Is a logical right shift by a power of 2 faster in AVR?

Let's look at the datasheet:

http://atmel.com/dyn/resources/prod_documents/8271S.pdf

As far as I can see, the ASR (arithmetic shift right) always shifts by one bit and cannot take the number of bits to shift; it takes one cycle to execute. Therefore, shifting right by n bits will take n cycles. Powers of two behave just the same as any other number.

In the AVR instruction set, arithmetic shift right and left happen one bit at a time. So, for this particular microcontroller, shifting >> n means the compiler actually makes n many individual asr ops, and I guess >>3 is one faster than >>4.

This makes the AVR fairly unsual, by the way.

You have to consult the documentation of your processor for this information. Even for a given instruction set, there may be different costs depending on the model. On a really small processor, shifting by one could conceivably be faster than by other values, for instance (it is the case for rotation instructions on some IA32 processors, but that's only because this instruction is so rarely produced by compilers).

According to http://atmel.com/dyn/resources/prod_documents/8271S.pdf all logical shifts are done in one cycle for the ATMega328. But of course, as pointed out in the comments, all logical shifts are by one bit. So the cost of a shift by n is n cycles in n instructions.