program Project12;

{$APPTYPE CONSOLE}

{$R *.res}

uses
  System.SysUtils;

function Epsilon(LimitEps: Real): Real;
var
   Eps: Real;
   IsCorrect: Boolean;
begin
   Writeln('Enter the precision value:');
   Readln(Eps);
   repeat
     try
        if (Eps < 1) and (Eps > LimitEps) then
        begin
           IsCorrect := True;
        end
        else
           Writeln('Enter a value between (1; 0.000001)');
     except
        IsCorrect := False;
        Writeln('Enter a number!');
     end;
   until IsCorrect ;
   Epsilon := Eps;
end;

function FunctionArgument(LimitX: Real): Real;
var
   x: Real;
   IsCorrect: Boolean;
begin
   Writeln('Enter the value of the function argument:');
   Readln(x);
   repeat
     try
        if (x < 0) and (x > LimitX) then
        begin
           IsCorrect := True;
        end
        else
           Writeln('Enter a value between (0; 10)');
     except
        IsCorrect := False;
        Writeln('Enter a number!');
     end;
   until IsCorrect ;
   FunctionArgument := x;
end;

 function MaclaurinSeries(Eps, x: Real): Real;
 var
    y, an: Real;
    n: Integer;
 begin
    y := x;
    an := x;
    n := 0;
    while abs(an) > Eps do
    begin
       Inc(n);
       an := -an * sqr(x)/ ( 2 * n * (2 * n + 1));
       y := y + an;
    end;
    MaclaurinSeries := y;
 end;

procedure Input(Eps, x, y: Real);
var
   i: Integer;
begin
   WriteLn('x =',x: 8: 4, ' eps =',eps: 8: 4, ' y =',y: 8: 4);
   Writeln;
end;

procedure ReadFileOutputName(var MyFile: TextFile);
var
   NewFName: string;
   CorrectName: Boolean;
begin
   Writeln('Enter a file name for data entry in the format Name.txt');
   repeat
      Readln(NewFName);
      if Copy(NewFName, length(NewFName) - 3, 4) = '.txt' then
         CorrectName := True
      else
      begin
         Writeln('The file name was entered incorrectly. Try again. Example: Name.txt');
         CorrectName := False;
      end;
   until CorrectName;
   AssignFile(MyFile, NewFName);
   Rewrite(MyFile);
end;


procedure WriteToFile(const y: Real; var NewFile: TextFile);
var
   i, n: Integer;
begin
   Dec(n);
   for i := 0 to n do
   begin
      Write(NewFile, 'y= ',y: 8: 4 );
      Write(NewFile, ' ');
   end;
   CloseFile(NewFile);
   Writeln('Saved to file. ');
end;

const
   LimitEps = 0.000001;
   LimitX = 124;
var
   Eps, x, y: Real;
   MyTFile: TextFile;
begin
   Writeln('This program calculates the value of a function y = sin(x) with precision e by expanding the function in a Maclaurin series');
   Eps := Epsilon(LimitEps);
   x := FunctionArgument(LimitX);
   y := MaclaurinSeries(Eps, x);
   Input(Eps, x, y);
   ReadFileOutputName(MyTFile);
   WriteToFile(y, MyTFile);
   Readln;
end.