CODEWITHSUNDEEP
c
newby
newby

Reputation: 189

implementation of round up function in c

Guys this is the function to implement ceil function Which is working fine,I want to ask what is the logic behind subtracting -1 from denominator ?
I am new to programming please Help 

int checkceil(int numerator,int denominator){

    return (numerator+denominator-1)/denominator;
}

Upvotes: 1

Views: 1147

Answers (2)

P.W
P.W

Reputation: 26800

Since dividing two integers a and b will always floor (truncate) the result, we need to find some d (delta) such that floor(d + a/b) == ceil (a/b).

How do we find d? Think about it this way:
ceil(a/b) > floor(a/b), except when (a/b) is a whole number. So, we want to bump (a/b) to (or past) the next whole number, unless (a/b) is a whole number, by adding d. This way floor(a/b + d) will be equal to ceil(a/b). We want to find d so that for whole numbers, it won’t quite push them up to the next whole number, but for non-whole numbers it will.

So how much d is just enough?

So assuming (a/b) is not a whole number, the smallest leftover we can have is (1/b). So in order to bump (a/b) to the next whole number, it suffices to add d = 1 - (1/b). This is less than 1, which will not bump (a/b) to the next whole number in case (a/b) is a whole number, but still enough to bump (a/b) to the next whole number in case (a/b) is not a whole number.

Summing it up, we know adding d = 1 - (1/b) to (a/b) will fulfill the equality:
floor(a/b + d) = ceil(a/b). Thus we get: 

 ceil(a/b) = floor(a/b + d)  = floor(a/b + 1 - 1/b) = floor((a + b - 1)/b)

When we write in terms of code it will be: 

int myceil = (a + b - 1)/b;

Upvotes: 2

Aki Suihkonen
Aki Suihkonen

Reputation: 20027

The numerator n is of form n = a * d + b, where b is the remainder of n / d. The remainder is by definition smaller than d.

In C, the division of n/d returns the integral part of a. When b == 0, one can add only d - 1 to n to get the same result (ad + 0)/d == (ad + d-1)/d. For all other remainders 0<b<d, the division returns the next integer a+1, ie the ceiling.

Upvotes: 2

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