static
long BKZ_XD(mat_ZZ& BB, mat_ZZ* UU, xdouble delta,
long beta, long prune, LLLCheckFct check)
{
long m = BB.NumRows();
long n = BB.NumCols();
long m_orig = m;
long i, j;
ZZ MU;
xdouble t1;
ZZ T1;
xdouble *tp;
init_red_fudge();
mat_ZZ B;
B = BB;
B.SetDims(m+1, n);
Unique2DArray<xdouble> B1_store;
B1_store.SetDimsFrom1(m+2, n+1);
xdouble **B1 = B1_store.get(); // approximates B
Unique2DArray<xdouble> mu_store;
mu_store.SetDimsFrom1(m+2, m+1);
xdouble **mu = mu_store.get();
UniqueArray<xdouble> c_store;
c_store.SetLength(m+2);
xdouble *c = c_store.get(); // squared lengths of Gramm-Schmidt basis vectors
UniqueArray<xdouble> b_store;
b_store.SetLength(m+2);
xdouble *b = b_store.get(); // squared lengths of basis vectors
xdouble cbar;
UniqueArray<xdouble> ctilda_store;
ctilda_store.SetLength(m+2);
xdouble *ctilda = ctilda_store.get();
UniqueArray<xdouble> vvec_store;
vvec_store.SetLength(m+2);
xdouble *vvec = vvec_store.get();
UniqueArray<xdouble> yvec_store;
yvec_store.SetLength(m+2);
xdouble *yvec = yvec_store.get();
UniqueArray<xdouble> uvec_store;
uvec_store.SetLength(m+2);
xdouble *uvec = uvec_store.get();
UniqueArray<xdouble> utildavec_store;
utildavec_store.SetLength(m+2);
xdouble *utildavec = utildavec_store.get();
UniqueArray<long> Deltavec_store;
Deltavec_store.SetLength(m+2);
long *Deltavec = Deltavec_store.get();
UniqueArray<long> deltavec_store;
deltavec_store.SetLength(m+2);
long *deltavec = deltavec_store.get();;
mat_ZZ Ulocal;
mat_ZZ *U;
if (UU) {
Ulocal.SetDims(m+1, m);
for (i = 1; i <= m; i++)
conv(Ulocal(i, i), 1);
U = &Ulocal;
}
else
U = 0;
long quit;
long new_m;
long z, jj, kk;
long s, t;
long h;
xdouble eta;
for (i = 1; i <=m; i++)
for (j = 1; j <= n; j++)
conv(B1[i][j], B(i, j));
for (i = 1; i <= m; i++) {
b[i] = InnerProduct(B1[i], B1[i], n);
}
// cerr << "\n";
// cerr << "first LLL\n";
m = ll_LLL_XD(B, U, delta, 0, check, B1, mu, b, c, m, 1, quit);
double tt;
double enum_time = 0;
unsigned long NumIterations = 0;
unsigned long NumTrivial = 0;
unsigned long NumNonTrivial = 0;
unsigned long NumNoOps = 0;
long verb = verbose;
verbose = 0;
if (m < m_orig) {
for (i = m_orig+1; i >= m+2; i--) {
// swap i, i-1
swap(B(i), B(i-1));
if (U) swap((*U)(i), (*U)(i-1));
}
}
long clean = 1;
if (!quit && m > 1) {
// cerr << "continuing\n";
if (beta > m) beta = m;
if (prune > 0)
ComputeBKZConstant(beta, prune);
z = 0;
jj = 0;
while (z < m-1) {
jj++;
kk = min(jj+beta-1, m);
if (jj == m) {
jj = 1;
kk = beta;
clean = 1;
}
if (verb) {
tt = GetTime();
