void
_arb_poly_log1p_series(arb_ptr res, arb_srcptr f, slong flen, slong n, slong prec)
{
arb_t a;
flen = FLINT_MIN(flen, n);
arb_init(a);
arb_log1p(a, f, prec);
if (flen == 1)
{
_arb_vec_zero(res + 1, n - 1);
}
else if (n == 2)
{
arb_add_ui(res, f + 0, 1, prec);
arb_div(res + 1, f + 1, res + 0, prec);
}
else if (_arb_vec_is_zero(f + 1, flen - 2)) /* f = a + bx^d */
{
slong i, j, d = flen - 1;
arb_add_ui(res, f + 0, 1, prec);
for (i = 1, j = d; j < n; j += d, i++)
{
if (i == 1)
arb_div(res + j, f + d, res, prec);
else
arb_mul(res + j, res + j - d, res + d, prec);
_arb_vec_zero(res + j - d + 1, flen - 2);
}
_arb_vec_zero(res + j - d + 1, n - (j - d + 1));
for (i = 2, j = 2 * d; j < n; j += d, i++)
arb_div_si(res + j, res + j, i % 2 ? i : -i, prec);
}
else
{
arb_ptr f_diff, f_inv;
slong alloc;
alloc = n + flen;
f_inv = _arb_vec_init(alloc);
f_diff = f_inv + n;
arb_add_ui(f_diff, f, 1, prec);
_arb_vec_set(f_diff + 1, f + 1, flen - 1);
_arb_poly_inv_series(f_inv, f_diff, flen, n, prec);
_arb_poly_derivative(f_diff, f, flen, prec);
_arb_poly_mullow(res, f_inv, n - 1, f_diff, flen - 1, n - 1, prec);
_arb_poly_integral(res, res, n, prec);
_arb_vec_clear(f_inv, alloc);
}
arb_swap(res, a);
arb_clear(a);
}
void
arb_atanh(arb_t z, const arb_t x, slong prec)
{
if (arb_is_zero(x))
{
arb_zero(z);
}
else
{
arb_t t;
arb_init(t);
arb_sub_ui(t, x, 1, prec + 4);
arb_div(t, x, t, prec + 4);
arb_mul_2exp_si(t, t, 1);
arb_neg(t, t);
arb_log1p(z, t, prec);
arb_mul_2exp_si(z, z, -1);
arb_clear(t);
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("log1p....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 20000; iter++)
{
arb_t a, b, c, d;
slong prec0, prec1, prec2;
if (iter % 10 == 0)
prec0 = 10000;
else
prec0 = 1000;
prec1 = 2 + n_randint(state, prec0);
prec2 = 2 + n_randint(state, prec0);
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_special(a, state, 1 + n_randint(state, prec0), 100);
arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100);
arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100);
arb_log1p(b, a, prec1);
arb_log1p(c, a, prec2);
if (!arb_overlaps(b, c))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
abort();
}
/* compare with log */
arb_add_ui(d, a, 1, prec2);
arb_log(d, d, prec2);
if (!arb_overlaps(c, d))
{
flint_printf("FAIL: comparison with log\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
abort();
}
arb_log1p(a, a, prec1);
if (!arb_overlaps(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
