--- Cristea Bogdan <cristeab@xxxxxxxxx> wrote: > I use an Athlon 64 double core processor under > openSuSE 10.2 (gcc > 4.2.2). The trouble is that implementing fixed point > operations in C++ > seems to be very slow with respect to floating-point > operations. I > have hoped to find something faster. > Ideally I would like to have a data type in C++ > with all common > operations in order to do some research with chaotic > maps. This doesn't make sense. You may want to check your math. Chaos can exist only on the reals because only with the reals can you have a bounded interval containing an infinite number of points. With all other kinds of number, such as integers, you can at most have long periodic orbits. The closest thing you will find, in a computer program, will be floating point numbers, and that only as long as your simulations are short enough to make the sequence, in fact drawn from a periodic orbit with a very long period, you generate statistically indistinguishable from a chaotic sequence that could be drawn from your map. There is some interesting research into how well one can obtain a chaotic sequence (limitations due in part to finite representation and in part to information production interacting with representation error). I can recall seeing results based on this kind of analysis twenty odd years ago which place upper and lower limits on how long your simulations can be and still adequately represent a chaotic sequence from the map you're interested in (a sequence, at that, with a small, unknowable difference delta between the numbers obtained in the computed sequence and the actual values that would have been drawn from the chaotic process). The best you can say is that the sequence you have represents a chaotic sequence from this chaotic process with an initial position X0+delta0, and the distance between the computed sequence and the "real" sequence is always less than delta1. But I digress. This fact of life in regard to the nature of chaos means the most useful type for the study of chaos is that floating point type with the greatest precision. The more precision you can get, the better! Why you would even begin to looking at fixed point is a mystery, unless you're using a template for it and routinely give it more precision than is possible for the largest floating point type. But then, I'd bet you'd be getting it all in software anyway since you're likely be working with numbers that won't fit in the processor's registers anyway. You have to make a choice. Either deal with slow performance associated with arbitrarily high precision obtained using software (you can make a numeric class that will give you megabyte numbers, if you wanted, but that would be silly overkill), or deal with the limitations of the representations available with the greatest possible precision from the largest floating point number. You have to make a choice since you can't have both. HTH Ted
