SigmaComparisons.swift

//: Playground - noun: a place where people can play

import UIKit

struct FloatRange {
    var minimum: Double;
    var maximum: Double;
}

var floatRange = FloatRange(minimum: 0.9999, maximum: 1.0001);

func == (lhs: Double, rhs: FloatRange) -> Bool {
    return (lhs >= rhs.minimum && lhs <= rhs.maximum);
}

func == (rhs: FloatRange, lhs: Double) -> Bool {
    return lhs == rhs;
}

func == (lhs: Int, rhs: FloatRange) -> Bool {
    return Double(lhs) == rhs;
}

func == (rhs: FloatRange, lhs: Int) -> Bool {
    return lhs == rhs;
}

func == (lhs: Float, rhs: FloatRange) -> Bool {
    return Double(lhs) == rhs;
}

func == (rhs: FloatRange, lhs: Float) -> Bool {
    return lhs == rhs;
}

var a: Float = 1.000;
var b = 1.001
var c = 1

a == floatRange
b == floatRange
c == floatRange

infix operator +-: RangeFormationPrecedence
func +- (lhs: Double, rhs: Double) -> FloatRange {
    return FloatRange(minimum: lhs - rhs, maximum: lhs + rhs);
}

func +- (lhs: Int, rhs: Double) -> FloatRange {
    return Double(lhs) +- rhs;
}

func +- (lhs: Int, rhs: Float) -> FloatRange {
    return Double(lhs) +- Double(rhs);
}

func +- (lhs: Float, rhs: Double) -> FloatRange {
    return Double(lhs) +- rhs;
}

func +- (lhs: Float, rhs: Float) -> FloatRange {
    return Double(lhs) +- Double(rhs);
}

func +- (lhs: Double, rhs: Float) -> FloatRange {
    return lhs +- Double(rhs);
}

infix operator ±: RangeFormationPrecedence
func ± (lhs: Double, rhs: Double) -> FloatRange {
    return lhs ± rhs;
}

func ± (lhs: Int, rhs: Double) -> FloatRange {
    return lhs ± rhs;
}

func ± (lhs: Int, rhs: Float) -> FloatRange {
    return lhs ± rhs;
}

func ± (lhs: Float, rhs: Double) -> FloatRange {
    return lhs ± rhs;
}

func ± (lhs: Float, rhs: Float) -> FloatRange {
    return lhs ± rhs;
}

func ± (lhs: Double, rhs: Float) -> FloatRange {
    return lhs ± rhs;
}

b == 1 +- 0.01 // true
b == 1 +- 0.001 // true
b == 1 +- 0.0001 // false
b == 1 +- 0.00001 // false

b == 1 +- 0 + 0.001 // true
b == 1 +- 0 + 0.0001 // false

b == 1 +- 1*0.001 // true
b == 1 +- 1*0.0001 // false