/* sample (x, y) so that x /in y */ void _sample_arf_in_arb(arf_t x, arb_t y, flint_rand_t state) { slong bits, prec, expbits; arf_t a, b; slong i, n; arf_init(a); arf_init(b); bits = 2 + n_randint(state, 1000); prec = 2 + n_randint(state, 1000); expbits = n_randint(state, 14); n = n_randint(state, 3); arf_randtest(x, state, bits, expbits); arf_set(a, x); arf_set(b, x); for (i = 0; i < n; i++) { arf_randtest(x, state, bits, expbits); arf_min(a, a, x); arf_max(b, b, x); } arb_set_interval_arf(y, a, b, prec); arf_clear(a); arf_clear(b); }
void arb_max(arb_t z, const arb_t x, const arb_t y, slong prec) { arf_t left, right, t, xr, yr; if (arf_is_nan(arb_midref(x)) || arf_is_nan(arb_midref(y))) { arb_indeterminate(z); return; } arf_init(left); arf_init(right); arf_init(t); arf_init_set_mag_shallow(xr, arb_radref(x)); arf_init_set_mag_shallow(yr, arb_radref(y)); arf_sub(left, arb_midref(x), xr, prec, ARF_RND_FLOOR); arf_sub(t, arb_midref(y), yr, prec, ARF_RND_FLOOR); arf_max(left, left, t); arf_add(right, arb_midref(x), xr, prec, ARF_RND_CEIL); arf_add(t, arb_midref(y), yr, prec, ARF_RND_CEIL); arf_max(right, right, t); arb_set_interval_arf(z, left, right, prec); arf_clear(left); arf_clear(right); arf_clear(t); }
int mag_close(const mag_t am, const mag_t bm) { arf_t t, a, b; int res1, res2; arf_init(t); arf_init(a); arf_init(b); arf_set_mag(a, am); arf_set_mag(b, bm); arf_mul_ui(t, b, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res1 = arf_cmp(a, t) <= 0; arf_mul_ui(t, a, 257, MAG_BITS, ARF_RND_UP); arf_mul_2exp_si(t, t, -8); res2 = arf_cmp(b, t) <= 0; arf_clear(t); arf_clear(a); arf_clear(b); return res1 && res2; }
int main() { #define ni 5 slong n, i, f; double b[ni][2] = { { 0, 1}, {-1, 1}, {0, 10}, {-20, 3}, {0, 3.14} }; const slong prec = 40; #define nf 5 arb_func_t func[nf] = { (arb_func_t)&f_1x2, (arb_func_t)&f_pol, (arb_func_t)&f_thsh, (arb_func_t)&f_thsh_shift, (arb_func_t)&f_aj }; #if VERBOSE char * fn[nf] = { "1/(1+x^2)", "1/p(x)", "th(sh(x))", "th(sh(x+.7I))" , "1/y" }; #endif params_t p[nf]; arf_t tmin, tmax; mag_t max; flint_printf("max_func..."); fflush(stdout); p[1].len = 3; p[1].z = _acb_vec_init(3); acb_set_d_d(p[1].z + 0, 2, 1); acb_set_d_d(p[1].z + 1, 2, .1); acb_set_d_d(p[1].z + 2, 1, .1); p[4] = p[1]; arf_init(tmin); arf_init(tmax); mag_init(max); for (i = 0; i < ni; i++) { arf_set_d(tmin, b[i][0]); arf_set_d(tmax, b[i][1]); for (f = 0; f < nf; f++) { for (n = 5; n < 100; n *= 2) { slong count; count = mag_func_arf(max, func[f], (void *)&p[f], tmin, tmax, n, prec); #if VERBOSE flint_printf("\nmax %s on [%lf, %lf] <= ",fn[f],b[i][0],b[i][1]); mag_printd(max,8); flint_printf(" [asked %ld, did %ld]", n, count); #endif } } } mag_clear(max); arf_clear(tmin); arf_clear(tmax); printf("PASS\n"); return 0; }
