// {{{ sieve()
void sieve(Polynomial &polynomial, Target &target, FactorBase &fb,
int pairs_needed, std::vector<int> &av, std::vector<int> &bv)
{
std::vector<double> normv;
int b = 0;
int pairs_found = 0;
normv.resize(2*target.C+1);
av.resize(pairs_needed);
bv.resize(pairs_needed);
int u = polynomial.d*target.t;
int i;
int p;
NTL::ZZ numZ;
NTL::ZZ valZ;
while(pairs_found < pairs_needed)
{
// Note: i-C = a
int a;
b++;
for(i=0; i<=2*target.C; i++)
{
valZ = (i-target.C) + b*polynomial.m;
if(NTL::GCD(i-target.C, b)!=1 || valZ==0)
normv[i] = SKIP;
else
normv[i] = 0.5 - log(abs(valZ));
}
// Test for RFB-smoothness
for(i=0; i < target.t; i++)
{
p = fb.RFB[i];
a = (int)(p * (-floor(target.C / p)) - (b * fb.RFBm[i])) + target.C;
while(a < 0)
a += p;
while(a <= 2*target.C)
{
if(normv[a] != SKIP)
normv[a] += fb.RFBlog[i];
a += p;
}
// Now check p^2, p^3, ....
int pPow = p * p;
while(pPow < 2 * target.C)
{
a = (int)(pPow * (-floor(target.C/pPow))-
(b*(polynomial.m % pPow))) + target.C;
while(a < 0)
a += pPow;
while(a <= 2*target.C)
{
if(normv[a] != SKIP)
normv[a] += fb.RFBlog[i];
a += pPow;
}
pPow *= p;
}
}
// Initialize normv with -ln( (-b)^d*f(-a/b) )
for(i=0; i<=2*target.C; i++)
{
if(normv[i] > 0)
{
// init Norm
numZ = abs(algebraic_norm(polynomial, i-target.C, b));
if(numZ == 0)
normv[i] = SKIP;
else
normv[i] = fb.AFBlog[u-1] - log(numZ);
}
else
normv[i] = SKIP;
}
// Test for AFB-smoothness
for(i=0; i<u; i++)
{
p = fb.AFB[i];
a = (int)(p * (-floor(target.C / p)) - (b * fb.AFBr[i])) + target.C;
while(a < 0)
a += p;
while(a <= 2*target.C)
{
if(normv[a] != SKIP)
normv[a] += fb.AFBlog[i];
a += p;
}
}
// Search for good (a,b)'s
for(int i=0; i<=2*target.C; i++)
{
if(normv[i] > 0)
{
if(pairs_found < pairs_needed)
{
av[pairs_found] = i-target.C;
bv[pairs_found++] = b;
}
}
}
// info
std::cout << "\tit: " << b << " relation: " << pairs_found
<< " needed: " << pairs_needed << " completed: ("
<< (pairs_found*100)/pairs_needed << "%)\r";
}
}
// {{{ linear_algebra()
void linear_algebra(
GNFS::Polynomial &polynomial,
GNFS::Target &target,
FactorBase &fb,
Matrix &matrix,
const std::vector<int> &av,
const std::vector<int> &bv)
{
NTL::ZZ aZ;
NTL::ZZ bZ;
NTL::ZZ pZ;
NTL::ZZ valZ;
NTL::ZZ numZ;
int i;
int j;
int k;
int u = polynomial.d*target.t;
// Initialize sM
for(j = 0; j <= matrix.sM.NumCols()-1; j++)
{
// Initialize row
for(k = 0; k < matrix.sM.NumCols()-1; k++)
matrix.sM[k][j] = 0;
// Set the first column
aZ = av[j];
bZ = bv[j];
valZ = aZ + bZ * polynomial.m;
if(valZ < 0)
{
valZ *= -1;
matrix.sM[0][j] = 1;
}
// Set a RFB row
i = 0;
while(i < target.t && valZ != 1)
{
pZ = fb.RFB[i];
if(valZ % pZ == 0)
{
if(matrix.sM[1+i][j]==0) matrix.sM[1+i][j]=1;
else matrix.sM[1+i][j]=0;
valZ = valZ / pZ;
}
else i++;
}
// Set a AFB row
valZ = algebraic_norm(polynomial, av[j], bv[j]);
if(valZ < 0)
valZ *= -1;
i = 0;
while(i<u && valZ!=1)
{
pZ = fb.AFB[i];
if(valZ % pZ == 0)
{
numZ = fb.AFBr[i];
//while((aZ + bZ * numZ) % pZ != 0 && i<target.t) // TODO
while((aZ + bZ * numZ) % pZ != 0) // TODO
{
pZ = fb.AFB[++i];
numZ = fb.AFBr[i];
}
if(matrix.sM[1+target.t+i][j]==0) matrix.sM[1+target.t+i][j]=1;
else matrix.sM[1+target.t+i][j]=0;
valZ = valZ / pZ;
}
else i++;
}
// Set a QCB row
for(i=0; i<target.digits; i++)
{
numZ = fb.QCB[i];
valZ = fb.QCBs[i];
valZ = aZ + bZ * valZ;
if(Legendre(valZ, numZ) != 1)
{
matrix.sM[1+target.t+u+i][j]=1;
}
}
}
std::cout << "\tSize: " << matrix.sM.NumRows() << "x" << matrix.sM.NumCols() << std::endl;
gaussian_elimination(matrix.sM);
matrix.sfreeCols = get_freecols(matrix.sM);
}
