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; }