FastECPP software and 50000 digit primality proof (reposted from NMBRTHRY) - Page 10

R. Gerbicz · 2022-05-19, 00:46

Quote:

Originally Posted by frmky

Looks like mpich. Did you install it through the package manager? If you did install it that way and don't have anything else relying on it, I recommend

Code:

sudo apt remove mpich
sudo apt install openmpi-bin libopenmpi-dev

Then do a full configure, make, and trial run.

With a newer gcc-10.3.0 using that it is worked, thank you all! Of course quickly proved that 1k, with a 4k:

Code:

gerbicz@gerbicz-MS-7972:~/cmexp3/cm-0.4.1dev/src$ mpirun ecpp-mpi -v -g -n '10^3999+4771' -c -f cert-4000
MPI with 3 workers initialised, of which 3 are local.
GMP: include 6.1.2, lib 6.1.2
MPFR: include 4.1.0, lib 4.1.0
MPC: include 1.2.1, lib 1.2.1
MPFRCX: include 0.6.3, lib 0.6.3
PARI: include 2.11.1, lib 2.11.1
Could not open file 'cert-4000.cert1' for reading.
Writing to 'cert-4000.cert1'.
-- Time for class numbers up to Dmax=44122804: 31.5 (10.5)
  ***   Warning:   ***   Warning: increasing stack size to 16777216.
  ***   Warning: increasing stack size to 16777216.
increasing stack size to 16777216.
  ***   Warning: increasing stack size to 33554432.
  ***   Warning: increasing stack size to 33554432.
  ***   Warning: increasing stack size to 33554432.
  ***   Warning: increasing stack size to 67108864.
  ***   Warning: increasing stack size to 67108864.
  ***   Warning: increasing stack size to 67108864.
-- Time for primorial of B=285893500: 11.9 (4.0)
-- hmaxprime: 29
-- Size [0]: 13285 bits
   Time for discriminant -35378335: 156.0 ( 56.3)
   largest prime of d: 523
   largest prime of h: 5
       discriminants: 6.4 (6.4)
      156 qroot:      45.5 (15.2)
    42229 Cornacchia: 37.8 (12.7)
      826 trial div:  7.9 (2.0)
      198 is_prime:   58.4 (19.9)
-- Size [1]: 13245 bits
   Time for discriminant   -36487:  69.9 ( 23.4)
   largest prime of d: 107
   largest prime of h: 19
       discriminants: 6.5 (6.5)
      189 qroot:      55.2 (18.8)
    58122 Cornacchia: 52.5 (17.7)
     1550 trial div:  15.5 (3.9)
      327 is_prime:   96.2 (32.9)
-- Size [2]: 13198 bits

paulunderwood · 2022-05-19, 10:13

Quote:

Originally Posted by paulunderwood

The attached code can be compiled with GWNUM (after that has compiled from P95 source) in the P95 directory

Then make the change to lib/nt.c of CM (FastECCP code):

Code:

int cm_nt_is_prime (mpz_t a) {
   char str[60000];
   if ( mpz_sizeinbase (a, 2) < 26000 ) { // is 26000 optimal?
      return (mpz_probab_prime_p(a, 0)>0);
   }
   strcpy (str, "/home/paul/Downloads/p95/gw_prp "); // note the space
   strcat (str, mpz_get_str(NULL, 10, a));
   return (system(str));
}

Obviously you'll need your own path for gw_prp!!!

I have not tried this on a cluster, but I guess you put the program in the mpi directories.

Note: running this code messes up CM's internal clock -- better to prefix the command with time to get wall time.

I am pretty sure it would be way better if the code was internal to CM instead of making use of system().

Check the sanity of the code!

I can't impress enough the usefulness of this hack. The threshold of ~26000 bits is optimal. At 44497 bits it is 30% quicker. Considering most of the time is spent at larger bit levels the hack could more than double the speed for a number of say 25k digits.

I just measured a ~25k digits (85349 bits) from "Size [0]" to "Size [2]" with a decrease in time from 39:49 minutes to 24:56 minutes -- about 60% speed up.

There is an error in the gw_prp.c attachment for the Lucas sequence: It should be LEN = bitlen(n) - 1; The fact that "-1" is missing is of no consequence because 2^2-2 == 2 and 2*a-a == a. Fix at will.

mart_r · 2022-05-19, 17:44

So when will R86453 be verified?

paulunderwood · 2022-05-19, 17:57

Quote:

Originally Posted by mart_r

So when will R86453 be verified?

