What is the behavior of integer division?

Question

For example,

int result;

result = 125/100;

or

result = 43/100;

Will result always be the floor of the division? What is the defined behavior?

Answer 1

Yes, the result is always truncated towards zero. It will round towards the smallest absolute value.

-5 / 2 = -2
 5 / 2 =  2

For unsigned and non-negative signed values, this is the same as floor (rounding towards -Infinity).

Answer 2

Will result always be the floor of the division? What is the defined behavior?

Yes, integer quotient of the two operands.

6.5.5 Multiplicative operators

6 When integers are divided, the result of the / operator is the algebraic quotient with any fractional part discarded.⁸⁸⁾ If the quotient a/b is representable, the expression (a/b)*b + a%b shall equal a.

and the corresponding footnote:

88) This is often called ‘‘truncation toward zero’’.

Of course two points to note are:

3 The usual arithmetic conversions are performed on the operands.

and:

5 The result of the / operator is the quotient from the division of the first operand by the second; the result of the % operator is the remainder. In both operations, if the value of the second operand is zero, the behavior is undefined.

[Note: Emphasis mine]

Answer 3

Where the result is negative, C truncates towards 0 rather than flooring - I learnt this reading about why Python integer division always floors here: Why Python's Integer Division Floors

Answer 4

Dirkgently gives an excellent description of integer division in C99, but you should also know that in C89 integer division with a negative operand has an implementation-defined direction.

From the ANSI C draft (3.3.5):

If either operand is negative, whether the result of the / operator is the largest integer less than the algebraic quotient or the smallest integer greater than the algebraic quotient is implementation-defined, as is the sign of the result of the % operator. If the quotient a/b is representable, the expression (a/b)*b + a%b shall equal a.

So watch out with negative numbers when you are stuck with a C89 compiler.

It's a fun fact that C99 chose truncation towards zero because that was how FORTRAN did it. See this message on comp.std.c.

Answer 5

Will result always be the floor of the division?

No. The result varies, but variation happens only for negative values.

What is the defined behavior?

To make it clear floor rounds towards negative infinity,while integer division rounds towards zero (truncates)

For positive values they are the same

int integerDivisionResultPositive= 125/100;//= 1
double flooringResultPositive= floor(125.0/100.0);//=1.0

For negative value this is different

int integerDivisionResultNegative= -125/100;//=-1
double flooringResultNegative= floor(-125.0/100.0);//=-2.0