Will the compiler optimize division into multiplication

Question

Depending on this question Floating point division vs floating point multiplication . Division is slower than multiplication due to some reasons.

Will the compiler, usually, replace division by multiplication if it is possibe?

For example:

float a;
// During runtime a=5.4f
float b = a/10.f;

Will it be:

float a;
// During runtime a=5.4f
float b = a*0.1f;

If it is considered a compiler dependable question, I am using VS2013 default compiler. However, it would be nice if I got a generic answer (theoretical validity of this optimization)

Answer 1

No, the compiler is not allowed to do that for the general case: the two operations could produce results that are not bit-identical due to the representation error of the reciprocal.

In your example, 0.1 does not have an exact representation as float . This causes the results of multiplication by 0.1 and division by 10 to differ:

float f = 21736517;
float a = f / 10.f;
float b = f * 0.1f;
cout << (a == b) << endl; // Prints zero

Demo.

Note: As njuffa correctly notes in the comment below, there are situations when the compiler could make some optimizations for a wide set of numbers, as described in this paper . For example, multiplying or dividing by a power of two is equivalent to addition to the exponent portion of the IEEE-754 float representation.