Explanation of the safe average of two numbers

Question

Whenever I need to average two numbers for an algorithm like binary search, I always do something like this:

int mid = low + ((high - low) / 2);

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Answer 1

You are safe from integer overflows by using the way you said you already use, which is:

int mid = low + ((high - low) / 2);

Let you compiler do it's job to optimize this if it needs to.