int main() { long iter; flint_rand_t state; printf("log_series...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { long m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; acb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); acb_poly_init(a); acb_poly_init(b); fmpq_poly_randtest_not_zero(A, state, m, qbits); fmpq_poly_set_coeff_ui(A, 0, 1UL); fmpq_poly_log_series(B, A, n); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); acb_poly_log_series(b, a, n, rbits2); if (!acb_poly_contains_fmpq_poly(b, B)) { printf("FAIL\n\n"); printf("bits2 = %ld\n", rbits2); printf("A = "); fmpq_poly_print(A); printf("\n\n"); printf("B = "); fmpq_poly_print(B); printf("\n\n"); printf("a = "); acb_poly_printd(a, 15); printf("\n\n"); printf("b = "); acb_poly_printd(b, 15); printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); acb_poly_clear(a); acb_poly_clear(b); } /* test aliasing */ for (iter = 0; iter < 10000; iter++) { long m, n, qbits, rbits1, rbits2; fmpq_poly_t A; acb_poly_t a, b; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); acb_poly_init(a); acb_poly_init(b); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (fmpz_sgn(A->coeffs + 0) <= 0); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_log_series(b, a, n, rbits2); acb_poly_log_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { printf("FAIL\n\n"); printf("bits2 = %ld\n", rbits2); printf("A = "); fmpq_poly_print(A); printf("\n\n"); printf("a = "); acb_poly_printd(a, 15); printf("\n\n"); printf("b = "); acb_poly_printd(b, 15); printf("\n\n"); abort(); } fmpq_poly_clear(A); acb_poly_clear(a); acb_poly_clear(b); } /* test that exp(log(f)) contains f */ for (iter = 0; iter < 10000; iter++) { long m, n, qbits, rbits1, rbits2, rbits3; fmpq_poly_t A; acb_poly_t a, b, c; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); fmpq_poly_init(A); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); do { fmpq_poly_randtest_not_zero(A, state, m, qbits); } while (fmpz_sgn(A->coeffs + 0) <= 0); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_randtest(b, state, 1 + n_randint(state, 20), rbits1, 5); acb_poly_log_series(b, a, n, rbits2); acb_poly_exp_series_basecase(c, b, n, rbits3); fmpq_poly_truncate(A, n); if (!acb_poly_contains_fmpq_poly(c, A)) { printf("FAIL\n\n"); printf("bits2 = %ld\n", rbits2); printf("bits3 = %ld\n", rbits3); printf("A = "); fmpq_poly_print(A); printf("\n\n"); printf("a = "); acb_poly_printd(a, 15); printf("\n\n"); printf("b = "); acb_poly_printd(b, 15); printf("\n\n"); printf("c = "); acb_poly_printd(c, 15); printf("\n\n"); abort(); } fmpq_poly_clear(A); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("li_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 200 * arb_test_multiplier(); iter++) { slong m, n1, n2, n3, bits1, bits2, bits3; acb_poly_t S, A, B, C, T, U; int offset; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 10); n1 = 1 + n_randint(state, 10); n2 = 1 + n_randint(state, 10); n3 = FLINT_MIN(n1, n2); offset = n_randint(state, 2); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_init(T); acb_poly_init(U); acb_poly_randtest(S, state, m, bits1, 3); acb_poly_randtest(A, state, m, bits1, 3); acb_poly_randtest(B, state, m, bits1, 3); acb_hypgeom_li_series(A, S, offset, n1, bits2); acb_hypgeom_li_series(B, S, offset, n2, bits3); acb_poly_set(C, A); acb_poly_truncate(C, n3); acb_poly_truncate(B, n3); /* [li(h(x))]' log(h(x)) = h'(x) */ acb_poly_derivative(T, A, bits2); acb_poly_log_series(U, S, n3, bits2); acb_poly_mullow(T, T, U, FLINT_MAX(0, n3 - 1), bits2); acb_poly_derivative(U, S, bits2); acb_poly_truncate(U, FLINT_MAX(0, n3 - 1)); if (!acb_poly_overlaps(B, C) || !acb_poly_overlaps(T, U)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); flint_printf("T = "); acb_poly_printd(T, 15); flint_printf("\n\n"); flint_printf("U = "); acb_poly_printd(U, 15); flint_printf("\n\n"); abort(); } acb_hypgeom_li_series(S, S, offset, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); acb_poly_clear(T); acb_poly_clear(U); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("pow_acb_series...."); fflush(stdout); flint_randinit(state); /* compare with exp/log */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong prec, trunc; acb_poly_t f, g, h1, h2; acb_t c; prec = 2 + n_randint(state, 200); trunc = n_randint(state, 20); acb_poly_init(f); acb_poly_init(g); acb_poly_init(h1); acb_poly_init(h2); acb_init(c); /* generate binomials */ if (n_randint(state, 20) == 0) { acb_randtest(c, state, prec, 10); acb_poly_set_coeff_acb(f, 0, c); acb_randtest(c, state, prec, 10); acb_poly_set_coeff_acb(f, 1 + n_randint(state, 20), c); } else { acb_poly_randtest(f, state, 1 + n_randint(state, 20), prec, 10); } acb_poly_randtest(h1, state, 1 + n_randint(state, 20), prec, 10); acb_randtest(c, state, prec, 10); acb_poly_set_acb(g, c); /* f^c */ acb_poly_pow_acb_series(h1, f, c, trunc, prec); /* f^c = exp(c*log(f)) */ acb_poly_log_series(h2, f, trunc, prec); acb_poly_mullow(h2, h2, g, trunc, prec); acb_poly_exp_series(h2, h2, trunc, prec); if (!acb_poly_overlaps(h1, h2)) { flint_printf("FAIL\n\n"); flint_printf("prec = %wd\n", prec); flint_printf("trunc = %wd\n", trunc); flint_printf("f = "); acb_poly_printd(f, 15); flint_printf("\n\n"); flint_printf("c = "); acb_printd(c, 15); flint_printf("\n\n"); flint_printf("h1 = "); acb_poly_printd(h1, 15); flint_printf("\n\n"); flint_printf("h2 = "); acb_poly_printd(h2, 15); flint_printf("\n\n"); abort(); } acb_poly_pow_acb_series(f, f, c, trunc, prec); if (!acb_poly_overlaps(f, h1)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(f); acb_poly_clear(g); acb_poly_clear(h1); acb_poly_clear(h2); acb_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("lgamma_series...."); fflush(stdout); flint_randinit(state); /* special accuracy test case */ { acb_poly_t a; acb_t c; acb_init(c); acb_poly_init(a); arb_set_str(acb_realref(c), "-20.25", 53); arb_set_str(acb_imagref(c), "1e1000", 53); acb_poly_set_coeff_acb(a, 0, c); acb_poly_set_coeff_si(a, 1, 1); acb_poly_lgamma_series(a, a, 3, 53); if (acb_rel_accuracy_bits(a->coeffs) < 40 || acb_rel_accuracy_bits(a->coeffs + 1) < 40 || acb_rel_accuracy_bits(a->coeffs + 2) < 40) { flint_printf("FAIL: accuracy (reflection formula)\n\n"); acb_poly_printd(a, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_clear(c); } for (iter = 0; iter < 500 * arb_test_multiplier(); iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_randtest(b, state, m, rbits1, 10); acb_poly_randtest(c, state, m, rbits1, 10); acb_poly_lgamma_series(b, a, n1, rbits2); acb_poly_lgamma_series(c, a, n2, rbits3); acb_poly_set(d, b); acb_poly_truncate(d, FLINT_MIN(n1, n2)); acb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check loggamma(a) + log(a) = loggamma(a+1) */ acb_poly_log_series(c, a, n1, rbits2); acb_poly_add(c, b, c, rbits2); acb_poly_set(d, a); acb_add_ui(d->coeffs, d->coeffs, 1, rbits2); acb_poly_lgamma_series(d, d, n1, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_lgamma_series(a, a, n1, rbits2); if (!acb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }