void acb_hypgeom_bessel_k_0f1_series(acb_poly_t res, const acb_poly_t nu, const acb_poly_t z, slong len, slong prec) { acb_poly_t s, u, A, B; acb_poly_struct b[2]; arb_t c; slong wlen; int singular; acb_poly_init(s); acb_poly_init(u); acb_poly_init(A); acb_poly_init(B); acb_poly_init(b + 0); acb_poly_init(b + 1); arb_init(c); singular = (nu->length == 0) || acb_is_int(nu->coeffs); wlen = len + (singular != 0); /* A = (z/2)^nu, B = 1/A */ acb_poly_scalar_mul_2exp_si(A, z, -1); acb_poly_pow_series(A, A, nu, wlen, prec); acb_poly_inv_series(B, A, wlen, prec); acb_poly_mullow(u, z, z, wlen, prec); acb_poly_scalar_mul_2exp_si(u, u, -2); acb_poly_one(b + 1); acb_poly_add_si(b + 0, nu, 1, prec); acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec); acb_poly_mullow(A, A, s, wlen, prec); acb_poly_add_si(b + 0, nu, -1, prec); acb_poly_neg(b + 0, b + 0); acb_hypgeom_pfq_series_direct(s, NULL, 0, b, 2, u, 1, -1, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_sub(A, B, A, prec); acb_poly_scalar_mul_2exp_si(A, A, -1); /* multiply by pi csc(pi nu) */ acb_poly_sin_pi_series(B, nu, wlen, prec); if (singular) { acb_poly_shift_right(A, A, 1); acb_poly_shift_right(B, B, 1); } acb_poly_div_series(res, A, B, len, prec); arb_const_pi(c, prec); _acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec); acb_poly_clear(s); acb_poly_clear(u); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(b + 0); acb_poly_clear(b + 1); arb_clear(c); }
void acb_hypgeom_pfq_series_sum_forward(acb_poly_t s, acb_poly_t t, const acb_poly_struct * a, long p, const acb_poly_struct * b, long q, const acb_poly_t z, int regularized, long n, long len, long prec) { acb_poly_t u, v; acb_poly_t tmp; long k, i; acb_poly_init(u); acb_poly_init(v); acb_poly_init(tmp); if (!regularized) { acb_poly_zero(s); acb_poly_one(t); for (k = 0; k < n && acb_poly_length(t) != 0; k++) { acb_poly_add(s, s, t, prec); if (p > 0) { acb_poly_add_si(u, a, k, prec); for (i = 1; i < p; i++) { acb_poly_add_si(v, a + i, k, prec); acb_poly_mullow(u, u, v, len, prec); } acb_poly_mullow(t, t, u, len, prec); } if (q > 0) { acb_poly_add_si(u, b, k, prec); for (i = 1; i < q; i++) { acb_poly_add_si(v, b + i, k, prec); acb_poly_mullow(u, u, v, len, prec); } acb_poly_div_series(t, t, u, len, prec); } acb_poly_mullow(t, t, z, len, prec); } } else { acb_poly_zero(s); for (i = 0; i < q; i++) { if (i == 0) { acb_poly_rgamma_series(t, b + i, len, prec); } else { acb_poly_rgamma_series(u, b + i, len, prec); acb_poly_mullow(tmp, t, u, len, prec); acb_poly_swap(tmp, t); } } for (k = 0; k < n; k++) { acb_poly_add(s, s, t, prec); if (p > 0) { acb_poly_add_si(u, a, k, prec); for (i = 1; i < p; i++) { acb_poly_add_si(v, a + i, k, prec); acb_poly_mullow(tmp, u, v, len, prec); acb_poly_swap(tmp, u); } acb_poly_mullow(tmp, t, u, len, prec); acb_poly_swap(tmp, t); } if (q > 0) { acb_poly_add_si(u, b, k, prec); for (i = 1; i < q; i++) { acb_poly_add_si(v, b + i, k, prec); acb_poly_mullow(tmp, u, v, len, prec); acb_poly_swap(tmp, u); } if (acb_poly_length(u) > 0 && !acb_contains_zero(u->coeffs)) { acb_poly_div_series(tmp, t, u, len, prec); acb_poly_mullow(t, tmp, z, len, prec); } else { /* compute term from scratch */ acb_poly_one(t); for (i = 0; i < p; i++) { acb_poly_rising_ui_series(v, a + i, k + 1, len, prec); acb_poly_mullow(t, t, v, len, prec); } for (i = 0; i < q; i++) { acb_poly_add_si(v, b + i, k + 1, prec); acb_poly_rgamma_series(v, v, len, prec); acb_poly_mullow(t, t, v, len, prec); } acb_poly_pow_ui_trunc_binexp(v, z, k + 1, len, prec); acb_poly_mullow(t, t, v, len, prec); } } else { acb_poly_mullow(tmp, t, z, len, prec); acb_poly_swap(tmp, t); } } } acb_poly_clear(u); acb_poly_clear(v); acb_poly_clear(tmp); }
