bool intVecCRT(vec_ZZ& vp, const ZZ& p, const zzvec& vq, long q)
{
long pInv = InvMod(rem(p,q), q); // p^{-1} mod q
long n = min(vp.length(),vq.length());
long q_over_2 = q/2;
ZZ tmp;
long vqi;
mulmod_precon_t pqInv = PrepMulModPrecon(pInv, q);
for (long i=0; i<n; i++) {
conv(vqi, vq[i]); // convert to single precision
long vq_minus_vp_mod_q = SubMod(vqi, rem(vp[i],q), q);
long delta_times_pInv = MulModPrecon(vq_minus_vp_mod_q, pInv, q, pqInv);
if (delta_times_pInv > q_over_2) delta_times_pInv -= q;
mul(tmp, delta_times_pInv, p); // tmp = [(vq_i-vp_i)*p^{-1}]_q * p
vp[i] += tmp;
}
// other entries (if any) are 0 mod q
for (long i=vq.length(); i<vp.length(); i++) {
long minus_vp_mod_q = NegateMod(rem(vp[i],q), q);
long delta_times_pInv = MulModPrecon(minus_vp_mod_q, pInv, q, pqInv);
if (delta_times_pInv > q_over_2) delta_times_pInv -= q;
mul(tmp, delta_times_pInv, p); // tmp = [(vq_i-vp_i)*p^{-1}]_q * p
vp[i] += tmp;
}
return (vp.length()==vq.length());
}
void mul(vec_ZZ& x, const vec_ZZ& a, long b)
{
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
mul(x[i], a[i], b);
}
void negate(vec_ZZ& x, const vec_ZZ& a)
{
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
negate(x[i], a[i]);
}
void mul(vec_ZZ& x, const vec_ZZ& a, const ZZ& b_in)
{
ZZ b = b_in;
long n = a.length();
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
mul(x[i], a[i], b);
}
void sub(vec_ZZ& x, const vec_ZZ& a, const vec_ZZ& b)
{
long n = a.length();
if (b.length() != n) LogicError("vector sub: dimension mismatch");
x.SetLength(n);
long i;
for (i = 0; i < n; i++)
sub(x[i], a[i], b[i]);
}
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);
}
void conv(vec_zz_p& x, const vec_ZZ& a)
{
long i, n;
n = a.length();
x.SetLength(n);
zz_p* xp = x.elts();
const ZZ* ap = a.elts();
for (i = 0; i < n; i++)
conv(xp[i], ap[i]);
}
NTL_START_IMPL
// NOTE: the signature for this is in lzz_p.h
void conv(vec_zz_p& x, const vec_ZZ& a)
{
long i, n;
n = a.length();
x.SetLength(n);
VectorConv(n, x.elts(), a.elts());
}
static
void SubDiv(vec_ZZ& e, const vec_ZZ& t, long p)
{
long n = e.length();
if (t.length() != n) Error("SubDiv: dimension mismatch");
ZZ s;
long i;
for (i = 0; i < n; i++) {
sub(s, e[i], t[i]);
div(e[i], s, p);
}
}
static void MulSubDiv(vec_ZZ& c, const vec_ZZ& c1, const vec_ZZ& c2,
const ZZ& x, const ZZ& y, const ZZ& z)
// c = (x*c1 + y*c2)/z
{
long n = c1.length();
if (c2.length() != n) Error("MulSubDiv: length mismatch");
c.SetLength(n);
long i;
for (i = 1; i <= n; i++)
MulSubDiv(c(i), c1(i), c2(i), x, y, z);
}
void clear(vec_ZZ& x)
{
long n = x.length();
long i;
for (i = 0; i < n; i++)
clear(x[i]);
}
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 VectorCopy(vec_ZZ& x, const vec_ZZ& 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);
long i;
