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); }