South Winds Games :: Blog » math http://www.southwindsgames.com/blog Casual Games Development Sat, 05 Mar 2011 17:32:29 +0000 http://wordpress.org/?v=2.9.2 en hourly 1 Fast Integer Log2 function in C/C++ http://www.southwindsgames.com/blog/2009/01/19/fast-integer-log2-function-in-cc/ http://www.southwindsgames.com/blog/2009/01/19/fast-integer-log2-function-in-cc/#comments Tue, 20 Jan 2009 03:14:14 +0000 Juan Pablo http://www.southwindsgames.com/blog/?p=48 Some times, it happens that you need to have a high performance function that you usually use in a not optimized way. And since you never needed to optimize it you hesitated before realising it can be severly improved. Probably, this is what you would think of the integer log2 function, in general this function is used on not critic code so it can be “slow” without creating any problem (often used to calculate the size of a power of 2 texture to hold an image)

The usual way of calculating this log2 function is testing until the base elevated to the log is bigger than the value. This is easy with the << operator.
This function returns the truncated to the integer unit log2 of value:

inline unsigned int iLog2(unsigned int value)
{
    unsigned int l = 0;
    while( (value >> l) > 1 ) ++l;
    return l;
}

Easy, isn’t it? And it is quite fast! you will do 8 comparations to return the log2 of 256.
But what if we do a binary search instead of this linear search …

inline unsigned int Log2(unsigned int value)
{
    unsigned int f=0, s=32;
    while(s) {
        s>>=1;
        if( value > 1<<(f+s) ) f+=s;
    }
    return f;
}

Even faster since we will be doing a fixed number of comparations.
And so, if they are fixed …

inline unsigned int ilog2(register unsigned int x)
{
    register unsigned int l=0;
    if(x >= 1<<16) { x>>=16; l|=16; }
    if(x >= 1<<8) { x>>=8; l|=8; }
    if(x >= 1<<4) { x>>=4; l|=4; }
    if(x >= 1<<2) { x>>=2; l|=2; }
    if(x >= 1<<1) l|=1;
    return l;
}

You can hardcode the answers and the bit settings, and this one compiles really well!
If you want to go further you can expand the ifs to 32 branches with 32 results, and so you will collapse the search time to the minimal (I cannot think on something better), but it is up to you if you want to go further. As well this function can be bounded with template arguments, but I don’t think this will ever pay off.

Probably you won’t find this function useful (except if you are here because you were looking for it), but in any case I liked this function so much and I wanted to share it because it shows us that even the most every day used things can be improved, refined, and can be prepared for different contexts. It isn’t all invented, you can keep discovering and creating :)

- Juan Pablo

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