if (tt > LastTime + LLLStatusInterval)
BKZStatus(tt, enum_time, NumIterations, NumTrivial,
NumNonTrivial, NumNoOps, m, B);
}
// ENUM
double tt1;
if (verb) {
tt1 = GetTime();
}
if (prune > 0)
ComputeBKZThresh(&c[jj], kk-jj+1);
cbar = c[jj];
utildavec[jj] = uvec[jj] = 1;
yvec[jj] = vvec[jj] = 0;
Deltavec[jj] = 0;
s = t = jj;
deltavec[jj] = 1;
for (i = jj+1; i <= kk+1; i++) {
ctilda[i] = uvec[i] = utildavec[i] = yvec[i] = 0;
Deltavec[i] = 0;
vvec[i] = 0;
deltavec[i] = 1;
}
long enum_cnt = 0;
while (t <= kk) {
if (verb) {
enum_cnt++;
if (enum_cnt > 100000) {
enum_cnt = 0;
tt = GetTime();
if (tt > LastTime + LLLStatusInterval) {
enum_time += tt - tt1;
tt1 = tt;
BKZStatus(tt, enum_time, NumIterations, NumTrivial,
NumNonTrivial, NumNoOps, m, B);
}
}
}
ctilda[t] = ctilda[t+1] +
(yvec[t]+utildavec[t])*(yvec[t]+utildavec[t])*c[t];
if (prune > 0 && t > jj) {
eta = BKZThresh(t-jj);
}
else
eta = 0;
if (ctilda[t] < cbar - eta) {
if (t > jj) {
t--;
t1 = 0;
for (i = t+1; i <= s; i++) {
t1 += utildavec[i]*mu[i][t];
}
yvec[t] = t1;
t1 = -t1;
if (t1 >= 0)
t1 = ceil(t1-0.5);
else
t1 = floor(t1+0.5);
utildavec[t] = vvec[t] = t1;
Deltavec[t] = 0;
if (utildavec[t] > -yvec[t])
deltavec[t] = -1;
else
deltavec[t] = 1;
}
else {
cbar = ctilda[jj];
for (i = jj; i <= kk; i++) {
uvec[i] = utildavec[i];
}
}
}
else {
t++;
s = max(s, t);
if (t < s) Deltavec[t] = -Deltavec[t];
if (Deltavec[t]*deltavec[t] >= 0) Deltavec[t] += deltavec[t];
utildavec[t] = vvec[t] + Deltavec[t];
}
}
if (verb) {
tt1 = GetTime() - tt1;
enum_time += tt1;
}
NumIterations++;
h = min(kk+1, m);
if ((delta-8*red_fudge)*c[jj] > cbar) {
clean = 0;
// we treat the case that the new vector is b_s (jj < s <= kk)
// as a special case that appears to occur most of the time.
s = 0;
for (i = jj+1; i <= kk; i++) {
if (uvec[i] != 0) {
if (s == 0)
s = i;
else
s = -1;
}
}
if (s == 0) LogicError("BKZ_XD: internal error");
if (s > 0) {
// special case
NumTrivial++;
for (i = s; i > jj; i--) {
// swap i, i-1
swap(B(i-1), B(i));
if (U) swap((*U)(i-1), (*U)(i));
tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp;
t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1;
}
// cerr << "special case\n";
new_m = ll_LLL_XD(B, U, delta, 0, check,
B1, mu, b, c, h, jj, quit);
if (new_m != h) LogicError("BKZ_XD: internal error");
if (quit) break;
}
else {
// the general case
NumNonTrivial++;
for (i = 1; i <= n; i++) conv(B(m+1, i), 0);
if (U) {
for (i = 1; i <= m_orig; i++)
conv((*U)(m+1, i), 0);
}
for (i = jj; i <= kk; i++) {
if (uvec[i] == 0) continue;
conv(MU, uvec[i]);
