c# - Fastest way to calculate the decimal length of an integer? (.NET)

Question

I have some code that does a lot of comparisons of 64-bit integers, however it must take into account the length of the number, as if it was formatted as a string. I can't change the calling code, only the function.

The easiest way (besides .ToString().Length) is:

(int)Math.Truncate(Math.Log10(x)) + 1;

However that performs rather poorly. Since my application only sends positive values, and the lengths are rather evenly distributed between 2 and 9 (with some bias towards 9), I precomputed the values and have if statements:

static int getLen(long x) {
    if (x < 1000000) {
        if (x < 100) return 2;
        if (x < 1000) return 3;
        if (x < 10000) return 4;
        if (x < 100000) return 5;
        return 6;
    } else {
        if (x < 10000000) return 7;
        if (x < 100000000) return 8;
        if (x < 1000000000) return 9; 
        return (int)Math.Truncate(Math.Log10(x)) + 1; // Very uncommon
    }
}

This lets the length be computed with an average of 4 compares.

So, are there any other tricks I can use to make this function faster?

Edit: This will be running as 32-bit code (Silverlight).

Update:

I took Norman's suggestion and changed the ifs around a bit to result in an average of only 3 compares. As per Sean's comment, I removed the Math.Truncate. Together, this boosted things about 10%. Thanks!

Answer 1

Two suggestions:

1. Profile and put the common cases first.
2. Do a binary search to minimize the number of comparions in the worst case. You can decide among 8 alternatives using exactly three comparisons.

This combination probably doesn't buy you much unless the distribution is very skew.