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 arb_richcmp_fallback(const arb_t x, const arb_t y, int op) { arf_t xa, xb, ya, yb; int res; arf_init(xa); arf_init(xb); arf_init(ya); arf_init(yb); arb_infimum(xa, x); arb_supremum(xb, x); arb_infimum(ya, y); arb_supremum(yb, y); if (arf_is_nan(xa) || arf_is_nan(ya)) { res = 0; } else { if (op == 0) /* eq */ { res = arf_equal(xa, xb) && arf_equal(ya, yb) && arf_equal(xa, ya); } else if (op == 1) /* ne */ { res = (arf_cmp(yb, xa) < 0) || (arf_cmp(xb, ya) < 0); } else if (op == 2) /* le */ { res = (arf_cmp(xb, ya) <= 0); } else if (op == 3) /* lt */ { res = (arf_cmp(xb, ya) < 0); } else if (op == 4) /* ge */ { res = (arf_cmp(xa, yb) >= 0); } else /* gt */ { res = (arf_cmp(xa, yb) > 0); } } arf_clear(xa); arf_clear(xb); arf_clear(ya); arf_clear(yb); return res; }
int main() { slong iter; flint_rand_t state; flint_printf("abs_bound_le_2exp_fmpz...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++) { arf_t x, y; fmpz_t b; int cmp1, cmp2; arf_init(x); arf_init(y); fmpz_init(b); arf_randtest_not_zero(x, state, 2 + n_randint(state, 1000), 100); arf_abs_bound_le_2exp_fmpz(b, x); arf_one(y); arf_mul_2exp_fmpz(y, y, b); cmp1 = (arf_cmpabs(x, y) <= 0); arf_mul_2exp_si(y, y, -1); cmp2 = (arf_cmpabs(y, x) < 0); arf_mul_2exp_si(y, y, 1); if (!cmp1 || !cmp2) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf("\n\n"); flint_printf("cmp1 = %d, cmp2 = %d\n\n", cmp1, cmp2); abort(); } arf_clear(x); arf_clear(y); fmpz_clear(b); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("set_interval_mpfr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x; arf_t a, b; mpfr_t aa, bb; arb_init(x); arf_init(a); arf_init(b); mpfr_init2(aa, 200); mpfr_init2(bb, 200); arf_randtest_special(a, state, 200, 10); arf_randtest_special(b, state, 200, 10); if (arf_cmp(a, b) > 0) arf_swap(a, b); arf_get_mpfr(aa, a, MPFR_RNDD); arf_get_mpfr(bb, b, MPFR_RNDU); arb_set_interval_mpfr(x, aa, bb, 2 + n_randint(state, 200)); if (!arb_contains_arf(x, a) || !arb_contains_arf(x, b)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); abort(); } arb_clear(x); arf_clear(a); arf_clear(b); mpfr_clear(aa); mpfr_clear(bb); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("set_fmpq...."); fflush(stdout); flint_randinit(state); /* test exact roundtrip R -> Q -> R */ for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { slong bits, res; arf_t x, z; fmpq_t y; bits = 2 + n_randint(state, 200); arf_init(x); arf_init(z); fmpq_init(y); arf_randtest(x, state, bits, 10); arf_randtest(z, state, bits, 10); arf_get_fmpq(y, x); res = arf_set_fmpq(z, y, bits, ARF_RND_DOWN); if (!arf_equal(x, z) || res != 0) { flint_printf("FAIL\n\n"); flint_printf("bits: %wd\n", bits); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("y = "); fmpq_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); fmpq_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
void partitions_fmpz_fmpz_hrr(fmpz_t p, const fmpz_t n, int use_doubles) { arb_t x; arf_t bound; slong N; arb_init(x); arf_init(bound); N = partitions_hrr_needed_terms(fmpz_get_d(n)); if (fmpz_cmp_ui(n, 4e8) >= 0 && flint_get_num_threads() > 1) { hrr_sum_threaded(x, n, N, use_doubles); } else { partitions_hrr_sum_arb(x, n, 1, N, use_doubles); } partitions_rademacher_bound(bound, n, N); arb_add_error_arf(x, bound); if (!arb_get_unique_fmpz(p, x)) { flint_printf("not unique!\n"); arb_printd(x, 50); flint_printf("\n"); abort(); } arb_clear(x); arf_clear(bound); }
