long CRT(vec_ZZ& gg, ZZ& a, const vec_zz_p& G) { long n = gg.length(); if (G.length() != n) Error("CRT: vector length mismatch"); long p = zz_p::modulus(); ZZ new_a; mul(new_a, a, p); long a_inv; a_inv = rem(a, p); a_inv = InvMod(a_inv, p); long p1; p1 = p >> 1; ZZ a1; RightShift(a1, a, 1); long p_odd = (p & 1); long modified = 0; long h; ZZ g; long i; for (i = 0; i < n; i++) { if (!CRTInRange(gg[i], a)) { modified = 1; rem(g, gg[i], a); if (g > a1) sub(g, g, a); } else g = gg[i]; h = rem(g, p); h = SubMod(rep(G[i]), h, p); h = MulMod(h, a_inv, p); if (h > p1) h = h - p; if (h != 0) { modified = 1; if (!p_odd && g > 0 && (h == p1)) MulSubFrom(g, a, h); else MulAddTo(g, a, h); } gg[i] = g; } a = new_a; return modified; }
static void MulSubFrom(vec_ZZ& c, const vec_ZZ& c2, long x) // c = c - x*c2 { long n = c.length(); if (c2.length() != n) Error("MulSubFrom: length mismatch"); long i; for (i = 1; i <= n; i++) MulSubFrom(c(i), c2(i), x); }
static void reduce(long k, long l, mat_ZZ& B, vec_long& P, vec_ZZ& D, vec_vec_ZZ& lam, mat_ZZ* U) { static ZZ t1; static ZZ r; if (P(l) == 0) return; add(t1, lam(k)(P(l)), lam(k)(P(l))); abs(t1, t1); if (t1 <= D[P(l)]) return; long j; long rr, small_r; BalDiv(r, lam(k)(P(l)), D[P(l)]); if (r.WideSinglePrecision()) { small_r = 1; rr = to_long(r); } else { small_r = 0; } if (small_r) { MulSubFrom(B(k), B(l), rr); if (U) MulSubFrom((*U)(k), (*U)(l), rr); for (j = 1; j <= l-1; j++) if (P(j) != 0) MulSubFrom(lam(k)(P(j)), lam(l)(P(j)), rr); MulSubFrom(lam(k)(P(l)), D[P(l)], rr); } else { MulSubFrom(B(k), B(l), r); if (U) MulSubFrom((*U)(k), (*U)(l), r); for (j = 1; j <= l-1; j++) if (P(j) != 0) MulSubFrom(lam(k)(P(j)), lam(l)(P(j)), r); MulSubFrom(lam(k)(P(l)), D[P(l)], r); } }
static void RowTransform(vec_ZZ& A, vec_ZZ& B, const ZZ& MU1) // x = x - y*MU { NTL_ZZRegister(T); NTL_ZZRegister(MU); long k; long n = A.length(); long i; MU = MU1; if (MU == 1) { for (i = 1; i <= n; i++) sub(A(i), A(i), B(i)); return; } if (MU == -1) { for (i = 1; i <= n; i++) add(A(i), A(i), B(i)); return; } if (MU == 0) return; if (NumTwos(MU) >= NTL_ZZ_NBITS) k = MakeOdd(MU); else k = 0; if (MU.WideSinglePrecision()) { long mu1; conv(mu1, MU); if (k > 0) { for (i = 1; i <= n; i++) { mul(T, B(i), mu1); LeftShift(T, T, k); sub(A(i), A(i), T); } } else { for (i = 1; i <= n; i++) { MulSubFrom(A(i), B(i), mu1); } } } else { for (i = 1; i <= n; i++) { mul(T, B(i), MU); if (k > 0) LeftShift(T, T, k); sub(A(i), A(i), T); } } }
long CRT(mat_ZZ& gg, ZZ& a, const mat_zz_p& G) { long n = gg.NumRows(); long m = gg.NumCols(); if (G.NumRows() != n || G.NumCols() != m) Error("CRT: dimension mismatch"); long p = zz_p::modulus(); ZZ new_a; mul(new_a, a, p); long a_inv; a_inv = rem(a, p); a_inv = InvMod(a_inv, p); long p1; p1 = p >> 1; ZZ a1; RightShift(a1, a, 1); long p_odd = (p & 1); long modified = 0; long h; ZZ g; long i, j; for (i = 0; i < n; i++) { for (j = 0; j < m; j++) { if (!CRTInRange(gg[i][j], a)) { modified = 1; rem(g, gg[i][j], a); if (g > a1) sub(g, g, a); } else g = gg[i][j]; h = rem(g, p); h = SubMod(rep(G[i][j]), h, p); h = MulMod(h, a_inv, p); if (h > p1) h = h - p; if (h != 0) { modified = 1; if (!p_odd && g > 0 && (h == p1)) MulSubFrom(g, a, h); else MulAddTo(g, a, h); } gg[i][j] = g; } } a = new_a; return modified; }