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Calculating Pi to arbitrary number of digits

The code calculates the value of Pi to arbitrary number of digits such as 100, 1000 etc. The article describes the theory behind the code.

Enumerable Interleave Extension Method

A recent stackoverflow question, which I didn’t bookmark and now I’m unable to find, inspired me to implement an extension method for Enumerable that allows to insert a constant element between each pair of elements in a sequence. Kind of what String.Join does for strings, but maintaining an enumerable as the return value. Having done the single element part I got a bit carried away and ended up expanding it adding overloads to support interleaving elements of another sequence and support for a predicate to control when interleaving takes place. I have to confess that I did this for fun and now I can’t think of any real usage scenario, nonetheless, it may prove useful for someone. First a simple example: var target = new string[] { "(", ")", "(", ")" }; var result = target.Interleave(".", (f, s) => f == "("); // Prints: (.)(.) Console.WriteLine(String.Join(string.Empty, result)); And now the untested but documented implementation: using System; using System.Collections; using System.Collections.Generic; using System.Linq; public static class EnumerableExtensions { /// <summary> /// Iterates infinitely over a constant element. /// </summary> /// <typeparam name="T"> /// The type of element in the sequence. /// </typeparam> private class InfiniteSequence<T> : IEnumerable<T>, IEnumerator<T> { public InfiniteSequence(T element) { this.Element = element; } public T Element { get; private set; } public IEnumerator<T> GetEnumerator() { return this; } IEnumerator IEnumerable.GetEnumerator() { return this; } T IEnumerator<T>.Current { get { return this.Element; } } void IDisposable.Dispose() { } object IEnumerator.Current { get { return this.Element; } } bool IEnumerator.MoveNext() { return true; } void IEnumerator.Reset() { } } /// <summary> /// Interleaves the specified <paramref name="element"/> between each pair of elements in the <paramref name="target"/> sequence. /// </summary> /// <typeparam name="T"> /// The type of elements in the sequence. /// </typeparam> /// <param name="target"> /// The target sequence to be interleaved. /// </param> /// <param name="element"> /// The element used to perform the interleave operation. /// </param> /// <exception cref="ArgumentNullException"> /// <paramref name="target"/> or <paramref name="element"/> is a null reference. /// </exception> /// <returns> /// The <paramref name="target"/> sequence interleaved with the specified <paramref name="element"/>. /// </returns> public static IEnumerable<T> Interleave<T>( this IEnumerable<T> target, T element) { if (target == null) throw new ArgumentNullException("target"); if (element == null) throw new ArgumentNullException("element"); return InterleaveInternal(target, new InfiniteSequence<T>(element), (f, s) => true); } /// <summary> /// Interleaves the specified <paramref name="element"/> between each pair of elements in the <paramref name="target"/> sequence. /// </summary> /// <remarks> /// The interleave operation is interrupted as soon as the <paramref name="target"/> sequence is exhausted; If the number of <paramref name="elements"/> to be interleaved are not enough to completely interleave the <paramref name="target"/> sequence then the remainder of the sequence is returned without being interleaved. /// </remarks> /// <typeparam name="T"> /// The type of elements in the sequence. /// </typeparam> /// <param name="target"> /// The target sequence to be interleaved. /// </param> /// <param name="elements"> /// The elements used to perform the interleave operation. /// </param> /// <exception cref="ArgumentNullException"> /// <paramref name="target"/> or <paramref name="element"/> is a null reference. /// </exception> /// <returns> /// The <paramref name="target"/> sequence interleaved with the specified <paramref name="elements"/>. /// </returns> public static IEnumerable<T> Interleave<T>( this IEnumerable<T> target, IEnumerable<T> elements) { if (target == null) throw new ArgumentNullException("target"); if (elements == null) throw new ArgumentNullException("elements"); return InterleaveInternal(target, elements, (f, s) => true); } /// <summary> /// Interleaves the specified <paramref name="element"/> between each pair of elements in the <paramref name="target"/> sequence that satisfy <paramref name="predicate"/>. /// </summary> /// <typeparam name="T"> /// The type of elements in the sequence. /// </typeparam> /// <param name="target"> /// The target sequence to be interleaved. /// </param> /// <param name="element"> /// The element used to perform the interleave operation. /// </param> /// <param name="predicate"> /// A predicate used to assert if interleaving should occur between two target elements. /// </param> /// <exception cref="ArgumentNullException"> /// <paramref name="target"/> or <paramref name="element"/> or <paramref name="predicate"/> is a null reference. /// </exception> /// <returns> /// The <paramref name="target"/> sequence interleaved with the specified <paramref name="element"/>. /// </returns> public static IEnumerable<T> Interleave<T>( this IEnumerable<T> target, T element, Func<T, T, bool> predicate) { if (target == null) throw new ArgumentNullException("target"); if (element == null) throw new ArgumentNullException("element"); if (predicate == null) throw new ArgumentNullException("predicate"); return InterleaveInternal(target, new InfiniteSequence<T>(element), predicate); } /// <summary> /// Interleaves the specified <paramref name="element"/> between each pair of elements in the <paramref name="target"/> sequence that satisfy <paramref name="predicate"/>. /// </summary> /// <remarks> /// The interleave operation is interrupted as soon as the <paramref name="target"/> sequence is exhausted; If the number of <paramref name="elements"/> to be interleaved are not enough to completely interleave the <paramref name="target"/> sequence then the remainder of the sequence is returned without being interleaved. /// </remarks> /// <typeparam name="T"> /// The type of elements in the sequence. /// </typeparam> /// <param name="target"> /// The target sequence to be interleaved. /// </param> /// <param name="elements"> /// The elements used to perform the interleave operation. /// </param> /// <param name="predicate"> /// A predicate used to assert if interleaving should occur between two target elements. /// </param> /// <exception cref="ArgumentNullException"> /// <paramref name="target"/> or <paramref name="element"/> or <paramref name="predicate"/> is a null reference. /// </exception> /// <returns> /// The <paramref name="target"/> sequence interleaved with the specified <paramref name="elements"/>. /// </returns> public static IEnumerable<T> Interleave<T>( this IEnumerable<T> target, IEnumerable<T> elements, Func<T, T, bool> predicate) { if (target == null) throw new ArgumentNullException("target"); if (elements == null) throw new ArgumentNullException("elements"); if (predicate == null) throw new ArgumentNullException("predicate"); return InterleaveInternal(target, elements, predicate); } private static IEnumerable<T> InterleaveInternal<T>( this IEnumerable<T> target, IEnumerable<T> elements, Func<T, T, bool> predicate) { var targetEnumerator = target.GetEnumerator(); if (targetEnumerator.MoveNext()) { var elementsEnumerator = elements.GetEnumerator(); while (true) { T first = targetEnumerator.Current; yield return first; if (!targetEnumerator.MoveNext()) yield break; T second = targetEnumerator.Current; bool interleave = true && predicate(first, second) && elementsEnumerator.MoveNext(); if (interleave) yield return elementsEnumerator.Current; } } } }

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