my own Integer-based LL-test not pass 3 Mprimes!?

[ktpn2011]

1. about your code: I just put main LL algo, instead of some 'modpow optimization'
2. back to sqrt. I looked in debugger, and Perl's BigInt
library is a GMP. And code executing was some written in MMX registers, possible name 'basecase_sqr', but from one glance, nothing like simple loops of MUL. need more info on that code.

[ktpn2011]

Originally Posted by science_man_88

... PARIdroid

Hi! I become interested and downloaded it, but some strange happens, 10^390625 is same, as (10^390625)^2 ; does [+++] means "more digits there"?

this just overflows 10^390625^2.

[science_man_88]

Originally Posted by ktpn2011

Hi! I become interested and downloaded it, but some strange happens, 10^390625 is same, as (10^390625)^2 ; this just overflows 10^390625^2.

allocatemem is you're friend that and parisizemax

[ktpn2011]

Originally Posted by science_man_88

allocatemem is you're friend that and parisizemax

i edited my question.. +++ means there are more number.

Now I just want to get 100m digit number in binary file. (not 100.. text)
Can I do it?

[ktpn2011]

got near
x=10^(390625*16); writebin ("outfile", x)

but not only number is inside, some other info

[CRGreathouse]

Originally Posted by ktpn2011

Now I just want to get 100m digit number in binary file. (not 100.. text)
Can I do it?

I mean, sure, but I wouldn't really recommend gp for this sort of thing.

Most directly you could do

binary(greatBigNumber)

and have it as a 332-million element vector. If that's too big you could do a bit more work to get it as a Vecsmall or peel off the digits one by one and write them to a file.

[ktpn2011]

Originally Posted by paulunderwood

If FFT is a bit daunting for you, you could easily implement Karatsuba.

today implemented Karatuba basic step..huh overcoming extra-bit problem

[danaj]

Regarding the Perl,

There are lots of little things one could do outside the powmod to be either cleaner or faster, but it is really irrelevent for this purpose.

Perl has multiple bigint backends, from the gawdawful-slow-but-super-portable pure Perl, old Pari, or GMP. Kriesel's script asks specifically for GMP though doesn't it will just whine and keep running if it isn't available.

Using the Math::BigInt front end has a lot of overhead for each operation. Math::GMPz is less portable (in that you *have* to have GMP) and more brittle for coding (get a type wrong and it barfs nastily), but has almost no overhead. Much more similar timings to using C+GMP.

Even so, for 86243 it is only about 15% slower than C+GMP using the same method (three step mul/pow, sub, mod). But it is about 5x slower than when we use the efficient mod for 2^p-1. E.g.

time perl -E 'use ntheory; say Math::Prime::Util::GMP::is_mersenne_prime(86243)'
1
user	0m11.391s

which uses code basically identical to what is shown at RosettaCode (since that was copied from the Perl module).

[kriesel]

Originally Posted by danaj

Regarding the Perl,

There are lots of little things one could do outside the powmod to be either cleaner or faster, but it is really irrelevent for this purpose.
...

Even so, for 86243 it is only about 15% slower than C+GMP using the same method (three step mul/pow, sub, mod). But it is about 5x slower than when we use the efficient mod for 2^p-1. E.g.

time perl -E 'use ntheory; say Math::Prime::Util::GMP::is_mersenne_prime(86243)'
1
user    0m11.391s

which uses code basically identical to what is shown at RosettaCode (since that was copied from the Perl module).

Very useful input.

That form of time is linux-specific; https://www.lifewire.com/command-ret...ommand-4054237
The following errors on windows 7;
perl -E 'use ntheory; say Math::Prime::Util::GMP::is_mersenne_prime(86243);'

Can't find string terminator "'" anywhere before EOF at -e line 1.

A Windows compatible rough equivalent but limited to one second resolution is pmp.pl

$t1=time();
use ntheory;
$p=86243;
$bool=Math::Prime::Util::GMP::is_mersenne_prime($p);
$dt=time()-$t1;
print "exponent $p yields $bool in $dt seconds\n";
# $bool 0 composite, 1 prime

On Windows, one could use cmd line time /T before and after but its resolution is only a minute then. One could use cmd line time with a <(file containing a carriage return) for a bit more time resolution, ~1/64 second.

time <cr.txt
time <cr.txt
perl pmp.pl
 time <cr.txt

On my i3-M370, one core, 86243 ntheory took ~149. seconds. I ran the ntheory version for several exponents and compensated the timings for the time required to get time at the cmd line (~.01 sec) It extrapolates to 4-8 times faster than the 3-step perl code, and 3 to 3200. times faster than the ASM code. All are orders of magnitude too slow for exponents at or beyond the GIMPS wavefront, hence irrelevant for GIMPS progress.

Interestingly, https://metacpan.org/pod/Math::Prime...mersenne_prime says it uses a list or table for various known Mersenne primes up to 37,156,667. The timings seem too long for that to be the case.

[danaj]

Originally Posted by kriesel

The following errors on windows 7;
perl -E 'use ntheory; say Math::Prime::Util::GMP::is_mersenne_prime(86243);'

The DOS shell is crippled in many ways. In this case it doesn't understand single quotes, so you need to use double quotes.

As for timing, I don't do a lot with it on Windows. It looks like you have to do some work yourself, maybe with Time::HiRes.

It extrapolates to 4-8 times faster than the 3-step perl code, and 3 to 3200. times faster than the ASM code. All are orders of magnitude too slow for exponents at or beyond the GIMPS wavefront, hence irrelevant for GIMPS progress.

This seems pretty close to what I see. It is using standard GMP calls so won't be remotely competitive with gwnum (used by prime95 / GIMPS) for large values. That is mentioned in the documentation.

Interestingly, https://metacpan.org/pod/Math::Prime...mersenne_prime says it uses a list or table for various known Mersenne primes up to 37,156,667. The timings seem too long for that to be the case.

Yes, the one-liner above is calling the GMP back-end directly, which bypasses those checks. If you took out the '::GMP' part you would get the standard C code (or Perl if you disable the C code) which has a list and checks it. It takes under a tenth of a second on my Macbook and would be much less for repeated calls.

[kriesel]

Originally Posted by danaj

The DOS shell is crippled in many ways. In this case it doesn't understand single quotes, so you need to use double quotes.

As for timing, I don't do a lot with it on Windows. It looks like you have to do some work yourself, maybe with Time::HiRes.

Yes. Or Powershell Measure Command. https://stackoverflow.com/questions/...-in-powershell

In http://perldoc.perl.org/Time/HiRes.html They're not kidding when stating "Some calls simply aren't available, real or emulated, on every platform."

use Time::HiRes qw( usleep ualarm gettimeofday tv_interval nanosleep          clock_gettime clock_getres clock_nanosleep clock stat lstat utime);

after a succession of messages similar to

Time::HiRes::ualarm(): unimplemented in this platform at hrt2.pl line 1.
BEGIN failed--compilation aborted at hrt2.pl line 3

. reduced to

use Time::HiRes qw( usleep gettimeofday tv_interval stat lstat );