int main() { slong iter; flint_rand_t state; flint_printf("exp_series_basecase...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong m, n, bits1, bits2, bits3; acb_poly_t a, b, c, d; bits1 = 2 + n_randint(state, 100); bits2 = 2 + n_randint(state, 100); bits3 = 2 + n_randint(state, 100); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, bits1, 5); acb_poly_randtest(b, state, m, bits1, 5); /* check exp(a+b) = exp(a) exp(b) */ acb_poly_exp_series_basecase(c, a, n, bits2); acb_poly_exp_series_basecase(d, b, n, bits2); acb_poly_mullow(c, c, d, n, bits2); acb_poly_add(d, a, b, bits3); acb_poly_exp_series_basecase(d, d, n, bits3); /* also aliasing test */ if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\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"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } 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; }
void acb_hypgeom_pfq_series_direct(acb_poly_t res, 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 s, t, err; arb_poly_t C, T; long i; int is_real; /* default algorithm to choose number of terms */ if (n < 0) { n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec); } acb_poly_init(s); acb_poly_init(t); acb_poly_init(err); arb_poly_init(C); arb_poly_init(T); acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec); if (acb_poly_length(t) != 0) { is_real = acb_poly_is_real(z); for (i = 0; i < p; i++) is_real = is_real && acb_poly_is_real(a + i); for (i = 0; i < q; i++) is_real = is_real && acb_poly_is_real(b + i); acb_poly_majorant(T, t, MAG_BITS); acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS); arb_poly_mullow(T, T, C, len, MAG_BITS); /* create polynomial of errors */ acb_poly_fit_length(err, len); for (i = 0; i < FLINT_MIN(len, T->length); i++) { arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i); if (!is_real) arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i); } _acb_poly_set_length(err, len); _acb_poly_normalise(err); acb_poly_add(s, s, err, prec); } acb_poly_set(res, s); acb_poly_clear(s); acb_poly_clear(t); acb_poly_clear(err); arb_poly_clear(C); arb_poly_clear(T); }
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); }
/* todo: do this using underscore methods */ static void bsplit(acb_poly_t A, acb_poly_t B, acb_poly_t C, acb_srcptr a, slong p, acb_srcptr b, slong q, const acb_t z, slong an, slong bn, slong prec) { if (bn - an == 1) { evaluate(A, a, p, z, an, prec); evaluate(B, b, q, NULL, an, prec); acb_poly_set(C, B); } else if (bn - an == 2) /* inlined */ { acb_poly_t A2, B2; acb_poly_init(A2); acb_poly_init(B2); evaluate(A, a, p, z, an, prec); evaluate(A2, a, p, z, an + 1, prec); evaluate(B, b, q, NULL, an, prec); evaluate(B2, b, q, NULL, an + 1, prec); acb_poly_mul(C, B, B2, prec); acb_poly_set(B, C); acb_poly_mul(C, A, B2, prec); acb_poly_add(C, C, B, prec); acb_poly_mul(A2, A, A2, prec); acb_poly_swap(A, A2); acb_poly_clear(A2); acb_poly_clear(B2); } else { slong m = an + (bn - an) / 2; acb_poly_t A2, B2, C2, T; acb_poly_init(A2); acb_poly_init(B2); acb_poly_init(C2); acb_poly_init(T); bsplit(A, B, C, a, p, b, q, z, an, m, prec); bsplit(A2, B2, C2, a, p, b, q, z, m, bn, prec); acb_poly_mul(T, B2, C, prec); acb_poly_mul(C, A, C2, prec); acb_poly_add(C, C, T, prec); acb_poly_mul(C2, B, B2, prec); acb_poly_swap(B, C2); acb_poly_mul(B2, A, A2, prec); acb_poly_swap(A, B2); acb_poly_clear(A2); acb_poly_clear(B2); acb_poly_clear(C2); acb_poly_clear(T); } }
int main() { slong iter; flint_rand_t state; flint_printf("digamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 300); rbits2 = 2 + n_randint(state, 300); rbits3 = 2 + n_randint(state, 300); m = n_randint(state, 25); n1 = n_randint(state, 25); n2 = n_randint(state, 25); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_digamma_series(b, a, n1, rbits2); acb_poly_digamma_series(c, a, n2, rbits3); acb_poly_set(d, b); acb_poly_truncate(d, FLINT_MIN(n1, n2)); acb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); flint_printf("a = "); acb_poly_printd(a, 50); flint_printf("\n\n"); flint_printf("b = "); acb_poly_printd(b, 50); flint_printf("\n\n"); flint_printf("c = "); acb_poly_printd(c, 50); flint_printf("\n\n"); flint_abort(); } /* check psi(a) + 1/a = psi(a+1) */ acb_poly_inv_series(c, a, n1, rbits2); acb_poly_add(c, b, c, rbits2); acb_poly_add_si(d, a, 1, rbits2); acb_poly_digamma_series(d, d, n1, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\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"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); flint_abort(); } acb_poly_digamma_series(a, a, n1, rbits2); if (!acb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); flint_abort(); } 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("add_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++) { acb_poly_t a, b, c, d; slong len, prec; acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, 1 + n_randint(state, 10), 100, 10); acb_poly_randtest(b, state, 1 + n_randint(state, 10), 100, 10); acb_poly_randtest(c, state, 1 + n_randint(state, 10), 100, 10); acb_poly_randtest(d, state, 1 + n_randint(state, 10), 100, 10); prec = 2 + n_randint(state, 100); len = n_randint(state, 10); acb_poly_add_series(c, a, b, len, prec); acb_poly_add(d, a, b, prec); acb_poly_truncate(d, len); if (!acb_poly_equal(c, d)) { flint_printf("FAIL\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"); flint_printf("c = "); acb_poly_printd(c, 15); flint_printf("\n\n"); flint_abort(); } acb_poly_set(d, a); acb_poly_add_series(d, d, b, len, prec); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); flint_abort(); } acb_poly_set(d, b); acb_poly_add_series(d, a, d, len, prec); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); flint_abort(); } 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("sin_cos_series_basecase...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++) { slong m, n, rbits1, rbits2; fmpq_poly_t B; acb_poly_t a, b, c, d, e; int times_pi; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); times_pi = n_randint(state, 2); fmpq_poly_init(B); 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_sin_cos_series_basecase(b, c, a, n, rbits2, times_pi); /* Check sin(x)^2 + cos(x)^2 = 1 */ acb_poly_mullow(d, b, b, n, rbits2); acb_poly_mullow(e, c, c, n, rbits2); acb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!acb_poly_contains_fmpq_poly(d, B)) { 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"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series_basecase(d, c, d, n, rbits2, times_pi); if (!acb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, a); acb_poly_sin_cos_series_basecase(b, d, d, n, rbits2, times_pi); if (!acb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(B); 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_2f1_transform_limit(acb_t