void
arb_rising_fmpq_ui(arb_t y, const fmpq_t x, ulong n, long prec)
{
if (n == 0)
{
arb_one(y);
}
else if (n == 1)
{
arb_set_fmpq(y, x, prec);
}
else
{
long wp;
wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
bsplit(y, fmpq_numref(x), fmpq_denref(x), 0, n, wp);
if (fmpz_is_one(fmpq_denref(x)))
{
arb_set_round(y, y, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set_fmpz(t, fmpq_denref(x));
arb_pow_ui(t, t, n, wp);
arb_div(y, y, t, prec);
arb_clear(t);
}
}
}
void
arb_mat_set_fmpq_mat(arb_mat_t dest, const fmpq_mat_t src, long prec)
{
long i, j;
if (arb_mat_ncols(dest) != 0)
{
for (i = 0; i < arb_mat_nrows(dest); i++)
for (j = 0; j < arb_mat_ncols(dest); j++)
arb_set_fmpq(arb_mat_entry(dest, i, j),
fmpq_mat_entry(src, i, j), prec);
}
}
renf_elem_class::operator double() const noexcept
{
if (nf == nullptr)
{
arb_t s;
arb_init(s);
arb_set_fmpq(s, b, 128);
double ans = arf_get_d(arb_midref(s), ARF_RND_NEAR);
arb_clear(s);
return ans;
}
else
return renf_elem_get_d(a, nf->renf_t(), ARF_RND_NEAR);
}
void
_acb_poly_roots_initial_values(acb_ptr roots, slong deg, slong prec)
{
slong i;
fmpq_t q;
fmpq_init(q);
fmpq_set_si(q, 4, 10);
arb_set_fmpq(acb_realref(roots + 0), q, prec);
mag_zero(arb_radref(acb_realref(roots + 0)));
fmpq_set_si(q, 9, 10);
arb_set_fmpq(acb_imagref(roots + 0), q, prec);
mag_zero(arb_radref(acb_imagref(roots + 0)));
fmpq_clear(q);
for (i = 1; i < deg; i++)
{
acb_mul(roots + i, roots + i - 1, roots + 0, prec);
mag_zero(arb_radref(acb_realref(roots + i)));
mag_zero(arb_radref(acb_imagref(roots + i)));
}
}
std::string renf_elem_class::to_string(int flags) const noexcept
{
std::string s;
assert(!((flags & EANTIC_STR_D) && (flags & EANTIC_STR_ARB)));
// call to renf_elem_get_str_pretty
if (nf == nullptr)
{
if (flags & EANTIC_STR_ALG)
{
char * u = fmpq_get_str(nullptr, 10, b);
s += u;
flint_free(u);
if (flags & (EANTIC_STR_D | EANTIC_STR_ARB)) s += " ~ ";
}
if (flags & EANTIC_STR_D)
{
char * u = (char *) flint_malloc(20 * sizeof(char));
sprintf(u, "%lf", fmpq_get_d(b));
s += u;
flint_free(u);
}
if (flags & EANTIC_STR_ARB)
{
char * u;
arb_t x;
arb_init(x);
arb_set_fmpq(x, b, 128);
u = arb_get_str(x, 64, 0);
s += u;
arb_clear(x);
flint_free(u);
}
}
else
{
char * u = renf_elem_get_str_pretty(renf_elem_t(), parent().gen_name().c_str(), parent().renf_t(), 10, flags);
s += u;
flint_free(u);
}
if (flags != EANTIC_STR_ALG && flags != EANTIC_STR_D && flags != EANTIC_STR_ARB)
return "(" + s + ")";
else
return s;
}
int main()
{
long iter;
flint_rand_t state;
printf("interpolate_fast....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
long i, n, qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_poly_t P;
arb_poly_t R, S;
fmpq_t t, u;
arb_ptr xs, ys;
fmpq_poly_init(P);
arb_poly_init(R);
arb_poly_init(S);
fmpq_init(t);
fmpq_init(u);
qbits1 = 2 + n_randint(state, 200);
qbits2 = 2 + n_randint(state, 5);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
