int main()
{
slong iter;
flint_rand_t state;
flint_printf("airy_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_poly_t ai, aip, bi, bip, ai2, aip2, bi2, bip2, z, w, t;
acb_t c;
slong n1, n2, prec1, prec2;
unsigned int mask;
acb_poly_init(ai); acb_poly_init(aip);
acb_poly_init(bi); acb_poly_init(bip);
acb_poly_init(ai2); acb_poly_init(aip2);
acb_poly_init(bi2); acb_poly_init(bip2);
acb_poly_init(z); acb_poly_init(w);
acb_poly_init(t); acb_init(c);
prec1 = 2 + n_randint(state, 300);
prec2 = 2 + n_randint(state, 300);
n1 = n_randint(state, 6);
n2 = n_randint(state, 6);
acb_poly_randtest(ai, state, 10, prec1, 10);
acb_poly_randtest(aip, state, 10, prec1, 10);
acb_poly_randtest(bi, state, 10, prec1, 10);
acb_poly_randtest(bip, state, 10, prec1, 10);
acb_poly_randtest(z, state, 1 + n_randint(state, 10), prec1, 10);
acb_hypgeom_airy_series(ai, aip, bi, bip, z, n1, prec1);
acb_poly_mullow(w, ai, bip, n1, prec1);
acb_poly_mullow(t, bi, aip, n1, prec1);
acb_poly_sub(w, w, t, prec1);
acb_const_pi(c, prec1);
acb_inv(c, c, prec1);
acb_poly_set_acb(t, c);
acb_poly_truncate(t, n1);
if (!acb_poly_overlaps(w, t))
{
flint_printf("FAIL: wronskian\n\n");
flint_printf("z = "); acb_poly_printd(z, 30); flint_printf("\n\n");
flint_printf("ai = "); acb_poly_printd(ai, 30); flint_printf("\n\n");
flint_printf("aip = "); acb_poly_printd(aip, 30); flint_printf("\n\n");
flint_printf("bi = "); acb_poly_printd(bi, 30); flint_printf("\n\n");
flint_printf("bip = "); acb_poly_printd(bip, 30); flint_printf("\n\n");
flint_printf("w = "); acb_poly_printd(w, 30); flint_printf("\n\n");
abort();
}
mask = n_randlimb(state);
acb_hypgeom_airy_series((mask & 1) ? ai2 : NULL,
(mask & 2) ? aip2 : NULL,
(mask & 4) ? bi2 : NULL,
(mask & 8) ? bip2 : NULL, z, n2, prec2);
acb_poly_truncate(ai, FLINT_MIN(n1, n2));
acb_poly_truncate(aip, FLINT_MIN(n1, n2));
acb_poly_truncate(bi, FLINT_MIN(n1, n2));
acb_poly_truncate(bip, FLINT_MIN(n1, n2));
acb_poly_truncate(ai2, FLINT_MIN(n1, n2));
acb_poly_truncate(aip2, FLINT_MIN(n1, n2));
acb_poly_truncate(bi2, FLINT_MIN(n1, n2));
acb_poly_truncate(bip2, FLINT_MIN(n1, n2));
if (((mask & 1) && (!acb_poly_overlaps(ai, ai2))) ||
((mask & 2) && (!acb_poly_overlaps(aip, aip2))) ||
((mask & 4) && (!acb_poly_overlaps(bi, bi2))) ||
((mask & 8) && (!acb_poly_overlaps(bip, bip2))))
{
flint_printf("FAIL: consistency (mask)\n\n");
flint_printf("mask = %u\n\n", mask);
flint_printf("len1 = %wd, len2 = %wd\n\n", n1, n2);
flint_printf("z = "); acb_poly_printd(z, 30); flint_printf("\n\n");
flint_printf("ai = "); acb_poly_printd(ai, 30); flint_printf("\n\n");
flint_printf("ai2 = "); acb_poly_printd(ai2, 30); flint_printf("\n\n");
flint_printf("aip = "); acb_poly_printd(aip, 30); flint_printf("\n\n");
flint_printf("aip2 = "); acb_poly_printd(aip2, 30); flint_printf("\n\n");
flint_printf("bi = "); acb_poly_printd(bi, 30); flint_printf("\n\n");
flint_printf("bi2 = "); acb_poly_printd(bi2, 30); flint_printf("\n\n");
flint_printf("bip = "); acb_poly_printd(bip, 30); flint_printf("\n\n");
flint_printf("bip2 = "); acb_poly_printd(bip2, 30); flint_printf("\n\n");
abort();
}
acb_poly_clear(ai); acb_poly_clear(aip);
acb_poly_clear(bi); acb_poly_clear(bip);
acb_poly_clear(ai2); acb_poly_clear(aip2);
acb_poly_clear(bi2); acb_poly_clear(bip2);
acb_poly_clear(z); acb_poly_clear(w);
acb_poly_clear(t); 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("cos_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m, n1, n2, bits1, bits2, bits3;
acb_poly_t S, A, B, C;
acb_t pi;
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 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(S);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(pi);
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_poly_cos_pi_series(A, S, n1, bits2);
