int main()
{
long iter;
flint_rand_t state;
printf("submul_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c, d;
fmpz_t x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
fmpz_init(x);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
fmpz_randtest(x, state, 1 + n_randint(state, 2000));
prec = 2 + n_randint(state, 2000);
arb_set_fmpz(b, x);
arb_set(d, c);
arb_submul_fmpz(c, a, x, prec);
arb_submul(d, a, b, prec);
if (!arb_equal(c, d))
{
printf("FAIL\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");
printf("d = "); arb_print(d); printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
fmpz_clear(x);
}
/* aliasing */
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
fmpz_t x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
fmpz_init(x);
arb_randtest_special(a, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(b, state, 1 + n_randint(state, 2000), 100);
arb_randtest_special(c, state, 1 + n_randint(state, 2000), 100);
fmpz_randtest(x, state, 1 + n_randint(state, 2000));
prec = 2 + n_randint(state, 2000);
arb_set_fmpz(b, x);
arb_set(c, a);
arb_submul_fmpz(c, a, x, prec);
arb_submul_fmpz(a, a, x, prec);
if (!arb_equal(a, c))
{
printf("FAIL (aliasing)\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);
fmpz_clear(x);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("cos_pi_fmpq_algebraic....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t c1, c2;
ulong p, q, g;
slong prec;
prec = 2 + n_randint(state, 5000);
q = 1 + n_randint(state, 500);
p = n_randint(state, q / 2 + 1);
g = n_gcd(q, p);
q /= g;
p /= g;
arb_init(c1);
arb_init(c2);
_arb_cos_pi_fmpq_algebraic(c1, p, q, prec);
arb_const_pi(c2, prec);
arb_mul_ui(c2, c2, p, prec);
arb_div_ui(c2, c2, q, prec);
arb_cos(c2, c2, prec);
if (!arb_overlaps(c1, c2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n");
flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n");
flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n");
abort();
}
if (arb_rel_accuracy_bits(c1) < prec - 2)
{
flint_printf("FAIL: accuracy\n\n");
flint_printf("p/q = %wu/%wu", p, q); flint_printf("\n\n");
flint_printf("prec=%wd eff=%wd\n", prec, arb_rel_accuracy_bits(c1));
flint_printf("c1 = "); arb_printd(c1, 15); flint_printf("\n\n");
flint_printf("c2 = "); arb_printd(c2, 15); flint_printf("\n\n");
abort();
}
arb_clear(c1);
arb_clear(c2);
}
flint_randclear(state);
flint_cleanup();
flint_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()
{
long iter;
flint_rand_t state;
printf("union....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
arb_t x, y, z;
long prec;
int alias;
arb_init(x);
arb_init(y);
arb_init(z);
arb_randtest_special(x, state, 200, 10);
arb_randtest_special(y, state, 200, 10);
arb_randtest_special(z, state, 200, 10);
prec = 2 + n_randint(state, 200);
arb_union(z, x, y, prec);
if (!arb_contains(z, x) || !arb_contains(z, y))
{
printf("FAIL:\n\n");
printf("x = "); arb_print(x); printf("\n\n");
printf("y = "); arb_print(y); printf("\n\n");
printf("z = "); arb_print(z); printf("\n\n");
abort();
}
if (n_randint(state, 2))
{
arb_union(x, x, y, prec);
alias = arb_equal(x, z);
}
else
{
arb_union(y, x, y, prec);
alias = arb_equal(y, z);
}
if (!alias)
{
printf("FAIL (aliasing):\n\n");
printf("x = "); arb_print(x); printf("\n\n");
printf("y = "); arb_print(y); printf("\n\n");
printf("z = "); arb_print(z); printf("\n\n");
abort();
}
arb_clear(x);
arb_clear(y);
arb_clear(z);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
void
_arb_poly_rgamma_series(arb_ptr res, arb_srcptr h, long hlen, long len, long prec)
{
int reflect;
long i, rflen, r, n, wp;
arb_ptr t, u, v;
arb_struct f[2];
hlen = FLINT_MIN(hlen, len);
wp = prec + FLINT_BIT_COUNT(prec);
t = _arb_vec_init(len);
u = _arb_vec_init(len);
v = _arb_vec_init(len);
arb_init(f);
arb_init(f + 1);
/* use zeta values at small integers */
if (arb_is_int(h) && (arf_cmpabs_ui(arb_midref(h), prec / 2) < 0))
{
r = arf_get_si(arb_midref(h), ARF_RND_DOWN);
_arb_poly_lgamma_series_at_one(u, len, wp);
_arb_vec_neg(u, u, len);
_arb_poly_exp_series(t, u, len, len, wp);
if (r == 1)
{
_arb_vec_swap(v, t, len);
}
else if (r <= 0)
{
arb_set(f, h);
arb_one(f + 1);
rflen = FLINT_MIN(len, 2 - r);
_arb_poly_rising_ui_series(u, f, FLINT_MIN(2, len), 1 - r, rflen, wp);
_arb_poly_mullow(v, t, len, u, rflen, len, wp);
}
else
{
arb_one(f);
arb_one(f + 1);
rflen = FLINT_MIN(len, r);
_arb_poly_rising_ui_series(v, f, FLINT_MIN(2, len), r - 1, rflen, wp);
/* TODO: use div_series? */
_arb_poly_inv_series(u, v, rflen, len, wp);
_arb_poly_mullow(v, t, len, u, len, len, wp);
}
}
else
{
/* otherwise use Stirling series */
arb_gamma_stirling_choose_param(&reflect, &r, &n, h, 1, 0, wp);
/* rgamma(h) = (gamma(1-h+r) sin(pi h)) / (rf(1-h, r) * pi), h = h0 + t*/
if (reflect)
{
/* u = gamma(r+1-h) */
arb_sub_ui(f, h, r + 1, wp);
arb_neg(f, f);
_arb_poly_gamma_stirling_eval(t, f, n, len, wp);
_arb_poly_exp_series(u, t, len, len, wp);
for (i = 1; i < len; i += 2)
arb_neg(u + i, u + i);
/* v = sin(pi x) */
arb_const_pi(f + 1, wp);
arb_mul(f, h, f + 1, wp);
_arb_poly_sin_series(v, f, 2, len, wp);
_arb_poly_mullow(t, u, len, v, len, len, wp);
/* rf(1-h,r) * pi */
if (r == 0)
{
arb_const_pi(u, wp);
_arb_vec_scalar_div(v, t, len, u, wp);
}
else
{
arb_sub_ui(f, h, 1, wp);
arb_neg(f, f);
arb_set_si(f + 1, -1);