fmpq_poly_randtest(P, state, 1 + n_randint(state, 20), qbits1);
n = P->length;
xs = _arb_vec_init(n);
ys = _arb_vec_init(n);
arb_poly_set_fmpq_poly(R, P, rbits1);
if (n > 0)
{
fmpq_randtest(t, state, qbits2);
arb_set_fmpq(xs, t, rbits2);
for (i = 1; i < n; i++)
{
fmpq_randtest_not_zero(u, state, qbits2);
fmpq_abs(u, u);
fmpq_add(t, t, u);
arb_set_fmpq(xs + i, t, rbits2);
}
}
for (i = 0; i < n; i++)
arb_poly_evaluate(ys + i, R, xs + i, rbits2);
arb_poly_interpolate_fast(S, xs, ys, n, rbits3);
if (!arb_poly_contains_fmpq_poly(S, P))
{
printf("FAIL:\n");
printf("P = "); fmpq_poly_print(P); printf("\n\n");
printf("R = "); arb_poly_printd(R, 15); printf("\n\n");
printf("S = "); arb_poly_printd(S, 15); printf("\n\n");
abort();
}
fmpq_poly_clear(P);
arb_poly_clear(R);
arb_poly_clear(S);
fmpq_clear(t);
fmpq_clear(u);
_arb_vec_clear(xs, n);
_arb_vec_clear(ys, n);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("evaluate_vec_fast....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
slong i, n, qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_poly_t F;
fmpq * X, * Y;
arb_poly_t f;
arb_ptr x, y;
qbits1 = 2 + n_randint(state, 100);
qbits2 = 2 + n_randint(state, 100);
rbits1 = 2 + n_randint(state, 200);
rbits2 = 2 + n_randint(state, 200);
rbits3 = 2 + n_randint(state, 200);
n = n_randint(state, 10);
fmpq_poly_init(F);
X = _fmpq_vec_init(n);
Y = _fmpq_vec_init(n);
arb_poly_init(f);
x = _arb_vec_init(n);
y = _arb_vec_init(n);
fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1);
for (i = 0; i < n; i++)
fmpq_randtest(X + i, state, qbits2);
for (i = 0; i < n; i++)
fmpq_poly_evaluate_fmpq(Y + i, F, X + i);
arb_poly_set_fmpq_poly(f, F, rbits1);
for (i = 0; i < n; i++)
arb_set_fmpq(x + i, X + i, rbits2);
arb_poly_evaluate_vec_fast(y, f, x, n, rbits3);
for (i = 0; i < n; i++)
{
if (!arb_contains_fmpq(y + i, Y + i))
{
flint_printf("FAIL (%wd of %wd)\n\n", i, n);
flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n");
flint_printf("X = "); fmpq_print(X + i); flint_printf("\n\n");
flint_printf("Y = "); fmpq_print(Y + i); flint_printf("\n\n");
flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("x = "); arb_printd(x + i, 15); flint_printf("\n\n");
flint_printf("y = "); arb_printd(y + i, 15); flint_printf("\n\n");
abort();
}
}
fmpq_poly_clear(F);
_fmpq_vec_clear(X, n);
_fmpq_vec_clear(Y, n);
arb_poly_clear(f);
_arb_vec_clear(x, n);
_arb_vec_clear(y, n);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("evaluate_horner....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
slong qbits1, qbits2, rbits1, rbits2, rbits3;
fmpq_poly_t F;
fmpq_t X, Y;
arb_poly_t f;
arb_t x, y;
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(F);
fmpq_init(X);
fmpq_init(Y);
arb_poly_init(f);
arb_init(x);
arb_init(y);
fmpq_poly_randtest(F, state, 1 + n_randint(state, 20), qbits1);
fmpq_randtest(X, state, qbits2);
fmpq_poly_evaluate_fmpq(Y, F, X);
arb_poly_set_fmpq_poly(f, F, rbits1);
arb_set_fmpq(x, X, rbits2);