RowTransform2(B(m+1), B(i), MU);
if (U) RowTransform2((*U)(m+1), (*U)(i), MU);
}
for (i = m+1; i >= jj+1; i--) {
// swap i, i-1
swap(B(i-1), B(i));
if (U) swap((*U)(i-1), (*U)(i));
tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp;
t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1;
}
for (i = 1; i <= n; i++)
conv(B1[jj][i], B(jj, i));
b[jj] = InnerProduct(B1[jj], B1[jj], n);
if (b[jj] == 0) LogicError("BKZ_XD: internal error");
// remove linear dependencies
// cerr << "general case\n";
new_m = ll_LLL_XD(B, U, delta, 0, 0, B1, mu, b, c, kk+1, jj, quit);
if (new_m != kk) LogicError("BKZ_XD: internal error");
// remove zero vector
for (i = kk+2; i <= m+1; i++) {
// swap i, i-1
swap(B(i-1), B(i));
if (U) swap((*U)(i-1), (*U)(i));
tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp;
t1 = b[i-1]; b[i-1] = b[i]; b[i] = t1;
}
quit = 0;
if (check) {
for (i = 1; i <= kk; i++)
if ((*check)(B(i))) {
quit = 1;
break;
}
}
if (quit) break;
if (h > kk) {
// extend reduced basis
new_m = ll_LLL_XD(B, U, delta, 0, check,
B1, mu, b, c, h, h, quit);
if (new_m != h) LogicError("BKZ_XD: internal error");
if (quit) break;
}
}
z = 0;
}
else {
// LLL_XD
// cerr << "progress\n";
NumNoOps++;
if (!clean) {
new_m =
ll_LLL_XD(B, U, delta, 0, check, B1, mu, b, c, h, h, quit);
if (new_m != h) LogicError("BKZ_XD: internal error");
if (quit) break;
}
z++;
}
}
}
if (verb) {
BKZStatus(GetTime(), enum_time, NumIterations, NumTrivial, NumNonTrivial,
NumNoOps, m, B);
}
// clean up
if (m_orig > m) {
// for consistency, we move zero vectors to the front
for (i = m+1; i <= m_orig; i++) {
swap(B(i), B(i+1));
if (U) swap((*U)(i), (*U)(i+1));
}
for (i = 0; i < m; i++) {
swap(B(m_orig-i), B(m-i));
if (U) swap((*U)(m_orig-i), (*U)(m-i));
}
}
B.SetDims(m_orig, n);
BB = B;
if (U) {
U->SetDims(m_orig, m_orig);
*UU = *U;
}
return m;
}
static
long LLL_XD(mat_ZZ& B, mat_ZZ* U, xdouble delta, long deep,
LLLCheckFct check)
{
long m = B.NumRows();
long n = B.NumCols();
long i, j;
long new_m, dep, quit;
xdouble s;
ZZ MU;
xdouble mu1;
xdouble t1;
ZZ T1;
init_red_fudge();
if (U) ident(*U, m);
Unique2DArray<xdouble> B1_store;
B1_store.SetDimsFrom1(m+1, n+1);
xdouble **B1 = B1_store.get(); // approximates B
Unique2DArray<xdouble> mu_store;
mu_store.SetDimsFrom1(m+1, m+1);
xdouble **mu = mu_store.get();
UniqueArray<xdouble> c_store;
c_store.SetLength(m+1);
xdouble *c = c_store.get(); // squared lengths of Gramm-Schmidt basis vectors
UniqueArray<xdouble> b_store;
b_store.SetLength(m+1);
