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

The provided code implements a 32-bit random number generator (RNG) using the PCG32 algorithm. It defines a PCG32 struct to hold the state and increment values for the generator.

Initialization and Seeding:

• The constructor PCG32(st, i) initializes the PCG32 with optional seed values st and i. By default, it uses pre-defined constants (0x853c49e6748fea9b for st and 0xda3e39cb94b95bdb for i).

Random Number Generation:

• The next_int! function generates a random 32-bit unsigned integer based on the current state and increment values. It uses bitwise operations to produce the random number and updates the state for subsequent calls.

• The next_float! function generates a random floating-point number between 0 and 1 by dividing the generated integer by 2^32.

• The seed! function allows you to initialize or reseed the generator with custom seed values.

Testing and Demonstration:

• The testPCG32 function demonstrates the usage of the RNG. It creates an instance, seeds it with specific values, and generates and prints random integers.

• It then re-seeds the generator and generates a histogram of 100_000 random floats divided into 5 bins. The histogram and bin counts are printed for analysis.

Overall, this code provides a simple and efficient implementation of the PCG32 random number generator in Julia, allowing for both integer and floating-point random number generation. The testing function demonstrates its functionality and provides insights into the distribution of generated numbers through a histogram.

const mask32, CONST = 0xffffffff, UInt(6364136223846793005)

mutable struct PCG32
    state::UInt64
    inc::UInt64
    PCG32(st=0x853c49e6748fea9b, i=0xda3e39cb94b95bdb) = new(st, i)
end

"""return random 32 bit unsigned int"""
function next_int!(x::PCG32)
    old = x.state
    x.state = (old * CONST) + x.inc
    xorshifted = (((old >> 18) ⊻ old) >> 27) & mask32
    rot = (old >> 59) & mask32
    return ((xorshifted >> rot) | (xorshifted << ((-rot) & 31))) & mask32
end

"""return random float between 0 and 1"""
next_float!(x::PCG32) = next_int!(x) / (1 << 32)

function seed!(x::PCG32, st, seq)
    x.state = 0x0
    x.inc = (UInt(seq) << 0x1) | 1
    next_int!(x)
    x.state = x.state + UInt(st)
    next_int!(x)
end

function testPCG32()
    random_gen = PCG32()
    seed!(random_gen, 42, 54)
    for _ in 1:5
        println(next_int!(random_gen))
    end
    seed!(random_gen, 987654321, 1)
    hist = fill(0, 5)
    for _ in 1:100_000
        hist[Int(floor(next_float!(random_gen) * 5)) + 1] += 1
    end
    println(hist)
    for n in 1:5
        print(n - 1, ": ", hist[n], "  ")
    end
end

testPCG32()