int main()
{
slong iter;
flint_rand_t state;
flint_printf("atan....");
fflush(stdout);
flint_randinit(state);
/* Compare with MPFR */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a, b;
fmpq_t q;
mpfr_t t;
slong prec = 2 + n_randint(state, 200);
arb_init(a);
arb_init(b);
fmpq_init(q);
mpfr_init2(t, prec + 100);
arb_randtest(a, state, 1 + n_randint(state, 200), 3);
arb_randtest(b, state, 1 + n_randint(state, 200), 3);
arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));
fmpq_get_mpfr(t, q, MPFR_RNDN);
mpfr_atan(t, t, MPFR_RNDN);
arb_atan(b, a, prec);
if (!arb_contains_mpfr(b, t))
{
flint_printf("FAIL: containment\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_abort();
}
arb_atan(a, a, prec);
if (!arb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(q);
mpfr_clear(t);
}
/* Check large arguments. */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c, d;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100);
arb_atan(b, a, prec1);
arb_atan(c, a, prec2);
if (!arb_overlaps(b, c))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_abort();
}
/* check tan(atan(x)) = x */
arb_sin_cos(c, d, b, prec1);
arb_div(c, c, d, prec1);
if (!arb_contains(c, a))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
}
/* Compare with MPFR, higher precision. */
for (iter = 0; iter < 200 * arb_test_multiplier(); iter++)
{
arb_t a, b;
fmpq_t q;
mpfr_t t;
slong prec = 2 + n_randint(state, 5000);
arb_init(a);
arb_init(b);
fmpq_init(q);
mpfr_init2(t, prec + 100);
arb_randtest(a, state, 1 + n_randint(state, 5000), 8);
arb_randtest(b, state, 1 + n_randint(state, 5000), 8);
arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));
fmpq_get_mpfr(t, q, MPFR_RNDN);
mpfr_atan(t, t, MPFR_RNDN);
arb_atan(b, a, prec);
if (!arb_contains_mpfr(b, t))
{
flint_printf("FAIL: containment\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("a = "); arb_printd(a, 50); flint_printf("\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_printd(b, 50); flint_printf("\n\n");
flint_abort();
}
arb_atan(a, a, prec);
if (!arb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(q);
mpfr_clear(t);
}
/* Higher precision + large arguments. */
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c, d;
slong prec1, prec2;
prec1 = 2 + n_randint(state, 5000);
prec2 = prec1 + 30;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_precise(a, state, 1 + n_randint(state, 5000), 100);
arb_atan(b, a, prec1);
arb_atan(c, a, prec2);
if (!arb_overlaps(b, c))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_abort();
}
/* check tan(atan(x)) = x */
arb_sin_cos(c, d, b, prec1);
arb_div(c, c, d, prec1);
if (!arb_contains(c, a))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
}
/* Check wide arguments. */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c, d;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_precise(a, state, 1 + n_randint(state, 1000), 100);
arb_randtest_precise(b, state, 1 + n_randint(state, 1000), 100);
if (n_randint(state, 2))
arb_add(a, a, b, 2 + n_randint(state, 1000));
arb_union(d, a, b, 2 + n_randint(state, 1000));
arb_atan(a, a, 2 + n_randint(state, 2000));
arb_atan(b, b, 2 + n_randint(state, 2000));
arb_atan(c, d, 2 + n_randint(state, 2000));
if (!arb_overlaps(c, a) || !arb_overlaps(c, b))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("reconstruct_fmpz_2....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
int result;
int modresult;
int special_case;
fmpq_t x, y;
fmpz_t mod, res, N, D, t;
mpz_t tmp;
fmpq_init(x);
fmpq_init(y);
fmpz_init(mod);
fmpz_init(res);
fmpz_init(N);
fmpz_init(D);
fmpz_init(t);
mpz_init(tmp);
fmpq_randtest(x, state, 100);
fmpz_abs(N, fmpq_numref(x));
fmpz_set(D, fmpq_denref(x));
/* Randomly generate larger bounds */
if (n_randint(state, 2))
{
fmpz_randtest_not_zero(t, state, 100);
fmpz_abs(t, t);
fmpz_mul(N, N, t);
}
if (n_randint(state, 2))
{
fmpz_randtest_not_zero(t, state, 100);
fmpz_abs(t, t);
fmpz_mul(D, D, t);
}
fmpz_mul(mod, N, D);
fmpz_mul_ui(mod, mod, UWORD(2));
/* Next prime greater than or equal */
fmpz_get_mpz(tmp, mod);
flint_mpz_sub_ui(tmp, tmp, UWORD(1));
mpz_nextprime(tmp, tmp);
fmpz_set_mpz(mod, tmp);
modresult = fmpq_mod_fmpz(res, x, mod);
result = fmpq_reconstruct_fmpz_2(y, res, mod, N, D);
/* Special case: both 1 and -1 have residue 1 mod 2.
