unit Unit2;

interface
uses
  Windows, Messages, SysUtils, Classes, Graphics, Controls, Forms, Dialogs;
procedure RATINT(XA, YA: array of real; N:integer; X:REAL; VAR Y, DY:real);

implementation
procedure RATINT(XA, YA: array of real; N:integer; X:REAL; VAR Y, DY:real);
const
    TINY=1E-25;
var
    C,D:array[0..10] of real;
    I,NS,M:integer;
    HH,H,DD,DX,W,T:real;
begin
    NS:=1;
    HH:=Abs(X - XA[1]);
    For I:=1 To N  do
    begin
        H:=Abs(X - XA[I]);
        If H = 0 Then
        begin
            Y:=YA[I];
            DY:=0;
            Exit;
        end
        Else If H < HH Then
        begin
            NS:=I;
            HH:=H;
        end;
        C[I]:=YA[I];
        D[I]:=YA[I] + TINY;
    end;
    Y:=YA[NS];
    NS:=NS - 1;
    For M:=1 To N - 1 do
    begin
        For I:=1 To N - M do
        begin
            W:=C[I + 1] - D[I];
            H:=XA[I + M] - X;
            T:=(XA[I] - X) * D[I] / H;
            DD:=T - C[I + 1];
            If DD = 0 Then
            begin
                ShowMessage('PAUSE');
                Exit;
            end;
            DD:=W / DD;
            D[I]:=C[I + 1] * DD;
            C[I]:=T * DD;
        end;
        If 2 * NS < N - M Then
            DY:=C[NS + 1]
        Else
        begin
            DY:=D[NS];
            NS:=NS - 1;
        end;
        Y:=Y + DY;
    end;
end;
end.