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;
}
