BasicThreadPool *ReleaseThreadPool()
{
NTL_TLS_GLOBAL_ACCESS(NTLThreadPool_stg);
BasicThreadPool *pool = NTLThreadPool_stg.release();
NTLThreadPool_ptr = 0;
return pool;
}
static
void ComputeBKZThresh(xdouble *c, long beta)
{
NTL_TLS_GLOBAL_ACCESS(BKZConstant);
NTL_TLS_GLOBAL_ACCESS(BKZThresh);
BKZThresh.SetLength(beta-1);
long i;
double x;
x = 0;
for (i = 1; i <= beta-1; i++) {
x += log(c[i-1]);
BKZThresh(i) = xexp(x/double(i))*BKZConstant(i);
}
}
static
void ComputeBKZConstant(long beta, long p)
{
NTL_TLS_GLOBAL_ACCESS(BKZConstant);
const double c_PI = 3.14159265358979323846264338328;
const double LogPI = 1.14472988584940017414342735135;
BKZConstant.SetLength(beta-1);
vec_double Log;
Log.SetLength(beta);
long i, j, k;
double x, y;
for (j = 1; j <= beta; j++)
Log(j) = log(double(j));
for (i = 1; i <= beta-1; i++) {
// First, we compute x = gamma(i/2)^{2/i}
k = i/2;
if ((i & 1) == 0) { // i even
x = 0;
for (j = 1; j <= k; j++)
x = x + Log(j);
x = x * (1/double(k));
x = exp(x);
}
else { // i odd
x = 0;
for (j = k + 2; j <= 2*k + 2; j++)
x = x + Log(j);
x = 0.5*LogPI + x - 2*(k+1)*Log(2);
x = x * (2.0/double(i));
x = exp(x);
}
// Second, we compute y = 2^{2*p/i}
y = -(2*p/double(i))*Log(2);
y = exp(y);
BKZConstant(i) = x*y/c_PI;
}
}
static void init_red_fudge()
{
NTL_TLS_GLOBAL_ACCESS(red_fudge);
long i;
log_red = long(0.50*NTL_DOUBLE_PRECISION);
red_fudge = 1;
for (i = log_red; i > 0; i--)
red_fudge = red_fudge*0.5;
}
static void inc_red_fudge()
{
NTL_TLS_GLOBAL_ACCESS(red_fudge);
red_fudge = red_fudge * 2;
log_red--;
cerr << "LLL_XD: warning--relaxing reduction (" << log_red << ")\n";
if (log_red < 4)
ResourceError("LLL_XD: can not continue...sorry");
}
void zz_pEContext::restore() const
{
NTL_TLS_GLOBAL_ACCESS(zz_pEInfo_stg);
zz_pEInfo_stg = ptr;
zz_pEInfo = zz_pEInfo_stg.get();
}
void zz_pEContext::save()
{
NTL_TLS_GLOBAL_ACCESS(zz_pEInfo_stg);
ptr = zz_pEInfo_stg;
}
void ResetThreadPool(BasicThreadPool *pool)
{
NTL_TLS_GLOBAL_ACCESS(NTLThreadPool_stg);
NTLThreadPool_stg.reset(pool);
NTLThreadPool_ptr = pool;
}
static
long BKZ_XD(mat_ZZ& BB, mat_ZZ* UU, xdouble delta,
long beta, long prune, LLLCheckFct check)
{
NTL_TLS_GLOBAL_ACCESS(red_fudge);
NTL_TLS_GLOBAL_ACCESS(BKZThresh);
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 ll_LLL_XD(mat_ZZ& B, mat_ZZ* U, xdouble delta, long deep,
LLLCheckFct check, xdouble **B1, xdouble **mu,
xdouble *b, xdouble *c,
long m, long init_k, long &quit)
{
NTL_TLS_GLOBAL_ACCESS(red_fudge);
long n = B.NumCols();
long i, j, k, Fc1;
ZZ MU;
xdouble mu1;
xdouble t1;
ZZ T1;
xdouble *tp;
NTL_TLS_LOCAL_INIT(xdouble, bound, (to_xdouble(0)));
if (bound == 0) {
// we tolerate a 15% loss of precision in computing
// inner products in ComputeGS.
