static CYTHON_INLINE void ZZX_xgcd(struct ZZX* x, struct ZZX* y, struct ZZ** r, struct ZZX** s,
struct ZZX** t, int proof)
{
*r = new ZZ();
*s = new ZZX();
*t = new ZZX();
XGCD(**r, **s, **t, *x, *y, proof);
}
void HNF(mat_ZZ& W, const mat_ZZ& A_in, const ZZ& D_in)
{
mat_ZZ A = A_in;
long n = A.NumRows();
long m = A.NumCols();
ZZ D = D_in;
if (D < 0)
negate(D, D);
if (n == 0 || m == 0 || D == 0)
Error("HNF: bad input");
W.SetDims(m, m);
clear(W);
long i, j, k;
ZZ d, u, v, c1, c2;
k = n;
for (i = m; i >= 1; i--) {
for (j = k-1; j >= 1; j--) {
if (A(j, i) != 0) {
XGCD(d, u, v, A(k, i), A(j, i));
div(c1, A(k, i), d);
div(c2, A(j, i), d);
negate(c2, c2);
EuclUpdate(A(j), A(k), c1, c2, v, u, D);
}
}
XGCD(d, u, v, A(k, i), D);
FixDiag(W(i), u, A(k), D, i);
if (W(i, i) == 0) W(i, i) = D;
for (j = i+1; j <= m; j++) {
div(c1, W(j, i), W(i, i));
ReduceW(W(j), c1, W(i), D, i);
}
div(D, D, d);
k--;
}
}
int main()
{
long n;
GF2X a, b, c, c1, ss, ss1, tt, tt1;
double t;
long iter, i;
cout << WD(12,"n") << WD(12,"OldGCD") << WD(12,"GCD") << WD(12,"OldXGCD")
<< WD(12, "XGCD") << "\n";
cout.precision(3);
cout.setf(ios::scientific);
for (n = 32; n <= (1L << 18); n = n << 3) {
random(a, n);
random(b, n);
OldGCD(c, a, b);
GCD(c1, a, b);
OldXGCD(c, ss, tt, a, b);
XGCD(c1, ss1, tt1, a, b);
if (c1 != c || ss1 != ss || tt1 != tt) {
cerr << "**** GF2XTest FAILED!\n";
return 1;
}
cout << WD(12,n);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
OldGCD(c, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
GCD(c, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
OldXGCD(c, ss, tt, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
iter = 0;
do {
iter = iter ? (2*iter) : 1;
t = GetTime();
for (i = 0; i < iter; i++)
XGCD(c, ss, tt, a, b);
t = GetTime()-t;
} while (t < 0.5);
cout << WD(12,t/iter);
cout << "\n";
}
return 0;
}
static
long swap(long k, mat_ZZ& B, vec_long& P, vec_ZZ& D,
vec_vec_ZZ& lam, mat_ZZ* U, long m, long verbose)
// swaps vectors k-1 and k; assumes P(k-1) != 0
// returns 1 if vector k-1 need to be reduced after the swap...
// this only occurs in 'case 2' when there are linear dependencies
{
long i, j;
static ZZ t1, t2, t3, e, x, y;
if (P(k) != 0) {
swap(B(k-1), B(k));
if (U) swap((*U)(k-1), (*U)(k));
for (j = 1; j <= k-2; j++)
if (P(j) != 0)
swap(lam(k-1)(P(j)), lam(k)(P(j)));
for (i = k+1; i <= m; i++) {
MulAddDiv(t1, lam(i)(P(k)-1), lam(i)(P(k)),
lam(k)(P(k)-1), D[P(k)-2], D[P(k)-1]);
MulSubDiv(t2, lam(i)(P(k)-1), lam(i)(P(k)),
D[P(k)], lam(k)(P(k)-1), D[P(k)-1]);
lam(i)(P(k)-1) = t1;
lam(i)(P(k)) = t2;
}
MulAddDiv(D[P(k)-1], D[P(k)], lam(k)(P(k)-1),
D[P(k)-2], lam(k)(P(k)-1), D[P(k)-1]);
return 0;
}
else if (!IsZero(lam(k)(P(k-1)))) {
XGCD(e, x, y, lam(k)(P(k-1)), D[P(k-1)]);
ExactDiv(t1, lam(k)(P(k-1)), e);
ExactDiv(t2, D[P(k-1)], e);
t3 = t2;
negate(t2, t2);
RowTransform(B(k-1), B(k), t1, t2, y, x);
if (U) RowTransform((*U)(k-1), (*U)(k), t1, t2, y, x);
for (j = 1; j <= k-2; j++)
if (P(j) != 0)
RowTransform(lam(k-1)(P(j)), lam(k)(P(j)), t1, t2, y, x);
sqr(t2, t2);
ExactDiv(D[P(k-1)], D[P(k-1)], t2);
for (i = k+1; i <= m; i++)
if (P(i) != 0) {
ExactDiv(D[P(i)], D[P(i)], t2);
for (j = i+1; j <= m; j++) {
ExactDiv(lam(j)(P(i)), lam(j)(P(i)), t2);
}
}
for (i = k+1; i <= m; i++) {
ExactDiv(lam(i)(P(k-1)), lam(i)(P(k-1)), t3);
}
swap(P(k-1), P(k));
return 1;
}
else {
swap(B(k-1), B(k));
if (U) swap((*U)(k-1), (*U)(k));
for (j = 1; j <= k-2; j++)
if (P(j) != 0)
swap(lam(k-1)(P(j)), lam(k)(P(j)));
swap(P(k-1), P(k));
return 0;
}
}
