#!/usr/bin/perl 
use strict;
use warnings;
# Script created for calculating e.
# Uses the Euler series.         
# e = infinite sum 0 to infinity  1/n!
#
#  e = 1 + 1/1! + 1/2! + 1/3! ...
#
#
# Author: Victor Odlivak August 3, 2007
#
# input:  an integer stating number of iterations desired for
# converging e series.
#
# output:  Approximation for  e to desired number of iterations of
# series. 
#
#  usage   perlR_e i
#  where   i is an integer between 1 and 10000.
# 
sub calc_e {
my ($numIterations)  = @_ ;# number of iterations of loop to
# calculate e. 
my $numerator = 1;
my $denominator = 1;# starting value, this will increment
my $calculatedVal = 1;# starting value for zeroth cycle.
# Note the  e to the zero power the first term is
#  equal to 1. Anything to the zero power is 1. Also zero! is by
#  definition 1.
my $j = 0;
# Number of iterations for loop to calculate e 
for  ($j = 0; $j < $numIterations; $j++) {
$calculatedVal +=  $numerator/(factorial($denominator));
# print "$calculatedVal is current value for iteration $j \n";
$denominator++;
# The denominator is incremented by one and we take the factorial.
}
return $calculatedVal;
}
sub factorial{
# input value to be factoralized and return it.
# It took me over three hours to figure this alorightm out!
# Note, this is a non recursive algorithm!
# 
my ($input_val) = @_;
my $result = 1;# This is the case for 0! or 1!
while ($input_val > 1)
# notice the DOUBLE Decrementation here. This is the
# gist of it. At first I did it without this and I kept
# getting factorials that were way too big.
#
#  Enjoy!!
#
# You start off with $result of 1. Then you walk the array,
# i.e.  Factorial(n) =  n* (n-1) * (n-2) .... 
# i.e. for Factorial(6)
#  $result = 1 * 6 * 5  
#  $result = 30 * 4 * 3
#  $result = 360  * 2
#  $result = 720  (done for loop with four iterations
#
    {
     $result = $result * $input_val * (--$input_val);
     --$input_val;
     
}
   return $result;
}


# Main Program Section

 my $num_cycles = shift(@ARGV);
 unless($num_cycles) {
 print " Sorry, you forgot to enter an iteration number for the ";
 print " e series.   \n\n usage:  perl_e i \n\n"; 
 print " where i is an integer between 1 and 1,000\n\n";
 exit;
 }
 if (($num_cycles > 1000) or ($num_cycles < 1)) {
 print " Sorry, you entered  an iteration number out of range";
 print " for the e series.   \n\n usage:  perl_e i \n\n"; 
 print " where i is an integer between 1 and 1,000\n\n";
 exit;
 }
 
my $approx_e = 0;

$approx_e = calc_e  ($num_cycles);
print "The calculated value of e  with $num_cycles";
print " cycles of the calculation loop is: \n";
print " $approx_e \n";
print " Note, the calculation loop starts at the zeroth cycle ";
print " which has a value of 1. \n";