There's probably no particular reason to disallow this. */
special_case = (fmpz_cmp_ui(mod, UWORD(2)) == 0 &&
fmpz_get_si(&x->num) == WORD(-1) &&
fmpz_cmp_ui(&x->den, UWORD(1)) == 0);
if (special_case)
{
if (!modresult || !result ||
!fmpz_is_one(&y->num) || !fmpz_is_one(&y->den))
{
flint_printf("FAIL: special case: -1 mod 2\n");
abort();
}
}
else if (!modresult || !result || !fmpq_equal(x, y))
{
flint_printf("FAIL: reconstruction failed\n");
flint_printf("input = ");
fmpq_print(x);
flint_printf("\nmodulus = ");
fmpz_print(mod);
flint_printf("\nresidue = ");
fmpz_print(res);
flint_printf("\nreconstructed = ");
fmpq_print(y);
flint_printf("\nfmpq_mod_fmpz return value = %d", modresult);
flint_printf("\nfmpq_reconstruct_fmpz return value = %d", result);
flint_printf("\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
fmpz_clear(mod);
fmpz_clear(res);
fmpz_clear(N);
fmpz_clear(D);
fmpz_clear(t);
mpz_clear(tmp);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main()
{
long iter;
flint_rand_t state;
printf("contains_arf....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; 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)
{
printf("FAIL:\n\n");
printf("a = "); arb_print(a); printf("\n\n");
printf("b = "); arf_print(b); printf("\n\n");
printf("am = "); fmpq_print(am); printf("\n\n");
printf("ar = "); fmpq_print(ar); printf("\n\n");
printf("bm = "); fmpq_print(bm); printf("\n\n");
printf("t = "); fmpq_print(t); printf("\n\n");
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();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("exp_sum_bs_powtab....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
slong N;
fmpz_t x, T, Q;
fmpq_t S, V;
mp_bitcnt_t Qexp, r;
fmpz_init(x);
fmpz_init(T);
fmpz_init(Q);
fmpq_init(S);
fmpq_init(V);
N = 1 + n_randint(state, 300);
r = n_randint(state, 10);
fmpz_randtest(x, state, 80);
_arb_exp_sum_bs_simple(T, Q, &Qexp, x, r, N);
fmpq_set_fmpz_frac(S, T, Q);
fmpq_div_2exp(S, S, Qexp);
_arb_exp_sum_bs_powtab(T, Q, &Qexp, x, r, N);
fmpq_set_fmpz_frac(V, T, Q);
fmpq_div_2exp(V, V, Qexp);
if (!fmpq_equal(S, V))
{
flint_printf("FAIL\n\n");
flint_printf("N = %wd\n\n", N);
flint_printf("r = %wu\n\n", r);
flint_printf("x = ");
fmpz_print(x);
flint_printf("\n\n");
flint_printf("T = ");
fmpz_print(T);
flint_printf("\n\n");
flint_printf("Q = ");
fmpz_print(T);
flint_printf("\n\n");
flint_printf("V = ");
fmpq_print(V);
flint_printf("\n\n");
flint_printf("S = ");
fmpq_print(S);
flint_printf("\n\n");
abort();
}
fmpz_clear(x);
fmpz_clear(T);
fmpz_clear(Q);
fmpq_clear(S);
fmpq_clear(V);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("interpolate_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 P;
acb_poly_t R, S;
fmpq_t t, u;
acb_ptr xs, ys;
fmpq_poly_init(P);
acb_poly_init(R);
acb_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 = _acb_vec_init(n);
ys = _acb_vec_init(n);
acb_poly_set_fmpq_poly(R, P, rbits1);
if (n > 0)
{
fmpq_randtest(t, state, qbits2);
acb_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);
