Indexed Summations in Swift (∑)

README.md

Sum

Perform generic indexed summations in Swift (sigma notation).

Usage

Here is an example showing the summation of exponential terms (all terms to the power of 2) from 3 to 6:

Translates to:

let squares: Double = sum(startIndex: 3, endIndex: 6) { i in 
  return pow(i, 2)
}
// squares = 3^2 + 4^2 + 5^2 + 6^2 = 86

License

The MIT License (MIT) Copyright (c) 2016 ALEXIS AUBRY RADANOVIC

Permission is hereby granted, free of charge, to any person obtaining a copy of this software and associated documentation files (the "Software"), to deal in the Software without restriction, including without limitation the rights to use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of the Software, and to permit persons to whom the Software is furnished to do so, subject to the following conditions:

The above copyright notice and this permission notice shall be included in all copies or substantial portions of the Software.

THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.

IndexedSum.swift

/*
 * ==---------------------------------------------------------------------------------==
 *
 *  File            :   IndexedSum.swift
 *  Author          :   ALEXIS AUBRY RADANOVIC
 *
 *  License         :   The MIT License (MIT)
 *
 * ==---------------------------------------------------------------------------------==
 *
 *    The MIT License (MIT)
 *    Copyright (c) 2016 ALEXIS AUBRY RADANOVIC
 *
 *    Permission is hereby granted, free of charge, to any person obtaining a copy of
 *    this software and associated documentation files (the "Software"), to deal in
 *    the Software without restriction, including without limitation the rights to
 *    use, copy, modify, merge, publish, distribute, sublicense, and/or sell copies of
 *    the Software, and to permit persons to whom the Software is furnished to do so,
 *    subject to the following conditions:
 *
 *    The above copyright notice and this permission notice shall be included in all
 *    copies or substantial portions of the Software.
 *
 *    THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
 *    IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY, FITNESS
 *    FOR A PARTICULAR PURPOSE AND NON-INFRINGEMENT. IN NO EVENT SHALL THE AUTHORS OR
 *    COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER LIABILITY, WHETHER
 *    IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM, OUT OF OR IN
 *    CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE SOFTWARE.
 *
 * ==---------------------------------------------------------------------------------==
 */

// MARK: - Protocols

/// A protocol for objects that can be constructed with a default value.
public protocol DefaultValueable {
    init()
}

/// A protocol for objects whose sum can be computed.
public protocol Addable {
    static func + (lhs: Self, rhs: Self) -> Self
}

/// A generic protocol for numbers.
public protocol Number: DefaultValueable, Addable {
    init(_ value: Int)
}

// MARK: - Extensions

extension Float: Number {}
extension Double: Number {}
extension Int: Number {}
extension Int8: Number {}
extension UInt8: Number {}
extension Int16: Number {}
extension UInt16: Number {}
extension Int32: Number {}
extension UInt32: Number {}
extension Int64: Number {}
extension UInt64: Number {}

extension Array where Element: Number {
    
    /// Computes the sum of every number stored in the array.
    public func sum() -> Element {
        return self.reduce(Element()) { $0 + $1 }
    }
    
}

// MARK: - Sum

///
/// Performs an indexed summation.
///
/// This function is equivalent to the [Capital-sigma notation](https://en.m.wikipedia.org/wiki/Summation#Capital-sigma_notation) for sums.
///
/// The index of summation, `i`, will be incremented by 1 for each successive term in startIndex...endIndex.
///
/// Example: computing the sum of the squares of numbers between 3 and 6.
///
/// ```
/// let squares: Double = sum(startIndex: 3, endIndex: 6) { i in 
///     return pow(i, 2) 
/// }
/// // squares = 3^2 + 4^2 + 5^2 + 6^2 = 86
/// ```
///
/// - parameter startIndex: The lower bound of summation.
/// - parameter endIndex: The upper bound of summation.
/// - parameter expression: The function mapping a summation index to a real number.
/// - parameter index: The current summation index.
///

func sum<T: Number>(startIndex: Int, endIndex: Int, expression: @escaping (_ index: T)->T) -> T {
    let summationIndexes = startIndex...endIndex
    return summationIndexes.map { expression( T($0) ) }.sum()
}