static void _fmpq_poly_oz_sqrt_approx_scale(fmpq_poly_t y, fmpq_poly_t z, const long n, const mpfr_prec_t prec) { /* We scale by about |det(y) · det(z)|^(-1/(2n)) to make it converge faster */ mpfr_t gamma; mpfr_init2(gamma, prec); mpfr_t tmp; mpfr_init2(tmp, prec); fmpq_t gamma_q; fmpq_init(gamma_q); /* det(y) */ fmpq_poly_oz_ideal_norm(gamma_q, y, n, 1); fmpq_get_mpfr(gamma, gamma_q, MPFR_RNDN); /* det(y) · det(z) */ fmpq_poly_oz_ideal_norm(gamma_q, z, n, 1); fmpq_get_mpfr(tmp, gamma_q, MPFR_RNDN); mpfr_mul(gamma, gamma, tmp, MPFR_RNDN); /* (det(y) · det(z))^(-1/(2n)) */ mpfr_root(gamma, gamma, 2*n, MPFR_RNDN); mpfr_ui_div(gamma, 1, gamma, MPFR_RNDN); mpfr_abs(gamma, gamma, MPFR_RNDN); fmpq_set_mpfr(gamma_q, gamma, MPFR_RNDN); fmpq_poly_scalar_mul_fmpq(y, y, gamma_q); fmpq_poly_scalar_mul_fmpq(z, z, gamma_q); fmpq_clear(gamma_q); mpfr_clear(gamma); mpfr_clear(tmp); }
int main() { slong iter; flint_rand_t state; flint_printf("sinh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_sinh(t, t, MPFR_RNDN); arb_sinh(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_abort(); } arb_sinh(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("log...."); fflush(stdout); flint_randinit(state); /* compare with mpfr */ for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); do { arb_randtest(a, state, 1 + n_randint(state, 200), 10); } while (arb_contains_nonpositive(a)); arb_randtest(b, state, 1 + n_randint(state, 200), 10); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); /* todo: estimate cancellation precisely */ if (mpfr_cmp_d(t, 1 - 1e-10) > 0 && mpfr_cmp_d(t, 1 + 1e-10) < 0) { mpfr_set_prec(t, prec + 1000); fmpq_get_mpfr(t, q, MPFR_RNDN); } mpfr_log(t, t, MPFR_RNDN); arb_log(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_log(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* compare with mpfr (higher precision) */ for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 6000); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); do { arb_randtest(a, state, 1 + n_randint(state, 6000), 10); } while (arb_contains_nonpositive(a)); arb_randtest(b, state, 1 + n_randint(state, 6000), 10); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); /* todo: estimate cancellation precisely */ if (mpfr_cmp_d(t, 1 - 1e-10) > 0 && mpfr_cmp_d(t, 1 + 1e-10) < 0) { mpfr_set_prec(t, prec + 10000); fmpq_get_mpfr(t, q, MPFR_RNDN); } mpfr_log(t, t, MPFR_RNDN); arb_log(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_log(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* test large numbers */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { arb_t a, b, ab, lab, la, lb, lalb; slong prec = 2 + n_randint(state, 6000); arb_init(a); arb_init(b); arb_init(ab); arb_init(lab); arb_init(la); arb_init(lb); arb_init(lalb); arb_randtest(a, state, 1 + n_randint(state, 400), 400); arb_randtest(b, state, 1 + n_randint(state, 400), 400); arb_log(la, a, prec); arb_log(lb, b, prec); arb_mul(ab, a, b, prec); arb_log(lab, ab, prec); arb_add(lalb, la, lb, prec); if (!arb_overlaps(lab, lalb)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("la = "); arb_print(la); flint_printf("\n\n"); flint_printf("lb = "); arb_print(lb); flint_printf("\n\n"); flint_printf("ab = "); arb_print(ab); flint_printf("\n\n"); flint_printf("lab = "); arb_print(lab); flint_printf("\n\n"); flint_printf("lalb = "); arb_print(lalb); flint_printf("\n\n"); abort(); } arb_log(a, a, prec); if (!arb_overlaps(a, la)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(ab); arb_clear(lab); arb_clear(la); arb_clear(lb); arb_clear(lalb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { long iter; flint_rand_t state; printf("asin...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000; iter++) { arb_t a, b; fmpq_t q; mpfr_t t; long prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_asin(t, t, MPFR_RNDN); arb_asin(b, a, prec); if (!arb_contains_mpfr(b, t)) { printf("FAIL: containment\n\n"); printf("a = "); arb_print(a); printf("\n\n"); printf("b = "); arb_print(b); printf("\n\n"); abort(); } arb_asin(a, a, prec); if (!arb_equal(a, b)) { printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 10000; iter++) { arb_t a, b, c; long prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100); arb_asin(b, a, prec1); arb_asin(c, a, prec2); if (!arb_overlaps(b, c)) { printf("FAIL: overlap\n\n"); printf("a = "); arb_print(a); printf("\n\n"); printf("b = "); arb_print(b); printf("\n\n"); printf("c = "); arb_print(c); printf("\n\n"); abort(); } /* check sin(asin(x)) = x */ arb_sin(c, b, prec1); if (!arb_contains(c, a)) { printf("FAIL: functional equation\n\n"); printf("a = "); arb_print(a); printf("\n\n"); printf("b = "); arb_print(b); printf("\n\n"); printf("c = "); arb_print(c); printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return EXIT_SUCCESS; }
