void
_arb_poly_asin_series(arb_ptr g, arb_srcptr h, slong hlen, slong n, slong prec)
{
arb_t c;
arb_init(c);
arb_asin(c, h, prec);
hlen = FLINT_MIN(hlen, n);
if (hlen == 1)
{
_arb_vec_zero(g + 1, n - 1);
}
else
{
arb_ptr t, u;
slong ulen;
t = _arb_vec_init(n);
u = _arb_vec_init(n);
/* asin(h(x)) = integral(h'(x)/sqrt(1-h(x)^2)) */
ulen = FLINT_MIN(n, 2 * hlen - 1);
_arb_poly_mullow(u, h, hlen, h, hlen, ulen, prec);
arb_sub_ui(u, u, 1, prec);
_arb_vec_neg(u, u, ulen);
_arb_poly_rsqrt_series(t, u, ulen, n, prec);
_arb_poly_derivative(u, h, hlen, prec);
_arb_poly_mullow(g, t, n, u, hlen - 1, n, prec);
_arb_poly_integral(g, g, n, prec);
_arb_vec_clear(t, n);
_arb_vec_clear(u, n);
}
arb_swap(g, c);
arb_clear(c);
}
int main()
{
long iter;
flint_rand_t state;
printf("asin....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b;
fmpq_t q;
mpfr_t t;
long prec = 2 + n_randint(state, 200);
arb_init(a);
arb_init(b);
fmpq_init(q);
mpfr_init2(t, prec + 100);
arb_randtest(a, state, 1 + n_randint(state, 200), 3);
arb_randtest(b, 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_asin(t, t, MPFR_RNDN);
arb_asin(b, a, prec);
if (!arb_contains_mpfr(b, t))
{
printf("FAIL: containment\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
abort();
}
arb_asin(a, a, prec);
if (!arb_equal(a, b))
{
printf("FAIL: aliasing\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(q);
mpfr_clear(t);
}
/* check large arguments */
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
long prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(a);
arb_init(b);
arb_init(c);
arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100);
arb_asin(b, a, prec1);
arb_asin(c, a, prec2);
if (!arb_overlaps(b, c))
{
printf("FAIL: overlap\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
/* check sin(asin(x)) = x */
arb_sin(c, b, prec1);
if (!arb_contains(c, a))
{
printf("FAIL: functional equation\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arb_print(b); printf("\n\n");
printf("c = "); arb_print(c); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