acb_set_fmpq(xs + i, t, rbits2);
}
}
for (i = 0; i < n; i++)
acb_poly_evaluate(ys + i, R, xs + i, rbits2);
acb_poly_interpolate_fast(S, xs, ys, n, rbits3);
if (!acb_poly_contains_fmpq_poly(S, P))
{
flint_printf("FAIL:\n");
flint_printf("P = "); fmpq_poly_print(P); flint_printf("\n\n");
flint_printf("R = "); acb_poly_printd(R, 15); flint_printf("\n\n");
flint_printf("S = "); acb_poly_printd(S, 15); flint_printf("\n\n");
flint_abort();
}
fmpq_poly_clear(P);
acb_poly_clear(R);
acb_poly_clear(S);
fmpq_clear(t);
fmpq_clear(u);
_acb_vec_clear(xs, n);
_acb_vec_clear(ys, n);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter, iter2;
flint_rand_t state;
flint_printf("addmul....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c;
fmpq_t x, y, z;
arb_init(a);
arb_init(b);
arb_init(c);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
arb_randtest(a, state, 1 + n_randint(state, 200), 10);
arb_randtest(b, state, 1 + n_randint(state, 200), 10);
arb_randtest(c, state, 1 + n_randint(state, 200), 10);
arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200));
arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200));
arb_get_rand_fmpq(z, state, c, 1 + n_randint(state, 200));
arb_addmul(c, a, b, 2 + n_randint(state, 200));
fmpq_addmul(z, x, y);
if (!arb_contains_fmpq(c, z))
{
flint_printf("FAIL: containment\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_printf("z = "); fmpq_print(z); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
}
/* aliasing of c and a */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a, b;
fmpq_t x, y, z;
arb_init(a);
arb_init(b);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
arb_randtest(a, state, 1 + n_randint(state, 200), 10);
arb_randtest(b, state, 1 + n_randint(state, 200), 10);
arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200));
arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200));
fmpq_set(z, x);
arb_addmul(a, a, b, 2 + n_randint(state, 200));
fmpq_addmul(z, x, y);
if (!arb_contains_fmpq(a, z))
{
flint_printf("FAIL: aliasing (c, a)\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpq_print(z); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
}
/* aliasing of c and b */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a, b;
fmpq_t x, y, z;
arb_init(a);
arb_init(b);
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
arb_randtest(a, state, 1 + n_randint(state, 200), 10);
arb_randtest(b, state, 1 + n_randint(state, 200), 10);
arb_get_rand_fmpq(x, state, a, 1 + n_randint(state, 200));
arb_get_rand_fmpq(y, state, b, 1 + n_randint(state, 200));
fmpq_set(z, y);
arb_addmul(b, a, b, 2 + n_randint(state, 200));
fmpq_addmul(z, x, y);
if (!arb_contains_fmpq(b, z))
{
flint_printf("FAIL: aliasing (c, b)\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("x = "); fmpq_print(x); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("y = "); fmpq_print(y); flint_printf("\n\n");
flint_printf("z = "); fmpq_print(z); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