res, const acb_poly_t a, const acb_poly_t b, const acb_poly_t c, const acb_poly_t z, int which, slong prec) { acb_poly_t ba, ca, cb, cab, ac1, bc1, ab1, ba1, w, t, u, v, s; acb_t tt; acb_poly_init(ba); acb_poly_init(ca); acb_poly_init(cb); acb_poly_init(cab); acb_poly_init(ac1); acb_poly_init(bc1); acb_poly_init(ab1); acb_poly_init(ba1); acb_poly_init(w); acb_poly_init(t); acb_poly_init(u); acb_poly_init(v); acb_poly_init(s); acb_init(tt); acb_poly_add_si(s, z, -1, prec); /* s = 1 - z */ acb_poly_neg(s, s); acb_poly_sub(ba, b, a, prec); /* ba = b - a */ acb_poly_sub(ca, c, a, prec); /* ca = c - a */ acb_poly_sub(cb, c, b, prec); /* cb = c - b */ acb_poly_sub(cab, ca, b, prec); /* cab = c - a - b */ acb_poly_add_si(ac1, ca, -1, prec); acb_poly_neg(ac1, ac1); /* ac1 = a - c + 1 */ acb_poly_add_si(bc1, cb, -1, prec); acb_poly_neg(bc1, bc1); /* bc1 = b - c + 1 */ acb_poly_add_si(ab1, ba, -1, prec); acb_poly_neg(ab1, ab1); /* ab1 = a - b + 1 */ acb_poly_add_si(ba1, ba, 1, prec); /* ba1 = b - a + 1 */ /* t = left term, u = right term (DLMF 15.8.1 - 15.8.5) */ if (which == 2) { acb_poly_inv_series(w, z, 2, prec); /* w = 1/z */ acb_hypgeom_2f1_series_direct(t, a, ac1, ab1, w, 1, 2, prec); acb_hypgeom_2f1_series_direct(u, b, bc1, ba1, w, 1, 2, prec); } else if (which == 3) { acb_poly_inv_series(w, s, 2, prec); /* w = 1/(1-z) */ acb_hypgeom_2f1_series_direct(t, a, cb, ab1, w, 1, 2, prec); acb_hypgeom_2f1_series_direct(u, b, ca, ba1, w, 1, 2, prec); } else if (which == 4) { acb_poly_set(w, s); /* w = 1-z */ acb_poly_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_series_direct(t, a, b, v, w, 1, 2, prec); acb_poly_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_hypgeom_2f1_series_direct(u, ca, cb, v, w, 1, 2, prec); } else if (which == 5) { acb_poly_inv_series(w, z, 2, prec); /* w = 1-1/z */ acb_poly_neg(w, w); acb_poly_add_si(w, w, 1, prec); acb_poly_add(v, ac1, b, prec); /* v = a+b-c+1 */ acb_hypgeom_2f1_series_direct(t, a, ac1, v, w, 1, 2, prec); acb_poly_add_si(v, cab, 1, prec); /* v = c-a-b+1 */ acb_poly_add_si(u, a, -1, prec); /* u = 1-a */ acb_poly_neg(u, u); acb_hypgeom_2f1_series_direct(u, ca, u, v, w, 1, 2, prec); } else { flint_printf("invalid transformation!\n"); flint_abort(); } /* gamma factors */ acb_poly_rgamma_series(v, a, 2, prec); acb_poly_mullow(u, u, v, 2, prec); acb_poly_rgamma_series(v, ca, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_rgamma_series(v, b, 2, prec); if (which == 2 || which == 3) acb_poly_mullow(t, t, v, 2, prec); else acb_poly_mullow(u, u, v, 2, prec); acb_poly_rgamma_series(v, cb, 2, prec); if (which == 2 || which == 3) acb_poly_mullow(u, u, v, 2, prec); else acb_poly_mullow(t, t, v, 2, prec); if (which == 2 || which == 3) { if (which == 2) acb_poly_neg(s, z); /* -z, otherwise 1-z since before */ acb_poly_neg(v, a); acb_poly_pow_series(v, s, v, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_neg(v, b); acb_poly_pow_series(v, s, v, 2, prec); acb_poly_mullow(u, u, v, 2, prec); } else { acb_poly_pow_series(v, s, cab, 2, prec); acb_poly_mullow(u, u, v, 2, prec); if (which == 5) { acb_poly_neg(v, a); acb_poly_pow_series(v, z, v, 2, prec); acb_poly_mullow(t, t, v, 2, prec); acb_poly_neg(v, ca); acb_poly_pow_series(v, z, v, 2, prec); acb_poly_mullow(u, u, v, 2, prec); } } acb_poly_sub(t, t, u, prec); if (which == 2 || which == 3) acb_poly_sin_pi_series(v, ba, 2, prec); else acb_poly_sin_pi_series(v, cab, 2, prec); acb_poly_get_coeff_acb(tt, t, 1); acb_poly_get_coeff_acb(res, v, 1); acb_div(res, tt, res, prec); acb_const_pi(tt, prec); acb_mul(res, res, tt, prec); acb_poly_clear(ba); acb_poly_clear(ca); acb_poly_clear(cb); acb_poly_clear(cab); acb_poly_clear(ac1); acb_poly_clear(bc1); acb_poly_clear(ab1); acb_poly_clear(ba1); acb_poly_clear(w); acb_poly_clear(t); acb_poly_clear(u); acb_poly_clear(v); acb_poly_clear(s); acb_clear(tt); }
