Re: Estimation of π using Leibniz series

[wiffel]

@alfrednewman

I tried to replicate your test. On my computer the following (slightly modified 
version) of the _nim_ program and the _julia_ program have the same runtime.

Whatever I do, I fail to run the _julia_ version in less than 2 seconds (as you 
had). Are you sure that test went OK?
    
    
    import times, math
    
    proc `/`(a, b: int): float =
      float(a) / float(b)
    
    proc leibniz(terms: int): float =
      for i in 0..terms:
        result += (-1)^i / (2*i+1)
      result *= 4.0
    
    let
      t0 = cpuTime()
      pi = leibniz(100_000_000)
      tt = cpuTime() - t0
    echo("Elapsed time: ", tt)
    echo("Pi: ", pi)
    

gives
    
    
    >> nim c -d:release pi.nim
    >> time ./pi
    Elapsed time: 5.671875
    Pi: 3.141592663589326
    
    real    0m5.706s
    user    0m5.672s
    sys     0m0.000s
    

and
    
    
    function leibniz(terms)
      res = 0.0
      for i in 0:terms
        res += (-1.0)^i/(2.0*i+1.0)
      end
      return res * 4.0
    end
    
    println("Pi: ", @time leibniz(100_000_000))
    

gives
    
    
    >> time julia pi.jl
      5.770856 seconds (4.48 k allocations: 226.962 KB)
    Pi: 3.141592663589326
    
    real    0m6.538s
    user    0m6.594s
    sys     0m0.234s