}
/* main test */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t x, y, z, v;
slong prec;
arb_init(x);
arb_init(y);
arb_init(z);
arb_init(v);
for (iter2 = 0; iter2 < 100; iter2++)
{
arb_randtest_special(x, state, n_randint(state,2) ? 2000 : 200, 200);
arb_randtest_special(y, state, n_randint(state,2) ? 2000 : 200, 200);
arb_randtest_special(z, state, n_randint(state,2) ? 2000 : 200, 200);
prec = 2 + n_randint(state, 2000);
switch (n_randint(state, 5))
{
case 0:
arb_set(v, z);
arb_addmul(z, x, y, prec);
arb_addmul_naive(v, x, y, prec);
if (!arf_equal(arb_midref(z), arb_midref(v))
|| !mag_close(arb_radref(z), arb_radref(v)))
{
flint_printf("FAIL!\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("y = "); arb_print(y); flint_printf("\n\n");
flint_printf("z = "); arb_print(z); flint_printf("\n\n");
flint_printf("v = "); arb_print(v); flint_printf("\n\n");
abort();
}
break;
case 1:
arb_set(y, x);
arb_set(z, v);
arb_addmul(z, x, y, prec);
arb_addmul(v, x, x, prec);
if (!arf_equal(arb_midref(z), arb_midref(v))
|| !mag_close(arb_radref(z), arb_radref(v)))
{
flint_printf("FAIL (aliasing 1)!\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("z = "); arb_print(z); flint_printf("\n\n");
flint_printf("v = "); arb_print(v); flint_printf("\n\n");
abort();
}
break;
case 2:
arb_set(v, x);
arb_addmul(v, x, x, prec);
arb_addmul(x, x, x, prec);
if (!arf_equal(arb_midref(x), arb_midref(v))
|| !mag_close(arb_radref(x), arb_radref(v)))
{
flint_printf("FAIL (aliasing 2)!\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("v = "); arb_print(v); flint_printf("\n\n");
abort();
}
break;
case 3:
arb_set(v, x);
arb_addmul(v, x, y, prec);
arb_addmul(x, x, y, prec);
if (!arf_equal(arb_midref(x), arb_midref(v))
|| !mag_close(arb_radref(x), arb_radref(v)))
{
flint_printf("FAIL (aliasing 3)!\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("y = "); arb_print(y); flint_printf("\n\n");
flint_printf("v = "); arb_print(v); flint_printf("\n\n");
abort();
}
break;
default:
arb_set(v, x);
arb_addmul(v, x, y, prec);
arb_addmul(x, y, x, prec);
if (!arf_equal(arb_midref(x), arb_midref(v))
|| !mag_close(arb_radref(x), arb_radref(v)))
{
flint_printf("FAIL (aliasing 4)!\n");
flint_printf("x = "); arb_print(x); flint_printf("\n\n");
flint_printf("y = "); arb_print(y); flint_printf("\n\n");
flint_printf("v = "); arb_print(v); flint_printf("\n\n");
abort();
}
break;
}
}
arb_clear(x);
arb_clear(y);
arb_clear(z);
arb_clear(v);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("exp....");
fflush(stdout);
flint_randinit(state);
/* check large arguments + compare with exp_simple */
for (iter = 0; iter < 100000 *arb_test_multiplier(); iter++)
{
arb_t a, b, c, d;
slong prec0, prec1, prec2, acc1, acc2;
if (iter % 10 == 0)
prec0 = 10000;
else
prec0 = 1000;
prec1 = 2 + n_randint(state, prec0);
prec2 = 2 + n_randint(state, prec0);
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_randtest_special(a, state, 1 + n_randint(state, prec0), 100);
arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100);