rflen = FLINT_MIN(len, r + 1);
_arb_poly_rising_ui_series(v, f, FLINT_MIN(2, len), r, rflen, wp);
arb_const_pi(u, wp);
_arb_vec_scalar_mul(v, v, rflen, u, wp);
/* divide by rising factorial */
/* TODO: might better to use div_series, when it has a good basecase */
_arb_poly_inv_series(u, v, rflen, len, wp);
_arb_poly_mullow(v, t, len, u, len, len, wp);
}
}
else
{
/* rgamma(h) = rgamma(h+r) rf(h,r) */
if (r == 0)
{
arb_add_ui(f, h, r, wp);
_arb_poly_gamma_stirling_eval(t, f, n, len, wp);
_arb_vec_neg(t, t, len);
_arb_poly_exp_series(v, t, len, len, wp);
}
else
{
arb_set(f, h);
arb_one(f + 1);
rflen = FLINT_MIN(len, r + 1);
_arb_poly_rising_ui_series(t, f, FLINT_MIN(2, len), r, rflen, wp);
arb_add_ui(f, h, r, wp);
_arb_poly_gamma_stirling_eval(v, f, n, len, wp);
_arb_vec_neg(v, v, len);
_arb_poly_exp_series(u, v, len, len, wp);
_arb_poly_mullow(v, u, len, t, rflen, len, wp);
}
}
}
/* compose with nonconstant part */
arb_zero(t);
_arb_vec_set(t + 1, h + 1, hlen - 1);
_arb_poly_compose_series(res, v, len, t, hlen, len, prec);
arb_clear(f);
arb_clear(f + 1);
_arb_vec_clear(t, len);
_arb_vec_clear(u, len);
_arb_vec_clear(v, len);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rising2_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
arb_t a, u, v, u2, v2;
fmpz *f;
arb_ptr g;
ulong n;
slong i, prec;
arb_init(a);
arb_init(u);
arb_init(v);
arb_init(u2);
arb_init(v2);
arb_randtest(a, state, 1 + n_randint(state, 4000), 10);
arb_randtest(u, state, 1 + n_randint(state, 4000), 10);
arb_randtest(v, state, 1 + n_randint(state, 4000), 10);
n = n_randint(state, 120);
f = _fmpz_vec_init(n + 1);
g = _arb_vec_init(n + 1);
prec = 2 + n_randint(state, 4000);
arb_rising2_ui(u, v, a, n, prec);
arith_stirling_number_1u_vec(f, n, n + 1);
for (i = 0; i <= n; i++)
arb_set_fmpz(g + i, f + i);
_arb_poly_evaluate(u2, g, n + 1, a, prec);
_arb_poly_derivative(g, g, n + 1, prec);
_arb_poly_evaluate(v2, g, n, a, prec);
if (!arb_overlaps(u, u2) || !arb_overlaps(v, v2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu\n", n);
flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n");
flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n");
flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n");
flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n");
flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n");
abort();
}
arb_set(u2, a);
arb_rising2_ui(u2, v, u2, n, prec);
if (!arb_equal(u2, u))
{
flint_printf("FAIL: aliasing 1\n\n");
flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n");
flint_printf("u = "); arb_printd(u, 15); flint_printf("\n\n");
flint_printf("u2 = "); arb_printd(u2, 15); flint_printf("\n\n");
flint_printf("n = %wu\n", n);
abort();
}
arb_set(v2, a);
arb_rising2_ui(u, v2, v2, n, prec);
if (!arb_equal(v2, v))
{
flint_printf("FAIL: aliasing 2\n\n");
flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n");
flint_printf("v = "); arb_printd(v, 15); flint_printf("\n\n");
flint_printf("v2 = "); arb_printd(v2, 15); flint_printf("\n\n");
flint_printf("n = %wu\n", n);
abort();
}
arb_clear(a);
arb_clear(u);
arb_clear(v);
arb_clear(u2);
arb_clear(v2);
_fmpz_vec_clear(f, n + 1);
_arb_vec_clear(g, n + 1);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("zeta_nzeros_gram....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 130 + 20 * arb_test_multiplier(); iter++)
{
arb_t t, x;
fmpz_t N, n;
slong prec1, prec2;
arb_init(t);
arb_init(x);
fmpz_init(n);
fmpz_init(N);
if (iter < 130)
{
fmpz_set_si(n, iter - 1);
}
else
{
fmpz_randtest_unsigned(n, state, 20);
fmpz_add_ui(n, n, 129);
}
prec1 = 2 + n_randtest(state) % 100;
prec2 = 2 + n_randtest(state) % 100;
acb_dirichlet_zeta_nzeros_gram(N, n);
acb_dirichlet_gram_point(t, n, NULL, NULL, prec1);
acb_dirichlet_zeta_nzeros(x, t, prec2);
if (!arb_contains_fmpz(x, N))
{
flint_printf("FAIL: containment\n\n");
flint_printf("n = "); fmpz_print(n);
flint_printf(" prec1 = %wd prec2 = %wd\n\n", prec1, prec2);
flint_printf("N = "); fmpz_print(N); flint_printf("\n\n");
flint_printf("t = "); arb_printn(t, 100, 0); flint_printf("\n\n");
flint_printf("x = "); arb_printn(x, 100, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(t);
arb_clear(x);
fmpz_clear(n);
fmpz_clear(N);
}
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_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 main()
{
slong iter;
flint_rand_t state;
flint_printf("taylor_shift....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000; iter++)
{
slong prec1, prec2;
arb_poly_t f, g;
arb_t c, d, e;
prec1 = 2 + n_randint(state, 500);
prec2 = 2 + n_randint(state, 500);
arb_poly_init(f);
arb_poly_init(g);
arb_init(c);
arb_init(d);
arb_init(e);
arb_poly_randtest(f, state, 1 + n_randint(state, 40), 1 + n_randint(state, 500), 10);
arb_poly_randtest(g, state, 1 + n_randint(state, 20), 1 + n_randint(state, 500), 10);
if (n_randint(state, 2))
arb_set_si(c, n_randint(state, 5) - 2);
else
arb_randtest(c, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
if (n_randint(state, 2))
arb_set_si(d, n_randint(state, 5) - 2);
else
arb_randtest(d, state, 1 + n_randint(state, 500), 1 + n_randint(state, 100));
arb_add(e, c, d, prec1);
/* check f(x+c)(x+d) = f(x+c+d) */
arb_poly_taylor_shift(g, f, e, prec2);
arb_poly_taylor_shift(f, f, c, prec1);
arb_poly_taylor_shift(f, f, d, prec1);
