// recursive factoring (precondition: n composite)
// currently only uses ECM
void factor_r(vec_pair_ZZ_long& factors, const ZZ& _n,
const ZZ& bnd, double failure_prob, bool verbose) {
ZZ q;
ZZ n(_n);
do {
// attempt to factor n
if (bnd>0)
ECM(q,n,bnd,failure_prob,verbose);
else
ECM(q,n,ZZ::zero(),0,verbose);
if (IsOne(q)) {
// give up
addFactor(factors,n);
return;
}
// compute other factor
div(n,n,q);
if (n<q) swap(n,q);
// q is small factor, n is large factor
if (ProbPrime_notd(q))
addFactor(factors,q);
else
factor_r(factors,q,bnd,failure_prob,verbose);
// check if n is still composite
if (ProbPrime_notd(n)) {
addFactor(factors,n);
return;
}
} while (true);
}
// trial division primitive
void TrialDivision(vec_pair_ZZ_long& factors, ZZ& q, const ZZ& n, long bnd) {
factors.SetLength(0);
if (&q!=&n) q=n;
if (bnd==0) {
bnd=10000; // should probably be higher
}
PrimeSeq s;
ZZ d;
for (long p=s.next(); (p>0 && p<=bnd); p=s.next()) {
if (DivRem(d,q,p)==0) {
long e=1;
q=d;
while (DivRem(d,q,p)==0) {
++e;
q=d;
}
addFactor(factors,to_ZZ(p),e);
if (IsOne(q))
return;
}
if (d<=p) {
// q must be prime
addFactor(factors,q);
set(q);
return;
}
}
}
// general purpose factoring method
void factor(vec_pair_ZZ_long& factors, const ZZ& _n,
const ZZ& bnd, double failure_prob,
bool verbose) {
ZZ n(_n);
if (n<=1) {
abs(n,n);
if (n<=1) {
factors.SetLength(0);
return;
}
}
// upper bound on size of smallest prime factor
ZZ upper_bound;
SqrRoot(upper_bound,n);
if (bnd>0 && bnd<upper_bound)
upper_bound=bnd;
// figure out appropriate lower_bound for trial division
long B1,B2,D;
double prob;
ECM_parameters(B1,B2,prob,D,NumBits(upper_bound),NumBits(n));
ZZ lower_bound;
conv(lower_bound,max(B2,1<<14));
if (lower_bound>upper_bound)
lower_bound=upper_bound;
// start factoring with trial division
TrialDivision(factors,n,n,to_long(lower_bound));
if (IsOne(n))
return;
if (upper_bound<=lower_bound || ProbPrime_notd(n)) {
addFactor(factors,n);
return;
}
/* n is composite and smallest prime factor is assumed to be such that
* lower_bound < factor <= upper_bound
*
* Ramp-up to searching for factors of size upper_bound. This is a good
* idea in cases where we have no idea what size factors N might have,
* but we don't want to spend too much time doing this.
*/
for(lower_bound<<=4; lower_bound<upper_bound; lower_bound<<=4) {
ZZ q;
ECM(q,n,lower_bound,1,verbose); // one curve only
if (!IsOne(q)) {
div(n,n,q);
if (n<q) swap(n,q);
// q is small factor, n is large factor
if (ProbPrime_notd(q))
addFactor(factors,q);
else
factor_r(factors,q,bnd,failure_prob,verbose);
if (ProbPrime_notd(n)) {
addFactor(factors,n);
return;
}
// new upper_bound
SqrRoot(upper_bound,n);
if (bnd>0 && bnd<upper_bound)
upper_bound=bnd;
}
}
// search for factors of size bnd
factor_r(factors,n,bnd,failure_prob,verbose);
}
void ExerciseFactorize::slotFactor19ButtonClicked()
{
addFactor(19);
return;
}
void ExerciseFactorize::slotFactor7ButtonClicked()
{
addFactor(7);
return;
}
