How to check if an integer is a power of 3?

Question

I saw this question, and pop up this idea.

Answer 1

Here is a nice and fast implementation of Ray Burns' method in C:

bool is_power_of_3(unsigned x) {
    if (x > 0x0000ffff)
        x *= 0xb0cd1d99;    // multiplicative inverse of 59049
    if (x > 0x000000ff)
        x *= 0xd2b3183b;    // multiplicative inverse of 243
    return x <= 243 && ((x * 0x71c5) & 0x5145) == 0x5145;
}

It uses the multiplicative inverse trick for to first divide by 3^10 and then by 3^5. Finally, it needs to check whether the result is 1, 3, 9, 27, 81, or 243, which is done by some simple hashing that I found by trial-and-error.

On my CPU (Intel Sandy Bridge), it is quite fast, but not as fast as the method of starblue that uses the binary logarithm (which is implemented in hardware on that CPU). But on a CPU without such an instruction, or when lookup tables are undesirable, it might be an alternative.