int
main(void)
{
int i, result;
flint_rand_t state;
printf("shift_left/right....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing of a and b for left shift */
for (i = 0; i < 1000; i++)
{
acb_poly_t a, b;
long shift = n_randint(state, 100);
acb_poly_init(a);
acb_poly_init(b);
acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10);
acb_poly_shift_left(b, a, shift);
acb_poly_shift_left(a, a, shift);
result = (acb_poly_equal(a, b));
if (!result)
{
printf("FAIL:\n");
acb_poly_printd(a, 10), printf("\n\n");
acb_poly_printd(b, 10), printf("\n\n");
abort();
}
acb_poly_clear(a);
acb_poly_clear(b);
}
/* Check aliasing of a and b for right shift */
for (i = 0; i < 1000; i++)
{
acb_poly_t a, b;
long shift = n_randint(state, 100);
acb_poly_init(a);
acb_poly_init(b);
acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10);
acb_poly_shift_right(b, a, shift);
acb_poly_shift_right(a, a, shift);
result = (acb_poly_equal(a, b));
if (!result)
{
printf("FAIL:\n");
acb_poly_printd(a, 10), printf("\n\n");
acb_poly_printd(b, 10), printf("\n\n");
abort();
}
acb_poly_clear(a);
acb_poly_clear(b);
}
/* Check shift left then right does nothing */
for (i = 0; i < 1000; i++)
{
acb_poly_t a, b, c;
long shift = n_randint(state, 100);
acb_poly_init(a);
acb_poly_init(b);
acb_poly_init(c);
acb_poly_randtest(a, state, n_randint(state, 100), 2 + n_randint(state, 200), 10);
acb_poly_shift_left(b, a, shift);
acb_poly_shift_right(c, b, shift);
result = (acb_poly_equal(c, a));
if (!result)
{
printf("FAIL:\n");
acb_poly_printd(a, 10), printf("\n\n");
acb_poly_printd(b, 10), printf("\n\n");
acb_poly_printd(c, 10), printf("\n\n");
abort();
}
acb_poly_clear(a);
acb_poly_clear(b);
acb_poly_clear(c);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return 0;
}
void
acb_hypgeom_bessel_k_0f1_series(acb_poly_t res,
const acb_poly_t nu, const acb_poly_t z,
slong len, slong prec)
{
acb_poly_t s, u, A, B;
acb_poly_struct b[2];
arb_t c;
slong wlen;
int singular;
acb_poly_init(s);
acb_poly_init(u);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(b + 0);
acb_poly_init(b + 1);
arb_init(c);
singular = (nu->length == 0) || acb_is_int(nu->coeffs);
wlen = len + (singular != 0);
/* A = (z/2)^nu, B = 1/A */
acb_poly_scalar_mul_2exp_si(A, z, -1);
acb_poly_pow_series(A, A, nu, wlen, prec);
acb_poly_inv_series(B, A, wlen, prec);
acb_poly_mullow(u, z, z, wlen, prec);
acb_poly_scalar_mul_2exp_si(u, u, -2);
acb_poly_one(b + 1);
acb_poly_add_si(b + 0, nu, 1, prec);
acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
acb_poly_mullow(A, A, s, wlen, prec);
acb_poly_add_si(b + 0, nu, -1, prec);
acb_poly_neg(b + 0, b + 0);
acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec);
acb_poly_mullow(B, B, s, wlen, prec);
acb_poly_sub(A, B, A, prec);
acb_poly_scalar_mul_2exp_si(A, A, -1);
/* multiply by pi csc(pi nu) */
acb_poly_sin_pi_series(B, nu, wlen, prec);
if (singular)
{
acb_poly_shift_right(A, A, 1);
acb_poly_shift_right(B, B, 1);
}
acb_poly_div_series(res, A, B, len, prec);
arb_const_pi(c, prec);
_acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec);
acb_poly_clear(s);
acb_poly_clear(u);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(b + 0);
acb_poly_clear(b + 1);
arb_clear(c);
}
void
acb_hypgeom_u_1f1_series(acb_poly_t res,
const acb_poly_t a, const acb_poly_t b, const acb_poly_t z,
long len, long prec)
{
acb_poly_t s, u, A, B;
acb_poly_struct aa[3];
arb_t c;
long wlen;
int singular;
acb_poly_init(s);
acb_poly_init(u);
acb_poly_init(A);
acb_poly_init(B);
acb_poly_init(aa + 0);
acb_poly_init(aa + 1);
acb_poly_init(aa + 2);
arb_init(c);
singular = (b->length == 0) || acb_is_int(b->coeffs);
wlen = len + (singular != 0);
/* A = rgamma(a-b+1) * 1F~1(a,b,z) */
acb_poly_sub(u, a, b, prec);
acb_poly_add_si(u, u, 1, prec);
acb_poly_rgamma_series(A, u, wlen, prec);
/* todo: handle a = 1 efficiently */
acb_poly_set(aa, a);
acb_poly_set(aa + 1, b);
acb_poly_one(aa + 2);
acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec);
acb_poly_mullow(A, A, s, wlen, prec);
/* B = rgamma(a) * 1F~1(a-b+1,2-b,z) * z^(1-b) */
acb_poly_set(aa, u);
acb_poly_add_si(aa + 1, b, -2, prec);
acb_poly_neg(aa + 1, aa + 1);
acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec);
acb_poly_rgamma_series(B, a, wlen, prec);
acb_poly_mullow(B, B, s, wlen, prec);
acb_poly_add_si(u, b, -1, prec);
acb_poly_neg(u, u);
acb_poly_pow_series(s, z, u, wlen, prec);
acb_poly_mullow(B, B, s, wlen, prec);
acb_poly_sub(A, A, B, prec);
/* multiply by pi csc(pi b) */
acb_poly_sin_pi_series(B, b, wlen, prec);
if (singular)
{
acb_poly_shift_right(A, A, 1);
acb_poly_shift_right(B, B, 1);
}
acb_poly_div_series(res, A, B, len, prec);
arb_const_pi(c, prec);
_acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec);
acb_poly_clear(s);
acb_poly_clear(u);
acb_poly_clear(A);
acb_poly_clear(B);
acb_poly_clear(aa + 0);
acb_poly_clear(aa + 1);
acb_poly_clear(aa + 2);
arb_clear(c);
}