if (!arb_poly_overlaps(f, g))
{
flint_printf("FAIL\n\n");
flint_printf("c = "); arb_printd(c, 15); flint_printf("\n\n");
flint_printf("d = "); arb_printd(d, 15); flint_printf("\n\n");
flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("g = "); arb_poly_printd(g, 15); flint_printf("\n\n");
abort();
}
arb_poly_clear(f);
arb_poly_clear(g);
arb_clear(c);
arb_clear(d);
arb_clear(e);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("atan_arf_bb....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 5000; iter++)
{
arb_t x, y, z;
slong prec, prec2;
arb_init(x);
arb_init(y);
arb_init(z);
prec = 2 + n_randint(state, 8000);
arb_randtest(x, state, 1 + n_randint(state, 8000), 3);
mag_zero(arb_radref(x));
if (n_randint(state, 2))
arb_mul_2exp_si(x, x, 1 + n_randint(state, 40));
else
arb_mul_2exp_si(x, x, -n_randint(state, 1.5 * prec));
if (!arf_is_special(arb_midref(x)))
prec2 = prec + 100 + 2 * (-ARF_EXP(arb_midref(x)));
else
prec2 = prec + 100;
arb_atan_arf_via_mpfr(y, arb_midref(x), prec2);
arb_atan_arf_bb(z, arb_midref(x), prec);
if (!arb_contains(z, y))
{
flint_printf("FAIL: containment\n\n");
flint_printf("prec = %wd\n\n", prec);
flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n");
flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n");
flint_printf("z = "); arb_printd(z, 50); flint_printf("\n\n");
abort();
}
if (arb_rel_accuracy_bits(z) < prec - 2)
{
flint_printf("FAIL: poor accuracy\n\n");
flint_printf("prec = %wd, acc = %wd\n\n", prec, arb_rel_accuracy_bits(z));
flint_printf("x = "); arb_printd(x, 50); flint_printf("\n\n");
flint_printf("y = "); arb_printd(y, 50); flint_printf("\n\n");
flint_printf("z = "); arb_printd(z, 50); flint_printf("\n\n");
abort();
}
arb_atan_arf_bb(x, arb_midref(x), prec);
if (!arb_overlaps(x, z))
{
flint_printf("FAIL: aliasing\n\n");
abort();
}
arb_clear(x);
arb_clear(y);
arb_clear(z);
}
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()
{
long iter;
flint_rand_t state;
printf("eta....");
fflush(stdout);
flint_randinit(state);
/* Test functional equation */
for (iter = 0; iter < 10000; iter++)
{
acb_t tau1, tau2, z1, z2, z3, t;
fmpq_t arg;
long e0, prec0, prec1, prec2;
psl2z_t g;
psl2z_init(g);
fmpq_init(arg);
acb_init(tau1);
acb_init(tau2);
acb_init(z1);
acb_init(z2);
acb_init(z3);
acb_init(t);
e0 = 1 + n_randint(state, 200);
prec0 = 2 + n_randint(state, 2000);
prec1 = 2 + n_randint(state, 2000);
prec2 = 2 + n_randint(state, 2000);
acb_randtest(tau1, state, prec0, e0);
acb_randtest(tau2, state, prec0, e0);
acb_randtest(z1, state, prec0, e0);
acb_randtest(z2, state, prec0, e0);
psl2z_randtest(g, state, 1 + n_randint(state, 200));
acb_modular_transform(tau2, g, tau1, prec0);
acb_modular_eta(z1, tau1, prec1);
acb_modular_eta(z2, tau2, prec2);
/* apply transformation */
fmpq_set_si(arg, acb_modular_epsilon_arg(g), 12);
arb_sin_cos_pi_fmpq(acb_imagref(t), acb_realref(t), arg, prec1);
acb_mul(z3, z1, t, prec1);
acb_mul_fmpz(t, tau1, &g->c, prec1);
acb_add_fmpz(t, t, &g->d, prec1);
acb_sqrt(t, t, prec1);
acb_mul(z3, z3, t, prec1);
if (!acb_overlaps(z3, z2))
{
printf("FAIL (overlap)\n");
printf("tau1 = "); acb_printd(tau1, 15); printf("\n\n");
printf("tau2 = "); acb_printd(tau2, 15); printf("\n\n");
printf("g = "); psl2z_print(g); printf("\n\n");
printf("z1 = "); acb_printd(z1, 15); printf("\n\n");
printf("z2 = "); acb_printd(z2, 15); printf("\n\n");
printf("z3 = "); acb_printd(z3, 15); printf("\n\n");
abort();
}
acb_modular_eta(tau1, tau1, prec2);
if (!acb_overlaps(z1, tau1))
{
printf("FAIL (aliasing)\n");
printf("tau1 = "); acb_print(tau1); printf("\n\n");
printf("tau2 = "); acb_print(tau2); printf("\n\n");
printf("z1 = "); acb_print(z1); printf("\n\n");
printf("z2 = "); acb_print(z2); printf("\n\n");
abort();
}
acb_clear(tau1);
acb_clear(tau2);
acb_clear(z1);
acb_clear(z2);
acb_clear(z3);
acb_clear(t);
psl2z_clear(g);
fmpq_clear(arg);
}
/* Test special values */
for (iter = 0; iter < 100; iter++)
{
acb_t tau, z;
arb_t t, u;
long prec;
acb_init(tau);
acb_init(z);
arb_init(t);
arb_init(u);
prec = 2 + n_randint(state, 2000);
acb_randtest(z, state, prec, 10);
acb_onei(tau);
acb_modular_eta(z, tau, prec);
arb_one(t);
arb_mul_2exp_si(t, t, -2);
arb_gamma(t, t, prec);
arb_const_pi(u, prec);
arb_root(u, u, 4, prec);
arb_pow_ui(u, u, 3, prec);
arb_div(t, t, u, prec);
arb_mul_2exp_si(t, t, -1);
if (!arb_overlaps(acb_realref(z), t) ||
!arb_contains_zero(acb_imagref(z)))
{
printf("FAIL (value 1)\n");
printf("tau = "); acb_print(tau); printf("\n\n");
printf("z = "); acb_print(z); printf("\n\n");
abort();
}
acb_clear(tau);
acb_clear(z);
arb_clear(t);
arb_clear(u);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
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;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("coth....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t x, y, a, b, c, d;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(x);
arb_init(y);
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_precise(x, state, 1 + n_randint(state, 1000), 100);
arb_randtest_precise(y, state, 1 + n_randint(state, 1000), 100);
arb_coth(a, x, prec1);
arb_coth(b, x, prec2);
/* check consistency */
if (!arb_overlaps(a, b))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("x = "); arb_print(x); 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_abort();
