How to resolve the algorithm Pseudo-random numbers/Combined recursive generator MRG32k3a step by step in the Java programming language
How to resolve the algorithm Pseudo-random numbers/Combined recursive generator MRG32k3a step by step in the Java programming language
Table of Contents
Problem Statement
numbers as shown above.
are as shown above
repetitions of
Is as follows:
Let's start with the solution:
Step by Step solution about How to resolve the algorithm Pseudo-random numbers/Combined recursive generator MRG32k3a step by step in the Java programming language
The provided Java code is related to random number generation using two Linear Congruential Generators (LCGs). A detailed explanation of the code is as follows:
-
mod
Function: This is a utility function that calculates the modulo of two long numbers, handling negative values to ensure a positive result. -
RNG
Class:- Instance Variables:
a1
anda2
: These are arrays of coefficients for two LCGs.m1
andm2
: Moduli for the two LCGs.x1
andx2
: Arrays for storing the current states of the two LCGs.
seed
Method: Initializes the LCGs with a specifiedstate
value.nextInt
Method: Generates the next random integer using the two LCGs and returns it.nextFloat
Method: Generates the next random float by dividing the integer result fromnextInt
byd
.
- Instance Variables:
-
main
Method:- Creates an
RNG
instance and seeds it with a value1234567
. - Prints five random integers generated using
nextInt
. - Seeds the
RNG
again with a different value987654321
. - Generates 100,000 random floats using
nextFloat
and counts how often each value from 0 to 4 (inclusive) occurs. The counts are then printed out.
- Creates an
In summary, this code is an implementation of two LCGs to generate random numbers. It demonstrates how to set a seed and generate both random integers and floats using this setup. The mod
function helps ensure positive modulo results for non-negative inputs. The main
method showcases the random number generation and provides a frequency count for testing the randomness.
Source code in the java programming language
public class App {
private static long mod(long x, long y) {
long m = x % y;
if (m < 0) {
if (y < 0) {
return m - y;
} else {
return m + y;
}
}
return m;
}
public static class RNG {
// first generator
private final long[] a1 = {0, 1403580, -810728};
private static final long m1 = (1L << 32) - 209;
private long[] x1;
// second generator
private final long[] a2 = {527612, 0, -1370589};
private static final long m2 = (1L << 32) - 22853;
private long[] x2;
// other
private static final long d = m1 + 1;
public void seed(long state) {
x1 = new long[]{state, 0, 0};
x2 = new long[]{state, 0, 0};
}
public long nextInt() {
long x1i = mod(a1[0] * x1[0] + a1[1] * x1[1] + a1[2] * x1[2], m1);
long x2i = mod(a2[0] * x2[0] + a2[1] * x2[1] + a2[2] * x2[2], m2);
long z = mod(x1i - x2i, m1);
// keep the last three values of the first generator
x1 = new long[]{x1i, x1[0], x1[1]};
// keep the last three values of the second generator
x2 = new long[]{x2i, x2[0], x2[1]};
return z + 1;
}
public double nextFloat() {
return 1.0 * nextInt() / d;
}
}
public static void main(String[] args) {
RNG rng = new RNG();
rng.seed(1234567);
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println(rng.nextInt());
System.out.println();
int[] counts = {0, 0, 0, 0, 0};
rng.seed(987654321);
for (int i = 0; i < 100_000; i++) {
int value = (int) Math.floor(rng.nextFloat() * 5.0);
counts[value]++;
}
for (int i = 0; i < counts.length; i++) {
System.out.printf("%d: %d%n", i, counts[i]);
}
}
}
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