Arbitrary precision integer arithmetic: ceiling?

Steven D'Aprano steve at
Sun Mar 9 03:31:15 CET 2008

On Sun, 09 Mar 2008 10:11:53 +1100, Alasdair wrote:

> I need to apply the ceiling function to arbitrary sized (long) integers.
> However, division automatically returns the type of its operands, so
> that, for example: math.ceil(7/4) returns 1.  I can use float, as in:
> math.ceil(7/float(4)), except that for very large integers float causes
> an unacceptable loss of precision.
> What is the best way of finding a ceiling of a quotient of arbitrary
> sized integers?

def quot_ceil(a, b):
    """Returns the integer ceiling of the quotient of longints."""
    q, r = divmod(a, b)
    if r: return q+1
    else: return q


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