates a new value and a new random generator) and the split function (which is not implemented in this case). The PCGen type holds two Word64 values, state and inc. The mkPCGen function creates a new PCGen generator from an initial state and a sequence value. The next function generates a new random number and a new PCGen generator from the current state and inc values. The toFloat function converts a Word64 value to a float in the range [0, 1). The randoms' function generates a list of random numbers from a given RandomGen generator g.

Source code in the haskell programming language

import Data.Bits
import Data.Word
import System.Random
import Data.List

data PCGen = PCGen !Word64 !Word64 

mkPCGen state sequence =
  let
    n = 6364136223846793005 :: Word64 
    inc = (sequence `shiftL` 1) .|. 1 :: Word64 
  in PCGen ((inc + state)*n + inc) inc 

instance RandomGen PCGen where
   next (PCGen state inc) =
     let
       n = 6364136223846793005 :: Word64
       xs = fromIntegral $ ((state `shiftR` 18) `xor` state) `shiftR` 27 :: Word32
       rot = fromIntegral $ state `shiftR` 59 :: Int
     in (fromIntegral $ (xs `shiftR` rot) .|. (xs `shiftL` ((-rot) .&. 31))
        , PCGen (state * n + inc) inc)

   split _ = error "PCG32 is not splittable"

randoms' :: RandomGen g => g -> [Int]
randoms' g = unfoldr (pure . next) g

toFloat n = fromIntegral n / (2^32 - 1)

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