void acb_poly_sin_cos_series_tangent(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec, int times_pi) { slong hlen = h->length; if (n == 0) { acb_poly_zero(s); acb_poly_zero(c); return; } if (hlen == 0) { acb_poly_zero(s); acb_poly_one(c); return; } acb_poly_fit_length(s, n); acb_poly_fit_length(c, n); _acb_poly_sin_cos_series_tangent(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec, times_pi); _acb_poly_set_length(s, n); _acb_poly_normalise(s); _acb_poly_set_length(c, n); _acb_poly_normalise(c); }
void acb_poly_sin_cos_pi_series(acb_poly_t s, acb_poly_t c, const acb_poly_t h, slong n, slong prec) { slong hlen = h->length; if (n == 0) { acb_poly_zero(s); acb_poly_zero(c); return; } if (hlen == 0) { acb_poly_zero(s); acb_poly_one(c); return; } if (hlen == 1) n = 1; acb_poly_fit_length(s, n); acb_poly_fit_length(c, n); _acb_poly_sin_cos_pi_series(s->coeffs, c->coeffs, h->coeffs, hlen, n, prec); _acb_poly_set_length(s, n); _acb_poly_normalise(s); _acb_poly_set_length(c, n); _acb_poly_normalise(c); }
void acb_hypgeom_2f1_series_direct(acb_poly_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t c, const acb_poly_t z, int regularized, slong len, slong prec) { acb_poly_struct aa[4]; aa[0] = *a; aa[1] = *b; aa[2] = *c; acb_poly_init(&aa[3]); acb_poly_one(&aa[3]); acb_hypgeom_pfq_series_direct(res, aa, 2, aa + 2, 2, z, regularized, -1, len, prec); acb_poly_clear(&aa[3]); }
void acb_poly_pow_ui(acb_poly_t res, const acb_poly_t poly, ulong exp, slong prec) { slong flen, rlen; flen = poly->length; if (exp == 0) { acb_poly_one(res); } else if (flen == 0) { acb_poly_zero(res); } else { rlen = exp * (flen - 1) + 1; if (res != poly) { acb_poly_fit_length(res, rlen); _acb_poly_pow_ui(res->coeffs, poly->coeffs, flen, exp, prec); _acb_poly_set_length(res, rlen); _acb_poly_normalise(res); } else { acb_poly_t t; acb_poly_init2(t, rlen); _acb_poly_pow_ui(t->coeffs, poly->coeffs, flen, exp, prec); _acb_poly_set_length(t, rlen); _acb_poly_normalise(t); acb_poly_swap(res, t); acb_poly_clear(t); } } }
void acb_poly_pow_ui_trunc_binexp(acb_poly_t res, const acb_poly_t poly, ulong exp, long len, long prec) { long flen, rlen; flen = poly->length; if (exp == 0 && len != 0) { acb_poly_one(res); } else if (flen == 0 || len == 0) { acb_poly_zero(res); } else { rlen = poly_pow_length(flen, exp, len); if (res != poly) { acb_poly_fit_length(res, rlen); _acb_poly_pow_ui_trunc_binexp(res->coeffs, poly->coeffs, flen, exp, rlen, prec); _acb_poly_set_length(res, rlen); _acb_poly_normalise(res); } else { acb_poly_t t; acb_poly_init2(t, rlen); _acb_poly_pow_ui_trunc_binexp(t->coeffs, poly->coeffs, flen, exp, rlen, prec); _acb_poly_set_length(t, rlen); _acb_poly_normalise(t); acb_poly_swap(res, t); acb_poly_clear(t); } } }
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("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); }