int main() { long iter; flint_rand_t state; printf("atan2...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t q, r; mpfr_t t, u; long prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); fmpq_init(q); fmpq_init(r); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_randtest(c, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(r, state, b, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); fmpq_get_mpfr(u, r, MPFR_RNDN); mpfr_atan2(t, u, t, MPFR_RNDN); arb_atan2(c, b, a, prec); if (!arb_contains_mpfr(c, t)) { printf("FAIL: containment\n\n"); printf("a = "); arb_print(a); printf("\n\n"); printf("b = "); arb_print(b); printf("\n\n"); printf("c = "); arb_print(c); printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(q); fmpq_clear(r); mpfr_clear(t); mpfr_clear(u); } flint_randclear(state); flint_cleanup(); printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("sin...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec0, prec; prec0 = 400; if (iter % 100 == 0) prec0 = 8000; prec = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec0 + 100); arb_randtest(a, state, 1 + n_randint(state, prec0), 6); arb_randtest(b, state, 1 + n_randint(state, prec0), 6); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_sin(t, t, MPFR_RNDN); arb_sin(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } arb_sin(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* check large arguments */ for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), prec0); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(c, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(d, state, 1 + n_randint(state, prec0), 100); arb_sin(b, a, prec1); arb_sin(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } /* check sin(2a) = 2sin(a)cos(a) */ arb_mul_2exp_si(c, a, 1); arb_sin(c, c, prec1); arb_cos(d, a, prec1); arb_mul(b, b, d, prec1); arb_mul_2exp_si(b, b, 1); if (!arb_overlaps(b, c)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("sinh_cosh...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t a, b, c; fmpq_t q; mpfr_t t, u; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); fmpq_init(q); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_randtest(c, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_sinh_cosh(t, u, t, MPFR_RNDN); arb_sinh_cosh(b, c, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment (sin)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); abort(); } if (!arb_contains_mpfr(c, u)) { flint_printf("FAIL: containment (cos)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(q); mpfr_clear(t); mpfr_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("agm...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t a, b, c; fmpq_t q, r; mpfr_t t, u; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); arb_init(c); fmpq_init(q); fmpq_init(r); mpfr_init2(t, prec + 100); mpfr_init2(u, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_randtest(c, state, 1 + n_randint(state, 200), 3); arb_agm(c, a, b, prec); if (arb_equal(a, b)) { if (!arb_contains(c, a)) { flint_printf("FAIL: containment (identity)\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } } else { arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); arb_get_rand_fmpq(r, state, b, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); fmpq_get_mpfr(u, r, MPFR_RNDN); mpfr_agm(t, t, u, MPFR_RNDN); if (!arb_contains_mpfr(c, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); abort(); } } arb_clear(a); arb_clear(b); arb_clear(c); fmpq_clear(q); fmpq_clear(r); mpfr_clear(t); mpfr_clear(u); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("atan...."); fflush(stdout); flint_randinit(state); /* Compare with