int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); 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, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_add(C, A, B); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_add(c, a, b, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); 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_add(d, d, b, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_add(d, a, d, rbits3); if (!acb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\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; }
void acb_hypgeom_pfq_series_direct(acb_poly_t res, 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 s, t, err; arb_poly_t C, T; long i; int is_real; int terminating; /* default algorithm to choose number of terms */ if (n < 0) { n = acb_hypgeom_pfq_series_choose_n(a, p, b, q, z, len, prec); } terminating = 0; /* check if it terminates due to a root of the numerator */ for (i = 0; i < p; i++) { if (acb_poly_length(a + i) == 0 && n > 0) { terminating = 1; } else if (acb_poly_length(a + i) == 1) { acb_srcptr c = acb_poly_get_coeff_ptr(a + i, 0); if (acb_is_int(c) && arb_is_negative(acb_realref(c)) && arf_cmpabs_ui(arb_midref(acb_realref(c)), n) < 0) { terminating = 1; } } } /* check if it terminates (to order n) due to z */ /* the following tests could be made stronger... */ if (z->length == 0 && n >= 1) { terminating = 1; } else if (!terminating && z->length > 0 && acb_is_zero(z->coeffs) && n >= len) { if (regularized) { terminating = 1; } else { terminating = 1; for (i = 0; i < q; i++) { acb_srcptr c = acb_poly_get_coeff_ptr(b + i, 0); if (!arb_is_positive(acb_realref(c)) && acb_contains_int(c)) terminating = 0; } } } acb_poly_init(s); acb_poly_init(t); acb_poly_init(err); arb_poly_init(C); arb_poly_init(T); acb_hypgeom_pfq_series_sum_forward(s, t, a, p, b, q, z, regularized, n, len, prec); if (!terminating) { is_real = acb_poly_is_real(z); for (i = 0; i < p; i++) is_real = is_real && acb_poly_is_real(a + i); for (i = 0; i < q; i++) is_real = is_real && acb_poly_is_real(b + i); acb_poly_majorant(T, t, MAG_BITS); acb_hypgeom_pfq_series_bound_factor(C, a, p, b, q, z, n, len, MAG_BITS); if (!_arb_vec_is_finite(T->coeffs, T->length) || !_arb_vec_is_finite(C->coeffs, C->length)) { arb_poly_fit_length(T, len); _arb_vec_indeterminate(T->coeffs, len); _arb_poly_set_length(T, len); } else { arb_poly_mullow(T, T, C, len, MAG_BITS); } /* create polynomial of errors */ acb_poly_fit_length(err, len); for (i = 0; i < FLINT_MIN(len, T->length); i++) { arb_add_error(acb_realref(err->coeffs + i), T->coeffs + i); if (!is_real) arb_add_error(acb_imagref(err->coeffs + i), T->coeffs + i); } _acb_poly_set_length(err, len); _acb_poly_normalise(err); acb_poly_add(s, s, err, prec); } acb_poly_set(res, s); acb_poly_clear(s); acb_poly_clear(t); acb_poly_clear(err); arb_poly_clear(C); arb_poly_clear(T); }