arb_exp(b, a, prec1);
arb_exp(c, a, prec2);
arb_exp_simple(d, a, prec1);
if (!arb_overlaps(b, c) || !arb_overlaps(b, d) || !arb_overlaps(c, d))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
flint_abort();
}
/* compare accuracy with exp_simple */
acc1 = arb_rel_accuracy_bits(b);
acc2 = arb_rel_accuracy_bits(d);
if (acc2 > 0 && acc1 < acc2 - 1)
{
flint_printf("FAIL: accuracy\n\n");
flint_printf("prec1 = %wd, acc1 = %wd, acc2 = %wd\n\n", prec1, acc1, acc2);
flint_printf("a = "); arb_printd(a, 50); flint_printf("\n\n");
flint_printf("b = "); arb_printd(b, 50); flint_printf("\n\n");
flint_printf("d = "); arb_printd(d, 50); flint_printf("\n\n");
flint_abort();
}
arb_randtest_special(b, state, 1 + n_randint(state, prec0), 100);
/* check exp(a)*exp(b) = exp(a+b) */
arb_exp(c, a, prec1);
arb_exp(d, b, prec1);
arb_mul(c, c, d, prec1);
arb_add(d, a, b, prec1);
arb_exp(d, d, prec1);
if (!arb_overlaps(c, d))
{
flint_printf("FAIL: functional equation\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
flint_printf("d = "); arb_print(d); flint_printf("\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
}
/* test union */
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arb_t a, b, c, d, e;
slong prec0, prec1, prec2, prec3, prec4;
if (iter % 10 == 0)
prec0 = 10000;
else
prec0 = 1000;
prec1 = 2 + n_randint(state, prec0);
prec2 = 2 + n_randint(state, prec0);
prec3 = 2 + n_randint(state, prec0);
prec4 = 2 + n_randint(state, prec0);
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
arb_init(e);
arb_randtest_special(a, state, 1 + n_randint(state, prec0), 200);
arb_randtest_special(b, state, 1 + n_randint(state, prec0), 200);
arb_randtest_special(c, state, 1 + n_randint(state, prec0), 200);
arb_randtest_special(d, state, 1 + n_randint(state, prec0), 200);
arb_randtest_special(e, state, 1 + n_randint(state, prec0), 200);
arb_exp(c, a, prec1);
arb_exp(d, b, prec2);
arb_union(e, a, b, prec3);
arb_exp(e, e, prec4);
if (!arb_overlaps(e, c) || !arb_overlaps(e, d))
{
flint_printf("FAIL: union\n\n");
flint_printf("a = "); arb_printn(a, 1000, 0); flint_printf("\n\n");
flint_printf("b = "); arb_printn(b, 1000, 0); flint_printf("\n\n");
flint_printf("c = "); arb_printn(c, 1000, 0); flint_printf("\n\n");
flint_printf("d = "); arb_printn(d, 1000, 0); flint_printf("\n\n");
flint_printf("e = "); arb_printn(e, 1000, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
arb_clear(d);
arb_clear(e);
}
/* comparison with mpfr */
for (iter = 0; iter < 100000 * arb_test_multiplier(); iter++)
{
arb_t a, b;
fmpq_t q;
mpfr_t t;
slong prec0, prec;
prec0 = 400;
if (iter % 100 == 0)
prec0 = 10000;
prec = 2 + n_randint(state, prec0);
arb_init(a);
arb_init(b);
fmpq_init(q);
mpfr_init2(t, prec + 100);
arb_randtest(a, state, 1 + n_randint(state, prec0), 4);
arb_randtest(b, state, 1 + n_randint(state, prec0), 4);
arb_get_rand_fmpq(q, state, a, 1 + n_randint(state, prec0));
fmpq_get_mpfr(t, q, MPFR_RNDN);
mpfr_exp(t, t, MPFR_RNDN);
arb_exp(b, a, prec);
