> Back in time it was known for being a fast way to multiply and divide by powers of 2. This hasn't been true for a long time now, and in the rare cases it is, most optimizing compilers will bitwise shift where in your source code you divide or multiply.

Shifting is still faster than multiplication--a shift is a 1-cycle operation, multiplication typically 3 cycles. Division is somewhere in the region of a dozen cycles or more. (Also, division is one of the assembly operations whose time is data-dependent). So it's faster to replace a multiplication with a single shift (but not multiple shifts), and to replace division with shifts or even multiplies--there's a fast division replacement that replaces a division by a small constant with a multiply-hi and shift.

Will compilers replace multiplies and divides with shifts? Kind of. If you multiply a value with a constant (after inlining/constant propagation/etc.) that's a power of two, or if you multiply it with an expression 1 << var, then that will be converted to a shift.

For division, it's even more complicated because shifts and division by power of 2 are not equivalent if the type is signed: -1 / 2 is 0 but -1 >> 1 is -1, so the transform is not legal unless the compiler can find out either a) the value is never negative or b) the division is exact.