int _arf_add_eps(arf_t s, const arf_t x, int sgn, long prec, arf_rnd_t rnd) { arf_t t; long bits; bits = arf_bits(x); if (bits == 0) { printf("_arf_add_eps\n"); abort(); } bits = FLINT_MAX(bits, prec) + 10; arf_init(t); arf_set_si(t, sgn); arf_mul_2exp_fmpz(t, t, ARF_EXPREF(x)); arf_mul_2exp_si(t, t, -bits); arf_add(s, x, t, prec, rnd); arf_clear(t); return 1; }
void arb_log_arf_huge(arb_t z, const arf_t x, slong prec) { arf_t t; arb_t c; fmpz_t exp; slong wp; arf_init(t); arb_init(c); fmpz_init(exp); fmpz_neg(exp, ARF_EXPREF(x)); arf_mul_2exp_fmpz(t, x, exp); wp = prec + 4 - fmpz_bits(exp); wp = FLINT_MAX(wp, 4); arb_log_arf(z, t, wp); arb_const_log2(c, prec + 4); arb_submul_fmpz(z, c, exp, prec); arf_clear(t); arb_clear(c); fmpz_clear(exp); }
int arb_calc_partition(arf_interval_t L, arf_interval_t R, arb_calc_func_t func, void * param, const arf_interval_t block, slong prec) { arb_t t, m; arf_t u; int msign; arb_init(t); arb_init(m); arf_init(u); /* Compute the midpoint (TODO: try other points) */ arf_add(u, &block->a, &block->b, ARF_PREC_EXACT, ARF_RND_DOWN); arf_mul_2exp_si(u, u, -1); /* Evaluate and get sign at midpoint */ arb_set_arf(m, u); func(t, m, param, 1, prec); msign = _arb_sign(t); /* L, R = block, split at midpoint */ arf_set(&L->a, &block->a); arf_set(&R->b, &block->b); arf_set(&L->b, u); arf_set(&R->a, u); arb_clear(t); arb_clear(m); arf_clear(u); return msign; }
void arb_set_interval_arf(arb_t x, const arf_t a, const arf_t b, slong prec) { arf_t t; int inexact; if (arf_is_inf(a) && arf_equal(a, b)) { /* [-inf, -inf] or [+inf, +inf] */ arf_set(arb_midref(x), a); mag_zero(arb_radref(x)); return; } arf_init(t); arf_sub(t, b, a, MAG_BITS, ARF_RND_UP); if (arf_sgn(t) < 0) { flint_printf("exception: arb_set_interval_arf: endpoints not ordered\n"); abort(); } arf_get_mag(arb_radref(x), t); inexact = arf_add(arb_midref(x), a, b, prec, ARB_RND); if (inexact) arf_mag_add_ulp(arb_radref(x), arb_radref(x), arb_midref(x), prec); arb_mul_2exp_si(x, x, -1); arf_clear(t); }
static __inline__ void arb_nonnegative_part(arb_t z, const arb_t x, long prec) { if (arb_contains_negative(x)) { arf_t t; arf_init(t); arf_set_mag(t, arb_radref(x)); arf_add(arb_midref(z), arb_midref(x), t, MAG_BITS, ARF_RND_CEIL); if (arf_sgn(arb_midref(z)) <= 0) { mag_zero(arb_radref(z)); } else { arf_mul_2exp_si(arb_midref(z), arb_midref(z), -1); arf_get_mag(arb_radref(z), arb_midref(z)); /* XXX: needed since arf_get_mag is inexact */ arf_set_mag(arb_midref(z), arb_radref(z)); } arf_clear(t); } else { arb_set(z, x); } }
