def asin(x, err=defaultError):
"""
asin(x [,err]) returns arc sine of x.
"""
if x > 1 or x < -1:
raise ValueError("%s is not in the range [-1, 1]." % str(x))
if x < 0:
return -asin(-x)
if err <= defaultError:
u = sqrt(rational.Rational(1, 2))
if x > u:
return pi(err) / 2 - asin(sqrt(1 - x**2))
if x == 0:
return rational.Integer(0)
y = rational.Rational(x)
y2 = y**2
i = 2
retval = y
term = rational.Rational(y)
oldvalue = 0
while not err.nearlyEqual(retval, oldvalue):
oldvalue = +retval
term *= y2 * (i - 1)**2 / (i * (i + 1))
i += 2
retval += term
else:
retval = rational.Rational(math.asin(x))
return retval