I'd say 4-5 months on 1024 cores with my above hack.

You'd need to increase the char array size!

xilman · 2022-05-19, 19:04

Quote:

Originally Posted by paulunderwood

I'd say 4-5 months on 1024 cores with my above hack.

Looking forward to it!

Should be possible to run this as an internet-wide project ...

Paul (another one)

paulunderwood · 2022-05-20, 15:00

I have made a number of changes gw_prp.c (attached):

mpz strings are now base 16 for the system call to gw_prp
added bound check for A in the calculation on the discriminant D
used mpz instead of giants for loops and bit tests
moved squareness test to after Fermat PRP test

Important: Correspondingly the hack to lib/nt.c is:

Code:

int cm_nt_is_prime (mpz_t a) {
   char str[100000];
   if ( mpz_sizeinbase (a, 2) < 26000 ) {
      return (mpz_probab_prime_p(a, 0)>0);
   }
   strcpy(str, "/home/paul/Downloads/p95/gw_prp "); // note space in the string
   strcat(str, mpz_get_str(NULL, 16, a));
   return (system(str));
}

You have to set your own path(s) in the hack!!

R. Gerbicz · 2022-05-20, 15:34

Btw what the current code is doing is already an overshoot, though not that much, in nt.c:

Code:

int cm_nt_is_prime (mpz_t a)

{
   return (mpz_probab_prime_p (a, 0) > 0);
}

Because with that you are duplicating a trial division work (up to a lower bound), because before any powmod the gmp is doing a trial division, so in this place the correct way is to write:
return (mpz_millerrabin (a, 0) > 0);
In fact from (guessing) version 6.2.1 it will do also a strong Lucas test (if one Rabin is successful), but that is not a big deal.
And for earlier versions it is doing one Fermat test with base=210 and not a Rabin test when you call with reps=0, quite misleading function names.

frmky · 2022-05-21, 05:20

I just had a run get stuck on a step working on

Code:

45316390803984097515431023631892103885612957392000594099100021285758792520443724709396391306543503268096190322837859515866673871625561592044705792807440803947708908907614737717025433414398430578398260429903808077745088260091316370076526004919904661424339969809743238680989607370378967547156281025932580968892507449962380632213318260278558168471787932101671044457923993675114665325483114146022945608637609714927479748896016791346070989278565341391464839930365199105838661766996064324518536195747905563233126962022401765032061915788521397224045868544728828888066389285374270193193921699426406648608799563456412467290295625321383590670674753769747480184537039898532025040338420361488986162265523401014656817685444454432395319998589181423147547850705423029123801255311562441883330224429919852265213127673745216174580743551516719939030616241169325853999625407148745744272499519117498444921281424268560398456565789365909105075743569412570618662434380044032248880895284644180183569684459368853498365561443529411385715571563246535767567594228546425499909216250456114112719196095445261078172225023041827598437236185512143513343618970510558447792177136151782087004330545713587472421718700959692043757695326442365344491373239179095947753040876772804212692709049818049781390959078742604855209957870038475129029957826593048062052152503580934197923659278295258774063329455211580004368647356965289853928420209038458278624645084251627035308603445374775194786882131768430465049313962009971153188701196641954065456046907700584404515434807981659524535813939654198710798271825408211199781009304429379390988517358616887337595461528095624744926599829978359180854694499797458446146508252607193086010793503485916616240785235892171665685647235201582758617481929728074052944072393422044276634929971593836999818684367532124636699472306940638812946243617276508895415995560654539298741470305930582498594229338540140129896890597311560561325167861412998579874899980683387475753770331397884521827280915933425312895810874049050912565362714366947679028506865607543651666944818622970037797556956715178252948886793818560464719115948115171169408343941987322533894845589533113480356690078580719815270440254962575183460599947582493004236203701261021582918505709026679971640724690337170804646405210574685058717186027965302418783598405880942950369026430011503326388460356235153275102394480152395056388932273121801895199087195745442930206743903771868961856127169027839003857248213902369862944728949002196064131390051440762701346867774426920652025742398415821171450860322627236463628944562740058080797054501740197712322742567908518519280554716749124817316784076462026964301643417817211685510598265108249508865436100549516144896078260422710486782560912672166095421979793545338979226789747907019113869683216283788746644801488133000274968754658943760421498305262976385502791737074343740607065141397080138191159814172747983779354628927883755154237881376104720343896450020686559390223052514573303179892049020874146739822750160987976605380694678469657337935343164401432187317845370990069380390103309418434806208897154033512709320671120903090034673196636759734871688011284689567723323850722452921387391490853271028387582351828105202918727911076314821291073600727825517820093204716975695731468687813034516672059565455292732486476909360320855203511721324824419088194601574065152935099940567351980497687840674750874573306890127682156886720333346451245731279530385844576422405733265402959295341314382839445523548515120089660018723042205768815384308974712638456944742086228398510289107279822432995196807013921993753105027971082127906199154734298768425018929239377829306963254438492897935666241521283516569138047719504130503287482074006712983233662325973225948335012687972440895046781948354479667155209040994734509279859515414052740463303848818829426804232968255007804292805132982902893283937185357904740888196203356049006382059409505147078996903441012383977575190101704740310495966851817015834912341924515907690440592696923574818129506140995021064759768715552614068566319317983183485630680265200320447035110209718706444078827318969919987680821106527734448380429809728300446705018019328279748116471907584255683214391652565135909803291237262218342682224858343846768424688014337880683578749729654852081390941767909226855880737355784059448652447047028352531751100120248662606425847095349473404087214795952172060188977960963733361962696101099265246407540679740814257732190588235207663651296880411214224288381444615541107992065020757092208937469771613451624239790315960478449836060659173305470358506086468219305921426025845832919623235701913958284288898088846230133697087063743906974504567013102079161938108694579777747144259440428052354975128874092684753490463489190489412318570068470193365721393937770074058430439348595615160604927954902272287409209856514399706780027578114317030153944168953758500581898788471172793830277194643819200602088800433297422107135985928693922214543564082398587195157163277040239976491178578641279899525230912876032407219276678948175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After a few hours, it stopped with the message

