Example of ceil divisions.

I have collected code that do ceil division (round up after division) from popular open source project using grep/git grep. For example, you can find (x + y - 1) / y expression in C (and C like) programming language using following command:

git grep -E "\([[:alnum:]_.]+ \+ [[:alnum:]_.]+ - 1\) / [[:alnum:]_.]+"

In case magic number is used like (x + 31) / 32

git grep -E "\([[:alnum:]_.]+ \+ [[:digit:]]+\) / [[:digit:]]+"

x is dividend and y is divisor.

• (x + y - 1) / y

  • Doesn't work with negative numbers
  • Doesn't work if x + y - 1 overflowed

• x / y + 1

  • results in one higher value in following case
    • x mod y == 0
    • x / y is negative value and integer division is always rounds towards to zero

• (x >> n) + ((x & (2^n - 1)) ? 1 : 0)

  • Assume divisor is a power of 2 number y = 2^n and n >= 0
  • works with any dividend even if it is negative

nim-lang/Nim#18596