void _acb_poly_zeta_cpx_series(acb_ptr z, const acb_t s, const acb_t a, int deflate, long d, long prec) { ulong M, N; long i; arf_t bound; arb_ptr vb; if (d < 1) return; if (!acb_is_finite(s) || !acb_is_finite(a)) { _acb_vec_indeterminate(z, d); return; } arf_init(bound); vb = _arb_vec_init(d); _acb_poly_zeta_em_choose_param(bound, &N, &M, s, a, FLINT_MIN(d, 2), prec, MAG_BITS); _acb_poly_zeta_em_bound(vb, s, a, N, M, d, MAG_BITS); _acb_poly_zeta_em_sum(z, s, a, deflate, N, M, d, prec); for (i = 0; i < d; i++) { arb_get_abs_ubound_arf(bound, vb + i, MAG_BITS); arb_add_error_arf(acb_realref(z + i), bound); arb_add_error_arf(acb_imagref(z + i), bound); } arf_clear(bound); _arb_vec_clear(vb, d); }
void Lib_Arb_Set_Mpfr(ArbPtr x, MpfrPtr a) { arf_t rop; arf_init(rop); arf_set_mpfr(rop, (mpfr_ptr) a); arb_set_arf((arb_ptr) x, rop); arf_clear(rop); }
void Lib_Arb_Set_D(ArbPtr x, double d) { arf_t rop; arf_init(rop); arf_set_d(rop, d); arb_set_arf((arb_ptr)x, rop); arf_clear(rop); }
int main() { slong iter; flint_rand_t state; flint_printf("get_interval_fmpz_2exp...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { arb_t x; arf_t y; fmpz_t a, b, exp; arb_init(x); arf_init(y); fmpz_init(a); fmpz_init(b); fmpz_init(exp); arb_randtest(x, state, 200, 10); arb_get_interval_fmpz_2exp(a, b, exp, x); arf_set_fmpz_2exp(y, a, exp); if (!arb_contains_arf(x, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); fmpz_print(a); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } arf_set_fmpz_2exp(y, b, exp); if (!arb_contains_arf(x, y)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("b = "); fmpz_print(b); flint_printf(" exp = "); fmpz_print(exp); flint_printf("\n\n"); abort(); } arb_clear(x); arf_clear(y); fmpz_clear(a); fmpz_clear(b); fmpz_clear(exp); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
void arb_log_ui(arb_t z, ulong x, slong prec) { arf_t t; arf_init(t); arf_set_ui(t, x); arb_log_arf(z, t, prec); arf_clear(t); }
void arb_log_fmpz(arb_t z, const fmpz_t x, slong prec) { arf_t t; arf_init(t); arf_set_fmpz(t, x); arb_log_arf(z, t, prec); arf_clear(t); }
int main() { slong iter; flint_rand_t state; flint_printf("get_interval_arf...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { arb_t x, y; arf_t a, b; arb_init(x); arf_init(a); arf_init(b); arb_init(y); arb_randtest_special(x, state, 200, 100); arb_get_interval_arf(a, b, x, 2 + n_randint(state, 200)); arb_set_interval_arf(y, a, b, 2 + n_randint(state, 200)); if (!arb_contains(y, x)) { flint_printf("FAIL:\n\n"); flint_printf("x = "); arb_print(x); flint_printf("\n\n"); flint_printf("a = "); arf_print(a); flint_printf("\n\n"); flint_printf("b = "); arf_print(b); flint_printf("\n\n"); flint_printf("y = "); arb_print(y); flint_printf("\n\n"); abort(); } arb_clear(x); arf_clear(a); arf_clear(b); arb_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("get_mpfr...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000; iter++) { slong bits; arf_t x, z; mpfr_t y; bits = 2 + n_randint(state, 200); arf_init(x); arf_init(z); mpfr_init2(y, bits); arf_randtest_special(x, state, bits, 10); arf_get_mpfr(y, x, MPFR_RNDN); arf_set_mpfr(z, y); if (!arf_equal(x, z)) { flint_printf("FAIL\n\n"); flint_printf("x = "); arf_print(x); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); abort(); } arf_clear(x); arf_clear(z); mpfr_clear(y); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
