Re: factorial and exponent

Richard Heathfield wrote:
Army1987 said:
"Richard Heathfield" <rjh@xxxxxxxxxxxxxxx> ha scritto nel messaggio
news:Gv6dnQ2-P8SDeunbnZ2dnUVZ8t_inZ2d@xxxxxxxxx
BiGYaN said:
<snip>
Use GMP library found in http://gmplib.org/
It will enable you to do "Arithmetic without Limitations" !!
Nonsense.

Consider an integer greater than or equal to 2. Call it A. Consider
another integer greater than or equal to 2. Call it B.

Raise A to the power B, storing the result in A. Now raise B to the
power A, storing the result in B. If you repeat this often enough,
you *will* hit a limit, no matter what numerical library you use.
But it is a limit of your computer, not of the library itself.

Nevertheless, it is a limit, and therefore the library *cannot* 'enable you to do "Arithmetic without Limitations"', and therefore BiGYaN's statement is nonsense.

Incidentally, you've just emerged from a 30-day spell in my sin bin. I hope I won't have to chuck you back in there.

Of course there are limits, but I don't agree that they necessarily have to be in the library. size_t is one limit, but if run on for example a windows box it will not be *the* limit. A win32 application is not allowed to allocate more than 2Gbytes of memory (and that's typically half of what size_t allows for), unless you buy a more expensive version of windows where that limit is raised to 3Gbytes.
It would also be possible for the mathematics library to internally use something else than a standard C pointer and internally use paging towards the system's hard disk or some internet based server or whatever (magnetic tape?) allowing for a *much* higher limit. Oh well the limit will still be there somewhere, but the calculation time will probably be the limiting factor instead...

No, I don't seriously suggest using magnetic tape as a paging media... but it would be possible!


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