def exp(x, err=defaultError):
"""
Return exponential of x.
"""
if err <= defaultError:
reduced = rational.Rational(x)
if reduced < 0:
reverse = -1
reduced = -reduced
else:
reverse = 1
i = 0
while reduced >= 2:
reduced /= 2
i += 1
if reduced == 0:
retval = rational.Integer(1)
else:
series = ExponentialPowerSeries(
itertools.cycle((rational.Integer(1), )))
retval = series(reduced, err)
if i > 0:
retval **= 2**i
if reverse < 0:
retval = 1 / retval
else:
retval = rational.Rational(math.exp(x))
return retval
