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  how to compute log2  (Read 2634 times)
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Offline shareme

Junior Devvie

Java games rock!

« Posted 2003-12-11 20:27:06 »

I want to speed up fixed point math computations by using shifting..

so how do I compute Log2 of a number considering that I do not have access to Math.log?

Offline tom
« Reply #1 - Posted 2003-12-11 22:48:32 »

Here is a fixed point math library:

Offline davidaprice

Junior Devvie

« Reply #2 - Posted 2003-12-12 05:32:34 »

Log2(x) is just the opposite of 2^x.  So where 2^x is just "1 shifted left x times", log2(x) is just "the position of the left-most 1". E.g.:

log2(00000001b) = 0   ('b' suffix means binary here)
log2(00000100b) = 2
log2(10000000b) = 7

For numbers which aren't powers of 2, you must decide whether to round to the nearest integer or just round down. Rounding down is much easier Smiley. In which case:

log2(00000111b) = 2

Then your code will look something like this:

int log2 = 0;
while (x > 1) {
   x >>>= 1;

Note that I'm assuming x is positive! Negative numbers or zero would be invalid arguments for a log2 method.

If you're emulating fixed point (e.g. by storing all numbers << 8 ) then just subtract the number of fractional binary digits (e.g. 8 ) from the result of log2.
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Offline shareme

Junior Devvie

Java games rock!

« Reply #3 - Posted 2003-12-12 06:37:38 »

I foudn it in my knuth vollumes of books Smiley

let me explain why I want to sue it..

you can speed up fp math on non FPU cpus such as arm by

6*32=6<<log2 32=192

25/4 25>>log2 4=6

of course division is truncated and you have to allow for that Smiley

of course if I convert to binary before any computation than division is no longer truncated Smiley hey that works!

Offline shareme

Junior Devvie

Java games rock!

« Reply #4 - Posted 2003-12-13 22:03:03 »

here is my solution and an example of where and how I am usng it:

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