void
_arb_poly_sinh_cosh_series(arb_ptr s, arb_ptr c, const arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sinh_cosh(s, c, h, prec);
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_set(t, h + 1);
arb_sinh_cosh(s, c, h, prec);
arb_mul(s + 1, c, t, prec);
arb_mul(c + 1, s, t, prec);
arb_clear(t);
}
else if (hlen < 60 || n < 120)
_arb_poly_sinh_cosh_series_basecase(s, c, h, hlen, n, prec);
else
_arb_poly_sinh_cosh_series_exponential(s, c, h, hlen, n, prec);
}
void
_arb_poly_sinh_cosh_series_exponential(arb_ptr s, arb_ptr c,
const arb_srcptr h, slong hlen, slong len, slong prec)
{
arb_ptr t, u, v;
arb_t s0, c0;
hlen = FLINT_MIN(hlen, len);
if (hlen == 1)
{
arb_sinh_cosh(s, c, h, prec);
_arb_vec_zero(s + 1, len - 1);
_arb_vec_zero(c + 1, len - 1);
return;
}
arb_init(s0);
arb_init(c0);
t = _arb_vec_init(3 * len);
u = t + len;
v = u + len;
arb_sinh_cosh(s0, c0, h, prec);
_arb_vec_set(t + 1, h + 1, hlen - 1);
_arb_poly_exp_series(t, t, len, len, prec);
/* todo: part of the inverse could be avoided since exp computes
it internally to half the length */
_arb_poly_inv_series(u, t, len, len, prec);
/* hyperbolic sine */
_arb_vec_sub(s, t, u, len, prec);
_arb_vec_scalar_mul_2exp_si(s, s, len, -1);
/* hyperbolic cosine */
_arb_vec_add(c, t, u, len, prec);
_arb_vec_scalar_mul_2exp_si(c, c, len, -1);
/* sinh(h0 + h1) = cosh(h0) sinh(h1) + sinh(h0) cosh(h1)
cosh(h0 + h1) = cosh(h0) cosh(h1) + sinh(h0) sinh(h1) */
if (!arb_is_zero(s0))
{
_arb_vec_scalar_mul(t, s, len, c0, prec);
_arb_vec_scalar_mul(u, c, len, s0, prec);
_arb_vec_scalar_mul(v, s, len, s0, prec);
_arb_vec_add(s, t, u, len, prec);
_arb_vec_scalar_mul(t, c, len, c0, prec);
_arb_vec_add(c, t, v, len, prec);
}
_arb_vec_clear(t, 3 * len);
arb_clear(s0);
arb_clear(c0);
}
void
acb_sin_cos_pi(acb_t s, acb_t c, const acb_t z, slong prec)
{
#define a acb_realref(z)
#define b acb_imagref(z)
if (arb_is_zero(b))
{
arb_sin_cos_pi(acb_realref(s), acb_realref(c), a, prec);
arb_zero(acb_imagref(s));
arb_zero(acb_imagref(c));
}
else if (arb_is_zero(a))
{
arb_t t;
arb_init(t);
arb_const_pi(t, prec);
arb_mul(t, t, b, prec);
arb_sinh_cosh(acb_imagref(s), acb_realref(c), t, prec);
arb_zero(acb_realref(s));
arb_zero(acb_imagref(c));
arb_clear(t);
}
else
{
arb_t sa, ca, sb, cb;
arb_init(sa);
arb_init(ca);
arb_init(sb);
arb_init(cb);
arb_const_pi(sb, prec);
arb_mul(sb, sb, b, prec);
arb_sin_cos_pi(sa, ca, a, prec);
arb_sinh_cosh(sb, cb, sb, prec);
arb_mul(acb_realref(s), sa, cb, prec);
arb_mul(acb_imagref(s), sb, ca, prec);
arb_mul(acb_realref(c), ca, cb, prec);
arb_mul(acb_imagref(c), sa, sb, prec);
arb_neg(acb_imagref(c), acb_imagref(c));
arb_clear(sa);
arb_clear(ca);
arb_clear(sb);
arb_clear(cb);
}
#undef a
#undef b
}
void
_arb_poly_sinh_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
{
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
arb_sinh(g, h, prec);
_arb_vec_zero(g + 1, n - 1);
}
else if (n == 2)
{
arb_t t;
arb_init(t);
arb_sinh_cosh(g, t, h, prec);
arb_mul(g + 1, h + 1, t, prec); /* safe since hlen >= 2 */
arb_clear(t);
}
else
{
arb_ptr t = _arb_vec_init(n);
_arb_poly_sinh_cosh_series(g, t, h, hlen, n, prec);
_arb_vec_clear(t, n);
}
}
void
_arb_poly_sinh_cosh_series_basecase(arb_ptr s, arb_ptr c, arb_srcptr h, slong hlen,
slong n, slong prec)
{
slong j, k, alen = FLINT_MIN(n, hlen);
arb_ptr a;
arb_t t, u;
arb_sinh_cosh(s, c, h, prec);
if (hlen == 1)
{
_arb_vec_zero(s + 1, n - 1);
_arb_vec_zero(c + 1, n - 1);
return;
}
arb_init(t);
arb_init(u);
a = _arb_vec_init(alen);
for (k = 1; k < alen; k++)
arb_mul_ui(a + k, h + k, k, prec);
for (k = 1; k < n; k++)
{
arb_zero(t);
arb_zero(u);
for (j = 1; j < FLINT_MIN(k + 1, hlen); j++)
{
arb_addmul(t, a + j, s + k - j, prec);
arb_addmul(u, a + j, c + k - j, prec);
}
arb_div_ui(c + k, t, k, prec);
arb_div_ui(s + k, u, k, prec);
}
arb_clear(t);
arb_clear(u);
_arb_vec_clear(a, alen);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sinh_cosh....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
arb_t a, b, c;
fmpq_t q;
mpfr_t t, u;
slong prec = 2 + n_randint(state, 200);
arb_init(a);
arb_init(b);
arb_init(c);
fmpq_init(q);
mpfr_init2(t, prec + 100);
mpfr_init2(u, prec + 100);
arb_randtest(a, state, 1 + n_randint(state, 200), 3);
arb_randtest(b, state, 1 + n_randint(state, 200), 3);
arb_randtest(c, state, 1 + n_randint(state, 200), 3);
arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));
fmpq_get_mpfr(t, q, MPFR_RNDN);
mpfr_sinh_cosh(t, u, t, MPFR_RNDN);
arb_sinh_cosh(b, c, a, prec);
if (!arb_contains_mpfr(b, t))
{
flint_printf("FAIL: containment (sin)\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
abort();
}
if (!arb_contains_mpfr(c, u))
{
flint_printf("FAIL: containment (cos)\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpq_clear(q);
mpfr_clear(t);
mpfr_clear(u);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
