Question

I recently encountered the following interview question:

How can you multiply a number by 7 in an efficient and optimized way?

I know that I can multiply by 8 (or left-shift by three bits) and then subtract the original value:

num = (num << 3) - num;

but are there any other solutions.

Answer 1

To get a multiple of 7 in an efficient way:

7

7 is a multiple of 7. That answers the question you asked, but I’m sure it doesn’t answer the question you mean to ask.

EDIT: The above is based on the question’s original title,which I’ve just corrected.

To multiply by 7 efficiently, just write, for example:

x * 7

and invoke your compiler with optimization. Let the compiler figure out whether a single MUL instruction or something like (x<<3) - x is more efficient for the current machine.

There’s yet another implicit question here: what answer was the interviewer looking for? I hope that “let the compiler worry about it” would be an acceptable answer. (x<<3) - x is probably the most obvious micro-optimization — but it can yield incorrect answers if x<<3 overflows, and depending on the system it might be slower than a MUL instruction.

(If I were the interviewer, I’d be more impressed by a good explanation and understanding of the issues than by any specific answer.)

EDIT

On further thought, the kinds of micro-optimizations that have been discussed here might be useful if you know more about the possible values of x than the compiler does. If you know, because of the nature of your program’s logic, that x will always be in the range 0..10, then a lookup table could easily be faster than a multiply operation. Or if you know that x is in that range 99% of the time, a lookup table with a fallback to an actual multiplication might be just the thing.

But if the compiler’s analysis of your program flow doesn’t allow it to prove that x is always in that range, then it can’t perform this kind of optimization.

But such circumstances are very rare. And when your code runs in a new environment where x can be 11 (perhaps it’s running on a device with a larger display), kaboom. And the performance improvement very likely wasn’t significant in the first place.

There are times when micro-optimization is appropriate, but there is a substantial cost in development and testing time. Do it only if actual measurements indicate that it’s worth it.