Arithmosophi alternatives and similar libraries
Based on the "Math" category.
Alternatively, view Arithmosophi alternatives based on common mentions on social networks and blogs.

VectorMath
A Swift library for Mac and iOS that implements common 2D and 3D vector and matrix functions, useful for games or vectorbased graphics 
SwiftMath
DISCONTINUED. 📐 A math framework for Swift. Includes: vectors, matrices, complex numbers, quaternions and polynomials. 
SwiftMathEagle
A general math framework to make using math easy. Currently supports function solving and optimisation, matrix and vector algebra, complex numbers, big int, big frac, big rational, graphs and general handy extensions and functions.
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README
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](Sources/Arithmosophi.swift)
Contents
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](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](Sources/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](Sources/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
.swift [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
.swift [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
.swift [1, 11, 19, 4, 12, 7].medianHigh // 11
Variance
with [Sigma.swift](Sources/Sigma.swift)
Computes variance.
 The sample variance: Σ( (Element  average)^{2} ) / (count  1)
[1.0, 11, 19.5, 4, 12, 7].varianceSample
 The population variance: Σ( (Element  average)^{2} ) / count
[1.0, 11, 19.5, 4, 12, 7].variancePopulation
Standard deviation
with [Sigma.swift](Sources/Sigma.swift)
Computes standard deviation.
 sample based
swift [1.0, 11, 19.5, 4, 12, 7].standardDeviationSample
 population based
swift [[1.0, 11, 19.5, 4, 12, 7].standardDeviationPopulation
Skewness
with [Sigma.swift](Sources/Sigma.swift)
Computes skewness.
[1.0, 11, 19.5, 4, 12, 7].skewness // or .moment.skewness
Kurtosis
with [Sigma.swift](Sources/Sigma.swift)
Computes kurtosis.
[1.0, 11, 19.5, 4, 12, 7].kurtosis // or .moment.kurtosis
Covariance
with [Sigma.swift](Sources/Sigma.swift)
Computes covariance with another CollectionType
 sample covariance
swift [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])
Pearson productmoment correlation coefficient
[1, 2, 3.5, 3.7, 8, 12].pearson([0.5, 1, 2.1, 3.4, 3.4, 4])
Complex
with [Complex.swift](Sources/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) {
box.value = box.value + addend
}
func =<T where T:Substractable> (inout box: Box<T>, addend: T) {
box.value = box.value  addend
}
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](Samples/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?
}
func +=<T where T:Addable, T:Initializable> (inout box: Box<T>, addend: T) {
box.value = (box.value ?? T()) + addend
}
Logical operations
[LogicalOperationsType
](Sources/LogicalOperationsType.swift) 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](Samples/Boolean.swift) 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](Samples/Optional.swift) which implement also LogicalOperationsType
Geometry
with Arithmos
(number) & Statheros
(constant)
[Arithmos
](Sources/Arithmos.swift) and [Statheros
](Sources/Statheros.swift) 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](Samples/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'
Using xcode
Drag files to your projects
*Note that all licence references and agreements mentioned in the Arithmosophi README section above
are relevant to that project's source code only.