}
/* check coth(x+y) = (1 + coth(x) coth(y)) / (coth(x) + coth(y)) */
arb_add(b, x, y, prec1);
arb_coth(b, b, prec1);
arb_coth(c, y, prec1);
arb_add(d, a, c, prec1);
arb_mul(c, a, c, prec1);
arb_add_ui(c, c, 1, prec1);
arb_div(d, c, d, prec1);
if (!arb_overlaps(b, d))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("y = "); arb_print(y); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
flint_abort();
}
arb_coth(x, x, prec1);
if (!arb_overlaps(a, x))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_abort();
}
arb_clear(x);
arb_clear(y);
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("asin....");
fflush(stdout);
flint_randinit(state);
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_asin(t, t, MPFR_RNDN);
arb_asin(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_asin(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;
slong 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))
{
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 sin(asin(x)) = x */
arb_sin(c, b, 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_abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void
gc_integrals_precomp(acb_ptr res, acb_srcptr u, slong d1, slong d, slong g, const gc_int_t gc, int flag, slong prec)
{
slong l;
arb_t w, x;
acb_t y, yxi;
void (*sqrt_pol) (acb_t y, acb_srcptr u, slong d1, slong d,
const arb_t x, slong prec);
arb_init(w);
arb_init(x);
acb_init(y);
acb_init(yxi);
#if DEBUG
flint_printf("\ngc integral : d1 = %ld, d = %ld, g = %ld, n = %ld, prec = %ld",
d1, d, g, gc->n, prec);
#endif
sqrt_pol = &sqrt_pol_turn;
if (flag & AJ_ROOT_DEF)
sqrt_pol = &sqrt_pol_def;
else if (flag & AJ_ROOT_TURN)
sqrt_pol = &sqrt_pol_turn;
/* compute integral */
_acb_vec_zero(res, g);
for (l = 0; l < gc->len; l++)
{
/* compute 1/y(x) */
sqrt_pol(y, u, d1, d, gc->x + l, prec);
acb_inv(y, y, prec);
/* differentials */
acb_vec_add_geom_arb(res, g, y, gc->x + l, prec);
/* now on -x */
arb_neg(x, gc->x + l);
sqrt_pol(y, u, d1, d, x, prec);
acb_inv(y, y, prec);
acb_vec_add_geom_arb(res, g, y, x, prec);
}
if (gc->n % 2)
{
arb_zero(x);
/* FIXME: pb with turn */
sqrt_pol_def(y, u, d1, d, x, prec);
#if DEBUG > 1
flint_printf("\nend integration sum");
_acb_vec_printd(res, g, 30, "\n");
flint_printf("\nroots (d1=%ld, d=%ld)\n",d1,d);
_acb_vec_printd(u, d, 30, "\n");
flint_printf("\n -> y = ");
acb_printd(y, 30);
#endif
acb_inv(y, y, prec);
acb_add(res + 0, res + 0, y, prec);
}
/* multiply by weight = Pi / n */
arb_const_pi(w, prec);
arb_div_ui(w, w, gc->n, prec);
_acb_vec_scalar_mul_arb(res, res, g, w, prec);
#if DEBUG > 1
flint_printf("\nend integration ");
_acb_vec_printd(res, g, 30, "\n");
#endif
arb_clear(x);
arb_clear(w);
acb_clear(y);
acb_clear(yxi);
}
int main()
{
flint_rand_t state;
flint_printf("wrappers....");
fflush(stdout);
flint_randinit(state);
{
arb_t a, b, c, d, z, r, u, v;
slong prec;
prec = 53;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_init(z);
arb_init(r);
arb_init(u);
arb_init(v);
arb_set_d(a, 0.5);
arb_set_d(b, 0.25);
arb_set_d(c, 0.125);
arb_set_d(z, 0.75);
arb_hypgeom_pfq(r, a, 1, b, 1, z, 0, prec);
arb_set_str(v, "[3.40725820729608 +/- 6.88e-15]", prec);
TEST(r, v, "pfq");
arb_hypgeom_pfq(r, a, 1, b, 1, z, 1, prec);
arb_set_str(v, "[0.93977518087904 +/- 3.26e-15]", prec);
TEST(r, v, "pfq regularized");
arb_hypgeom_0f1(r, a, z, 0, prec);
arb_set_str(v, "[2.91457744017593 +/- 4.17e-15]", prec);
TEST(r, v, "0f1");
arb_hypgeom_0f1(r, a, z, 1, prec);
arb_set_str(v, "[1.64437423219054 +/- 3.77e-15]", prec);
TEST(r, v, "0f1 regularized");
arb_hypgeom_1f1(r, a, b, z, 0, prec);
arb_set_str(v, "[3.40725820729608 +/- 6.88e-15]", prec);
TEST(r, v, "1f1");
arb_hypgeom_1f1(r, a, b, z, 1, prec);
arb_set_str(v, "[0.93977518087904 +/- 3.26e-15]", prec);
TEST(r, v, "1f1 regularized");
arb_hypgeom_u(r, a, b, z, prec);
arb_set_str(v, "[0.7761320390950 +/- 3.89e-14]", prec);
TEST(r, v, "u");
arb_hypgeom_2f1(r, a, b, c, z, 0, prec);
arb_set_str(v, "[3.2569394189980 +/- 8.18e-14]", prec);
TEST(r, v, "2f1");
arb_hypgeom_2f1(r, a, b, c, z, 1, prec);
arb_set_str(v, "[0.4323021855542 +/- 1.67e-14]", prec);
TEST(r, v, "2f1 regularized");
arb_hypgeom_erf(r, z, prec);
arb_set_str(v, "[0.711155633653515 +/- 2.35e-16]", prec);
TEST(r, v, "erf");
arb_hypgeom_erfc(r, z, prec);
arb_set_str(v, "[0.288844366346485 +/- 2.34e-16]", prec);
TEST(r, v, "erfc");
arb_hypgeom_erfi(r, z, prec);
arb_set_str(v, "[1.03575728441196 +/- 3.17e-15]", prec);
TEST(r, v, "erfi");
arb_hypgeom_fresnel(r, NULL, z, 0, prec);
arb_set_str(v, "[0.137478632382610 +/- 1.79e-16]", prec);
TEST(r, v, "fresnel_s");
arb_hypgeom_fresnel(r, NULL, z, 1, prec);
arb_set_str(v, "[0.208877111233384 +/- 4.63e-16]", prec);
TEST(r, v, "fresnel_s normalized");
arb_hypgeom_fresnel(NULL, r, z, 0, prec);
arb_set_str(v, "[0.726614618304550 +/- 2.11e-16]", prec);
TEST(r, v, "fresnel_c");
arb_hypgeom_fresnel(NULL, r, z, 1, prec);
arb_set_str(v, "[0.693525990787136 +/- 2.76e-16]", prec);
TEST(r, v, "fresnel_c normalized");
arb_hypgeom_gamma_lower(r, a, z, 0, prec);
arb_set_str(v, "[1.38132404568612 +/- 3.66e-15]", prec);
TEST(r, v, "gamma_lower");
arb_hypgeom_gamma_lower(r, a, z, 1, prec);
arb_set_str(v, "[0.77932863808015 +/- 4.17e-15]", prec);
TEST(r, v, "gamma_lower 1");
arb_hypgeom_gamma_lower(r, a, z, 2, prec);
arb_set_str(v, "[0.89989119796552 +/- 2.76e-15]", prec);
TEST(r, v, "gamma_lower 2");
arb_hypgeom_gamma_upper(r, a, z, 0, prec);
arb_set_str(v, "[0.39112980521940 +/- 4.21e-15]", prec);
TEST(r, v, "gamma_upper");
arb_hypgeom_gamma_upper(r, a, z, 1, prec);
arb_set_str(v, "[0.22067136191985 +/- 4.08e-15]", prec);
TEST(r, v, "gamma_upper 1");
arb_hypgeom_beta_lower(r, a, b, z, 0, prec);
arb_set_str(v, "[2.3363313667086 +/- 3.14e-14]", prec);
TEST(r, v, "beta_lower");
arb_hypgeom_beta_lower(r, a, b, z, 1, prec);
arb_set_str(v, "[0.44551489018313 +/- 6.22e-15]", prec);
TEST(r, v, "beta_lower 1");
arb_hypgeom_expint(r, a, z, prec);
arb_set_str(v, "[0.45163779666301 +/- 3.10e-15]", prec);
TEST(r, v, "expint");
arb_hypgeom_ei(r, z, prec);
arb_set_str(v, "[1.20733281600122 +/- 2.72e-15]", prec);
TEST(r, v, "ei");
arb_hypgeom_si(r, z, prec);
arb_set_str(v, "[0.72695424715009 +/- 3.99e-15]", prec);
TEST(r, v, "si");
arb_hypgeom_ci(r, z, prec);
arb_set_str(v, "[0.152163600980330 +/- 5.49e-16]", prec);
TEST(r, v, "ci");
arb_hypgeom_shi(r, z, prec);
arb_set_str(v, "[0.77383681445623 +/- 5.97e-15]", prec);
TEST(r, v, "shi");
arb_hypgeom_chi(r, z, prec);
arb_set_str(v, "[0.433496001544996 +/- 7.91e-16]", prec);
TEST(r, v, "chi");
arb_hypgeom_li(r, z, 0, prec);
arb_set_str(v, "[-0.93693001101265 +/- 5.67e-15]", prec);
TEST(r, v, "li");
arb_hypgeom_li(r, z, 1, prec);
arb_set_str(v, "[-1.98209379113014 +/- 3.56e-15]", prec);
TEST(r, v, "li offset");
arb_hypgeom_bessel_j(r, a, z, prec);
arb_set_str(v, "[0.62800587637589 +/- 4.06e-15]", prec);
TEST(r, v, "bessel_j");
arb_hypgeom_bessel_y(r, a, z, prec);
arb_set_str(v, "[-0.67411792914454 +/- 5.27e-15]", prec);
TEST(r, v, "bessel_y");
arb_hypgeom_bessel_jy(r, u, a, z, prec);
arb_set_str(v, "[0.62800587637589 +/- 4.06e-15]", prec);
TEST(r, v, "bessel_jy");
arb_set_str(v, "[-0.67411792914454 +/- 5.27e-15]", prec);
TEST(u, v, "bessel_jy");
arb_hypgeom_bessel_i(r, a, z, prec);
arb_set_str(v, "[0.75761498638991 +/- 4.63e-15]", prec);
TEST(r, v, "bessel_i");
arb_hypgeom_bessel_k(r, a, z, prec);
arb_set_str(v, "[0.68361006034952 +/- 7.89e-15]", prec);
TEST(r, v, "bessel_k");
arb_hypgeom_airy(r, NULL, NULL, NULL, z, prec);
arb_set_str(v, "[0.179336305478645 +/- 2.36e-16]", prec);
TEST(r, v, "airy ai");
arb_hypgeom_airy(NULL, r, NULL, NULL, z, prec);
arb_set_str(v, "[-0.193175208104376 +/- 4.67e-16]", prec);
TEST(r, v, "airy ai'");
arb_hypgeom_airy(NULL, NULL, r, NULL, z, prec);
arb_set_str(v, "[1.00693090863322 +/- 3.90e-15]", prec);
TEST(r, v, "airy bi");
arb_hypgeom_airy(NULL, NULL, NULL, r, z, prec);
arb_set_str(v, "[0.690299702736886 +/- 2.34e-16]", prec);
TEST(r, v, "airy bi'");
arb_hypgeom_chebyshev_t(r, a, z, prec);
arb_set_str(v, "[0.935414346693485 +/- 7.02e-16]", prec);
TEST(r, v, "chebyshev_t");
arb_hypgeom_chebyshev_u(r, a, z, prec);
arb_set_str(v, "[1.33630620956212 +/- 3.41e-15]", prec);
TEST(r, v, "chebyshev_u");
arb_hypgeom_jacobi_p(r, a, b, c, z, prec);
arb_set_str(v, "[1.03224258095454 +/- 6.54e-15]", prec);
TEST(r, v, "jacobi_p");
arb_hypgeom_gegenbauer_c(r, a, b, z, prec);
arb_set_str(v, "[0.58153237382485 +/- 3.74e-15]", prec);
TEST(r, v, "gegenbauer_c");
arb_hypgeom_laguerre_l(r, a, b, z, prec);
arb_set_str(v, "[0.76858987769621 +/- 3.19e-15]", prec);
TEST(r, v, "laguerre_l");
arb_hypgeom_hermite_h(r, a, z, prec);
arb_set_str(v, "[1.31600493243946 +/- 6.52e-15]", prec);
TEST(r, v, "hermite_h");
arb_hypgeom_legendre_p(r, a, b, z, 0, prec);
arb_set_str(v, "[0.90435295129350 +/- 5.79e-15]", prec);
TEST(r, v, "legendre_q");
arb_hypgeom_legendre_q(r, a, b, z, 0, prec);
arb_set_str(v, "[-0.3763617490859 +/- 3.83e-14]", prec);
TEST(r, v, "legendre_q");
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
arb_clear(z);
arb_clear(r);
arb_clear(u);
arb_clear(v);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
/* derivatives: |8/sqrt(pi) sin(2z^2)|, |8/sqrt(pi) cos(2z^2)| <= 5 exp(4|xy|) */
void
acb_hypgeom_fresnel_erf_error(acb_t res1, acb_t res2, const acb_t z, slong prec)
{
mag_t re;
mag_t im;
acb_t zmid;
mag_init(re);
mag_init(im);
acb_init(zmid);
if (arf_cmpabs_ui(arb_midref(acb_realref(z)), 1000) < 0 &&
arf_cmpabs_ui(arb_midref(acb_imagref(z)), 1000) < 0)
{
arb_get_mag(re, acb_realref(z));
arb_get_mag(im, acb_imagref(z));
mag_mul(re, re, im);
mag_mul_2exp_si(re, re, 2);
mag_exp(re, re);
mag_mul_ui(re, re, 5);
}
else
{
arb_t t;
arb_init(t);
arb_mul(t, acb_realref(z), acb_imagref(z), prec);
arb_abs(t, t);
arb_mul_2exp_si(t, t, 2);
arb_exp(t, t, prec);
arb_get_mag(re, t);
mag_mul_ui(re, re, 5);
arb_clear(t);
}
mag_hypot(im, arb_radref(acb_realref(z)), arb_radref(acb_imagref(z)));
mag_mul(re, re, im);
if (arb_is_zero(acb_imagref(z)))
{
mag_set_ui(im, 8); /* For real x, |S(x)| < 4, |C(x)| < 4. */
mag_min(re, re, im);
mag_zero(im);
}
else if (arb_is_zero(acb_realref(z)))
{
mag_set_ui(im, 8);
mag_min(im, re, im);
mag_zero(re);
}
else
{
mag_set(im, re);
}
arf_set(arb_midref(acb_realref(zmid)), arb_midref(acb_realref(z)));
arf_set(arb_midref(acb_imagref(zmid)), arb_midref(acb_imagref(z)));
acb_hypgeom_fresnel_erf(res1, res2, zmid, prec);
if (res1 != NULL)
{
arb_add_error_mag(acb_realref(res1), re);
arb_add_error_mag(acb_imagref(res1), im);
}
if (res2 != NULL)
{
arb_add_error_mag(acb_realref(res2), re);
arb_add_error_mag(acb_imagref(res2), im);
}
