Precision of multiplication by 1.0 and int to float conversion

Question

Is it safe to assume that the condition (int)(i * 1.0f) == i is true for any integer i?

Answer 1

No.

If i is sufficiently large that int(float(i)) != i (assuming float is IEEE-754 single precision, i = 0x1000001 suffices to exhibit this) then this is false, because multiplication by 1.0f forces a conversion to float, which changes the value even though the subsequent multiplication does not.

However, if i is a 32-bit integer and double is IEEE-754 double, then it is true that int(i*1.0) == i.

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Just to be totally clear, multiplication by 1.0f is exact. It's the conversion from int to float that may not be.