void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b, long offset) { if (offset < 0) LogicError("InnerProduct: negative offset"); if (NTL_OVERFLOW(offset, 1, 0)) ResourceError("InnerProduct: offset too big"); long n = min(a.length(), b.length()+offset); long i; long accum, t; long p = zz_p::modulus(); mulmod_t pinv = zz_p::ModulusInverse(); const zz_p *ap = a.elts(); const zz_p *bp = b.elts(); accum = 0; for (i = offset; i < n; i++) { t = MulMod(rep(ap[i]), rep(bp[i-offset]), p, pinv); accum = AddMod(accum, t, p); } x.LoopHole() = accum; }
void sub(vec_zz_p& x, const vec_zz_p& a, const vec_zz_p& b) { long n = a.length(); if (b.length() != n) Error("vector sub: dimension mismatch"); x.SetLength(n); long i; for (i = 0; i < n; i++) sub(x[i], a[i], b[i]); }
void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b) { long n = min(a.length(), b.length()); long i; zz_p accum, t; clear(accum); for (i = 0; i < n; i++) { mul(t, a[i], b[i]); add(accum, accum, t); } x = accum; }
void clear(vec_zz_p& x) { long n = x.length(); long i; for (i = 0; i < n; i++) clear(x[i]); }
void InnerProduct(zz_pX& x, const vec_zz_p& v, long low, long high, const vec_zz_pX& H, long n, vec_zz_p& t) { zz_p s; long i, j; zz_p *tp = t.elts(); for (j = 0; j < n; j++) clear(tp[j]); long p = zz_p::modulus(); double pinv = zz_p::ModulusInverse(); high = min(high, v.length()-1); for (i = low; i <= high; i++) { const vec_zz_p& h = H[i-low].rep; long m = h.length(); zz_p w = (v[i]); long W = rep(w); mulmod_precon_t Wpinv = PrepMulModPrecon(W, p, pinv); // ((double) W)*pinv; const zz_p *hp = h.elts(); for (j = 0; j < m; j++) { long S = MulModPrecon(rep(hp[j]), W, p, Wpinv); S = AddMod(S, rep(tp[j]), p); tp[j].LoopHole() = S; } } x.rep = t; x.normalize(); }
void ProjectPowers(vec_zz_p& x, const vec_zz_p& a, long k, const zz_pXArgument& H, const zz_pXModulus& F) { long n = F.n; if (a.length() > n || k < 0 || NTL_OVERFLOW(k, 1, 0)) Error("ProjectPowers: bad args"); long m = H.H.length()-1; long l = (k+m-1)/m - 1; zz_pXMultiplier M; build(M, H.H[m], F); vec_zz_p s(INIT_SIZE, n); s = a; StripZeroes(s); x.SetLength(k); for (long i = 0; i <= l; i++) { long m1 = min(m, k-i*m); zz_p* w = &x[i*m]; for (long j = 0; j < m1; j++) InnerProduct(w[j], H.H[j].rep, s); if (i < l) UpdateMap(s, s, M, F); } }
void mul(vec_zz_p& x, const vec_zz_p& a, zz_p b) { long n = a.length(); x.SetLength(n); long i; if (n <= 1) { for (i = 0; i < n; i++) mul(x[i], a[i], b); } else { long p = zz_p::modulus(); double pinv = zz_p::ModulusInverse(); long bb = rep(b); mulmod_precon_t bpinv = PrepMulModPrecon(bb, p, pinv); const zz_p *ap = a.elts(); zz_p *xp = x.elts(); for (i = 0; i < n; i++) xp[i].LoopHole() = MulModPrecon(rep(ap[i]), bb, p, bpinv); } }
static void StripZeroes(vec_zz_p& x) { long n = x.length(); while (n > 0 && IsZero(x[n-1])) n--; x.SetLength(n); }
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; }
void conv(vec_ZZ& x, const vec_zz_p& a) { long n = a.length(); x.SetLength(n); long i; for (i = 0; i < n; i++) x[i] = rep(a[i]); }
void negate(vec_zz_p& x, const vec_zz_p& a) { long n = a.length(); x.SetLength(n); long i; for (i = 0; i < n; i++) negate(x[i], a[i]); }