int main() { slong iter; flint_rand_t state; flint_printf("cot_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, bits1, bits2, bits3; acb_poly_t S, A, B, C; bits1 = 2 + n_randint(state, 200); bits2 = 2 + n_randint(state, 200); bits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); acb_poly_init(S); acb_poly_init(A); acb_poly_init(B); acb_poly_init(C); acb_poly_randtest(S, state, m, bits1, 10); acb_poly_randtest(A, state, m, bits1, 10); acb_poly_randtest(B, state, m, bits1, 10); acb_poly_cot_pi_series(A, S, n1, bits2); acb_poly_sin_cos_pi_series(B, C, S, n1, bits3); acb_poly_div_series(B, C, B, n1, bits3); if (!acb_poly_overlaps(A, B)) { flint_printf("FAIL\n\n"); flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n"); flint_printf("A = "); acb_poly_printd(A, 15); flint_printf("\n\n"); flint_printf("B = "); acb_poly_printd(B, 15); flint_printf("\n\n"); abort(); } acb_poly_cot_pi_series(S, S, n1, bits2); if (!acb_poly_overlaps(A, S)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(S); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(C); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("div_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong m, n, p, qbits, rbits1, rbits2; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); p = 1 + n_randint(state, 20); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); do { fmpq_poly_randtest_not_zero(B, state, n, qbits); } while (B->coeffs[0] == 0); fmpq_poly_div_series(C, A, B, p); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits1); acb_poly_div_series(c, a, b, p, rbits2); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpq_poly_print(B); flint_printf("\n\n"); flint_printf("C = "); fmpq_poly_print(C); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_div_series(d, d, b, p, rbits2); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_div_series(d, a, d, p, rbits2); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_div_series(c, d, d, p, rbits2); acb_poly_div_series(d, d, d, p, rbits2); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 3)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("tan_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++) { slong m, n, rbits1, rbits2; acb_poly_t a, b, c, d, e; rbits1 = 2 + n_randint(state, 100); rbits2 = 2 + n_randint(state, 100); if (n_randint(state, 10) == 0) { m = 1 + n_randint(state, 50); n = 1 + n_randint(state, 50); } else { m = 1 + n_randint(state, 20); n = 1 + n_randint(state, 20); } acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_init(e); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_tan_series(b, a, n, rbits2); /* check tan(x) = 2*tan(x/2)/(1-tan(x/2)^2) */ acb_poly_scalar_mul_2exp_si(c, a, -1); acb_poly_tan_series(c, c, n, rbits2); acb_poly_mullow(d, c, c, n, rbits2); acb_poly_one(e); acb_poly_sub(e, e, d, rbits2); acb_poly_div_series(c, c, e, n, rbits2); acb_poly_scalar_mul_2exp_si(c, c, 1); if (!acb_poly_overlaps(b, c)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } acb_poly_tan_series(a, a, n, rbits2); if (!acb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(d); acb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
void acb_hypgeom_u_1f1_series(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t z, long len, long prec) { acb_poly_t s, u, A, B; acb_poly_struct aa[3]; arb_t c; long wlen; int singular; acb_poly_init(s); acb_poly_init(u); acb_poly_init(A); acb_poly_init(B); acb_poly_init(aa + 0); acb_poly_init(aa + 1); acb_poly_init(aa + 2); arb_init(c); singular = (b->length == 0) || acb_is_int(b->coeffs); wlen = len + (singular != 0); /* A = rgamma(a-b+1) * 1F~1(a,b,z) */ acb_poly_sub(u, a, b, prec); acb_poly_add_si(u, u, 1, prec); acb_poly_rgamma_series(A, u, wlen, prec); /* todo: handle a = 1 efficiently */ acb_poly_set(aa, a); acb_poly_set(aa + 1, b); acb_poly_one(aa + 2); acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec); acb_poly_mullow(A, A, s, wlen, prec); /* B = rgamma(a) * 1F~1(a-b+1,2-b,z) * z^(1-b) */ acb_poly_set(aa, u); acb_poly_add_si(aa + 1, b, -2, prec); acb_poly_neg(aa + 1, aa + 1); acb_hypgeom_pfq_series_direct(s, aa, 1, aa + 1, 2, z, 1, -1, wlen, prec); acb_poly_rgamma_series(B, a, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_add_si(u, b, -1, prec); acb_poly_neg(u, u); acb_poly_pow_series(s, z, u, wlen, prec); acb_poly_mullow(B, B, s, wlen, prec); acb_poly_sub(A, A, B, prec); /* multiply by pi csc(pi b) */ acb_poly_sin_pi_series(B, b, wlen, prec); if (singular) { acb_poly_shift_right(A, A, 1); acb_poly_shift_right(B, B, 1); } acb_poly_div_series(res, A, B, len, prec); arb_const_pi(c, prec); _acb_vec_scalar_mul_arb(res->coeffs, res->coeffs, res->length, c, prec); acb_poly_clear(s); acb_poly_clear(u); acb_poly_clear(A); acb_poly_clear(B); acb_poly_clear(aa + 0); acb_poly_clear(aa + 1); acb_poly_clear(aa + 2); arb_clear(c); }