Space for speed

[czurnieden]

First sketch of a method to implement optional speed (big-O) optimization.

The example used is a O(1) replacement for the O(n^2) method currently used in mp_radix_size(). The method presented here works well for the replacements of a function in a single file, not so well if there is more than one function/file involved, for example: the balancing of multiplication which would need a file for the function itself and a hook in bn_mp_mul.c. Others, like an O(M(n) log(n)) version of the mp_toradix() (currently O(n^2)) would depend on the fast version of mp_radix_size() to function.

[czurnieden]

After a lot of time-outs I decided to give the original version of mp_n_root() a proper start-value. It's usable now. And Travis, too, seems to be OK with it.

[minad]

Could you split this PR? For example one PR per function which has been improved? Otherwise I don't really get what you are doing here.

[czurnieden]

Could you split this PR?

Of course I can, no problem, I just found it easier for the user to bundle all of the "space for speed" optimizations into one packet. I mean: the current method via macros (e.g.: tommath_superclass.h) is a pain in the behind, isn't it? ;-)

But, as I said above: no problem, all what I already have and what is planned is independent of each other. Most of them are not independent of LTM, but they need only small changes, like the multiplication balancing and all of them can be put into preprocessor brackets (like the one in bn_mp_div.c switching between "normal" and "small").

Before somebody thinks that I already started splitting: the nth-root algorithm in this PR is the optimized one, the one in #189 is only a bugfix of Tom's original.

[minad]

Close, see #160 for the reason