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/**************************************************************************
* *
* Regina - A Normal Surface Theory Calculator *
* Computational Engine *
* *
* Copyright (c) 1999-2016, Ben Burton *
* For further details contact Ben Burton (bab@debian.org). *
* *
* This program is free software; you can redistribute it and/or *
* modify it under the terms of the GNU General Public License as *
* published by the Free Software Foundation; either version 2 of the *
* License, or (at your option) any later version. *
* *
* As an exception, when this program is distributed through (i) the *
* App Store by Apple Inc.; (ii) the Mac App Store by Apple Inc.; or *
* (iii) Google Play by Google Inc., then that store may impose any *
* digital rights management, device limits and/or redistribution *
* restrictions that are required by its terms of service. *
* *
* This program is distributed in the hope that it will be useful, but *
* WITHOUT ANY WARRANTY; without even the implied warranty of *
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU *
* General Public License for more details. *
* *
* You should have received a copy of the GNU General Public *
* License along with this program; if not, write to the Free *
* Software Foundation, Inc., 51 Franklin St, Fifth Floor, Boston, *
* MA 02110-1301, USA. *
* *
**************************************************************************/
#include "maths/primes.h"
namespace regina {
std::vector<Integer> Primes::largePrimes;
std::mutex Primes::largeMutex;
Integer Primes::prime(unsigned long which, bool autoGrow) {
// Can we grab it straight out of the hard-coded seed list?
if (which < numPrimeSeeds)
return primeSeedList[which];
// From here we need to ensure thread safety.
std::lock_guard<std::mutex> lock(largeMutex);
// Do we even have the requested prime stored?
if (which >= numPrimeSeeds + largePrimes.size()) {
if (autoGrow)
growPrimeList(which - numPrimeSeeds - largePrimes.size() + 1);
else
return Integer::zero;
}
// Got it.
return largePrimes[which - numPrimeSeeds];
}
void Primes::growPrimeList(unsigned long extras) {
Integer lastPrime = (largePrimes.empty() ?
primeSeedList[numPrimeSeeds - 1] :
largePrimes[largePrimes.size() - 1]);
Integer newPrime;
// Since this is all being done through GMP, just bite the bullet
// and make them all GMP integers (not native integers).
// This means we can call rawData() with abandon.
while (extras) {
mpz_nextprime(newPrime.rawData(), lastPrime.rawData());
newPrime.tryReduce(); // since rawData() forced it into GMP format
largePrimes.push_back(newPrime);
lastPrime = newPrime;
extras--;
}
}
std::vector<Integer> Primes::primeDecomp(const Integer& n) {
std::vector<Integer> retval;
// Deal with n=0 first.
if (n == Integer::zero) {
retval.push_back(Integer::zero);
return retval;
}
Integer temp(n);
Integer r,q;
// if the number is negative, put -1 as first factor.
if (temp < Integer::zero) {
temp.negate();
retval.push_back(Integer(-1));
}
// repeatedly divide the number by the smallest primes until no
// longer divisible.
// at present the algorithm is only guaranteed to factorize the integer
// into its prime factors if none of them are larger than the 500th smallest
// prime. it always produces a factorization, but after the 500th it uses
// a probabilistic test to speed things up. This algorithm is at present
// ad-hoc since the current usage in Regina rarely demands the
// factorization of even a 4-digit number.
unsigned long cpi=0; // current prime index.
unsigned long iterSinceDivision=0; // keeps track of how many iterations
// since the last successful division
while ( temp != Integer::one ) {
// now cpi<size(), check to see if temp % prime(cpi) == 0
q = temp.divisionAlg(prime(cpi), r); // means temp = q*prime(cpi) + r
if (r == Integer::zero) {
temp=q;
retval.push_back(prime(cpi));
iterSinceDivision=0;
continue;
}
cpi++;
iterSinceDivision++;
// after 500 unsuccessful divisions,
// check to see if it is probably prime.
if (iterSinceDivision == 500) {
int res = mpz_probab_prime_p (temp.rawData(), 10);
// Calling rawData() made temp fat (GMP); try to make it
// native again if we can (for performance).
temp.tryReduce();
if (res) {
// temp is likely prime.
// end the search.
retval.push_back(temp);
break;
}
}
}
return retval; // now it's reasonably fast for small numbers.
// it tends to bog down on numbers with two or more large
// prime factors. the GAP algorithm is better, whatever
// that is... should consider importing it.
}
std::vector<std::pair<Integer, unsigned long> >
Primes::primePowerDecomp(const Integer& n) {
std::vector<Integer> list1(primeDecomp(n));
std::vector< std::pair<Integer, unsigned long> > retlist;
// go through list1, record number of each prime, put in retlist.
if (! list1.empty()) {
Integer cp(list1.front()); // current prime
unsigned long cc(1); // current count
std::vector<Integer>::const_iterator it = list1.begin();
for (++it; it != list1.end(); ++it) {
if (*it == cp)
cc++;
else {
// a new prime is coming up.
retlist.push_back(std::make_pair( cp, cc ) );
cp = *it;
cc = 1;
}
}
retlist.push_back(std::make_pair( cp, cc ) );
}
return retlist;
}
} // namespace regina
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