acb_const_pi(pi, bits3);
acb_poly_set_acb(B, pi);
acb_poly_mul(B, S, B, bits3);
acb_poly_cos_series(B, B, n2, bits3);
acb_poly_set(C, A);
acb_poly_truncate(C, FLINT_MIN(n1, n2));
acb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(B, C))
{
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");
abort();
}
acb_poly_cos_pi_series(S, S, 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_clear(pi);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("digamma_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m, n1, n2, rbits1, rbits2, rbits3;
acb_poly_t a, b, c, d;
rbits1 = 2 + n_randint(state, 300);
rbits2 = 2 + n_randint(state, 300);
rbits3 = 2 + n_randint(state, 300);
m = n_randint(state, 25);
n1 = n_randint(state, 25);
n2 = n_randint(state, 25);
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_digamma_series(b, a, n1, rbits2);
acb_poly_digamma_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, 50); flint_printf("\n\n");
flint_printf("b = "); acb_poly_printd(b, 50); flint_printf("\n\n");
flint_printf("c = "); acb_poly_printd(c, 50); flint_printf("\n\n");
flint_abort();
}
/* check psi(a) + 1/a = psi(a+1) */
acb_poly_inv_series(c, a, n1, rbits2);
acb_poly_add(c, b, c, rbits2);
acb_poly_add_si(d, a, 1, rbits2);
acb_poly_digamma_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");
flint_abort();
}
acb_poly_digamma_series(a, a, n1, rbits2);
if (!acb_poly_overlaps(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
flint_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;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("hardy_z_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 200 * arb_test_multiplier(); iter++)
{
slong m, n1, n2, bits1, bits2, bits3;
acb_poly_t S, A, B, C;
dirichlet_group_t G;
dirichlet_char_t chi;
ulong q;
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 8);
n1 = 1 + n_randint(state, 8);
n2 = 1 + n_randint(state, 8);
do {
q = 1 + n_randint(state, 15);
} while (q % 4 == 2);
dirichlet_group_init(G, q);
dirichlet_char_init(chi, G);
do {
dirichlet_char_index(chi, G, n_randint(state, G->phi_q));
} while (!dirichlet_char_is_primitive(G, chi));
acb_poly_init(S);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_poly_randtest(S, state, m, bits1, 3);
acb_dirichlet_hardy_z_series(A, S, G, chi, n1, bits2);
acb_poly_set(B, S); /* aliasing */
if (q == 1 && n_randint(state, 2))
acb_poly_neg(B, B);
acb_dirichlet_hardy_z_series(B, B, G, chi, n2, bits3);
acb_poly_set(C, A);
acb_poly_truncate(C, FLINT_MIN(n1, n2));
acb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(B, C))
{
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");
abort();
}
acb_poly_clear(S);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
dirichlet_char_clear(chi);
dirichlet_group_clear(G);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sinh_cosh_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_poly_t a, b, c, d, e;
slong n1, n2, prec;
int alg1, alg2;
prec = 2 + n_randint(state, 200);
if (n_randint(state, 40) == 0)
{
n1 = n_randint(state, 300);
n2 = n_randint(state, 300);
}
else
{
n1 = n_randint(state, 30);
n2 = n_randint(state, 30);
}
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_poly_init(d);
acb_poly_init(e);
acb_poly_randtest(a, state, 20, prec, 3);
acb_poly_randtest(b, state, 20, prec, 10);
acb_poly_randtest(c, state, 20, prec, 10);
acb_poly_randtest(d, state, 20, prec, 10);
acb_poly_randtest(e, state, 20, prec, 10);
alg1 = n_randint(state, 4);
alg2 = n_randint(state, 7);
switch (alg1)
{
case 0:
acb_poly_sinh_cosh_series(b, c, a, n1, prec);
break;
case 1:
acb_poly_sinh_cosh_series_basecase(b, c, a, n1, prec);
break;
case 2:
acb_poly_sinh_cosh_series_exponential(b, c, a, n1, prec);
break;
default:
acb_poly_sinh_series(b, a, n1, prec);
acb_poly_cosh_series(c, a, n1, prec);
break;
}
switch (alg2)
{
case 0:
acb_poly_sinh_cosh_series(d, e, a, n2, prec);
break;
case 1:
acb_poly_sinh_cosh_series_basecase(d, e, a, n2, prec);
break;
case 2:
acb_poly_sinh_cosh_series_exponential(d, e, a, n2, prec);
break;
case 3:
acb_poly_sinh_series(d, a, n2, prec);
acb_poly_cosh_series(e, a, n2, prec);
break;
case 4:
acb_poly_set(d, a);
acb_poly_sinh_cosh_series(d, e, d, n2, prec);
break;
case 5:
acb_poly_set(e, a);
acb_poly_sinh_cosh_series(d, e, e, n2, prec);
break;
default:
acb_poly_set(d, a);
acb_poly_sinh_series(d, d, n2, prec);
acb_poly_set(e, a);
acb_poly_cosh_series(e, e, n2, prec);
break;
}
acb_poly_truncate(b, FLINT_MIN(n1, n2));
acb_poly_truncate(c, FLINT_MIN(n1, n2));
acb_poly_truncate(d, FLINT_MIN(n1, n2));
acb_poly_truncate(e, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(b, d) || !acb_poly_overlaps(c, e))
{
flint_printf("FAIL\n\n");
flint_printf("alg1 = %d, alg2 = %d, n1 = %wd, n2 = %wd\n\n", alg1, alg2, n1, n2);
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");
flint_printf("d = "); acb_poly_printd(e, 15); flint_printf("\n\n");
abort();
}
acb_poly_clear(a);
acb_poly_clear(b);
acb_poly_clear(c);
acb_poly_clear(d);
acb_poly_clear(e);
}
flint_randclear(state);
flint_cleanup();
flint_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("gamma_upper_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m, n1, n2, bits1, bits2, bits3;
acb_poly_t S, A, B, C;
acb_t s, t, c;
int regularized;
regularized = n_randint(state, 3);
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);
acb_poly_init(S);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(s);
acb_init(t);
acb_init(c);
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_randtest(s, state, bits1, 3);
acb_hypgeom_gamma_upper_series(A, s, S, regularized, n1, bits2);
acb_hypgeom_gamma_upper_series(B, s, S, regularized, n2, bits3);
acb_poly_set(C, A);
acb_poly_truncate(C, FLINT_MIN(n1, n2));
acb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(B, C))
{
flint_printf("FAIL (consistency)\n\n");
flint_printf("regularized = %d\n\n", regularized);
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("C = "); acb_poly_printd(C, 15); flint_printf("\n\n");
flint_abort();
}
/* f(h(x)) = -exp(-h(x)) h(x)^(s-1) */
acb_poly_neg(C, S);
acb_poly_exp_series(C, C, n1, bits2);
acb_sub_ui(t, s, 1, bits2);
acb_poly_pow_acb_series(B, S, t, n1, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_poly_neg(C, C);
if (regularized == 0)
{
/* integral(f(h(x)) h'(x))' = f(h(x)) h'(x) */
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_poly_truncate(C, n1 - 1);
}
else if (regularized == 1)
{
/* (integral(f(h(x)) h'(x)) / c)' = (f(h(x)) h'(x)) / c */
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_gamma(c, s, bits2);
acb_poly_scalar_div(C, C, c, bits2);
acb_poly_truncate(C, n1 - 1);
}
else if (regularized == 2)
{
/* (h(x)^-s integral(f(h(x)) h'(x)))' =
* h(x)^-(s+1) (h(x) f(h(x)) - s integral(f(h(x)) h'(x))) h'(x) */
acb_poly_t D;
acb_poly_init(D);
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(D, C, B, n1, bits2);
acb_poly_integral(D, D, bits2);
acb_poly_scalar_mul(D, D, s, bits2);
acb_poly_mullow(C, C, S, n1, bits2);
acb_poly_sub(D, C, D, bits2);
acb_add_ui(t, s, 1, bits2);
acb_neg(t, t);
acb_poly_pow_acb_series(B, S, t, n1, bits2);
acb_poly_mullow(C, D, B, n1, bits2);
acb_poly_derivative(B, S, bits2);
acb_poly_mullow(C, C, B, n1, bits2);
acb_poly_truncate(C, n1 - 1);
acb_poly_clear(D);
}
acb_poly_derivative(B, A, bits2);
if (!acb_poly_overlaps(B, C))
{
flint_printf("FAIL (derivative)\n\n");
flint_printf("regularized = %d\n\n", regularized);
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("C = "); acb_poly_printd(C, 15); flint_printf("\n\n");