mag_clear(re);
mag_clear(im);
acb_clear(zmid);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("contains_arf....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a;
arf_t b;
fmpq_t am, ar, bm, t;
int c1, c2;
arb_init(a);
arf_init(b);
fmpq_init(am);
fmpq_init(ar);
fmpq_init(bm);
fmpq_init(t);
arb_randtest(a, state, 1 + n_randint(state, 500), 14);
arf_randtest(b, state, 1 + n_randint(state, 500), 14);
arf_get_fmpq(am, arb_midref(a));
mag_get_fmpq(ar, arb_radref(a));
arf_get_fmpq(bm, b);
c1 = arb_contains_arf(a, b);
fmpq_sub(t, am, ar);
c2 = fmpq_cmp(t, bm) <= 0;
fmpq_add(t, am, ar);
c2 = c2 && (fmpq_cmp(t, bm) >= 0);
if (c1 != c2)
{
flint_printf("FAIL:\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arf_print(b); flint_printf("\n\n");
flint_printf("am = "); fmpq_print(am); flint_printf("\n\n");
flint_printf("ar = "); fmpq_print(ar); flint_printf("\n\n");
flint_printf("bm = "); fmpq_print(bm); flint_printf("\n\n");
flint_printf("t = "); fmpq_print(t); flint_printf("\n\n");
flint_printf("c1 = %d, c2 = %d\n\n", c1, c2);
abort();
}
arb_clear(a);
arf_clear(b);
fmpq_clear(am);
fmpq_clear(ar);
fmpq_clear(bm);
fmpq_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("euler_product_real_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 3000 * arb_test_multiplier(); iter++)
{
arb_t res1, res2;
ulong s;
slong prec1, prec2, accuracy;
int choice, reciprocal1, reciprocal2;
if (iter % 10 == 0)
{
s = n_randtest(state);
prec1 = 2 + n_randint(state, 300);
prec2 = 2 + n_randint(state, 300);
}
else
{
s = 6 + n_randint(state, 1 << n_randint(state, 12));
prec1 = 2 + n_randint(state, 12 * s);
prec2 = 2 + n_randint(state, 12 * s);
}
if (n_randint(state, 30) == 0)
prec1 = 2 + n_randint(state, 4000);
choice = n_randint(state, 7);
reciprocal1 = n_randint(state, 2);
reciprocal2 = n_randint(state, 2);
arb_init(res1);
arb_init(res2);
arb_randtest(res1, state, 200, 100);
_acb_dirichlet_euler_product_real_ui(res1, s, chi[choice] + 1,
chi[choice][0], reciprocal1, prec1);
_acb_dirichlet_euler_product_real_ui(res2, s, chi[choice] + 1,
chi[choice][0], reciprocal2, prec2);
if (reciprocal1 != reciprocal2)
arb_inv(res2, res2, prec2);
if (!arb_overlaps(res1, res2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("s = %wu\n\n", s);
flint_printf("chi: %d\n", choice);
flint_printf("res1 = "); arb_printd(res1, prec1 / 3.33); flint_printf("\n\n");
flint_printf("res2 = "); arb_printd(res2, prec2 / 3.33); flint_printf("\n\n");
abort();
}
if (s >= 6 && prec1 < 2 * s * log(s))
{
accuracy = arb_rel_accuracy_bits(res1);
if (accuracy < prec1 - 4)
{
flint_printf("FAIL: accuracy = %wd, prec = %wd\n\n", accuracy, prec1);
flint_printf("res1 = "); arb_printd(res1, prec1 / 3.33); flint_printf("\n\n");
abort();
}
}
if (s == 10)
{
arf_set_d(arb_midref(res2), L10[choice]);
mag_set_d(arb_radref(res2), 1e-15);
if (reciprocal1)
arb_inv(res2, res2, 53);
if (!arb_overlaps(res1, res2))
{
flint_printf("FAIL: overlap (2)\n\n");
flint_printf("s = %wu\n\n", s);
flint_printf("chi: %d\n", choice);
flint_printf("res1 = "); arb_printd(res1, prec1 / 3.33); flint_printf("\n\n");
flint_printf("res2 = "); arb_printd(res2, prec2 / 3.33); flint_printf("\n\n");
abort();
}
}
arb_clear(res1);
arb_clear(res2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sin_pi_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
slong m, n1, n2, bits1, bits2, bits3;
arb_poly_t S, A, B, C;
arb_t pi;
bits1 = 2 + n_randint(state, 200);
bits2 = 2 + n_randint(state, 200);
bits3 = 2 + n_randint(state, 200);
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_init(pi);
arb_poly_randtest(S, state, m, bits1, 3);
arb_poly_randtest(A, state, m, bits1, 3);
arb_poly_randtest(B, state, m, bits1, 3);
arb_poly_sin_pi_series(A, S, n1, bits2);
arb_const_pi(pi, bits3);
arb_poly_set_arb(B, pi);
arb_poly_mul(B, S, B, bits3);
arb_poly_sin_series(B, B, 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))
{
flint_printf("FAIL\n\n");
flint_printf("S = "); arb_poly_printd(S, 15); 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");
abort();
}
arb_poly_sin_pi_series(S, S, n1, bits2);
if (!arb_poly_overlaps(A, S))
{
flint_printf("FAIL (aliasing)\n\n");
abort();
}
arb_poly_clear(S);
arb_poly_clear(A);
arb_poly_clear(B);
arb_poly_clear(C);
arb_clear(pi);
}
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("legendre_p_ui_root....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100 * arb_test_multiplier(); iter++)
{
ulong n, k;
slong prec;
arb_ptr roots, weights;
arb_poly_t pol;
arb_t s;
fmpq_poly_t pol2;
n = 1 + n_randint(state, 100);
prec = 20 + n_randint(state, 500);
roots = _arb_vec_init(n);
weights = _arb_vec_init(n);
arb_poly_init(pol);
fmpq_poly_init(pol2);
arb_init(s);
for (k = 0; k < n; k++)
{
if (k > n / 2 && n_randint(state, 2))
{
arb_neg(roots + k, roots + n - k - 1);
arb_set(weights + k, weights + n - k - 1);
}
else
{
arb_hypgeom_legendre_p_ui_root(roots + k, weights + k, n, k, prec);
}
}
arb_poly_product_roots(pol, roots, n, prec);
/* fmpq_poly_legendre_p(pol2, n); */
arith_legendre_polynomial(pol2, n);
arb_set_fmpz(s, pol2->coeffs + n);
arb_div_fmpz(s, s, pol2->den, prec);
arb_poly_scalar_mul(pol, pol, s, prec);
if (!arb_poly_contains_fmpq_poly(pol, pol2))
{
flint_printf("FAIL: polynomial containment\n\n");
flint_printf("n = %wu, prec = %wd\n\n", n, prec);