int main() { slong iter; flint_rand_t state; flint_printf("set_d...."); fflush(stdout); flint_randinit(state); for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++) { double x; arf_t y, z; mpfr_t m; arf_init(y); arf_init(z); mpfr_init2(m, 53); x = d_randtest_special(state, -1200, 1200); arf_set_d(y, x); mpfr_set_d(m, x, MPFR_RNDN); arf_set_mpfr(z, m); if (!arf_equal(y, z)) { flint_printf("FAIL:\n\n"); flint_printf("x = %.17g\n\n", x); flint_printf("y = "); arf_print(y); flint_printf("\n\n"); flint_printf("z = "); arf_print(z); flint_printf("\n\n"); flint_abort(); } arf_clear(y); arf_clear(z); mpfr_clear(m); } flint_randclear(state); flint_cleanup(); flint_printf("PASS\n"); return EXIT_SUCCESS; }
void acb_modular_lambda(acb_t r, const acb_t tau, long prec) { psl2z_t g; arf_t one_minus_eps; acb_t tau_prime, q; acb_struct thetas[4]; int R[4], S[4], C; int Rsum, qpower; psl2z_init(g); arf_init(one_minus_eps); acb_init(tau_prime); acb_init(q); acb_init(thetas + 0); acb_init(thetas + 1); acb_init(thetas + 2); acb_init(thetas + 3); arf_set_ui_2exp_si(one_minus_eps, 63, -6); acb_modular_fundamental_domain_approx(tau_prime, g, tau, one_minus_eps, prec); acb_modular_theta_transform(R, S, &C, g); acb_exp_pi_i(q, tau_prime, prec); acb_modular_theta_const_sum(thetas + 1, thetas + 2, thetas + 3, q, prec); acb_zero(thetas + 0); /* divide the transformation factors */ Rsum = 4 * (R[1] - R[2]); /* possible factor [q^(+/- 1/4)]^4 needed for theta_1^4 or theta_2^4 */ qpower = (S[1] == 0 || S[1] == 1) - (S[2] == 0 || S[2] == 1); acb_div(r, thetas + S[1], thetas + S[2], prec); acb_mul(r, r, r, prec); acb_mul(r, r, r, prec); if ((Rsum & 7) == 4) acb_neg(r, r); if (qpower == 1) acb_mul(r, r, q, prec); else if (qpower == -1) acb_div(r, r, q, prec); psl2z_clear(g); arf_clear(one_minus_eps); acb_clear(tau_prime); acb_clear(q); acb_clear(thetas + 0); acb_clear(thetas + 1); acb_clear(thetas + 2); acb_clear(thetas + 3); }
int arb_contains_si(const arb_t x, slong y) { int ans; arf_t t; arf_init(t); arf_set_si(t, y); ans = arb_contains_arf(x, t); arf_clear(t); return ans; }
int arf_mul_fmpz_naive(arf_t z, const arf_t x, const fmpz_t y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz(t, y); r = arf_mul(z, x, t, prec, rnd); arf_clear(t); return r; }
int arb_contains_fmpz(const arb_t x, const fmpz_t y) { int ans; arf_t t; arf_init(t); arf_set_fmpz(t, y); ans = arb_contains_arf(x, t); arf_clear(t); return ans; }
int arf_add_si_naive(arf_t z, const arf_t x, slong y, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_si(t, y); r = arf_add(z, x, t, prec, rnd); arf_clear(t); return r; }
int arf_add_fmpz_2exp_naive(arf_t z, const arf_t x, const fmpz_t y, const fmpz_t e, slong prec, arf_rnd_t rnd) { arf_t t; int r; arf_init(t); arf_set_fmpz_2exp(t, y, e); r = arf_add(z, x, t, prec, rnd); arf_clear(t); return r; }