for (i = 0; i < m; i++)
x[i] = a[i];
for (i = m; i < n; i++)
clear(x[i]);
}
NTL_START_IMPL
void InnerProduct(ZZ& xx, const vec_ZZ& a, const vec_ZZ& b)
{
ZZ t1, x;
long n = min(a.length(), b.length());
long i;
clear(x);
for (i = 1; i <= n; i++) {
mul(t1, a(i), b(i));
add(x, x, t1);
}
xx = x;
}
static
void ExactDiv(vec_ZZ& x, const ZZ& d)
{
long n = x.length();
long i;
for (i = 0; i < n; i++)
if (!divide(x[i], x[i], d))
Error("inexact division");
}
long IsZero(const vec_ZZ& a)
{
long n = a.length();
long i;
for (i = 0; i < n; i++)
if (!IsZero(a[i]))
return 0;
return 1;
}
vec_ZZ vec_shift(vec_ZZ v, int dim)
{
vec_ZZ shifted_vec;
int len;
len = v.length();
shifted_vec.SetLength(dim);
// if (len>dim-1)
// cout<<"incorrect length "<<len<<" "<<dim<<endl;
for (int i=0; i<len-1;i++)
shifted_vec[i+1] = v[i];
return shifted_vec;
}
static void RowTransform2(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++)
add(A(i), A(i), B(i));
return;
}
if (MU == -1) {
for (i = 1; i <= n; i++)
sub(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);
for (i = 1; i <= n; i++) {
mul(T, B(i), mu1);
if (k > 0) LeftShift(T, T, k);
add(A(i), A(i), T);
}
}
else {
for (i = 1; i <= n; i++) {
mul(T, B(i), MU);
if (k > 0) LeftShift(T, T, k);
add(A(i), A(i), T);
}
}
}
static
void mul_aux(vec_ZZ& x, const vec_ZZ& 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, a(k), B(k,i));
add(acc, acc, tmp);
}
x(i) = acc;
}
}
NTL_CLIENT
long SubsetSumSolution(const vec_ZZ& z)
{
long n = z.length()-3;
long j;
if (z(n+1) != 0) return 0;
if (z(n+2) != -1 && z(n+2) != 1) return 0;
for (j = 1; j <= n; j++)
if (z(j) != -1 && z(j) != 1) 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);
}
}
static
void mul_aux(vec_ZZ& x, const mat_ZZ& A, const vec_ZZ& b)
{
long n = A.NumRows();
long l = A.NumCols();
if (l != b.length())
Error("matrix mul: dimension mismatch");
x.SetLength(n);
long i, k;
ZZ acc, tmp;
for (i = 1; i <= n; i++) {
clear(acc);
for (k = 1; k <= l; k++) {
mul(tmp, A(i,k), b(k));
add(acc, acc, tmp);
}
x(i) = acc;
}
}
static void RowTransform(vec_ZZ& c1, vec_ZZ& c2,
const ZZ& x, const ZZ& y, const ZZ& u, const ZZ& v)
// (c1, c2) = (x*c1 + y*c2, u*c1 + v*c2)
{
long n = c1.length();
if (c2.length() != n) Error("MulSubDiv: length mismatch");
static ZZ t1, t2, t3, t4;
long i;
for (i = 1; i <= n; i++) {
mul(t1, x, c1(i));
mul(t2, y, c2(i));
add(t1, t1, t2);
mul(t3, u, c1(i));
mul(t4, v, c2(i));
add(t3, t3, t4);
c1(i) = t1;
c2(i) = t3;
}
}
NTL_START_IMPL
// This implements a variation of an algorithm in
// [P. Domich, R. Kannan and L. Trotter, Math. Oper. Research 12:50-59, 1987].
// I started with the description in Henri Cohen's book, but had to modify
// that because Cohen does not actually keep the numbers reduced modulo
// the determinant, which leads to larger than necessary numbers.