xdouble *b = b_store.get(); // squared lengths of basis vectors
for (i = 1; i <=m; i++)
for (j = 1; j <= n; j++)
conv(B1[i][j], B(i, j));
for (i = 1; i <= m; i++) {
b[i] = InnerProduct(B1[i], B1[i], n);
}
new_m = ll_LLL_XD(B, U, delta, deep, check, B1, mu, b, c, m, 1, quit);
dep = m - new_m;
m = new_m;
if (dep > 0) {
// for consistency, we move all of the zero rows to the front
for (i = 0; i < m; i++) {
swap(B(m+dep-i), B(m-i));
if (U) swap((*U)(m+dep-i), (*U)(m-i));
}
}
return m;
}
static
long G_BKZ_XD(mat_ZZ& BB, mat_ZZ* UU, xdouble delta,
long beta, long prune, LLLCheckFct check)
{
long m = BB.NumRows();
long n = BB.NumCols();
long m_orig = m;
long i, j;
ZZ MU;
xdouble t1;
ZZ T1;
xdouble *tp;
init_red_fudge();
mat_ZZ B;
B = BB;
B.SetDims(m+1, n);
xdouble **B1; // approximates B
typedef xdouble *xdoubleptr;
B1 = NTL_NEW_OP xdoubleptr[m+2];
if (!B1) Error("G_BKZ_XD: out of memory");
for (i = 1; i <= m+1; i++) {
B1[i] = NTL_NEW_OP xdouble[n+1];
if (!B1[i]) Error("G_BKZ_XD: out of memory");
}
xdouble **mu;
mu = NTL_NEW_OP xdoubleptr[m+2];
if (!mu) Error("G_BKZ_XD: out of memory");
for (i = 1; i <= m+1; i++) {
mu[i] = NTL_NEW_OP xdouble[n+2];
if (!mu[i]) Error("G_BKZ_XD: out of memory");
}
xdouble **aux;
aux = NTL_NEW_OP xdoubleptr[m+2];
if (!aux) Error("G_BKZ_XD: out of memory");
for (i = 1; i <= m+1; i++) {
aux[i] = NTL_NEW_OP xdouble[n+1];
if (!aux[i]) Error("G_BKZ_XD: out of memory");
}
xdouble *c; // squared lengths of Gramm-Schmidt basis vectors
c = NTL_NEW_OP xdouble[m+2];
if (!c) Error("G_BKZ_XD: out of memory");
xdouble cbar;
xdouble *ctilda;
ctilda = NTL_NEW_OP xdouble[m+2];
if (!ctilda) Error("G_BKZ_XD: out of memory");
xdouble *vvec;
vvec = NTL_NEW_OP xdouble[m+2];
if (!vvec) Error("G_BKZ_XD: out of memory");
xdouble *yvec;
yvec = NTL_NEW_OP xdouble[m+2];
if (!yvec) Error("G_BKZ_XD: out of memory");
xdouble *uvec;
uvec = NTL_NEW_OP xdouble[m+2];
if (!uvec) Error("G_BKZ_XD: out of memory");
xdouble *utildavec;
utildavec = NTL_NEW_OP xdouble[m+2];
if (!utildavec) Error("G_BKZ_XD: out of memory");
long *Deltavec;
Deltavec = NTL_NEW_OP long[m+2];
if (!Deltavec) Error("G_BKZ_XD: out of memory");
long *deltavec;
deltavec = NTL_NEW_OP long[m+2];
if (!deltavec) Error("G_BKZ_XD: out of memory");
mat_ZZ Ulocal;
mat_ZZ *U;
if (UU) {
Ulocal.SetDims(m+1, m);
for (i = 1; i <= m; i++)
conv(Ulocal(i, i), 1);
U = &Ulocal;
}
else
U = 0;
long quit;
long new_m;
long z, jj, kk;
long s, t;
long h;
xdouble eta;
for (i = 1; i <=m; i++)
for (j = 1; j <= n; j++)
conv(B1[i][j], B(i, j));
// cerr << "\n";
// cerr << "first G_LLL\n";
GivensCache_XD cache(m, n);
m = ll_G_LLL_XD(B, U, delta, 0, check, B1, mu, aux, m, 1, quit, cache);
double tt;
double enum_time = 0;
unsigned long NumIterations = 0;
unsigned long NumTrivial = 0;
unsigned long NumNonTrivial = 0;
unsigned long NumNoOps = 0;
long verb = verbose;
verbose = 0;
if (m < m_orig) {
for (i = m_orig+1; i >= m+2; i--) {
// swap i, i-1
swap(B(i), B(i-1));
if (U) swap((*U)(i), (*U)(i-1));
}
}
long clean = 1;
if (!quit && m > 1) {
// cerr << "continuing\n";
if (beta > m) beta = m;
if (prune > 0)
ComputeG_BKZConstant(beta, prune);
z = 0;
jj = 0;
while (z < m-1) {
jj++;
kk = min(jj+beta-1, m);
if (jj == m) {
jj = 1;
kk = beta;
clean = 1;
}
if (verb) {
tt = GetTime();
if (tt > LastTime + LLLStatusInterval)
G_BKZStatus(tt, enum_time, NumIterations, NumTrivial,
NumNonTrivial, NumNoOps, m, B);
}
// ENUM
double tt1;
if (verb) {
tt1 = GetTime();
}
for (i = jj; i <= kk; i++)
c[i] = mu[i][i]*mu[i][i];
if (prune > 0)
ComputeG_BKZThresh(&c[jj], kk-jj+1);
cbar = c[jj];
utildavec[jj] = uvec[jj] = 1;
yvec[jj] = vvec[jj] = 0;
Deltavec[jj] = 0;
s = t = jj;
deltavec[jj] = 1;
for (i = jj+1; i <= kk+1; i++) {
ctilda[i] = uvec[i] = utildavec[i] = yvec[i] = 0;
Deltavec[i] = 0;
vvec[i] = 0;
deltavec[i] = 1;
}
long enum_cnt = 0;
while (t <= kk) {
if (verb) {
enum_cnt++;
if (enum_cnt > 100000) {
enum_cnt = 0;
tt = GetTime();
if (tt > LastTime + LLLStatusInterval) {
enum_time += tt - tt1;
tt1 = tt;
G_BKZStatus(tt, enum_time, NumIterations, NumTrivial,
NumNonTrivial, NumNoOps, m, B);
}
}
}
ctilda[t] = ctilda[t+1] +
(yvec[t]+utildavec[t])*(yvec[t]+utildavec[t])*c[t];
if (prune > 0 && t > jj) {
eta = G_BKZThresh(t-jj);
}
else
eta = 0;
if (ctilda[t] < cbar - eta) {
if (t > jj) {
t--;
t1 = 0;
for (i = t+1; i <= s; i++) {
t1 += utildavec[i]*mu[i][t];
}
yvec[t] = t1;
t1 = -t1;
if (t1 >= 0)
t1 = ceil(t1-0.5);
else
t1 = floor(t1+0.5);
utildavec[t] = vvec[t] = t1;
Deltavec[t] = 0;
if (utildavec[t] > -yvec[t])
deltavec[t] = -1;
else
deltavec[t] = 1;
}
else {
cbar = ctilda[jj];
for (i = jj; i <= kk; i++) {
uvec[i] = utildavec[i];
}
}
}
else {
t++;
s = max(s, t);
if (t < s) Deltavec[t] = -Deltavec[t];
if (Deltavec[t]*deltavec[t] >= 0) Deltavec[t] += deltavec[t];
utildavec[t] = vvec[t] + Deltavec[t];
}
}
if (verb) {
tt1 = GetTime() - tt1;
enum_time += tt1;
}
NumIterations++;
h = min(kk+1, m);
if ((delta-8*red_fudge)*c[jj] > cbar) {
clean = 0;
// we treat the case that the new vector is b_s (jj < s <= kk)
// as a special case that appears to occur most of the time.
