Digit generator for the base of the natural logarithms

by Stephen R. Schmitt

Definition

The constant irrational number e is one of the most important constants in mathematics. It is the base number for natural logarithms. It has the property that the area under the hyperbola y = 1/x from x = 1...e equals 1.

The sample program, below, uses a spigot algorithm to compute the first 10,000 digits. A spigot algorithm yields its outputs incrementally, and does not reuse them after producing them.

Zeno source code

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var   A : array[3302] of int
const B : int := 3301

program

    var f, i, j, k, n : int

    % assign each element of array 1
    for i := 1...B do
        A[i] := 1
    end for
    % except this element
    A[3301] := 2    

    % initialize counters
    i := 0
    j := 2001
    f := 0
    put i:5, ":  "...           % total digits thus far

    while j > 0

        decr j
        k := 1
        n := B

        while n > 0
            f    := f + A[k]*100000
            A[k] := f mod n
            f    := f div n
            incr k
            decr n
        end while

        put_five( f )           % group of five digits

        if j mod 10 = 1 then    % start a new line
            i := i + 50
            put ""
            put i:5, ":   "...  % total digits thus far
        end if

    end while
    
end program

procedure put_five( n : int )

    var s : string := intstr( n, 0 )
    var z : int := 5 - strlen( s )

    while z > 0
        put "0"...
        decr z
    end while
    put s, " "...

end procedure

Sample output

    0:  271828 18284 59045 23536 02874 71352 66249 77572 47093 69995  
   50:   95749 66967 62772 40766 30353 54759 45713 82178 52516 64274  
  100:   27466 39193 20030 59921 81741 35966 29043 57290 03342 95260  
  150:   59563 07381 32328 62794 34907 63233 82988 07531 95251 01901  
  200:   15738 34187 93070 21540 89149 93488 41675 09244 76146 06680

Reference

1. Mathworld: e
2. Numbers, constants and computation