import builtins
def Round(a,base_place=0,base=10):
'''
implement Rounding to bases other than 10.
known deficiencies:
fails with decimal input
fails with fractions input
Beware of 0 < base < 1 since b**(-p) == (1/b)**(p)
>>> [Round(x,-1,5) for x in (142,143,147,)]
[140, 145, 145]
>>>
>>> [(p,Round(12.345,p,2)) for p in range(-3,3)]
[(-3, 16.0), (-2, 12.0), (-1, 12.0), (0, 12.0), (1, 12.5), (2, 12.25)]
>>>
>>> # Use for base < 1
>>> # one might want decimal input
>>> # Round to the nearest US nickel
>>> no_pennies = Round(12.07,-1,0.05)
>>> print('{0:.2f}'.format(no_pennies))
12.05
>>> # The advertising game
>>> price_per_gallon = Round(12.379999999999,-1,1/100)
>>> print('{0:.2f}'.format(price_per_gallon))
12.38
>>>
>>> # round to nearest multiple of square root of two
>>> x = Round(12.379999999999,1/2,2)
>>> print (x / 2**(1/2))
9.0
>>>
'''
# consider using sign transfer for negative a
if base == 10:
return builtins.round(a,base_place)
if base <= 0:
raise ValueError('base too complex')
b = base**base_place
return type(a)(int(a*b+0.5)/b)
