alternative to log?

I am multiplying a lot of small numbers (probabilities). in order to avoid underflow, i use the log transformation. this is rather time consuming, so i was wondering whether there is a faster alternative

[the cyclist]

Maybe you could post some code, to get some hints? If taking the log of many numbers is your bottleneck, there is probably something that can be done to speed it up, but it is impossible to help without seeing code.

[bym]

can I ask why you are multiplying a lot of small probabilities? perhaps there is another way to formulate your problem

[Daniel Shub]

Have you profiled your code to know this is the bottleneck? Is it possible to distrbute the log and multiplication to across a cluster?

[Grzegorz Knor]

Maybe you could use complementary events?

Answer 1

[Walter Roberson]

There is a possibility that the fixed-point toolbox might be faster (you would define a fixed point format with a large enough exponent field to take care of your final value), but I suspect that the cost of converting the values into fixed point and doing the software multiplications would be higher than the cost of taking the log.

The symbolic toolbox can handle very small numbers, but again there is the cost of the conversion and software multiplication (but the software multiplication library would at be a fairly well-tuned and robust one in this case.)

Answer 2

[Derek O'Connor]

No matter what transformation you use, the result, prod(pi, i=1:n) --> 0, so eventually you will get underflow in fixed precision or run out of memory in variable precision or rational arithmetic.

You need to give us more information.