void add(vec_zz_p& x, const vec_zz_p& a, const vec_zz_p& b) { long n = a.length(); if (b.length() != n) LogicError("vector add: dimension mismatch"); long p = zz_p::modulus(); x.SetLength(n); const zz_p *ap = a.elts(); const zz_p *bp = b.elts(); zz_p *xp = x.elts(); long i; for (i = 0; i < n; i++) xp[i].LoopHole() = AddMod(rep(ap[i]), rep(bp[i]), p); }
void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b, long offset) { if (offset < 0) Error("InnerProduct: negative offset"); if (NTL_OVERFLOW(offset, 1, 0)) Error("InnerProduct: offset too big"); long n = min(a.length(), b.length()+offset); long i; zz_p accum, t; clear(accum); for (i = offset; i < n; i++) { mul(t, a[i], b[i-offset]); add(accum, accum, t); } x = accum; }
void mul_aux(vec_zz_p& x, const mat_zz_p& A, const vec_zz_p& b) { long n = A.NumRows(); long l = A.NumCols(); if (l != b.length()) LogicError("matrix mul: dimension mismatch"); x.SetLength(n); zz_p* xp = x.elts(); long p = zz_p::modulus(); mulmod_t pinv = zz_p::ModulusInverse(); long i, k; long acc, tmp; const zz_p* bp = b.elts(); if (n <= 1) { for (i = 0; i < n; i++) { acc = 0; const zz_p* ap = A[i].elts(); for (k = 0; k < l; k++) { tmp = MulMod(rep(ap[k]), rep(bp[k]), p, pinv); acc = AddMod(acc, tmp, p); } xp[i].LoopHole() = acc; } } else { Vec<mulmod_precon_t>::Watcher watch_precon_vec(precon_vec); precon_vec.SetLength(l); mulmod_precon_t *bpinv = precon_vec.elts(); for (k = 0; k < l; k++) bpinv[k] = PrepMulModPrecon(rep(bp[k]), p, pinv); for (i = 0; i < n; i++) { acc = 0; const zz_p* ap = A[i].elts(); for (k = 0; k < l; k++) { tmp = MulModPrecon(rep(ap[k]), rep(bp[k]), p, bpinv[k]); acc = AddMod(acc, tmp, p); } xp[i].LoopHole() = acc; } } }
void MinPolySeq(zz_pX& h, const vec_zz_p& a, long m) { if (m < 0 || NTL_OVERFLOW(m, 1, 0)) Error("MinPoly: bad args"); if (a.length() < 2*m) Error("MinPoly: sequence too short"); if (m > NTL_zz_pX_BERMASS_CROSSOVER) GCDMinPolySeq(h, a, m); else BerlekampMassey(h, a, m); }
void clear(vec_zz_p& x) { long n = x.length(); zz_p *xp = x.elts(); long i; for (i = 0; i < n; i++) clear(xp[i]); }
void InnerProduct(zz_p& x, const vec_zz_p& a, const vec_zz_p& b) { long n = min(a.length(), b.length()); long i; long accum, t; long p = zz_p::modulus(); mulmod_t pinv = zz_p::ModulusInverse(); const zz_p *ap = a.elts(); const zz_p *bp = b.elts(); accum = 0; for (i = 0; i < n; i++) { t = MulMod(rep(ap[i]), rep(bp[i]), p, pinv); accum = AddMod(accum, t, p); } x.LoopHole() = accum; }
void cvt(vec_GF2& x, const vec_zz_p& a) { long n = a.length(); x.SetLength(n); long i; for (i = 0; i < n; i++) x.put(i, rep(a[i])); }
long IsZero(const vec_zz_p& a) { long n = a.length(); long i; for (i = 0; i < n; i++) if (!IsZero(a[i])) return 0; return 1; }
static void MulAdd(vec_ZZ& x, const ZZ& prod, const vec_zz_p& h) { long n = x.length(); if (h.length() != n) Error("MulAdd: dimension mismatch"); ZZ t; long i; for (i = 0; i < n; i++) { mul(t, prod, rep(h[i])); add(x[i], x[i], t); } }
void negate(vec_zz_p& x, const vec_zz_p& a) { long n = a.length(); long p = zz_p::modulus(); x.SetLength(n); const zz_p *ap = a.elts(); zz_p *xp = x.elts(); long i; for (i = 0; i < n; i++) xp[i].LoopHole() = NegateMod(rep(ap[i]), p); }
