void
acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, slong n, slong prec, int times_pi)
{
slong hlen = h->length;
if (n == 0)
{
acb_poly_zero(s);
acb_poly_zero(c);
return;
}
if (hlen == 0)
{
acb_poly_zero(s);
acb_poly_one(c);
return;
}
acb_poly_fit_length(s, n);
acb_poly_fit_length(c, n);
_acb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs,
h->coeffs, hlen, n, prec, times_pi);
_acb_poly_set_length(s, n);
_acb_poly_normalise(s);
_acb_poly_set_length(c, n);
_acb_poly_normalise(c);
}
void
acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c,
const acb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
acb_poly_zero(s);
acb_poly_zero(c);
return;
}
if (hlen == 0)
{
acb_poly_zero(s);
acb_poly_one(c);
return;
}
if (hlen == 1)
n = 1;
acb_poly_fit_length(s, n);
acb_poly_fit_length(c, n);
_acb_poly_sin_cos_pi_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec);
_acb_poly_set_length(s, n);
_acb_poly_normalise(s);
_acb_poly_set_length(c, n);
_acb_poly_normalise(c);
}
void
acb_hypgeom_2f1_series_direct(acb_poly_t res,
const acb_poly_t a, const acb_poly_t b,
const acb_poly_t c, const acb_poly_t z, int regularized, slong len, slong prec)
{
acb_poly_struct aa[4];
aa[0] = *a;
aa[1] = *b;
aa[2] = *c;
acb_poly_init(&aa[3]);
acb_poly_one(&aa[3]);
acb_hypgeom_pfq_series_direct(res, aa, 2, aa + 2, 2, z,
regularized, -1, len, prec);
acb_poly_clear(&aa[3]);
}
void
acb_poly_pow_ui(acb_poly_t res,
const acb_poly_t poly, ulong exp, slong prec)
{
slong flen, rlen;
flen = poly->length;
if (exp == 0)
{
acb_poly_one(res);
}
else if (flen == 0)
{
acb_poly_zero(res);
}
else
{
rlen = exp * (flen - 1) + 1;
if (res != poly)
{
acb_poly_fit_length(res, rlen);
_acb_poly_pow_ui(res->coeffs,
poly->coeffs, flen, exp, prec);
_acb_poly_set_length(res, rlen);
_acb_poly_normalise(res);
}
else
{
acb_poly_t t;
acb_poly_init2(t, rlen);
_acb_poly_pow_ui(t->coeffs,
poly->coeffs, flen, exp, prec);
_acb_poly_set_length(t, rlen);
_acb_poly_normalise(t);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
}
}
void
acb_poly_pow_ui_trunc_binexp(acb_poly_t res,
const acb_poly_t poly, ulong exp, long len, long prec)
{
long flen, rlen;
flen = poly->length;
if (exp == 0 && len != 0)
{
acb_poly_one(res);
}
else if (flen == 0 || len == 0)
{
acb_poly_zero(res);
}
else
{
rlen = poly_pow_length(flen, exp, len);
if (res != poly)
{
acb_poly_fit_length(res, rlen);
_acb_poly_pow_ui_trunc_binexp(res->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_acb_poly_set_length(res, rlen);
_acb_poly_normalise(res);
}
else
{
acb_poly_t t;
acb_poly_init2(t, rlen);
_acb_poly_pow_ui_trunc_binexp(t->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_acb_poly_set_length(t, rlen);
_acb_poly_normalise(t);
acb_poly_swap(res, t);
acb_poly_clear(t);
}
}
}
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_pfq_series_sum_forward(acb_poly_t s, acb_poly_t t,
const acb_poly_struct * a, long p,
const acb_poly_struct * b, long q,
const acb_poly_t z, int regularized,
long n, long len, long prec)
{
acb_poly_t u, v;
acb_poly_t tmp;
long k, i;
acb_poly_init(u);
acb_poly_init(v);
acb_poly_init(tmp);
if (!regularized)
