void
arb_poly_exp_series(arb_poly_t f, const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(f);
return;
}
if (hlen == 0)
{
arb_poly_one(f);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(f, n);
_arb_poly_exp_series(f->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(f, n);
_arb_poly_normalise(f);
}
void
arb_poly_sinh_cosh_series_exponential(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(s);
arb_poly_zero(c);
return;
}
if (hlen == 0)
{
arb_poly_zero(s);
arb_poly_one(c);
return;
}
arb_poly_fit_length(s, n);
arb_poly_fit_length(c, n);
_arb_poly_sinh_cosh_series_exponential(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(s, n);
_arb_poly_normalise(s);
_arb_poly_set_length(c, n);
_arb_poly_normalise(c);
}
void
arb_poly_rising_ui_series(arb_poly_t res, const arb_poly_t f, ulong r, slong trunc, slong prec)
{
slong len;
if ((f->length == 0 && r != 0) || trunc == 0)
{
arb_poly_zero(res);
return;
}
if (r == 0)
{
arb_poly_one(res);
return;
}
len = poly_pow_length(f->length, r, trunc);
if (f == res)
{
arb_poly_t tmp;
arb_poly_init(tmp);
arb_poly_rising_ui_series(tmp, f, r, len, prec);
arb_poly_swap(tmp, res);
arb_poly_clear(tmp);
}
else
{
arb_poly_fit_length(res, len);
_arb_poly_rising_ui_series(res->coeffs, f->coeffs, f->length, r, len, prec);
_arb_poly_set_length(res, len);
_arb_poly_normalise(res);
}
}
void
arb_poly_sin_cos_series_tangent(arb_poly_t s, arb_poly_t c,
const arb_poly_t h, slong n, slong prec, int times_pi)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(s);
arb_poly_zero(c);
return;
}
if (hlen == 0)
{
arb_poly_zero(s);
arb_poly_one(c);
return;
}
arb_poly_fit_length(s, n);
arb_poly_fit_length(c, n);
_arb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs,
h->coeffs, hlen, n, prec, times_pi);
_arb_poly_set_length(s, n);
_arb_poly_normalise(s);
_arb_poly_set_length(c, n);
_arb_poly_normalise(c);
}
void
arb_poly_cosh_series(arb_poly_t g, const arb_poly_t h, slong n, slong prec)
{
slong hlen = h->length;
if (n == 0)
{
arb_poly_zero(g);
return;
}
if (hlen == 0)
{
arb_poly_one(g);
return;
}
if (hlen == 1)
n = 1;
arb_poly_fit_length(g, n);
_arb_poly_cosh_series(g->coeffs, h->coeffs, hlen, n, prec);
_arb_poly_set_length(g, n);
_arb_poly_normalise(g);
}
static void
bsplit(arb_poly_t pol, const arb_t sqrtD,
const slong * qbf, slong a, slong b, slong prec)
{
if (b - a == 0)
{
arb_poly_one(pol);
}
else if (b - a == 1)
{
acb_t z;
acb_init(z);
/* j((-b+sqrt(-D))/(2a)) */
arb_set_si(acb_realref(z), -FLINT_ABS(qbf[3 * a + 1]));
arb_set(acb_imagref(z), sqrtD);
acb_div_si(z, z, 2 * qbf[3 * a], prec);
acb_modular_j(z, z, prec);
if (qbf[3 * a + 1] < 0)
{
/* (x^2 - 2re(j) x + |j|^2) */
arb_poly_fit_length(pol, 3);
arb_mul(pol->coeffs, acb_realref(z), acb_realref(z), prec);
arb_addmul(pol->coeffs, acb_imagref(z), acb_imagref(z), prec);
arb_mul_2exp_si(pol->coeffs + 1, acb_realref(z), 1);
arb_neg(pol->coeffs + 1, pol->coeffs + 1);
arb_one(pol->coeffs + 2);
_arb_poly_set_length(pol, 3);
}
else
{
/* (x-j) */
arb_poly_fit_length(pol, 2);
arb_neg(pol->coeffs, acb_realref(z));
arb_one(pol->coeffs + 1);
