Exponentiation in O(log n)

src/math/Math.jl

@@ -36,6 +36,7 @@ export combination
 export divisors
 export eratosthenes
 export euler_method
+export exp_logn
 export is_mersenne_prime
 export totient
 export factorial_iterative
@@ -101,6 +102,7 @@ include("combination.jl")
 include("divisors.jl")
 include("euler_method.jl")
 include("eulers_totient.jl")
+include("exp_logn.jl")
 include("factorial.jl")
 include("fibonacci.jl")
 include("floor.jl")

src/math/exp_logn.jl

@@ -0,0 +1,59 @@
+"""
+    exp_logn(x::Number, n::Int)
+
+Recursive function which calculates 'x' to the power of 'n' in O(log n) complexity.
+
+# Arguments:
+- `x` : Base
+- `n` : Exponent
+
+# Examples/Tests
+```julia
+exp_logn(0, 5)    # returns 0
+exp_logn(3.14, 0) # returns 1
+exp_logn(2, 5)    # returns 32
+exp_logn(2, -2)   # returns 0.25
+exp_logn(2, -5)   # returns 0.03125
+```
+
+# Implementation
+```julia
+function exp_logn(x::Number, n::Int)
+    if n == 0
+        return 1
+    elseif n < 0
+        return 1/exp_logn(x, -n)
+    else
+        tmp = exp_logn(x, div(n,2))
+
+        if n%2 == 0
+            # If n is even, x^n = x^(n/2) * x^(n/2)
+            return tmp * tmp
+        else
+            # else, x^n = x^(n/2) * x^(n/2) * x
+            return tmp * tmp * x
+        end
+    end
+end
+```
+
+Contributed by [Nikola Mircic](https://www.github.com/Nikola-Mircic)
+"""
+
+function exp_logn(x::Number, n::Int)
+    if n == 0
+        return 1
+    elseif n < 0
+        return 1/exp_logn(x, -n)
+    else
+        tmp = exp_logn(x, div(n,2))
+
+        if n%2 == 0
+            # If n is even, x^n = x^(n/2) * x^(n/2)
+            return tmp * tmp
+        else
+            # else, x^n = x^(n/2) * x^(n/2) * x
+            return tmp * tmp * x
+        end
+    end
+end

test/math.jl

@@ -239,6 +239,14 @@ using TheAlgorithms.Math
         @test_throws DomainError totient(-1)
     end
 
+    @testset "Math: Exponentiation in O(log n)" begin
+        @test exp_logn(0, 5)    == 0
+        @test exp_logn(3.14, 0) == 1
+        @test exp_logn(2, 5)    == 32
+        @test exp_logn(2, -2)   == 0.25
+        @test exp_logn(2, -5)   == 0.03125
+    end
+
     @testset "Math: Factorial Related" begin
         @test factorial_iterative(5) == 120
         @test factorial_iterative(0) == 1