Question

How to multiply two long numbers in Pascal

Answer 1

program LongMultiDemo;

{$mode objfpc}{$H+}

{ Multiply Two Long Numbers
  ------------------------------------
  Implements manual big‑integer multiplication
  using decimal strings.
}

(* Multiply two integer strings a * b and return the result as a string.
   Caller receives a normal Pascal string.
   No aliasing issues because strings are value types. *)
function LongMulti(const A, B: string): string;
var
  a2, b2: string;
  sign: Boolean;
  la, lb: Integer;
  digits: array of Integer;
  i, j, pos, sum: Integer;

  function TrimLeftSpaces(const s: string): string;
  var
    k: Integer;
  begin
    k := 1;
    while (k <= Length(s)) and (s[k] = ' ') do
      Inc(k);
    Result := Copy(s, k, MaxInt);
  end;

  function StripLeadingZeros(const s: string): string;
  var
    k: Integer;
  begin
    k := 1;
    while (k < Length(s)) and (s[k] = '0') do
      Inc(k);
    Result := Copy(s, k, MaxInt);
    if Result = '' then
      Result := '0';
  end;

begin
  (* Skip leading spaces *)
  a2 := TrimLeftSpaces(A);
  b2 := TrimLeftSpaces(B);

  (* Handle sign *)
  sign := False;
  if (a2 <> '') and (a2[1] = '-') then
  begin
    sign := not sign;
    Delete(a2, 1, 1);
  end;
  if (b2 <> '') and (b2[1] = '-') then
  begin
    sign := not sign;
    Delete(b2, 1, 1);
  end;

  (* Skip leading zeros *)
  a2 := StripLeadingZeros(a2);
  b2 := StripLeadingZeros(b2);

  (* If either is "0", return "0" *)
  if (a2 = '0') or (b2 = '0') then
  begin
    Result := '0';
    Exit;
  end;

  la := Length(a2);
  lb := Length(b2);

  (* Initialize result buffer with zeros *)
  SetLength(digits, la + lb);
  for i := 0 to High(digits) do
    digits[i] := 0;

  (* Multiply from right to left *)
  for i := la downto 1 do
  begin
    if not (a2[i] in ['0'..'9']) then
      Continue;

    for j := lb downto 1 do
    begin
      if not (b2[j] in ['0'..'9']) then
        Continue;

      pos := (i - 1) + (j - 1) + 1;  (* zero-based array index *)
      sum := digits[pos] + (Ord(a2[i]) - Ord('0')) * (Ord(b2[j]) - Ord('0'));
      digits[pos] := sum mod 10;
      digits[pos - 1] := digits[pos - 1] + (sum div 10);
    end;
  end;

  (* Convert digits[] to string, skipping leading zero *)
  Result := '';
  i := 0;
  if digits[0] = 0 then
    i := 1;

  while i < Length(digits) do
  begin
    Result := Result + Chr(digits[i] + Ord('0'));
    Inc(i);
  end;

  (* Add sign if needed *)
  if sign then
    Result := '-' + Result;
end;

begin
  WriteLn(
    LongMulti(
      ' 18361891827367132321',
      '-18361891827367132321'
    )
  );
end.


(*
run:

-337159071479931885857929667075122847041

*)

 

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