{
acb_poly_zero(s);
acb_poly_one(t);
for (k = 0; k < n && acb_poly_length(t) != 0; k++)
{
acb_poly_add(s, s, t, prec);
if (p > 0)
{
acb_poly_add_si(u, a, k, prec);
for (i = 1; i < p; i++)
{
acb_poly_add_si(v, a + i, k, prec);
acb_poly_mullow(u, u, v, len, prec);
}
acb_poly_mullow(t, t, u, len, prec);
}
if (q > 0)
{
acb_poly_add_si(u, b, k, prec);
for (i = 1; i < q; i++)
{
acb_poly_add_si(v, b + i, k, prec);
acb_poly_mullow(u, u, v, len, prec);
}
acb_poly_div_series(t, t, u, len, prec);
}
acb_poly_mullow(t, t, z, len, prec);
}
}
else
{
acb_poly_zero(s);
for (i = 0; i < q; i++)
{
if (i == 0)
{
acb_poly_rgamma_series(t, b + i, len, prec);
}
else
{
acb_poly_rgamma_series(u, b + i, len, prec);
acb_poly_mullow(tmp, t, u, len, prec);
acb_poly_swap(tmp, t);
}
}
for (k = 0; k < n; k++)
{
acb_poly_add(s, s, t, prec);
if (p > 0)
{
acb_poly_add_si(u, a, k, prec);
for (i = 1; i < p; i++)
{
acb_poly_add_si(v, a + i, k, prec);
acb_poly_mullow(tmp, u, v, len, prec);
acb_poly_swap(tmp, u);
}
acb_poly_mullow(tmp, t, u, len, prec);
acb_poly_swap(tmp, t);
}
if (q > 0)
{
acb_poly_add_si(u, b, k, prec);
for (i = 1; i < q; i++)
{
acb_poly_add_si(v, b + i, k, prec);
acb_poly_mullow(tmp, u, v, len, prec);
acb_poly_swap(tmp, u);
}
if (acb_poly_length(u) > 0 && !acb_contains_zero(u->coeffs))
{
acb_poly_div_series(tmp, t, u, len, prec);
acb_poly_mullow(t, tmp, z, len, prec);
}
else
{
/* compute term from scratch */
acb_poly_one(t);
for (i = 0; i < p; i++)
{
acb_poly_rising_ui_series(v, a + i, k + 1, len, prec);
acb_poly_mullow(t, t, v, len, prec);
}
for (i = 0; i < q; i++)
{
acb_poly_add_si(v, b + i, k + 1, prec);
acb_poly_rgamma_series(v, v, len, prec);
acb_poly_mullow(t, t, v, len, prec);
}
acb_poly_pow_ui_trunc_binexp(v, z, k + 1, len, prec);
acb_poly_mullow(t, t, v, len, prec);
}
}
else
{
acb_poly_mullow(tmp, t, z, len, prec);
acb_poly_swap(tmp, t);
}
}
}
acb_poly_clear(u);
acb_poly_clear(v);
acb_poly_clear(tmp);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("tan_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
slong m, n, rbits1, rbits2;
acb_poly_t a, b, c, d, e;
rbits1 = 2 + n_randint(state, 100);
rbits2 = 2 + n_randint(state, 100);
if (n_randint(state, 10) == 0)
{
m = 1 + n_randint(state, 50);
n = 1 + n_randint(state, 50);
}
else
{
m = 1 + n_randint(state, 20);
n = 1 + n_randint(state, 20);
}
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, m, rbits1, 10);
acb_poly_tan_series(b, a, n, rbits2);
/* check tan(x) = 2*tan(x/2)/(1-tan(x/2)^2) */
acb_poly_scalar_mul_2exp_si(c, a, -1);
acb_poly_tan_series(c, c, n, rbits2);
acb_poly_mullow(d, c, c, n, rbits2);
acb_poly_one(e);
acb_poly_sub(e, e, d, rbits2);
acb_poly_div_series(c, c, e, n, rbits2);
acb_poly_scalar_mul_2exp_si(c, c, 1);
if (!acb_poly_overlaps(b, c))
{
flint_printf("FAIL\n\n");
flint_printf("bits2 = %wd\n", rbits2);
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_tan_series(a, a, n, rbits2);
if (!acb_poly_equal(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);
acb_poly_clear(e);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
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);
}