void eval(vec_zz_p& b, const zz_pX& f, const vec_zz_p& a) // naive algorithm: repeats Horner { if (&b == &f.rep) { vec_zz_p bb; eval(bb, f, a); b = bb; return; } long m = a.length(); b.SetLength(m); long i; for (i = 0; i < m; i++) eval(b[i], f, a[i]); }
void VectorCopy(vec_zz_p& x, const vec_zz_p& a, long n) { if (n < 0) Error("VectorCopy: negative length"); if (NTL_OVERFLOW(n, 1, 0)) Error("overflow in VectorCopy"); long m = min(n, a.length()); x.SetLength(n); long i; for (i = 0; i < m; i++) x[i] = a[i]; for (i = m; i < n; i++) clear(x[i]); }
void ProjectPowers(vec_zz_p& x, const vec_zz_p& a, long k, const zz_pX& h, const zz_pXModulus& F) { if (a.length() > F.n || k < 0) Error("ProjectPowers: bad args"); if (k == 0) { x.SetLength(0); return; } long m = SqrRoot(k); zz_pXArgument H; build(H, h, F, m); ProjectPowers(x, a, k, H, F); }
void VectorCopy(vec_zz_p& x, const vec_zz_p& a, long n) { if (n < 0) LogicError("VectorCopy: negative length"); if (NTL_OVERFLOW(n, 1, 0)) ResourceError("overflow in VectorCopy"); long m = min(n, a.length()); x.SetLength(n); const zz_p *ap = a.elts(); zz_p *xp = x.elts(); long i; for (i = 0; i < m; i++) xp[i] = ap[i]; for (i = m; i < n; i++) clear(xp[i]); }
static void MixedMul(vec_ZZ& x, const vec_zz_p& a, const mat_ZZ& B) { long n = B.NumRows(); long l = B.NumCols(); if (n != a.length()) Error("matrix mul: dimension mismatch"); x.SetLength(l); long i, k; ZZ acc, tmp; for (i = 1; i <= l; i++) { clear(acc); for (k = 1; k <= n; k++) { mul(tmp, B(k, i), rep(a(k))); add(acc, acc, tmp); } x(i) = acc; } }
void mul(vec_zz_p& x, const vec_zz_p& a, const mat_zz_p& B) { long l = a.length(); long m = B.NumCols(); if (l != B.NumRows()) LogicError("matrix mul: dimension mismatch"); if (m == 0) { x.SetLength(0); } else if (m == 1) { long p = zz_p::modulus(); mulmod_t pinv = zz_p::ModulusInverse(); long acc, tmp; long k; acc = 0; for(k = 1; k <= l; k++) { tmp = MulMod(rep(a(k)), rep(B(k,1)), p, pinv); acc = AddMod(acc, tmp, p); } x.SetLength(1); x(1).LoopHole() = acc; } else { // m > 1. precondition long p = zz_p::modulus(); mulmod_t pinv = zz_p::ModulusInverse(); vec_long::Watcher watch_mul_aux_vec(mul_aux_vec); mul_aux_vec.SetLength(m); long *acc = mul_aux_vec.elts(); long j, k; const zz_p* ap = a.elts(); for (j = 0; j < m; j++) acc[j] = 0; for (k = 0; k < l; k++) { long aa = rep(ap[k]); if (aa != 0) { const zz_p* bp = B[k].elts(); long T1; mulmod_precon_t aapinv = PrepMulModPrecon(aa, p, pinv); for (j = 0; j < m; j++) { T1 = MulModPrecon(rep(bp[j]), aa, p, aapinv); acc[j] = AddMod(acc[j], T1, p); } } } x.SetLength(m); zz_p *xp = x.elts(); for (j = 0; j < m; j++) xp[j].LoopHole() = acc[j]; } }
void interpolate(zz_pX& f, const vec_zz_p& a, const vec_zz_p& b) { long m = a.length(); if (b.length() != m) Error("interpolate: vector length mismatch"); if (m == 0) { clear(f); return; } vec_zz_p prod; prod = a; zz_p t1, t2; long k, i; vec_zz_p res; res.SetLength(m); for (k = 0; k < m; k++) { const zz_p& aa = a[k]; set(t1); for (i = k-1; i >= 0; i--) { mul(t1, t1, aa); add(t1, t1, prod[i]); } clear(t2); for (i = k-1; i >= 0; i--) { mul(t2, t2, aa); add(t2, t2, res[i]); } inv(t1, t1); sub(t2, b[k], t2); mul(t1, t1, t2); for (i = 0; i < k; i++) { mul(t2, prod[i], t1); add(res[i], res[i], t2); } res[k] = t1; if (k < m-1) { if (k == 0) negate(prod[0], prod[0]); else { negate(t1, a[k]); add(prod[k], t1, prod[k-1]); for (i = k-1; i >= 1; i--) { mul(t2, prod[i], t1); add(prod[i], t2, prod[i-1]); } mul(prod[0], prod[0], t1); } } } while (m > 0 && IsZero(res[m-1])) m--; res.SetLength(m); f.rep = res; }
