How to Calculate the Ceiling of Integer Division in C/C without Multiplication or Floating-Point Operations?

Ceiling of Integer Division without Multiplication or Floating-Point Casting

In C and C , integer division (x/y) returns the floor of the result. To calculate the ceiling instead, avoiding floating-point casting and additional multiplication, consider the following methods:

1. Using (x y - 1) / y:

unsigned int x, y, q;
// Round up
q = (x + y - 1) / y;

This formula ensures that the ceiling is computed, as it adds 1 before performing division.

2. Avoiding Overflow in (x y):

To prevent integer overflow when adding x and y, an alternative method is:

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

This formulation effectively increments the ceiling by 1, except when x is 0, where it remains 0.

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