How to Efficiently Round Up Integer Division in C/C ?

Rounding Integer Division Upwards in C/C

When dividing two integers x and y in C/C , the result q = x/y yields the floor of the floating-point equivalent. However, there are scenarios where it may be desirable to obtain the ceiling instead, such as ceil(10/5) = 2 or ceil(11/5) = 3.

Inefficient Approach to Ceiling Division

One common approach for ceiling division involves comparing and incrementing the floor value:

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

While effective, this method entails an additional comparison and multiplication, which can impact performance.

Efficient Ceiling Division Algorithm

To circumvent the limitations of the inefficient approach, consider the following algorithm for positive numbers where q is the ceiling of x divided by y:

unsigned int x, y, q;

// Round up using (x + y - 1) / y
q = (x + y - 1) / y;

Alternative Overflow-Avoidant Algorithm

Alternatively, to prevent potential overflow in x y, use the following formula:

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

By employing these efficient algorithms, you can avoid the pitfalls of additional comparisons, multiplications, and floating-point casting, resulting in faster and more precise ceiling division operations.

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