How can I compute a base 2 logarithm without using the built-in math functions in C#?

Question

How can I compute a base 2 logarithm without using the built-in math functions in C#?

I use Math.Log and BigInteger.Log repeatedly in an application millions of times and it becomes painfully slow.

I am interested in alternatives that use binary manipulation to achieve the same. Please bear in mind that I can make do with Log approximations in case that helps speed up execution times.

Answer 1

Assuming you're only interested in the integral part of the logarithm, you can do something like that:

static int LogBase2(uint value)
{
    int log = 31;
    while (log >= 0)
    {
        uint mask = (1 << log);
        if ((mask & value) != 0)
            return (uint)log;
        log--;
    }
    return -1;
}

(note that the return value for 0 is wrong; it should be negative infinity, but there is no such value for integral datatypes so I return -1 instead)

Answer 2

http://graphics.stanford.edu/~seander/bithacks.html

Answer 3

For the BigInteger you could use the toByteArray() method and then manually find the most significant 1 and count the number of zeroes afterward. This would give you the base-2 logarithm with integer precision.

Answer 4

The bit hacks page is useful for things like this.

• Find the log base 2 of an integer with a lookup table

The code there is in C, but the basic idea will work in C# too.

Answer 5

If you can make due with approximations then use a trick that Intel chips use: precalculate the values into an array of suitable size and then reference that array. You can make the array start and end with any min/max values, and you can create as many in-between values as you need to achieve the desired accuracy.