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);
}
int main()
{
long i, j;
int sign;
fmpz_t input;
fmpz_t result;
fmpz_t r1;
fmpz_t m1;
fmpz_t mprod;
ulong r2, m2;
flint_rand_t state;
printf("CRT_ui....");
fflush(stdout);
fmpz_init(input);
fmpz_init(result);
fmpz_init(r1);
fmpz_init(m1);
fmpz_init(mprod);
flint_randinit(state);
for (i = 0; i < 10000; i++)
{
long nprimes;
m2 = n_randtest_prime(state, 0);
nprimes = 1 + n_randint(state, 4);
fmpz_set_ui(m1, 1UL);
for (j = 0; j < nprimes; )
{
ulong t = n_randtest_prime(state, 0);
if (t != m2)
{
fmpz_mul_ui(m1, m1, t);
j++;
}
}
fmpz_mul_ui(mprod, m1, m2);
sign = n_randint(state, 2);
if (sign)
fmpz_randtest_mod_signed(input, state, mprod);
else
fmpz_randtest_mod(input, state, mprod);
fmpz_mod(r1, input, m1);
r2 = fmpz_fdiv_ui(input, m2);
if (sign)
fmpz_CRT_ui(result, r1, m1, r2, m2);
else
fmpz_CRT_ui_unsigned(result, r1, m1, r2, m2);
if (!fmpz_equal(result, input))
{
printf("FAIL:\n");
printf("m1: "); fmpz_print(m1); printf("\n");
printf("m2: %lu\n", m2);
printf("m1*m2: "); fmpz_print(mprod); printf("\n");
printf("input: "); fmpz_print(input); printf("\n");
printf("r1: "); fmpz_print(r1); printf("\n");
printf("r2: %lu\n", r2);
printf("result: "); fmpz_print(result); printf("\n");
printf("%ld Equalness: %d\n", i, fmpz_equal(result, input));
printf("\n");
abort();
}
}
fmpz_clear(input);
fmpz_clear(result);
fmpz_clear(r1);
fmpz_clear(m1);
fmpz_clear(mprod);
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int main()
{
slong i, j;
int sign;
fmpz_t input;
fmpz_t result;
fmpz_t r1;
fmpz_t m1;
fmpz_t mprod;
ulong r2, m2;
FLINT_TEST_INIT(state);
flint_printf("CRT_ui....");
fflush(stdout);
fmpz_init(input);
fmpz_init(result);
fmpz_init(r1);
fmpz_init(m1);
fmpz_init(mprod);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
slong nprimes;
m2 = n_randtest_prime(state, 0);
nprimes = 1 + n_randint(state, 4);
fmpz_set_ui(m1, UWORD(1));
for (j = 0; j < nprimes; )
{
ulong t = n_randtest_prime(state, 0);
if (t != m2)
{
fmpz_mul_ui(m1, m1, t);
j++;
}
}
fmpz_mul_ui(mprod, m1, m2);
sign = n_randint(state, 2);
if (sign)
fmpz_randtest_mod_signed(input, state, mprod);
else
fmpz_randtest_mod(input, state, mprod);
fmpz_mod(r1, input, m1);
r2 = fmpz_fdiv_ui(input, m2);
fmpz_CRT_ui(result, r1, m1, r2, m2, sign);
if (!fmpz_equal(result, input))
{
flint_printf("FAIL:\n");
flint_printf("m1: "); fmpz_print(m1); flint_printf("\n");
flint_printf("m2: %wu\n", m2);
flint_printf("m1*m2: "); fmpz_print(mprod); flint_printf("\n");
flint_printf("input: "); fmpz_print(input); flint_printf("\n");
flint_printf("r1: "); fmpz_print(r1); flint_printf("\n");
flint_printf("r2: %wu\n", r2);
flint_printf("result: "); fmpz_print(result); flint_printf("\n");
flint_printf("%wd Equalness: %d\n", i, fmpz_equal(result, input));
flint_printf("\n");
abort();
}
}
fmpz_clear(input);
fmpz_clear(result);
fmpz_clear(r1);
fmpz_clear(m1);
fmpz_clear(mprod);
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