_arb_poly_set_length(pol, 2);
}
acb_clear(z);
}
else
{
arb_poly_t tmp;
arb_poly_init(tmp);
bsplit(pol, sqrtD, qbf, a, a + (b - a) / 2, prec);
bsplit(tmp, sqrtD, qbf, a + (b - a) / 2, b, prec);
arb_poly_mul(pol, pol, tmp, prec);
arb_poly_clear(tmp);
}
}
void
arb_poly_pow_ui_trunc_binexp(arb_poly_t res,
const arb_poly_t poly, ulong exp, slong len, slong prec)
{
slong flen, rlen;
flen = poly->length;
if (exp == 0 && len != 0)
{
arb_poly_one(res);
}
else if (flen == 0 || len == 0)
{
arb_poly_zero(res);
}
else
{
rlen = poly_pow_length(flen, exp, len);
if (res != poly)
{
arb_poly_fit_length(res, rlen);
_arb_poly_pow_ui_trunc_binexp(res->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_arb_poly_set_length(res, rlen);
_arb_poly_normalise(res);
}
else
{
arb_poly_t t;
arb_poly_init2(t, rlen);
_arb_poly_pow_ui_trunc_binexp(t->coeffs,
poly->coeffs, flen, exp, rlen, prec);
_arb_poly_set_length(t, rlen);
_arb_poly_normalise(t);
arb_poly_swap(res, t);
arb_poly_clear(t);
}
}
}
/* F = 1 + U + U^2 + ... = 1/(1-U) assuming that U[0] is positive;
indeterminate if not convergent */
static void
arb_poly_geometric_sum(arb_poly_t F, const arb_poly_t U, long len, long prec)
{
if (U->length == 0)
{
arb_poly_one(F);
return;
}
arb_poly_add_si(F, U, -1, prec);
arb_poly_neg(F, F);
if (F->length > 0 && arb_is_positive(F->coeffs))
{
arb_poly_inv_series(F, F, len, prec);
}
else
{
arb_poly_fit_length(F, len);
_arb_vec_indeterminate(F->coeffs, len);
_arb_poly_set_length(F, len);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("atan_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
slong m, n, qbits, rbits1, rbits2;
fmpq_poly_t A;
arb_poly_t a, b, c, d;
qbits = 2 + n_randint(state, 200);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
m = 1 + n_randint(state, 30);
n = 1 + n_randint(state, 30);
fmpq_poly_init(A);
arb_poly_init(a);
arb_poly_init(b);
arb_poly_init(c);
arb_poly_init(d);
fmpq_poly_randtest(A, state, m, qbits);
arb_poly_set_fmpq_poly(a, A, rbits1);
arb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5);
arb_poly_atan_series(b, a, n, rbits2);
/* Check 2 atan(x) = atan(2x/(1-x^2)) + C */
arb_poly_mullow(c, a, a, n, rbits2);
arb_poly_one(d);
arb_poly_sub(c, d, c, rbits2);
arb_poly_add(d, a, a, rbits2);
if (arb_poly_length(c) != 0)
{
arb_poly_div_series(c, d, c, n, rbits2);
arb_poly_atan_series(c, c, n, rbits2);
arb_poly_add(d, b, b, rbits2);
/* TODO: also check the first coefficient */
arb_poly_set_coeff_si(c, 0, 0);
arb_poly_set_coeff_si(d, 0, 0);
if (!arb_poly_overlaps(c, d))
{
flint_printf("FAIL\n\n");
flint_printf("bits2 = %wd\n", rbits2);
flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n");
flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n");
flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n");
flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n");
abort();
}
}
arb_poly_atan_series(a, a, n, rbits2);
if (!arb_poly_equal(a, b))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
fmpq_poly_clear(A);
arb_poly_clear(a);
arb_poly_clear(b);
arb_poly_clear(c);
arb_poly_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}