divide_and_round_up.h

// Description: Ceil(a/b) for integers

#ifndef PASTELMATH_DIVIDE_AND_ROUND_UP_H
#define PASTELMATH_DIVIDE_AND_ROUND_UP_H

#include "pastel/sys/integer/integer_concept.h"
#include "pastel/sys/ensure.h"

namespace Pastel
{

    //! Returns ceil(divide / byThis).
    /*!
   Time complexity: O(1)
   Exception safety: nothrow
   */
    template <
        typename Integer,
        Requires<
            Models<Integer, Integer_Concept>
        > = 0
    >
    Integer divideAndRoundUp(
        const Integer& divide, 
        const Integer& byThis)
    {
        PENSURE(!zero(byThis));

        if ((!negative(divide)) != (!negative(byThis)))
        {
            // If the signs differ, then the integer division
            // computes ceil(a / b), which is what we want.
            return divide / byThis;
        }

        if (!negative(divide))
        {
            // Both are non-negative, and the integer division
            // computes floor(a / b). We use the formula
            // ceil(a / b) = floor((a + (b - 1)) / b).
            return (divide + byThis - 1) / byThis;
        }

        // Both are negative. Turn them positive,
        // and do as above:
        //
        // ceil(a / b) = ceil((-a) / (-b))
        //             = floor((-a + ((-b) - 1)) / (-b))
        //             = floor((-a - b - 1) / (-b))
        //             = floor(-(a + b + 1) / (-b))
        //             = floor((a + b + 1) / b)

        return (divide + byThis + 1) / byThis;
    }

}

#endif