flint_abort();
}
acb_hypgeom_gamma_upper_series(S, s, S, regularized, n1, bits2);
if (!acb_poly_overlaps(A, S))
{
flint_printf("FAIL (aliasing)\n\n");
flint_printf("regularized = %d\n\n", regularized);
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_abort();
}
acb_poly_clear(S);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
acb_clear(s);
acb_clear(t);
acb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
long iter;
flint_rand_t state;
printf("polylog_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100; iter++)
{
long m, n1, n2, bits1, bits2, bits3;
acb_poly_t S, A, B, C;
acb_t z;
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);
acb_poly_init(S);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(C);
acb_init(z);
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_randtest(z, state, bits1, 3);
acb_poly_polylog_series(A, S, z, n1, bits2);
acb_poly_polylog_series(B, S, z, n2, bits3);
acb_poly_set(C, A);
acb_poly_truncate(C, FLINT_MIN(n1, n2));
acb_poly_truncate(B, FLINT_MIN(n1, n2));
if (!acb_poly_overlaps(B, C))
{
printf("FAIL\n\n");
printf("S = "); acb_poly_printd(S, 15); printf("\n\n");
printf("z = "); acb_printd(z, 15); printf("\n\n");
printf("A = "); acb_poly_printd(A, 15); printf("\n\n");
printf("B = "); acb_poly_printd(B, 15); printf("\n\n");
abort();
}
acb_poly_polylog_series(S, S, z, n1, bits2);
if (!acb_poly_overlaps(A, S))
{
printf("FAIL (aliasing)\n\n");
abort();
}
acb_poly_clear(S);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(C);
acb_clear(z);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("add_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_poly_t a, b, c, d;
slong len, prec;
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_poly_init(d);
acb_poly_randtest(a, state, 1 + n_randint(state, 10), 100, 10);
acb_poly_randtest(b, state, 1 + n_randint(state, 10), 100, 10);
acb_poly_randtest(c, state, 1 + n_randint(state, 10), 100, 10);
acb_poly_randtest(d, state, 1 + n_randint(state, 10), 100, 10);
prec = 2 + n_randint(state, 100);
len = n_randint(state, 10);
acb_poly_add_series(c, a, b, len, prec);
acb_poly_add(d, a, b, prec);
acb_poly_truncate(d, len);
if (!acb_poly_equal(c, d))
{
flint_printf("FAIL\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("c = "); acb_poly_printd(c, 15); flint_printf("\n\n");
flint_abort();
}
acb_poly_set(d, a);
acb_poly_add_series(d, d, b, len, prec);
if (!acb_poly_equal(d, c))
{
flint_printf("FAIL (aliasing 1)\n\n");
flint_abort();
}
acb_poly_set(d, b);
acb_poly_add_series(d, a, d, len, prec);
if (!acb_poly_equal(d, c))
{
flint_printf("FAIL (aliasing 2)\n\n");
flint_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;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("binomial_transform....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 500 * arb_test_multiplier(); iter++)
{
acb_poly_t a, b, c, d;
slong j, n, prec;
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_poly_init(d);
n = n_randint(state, 20);
prec = 2 + n_randint(state, 200);
acb_poly_randtest(a, state, n, prec, 10);
acb_poly_randtest(b, state, n, prec, 10);
acb_poly_randtest(c, state, n, prec, 10);
/* check self-inversion property */
acb_poly_binomial_transform(b, a, n, prec);
acb_poly_binomial_transform(c, b, n, prec);
acb_poly_set(d, a);
acb_poly_truncate(d, n);
if (!acb_poly_contains(c, d))
{
flint_printf("FAIL (containment)\n\n");
flint_printf("n = %wd, prec = %wd\n\n", n, prec);
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_set(d, a);
acb_poly_binomial_transform(d, d, n, prec);
if (!acb_poly_equal(d, b))
{
flint_printf("FAIL (aliasing)\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("d: "); acb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