int main() { slong iter; flint_rand_t state; flint_printf("lgamma_series...."); fflush(stdout); flint_randinit(state); /* special accuracy test case */ { acb_poly_t a; acb_t c; acb_init(c); acb_poly_init(a); arb_set_str(acb_realref(c), "-20.25", 53); arb_set_str(acb_imagref(c), "1e1000", 53); acb_poly_set_coeff_acb(a, 0, c); acb_poly_set_coeff_si(a, 1, 1); acb_poly_lgamma_series(a, a, 3, 53); if (acb_rel_accuracy_bits(a->coeffs) < 40 || acb_rel_accuracy_bits(a->coeffs + 1) < 40 || acb_rel_accuracy_bits(a->coeffs + 2) < 40) { flint_printf("FAIL: accuracy (reflection formula)\n\n"); acb_poly_printd(a, 15); flint_printf("\n\n"); abort(); } acb_poly_clear(a); acb_clear(c); } for (iter = 0; iter < 500 * arb_test_multiplier(); iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; acb_poly_t a, b, c, d; rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(d); acb_poly_randtest(a, state, m, rbits1, 10); acb_poly_randtest(b, state, m, rbits1, 10); acb_poly_randtest(c, state, m, rbits1, 10); acb_poly_lgamma_series(b, a, n1, rbits2); acb_poly_lgamma_series(c, a, n2, rbits3); acb_poly_set(d, b); acb_poly_truncate(d, FLINT_MIN(n1, n2)); acb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("n1 = %wd, n2 = %wd, bits2 = %wd, bits3 = %wd\n", n1, n2, rbits2, rbits3); 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(); } /* check loggamma(a) + log(a) = loggamma(a+1) */ acb_poly_log_series(c, a, n1, rbits2); acb_poly_add(c, b, c, rbits2); acb_poly_set(d, a); acb_add_ui(d->coeffs, d->coeffs, 1, rbits2); acb_poly_lgamma_series(d, d, n1, rbits2); if (!acb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\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"); flint_printf("d = "); acb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } acb_poly_lgamma_series(a, a, n1, rbits2); if (!acb_poly_overlaps(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); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("get_unique_fmpz_poly...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong prec, c; fmpz_poly_t A, B, C; acb_poly_t a, b; fmpz_poly_init(A); fmpz_poly_init(B); fmpz_poly_init(C); acb_poly_init(a); acb_poly_init(b); fmpz_poly_randtest(A, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); fmpz_poly_randtest(B, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); fmpz_poly_randtest(C, state, 1 + n_randint(state, 10), 1 + n_randint(state, 1000)); c = 1 + n_randint(state, 1000); prec = 2 + n_randint(state, 100); for ( ; ; ) { acb_poly_set_fmpz_poly(a, A, prec); acb_poly_set2_fmpz_poly(b, B, C, prec); acb_poly_scalar_mul_2exp_si(b, b, -c); acb_poly_add(a, a, b, prec); acb_poly_sub(a, a, b, prec); if (acb_poly_get_unique_fmpz_poly(B, a)) { if (!fmpz_poly_equal(A, B)) { flint_printf("FAIL\n\n"); flint_printf("A = "); fmpz_poly_print(A); flint_printf("\n\n"); flint_printf("B = "); fmpz_poly_print(B); flint_printf("\n\n"); flint_printf("a = "); acb_poly_printd(a, 15); flint_printf("\n\n"); abort(); } break; } else { prec *= 2; } } fmpz_poly_clear(A); fmpz_poly_clear(B); fmpz_poly_clear(C); acb_poly_clear(a); acb_poly_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { long iter; flint_rand_t state; printf("mullow_classical...."); fflush(stdout); flint_randinit(state); /* compare with fmpq_poly */ for (iter = 0; iter < 10000; iter++) { long qbits1, qbits2, rbits1, rbits2, rbits3, trunc; fmpq_poly_t A, B, C; acb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 