John D'Errico

The point of Matthew's comment is not that MATLAB is required, but that you have failed to tell anyone that there is at least one toolbox required, one that not everyone may have. Have you used any functions in this code that are in some toolbox? (Yes.) The important question is, do you really need that tool you used? It prevents many people from using this utility.

As for globals being used in this code, they are a bit of a crutch here. So why not learn to write better code?

Hi Michael,

This is not really intended as a replacement for VPI, as the VPI tool concentrates entirely on large integers. In HPF you will see I've not given you tools to factor integers, or to test for primality, modular inverses, modular roots, or a powermod function.

Here I've concentrated on numerical methods, so I've provided computations for trig functions, exponentials, logs, erf, etc. HPF might be used to get around the dynamic range limitation of a double, or for someone who desperately wants to work in a given number of digits. It would seem to be a good tool for a student to learn about numerical precision problems. As well, I've found HPF to be quite useful in showing what MATLAB stores when we represent a number as an IEEE 754 double. (My own version of a tool like num2strexact that need not be compiled.) And it is a nice tool to test an algorithm to determine if a problem is due to a lack of numerical precision. I've even heard of a version of chol that will run with HPF numbers.

In general, I'd expect that most users of HPF will work with numbers in the range of 30 to perhaps 50 or so digits at most, except for those individuals who love to play in the huge digit sandbox.

As far as VPI goes, I plan on offering a new version to give a speed bump. (When I do, I'd like to play with some quadratic sieve factoring schemes to update factor.) I'd been debating in my own mind if I should leave the old VPI up there or not, for those users who have older releases of MATLAB.

By the way, that speed bump for VPI can come from one of two sources. For example, I could re-write VPI as a wrapper class for an existing Big Integer tool. I looked at such a question when I wrote HPF. (In fact, I wrote HPF in three separate versions, choosing the migit version as it ran the fastest.) Alternatively, I could in theory write the new VPI version to use migits, much like HPF uses now. The problem with migits is, they work well for numbers where the length of the mantissa does not change.

The issue is there are limits on the size of a number that can be operated on with migits, and integer arithmetic can cause integers to grow arbitrarily large. As such I would be forced to limit the size of the migits to be rather small. Thus with 3-migits, one can generate integers up to a few hundred millions of decimal digits. That would surely be adequate for the conceivable future, but perhaps one day it might be a limitation. (Somebody always wants to push the limits of any computational tool.)

Finally, a migital version of VPI would be simpler (and more efficient) to write than my HPF implementation, since it would not be forced to work in a fixed umber of digits. And there is no need for guard digits when you work with pure integers. (Is migital a word? I guess it is now.)

I'd be willing to take any advice people have to offer on these matters. Vote now.

John

New version submitted - thanks to Felipe.

Lovely, thanks