def atan(x, err=defaultError):
"""
atan(x [,err]) returns arc tangent of x.
"""
if not isinstance(err, defaultError.__class__) or err <= defaultError:
# atan(x) = -atan(-x)
if x < 0:
return -atan(-x, err)
# atan(x) = pi/2 - atan(1/x)
elif x > 1:
return pi(err) / 2 - atan(1 / x, err)
elif x == 1:
return pi(err) / 4
elif x == 0:
return rational.Integer(0)
y = rational.Rational(x)
y2 = y**2
retval = y
oldvalue = 0
term = rational.Rational(x)
i = 1
while not err.nearlyEqual(retval, oldvalue):
oldvalue = +retval
i += 2
term *= -y2 * (i - 2) / i
retval += term
else:
retval = rational.Rational(math.atan(x))
return retval