arb_poly_evaluate_horner(y, f, x, rbits3);
if (!arb_contains_fmpq(y, Y))
{
flint_printf("FAIL\n\n");
flint_printf("F = "); fmpq_poly_print(F); flint_printf("\n\n");
flint_printf("X = "); fmpq_print(X); flint_printf("\n\n");
flint_printf("Y = "); fmpq_print(Y); flint_printf("\n\n");
flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n");
flint_printf("y = "); arb_printd(y, 15); flint_printf("\n\n");
abort();
}
/* aliasing */
arb_poly_evaluate_horner(x, f, x, rbits3);
if (!arb_contains_fmpq(x, Y))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
fmpq_poly_clear(F);
fmpq_clear(X);
fmpq_clear(Y);
arb_poly_clear(f);
arb_clear(x);
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("gamma_fmpq....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t r, s;
fmpq_t q;
slong accuracy, prec, pp, qq;
prec = 2 + n_randint(state, 1 << n_randint(state, 12));
prec += 20;
arb_init(r);
arb_init(s);
fmpq_init(q);
pp = -100 + n_randint(state, 10000);
qq = 1 + n_randint(state, 20);
fmpq_set_si(q, pp, qq);
arb_gamma_fmpq(r, q, prec);
arb_set_fmpq(s, q, prec);
arb_gamma(s, s, prec);
if (!arb_overlaps(r, s))
{
flint_printf("FAIL: containment\n\n");
flint_printf("prec = %wd\n", prec);
flint_printf("q = "); fmpq_print(q); flint_printf("\n\n");
flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n");
flint_printf("s = "); arb_printd(s, prec / 3.33); flint_printf("\n\n");
abort();
}
if (!(fmpz_is_one(fmpq_denref(q)) && fmpz_sgn(fmpq_numref(q)) <= 0)
&& FLINT_ABS(pp / qq) < 10)
{
accuracy = arb_rel_accuracy_bits(r);
if (accuracy < prec - 6)
{
flint_printf("FAIL: poor accuracy\n\n");
flint_printf("prec = %wd\n", prec);
flint_printf("q = "); fmpq_print(q); flint_printf("\n\n");
flint_printf("r = "); arb_printd(r, prec / 3.33); flint_printf("\n\n");
abort();
}
}
arb_clear(r);
arb_clear(s);
fmpq_clear(q);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("fundamental_domain_approx....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
fmpq_t x, y;
psl2z_t g;
arf_t one_minus_eps, tol;
acb_t z, w, w2;
arb_t t;
slong prec;
fmpq_init(x);
fmpq_init(y);
psl2z_init(g);
acb_init(z);
acb_init(w);
acb_init(w2);
arf_init(one_minus_eps);
arf_init(tol);
arb_init(t);
/* pick an exact point in the upper half plane */
fmpq_randtest(x, state, 1 + n_randint(state, 500));
do {
fmpq_randtest(y, state, 1 + n_randint(state, 500));
} while (fmpz_sgn(fmpq_numref(y)) <= 0);
/* pick a tolerance */
arf_set_ui_2exp_si(tol, 1, -(slong) n_randint(state, 500));
/* now increase the precision until convergence */
for (prec = 32; ; prec *= 2)
{
if (prec > 16384)
{
flint_printf("FAIL (no convergence)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
arb_set_fmpq(acb_realref(z), x, prec);
arb_set_fmpq(acb_imagref(z), y, prec);
arf_set_ui_2exp_si(one_minus_eps, 1, -prec / 4);
arf_sub_ui(one_minus_eps, one_minus_eps, 1, prec, ARF_RND_DOWN);
arf_neg(one_minus_eps, one_minus_eps);
acb_modular_fundamental_domain_approx(w, g, z, one_minus_eps, prec);
