Private Sub cmdcalculate_Click()
Dim x(100), y(100), yprime(100), step
Call getarray(x, y, yprime, length, step)
Call derivative(x, y, yprime, length, step)
Call writearray(x, y, yprime, length) 'used just to test if derivate sub is working
xval = Val(txtx.Text)
j = 0
For i = 0 To length - 1
    If xval = x(i) Then
    lbloutputyprime.Caption = Format(yprime(i), "0.0000")
    lbloutputy.Caption = Format(y(i), "0.0000")
    End If
    j = j + 1
Next i
If j = length Then Call interpolate(x, y, yprime, length, step, xval)
End Sub
Private Sub cmdquit_Click()
End
End Sub
Sub getarray(x, y, yprime, length, step)
CommonDialog1.ShowOpen
file = CommonDialog1.FileName
Open file For Input As #1
length = 0
    Do While Not EOF(1)
        Input #1, x(length), y(length)
        length = length + 1
    Loop
step = (x(length - 1) - x(0)) / (length - 1)
Close #1
End Sub

Sub derivative(x, y, yprime, length, step)
For i = 0 To length - 1
    If i < 2 Then
        yprime(i) = (-y(i + 2) + 4 * y(i + 1) - 3 * y(i)) / (2 * step)
    ElseIf i > 1 And i < (length - 2) Then
        yprime(i) = (-y(i + 2) + 8 * y(i + 1) - 8 * y(i - 1) + y(i - 2)) / (12 * step)
    ElseIf i > (length - 3) Then
    yprime(i) = (3 * y(i) - 4 * y(i - 1) + y(i - 2)) / (2 * step)
    End If
Next i
End Sub
Sub interpolate(x, y, yprime, length, step, xval)
For i = 0 To length - 3
    If xval > x(i) And xval < x(i + 1) Then
        p = (xval - x(i)) / step
        yinterpolate = y(i) + p * (y(i + 1) - y(i)) + (p * (p - 1) / 2) * (y(i + 2) - 2 * y(i + 1) + y(i))
        yprimeinterpolate = yprime(i) + p * (yprime(i + 1) - yprime(i)) + (p * (p - 1) / 2) * (yprime(i + 2) - 2 * yprime(i + 1) + yprime(i))
        lbloutputyprime.Caption = Format(yprimeinterpolate, "0.0000")
        lbloutputy.Caption = Format(yinterpolate, "0.0000")
        End If
Next i

For i = length - 2 To length - 1
    If xval > x(i) And xval < x(i + 1) Then
        p = (xval - x(i)) / step
        yinterpolate = y(i) + p * (y(i) - y(i - 1)) + (p * (p + 1) / 2) * (y(i) - 2 * y(i - 1) + y(i - 2))
        yprimeinterpolate = yprime(i) + p * (yprime(i) - yprime(i - 1)) + (p * (p + 1) / 2) * (yprime(i) - 2 * yprime(i - 1) + yprime(i - 2))
        lbloutputyprime.Caption = Format(yprimeinterpolate, "0.0000")
        lbloutputy.Caption = Format(yinterpolate, "0.0000")
        End If
Next i

End Sub

Sub writearray(x, y, yprime, length)
CommonDialog1.ShowSave
file = CommonDialog1.FileName
Open file For Output As #1
For i = 0 To length - 1
    Print #1, x(i), y(i), yprime(i)
Next i
Close #1
End Sub