// This modifiaction was put in place in v3.9b.
static
void EuclUpdate(vec_ZZ& u, vec_ZZ& v,
const ZZ& a, const ZZ& b, const ZZ& c, const ZZ& d,
const ZZ& M)
{
long m = u.length();
long i;
ZZ M1;
RightShift(M1, M, 1);
ZZ t1, t2, t3;
for (i = 1; i <= m; i++) {
mul(t1, u(i), a);
mul(t2, v(i), b);
add(t1, t1, t2);
rem(t1, t1, M);
if (t1 > M1)
sub(t1, t1, M);
t3 = t1;
mul(t1, u(i), c);
mul(t2, v(i), d);
add(t1, t1, t2);
rem(t1, t1, M);
if (t1 > M1)
sub(t1, t1, M);
u(i) = t3;
v(i) = t1;
}
}
//Ideal lattice challenge problem generator
//modified from generate_ideal.cpp in Ideal lattice Challenge web page
void gen_idealsvpchallenge(mat_ZZ& B,int index,ZZ seed,vec_ZZ& phivec) {
ZZX phi=find_cyclotomic(index);
long n=deg(phi);
ZZ det=find_determinant(index,10*n,seed);
ZZ alpha=find_unity_root(index,det,phi);
B.SetDims(n,n);
clear(B);
B(1,1) = det;
for (long i=2; i<=n; i++)
{
B(i,1)=det-PowerMod(alpha,i-1,det);
B(i,i)=1;
}
phivec.SetLength(n+1);
for (int i=0;i<=n;i++) phivec[i] = coeff(phi,i);
}
mat_ZZ mat_expand(mat_ZZ M, vec_ZZ v)
{
int len, col, row;
mat_ZZ mat_exp;
len = v.length();
col = M.NumCols();
row = M.NumRows();
if (len!=col)
cout<<"Incompatible rows"<<endl;
mat_exp = M;
mat_exp.SetDims(row+1, col);
mat_exp[row] = v;
return mat_exp;
}
template <typename T> T ProjectedLength(LatticeBasis<T>& B,int istart,int iend, vec_ZZ& vector) {
B.updateGSBasis(1,iend);
ZZ ip;
T ipapprox;
T* mu = (T*)shared_memory::allocate1<T>(123,iend+1);
T result = LengthOf<T>(vector);
result *= result;
for (int j=istart;j<=iend;j++) {
ipapprox = 0;
for (int i=0;i<vector.length();i++) {
//inner product of two vectors
if ((vector[i]!=0) && (B.L[j-1][i]!=0)) {
T part;
part = log(to_double( log(abs(vector[i] )))) + log(to_double( log(abs( B.L[j-1][i] ))));
char sign1=1;
char sign2=1;
if (vector[i] < 0) sign1 = -1;
if (B.L[j-1][i] < 0) sign2 = -1;
if (sign1*sign2==1) {
ipapprox += exp(part);
} else {
ipapprox -= exp(part);
}
}
}
mu[j] = ipapprox;
for (int k=1;k<j;k++) {
mu[j] -= B.gs.mu[j][k] * mu[k] * B.gs.cd[k];
}
mu[j] /= B.gs.cd[j];
result -= mu[j] * mu[j] * B.gs.cd[j];
if (result < 0.5) return 0;
}
return sqrt(result);
}
void solve(ZZ& d_out, vec_ZZ& x_out,
const mat_ZZ& A, const vec_ZZ& b,
long deterministic)
{
long n = A.NumRows();
if (A.NumCols() != n)
Error("solve: nonsquare matrix");
if (b.length() != n)
Error("solve: dimension mismatch");
if (n == 0) {
set(d_out);
x_out.SetLength(0);
return;
}
zz_pBak zbak;
zbak.save();
ZZ_pBak Zbak;
Zbak.save();
vec_ZZ x(INIT_SIZE, n);
ZZ d, d1;
ZZ d_prod, x_prod;
set(d_prod);
set(x_prod);
long d_instable = 1;
long x_instable = 1;
long check = 0;
long gp_cnt = 0;
vec_ZZ y, b1;
long i;
long bound = 2+DetBound(A);
for (i = 0; ; i++) {
if ((check || IsZero(d)) && !d_instable) {
if (NumBits(d_prod) > bound) {
break;
}
else if (!deterministic &&
bound > 1000 && NumBits(d_prod) < 0.25*bound) {
ZZ P;