acb_modular_transform(w2, g, z, prec);
if (!psl2z_is_correct(g) || !acb_overlaps(w, w2))
{
flint_printf("FAIL (incorrect transformation)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
/* success */
if (acb_modular_is_in_fundamental_domain(w, tol, prec))
break;
}
/* check that g^(-1) * w contains x+yi */
psl2z_inv(g, g);
acb_modular_transform(w2, g, w, 2 + n_randint(state, 1000));
if (!arb_contains_fmpq(acb_realref(w2), x) ||
!arb_contains_fmpq(acb_imagref(w2), y))
{
flint_printf("FAIL (inverse containment)\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); acb_printd(z, 50); flint_printf("\n\n");
flint_printf("w = "); acb_printd(w, 50); flint_printf("\n\n");
flint_printf("w2 = "); acb_printd(w2, 50); flint_printf("\n\n");
flint_printf("g = "); psl2z_print(g); flint_printf("\n\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
psl2z_clear(g);
acb_clear(z);
acb_clear(w);
acb_clear(w2);
arf_clear(one_minus_eps);
arf_clear(tol);
arb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int renf_elem_cmp_fmpq(renf_elem_t a, const fmpq_t b, renf_t nf)
{
int s;
slong prec, cond;
arb_t diffball;
renf_elem_t diffnf;
if (fmpq_is_zero(b))
return renf_elem_sgn(a, nf);
if (nf_elem_is_rational(a->elem, nf->nf))
{
if (nf->nf->flag & NF_LINEAR)
return _fmpq_cmp(LNF_ELEM_NUMREF(a->elem),
LNF_ELEM_DENREF(a->elem),
fmpq_numref(b),
fmpq_denref(b));
else if (nf->nf->flag & NF_QUADRATIC)
return _fmpq_cmp(QNF_ELEM_NUMREF(a->elem),
QNF_ELEM_DENREF(a->elem),
fmpq_numref(b),
fmpq_denref(b));
else
return _fmpq_cmp(NF_ELEM_NUMREF(a->elem),
NF_ELEM_DENREF(a->elem),
fmpq_numref(b),
fmpq_denref(b));
}
arb_init(diffball);
arb_set_fmpq(diffball, b, nf->prec);
arb_sub(diffball, a->emb, diffball, nf->prec);
if (!arb_contains_zero(diffball))
{
s = arf_sgn(arb_midref(diffball));
arb_clear(diffball);
return s;
}
renf_elem_relative_condition_number_2exp(&cond, a, nf);
prec = FLINT_MAX(nf->prec, arb_rel_accuracy_bits(nf->emb));
renf_elem_set_evaluation(a, nf, prec + cond);
arb_set_fmpq(diffball, b, prec);
arb_sub(diffball, a->emb, diffball, prec);
if (!arb_contains_zero(diffball))
{
s = arf_sgn(arb_midref(diffball));
arb_clear(diffball);
return s;
}
arb_clear(diffball);
renf_elem_init(diffnf, nf);
renf_elem_set(diffnf, a, nf);
renf_elem_sub_fmpq(diffnf, diffnf, b, nf);
s = renf_elem_sgn(diffnf, nf);
renf_elem_clear(diffnf, nf);
return s;
}
int main()
{
slong iter;
FLINT_TEST_INIT(state);
{
ulong k;
arb_t a,b;
arf_t c,d;
fmpq_poly_t p;
arb_init(a);
arb_init(b);
arf_init(c);
arf_init(d);
/* x+1 */
fmpq_poly_init(p);
fmpq_poly_set_coeff_si(p, 0, 1);
fmpq_poly_set_coeff_si(p, 1, 1);
for (iter = 0; iter < 5000; iter++)
{
k = n_randint(state, 10000);
arb_set_si(a, k);
fmpq_poly_evaluate_arb(b, p, a, 30 + n_randint(state, 100));
if (!arb_equal_si(b, k + 1))
{
printf("FAIL (fmpq_poly_evaluate_arb):\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
arf_set_si(c, k);
fmpq_poly_evaluate_arf(d, p, c, 30 + n_randint(state, 100));