200); qbits2 = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); rbits3 = 2 + n_randint(state, 200); trunc = n_randint(state, 10); 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, 1 + n_randint(state, 10), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 10), qbits2); fmpq_poly_mullow(C, A, B, trunc); acb_poly_set_fmpq_poly(a, A, rbits1); acb_poly_set_fmpq_poly(b, B, rbits2); acb_poly_mullow_classical(c, a, b, trunc, rbits3); if (!acb_poly_contains_fmpq_poly(c, C)) { printf("FAIL\n\n"); printf("bits3 = %ld\n", rbits3); printf("trunc = %ld\n", trunc); printf("A = "); fmpq_poly_print(A); printf("\n\n"); printf("B = "); fmpq_poly_print(B); printf("\n\n"); printf("C = "); fmpq_poly_print(C); printf("\n\n"); printf("a = "); acb_poly_printd(a, 15); printf("\n\n"); printf("b = "); acb_poly_printd(b, 15); printf("\n\n"); printf("c = "); acb_poly_printd(c, 15); printf("\n\n"); abort(); } acb_poly_set(d, a); acb_poly_mullow_classical(d, d, b, trunc, rbits3); if (!acb_poly_equal(d, c)) { printf("FAIL (aliasing 1)\n\n"); abort(); } acb_poly_set(d, b); acb_poly_mullow_classical(d, a, d, trunc, rbits3); if (!acb_poly_equal(d, c)) { printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ acb_poly_set(b, a); acb_poly_mullow_classical(c, a, b, trunc, rbits3); acb_poly_mullow_classical(d, a, a, trunc, rbits3); if (!acb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { printf("FAIL (squaring)\n\n"); printf("a = "); acb_poly_printd(a, 15); printf("\n\n"); printf("b = "); acb_poly_printd(b, 15); printf("\n\n"); printf("c = "); acb_poly_printd(c, 15); printf("\n\n"); abort(); } acb_poly_mullow_classical(a, a, a, trunc, rbits3); if (!acb_poly_equal(d, a)) { printf("FAIL (aliasing, squaring)\n\n"); printf("a = "); acb_poly_printd(a, 15); printf("\n\n"); printf("b = "); acb_poly_printd(b, 15); printf("\n\n"); printf("d = "); acb_poly_printd(d, 15); printf("\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); } /* check a*(b+c) = a*b+a*c */ for (iter = 0; iter < 10000; iter++) { long bits, trunc; acb_poly_t a, b, c, bc, abc, ab, ac, abac; bits = 2 + n_randint(state, 200); trunc = n_randint(state, 10); acb_poly_init(a); acb_poly_init(b); acb_poly_init(c); acb_poly_init(bc); acb_poly_init(abc); acb_poly_init(ab); acb_poly_init(ac); acb_poly_init(abac); acb_poly_randtest(a, state, 1 + n_randint(state, 10), bits, 5); acb_poly_randtest(b, state, 1 + n_randint(state, 10), bits, 5); acb_poly_randtest(c, state, 1 + n_randint(state, 10), bits, 5); acb_poly_add(bc, b, c, bits); acb_poly_mullow_classical(abc, a, bc, trunc, bits); acb_poly_mullow_classical(ab, a, b, trunc, bits); acb_poly_mullow_classical(ac, a, c, trunc, bits); acb_poly_add(abac, ab, ac, bits); if (!acb_poly_overlaps(abc, abac)) { printf("FAIL\n\n"); printf("bits = %ld\n", bits); printf("trunc = %ld\n", trunc); printf("a = "); acb_poly_printd(a, 15); printf("\n\n"); printf("b = "); acb_poly_printd(b, 15); printf("\n\n"); printf("c = "); acb_poly_printd(c, 15); printf("\n\n"); printf("abc = "); acb_poly_printd(abc, 15); printf("\n\n"); printf("abac = "); acb_poly_printd(abac, 15); printf("\n\n"); abort(); } acb_poly_clear(a); acb_poly_clear(b); acb_poly_clear(c); acb_poly_clear(bc); acb_poly_clear(abc); acb_poly_clear(ab); acb_poly_clear(ac); acb_poly_clear(abac); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return EXIT_SUCCESS; }