Adding floats with gmp gives "correct" results, sort of

Question

In the code below I use mpf_add to add the string representation of two floating values. What I don't understand at this point is why 2.2 + 3.2 = 5.39999999999999999999999999999999999999. I would have thought that gmp was smart enough to give 5.4.

What am I not comprehending about how gmp does floats?

(BTW, when I first wrote this I wasn't sure how to insert a decimal point, thus the plus/minus digit stuff at the end)

BSTR __stdcall FBIGSUM(BSTR p1, BSTR p2 ) {
  USES_CONVERSION;

  F(n1);
  F(n2);
  F(res);

  LPSTR sNum1 = W2A( p1 );
  LPSTR sNum2 = W2A( p2 );

  mpf_set_str( n1, sNum1, 10 );
  mpf_set_str( n2, sNum2, 10 );

  mpf_add( res, n1, n2 );

  char * buff =  (char *) _alloca( 1024 );
  char expBuffer[ 20 ];
  mp_exp_t exp;

  mpf_get_str(buff, &exp, 10, 0, res);

  char * temp = ltoa( (long) exp, expBuffer, 10 );
  if (exp >= 0) {
    strcat(buff, "+" );
  }
  strcat(buff, expBuffer );

  BSTR bResult = _com_util::ConvertStringToBSTR( buff );
  return bResult;
}

Answer 1

This is because of the inherent error of using floating-point arithmetic in a binary environment.

See the IEEE 754 standard for more information.