Python vs. PyPy vs. Julia comparison - Factorials & Looping

python-pypy-julia.py

#Python/pypy
import math
def smallestdivisall(n):
    for i in xrange(1, math.factorial(n)+1):
        for j in xrange(1, n+1):
            if i % j != 0:
                break
            elif j == n:
                return i
                

#IPython timer
In [1]: %time smallestdivisall(20)
    
#Python w/ Numba @autojit
import math
from numba import autojit

@autojit
def smallestdivisall(n):
    for i in xrange(1, math.factorial(n)+1):
        for j in xrange(1, n+1):
            if i % j != 0:
                break
            elif j == n:
                return i

#IPython timer
In [1]: %time smallestdivisall(20)

#Julia, 2nd run to remove compilation time
function smallestdivisall(n::Int64)
    for i = 1:factorial(n)
        for j = 1:n
            if i % j !=0
                break
            elseif j == n
                return i
            end
        end
    end
end

#Julia time macro
julia> @time smallestdivisall(20)

#R
smallestdivisall <- function(n){
  require("iterators") #Need because large values for n don't fit in vector, so use iterator
  
  m <- icount(factorial(n))
  i <- nextElem(m)
  
  while(i < factorial(n)) {
    for (j in 1:n) {
      if (i %% j != 0) {
        break
      } else if (j == n) {
        return(i)
      }
    }
    i <- nextElem(m)
  }
}

#R timer
system.time(smallestdivisall(20))


#Compile function to see speed up
library(compiler)
enableJIT(1)
smallestdivisall_c <- cmpfun(smallestdivisall)

#R timer
system.time(smallestdivisall_c(20))

What values of n are you using in the Julia code? factorial(n) overflows very quickly.

The Julia function is only valid at n < 21 to avoid overflow, which is why my graphs are from 4 < n < 21