Num sq_exp(Num sq) //up > down
        {
            int i0, i1 = IDS.sqr_exp_bits;
            if (sq.down.IsEven && (up.Sign < 0)) IDS.sys.error("exp: neg sqr");
            Num res = new Num(1), _sq = new Num(sq), tmp = new Num(1), _t = new Num(this); // (5/11-1/2)*2 = ((5*2-11)/(11*2))*2
            BigInteger _ud = up / down;
            if (_ud > 3)
            {
                int l2 = Num._l2(_ud);
                while (l2 > 1)
                {
                    _t._sq2_n(tmp, IDS.sqr2[l2]); i0 = IDS.sqr_steps; while (i0-- > 0) _t._sq2_n(tmp, tmp);
                    _sq.up <<= 1; if (_sq.up >= _sq.down)
                    {
                        _sq.up -= _sq.down;
                        res.mul(tmp);
                    }
                    if (_sq.up.IsZero || (i1 < 0)) return res.simple();
                    _t.up = tmp.up; _t.down = tmp.down; l2 >>= 1; i1--;
                }
            }
            while ((!_sq.up.IsZero) && (i1 > 0))
            {
                tmp.up = _t.up + _t.down; if (tmp.up.IsEven) { tmp.up >>= 1; tmp.down = BigInteger.Abs(_t.down); } else tmp.down = _t.down << 1;
                i0 = IDS.sqr_steps; while (i0-- > 0) _t._sq2_n(tmp, tmp);
                _sq.up <<= 1; if (_sq.up >= _sq.down)
                {
                    _sq.up -= _sq.down;
                    res.mul(tmp); res.prec_this();
                }
                _t.up = tmp.up; _t.down = tmp.down; i1--;
            }
            return res.simple();
        }