# On Bits

A quick review of non-negative binary numbers and bitwise operators.

Read MoreA quick glimpse at a Java 8 implementation for taking derivatives of functions using functional interfaces and lambda expressions.

Read More*A while ago, I wrote a post on a Stream-Based Linear Congruential Generator in Scala. This post is a similar implementation using the Java 8 Stream API.*

Here is a Java 8 stream-based implementation of a pseudo-random number generator using a linear congruential generator (LCG):

package com.michaelcotterell.util; import java.util.stream.DoubleStream; import java.util.stream.IntStream; import java.util.stream.LongStream; public class Random { private final long a; // multiplier private final long c; // increment private final long m; // modulus private final long seed; // start value private final LongStream stream; public Random(long a, long c, long m, long seed) { this.a = a; this.c = c; this.m = m; this.seed = seed % m; this.stream = LongStream.iterate(this.seed, x -> (a * x + c) % m); } // Random public Random(long a, long c, long m) { this(a, c, m, System.currentTimeMillis()); } // Random public LongStream longs() { return stream.map(e -> e); } // longs public IntStream ints() { return stream.mapToInt(e -> (int) (e % (Integer.MAX_VALUE + 1L))); } // ints public DoubleStream doubles() { final double ONE_OVER_M = 1.0 / m; return stream.mapToDouble(e -> e * ONE_OVER_M); } // doubles } // Random

To use this class, you might do something like the following:

Random lcg = new Random(48271, 0, (2L << 31) - 1, System.currentTimeMillis()); Iterator<Double> rand = lcg.doubles().iterator(); for (int i = 0; i < 10; ++i) System.out.println(rand.next());

To test different LCGs, you might do the following:

long iters = 100_000; long seed = System.currentTimeMillis(); Random[] lcgs = new Random[] { new Random(48271, 0, (2L << 31) - 1, seed), // MINSTD (updated) new Random(16807, 0, (2L << 31) - 1, seed), // MINSTD (old) new Random(65539, 0, (2L << 31), seed) // RANDU }; for (Random lcg : lcgs) { System.out.println(lcg.doubles().limit(iters).summaryStatistics()); } // for

Finding the k-th smallest (or largest) element of an unordered array is a problem that's been approached by many programmers and computer scientists. There are many methods for solving this problem. To me, one of the more interesting implementations is a purely tail recursive implementation that uses the partition algorithm.

A purely tail recursive function or method is one in which there are no deferred operations. A deferred operation in this case, is one that must wait until a recursive call returns before it can complete. This article goes into this a little detail about the differences between "ordinary" and "pure" tail recursive methods.

Given a function that can swap two elements of an array and the partition function, it is possible to find the k-th smallest element of an array of distinct integers using the following purely tail recursive implementation (the accumulator parameters act in a fashion that is similar to a binary search):

private static int kthMin(int[] a,intleft,intright,intk) {intnewPivot =partition(a, left, right, k - 1); if (newPivot == k - 1)returna[k - 1]; if (newPivot < k - 1) left = newPivot + 1; if (newPivot > k - 1) right = newPivot - 1; returnkthMin(a, left, right, k); } // kthMin

If you have any questions, then please post them in the comments.