Power of an Natural by the left-to-right repeated squaring algorithm. This needs two multiplications in each step while the right-to-left algorithm needs only one multiplication for 0-bits, but here the two factors always have approximately the same size, which on average gains a bit when the result is large.
For small results, it is unlikely to be any faster than (^), quite
possibly slower (though the difference shouldn't be large), and for
exponents with few bits set, the same holds. But for exponents with
many bits set, the speedup can be significant.
Warning: No check for the negativity of the exponent is performed, a negative exponent is interpreted as a large positive exponent.