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); }
static void evaluate(acb_poly_t A, acb_srcptr a, slong p, const acb_t z, slong n, slong prec) { acb_poly_fit_length(A, p + 1); if (p == 1) { acb_add_ui(A->coeffs, a, n, prec); if (z != NULL) acb_mul(A->coeffs, A->coeffs, z, prec); } else if (p == 2) { acb_add(A->coeffs, a + 0, a + 1, prec); acb_add_ui(A->coeffs + 1, A->coeffs, 2 * n, prec); acb_add_ui(A->coeffs, A->coeffs, n, prec); acb_mul_ui(A->coeffs, A->coeffs, n, prec); acb_addmul(A->coeffs, a + 0, a + 1, prec); if (z != NULL) { acb_mul(A->coeffs, A->coeffs, z, prec); acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec); } } else if (p == 3) { acb_t t, u; acb_init(t); acb_init(u); acb_add(t, a + 0, a + 1, prec); acb_add(t, t, a + 2, prec); acb_mul(u, a + 0, a + 1, prec); acb_mul(A->coeffs, u, a + 2, prec); acb_addmul(u, a + 0, a + 2, prec); acb_addmul(u, a + 1, a + 2, prec); /* (a0 + n)(a1 + n)(a2 + n) = a0 a1 a2 + (a0 a1 + a0 a2 + a1 a2) n + (a0 + a1 + a2) n^2 + n^3 (a0 a1 + a0 a2 + a1 a2) + 2 (a0 + a1 + a2) n + 3 n^2 (a0 + a1 + a2) + 3n 1 */ acb_addmul_ui(A->coeffs, u, n, prec); acb_addmul_ui(A->coeffs, t, n * n, prec); acb_add_ui(A->coeffs, A->coeffs, n * n * n, prec); acb_set(A->coeffs + 1, u); acb_addmul_ui(A->coeffs + 1, t, 2 * n, prec); acb_add_ui(A->coeffs + 1, A->coeffs + 1, 3 * n * n, prec); acb_add_ui(A->coeffs + 2, t, 3 * n, prec); if (z != NULL) { acb_mul(A->coeffs + 0, A->coeffs + 0, z, prec); acb_mul(A->coeffs + 1, A->coeffs + 1, z, prec); acb_mul(A->coeffs + 2, A->coeffs + 2, z, prec); } acb_clear(t); acb_clear(u); } else if (p != 0) { flint_abort(); } if (z != NULL) acb_set(A->coeffs + p, z); else acb_one(A->coeffs + p); _acb_poly_set_length(A, p + 1); _acb_poly_normalise(A); }
int main() { slong iter; flint_rand_t state; flint_printf("elliptic_p...."); fflush(stdout); flint_randinit(state); /* check test values */ for (iter = 0; iter < 100; iter++) { slong i; acb_t z, tau, p1, p2; acb_init(z); acb_init(tau); acb_init(p1); acb_init(p2); for (i = 0; i < NUM_TESTS; i++) { acb_set_dddd(z, testdata[i][0], 0.0, testdata[i][1], 0.0); acb_set_dddd(tau, testdata[i][2], 0.0, testdata[i][3], 0.0); acb_set_dddd(p2, testdata[i][4], EPS, testdata[i][5], EPS); acb_modular_elliptic_p(p1, z, tau, 2 + n_randint(state, 1000)); if (!acb_overlaps(p1, p2)) { flint_printf("FAIL (test value)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z = "); acb_printd(z, 15); flint_printf("\n\n"); flint_printf("p1 = "); acb_printd(p1, 15); flint_printf("\n\n"); flint_printf("p2 = "); acb_printd(p2, 15); flint_printf("\n\n"); abort(); } } acb_clear(z); acb_clear(tau); acb_clear(p1); acb_clear(p2); } /* Test periods */ for (iter = 0; iter < 2000; iter++) { acb_t tau, z1, z2, p1, p2; slong m, n, e0, prec0, prec1, prec2; acb_init(tau); acb_init(z1); acb_init(z2); acb_init(p1); acb_init(p2); e0 = 1 + n_randint(state, 10); prec0 = 2 + n_randint(state, 1000); prec1 = 2 + n_randint(state, 1000); prec2 = 2 + n_randint(state, 1000); acb_randtest(tau, state, prec0, e0); if (arf_sgn(arb_midref(acb_imagref(tau))) < 0) acb_neg(tau, tau); acb_randtest(z1, state, prec0, e0); acb_randtest(p1, state, prec0, e0); acb_randtest(p2, state, prec0, e0); /* z2 = z1 + m + n*tau */ m = n_randint(state, 10); n = n_randint(state, 10); acb_add_ui(z2, z1, m, prec0); acb_addmul_ui(z2, tau, n, prec0); acb_modular_elliptic_p(p1, z1, tau, prec1); acb_modular_elliptic_p(p2, z2, tau, prec2); if (!acb_overlaps(p1, p2)) { flint_printf("FAIL (overlap)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("z2 = "); acb_printd(z2, 15); flint_printf("\n\n"); flint_printf("p1 = "); acb_printd(p1, 15); flint_printf("\n\n"); flint_printf("p2 = "); acb_printd(p2, 15); flint_printf("\n\n"); abort(); } acb_modular_elliptic_p(z1, z1, tau, prec1); if (!acb_overlaps(z1, p1)) { flint_printf("FAIL (aliasing)\n"); flint_printf("tau = "); acb_printd(tau, 15); flint_printf("\n\n"); flint_printf("z1 = "); acb_printd(z1, 15); flint_printf("\n\n"); flint_printf("p1 = "); acb_printd(p1, 15); flint_printf("\n\n"); abort(); } acb_clear(tau); acb_clear(z1); acb_clear(z2); acb_clear(p1); acb_clear(p2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }