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# Arithmosophi - Arithmosoϕ Arithmosophi is a set of missing protocols that simplify arithmetic and statistics on generic objects or functions. As `Equatable` define the `==` operator , `Addable` will define the `+` operator.

``````protocol Addable {
func + (lhs: Self, rhs: Self) -> Self
}
[1, 2, 3, 4].sum //  1 + 2 + 3 + 4
[0, 1, 2, 3, 4].average // 2
[13, 2.4, 3, 4].varianceSample
``````
• As you might guess `Substractable` define `-` operator, `Multiplicatable` define `*` operator, etc..., all defined in Arithmosophi.swift

## Generic functions

Take a look at `sumOf` function

``````func sumOf<T where T:Addable, T:Initializable>(input : [T]) -> T {
return reduce(input, T()) {\$0 + \$1}
}
``````

Array of `Int`, `Double` and even `String` could be passed as argument to this function. Any `Addable` objects.

No need to implement a function for `Double`, one for `Float`, one more for `Int`, etc...

`sumOf` and `productOf` functions are available in Arithmosophi.swift

## CollectionType

This framework contains some useful extensions on `CollectionType`

``````[1, 2, 3, 4].sum //  1 + 2 + 3 + 4
[1, 2, 3, 4].product //  1 * 2 * 3 * 4

["a","b","c","d"].sum // "abcd" same as joinWithSeparator("")
[["a","b"],["c"],["d"]].sum // ["a","b","c","d"] same as flatMap{\$0}
``````

### Average

with MesosOros.swift

Computes arithmetic average/mean

``````[1, 2, 3, 4].average //  (1 + 2 + 3 + 4) / 4
``````

A type is `Averagable` if it can be dividable by an `Int` and define an operator to do that

``````func /(lhs: Self, rhs: Int) -> Self
``````

All arithmetic type conform to this protocol and you can get an average for a `CollectionType`

P.S. You can conform to this protocol and `Addable` to make a custom average.

### Median

with MesosOros.swift

Get the median value from the array

• Returns the average of the two middle values if there is an even number of elements in the `CollectionType`.
``````[1, 11, 19, 4, -7].median // 4
``````
• Returns the lower of the two middle values if there is an even number of elements in the `CollectionType`.
``````[1.0, 11, 19.5, 4, 12, -7].medianLow // 4
``````
• Returns the higher of the two middle values if there is an even number of elements in the `CollectionType`.
``````[1, 11, 19, 4, 12, -7].medianHigh // 11
``````

### Variance

with Sigma.swift

Computes variance.

``````[1.0, 11, 19.5, 4, 12, -7].varianceSample
``````
``````[1.0, 11, 19.5, 4, 12, -7].variancePopulation
``````

### Standard deviation

with Sigma.swift

Computes standard deviation.

``````[1.0, 11, 19.5, 4, 12, -7].standardDeviationSample
``````
``````[[1.0, 11, 19.5, 4, 12, -7].standardDeviationPopulation
``````

### Skewness

with Sigma.swift

Computes skewness.

``````[1.0, 11, 19.5, 4, 12, -7].skewness // or .moment.skewness
``````

### Kurtosis

with Sigma.swift

Computes kurtosis.

``````[1.0, 11, 19.5, 4, 12, -7].kurtosis // or .moment.kurtosis
``````

### Covariance

with Sigma.swift

Computes covariance with another `CollectionType`

``````[1, 2, 3.5, 3.7, 8, 12].covarianceSample([0.5, 1, 2.1, 3.4, 3.4, 4])
``````
• population covariance
``````[1, 2, 3.5, 3.7, 8, 12].covariancePopulation([0.5, 1, 2.1, 3.4, 3.4, 4])
``````
``````[1, 2, 3.5, 3.7, 8, 12].pearson([0.5, 1, 2.1, 3.4, 3.4, 4])
``````

## Complex

with Complex.swift `Complex` is a struct of two `ArithmeticType`, the real and the imaginary component

``````var complex = Complex(real: 12, imaginary: 9)
complex = 12 + 9.i
``````

You can apply operation on it `(+, -, *, /, ++, --, -)`

``````result = complex + 8 // Complex(real: 20, imaginary: 9)

Complex(real: 12, imaginary: 9) + Complex(real: 8, imaginary: 1)
// Complex(real: 20, imaginary: 10)
``````

## Object attributes

The power of this simple arithmetic protocols are released when using operators

If we implement a box object containing a generic `T` value

``````class Box<T> {
var value: T
}
``````

we can define some operators on it, in a generic way, like we can do with `Equatable` or `Comparable`

``````func +=<T where T:Addable> (inout box: Box<T>, addend: T) {
}
func -=<T where T:Substractable> (inout box: Box<T>, addend: T) {
}
``````

how to use this operator:

``````var myInt: Box<Int>(5)
myInt += 37
``````

For a full example, see Prephirence file from Prephirences framework, or sample Box.swift

### Optional trick

For optional attribute you can use `Initializable` or any protocol which define a way to get a value

``````class Box<T> {
var value: T?
}
box.value = (box.value ?? T()) + addend
}
``````

## Logical operations

`LogicalOperationsType` is a missing protocol for `Bool` inspired from `BitwiseOperationsType` (or `IntegerArithmeticType`)

The purpose is the same, implement functions without knowing the base type

You can for instance implement your own `Boolean` enum and implement the protocol

``````enum Boolean: LogicalOperationsType {case True, False}
func && (left: Boolean, @autoclosure right:  () -> Boolean) -> Boolean {
switch left {
case .False: return .False
case .True:  return right()
}
}
...
``````

then create only one operator on `Box` for `Bool`, `Boolean` and any `LogicalOperationsType`

``````func &&=<T:LogicalOperationsType> (inout box: Box<T>, @autoclosure right:  () -> TT) {
box.value = box.value && right()
}
``````

Take a look at a more complex enum Optional which implement also `LogicalOperationsType`

## Geometry

with `Arithmos`(number) & `Statheros`(constant)

`Arithmos` and `Statheros` add respectively functions and mathematical constants for `Double`, `Float` and `CGFloat`, allowing to implement generic functions without taking care of type

``````func distance<T: Arithmos>(#x: T, y: T) -> T {
return x.hypot(y)
}

func radiansFromDegrees<T where T: Multiplicable, Dividable, T: Arithmos, T: Statheros>(degrees: T) -> T {
return degrees * T.PI / T(180.0)
}
``````

Take a look at Geometry.swift for more examples

## Setup

### Using cocoapods

``````pod 'Arithmosophi'
``````

Not interested in full framework ? install a subset with:

``````pod 'Arithmosophi/Core' # Arithmosophi.swift
pod 'Arithmosophi/Logical' # LogicalOperationsType.swift
pod 'Arithmosophi/Complex' # Complex.swift
pod 'Arithmosophi/MesosOros' # MesosOros.swift
pod 'Arithmosophi/Arithmos' # Arithmos.swift
pod 'Arithmosophi/Sigma' # Sigma.swift
pod 'Arithmosophi/Statheros' # Statheros.swift

pod 'Arithmosophi/Samples' # Samples/*.swift (not installed by default)
``````

Add `use_frameworks!` to the end of the `Podfile`.

#### Make your own framework dependent

In podspec file

``````s.dependency 'Arithmosophi'
``````

or define only wanted targets

``````s.dependency 'Arithmosophi/Core'
s.dependency 'Arithmosophi/Logical'
``````

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