s = 0;
for (i = jj+1; i <= kk; i++) {
if (uvec[i] != 0) {
if (s == 0)
s = i;
else
s = -1;
}
}
if (s == 0) Error("G_BKZ_XD: internal error");
if (s > 0) {
// special case
NumTrivial++;
for (i = s; i > jj; i--) {
// swap i, i-1
swap(B(i-1), B(i));
if (U) swap((*U)(i-1), (*U)(i));
tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp;
}
// cerr << "special case\n";
new_m = ll_G_LLL_XD(B, U, delta, 0, check,
B1, mu, aux, h, jj, quit, cache);
if (new_m != h) Error("G_BKZ_XD: internal error");
if (quit) break;
}
else {
// the general case
NumNonTrivial++;
for (i = 1; i <= n; i++) conv(B(m+1, i), 0);
if (U) {
for (i = 1; i <= m_orig; i++)
conv((*U)(m+1, i), 0);
}
for (i = jj; i <= kk; i++) {
if (uvec[i] == 0) continue;
conv(MU, uvec[i]);
RowTransform2(B(m+1), B(i), MU);
if (U) RowTransform2((*U)(m+1), (*U)(i), MU);
}
for (i = m+1; i >= jj+1; i--) {
// swap i, i-1
swap(B(i-1), B(i));
if (U) swap((*U)(i-1), (*U)(i));
tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp;
}
for (i = 1; i <= n; i++)
conv(B1[jj][i], B(jj, i));
if (IsZero(B(jj))) Error("G_BKZ_XD: internal error");
// remove linear dependencies
// cerr << "general case\n";
new_m = ll_G_LLL_XD(B, U, delta, 0, 0, B1, mu, aux,
kk+1, jj, quit, cache);
if (new_m != kk) Error("G_BKZ_XD: internal error");
// remove zero vector
for (i = kk+2; i <= m+1; i++) {
// swap i, i-1
swap(B(i-1), B(i));
if (U) swap((*U)(i-1), (*U)(i));
tp = B1[i-1]; B1[i-1] = B1[i]; B1[i] = tp;
}
quit = 0;
if (check) {
for (i = 1; i <= kk; i++)
if ((*check)(B(i))) {
quit = 1;
break;
}
}
if (quit) break;
if (h > kk) {
// extend reduced basis
new_m = ll_G_LLL_XD(B, U, delta, 0, check,
B1, mu, aux, h, h, quit, cache);
if (new_m != h) Error("G_BKZ_XD: internal error");
if (quit) break;
}
}
z = 0;
}
else {
// G_LLL_XD
// cerr << "progress\n";
NumNoOps++;
if (!clean) {
new_m = ll_G_LLL_XD(B, U, delta, 0, check, B1, mu, aux,
h, h, quit, cache);
if (new_m != h) Error("G_BKZ_XD: internal error");
if (quit) break;
}
z++;
}
}
}
if (verb) {
G_BKZStatus(GetTime(), enum_time, NumIterations, NumTrivial, NumNonTrivial,
NumNoOps, m, B);
}
// clean up
if (m_orig > m) {
// for consistency, we move zero vectors to the front
for (i = m+1; i <= m_orig; i++) {
swap(B(i), B(i+1));
if (U) swap((*U)(i), (*U)(i+1));
}
for (i = 0; i < m; i++) {
swap(B(m_orig-i), B(m-i));
if (U) swap((*U)(m_orig-i), (*U)(m-i));
}
}
B.SetDims(m_orig, n);
BB = B;
if (U) {
U->SetDims(m_orig, m_orig);
*UU = *U;
}
for (i = 1; i <= m_orig+1; i++) {
delete [] B1[i];
}
delete [] B1;
for (i = 1; i <= m_orig+1; i++) {
delete [] mu[i];
}
delete [] mu;
for (i = 1; i <= m_orig+1; i++) {
delete [] aux[i];
}
delete [] aux;
delete [] c;
delete [] ctilda;
delete [] vvec;
delete [] yvec;
delete [] uvec;
delete [] utildavec;
delete [] Deltavec;
delete [] deltavec;
return m;
}
static
long LLL_XD(mat_ZZ& B, mat_ZZ* U, xdouble delta, long deep,
LLLCheckFct check)
{
long m = B.NumRows();
long n = B.NumCols();
