def to_rational(ctx, s, limit=True):
        p, q = to_rational(s._mpf_)

        if not limit or q <= ctx.max_denom:
            return p, q

        p0, q0, p1, q1 = 0, 1, 1, 0
        n, d = p, q

        while True:
            a = n//d
            q2 = q0 + a*q1
            if q2 > ctx.max_denom:
                break
            p0, q0, p1, q1 = p1, q1, p0 + a*p1, q2
            n, d = d, n - a*d

        k = (ctx.max_denom - q0)//q1

        number = mpq(p, q)
        bound1 = mpq(p0 + k*p1, q0 + k*q1)
        bound2 = mpq(p1, q1)

        if not bound2 or not bound1:
            return p, q
        elif abs(bound2 - number) <= abs(bound1 - number):
            return bound2._mpq_
        else:
            return bound1._mpq_
dataset/ETHPy150Open sympy/sympy/sympy/polys/domains/mpelements.py/MPContext.to_rational/original