def _sum (data, start=None):
    if start is not None:
        t = set((type(start),))
        n, d = _exact_ratio(start)
    else:
        t = set()
        n = 0
        d = 1
    partials = {d: n}  # map {denominator: sum of numerators}

    # Micro-optimizations.
    exact_ratio = _exact_ratio
    partials_get = partials.get

    # Add numerators for each denominator, and build up a set of all types.
    for x in data:
        t.add(type(x))
        n, d = exact_ratio(x)
        partials[d] = partials_get(d, 0) + n
    T = _coerce_types(t) # decide which type to use based on set of all types
    if None in partials:
        assert issubclass(T, (float, Decimal))
        assert not math.isfinite(partials[None])
        return T(partials[None])
    total = Fraction()
    for d, n in sorted(partials.items()):
        total += Fraction(n, d)
    if issubclass(T, int):
        assert total.denominator == 1
        return T(total.numerator)
    if issubclass(T, Decimal):
        return T(total.numerator)/total.denominator
    return T(total)

def _coerce_types (types):
    if len(types) == 1:
        return next(iter(types))
    if all(issubclass(t, numbers.Integral) for t in types):
        return int
    if all(issubclass(t, numbers.Rational) for t in types):
        return Fraction
    if any(issubclass(t, Decimal) for t in types):
        if all(issubclass(t, (numbers.Integral, Decimal)) for t in types):
            return Decimal
        raise TypeError('cannot coerce type Decimal and non-Integral type(s)')    
    return float

def _coerce_types_2 (types):
    if len(types) == 1:
        return next(iter(types))
    if all(issubclass(t, numbers.Integral) for t in types):
        return int
    if all(issubclass(t, numbers.Rational) for t in types):
        return Fraction
    if any(issubclass(t, Decimal) for t in types):
        if all(issubclass(t, (numbers.Integral, Decimal)) for t in types):
            return Decimal
        if not all(issubclass(t, (numbers.Integral, Decimal, float)) for t in types):
            raise TypeError('cannot coerce type Decimal and non-Integral type(s) {0}'
                            .format(', '.join(str(t) for t in types if not issubclass(t, (numbers.Integral, Decimal, float)))))        
    return float