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;
}