bound = 1;
for (i = 2*long(0.15*NTL_DOUBLE_PRECISION); i > 0; i--) {
bound = bound * 2;
}
}
xdouble half = to_xdouble(0.5);
xdouble half_plus_fudge = 0.5 + red_fudge;
quit = 0;
k = init_k;
vec_long st_mem;
st_mem.SetLength(m+2);
long *st = st_mem.elts();
for (i = 1; i < k; i++)
st[i] = i;
for (i = k; i <= m+1; i++)
st[i] = 1;
UniqueArray<xdouble> buf_store;
buf_store.SetLength(m+1);
xdouble *buf = buf_store.get();
long rst;
long counter;
long trigger_index;
long small_trigger;
long cnt;
long max_k = 0;
double tt;
while (k <= m) {
if (k > max_k) {
max_k = k;
}
if (verbose) {
tt = GetTime();
if (tt > LastTime + LLLStatusInterval)
LLLStatus(max_k, tt, m, B);
}
if (st[k] == k)
rst = 1;
else
rst = k;
if (st[k] < st[k+1]) st[k+1] = st[k];
ComputeGS(B, B1, mu, b, c, k, bound, st[k], buf);
st[k] = k;
counter = 0;
trigger_index = k;
small_trigger = 0;
cnt = 0;
do {
// size reduction
counter++;
if (counter > 10000) {
cerr << "LLL_XD: warning--possible infinite loop\n";
counter = 0;
}
Fc1 = 0;
for (j = rst-1; j >= 1; j--) {
t1 = fabs(mu[k][j]);
if (t1 > half_plus_fudge) {
if (!Fc1) {
if (j > trigger_index ||
(j == trigger_index && small_trigger)) {
cnt++;
if (cnt > 10) {
inc_red_fudge();
half_plus_fudge = 0.5 + red_fudge;
cnt = 0;
}
}
trigger_index = j;
small_trigger = (t1 < 4);
}
Fc1 = 1;
mu1 = mu[k][j];
if (mu1 >= 0)
mu1 = ceil(mu1-half);
else
mu1 = floor(mu1+half);
xdouble *mu_k = mu[k];
xdouble *mu_j = mu[j];
if (mu1 == 1) {
for (i = 1; i <= j-1; i++)
mu_k[i] -= mu_j[i];
}
else if (mu1 == -1) {
for (i = 1; i <= j-1; i++)
mu_k[i] += mu_j[i];
}
else {
for (i = 1; i <= j-1; i++)
MulSub(mu_k[i], mu_k[i], mu1, mu_j[i]);
}
mu_k[j] -= mu1;
conv(MU, mu1);
// cout << j << " " << MU << "\n";
RowTransform(B(k), B(j), MU);
if (U) RowTransform((*U)(k), (*U)(j), MU);
}
}
if (Fc1) {
for (i = 1; i <= n; i++)
conv(B1[k][i], B(k, i));
b[k] = InnerProduct(B1[k], B1[k], n);
ComputeGS(B, B1, mu, b, c, k, bound, 1, buf);
}
} while (Fc1);
if (check && (*check)(B(k)))
quit = 1;
if (b[k] == 0) {
for (i = k; i < m; i++) {
// swap i, i+1
swap(B(i), B(i+1));
tp = B1[i]; B1[i] = B1[i+1]; B1[i+1] = tp;
t1 = b[i]; b[i] = b[i+1]; b[i+1] = t1;
if (U) swap((*U)(i), (*U)(i+1));
}
for (i = k; i <= m+1; i++) st[i] = 1;
m--;
if (quit) break;
continue;
}
if (quit) break;
if (deep > 0) {
// deep insertions
xdouble cc = b[k];
long l = 1;
while (l <= k-1 && delta*c[l] <= cc) {
cc = cc - mu[k][l]*mu[k][l]*c[l];
l++;
}
if (l <= k-1 && (l <= deep || k-l <= deep)) {
// deep insertion at position l
for (i = k; i > l; i--) {
// swap rows i, i-1
swap(B(i), B(i-1));
tp = B1[i]; B1[i] = B1[i-1]; B1[i-1] = tp;
tp = mu[i]; mu[i] = mu[i-1]; mu[i-1] = tp;
t1 = b[i]; b[i] = b[i-1]; b[i-1] = t1;
if (U) swap((*U)(i), (*U)(i-1));
}
k = l;
continue;
}
} // end deep insertions
// test LLL reduction condition
if (k > 1 && delta*c[k-1] > c[k] + mu[k][k-1]*mu[k][k-1]*c[k-1]) {
// swap rows k, k-1
swap(B(k), B(k-1));
tp = B1[k]; B1[k] = B1[k-1]; B1[k-1] = tp;
tp = mu[k]; mu[k] = mu[k-1]; mu[k-1] = tp;
t1 = b[k]; b[k] = b[k-1]; b[k-1] = t1;
if (U) swap((*U)(k), (*U)(k-1));
k--;
NumSwaps++;
// cout << "- " << k << "\n";
}
else {
k++;
// cout << "+ " << k << "\n";
}
}
if (verbose) {
LLLStatus(m+1, GetTime(), m, B);
}
return m;
}