/* compare with power series operations */
acb_poly_zero(d);
for (j = 1; j < n; j++)
acb_poly_set_coeff_si(d, j, -1);
acb_poly_compose_series(c, a, d, n, prec);
for (j = 0; j < n; j++)
acb_poly_set_coeff_si(d, j, 1);
acb_poly_mullow(c, c, d, n, prec);
if (!acb_poly_overlaps(b, c))
{
flint_printf("FAIL (power series)\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");
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;
}
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;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("pfq_series_direct....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
acb_poly_struct a[4], b[4];
acb_poly_t z, s1, s2;
slong i, p, q, len1, len2, n1, n2, prec1, prec2;
int regularized;
p = n_randint(state, 3);
q = n_randint(state, 3);
len1 = n_randint(state, 8);
len2 = n_randint(state, 8);
prec1 = 2 + n_randint(state, 400);
prec2 = 2 + n_randint(state, 400);
if (n_randint(state, 2))
n1 = -1;
else
n1 = n_randint(state, 50);
if (n_randint(state, 2))
n2 = -1;
else
n2 = n_randint(state, 50);
regularized = n_randint(state, 2);
acb_poly_init(z);
acb_poly_init(s1);
acb_poly_init(s2);
for (i = 0; i < p; i++)
acb_poly_init(a + i);
for (i = 0; i < q; i++)
acb_poly_init(b + i);
acb_poly_randtest(z, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 10);
for (i = 0; i < p; i++)
acb_poly_randtest(a + i, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 3);
for (i = 0; i < q; i++)
acb_poly_randtest(b + i, state, 1 + n_randint(state, 10), 1 + n_randint(state, 500), 3);
acb_hypgeom_pfq_series_direct(s1, a, p, b, q, z, regularized, n1, len1, prec1);
acb_hypgeom_pfq_series_direct(s2, a, p, b, q, z, regularized, n2, len2, prec2);
acb_poly_truncate(s1, FLINT_MIN(len1, len2));
acb_poly_truncate(s2, FLINT_MIN(len1, len2));
if (!acb_poly_overlaps(s1, s2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %wd\n", iter);
flint_printf("n1 = %wd, n2 = %wd prec1 = %wd, prec2 = %wd\n\n", n1, n2, prec1, prec2);
flint_printf("p = %wd, q = %wd\n\n", p, q);
flint_printf("z = "); acb_poly_printd(z, 15); flint_printf("\n\n");
for (i = 0; i < p; i++)
{
flint_printf("a[%wd] = ", i); acb_poly_printd(a + i, 15); flint_printf("\n\n");
}
for (i = 0; i < q; i++)
{
flint_printf("b[%wd] = ", i); acb_poly_printd(b + i, 15); flint_printf("\n\n");
}
flint_printf("s1 = "); acb_poly_printd(s1, 15); flint_printf("\n\n");
flint_printf("s2 = "); acb_poly_printd(s2, 15); flint_printf("\n\n");
acb_poly_sub(s1, s1, s2, prec1);
flint_printf("diff = "); acb_poly_printd(s1, 15); flint_printf("\n\n");
abort();
}
acb_poly_clear(z);
acb_poly_clear(s1);
acb_poly_clear(s2);
for (i = 0; i < p; i++)
acb_poly_clear(a + i);
for (i = 0; i < q; i++)
acb_poly_clear(b + i);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("exp_pi_i_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong m, n, prec;
acb_poly_t a, b, c;
acb_t t;
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_init(t);
prec = 2 + n_randint(state, 100);
acb_poly_randtest(a, state, 1 + n_randint(state, 20), prec, 5);
acb_poly_randtest(b, state, 1 + n_randint(state, 20), prec, 5);
acb_poly_randtest(c, state, 1 + n_randint(state, 20), prec, 5);
m = n_randint(state, 20);
n = n_randint(state, 20);
if (n_randint(state, 2) == 0)
acb_poly_exp_pi_i_series(b, a, m, prec);
else
{
acb_poly_set(b, a);
acb_poly_exp_pi_i_series(b, b, m, prec);
}
acb_const_pi(t, prec);
acb_mul_onei(t, t);
acb_poly_scalar_mul(c, a, t, prec);
acb_poly_exp_series(c, c, n, prec);
acb_poly_truncate(b, FLINT_MIN(m, n));
acb_poly_truncate(c, FLINT_MIN(m, n));
if (!acb_poly_overlaps(b, c))
{
flint_printf("FAIL\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_abort();
}
acb_poly_clear(a);
acb_poly_clear(b);
acb_poly_clear(c);
acb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