flint_printf("pol = "); arb_poly_printd(pol, 30); flint_printf("\n\n");
flint_printf("pol2 = "); fmpq_poly_print(pol2); flint_printf("\n\n");
flint_abort();
}
arb_zero(s);
for (k = 0; k < n; k++)
{
arb_add(s, s, weights + k, prec);
}
if (!arb_contains_si(s, 2))
{
flint_printf("FAIL: sum of weights\n\n");
flint_printf("n = %wu, prec = %wd\n\n", n, prec);
flint_printf("s = "); arb_printn(s, 30, 0); flint_printf("\n\n");
flint_abort();
}
_arb_vec_clear(roots, n);
_arb_vec_clear(weights, n);
arb_poly_clear(pol);
fmpq_poly_clear(pol2);
arb_clear(s);
}
for (iter = 0; iter < 500 * arb_test_multiplier(); iter++)
{
arb_t x1, x2, w1, w2;
ulong n, k;
slong prec1, prec2;
arb_init(x1);
arb_init(x2);
arb_init(w1);
arb_init(w2);
n = 1 + n_randtest(state) % 100000;
if (n_randint(state, 2) || n == 1)
k = n_randtest(state) % n;
else
k = n / 2 - (n_randtest(state) % (n / 2));
prec1 = 2 + n_randtest(state) % 2000;
prec2 = 2 + n_randtest(state) % 2000;
arb_hypgeom_legendre_p_ui_root(x1, w1, n, k, prec1);
if (n_randint(state, 10) == 0)
arb_hypgeom_legendre_p_ui_root(x1, NULL, n, k, prec1);
arb_hypgeom_legendre_p_ui_root(x2, w2, n, k, prec2);
if (!arb_overlaps(x1, x2) || !arb_overlaps(w1, w2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu, k = %wu, prec1 = %wd, prec2 = %wd\n\n", n, k, prec1, prec2);
flint_printf("x1 = "); arb_printn(x1, 100, 0); flint_printf("\n\n");
flint_printf("x2 = "); arb_printn(x2, 100, 0); flint_printf("\n\n");
flint_printf("w1 = "); arb_printn(w1, 100, 0); flint_printf("\n\n");
flint_printf("w2 = "); arb_printn(w2, 100, 0); flint_printf("\n\n");
flint_abort();
}
if (arb_rel_accuracy_bits(x1) < prec1 - 3 || arb_rel_accuracy_bits(w1) < prec1 - 3)
{
flint_printf("FAIL: accuracy\n\n");
flint_printf("n = %wu, k = %wu, prec1 = %wd\n\n", n, k, prec1);
flint_printf("acc(x1) = %wd, acc(w1) = %wd\n\n", arb_rel_accuracy_bits(x1), arb_rel_accuracy_bits(w1));
flint_printf("x1 = "); arb_printn(x1, prec1, ARB_STR_CONDENSE * 30); flint_printf("\n\n");
flint_printf("w1 = "); arb_printn(w1, prec1, ARB_STR_CONDENSE * 30); flint_printf("\n\n");
flint_abort();
}
if (arb_rel_accuracy_bits(x2) < prec2 - 3 || arb_rel_accuracy_bits(w2) < prec2 - 3)
{
flint_printf("FAIL: accuracy 2\n\n");
flint_printf("n = %wu, k = %wu, prec2 = %wd\n\n", n, k, prec2);
flint_printf("acc(x2) = %wd, acc(w2) = %wd\n\n", arb_rel_accuracy_bits(x2), arb_rel_accuracy_bits(w2));
flint_printf("x2 = "); arb_printn(x2, prec2, ARB_STR_CONDENSE * 30); flint_printf("\n\n");
flint_printf("w2 = "); arb_printn(w2, prec2, ARB_STR_CONDENSE * 30); flint_printf("\n\n");
flint_abort();
}
arb_clear(x1);
arb_clear(x2);
arb_clear(w1);
arb_clear(w2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("power_sum_vec....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
arb_t a, b, s, t;
arb_ptr res;
slong aa, bb, k, n, len;
slong prec;
len = n_randint(state, 30);
prec = 2 + n_randint(state, 500);
aa = n_randint(state, 50) - 50;
bb = aa + n_randint(state, 50);
arb_init(a);
arb_init(b);
arb_init(s);
arb_init(t);
res = _arb_vec_init(len);
arb_set_si(a, aa);
arb_set_si(b, bb);
arb_power_sum_vec(res, a, b, len, prec);
for (n = 0; n < len; n++)
{
arb_zero(s);
for (k = aa; k < bb; k++)
{
arb_set_si(t, k);
arb_pow_ui(t, t, n, prec);
arb_add(s, s, t, prec);
}
if (!arb_overlaps(res + n, s))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = %wd, b = %wd, n = %wd\n\n", aa, bb, n);
flint_printf("res = "); arb_printd(res + n, 30); flint_printf("\n\n");
flint_printf("s = "); arb_printd(s, 30); flint_printf("\n\n");
abort();
}
}
arb_clear(a);
arb_clear(b);
arb_clear(s);
arb_clear(t);
_arb_vec_clear(res, len);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("atanh....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t x, a, b;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(x);
arb_init(a);
arb_init(b);
arb_randtest_special(x, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100));
arb_randtest_special(a, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100));
arb_randtest_special(b, state, 1 + n_randint(state, 1000), 2 + n_randint(state, 100));
arb_atanh(a, x, prec1);
arb_atanh(b, x, prec2);
/* check consistency */
if (!arb_overlaps(a, b))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n");
flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n");
flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n");
abort();
}
/* check tanh(atanh(x)) = x */
arb_tanh(b, b, prec1);
if (!arb_contains(b, x))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n");
flint_printf("b = "); arb_printd(b, 15); flint_printf("\n\n");
abort();
}
arb_atanh(x, x, prec1);
if (!arb_overlaps(a, x))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("a = "); arb_printd(a, 15); flint_printf("\n\n");
flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n");
abort();
}
arb_clear(x);
arb_clear(a);
arb_clear(b);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("isolate_roots....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 40; iter++)
{
slong m, r, a, b, maxdepth, maxeval, maxfound, prec, i, j, num;
arf_interval_ptr blocks;
int * info;
arf_interval_t interval;
arb_t t;
fmpz_t nn;
prec = 2 + n_randint(state, 50);
m = n_randint(state, 80);
r = 1 + n_randint(state, 80);
a = m - r;
b = m + r;
maxdepth = 1 + n_randint(state, 60);
