int main() { slong iter; flint_rand_t state; flint_printf("backlund_s_bound...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 500 * arb_test_multiplier(); iter++) { arb_t a, b; mag_t u, v; slong aprec, bprec; slong abits, bbits; aprec = 2 + n_randint(state, 1000); bprec = 2 + n_randint(state, 1000); abits = 2 + n_randint(state, 100); bbits = 2 + n_randint(state, 100); arb_init(a); arb_init(b); mag_init(u); mag_init(v); arb_randtest(a, state, aprec, abits); arb_randtest(b, state, bprec, bbits); if (arb_is_nonnegative(a) && arb_is_nonnegative(b)) { acb_dirichlet_backlund_s_bound(u, a); acb_dirichlet_backlund_s_bound(v, b); if ((arb_lt(a, b) && mag_cmp(u, v) > 0) || (arb_gt(a, b) && mag_cmp(u, v) < 0)) { flint_printf("FAIL: increasing on t >= 0\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("u = "); mag_print(u); flint_printf("\n\n"); flint_printf("v = "); mag_print(v); flint_printf("\n\n"); flint_abort(); } } arb_clear(a); arb_clear(b); mag_clear(u); mag_clear(v); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("cmp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { fmpr_t x, y; mag_t xb, yb; int c1, c2; fmpr_init(x); fmpr_init(y); mag_init(xb); mag_init(yb); mag_randtest_special(xb, state, 100); mag_randtest_special(yb, state, 100); mag_get_fmpr(x, xb); mag_get_fmpr(y, yb); c1 = fmpr_cmp(x, y); c2 = mag_cmp(xb, yb); if (c1 != c2) { flint_printf("FAIL\n\n"); flint_printf("x = "); fmpr_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpr_print(y); flint_printf("\n\n"); flint_printf("xb = "); mag_print(xb); flint_printf("\n\n"); flint_printf("yb = "); mag_print(yb); flint_printf("\n\n"); abort(); } fmpr_clear(x); fmpr_clear(y); mag_clear(xb); mag_clear(yb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("get_mag...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { acb_t a; arf_t m2, x, y, s; mag_t m; acb_init(a); mag_init(m); arf_init(m2); arf_init(x); arf_init(y); arf_init(s); acb_randtest_special(a, state, 200, 10); acb_get_mag(m, a); MAG_CHECK_BITS(m) /* check m^2 >= x^2 + y^2 */ arf_set_mag(m2, m); arf_mul(m2, m2, m2, ARF_PREC_EXACT, ARF_RND_DOWN); arb_get_abs_ubound_arf(x, acb_realref(a), ARF_PREC_EXACT); arb_get_abs_ubound_arf(y, acb_imagref(a), ARF_PREC_EXACT); arf_sosq(s, x, y, ARF_PREC_EXACT, ARF_RND_DOWN); if (arf_cmp(m2, s) < 0) { flint_printf("FAIL:\n\n"); flint_printf("a = "); acb_print(a); flint_printf("\n\n"); flint_printf("m = "); mag_print(m); flint_printf("\n\n"); flint_abort(); } acb_clear(a); mag_clear(m); arf_clear(m2); arf_clear(x); arf_clear(y); arf_clear(s); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("frobenius_norm...."); fflush(stdout); flint_randinit(state); /* compare to the exact rational norm */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { fmpq_mat_t Q; fmpq_t q; arb_mat_t A; slong n, qbits, prec; n = n_randint(state, 8); qbits = 1 + n_randint(state, 100); prec = 2 + n_randint(state, 200); fmpq_mat_init(Q, n, n); fmpq_init(q); arb_mat_init(A, n, n); fmpq_mat_randtest(Q, state, qbits); _fmpq_mat_sum_of_squares(q, Q); arb_mat_set_fmpq_mat(A, Q, prec); /* check that the arb interval contains the exact value */ { arb_t a; arb_init(a); arb_mat_frobenius_norm(a, A, prec); arb_mul(a, a, a, prec); if (!arb_contains_fmpq(a, q)) { flint_printf("FAIL (containment, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("frobenius_norm(Q)^2 = \n"); fmpq_print(q); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("frobenius_norm(A)^2 = \n"); arb_printd(a, 15); flint_printf("\n\n"); flint_printf("frobenius_norm(A)^2 = \n"); arb_print(a); flint_printf("\n\n"); abort(); } arb_clear(a); } /* check that the upper bound is not less than the exact value */ { mag_t b; fmpq_t y; mag_init(b); fmpq_init(y); arb_mat_bound_frobenius_norm(b, A); mag_mul(b, b, b); mag_get_fmpq(y, b); if (fmpq_cmp(q, y) > 0) { flint_printf("FAIL (bound, iter = %wd)\n", iter); flint_printf("n = %wd, prec = %wd\n", n, prec); flint_printf("\n"); flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n"); flint_printf("frobenius_norm(Q)^2 = \n"); fmpq_print(q); flint_printf("\n\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("bound_frobenius_norm(A)^2 = \n"); mag_printd(b, 