int main()
{
long iter;
flint_rand_t state;
printf("forward_nmod_mat....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
fmpz_holonomic_t op;
fmpz_mat_t M1;
fmpz_t Q1;
nmod_mat_t M2, L, R;
mp_limb_t Q2;
long start, n, r;
mp_limb_t p;
fmpz_holonomic_init(op);
fmpz_holonomic_randtest(op, state, 4, 4, 10);
r = fmpz_holonomic_order(op);
start = n_randint(state, 10);
n = n_randint(state, 100);
p = n_randtest_prime(state, 0);
fmpz_mat_init(M1, r, r);
fmpz_init(Q1);
nmod_mat_init(M2, r, r, p);
nmod_mat_init(L, r, r, p);
nmod_mat_init(R, r, r, p);
fmpz_holonomic_forward_fmpz_mat(M1, Q1, op, start, n);
fmpz_holonomic_forward_nmod_mat(M2, &Q2, op, start, n);
fmpz_mat_get_nmod_mat(L, M1);
nmod_mat_scalar_mul(L, L, Q2);
nmod_mat_scalar_mul(R, M2, fmpz_fdiv_ui(Q1, p));
/* check Q2 * M1 = Q1 * M2 */
if (!nmod_mat_equal(L, R))
{
printf("FAIL\n");
fmpz_holonomic_print(op, "n", "Sn"); printf("\n\n");
printf("start = %lu, n = %lu\n", start, n);
fmpz_mat_print_pretty(M1); printf("\n\n");
fmpz_print(Q1); printf("\n\n");
nmod_mat_print_pretty(M2); printf("\n\n");
printf("%lu\n\n", Q2);
abort();
}
fmpz_mat_clear(M1);
fmpz_clear(Q1);
nmod_mat_clear(M2);
nmod_mat_clear(L);
nmod_mat_clear(R);
fmpz_holonomic_clear(op);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
fmpz_mat_det_modular_given_divisor_8arg(mpz_t det, nmod_mat_t Amod,
mpfr_t hadamard_log2, mpfr_prec_t pr, p_k_pk_t* pp, n_primes_rev_t iT,
mp_limb_t xmod, const fmpz_mat_t A)
/*
act like fmpz_mat_det_modular_given_divisor_4block(), but
* decrease primes using iT, rather than increase them
* don't count H.B., use hadamard_log2 which is 1+log2(H.B.)
* sum logarithms instead of multiplying together found primes
* re-use found prime pp->p and xmod which is determinant of A modulo pp->p
hadamard_log2 on entry is upper bound on log2(2*H.B)
on exit, decreased to an unspecified value
iT on entry just found prime pp->p
possibly gets shifted
*/
{
// loop bound = 2*H.B / known det divisor
decrease_bound_mpz(hadamard_log2,pr,det);
#if 0
flint_printf("det modulo %llX = %llX\n",pp->p_deg_k,xmod);
#endif
// re-use known det A modulo pp->p_deg_k
mp_limb_t divisor_inv=invert_det_divisor_modulo_pk(det,pp,&Amod->mod);
xmod=n_mulmod2_preinv(xmod,divisor_inv, Amod->mod.n,Amod->mod.ninv);
fmpz_t xnew,x;
fmpz_init(xnew);
fmpz_init(x);
fmpz_t prod; fmpz_init_set_ui(prod, UWORD(1) );
fmpz_CRT_ui(xnew, x, prod, xmod, pp->p_deg_k, 1);
fmpz_set_ui(prod, pp->p_deg_k);
fmpz_set(x, xnew);
#if LOUD_DET_BOUND
mpfr_printf("fmpz_mat_det_modular_given_divisor_8arg(): log2 bound=%Rf\n",
hadamard_log2);
slong primes_used=1;
#endif
// for orthogonal matrice the bound might be reached at this point.
// Attempt to skip main loop
if(comp_bound_ui(hadamard_log2,pp->p_deg_k))
{
mp_limb_t* scratch=flint_malloc( 4*(A->r-4)*sizeof(mp_limb_t) );
mp_limb_t bound=mpfr_get_uj(hadamard_log2,MPFR_RNDU);
for(;;)
{
divisor_inv=choose_prime_and_degree( pp, &Amod->mod, iT, det );
// TODO: optimize fmpz_mat_get_nmod_mat()
fmpz_mat_get_nmod_mat(Amod, A);
// TODO: call a faster subroutine instead of nmod_mat_det_mod_pk_4block()
// when pp->p is 64 bit long
xmod=nmod_mat_det_mod_pk_4block(Amod,pp[0],scratch);
xmod=n_mulmod2_preinv(xmod,divisor_inv, Amod->mod.n,Amod->mod.ninv);
// TODO: rewrite fmpz_CRT_ui() -> mpz_CRT_ui_5arg()
fmpz_CRT_ui(xnew, x, prod, xmod, pp->p_deg_k, 1);
fmpz_mul_ui(prod, prod, pp->p_deg_k);
#if LOUD_DET_BOUND
primes_used++;
#endif
if(cmp_positive_log2(prod,bound) >= 0)
break;
fmpz_set(x, xnew);
}
flint_free(scratch);
}
#if LOUD_DET_BOUND
flint_printf("fmpz_mat_det_modular_given_divisor_8arg() primes used: %d\n\n\n",
primes_used);
#endif
fmpz_clear(prod);
mpz_fmpz_mul_det_2arg(det,xnew);
fmpz_clear(prod);
fmpz_clear(x);
fmpz_clear(xnew);
}
