How Can I Efficiently Calculate the Ceiling of Integer Division in C/C ?

Optimizing Integer Division Ceiling in C / C

The integer division operator (/) in C and C calculates the quotient of two integers, resulting in the floor value. However, situations may arise where the ceiling value, which rounds up to the nearest integer, is desired.

In contrast to the standard approach, which involves an additional comparison and multiplication, this article presents a more efficient method to compute the ceiling of integer division while avoiding casting to floating-point numbers and unnecessary floating-point operations.

Fast Ceiling Algorithm

Given positive integers x and y, the ceiling of x divided by y can be calculated using the following formulas:

• Rounding Up:

  • q = (x y - 1) / y

• Avoiding Overflow (when x != 0):

  • q = 1 ((x - 1) / y)

These formulas offer a direct and efficient method to determine the ceiling value, eliminating the need for extra branches and floating-point conversions. By using these formulas, developers can optimize their code for integer division and improve performance.

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