At last night's clinic, we were discussing the problem of calculating
the factorial of large numbers in full precision. When the building
alarm kicked us out at 9:30, I was waiting for a compile to complete.
Here's a followup (mostly for Neil's benefit, since he seemed to be
somewhat interested).
I downloaded and built this library.
CLN - Class Library for Numbers
http://www.ginac.de/CLN/
Then I compiled and linked this program with it.
#include <cln/integer.h>
#include <cln/io.h>
#include <cln/integer_io.h>
main(int argc, const char *argv[])
{
for (int i = 1; i < argc; i++) {
char *endptr = NULL;
unsigned long n = strtoul(argv[i], &endptr, 10);
if (*endptr) {
std::cerr << argv[i] << " not numeric" << std::endl;
} else {
cln::cl_I nf = cln::factorial(n);
std::cout << n << "! = " << nf << std::endl;
}
}
}
Then I ran it:
bash$ time ./factorial 1000000 > /tmp/1000000!
real 1m6.455s
user 1m5.445s
sys 0m1.010s
bash$ wc /tmp/1000000!
1 3 5565721 /tmp/1000000!
bash$ echo `head -30c /tmp/1000000\!` ... `tail -30c /tmp/1000000\!`
1000000! = 8263931688331240062 ... 00000000000000000000000000000
Just over a minute, including the I/O. Pretty speedy...
I read somewhere that 1,000,000! was first computed in full precision
in 1986 on a VAX. I don't remember how many days or weeks the
computation ran, and I can't find the book where I read it.
--
Bob Miller K<bob>
kbobsoft software consulting
http://kbobsoft.com [EMAIL PROTECTED]
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