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++) { arb_poly_t a, b, c, d; slong len, prec; arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_randtest(a, state, 1 + n_randint(state, 10), 100, 10); arb_poly_randtest(b, state, 1 + n_randint(state, 10), 100, 10); arb_poly_randtest(c, state, 1 + n_randint(state, 10), 100, 10); arb_poly_randtest(d, state, 1 + n_randint(state, 10), 100, 10); prec = 2 + n_randint(state, 100); len = n_randint(state, 10); arb_poly_add_series(c, a, b, len, prec); arb_poly_add(d, a, b, prec); arb_poly_truncate(d, len); if (!arb_poly_equal(c, d)) { flint_printf("FAIL\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_add_series(d, d, b, len, prec); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_add_series(d, a, d, len, prec); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { long iter; flint_rand_t state; printf("zeta_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 500; iter++) { long m, n1, n2, bits1, bits2, bits3; int deflate; arb_poly_t S, A, B, C, D, E, F; arb_t a, a1; bits1 = 2 + n_randint(state, 300); bits2 = 2 + n_randint(state, 300); bits3 = 2 + n_randint(state, 300); m = 1 + n_randint(state, 30); n1 = 1 + n_randint(state, 30); n2 = 1 + n_randint(state, 30); arb_poly_init(S); arb_poly_init(A); arb_poly_init(B); arb_poly_init(C); arb_poly_init(D); arb_poly_init(E); arb_poly_init(F); arb_init(a); arb_init(a1); deflate = n_randint(state, 2); arb_poly_randtest(S, state, m, bits1, 3); arb_randtest_precise(a, state, bits1, 3); arb_poly_set_coeff_arb(S, 0, a); if (n_randint(state, 2)) arb_randtest(a, state, bits1, 3); else arb_one(a); arb_poly_zeta_series(A, S, a, deflate, n1, bits2); arb_poly_zeta_series(B, S, a, deflate, n2, bits3); arb_poly_set(C, A); arb_poly_truncate(C, FLINT_MIN(n1, n2)); arb_poly_truncate(B, FLINT_MIN(n1, n2)); if (!arb_poly_overlaps(B, C)) { printf("FAIL\n\n"); printf("S = "); arb_poly_printd(S, 15); printf("\n\n"); printf("a = "); arb_printd(a, 15); printf("\n\n"); printf("A = "); arb_poly_printd(A, 15); printf("\n\n"); printf("B = "); arb_poly_printd(B, 15); printf("\n\n"); abort(); } /* check zeta(s,a) = zeta(s,a+1) + a^(-s) */ arb_poly_set_arb(D, a); arb_poly_log_series(D, D, n1, bits2); arb_poly_mullow(D, D, S, n1, bits2); arb_poly_neg(D, D); arb_poly_exp_series(D, D, n1, bits2); arb_add_ui(a1, a, 1, bits2); arb_poly_zeta_series(E, S, a1, deflate, n1, bits2); arb_poly_add(E, E, D, bits2); if (!arb_poly_overlaps(A, E)) { printf("FAIL (functional equation)\n\n"); printf("S = "); arb_poly_printd(S, 15); printf("\n\n"); printf("a = "); arb_printd(a, 15); printf("\n\n"); printf("A = "); arb_poly_printd(A, 15); printf("\n\n"); printf("E = "); arb_poly_printd(A, 15); printf("\n\n"); abort(); } arb_poly_zeta_series(S, S, a, deflate, n1, bits2); if (!arb_poly_overlaps(A, S)) { printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(S); arb_poly_clear(A); arb_poly_clear(B); arb_poly_clear(C); arb_poly_clear(D); arb_poly_clear(E); arb_poly_clear(F); arb_clear(a); arb_clear(a1); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("sin_cos_pi_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A, B; arb_poly_t a, b, c, d, e; qbits = 2 + n_randint(state, 200); rbits1 = 2 + n_randint(state, 200); rbits2 = 2 + n_randint(state, 200); m = 1 + n_randint(state, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); fmpq_poly_init(B); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_init(e); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_sin_cos_pi_series(b, c, a, n, rbits2); /* Check sin(x)^2 + cos(x)^2 = 1 */ arb_poly_mullow(d, b, b, n, rbits2); arb_poly_mullow(e, c, c, n, rbits2); arb_poly_add(d, d, e, rbits2); fmpq_poly_one(B); if (!arb_poly_contains_fmpq_poly(d, B)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_pi_series(d, c, d, n, rbits2); if (!arb_poly_equal(b, d)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, a); arb_poly_sin_cos_pi_series(b, d, d, n, rbits2); if (!arb_poly_equal(c, d)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); arb_poly_clear(e); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("digamma_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000; iter++) { slong m, n1, n2, rbits1, rbits2, rbits3; arb_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); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); arb_poly_randtest(a, state, m, rbits1, 10); arb_poly_digamma_series(b, a, n1, rbits2); arb_poly_digamma_series(c, a, n2, rbits3); arb_poly_set(d, b); arb_poly_truncate(d, FLINT_MIN(n1, n2)); arb_poly_truncate(c, FLINT_MIN(n1, n2)); if (!arb_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 = "); arb_poly_printd(a, 50); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 50); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 50); flint_printf("\n\n"); abort(); } /* check psi(a) + 1/a = psi(a+1) */ arb_poly_inv_series(c, a, n1, rbits2); arb_poly_add(c, b, c, rbits2); arb_poly_add_si(d, a, 1, rbits2); arb_poly_digamma_series(d, d, n1, rbits2); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL (functional equation)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } arb_poly_digamma_series(a, a, n1, rbits2); if (!arb_poly_overlaps(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_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("atan_series...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { slong m, n, qbits, rbits1, rbits2; fmpq_poly_t A; arb_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, 30); n = 1 + n_randint(state, 30); fmpq_poly_init(A); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, m, qbits); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_randtest(b, state, 1 + n_randint(state, 30), rbits1, 5); arb_poly_atan_series(b, a, n, rbits2); /* Check 2 atan(x) = atan(2x/(1-x^2)) + C */ arb_poly_mullow(c, a, a, n, rbits2); arb_poly_one(d); arb_poly_sub(c, d, c, rbits2); arb_poly_add(d, a, a, rbits2); if (arb_poly_length(c) != 0) { arb_poly_div_series(c, d, c, n, rbits2); arb_poly_atan_series(c, c, n, rbits2); arb_poly_add(d, b, b, rbits2); /* TODO: also check the first coefficient */ arb_poly_set_coeff_si(c, 0, 0); arb_poly_set_coeff_si(d, 0, 0); if (!arb_poly_overlaps(c, d)) { flint_printf("FAIL\n\n"); flint_printf("bits2 = %wd\n", rbits2); flint_printf("A = "); fmpq_poly_print(A); flint_printf("\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } } arb_poly_atan_series(a, a, n, rbits2); if (!arb_poly_equal(a, b)) { flint_printf("FAIL (aliasing)\n\n"); abort(); } fmpq_poly_clear(A); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_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("mullow_block...."); 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; arb_poly_t a, b, c, d; qbits1 = 2 + n_randint(state, 1000); qbits2 = 2 + n_randint(state, 1000); rbits1 = 2 + n_randint(state, 1000); rbits2 = 2 + n_randint(state, 1000); rbits3 = 2 + n_randint(state, 1000); trunc = n_randint(state, 100); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(d); fmpq_poly_randtest(A, state, 1 + n_randint(state, 100), qbits1); fmpq_poly_randtest(B, state, 1 + n_randint(state, 100), qbits2); fmpq_poly_mullow(C, A, B, trunc); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_mullow_block(c, a, b, trunc, rbits3); if (!arb_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 = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_set(d, a); arb_poly_mullow_block(d, d, b, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 1)\n\n"); abort(); } arb_poly_set(d, b); arb_poly_mullow_block(d, a, d, trunc, rbits3); if (!arb_poly_equal(d, c)) { flint_printf("FAIL (aliasing 2)\n\n"); abort(); } /* test squaring */ arb_poly_set(b, a); arb_poly_mullow_block(c, a, b, trunc, rbits3); arb_poly_mullow_block(d, a, a, trunc, rbits3); if (!arb_poly_overlaps(c, d)) /* not guaranteed to be identical */ { flint_printf("FAIL (squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } arb_poly_mullow_block(a, a, a, trunc, rbits3); if (!arb_poly_equal(d, a)) { flint_printf("FAIL (aliasing, squaring)\n\n"); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("d = "); arb_poly_printd(d, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(d); } for (iter = 0; iter < 3000 * arb_test_multiplier(); iter++) { slong rbits1, rbits2, rbits3, trunc; arb_poly_t a, b, c, ab, ac, bc, abc, abc2; rbits1 = 2 + n_randint(state, 300); rbits2 = 2 + n_randint(state, 300); rbits3 = 2 + n_randint(state, 300); trunc = n_randint(state, 100); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); arb_poly_init(ab); arb_poly_init(ac); arb_poly_init(bc); arb_poly_init(abc); arb_poly_init(abc2); arb_poly_randtest(a, state, 1 + n_randint(state, 100), rbits1, 1 + n_randint(state, 100)); arb_poly_randtest(b, state, 1 + n_randint(state, 100), rbits2, 1 + n_randint(state, 100)); arb_poly_randtest(c, state, 1 + n_randint(state, 100), rbits2, 1 + n_randint(state, 100)); /* check a*(b+c) = a*b + a*c */ arb_poly_mullow_block(ab, a, b, trunc, rbits3); arb_poly_mullow_block(ac, a, c, trunc, rbits3); arb_poly_add(abc, ab, ac, rbits3); arb_poly_add(bc, b, c, rbits3); arb_poly_mullow_block(abc2, a, bc, trunc, rbits3); if (!arb_poly_overlaps(abc, abc2)) { flint_printf("FAIL (a*(b+c) = a*b + a*c) \n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("a = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } /* check (b+c)^2 = b^2 + 2bc + c^2 */ arb_poly_mullow_block(a, b, c, trunc, rbits3); arb_poly_scalar_mul_2exp_si(a, a, 1); arb_poly_mullow_block(abc, b, b, trunc, rbits3); arb_poly_mullow_block(abc2, c, c, trunc, rbits3); arb_poly_add(abc, abc, a, rbits3); arb_poly_add(abc, abc, abc2, rbits3); arb_poly_mullow_block(abc2, bc, bc, trunc, rbits3); if (!arb_poly_overlaps(abc, abc2)) { flint_printf("FAIL ((b+c)^2 = b^2 + 2bc + c^2) \n\n"); flint_printf("bits3 = %wd\n", rbits3); flint_printf("trunc = %wd\n", trunc); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); flint_printf("abc = "); arb_poly_printd(abc, 15); flint_printf("\n\n"); flint_printf("abc2 = "); arb_poly_printd(abc2, 15); flint_printf("\n\n"); abort(); } arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); arb_poly_clear(ab); arb_poly_clear(ac); arb_poly_clear(bc); arb_poly_clear(abc); arb_poly_clear(abc2); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("add...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong qbits1, qbits2, rbits1, rbits2, rbits3; fmpq_poly_t A, B, C; arb_poly_t a, b, c; 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); fmpq_poly_init(A); fmpq_poly_init(B); fmpq_poly_init(C); arb_poly_init(a); arb_poly_init(b); arb_poly_init(c); 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); arb_poly_set_fmpq_poly(a, A, rbits1); arb_poly_set_fmpq_poly(b, B, rbits2); arb_poly_add(c, a, b, rbits3); if (!arb_poly_contains_fmpq_poly(c, C)) { flint_printf("FAIL\n\n"); flint_printf("bits3 = %wd\n", rbits3); 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 = "); arb_poly_printd(a, 15); flint_printf("\n\n"); flint_printf("b = "); arb_poly_printd(b, 15); flint_printf("\n\n"); flint_printf("c = "); arb_poly_printd(c, 15); flint_printf("\n\n"); abort(); } fmpq_poly_clear(A); fmpq_poly_clear(B); fmpq_poly_clear(C); arb_poly_clear(a); arb_poly_clear(b); arb_poly_clear(c); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }