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const
  BUFFER_SIZE = 64 * 1024;

var
  Stream: TStream;
  Count: Int64;
  SHA: THash_SHA1;
  TmpBuf: TBytes;
  BufCount: integer;
  Buf: TBytes;
  Hash: string;
...

  SHA := THash_SHA1.Create;
  try
    Stream.Position := 0;
    Count := Stream.Size;

    SetLength(TmpBuf, BUFFER_SIZE);

    while Count > 0 do begin
      if Count > BUFFER_SIZE then
        BufCount := BUFFER_SIZE
      else
        BufCount := Count;

      Stream.ReadBuffer(TmpBuf[0], BufCount);
      SHA.TransformBlock(TmpBuf, 0, BufCount);
      Dec(Count, BufCount);
    end;
    SHA.TransformFinalBlock(nil, 0, 0);
    Buf := SHA.Hash;
    Hash := BytesToHexStr(Buf);
  finally
    SHA.Free;
  end;