long plen = 90 + NumBits(max(bound, NumBits(d)));
GenPrime(P, plen, 90 + 2*NumBits(gp_cnt++));
ZZ_p::init(P);
mat_ZZ_p AA;
conv(AA, A);
ZZ_p dd;
determinant(dd, AA);
if (CRT(d, d_prod, rep(dd), P))
d_instable = 1;
else
break;
}
}
zz_p::FFTInit(i);
long p = zz_p::modulus();
mat_zz_p AA;
conv(AA, A);
if (!check) {
vec_zz_p bb, xx;
conv(bb, b);
zz_p dd;
solve(dd, xx, AA, bb);
d_instable = CRT(d, d_prod, rep(dd), p);
if (!IsZero(dd)) {
mul(xx, xx, dd);
x_instable = CRT(x, x_prod, xx);
}
else
x_instable = 1;
if (!d_instable && !x_instable) {
mul(y, x, A);
mul(b1, b, d);
if (y == b1) {
d1 = d;
check = 1;
}
}
}
else {
zz_p dd;
determinant(dd, AA);
d_instable = CRT(d, d_prod, rep(dd), p);
}
}
if (check && d1 != d) {
mul(x, x, d);
ExactDiv(x, d1);
}
d_out = d;
if (check) x_out = x;
zbak.restore();
Zbak.restore();
}
void solve1(ZZ& d_out, vec_ZZ& x_out, const mat_ZZ& A, const vec_ZZ& b)
{
long n = A.NumRows();
if (A.NumCols() != n)
Error("solve1: nonsquare matrix");
if (b.length() != n)
Error("solve1: dimension mismatch");
if (n == 0) {
set(d_out);
x_out.SetLength(0);
return;
}
ZZ num_bound, den_bound;
hadamard(num_bound, den_bound, A, b);
if (den_bound == 0) {
clear(d_out);
return;
}
zz_pBak zbak;
zbak.save();
long i;
long j;
ZZ prod;
prod = 1;
mat_zz_p B;
for (i = 0; ; i++) {
zz_p::FFTInit(i);
mat_zz_p AA, BB;
zz_p dd;
conv(AA, A);
inv(dd, BB, AA);
if (dd != 0) {
transpose(B, BB);
break;
}
mul(prod, prod, zz_p::modulus());
if (prod > den_bound) {
d_out = 0;
return;
}
}
long max_A_len = MaxBits(A);
long use_double_mul1 = 0;
long use_double_mul2 = 0;
long double_limit = 0;
if (max_A_len + NTL_SP_NBITS + NumBits(n) <= NTL_DOUBLE_PRECISION-1)
use_double_mul1 = 1;
if (!use_double_mul1 && max_A_len+NTL_SP_NBITS+2 <= NTL_DOUBLE_PRECISION-1) {
use_double_mul2 = 1;
double_limit = (1L << (NTL_DOUBLE_PRECISION-1-max_A_len-NTL_SP_NBITS));
}
long use_long_mul1 = 0;
long use_long_mul2 = 0;
long long_limit = 0;
if (max_A_len + NTL_SP_NBITS + NumBits(n) <= NTL_BITS_PER_LONG-1)
use_long_mul1 = 1;
if (!use_long_mul1 && max_A_len+NTL_SP_NBITS+2 <= NTL_BITS_PER_LONG-1) {
use_long_mul2 = 1;
long_limit = (1L << (NTL_BITS_PER_LONG-1-max_A_len-NTL_SP_NBITS));
}
if (use_double_mul1 && use_long_mul1)
use_long_mul1 = 0;
else if (use_double_mul1 && use_long_mul2)
use_long_mul2 = 0;
else if (use_double_mul2 && use_long_mul1)
use_double_mul2 = 0;
else if (use_double_mul2 && use_long_mul2) {
if (long_limit > double_limit)
use_double_mul2 = 0;
else
use_long_mul2 = 0;
}
double **double_A;
double *double_h;
typedef double *double_ptr;
if (use_double_mul1 || use_double_mul2) {
double_h = NTL_NEW_OP double[n];
double_A = NTL_NEW_OP double_ptr[n];
if (!double_h || !double_A) Error("solve1: out of mem");
for (i = 0; i < n; i++) {
double_A[i] = NTL_NEW_OP double[n];
if (!double_A[i]) Error("solve1: out of mem");
}
for (i = 0; i < n; i++)
for (j = 0; j < n; j++)
double_A[j][i] = to_double(A[i][j]);
}