maxeval = 1 + n_randint(state, 5000);
maxfound = 1 + n_randint(state, 100);
arf_interval_init(interval);
arb_init(t);
fmpz_init(nn);
arf_set_si(&interval->a, a);
arf_set_si(&interval->b, b);
num = arb_calc_isolate_roots(&blocks, &info, sin_pi2_x, NULL,
interval, maxdepth, maxeval, maxfound, prec);
/* check that all roots are accounted for */
for (i = a; i <= b; i++)
{
if (i % 2 == 0)
{
int found = 0;
for (j = 0; j < num; j++)
{
arf_interval_get_arb(t, blocks + j, ARF_PREC_EXACT);
if (arb_contains_si(t, i))
{
found = 1;
break;
}
}
if (!found)
{
flint_printf("FAIL: missing root %wd\n", i);
flint_printf("a = %wd, b = %wd, maxdepth = %wd, maxeval = %wd, maxfound = %wd, prec = %wd\n",
a, b, maxdepth, maxeval, maxfound, prec);
for (j = 0; j < num; j++)
{
arf_interval_printd(blocks + j, 15);
flint_printf(" %d \n", info[i]);
}
abort();
}
}
}
/* check that all reported single roots are good */
for (i = 0; i < num; i++)
{
if (info[i] == 1)
{
/* b contains unique 2n -> b/2 contains unique n */
arf_interval_get_arb(t, blocks + i, ARF_PREC_EXACT);
arb_mul_2exp_si(t, t, -1);
if (!arb_get_unique_fmpz(nn, t))
{
flint_printf("FAIL: bad root %wd\n", i);
flint_printf("a = %wd, b = %wd, maxdepth = %wd, maxeval = %wd, maxfound = %wd, prec = %wd\n",
a, b, maxdepth, maxeval, maxfound, prec);
for (j = 0; j < num; j++)
{
arf_interval_printd(blocks + j, 15);
flint_printf(" %d \n", info[i]);
}
abort();
}
}
}
_arf_interval_vec_clear(blocks, num);
flint_free(info);
arf_interval_clear(interval);
arb_clear(t);
fmpz_clear(nn);
}
flint_randclear(state);
flint_cleanup();
flint_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(int argc, char *argv[])
{
arf_interval_ptr blocks;
arb_calc_func_t function;
int * info;
long digits, low_prec, high_prec, i, num, found_roots, found_unknown;
long maxdepth, maxeval, maxfound;
int refine;
double a, b;
arf_t C;
arf_interval_t t, interval;
arb_t v, w, z;
if (argc < 4)
{
printf("real_roots function a b [-refine d] [-verbose] "
"[-maxdepth n] [-maxeval n] [-maxfound n] [-prec n]\n");
printf("available functions:\n");
printf(" 0 Z(x), Riemann-Siegel Z-function\n");
printf(" 1 sin(x)\n");
printf(" 2 sin(x^2)\n");
printf(" 3 sin(1/x)\n");
return 1;
}
switch (atoi(argv[1]))
{
case 0:
function = z_function;
break;
case 1:
function = sin_x;
break;
case 2:
function = sin_x2;
break;
case 3:
function = sin_1x;
break;
default:
printf("require a function 0-3\n");
return 1;
}
a = atof(argv[2]);
b = atof(argv[3]);
if (a >= b)
{
printf("require a < b!\n");
return 1;
}
refine = 0;
digits = 0;
maxdepth = 30;
maxeval = 100000;
maxfound = 100000;
low_prec = 30;
for (i = 4; i < argc; i++)
{
if (!strcmp(argv[i], "-refine"))
{
refine = 1;
digits = atol(argv[i+1]);
}
else if (!strcmp(argv[i], "-verbose"))
{
arb_calc_verbose = 1;
}
else if (!strcmp(argv[i], "-maxdepth"))
{
maxdepth = atol(argv[i+1]);
}
else if (!strcmp(argv[i], "-maxeval"))
{
maxeval = atol(argv[i+1]);
}
else if (!strcmp(argv[i], "-maxfound"))
{
maxfound = atol(argv[i+1]);
}
else if (!strcmp(argv[i], "-prec"))
{
low_prec = atol(argv[i+1]);
}
}
high_prec = digits * 3.32192809488736 + 10;
found_roots = 0;
found_unknown = 0;
arf_init(C);
arf_interval_init(t);
arf_interval_init(interval);
arb_init(v);
arb_init(w);
arb_init(z);
arf_set_d(&interval->a, a);
arf_set_d(&interval->b, b);
printf("interval: ");
arf_interval_printd(interval, 15);
printf("\n");
printf("maxdepth = %ld, maxeval = %ld, maxfound = %ld, low_prec = %ld\n",
maxdepth, maxeval, maxfound, low_prec);
TIMEIT_ONCE_START
num = arb_calc_isolate_roots(&blocks, &info, function,
NULL, interval, maxdepth, maxeval, maxfound, low_prec);
for (i = 0; i < num; i++)
{
if (info[i] != 1)
{
if (arb_calc_verbose)
{
printf("unable to count roots in ");
arf_interval_printd(blocks + i, 15);
printf("\n");
}
found_unknown++;
continue;
}
found_roots++;
if (!refine)
continue;
if (arb_calc_refine_root_bisect(t,
function, NULL, blocks + i, 5, low_prec)
!= ARB_CALC_SUCCESS)
{
printf("warning: some bisection steps failed!\n");
}
if (arb_calc_verbose)
{
printf("after bisection 1: ");
arf_interval_printd(t, 15);
printf("\n");
}
if (arb_calc_refine_root_bisect(blocks + i,
function, NULL, t, 5, low_prec)
!= ARB_CALC_SUCCESS)
{
printf("warning: some bisection steps failed!\n");
}
if (arb_calc_verbose)
{
printf("after bisection 2: ");
arf_interval_printd(blocks + i, 15);
printf("\n");
}
arf_interval_get_arb(v, t, high_prec);
arb_calc_newton_conv_factor(C, function, NULL, v, low_prec);
arf_interval_get_arb(w, blocks + i, high_prec);
if (arb_calc_refine_root_newton(z, function, NULL,
w, v, C, 10, high_prec) != ARB_CALC_SUCCESS)
{
printf("warning: some newton steps failed!\n");
}
printf("refined root:\n");
arb_printd(z, digits + 2);
printf("\n\n");
}
printf("---------------------------------------------------------------\n");
printf("Found roots: %ld\n", found_roots);
printf("Subintervals possibly containing undetected roots: %ld\n", found_unknown);
printf("Function evaluations: %ld\n", eval_count);
TIMEIT_ONCE_STOP
SHOW_MEMORY_USAGE
for (i = 0; i < num; i++)
arf_interval_clear(blocks + i);
flint_free(blocks);
flint_free(info);
arf_interval_clear(t);
arf_interval_clear(interval);
arf_clear(C);
arb_clear(v);
arb_clear(w);
arb_clear(z);
flint_cleanup();
return 0;
}
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;
}
