XProfan

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p.specht

one the first programs the world employed itself with the Berechnung the undertow. Bernoulli-numbers [...]

, The u.a. in höherdimensionalen Reihenformeln a large strain play. The Algorithmus stammt of 1843, a publication of Lady Ada Lovelace, the first Programmiererin the world, and was for first real (Turing-mighty) computer the world virtual, The "Analytical Engine" of charles Babbage (... unfortunately never completed).

Compile Mark Separation

Window Title "Die BERNOULLI-ZAHLEN To B_28 berechnen":Window Style 24:CLS
Set("decimals",17)
'*********************************************************************
'* Diese program computes Bernoulli number Bn using subroutine BERNOA *
'* ----------------------------------------------------------------- *
'* SAMPLE RUN:                                                       *
'*                                                                   *
'*  Compute Bernoulli number Bn for n = 0,1,...,10.                  *
'*                                                                   *
'*  Please enter Nmax: 10                                            *
'*                                                                   *
'*    n            Bn                                                *
'*  --------------------------                                       *
'*    0    0.100000000000D+01                                        *
'*    1   -0.500000000000D+00                                        *
'*    2    0.166666666667D+00                                        *
'*    4   -0.333333333333D-01                                        *
'*    6    0.238095238095D-01                                        *
'*    8   -0.333333333333D-01                                        *
'*   10    0.757575757576D-01                                        *
'*  --------------------------                                       *
'*                                                                   *
'* ----------------------------------------------------------------- *
'* REFERENCE: "Fortran Routines for Computation of Special Functions,*
'*             jin.ece.uiuc.edu/routines/routines.html".             *
'*                                 F90 Release By J-P Moreau, Paris. *
'*                                         (www.jpmoreau.fr)         *
'*                                                                   *
'* XProfan 11.2a-Version by P.woodpecker, Vienna/Austria                 *
'* No warranty whatsoever!                                           *
'*********************************************************************
'    PROGRAM MBERNOA
Declare B![200],n&,k&
Print
nochma:
Print "\n Please Nmax prompt: ";:Input N&

If n&>29:Print " To big!":goto "nochma":endif

    BERNOA(N&,B![])
    Print "\n  n            Bn    "
    Print "---------------------------"
    Print "  ";0,tab(11);stature$("%g",B![0])
    Print "  ";1,tab(11);stature$("%g",B![1])

    WhileLoop 2,N&,2:k&=&Loop

        Print "  ";k&,tab(11);stature$("%g",B![k&])

    EndWhile

    Print "---------------------------"
    WaitInput
    END

    Proc BERNOA :Parameters N&,BN![]

        ' ======================================
        '  Purpose: Compute Bernoulli number Bn
        '  Input :  n --- Serial number
        '  output:  BN(n) --- Bn
        ' ======================================
        '    IMPLICIT DOUBLE PRECISION (A-H,O-Z)
        Declare s!,R!,j&,k&,m&
        BN![0]=1
        BN![1]=-0.5

        WhileLoop 2,n&:m&=&Loop

            s!=-(1.0e0/(M&+1)-0.5)

            WhileLoop 2,M&-1:k&=&Loop

                R!=1

                WhileLoop 2,K&:j&=&Loop

                    R!=R!*(J&+M&-K&)/J&

                EndWhile

                s!=s!-R!*BN![K&]

            EndWhile

            BN![M&]=s!

        EndWhile

        WhileLoop 3,N&,2:m&=&Loop

            BN![M&]=0

        EndWhile

        Return

    ENDPROC

    ' end of file mbernoa.prf