if (!arf_equal_si(d, k + 1))
{
printf("FAIL (fmpq_poly_evaluate_arf):\n");
printf("c = "); arf_print(c); printf("\n");
printf("d = "); arf_print(d); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
}
/* x^2 */
fmpq_poly_zero(p);
fmpq_poly_set_coeff_si(p, 2, 1);
for (iter = 0; iter < 1000; iter++)
{
k = n_randint(state, 10000);
arb_set_si(a, k);
fmpq_poly_evaluate_arb(b, p, a, 30 + n_randint(state, 100));
if (!arb_equal_si(b, k * k))
{
printf("Error (test_fmpq_poly_evaluate_arb):\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
arf_set_si(c, k);
fmpq_poly_evaluate_arf(d, p, c, 30 + n_randint(state, 100));
if (!arf_equal_si(d, k * k))
{
printf("Error (test_fmpq_poly_evaluate_arf):\n");
printf("c = "); arf_print(c); printf("\n");
printf("d = "); arf_print(d); printf("\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
abort();
}
}
fmpq_poly_clear(p);
arb_clear(a);
arb_clear(b);
arf_clear(c);
arf_clear(d);
}
/* check evaluate_arb agains exact evaluate_fmpq */
for (iter = 0; iter < 1000; iter++)
{
fmpq_poly_t p;
fmpq_t x,y;
arb_t a,b;
fmpq_poly_init(p);
fmpq_init(x);
fmpq_init(y);
arb_init(a);
arb_init(b);
fmpq_poly_randtest(p, state, 1 + n_randint(state,100), 10);
fmpq_randtest(x, state, 10);
arb_set_fmpq(a, x, 64);
fmpq_poly_evaluate_fmpq(y, p, x);
fmpq_poly_evaluate_arb(b, p, a, 60);
if (!arb_contains_fmpq(b, y))
{
printf("FAIL (y not in b):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("x = "); fmpq_print(x); printf("\n");
printf("y = "); fmpq_print(y); printf("\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
abort();
}
fmpq_poly_evaluate_arb(a, p, a, 60);
if (!arb_equal(a,b))
{
printf("FAIL (a not equal b):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("x = "); fmpq_print(x); printf("\n");
printf("y = "); fmpq_print(y); printf("\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
abort();
}
fmpq_poly_clear(p);
fmpq_clear(x);
fmpq_clear(y);
arb_clear(a);
arb_clear(b);
}
/* test aliasing */
for (iter = 0; iter < 1000; iter++)
{
fmpq_poly_t p;
arb_t a,b;
arf_t c,d;
fmpq_poly_init(p);
arb_init(a);
arb_init(b);
arf_init(c);
arf_init(d);
fmpq_poly_randtest(p, state, 1 + n_randint(state,100), 10);
arb_randtest(a, state, 60, 10);
arb_randtest(b, state, 60, 10);
arf_randtest(c, state, 60, 10);
arf_randtest(d, state, 60, 10);
fmpq_poly_evaluate_arb(b, p, a, 60);
fmpq_poly_evaluate_arb(a, p, a, 60);
if (!arb_equal(a, b))
{
printf("FAIL (a not equal b):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("a = "); arb_print(a); printf("\n");
printf("b = "); arb_print(b); printf("\n");
abort();
}
fmpq_poly_evaluate_arf(d, p, c, 60);
fmpq_poly_evaluate_arf(c, p, c, 60);
if (!arf_equal(c, d))
{
printf("FAIL (c not equal d):\n");
printf("p = "); fmpq_poly_print(p); printf("\n");
printf("c = "); arf_print(c); printf("\n");
printf("d = "); arf_print(d); printf("\n");
}
fmpq_poly_clear(p);
arb_clear(a);
arb_clear(b);
arf_clear(c);
arf_clear(d);
}
FLINT_TEST_CLEANUP(state);
return 0;
}