void solve(zz_p& d, vec_zz_p& X, const mat_zz_p& A, const vec_zz_p& b) { long n = A.NumRows(); if (A.NumCols() != n) LogicError("solve: nonsquare matrix"); if (b.length() != n) LogicError("solve: dimension mismatch"); if (n == 0) { set(d); X.SetLength(0); return; } long i, j, k, pos; zz_p t1, t2, t3; zz_p *x, *y; mat_zz_p M; M.SetDims(n, n+1); for (i = 0; i < n; i++) { for (j = 0; j < n; j++) M[i][j] = A[j][i]; M[i][n] = b[i]; } zz_p det; set(det); long p = zz_p::modulus(); mulmod_t pinv = zz_p::ModulusInverse(); for (k = 0; k < n; k++) { pos = -1; for (i = k; i < n; i++) { if (!IsZero(M[i][k])) { pos = i; break; } } if (pos != -1) { if (k != pos) { swap(M[pos], M[k]); negate(det, det); } mul(det, det, M[k][k]); inv(t3, M[k][k]); M[k][k] = t3; for (i = k+1; i < n; i++) { // M[i] = M[i] - M[k]*M[i,k]*t3 mul(t1, M[i][k], t3); negate(t1, t1); x = M[i].elts() + (k+1); y = M[k].elts() + (k+1); long T1 = rep(t1); mulmod_precon_t t1pinv = PrepMulModPrecon(T1, p, pinv); // T1*pinv; long T2; for (j = k+1; j <= n; j++, x++, y++) { // *x = *x + (*y)*t1 T2 = MulModPrecon(rep(*y), T1, p, t1pinv); x->LoopHole() = AddMod(rep(*x), T2, p); } } } else { clear(d); return; } } X.SetLength(n); for (i = n-1; i >= 0; i--) { clear(t1); for (j = i+1; j < n; j++) { mul(t2, X[j], M[i][j]); add(t1, t1, t2); } sub(t1, M[i][n], t1); mul(X[i], t1, M[i][i]); } d = det; }
void BuildFromRoots(zz_pX& x, const vec_zz_p& a) { long n = a.length(); if (n == 0) { set(x); return; } long k0 = NextPowerOfTwo(NTL_zz_pX_MUL_CROSSOVER)-1; long crossover = 1L << k0; if (n <= NTL_zz_pX_MUL_CROSSOVER) { x.rep.SetMaxLength(n+1); x.rep = a; IterBuild(&x.rep[0], n); x.rep.SetLength(n+1); SetCoeff(x, n); return; } long k = NextPowerOfTwo(n); long m = 1L << k; long i, j; long l, width; zz_pX b(INIT_SIZE, m+1); b.rep = a; b.rep.SetLength(m+1); for (i = n; i < m; i++) clear(b.rep[i]); set(b.rep[m]); fftRep R1(INIT_SIZE, k), R2(INIT_SIZE, k); zz_p t1, one; set(one); vec_zz_p G(INIT_SIZE, crossover), H(INIT_SIZE, crossover); zz_p *g = G.elts(); zz_p *h = H.elts(); zz_p *tmp; for (i = 0; i < m; i+= crossover) { for (j = 0; j < crossover; j++) negate(g[j], b.rep[i+j]); if (k0 > 0) { for (j = 0; j < crossover; j+=2) { mul(t1, g[j], g[j+1]); add(g[j+1], g[j], g[j+1]); g[j] = t1; } } for (l = 1; l < k0; l++) { width = 1L << l; for (j = 0; j < crossover; j += 2*width) mul(&h[j], &g[j], &g[j+width], width); tmp = g; g = h; h = tmp; } for (j = 0; j < crossover; j++) b.rep[i+j] = g[j]; } for (l = k0; l < k; l++) { width = 1L << l; for (i = 0; i < m; i += 2*width) { t1 = b.rep[i+width]; set(b.rep[i+width]); TofftRep(R1, b, l+1, i, i+width); b.rep[i+width] = t1; t1 = b.rep[i+2*width]; set(b.rep[i+2*width]); TofftRep(R2, b, l+1, i+width, i+2*width); b.rep[i+2*width] = t1; mul(R1, R1, R2); FromfftRep(&b.rep[i], R1, 0, 2*width-1); sub(b.rep[i], b.rep[i], one); } } x.rep.SetLength(n+1); long delta = m-n; for (i = 0; i <= n; i++) x.rep[i] = b.rep[i+delta]; // no need to normalize }