15); flint_printf("\n\n"); flint_printf("bound_frobenius_norm(A)^2 = \n"); mag_print(b); flint_printf("\n\n"); abort(); } mag_clear(b); fmpq_clear(y); } fmpq_mat_clear(Q); fmpq_clear(q); arb_mat_clear(A); } /* check trace(A^T A) = frobenius_norm(A)^2 */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { slong m, n, prec; arb_mat_t A, AT, ATA; arb_t t; prec = 2 + n_randint(state, 200); m = n_randint(state, 10); n = n_randint(state, 10); arb_mat_init(A, m, n); arb_mat_init(AT, n, m); arb_mat_init(ATA, n, n); arb_init(t); arb_mat_randtest(A, state, 2 + n_randint(state, 100), 10); arb_mat_transpose(AT, A); arb_mat_mul(ATA, AT, A, prec); arb_mat_trace(t, ATA, prec); arb_sqrt(t, t, prec); /* check the norm bound */ { mag_t low, frobenius; mag_init(low); arb_get_mag_lower(low, t); mag_init(frobenius); arb_mat_bound_frobenius_norm(frobenius, A); if (mag_cmp(low, frobenius) > 0) { flint_printf("FAIL (bound)\n", iter); flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec); flint_printf("\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("lower(sqrt(trace(A^T A))) = \n"); mag_printd(low, 15); flint_printf("\n\n"); flint_printf("bound_frobenius_norm(A) = \n"); mag_printd(frobenius, 15); flint_printf("\n\n"); abort(); } mag_clear(low); mag_clear(frobenius); } /* check the norm interval */ { arb_t frobenius; arb_init(frobenius); arb_mat_frobenius_norm(frobenius, A, prec); if (!arb_overlaps(t, frobenius)) { flint_printf("FAIL (overlap)\n", iter); flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec); flint_printf("\n"); flint_printf("A = \n"); arb_mat_printd(A, 15); flint_printf("\n\n"); flint_printf("sqrt(trace(A^T A)) = \n"); arb_printd(t, 15); flint_printf("\n\n"); flint_printf("frobenius_norm(A) = \n"); arb_printd(frobenius, 15); flint_printf("\n\n"); abort(); } arb_clear(frobenius); } arb_mat_clear(A); arb_mat_clear(AT); arb_mat_clear(ATA); arb_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("sum...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 1000000 * arb_test_multiplier(); iter++) { slong i, len, prec, bits, expbits; int res1, res2; arf_t s1, s2, s3, err; mag_t err_bound; arf_struct terms[20]; arf_rnd_t rnd; len = n_randint(state, 20); bits = 2 + n_randint(state, 1000); prec = 2 + n_randint(state, 1000); expbits = n_randint(state, 14); arf_init(s1); arf_init(s2); arf_init(s3); arf_init(err); mag_init(err_bound); for (i = 0; i < len; i++) { arf_init(terms + i); arf_randtest_special(terms + i, state, bits, expbits); } switch (n_randint(state, 4)) { case 0: rnd = ARF_RND_DOWN; break; case 1: rnd = ARF_RND_UP; break; case 2: rnd = ARF_RND_FLOOR; break; default: rnd = ARF_RND_CEIL; break; } res1 = arf_sum(s1, terms, len, prec, rnd); arf_zero(s2); for (i = 0; i < len; i++) arf_add(s2, s2, terms + i, ARF_PREC_EXACT, ARF_RND_DOWN); res2 = arf_set_round(s3, s2, prec, rnd); if (!arf_equal(s1, s3) || res1 != res2) { flint_printf("FAIL (%wd)\n\n", iter); flint_printf("prec = %wd\n\n", prec); for (i = 0; i < len; i++) { flint_printf("terms[%wd] = ", i); arf_print(terms + i); flint_printf("\n\n"); } flint_printf("s1 = "); arf_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); arf_print(s2); flint_printf("\n\n"); flint_printf("s3 = "); arf_print(s3); flint_printf("\n\n"); flint_printf("res1 = %d, res2 = %d\n\n", res1, res2); abort(); } arf_sub(err, s1, s2, ARF_PREC_EXACT, ARF_RND_DOWN); arf_abs(err, err); if (res1) arf_mag_set_ulp(err_bound, s1, prec); else mag_zero(err_bound); if (arf_cmpabs_mag(err, err_bound) > 0) { flint_printf("FAIL (error bound)!\n"); flint_printf("prec = %wd\n\n", prec); for (i = 0; i < len; i++) { flint_printf("terms[%wd] = ", i); arf_print(terms + i); flint_printf("\n\n"); } flint_printf("s1 = "); arf_print(s1); flint_printf("\n\n"); flint_printf("s2 = "); arf_print(s2); flint_printf("\n\n"); flint_printf("s3 = "); arf_print(s3); flint_printf("\n\n"); flint_printf("error: "); arf_print(err); flint_printf("\n\n"); flint_printf("error bound: "); mag_print(err_bound); flint_printf("\n\n"); flint_printf("res1 = %d, res2 = %d\n\n", res1, res2); abort(); } arf_clear(s1); arf_clear(s2); arf_clear(s3); arf_clear(err); mag_clear(err_bound); for (i = 0; i < len; i++) arf_clear(terms + i); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }