Count the digits of an integer in any base efficiently.

lib.rs

// We can use log2(x) = size_of(x) - 1 - clz(x).
// And then do a base conversion log_b(x) = log2(x) / log2(b).
// Then log_b(x) + 1 is the number of digits in base b for x > 0.
fn count_digits(x: usize, base: u8) -> usize {
    1 + (8 * mem::size_of::<usize>() - 1 - x.leading_zeros() as usize) / (7 - base.leading_zeros() as usize)
}

// Say we know we're counting in base 10 or base 16. We can calculate the divisor.
fn count_base10_digits(x: usize) -> usize {
    1 + (8 * mem::size_of::<usize>() - 1 - x.leading_zeros() as usize) / 3
}

// Rust and LLVM will calculate part of the dividend too
// But you can also do it yourself if the integer size is already clear.
fn count_base10_digits_u32(x: u32) -> u32 {
    1 + (31 - x.leading_zeros()) / 3
}

// Here's another example of counting hex digits.
fn count_base16_digits_u32(x: u32) -> u32 {
    1 + (31 - x.leading_zeros()) / 4
}