void
_acb_poly_agm1_series(acb_ptr res, acb_srcptr z, long zlen, long len, long prec)
{
acb_ptr t, u;
zlen = FLINT_MIN(zlen, len);
t = _acb_vec_init(len);
u = _acb_vec_init(len);
acb_agm1_cpx(t, z, len, prec);
/* compose with nonconstant part */
acb_zero(u);
_acb_vec_set(u + 1, z + 1, zlen - 1);
_acb_poly_compose_series(res, t, len, u, zlen, len, prec);
_acb_vec_clear(t, len);
_acb_vec_clear(u, len);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("agm1....");
fflush(stdout);
flint_randinit(state);
/* check particular values against table */
{
acb_t z, t;
acb_ptr w1;
slong i, j, prec, cnj;
acb_init(z);
acb_init(t);
w1 = _acb_vec_init(NUM_DERIVS);
for (prec = 32; prec <= 512; prec *= 4)
{
for (i = 0; i < NUM_TESTS; i++)
{
for (cnj = 0; cnj < 2; cnj++)
{
if (cnj == 1 && agm_testdata[i][0] < 0 &&
agm_testdata[i][1] == 0)
continue;
acb_zero(z);
arf_set_d(arb_midref(acb_realref(z)), agm_testdata[i][0]);
arf_set_d(arb_midref(acb_imagref(z)), cnj ? -agm_testdata[i][1] : agm_testdata[i][1]);
acb_agm1_cpx(w1, z, NUM_DERIVS, prec);
for (j = 0; j < NUM_DERIVS; j++)
{
arf_set_d(arb_midref(acb_realref(t)), agm_testdata[i][2+2*j]);
mag_set_d(arb_radref(acb_realref(t)), fabs(agm_testdata[i][2+2*j]) * EPS);
arf_set_d(arb_midref(acb_imagref(t)), cnj ? -agm_testdata[i][2+2*j+1] : agm_testdata[i][2+2*j+1]);
mag_set_d(arb_radref(acb_imagref(t)), fabs(agm_testdata[i][2+2*j+1]) * EPS);
if (!acb_overlaps(w1 + j, t))
{
flint_printf("FAIL\n\n");
flint_printf("j = %wd\n\n", j);
flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n");
flint_printf("t = "); acb_printd(t, 15); flint_printf("\n\n");
flint_printf("w1 = "); acb_printd(w1 + j, 15); flint_printf("\n\n");
abort();
}
}
}
}
}
_acb_vec_clear(w1, NUM_DERIVS);
acb_clear(z);
acb_clear(t);
}
/* self-consistency test */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_ptr m1, m2;
acb_t z1, z2, t;
slong i, len1, len2, prec1, prec2;
len1 = n_randint(state, 10);
len2 = n_randint(state, 10);
prec1 = 2 + n_randint(state, 2000);
prec2 = 2 + n_randint(state, 2000);
m1 = _acb_vec_init(len1);
m2 = _acb_vec_init(len2);
acb_init(z1);
acb_init(z2);
acb_init(t);
acb_randtest(z1, state, prec1, 1 + n_randint(state, 100));
if (n_randint(state, 2))
{
acb_set(z2, z1);
}
else
{
acb_randtest(t, state, prec2, 1 + n_randint(state, 100));
acb_add(z2, z1, t, prec2);
acb_sub(z2, z2, t, prec2);
}
acb_agm1_cpx(m1, z1, len1, prec1);
acb_agm1_cpx(m2, z2, len2, prec2);
for (i = 0; i < FLINT_MIN(len1, len2); i++)
{
if (!acb_overlaps(m1 + i, m2 + i))
{
flint_printf("FAIL (overlap)\n\n");
flint_printf("iter = %wd, i = %wd, len1 = %wd, len2 = %wd, prec1 = %wd, prec2 = %wd\n\n",
iter, i, len1, len2, prec1, prec2);
flint_printf("z1 = "); acb_printd(z1, 30); flint_printf("\n\n");
flint_printf("z2 = "); acb_printd(z2, 30); flint_printf("\n\n");
flint_printf("m1 = "); acb_printd(m1, 30); flint_printf("\n\n");
flint_printf("m2 = "); acb_printd(m2, 30); flint_printf("\n\n");
abort();
}
}
_acb_vec_clear(m1, len1);
_acb_vec_clear(m2, len2);
acb_clear(z1);
acb_clear(z2);
acb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
acb_modular_elliptic_k_cpx(acb_ptr w, const acb_t m, slong len, slong prec)
{
acb_t t, u, msub1m, m2sub1;
slong k, n;
if (len < 1)
return;
if (len == 1)
{
acb_modular_elliptic_k(w, m, prec);
return;
}
if (acb_is_zero(m))
{
acb_const_pi(w, prec);
acb_mul_2exp_si(w, w, -1);
for (k = 1; k < len; k++)
{
acb_mul_ui(w + k, w + k - 1, (2 * k - 1) * (2 * k - 1), prec);
acb_div_ui(w + k, w + k, 4 * k * k, prec);
}
return;
}
acb_init(t);
acb_init(u);
acb_init(msub1m);
acb_init(m2sub1);
acb_sub_ui(msub1m, m, 1, prec);
acb_neg(t, msub1m);
acb_sqrt(t, t, prec);
acb_mul(msub1m, msub1m, m, prec);
acb_mul_2exp_si(m2sub1, m, 1);
acb_sub_ui(m2sub1, m2sub1, 1, prec);
acb_agm1_cpx(w, t, 2, prec);
/* pi M'(t) / (4 t M(t)^2) */
acb_mul(u, w, w, prec);
acb_mul(t, t, u, prec);
acb_div(w + 1, w + 1, t, prec);
acb_const_pi(u, prec);
acb_mul(w + 1, w + 1, u, prec);
acb_mul_2exp_si(w + 1, w + 1, -2);
/* pi / (2 M(t)) */
acb_const_pi(u, prec);
acb_div(w, u, w, prec);
acb_mul_2exp_si(w, w, -1);
acb_inv(t, msub1m, prec);
for (k = 2; k < len; k++)
{
n = k - 2;
acb_mul_ui(w + k, w + n, (2 * n + 1) * (2 * n + 1), prec);
acb_mul(u, w + n + 1, m2sub1, prec);
acb_addmul_ui(w + k, u, (n + 1) * (n + 1) * 4, prec);
acb_mul(w + k, w + k, t, prec);
acb_div_ui(w + k, w + k, 4 * (n + 1) * (n + 2), prec);
acb_neg(w + k, w + k);
}
acb_clear(t);
acb_clear(u);
acb_clear(msub1m);
acb_clear(m2sub1);
}