MPFR */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 200); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 200), 3); arb_randtest(b, state, 1 + n_randint(state, 200), 3); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_atan(t, t, MPFR_RNDN); arb_atan(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_abort(); } arb_atan(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* Check large arguments. */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { arb_t a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 1000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100); arb_atan(b, a, prec1); arb_atan(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_abort(); } /* check tan(atan(x)) = x */ arb_sin_cos(c, d, b, prec1); arb_div(c, c, d, prec1); if (!arb_contains(c, a)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* Compare with MPFR, higher precision. */ for (iter = 0; iter < 200 * arb_test_multiplier(); iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec = 2 + n_randint(state, 5000); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, 5000), 8); arb_randtest(b, state, 1 + n_randint(state, 5000), 8); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_atan(t, t, MPFR_RNDN); arb_atan(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("a = "); arb_printd(a, 50); flint_printf("\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 50); flint_printf("\n\n"); flint_abort(); } arb_atan(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } /* Higher precision + large arguments. */ for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++) { arb_t a, b, c, d; slong prec1, prec2; prec1 = 2 + n_randint(state, 5000); prec2 = prec1 + 30; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_precise(a, state, 1 + n_randint(state, 5000), 100); arb_atan(b, a, prec1); arb_atan(c, a, prec2); if (!arb_overlaps(b, c)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_abort(); } /* check tan(atan(x)) = x */ arb_sin_cos(c, d, b, prec1); arb_div(c, c, d, prec1); if (!arb_contains(c, a)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* Check wide arguments. */ for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t a, b, c, d; arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100); arb_randtest_precise(b, state, 1 + n_randint(state, 1000), 100); if (n_randint(state, 2)) arb_add(a, a, b, 2 + n_randint(state, 1000)); arb_union(d, a, b, 2 + n_randint(state, 1000)); arb_atan(a, a, 2 + n_randint(state, 2000)); arb_atan(b, b, 2 + n_randint(state, 2000)); arb_atan(c, d, 2 + n_randint(state, 2000)); if (!arb_overlaps(c, a) || !arb_overlaps(c, b)) { flint_printf("FAIL: overlap\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("exp...."); fflush(stdout); flint_randinit(state); /* check large arguments + compare with exp_simple */ for (iter = 0; iter < 100000 *arb_test_multiplier(); iter++) { arb_t a, b, c, d; slong prec0, prec1, prec2, acc1, acc2; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_randtest_special(a, state, 1 + n_randint(state, prec0), 100); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); arb_exp(b, a, prec1); arb_exp(c, a, prec2); arb_exp_simple(d, a, prec1); if (!arb_overlaps(b, c) || !arb_overlaps(b, d) || !arb_overlaps(c, d)) { flint_printf("FAIL: overlap\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_abort(); } /* compare accuracy with exp_simple */ acc1 = arb_rel_accuracy_bits(b); acc2 = arb_rel_accuracy_bits(d); if (acc2 > 0 && acc1 < acc2 - 1) { flint_printf("FAIL: accuracy\n\n"); flint_printf("prec1 = %wd, acc1 = %wd, acc2 = %wd\n\n", prec1, acc1, acc2); flint_printf("a = "); arb_printd(a, 50); flint_printf("\n\n"); flint_printf("b = "); arb_printd(b, 50); flint_printf("\n\n"); flint_printf("d = "); arb_printd(d, 50); flint_printf("\n\n"); flint_abort(); } arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100); /* check exp(a)*exp(b) = exp(a+b) */ arb_exp(c, a, prec1); arb_exp(d, b, prec1); arb_mul(c, c, d, prec1); arb_add(d, a, b, prec1); arb_exp(d, d, prec1); if (!arb_overlaps(c, d)) { flint_printf("FAIL: functional equation\n\n"); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_printf("c = "); arb_print(c); flint_printf("\n\n"); flint_printf("d = "); arb_print(d); flint_printf("\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); } /* test union */ for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { arb_t a, b, c, d, e; slong prec0, prec1, prec2, prec3, prec4; if (iter % 10 == 0) prec0 = 10000; else prec0 = 1000; prec1 = 2 + n_randint(state, prec0); prec2 = 2 + n_randint(state, prec0); prec3 = 2 + n_randint(state, prec0); prec4 = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); arb_init(c); arb_init(d); arb_init(e); arb_randtest_special(a, state, 1 + n_randint(state, prec0), 200); arb_randtest_special(b, state, 1 + n_randint(state, prec0), 200); arb_randtest_special(c, state, 1 + n_randint(state, prec0), 200); arb_randtest_special(d, state, 1 + n_randint(state, prec0), 200); arb_randtest_special(e, state, 1 + n_randint(state, prec0), 200); arb_exp(c, a, prec1); arb_exp(d, b, prec2); arb_union(e, a, b, prec3); arb_exp(e, e, prec4); if (!arb_overlaps(e, c) || !arb_overlaps(e, d)) { flint_printf("FAIL: union\n\n"); flint_printf("a = "); arb_printn(a, 1000, 0); flint_printf("\n\n"); flint_printf("b = "); arb_printn(b, 1000, 0); flint_printf("\n\n"); flint_printf("c = "); arb_printn(c, 1000, 0); flint_printf("\n\n"); flint_printf("d = "); arb_printn(d, 1000, 0); flint_printf("\n\n"); flint_printf("e = "); arb_printn(e, 1000, 0); flint_printf("\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); arb_clear(c); arb_clear(d); arb_clear(e); } /* comparison with mpfr */ for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t a, b; fmpq_t q; mpfr_t t; slong prec0, prec; prec0 = 400; if (iter % 100 == 0) prec0 = 10000; prec = 2 + n_randint(state, prec0); arb_init(a); arb_init(b); fmpq_init(q); mpfr_init2(t, prec + 100); arb_randtest(a, state, 1 + n_randint(state, prec0), 4); arb_randtest(b, state, 1 + n_randint(state, prec0), 4); arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0)); fmpq_get_mpfr(t, q, MPFR_RNDN); mpfr_exp(t, t, MPFR_RNDN); arb_exp(b, a, prec); if (!arb_contains_mpfr(b, t)) { flint_printf("FAIL: containment\n\n"); flint_printf("iter = %wd, prec = %wd\n\n", iter, prec); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_abort(); } arb_exp(a, a, prec); if (!arb_equal(a, b)) { flint_printf("FAIL: aliasing\n\n"); flint_printf("iter = %wd, prec = %wd\n\n", iter, prec); flint_printf("a = "); arb_print(a); flint_printf("\n\n"); flint_printf("b = "); arb_print(b); flint_printf("\n\n"); flint_abort(); } arb_clear(a); arb_clear(b); fmpq_clear(q); mpfr_clear(t); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main(void) { int i; flint_rand_t state; flint_randinit(state); printf("bsplit_sum_abpq...."); fflush(stdout); for (i = 0; i < 10000; i++) { fmpq *ab, *pq; fmpq_t s1, s2, t, pqp; fmpq_bsplit_t sum; long k, n; n = n_randint(state, 40); ab = _fmpq_vec_init(n); pq = _fmpq_vec_init(n); fmpq_init(s1); fmpq_init(s2); fmpq_init(pqp); fmpq_init(t); for (k = 0; k < n; k++) fmpq_randtest(ab + k, state, 10); for (k = 0; k < n; k++) fmpq_randtest(pq + k, state, 10); fmpq_bsplit_init(sum); fmpq_bsplit_sum_abpq(sum, ab, pq, 0, n); fmpq_bsplit_get_fmpq(s1, sum); fmpq_zero(s2); fmpq_one(pqp); for (k = 0; k < n; k++) { fmpq_mul(pqp, pqp, pq + k); fmpq_mul(t, pqp, ab + k); fmpq_add(s2, s2, t); } if (!fmpq_is_canonical(s1) || !fmpq_equal(s1, s2)) { printf("FAIL\n"); printf("(a/b) = "); for (k = 0; k < n; k++) fmpq_print(ab+k), printf(" "); printf("\n"); printf("(p/q) = "); for (k = 0; k < n; k++) fmpq_print(pq+k), printf(" "); printf("\n"); printf("s1: "); fmpq_print(s1); printf("\n"); printf("s2: "); fmpq_print(s2); printf("\n"); abort(); } /* Check numerical evaluation */ { mpfr_t f1, f2; mpfr_prec_t prec; prec = 5 + n_randint(state, 1000); mpfr_init2(f1, prec); mpfr_init2(f2, prec); fmpq_bsplit_get_mpfr(f1, sum); fmpq_get_mpfr(f2, s1, MPFR_RNDN); mpfr_sub(f1, f1, f2, MPFR_RNDN); if (!mpfr_zero_p(f1) && !(mpfr_get_exp(f1) <= mpfr_get_exp(f2) - prec + 3)) { printf("FAIL: numerical evaluation\n"); printf("%ld, %ld, %ld\n", prec, mpfr_get_exp(f1), mpfr_get_exp(f2) - prec + 3); abort(); } mpfr_clear(f1); mpfr_clear(f2); } fmpq_bsplit_clear(sum); fmpq_clear(s1); fmpq_clear(s2); fmpq_clear(pqp); fmpq_clear(t); _fmpq_vec_clear(ab, n); _fmpq_vec_clear(pq, n); } flint_randclear(state); _fmpz_cleanup(); printf("PASS\n"); return 0; }