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c++calgorithmmathinteger-division

Fast ceiling of an integer division in C / C++

Given integer values x and y, C and C++ both return as the quotient q = x/y the floor of the floating point equivalent. I'm interested in a method of returning the ceiling instead. For example, ceil(10/5)=2 and ceil(11/5)=3.

The obvious approach involves something like:

q = x / y;
if (q * y < x) ++q;

This requires an extra comparison and multiplication; and other methods I've seen (used in fact) involve casting as a float or double. Is there a more direct method that avoids the additional multiplication (or a second division) and branch, and that also avoids casting as a floating point number?

Solution

  • For positive numbers where you want to find the ceiling (q) of x when divided by y.

    unsigned int x, y, q;

    To round up ...

    q = (x + y - 1) / y;

    or (avoiding overflow in x+y)

    q = 1 + ((x - 1) / y); // if x != 0