Code:

***** Error: cm_nt_next_prime called with an argument
that is too large for the precomputed list.

paulunderwood · 2022-05-21, 06:11

Quote:

Originally Posted by frmky

I just had a run get stuck on a step working on

Code:

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After a few hours, it stopped with the message

Code:

***** Error: cm_nt_next_prime called with an argument
that is too large for the precomputed list.

Have you tried recompiling the code in the cm_nt_next_prime function within lib/nt.c with:

Code:

#ifdef WITH_MPI
//   static unsigned long int P [664579];
//      /* primes up to 10^7 */
   static unsigned long int P [5761455];
      /* primes up to 10^8 */
#else
   static unsigned long int P [9592];
      /* primes up to 10^5 */
#endif

mart_r · 2022-05-21, 09:35

Quote:

Originally Posted by paulunderwood

I'd say 4-5 months on 1024 cores with my above hack.

Awesome!

Quote:

Originally Posted by sweety439

When will 8*13^32020+183 [...] be verified?

That should be doable in about a week or two on a reasonably fast PC.

I'm pondering testing a couple of numbers once the program is easy enough for me to use. I'm really lost when it comes to compiling like the way it's being discussed here.

xilman · 2022-05-21, 10:24

Quote:

Originally Posted by mart_r

I'm really lost when it comes to compiling like the way it's being discussed here.

That is readily fixable. All it needs is practice. I'm sure that a number of people here will help you to learn.

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2022-05-19, 17:44	#102
mart_r Dec 2008 you know...around... 762₁₀ Posts	So when will R86453 be verified?

2022-05-20, 15:34	#106
R. Gerbicz "Robert Gerbicz" Oct 2005 Hungary 11²·13 Posts	Btw what the current code is doing is already an overshoot, though not that much, in nt.c: Code: int cm_nt_is_prime (mpz_t a) { return (mpz_probab_prime_p (a, 0) > 0); } Because with that you are duplicating a trial division work (up to a lower bound), because before any powmod the gmp is doing a trial division, so in this place the correct way is to write: return (mpz_millerrabin (a, 0) > 0); In fact from (guessing) version 6.2.1 it will do also a strong Lucas test (if one Rabin is successful), but that is not a big deal. And for earlier versions it is doing one Fermat test with base=210 and not a Rabin test when you call with reps=0, quite misleading function names.