Digits of e calculation
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| <DPL>
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[edit] Implementations
[edit] C++
double e(int n)
{
int fact = 1;
double sum = 0;
for (int i = 1; i <= n; i++) {
sum += 1. / fact;
fact *= i;
}
return sum;
}
[edit] Common Lisp
Implements the above algorithm (which is in PHP) in Common Lisp
;;; Note that we already have the very first iteration (n = 0 in PHP code)
;;; calculated (result = 1), so we'll return a more accurate result on a
;;; same accuracy request.
(defun e (accuracy)
(let ((lastfactorial 1)
(result 1))
(dotimes (i accuracy)
(progn
(incf result (/ 1 lastfactorial))
(setf lastfactorial (* lastfactorial (+ i 2)))))
(return-from e result)))
;;; Usage:
* (e 10)
13563139/4989600
* (float * 1.0L0) ;; Use Long float.
2.7182818261984928651L0
[edit] OCaml
# let rec e ?(fact=1) ?(i=1) = function
| 0 -> 0.
| n -> 1. /. float fact +. e ~fact:(i*fact) ~i:(i+1) (n-1);;
val e : ?fact:int -> ?i:int -> int -> float = <fun>
For example:
# e 10;; - : float = 2.71828152557319225
[edit] PHP
Uses the formula: e = 1/0! + 1/1! + 1/2! + 1/3! + 1/4! + ... 1/N!
<?PHP
/*
Example usage:
echo number_format(e(15),20,'.','')
*/
function factorial($num) {
if ($num >= 0) {
$factorial = 1;
for($i=0;$i<$num;$i++) {
$factorial *= $num - $i;
}
return $factorial;
}
}
function e($accuracy) {
for($n=0;$n<$accuracy;$n++) {
$total += 1 / factorial($n);
}
return $total;
}
?>
[edit] Ruby
def e(n)
sum = 0.0
fact = 1
for i in 1..n
sum += 1.0 / fact
fact *= i
end
sum
end