long i, j;
long new_m, dep, quit;
xdouble s;
ZZ MU;
xdouble mu1;
xdouble t1;
ZZ T1;
init_red_fudge();
if (U) ident(*U, m);
xdouble **B1; // approximates B
typedef xdouble *xdoubleptr;
B1 = NTL_NEW_OP xdoubleptr[m+1];
if (!B1) Error("LLL_XD: out of memory");
for (i = 1; i <= m; i++) {
B1[i] = NTL_NEW_OP xdouble[n+1];
if (!B1[i]) Error("LLL_XD: out of memory");
}
xdouble **mu;
mu = NTL_NEW_OP xdoubleptr[m+1];
if (!mu) Error("LLL_XD: out of memory");
for (i = 1; i <= m; i++) {
mu[i] = NTL_NEW_OP xdouble[m+1];
if (!mu[i]) Error("LLL_XD: out of memory");
}
xdouble *c; // squared lengths of Gramm-Schmidt basis vectors
c = NTL_NEW_OP xdouble[m+1];
if (!c) Error("LLL_XD: out of memory");
xdouble *b; // squared lengths of basis vectors
b = NTL_NEW_OP xdouble[m+1];
if (!b) Error("LLL_XD: out of memory");
for (i = 1; i <=m; i++)
for (j = 1; j <= n; j++)
conv(B1[i][j], B(i, j));
for (i = 1; i <= m; i++) {
b[i] = InnerProduct(B1[i], B1[i], n);
}
new_m = ll_LLL_XD(B, U, delta, deep, check, B1, mu, b, c, m, 1, quit);
dep = m - new_m;
m = new_m;
if (dep > 0) {
// for consistency, we move all of the zero rows to the front
for (i = 0; i < m; i++) {
swap(B(m+dep-i), B(m-i));
if (U) swap((*U)(m+dep-i), (*U)(m-i));
}
}
// clean-up
for (i = 1; i <= m+dep; i++) {
delete [] B1[i];
}
delete [] B1;
for (i = 1; i <= m+dep; i++) {
delete [] mu[i];
}
delete [] mu;
delete [] c;
delete [] b;
return m;
}
static
long G_LLL_XD(mat_ZZ& B, mat_ZZ* U, xdouble delta, long deep,
LLLCheckFct check)
{
long m = B.NumRows();
long n = B.NumCols();
long i, j;
long new_m, dep, quit;
xdouble s;
ZZ MU;
xdouble mu1;
xdouble t1;
ZZ T1;
init_red_fudge();
if (U) ident(*U, m);
xdouble **B1; // approximates B
typedef xdouble *xdoubleptr;
B1 = NTL_NEW_OP xdoubleptr[m+1];
if (!B1) Error("G_LLL_XD: out of memory");
for (i = 1; i <= m; i++) {
B1[i] = NTL_NEW_OP xdouble[n+1];
if (!B1[i]) Error("G_LLL_XD: out of memory");
}
xdouble **mu;
mu = NTL_NEW_OP xdoubleptr[m+1];
if (!mu) Error("G_LLL_XD: out of memory");
for (i = 1; i <= m; i++) {
mu[i] = NTL_NEW_OP xdouble[n+2];
if (!mu[i]) Error("G_LLL_XD: out of memory");
}
xdouble **aux;
aux = NTL_NEW_OP xdoubleptr[m+1];
if (!aux) Error("G_LLL_XD: out of memory");
for (i = 1; i <= m; i++) {
aux[i] = NTL_NEW_OP xdouble[n+1];
if (!aux[i]) Error("G_LLL_XD: out of memory");
}
for (i = 1; i <=m; i++)
for (j = 1; j <= n; j++)
conv(B1[i][j], B(i, j));
GivensCache_XD cache(m, n);
new_m =
ll_G_LLL_XD(B, U, delta, deep, check, B1, mu, aux, m, 1, quit, cache);
dep = m - new_m;
m = new_m;
if (dep > 0) {
// for consistency, we move all of the zero rows to the front
for (i = 0; i < m; i++) {
swap(B(m+dep-i), B(m-i));
if (U) swap((*U)(m+dep-i), (*U)(m-i));
}
}
// clean-up
for (i = 1; i <= m+dep; i++) {
delete [] B1[i];
}
delete [] B1;
for (i = 1; i <= m+dep; i++) {
delete [] mu[i];
}
delete [] mu;
for (i = 1; i <= m+dep; i++) {
delete [] aux[i];
}
delete [] aux;
return m;
}