if (!arb_contains_mpfr(b, t))
{
flint_printf("FAIL: containment\n\n");
flint_printf("iter = %wd, prec = %wd\n\n", iter, prec);
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_abort();
}
arb_exp(a, a, prec);
if (!arb_equal(a, b))
{
flint_printf("FAIL: aliasing\n\n");
flint_printf("iter = %wd, prec = %wd\n\n", iter, prec);
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_abort();
}
arb_clear(a);
arb_clear(b);
fmpq_clear(q);
mpfr_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("solve_dixon....");
fflush(stdout);
/* Solve nonsingular systems */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpq_mat_t A, B, X, AX;
fmpq_t d;
int success;
slong n, m, bits;
n = n_randint(state, 10);
m = n_randint(state, 10);
bits = 1 + n_randint(state, 100);
fmpq_mat_init(A, n, n);
fmpq_mat_init(B, n, m);
fmpq_mat_init(X, n, m);
fmpq_mat_init(AX, n, m);
fmpq_init(d);
/* XXX: replace with a randtest function */
do {
fmpq_mat_randtest(A, state, bits);
fmpq_mat_det(d, A);
} while (fmpq_is_zero(d));
fmpq_clear(d);
fmpq_mat_randtest(B, state, bits);
success = fmpq_mat_solve_dixon(X, A, B);
fmpq_mat_mul(AX, A, X);
if (!fmpq_mat_equal(AX, B) || !success)
{
flint_printf("FAIL!\n");
flint_printf("success: %d\n", success);
flint_printf("A:\n");
fmpq_mat_print(A);
flint_printf("B:\n");
fmpq_mat_print(B);
flint_printf("X:\n");
fmpq_mat_print(X);
flint_printf("AX:\n");
fmpq_mat_print(AX);
abort();
}
fmpq_mat_clear(A);
fmpq_mat_clear(B);
fmpq_mat_clear(X);
fmpq_mat_clear(AX);
}
/* Check singular systems */
for (i = 0; i < 100 * flint_test_multiplier(); i++)
{
fmpq_mat_t A, B, X;
fmpz_mat_t M;
fmpz_t den;
slong n, m, bits;
int success;
n = 1 + n_randint(state, 10);
m = 1 + n_randint(state, 10);
bits = 1 + n_randint(state, 100);
fmpz_init(den);
fmpz_mat_init(M, n, n);
fmpz_mat_randrank(M, state, n_randint(state, n), bits);
if (i % 2)
fmpz_mat_randops(M, state, n_randint(state, 2*m*n + 1));
fmpz_randtest_not_zero(den, state, bits);
fmpq_mat_init(A, n, n);
fmpq_mat_set_fmpz_mat_div_fmpz(A, M, den);
fmpq_mat_init(B, n, m);
fmpq_mat_randtest(B, state, bits);
fmpq_mat_init(X, n, m);
success = fmpq_mat_solve_dixon(X, A, B);
if (success != 0)
{
flint_printf("FAIL!\n");
flint_printf("Expected success = 0\n");
fmpq_mat_print(A);
flint_printf("\n");
abort();
}
fmpq_mat_clear(A);
fmpq_mat_clear(B);
fmpq_mat_clear(X);
fmpz_mat_clear(M);
fmpz_clear(den);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int fmpq_poly_check_unique_real_root(const fmpq_poly_t pol, const arb_t a, slong prec)
{
if (pol->length < 2)
return 0;
else if (pol->length == 2)
{
/* linear polynomial */
fmpq_t root;
int ans;
fmpq_init(root);
fmpq_set_fmpz_frac(root, fmpq_poly_numref(pol), fmpq_poly_numref(pol) + 1);
fmpq_neg(root, root);
ans = arb_contains_fmpq(a, root);
fmpq_clear(root);
return ans;
}
else
{
arb_t b, c;
arf_t l, r;
fmpz * der;
int lsign, rsign;
fmpz_poly_t pol2;
slong n;
/* 1 - cheap test: */
/* - sign(left) * sign(right) = -1 */
/* - no zero of the derivative */
arb_init(b);
arb_init(c);
arf_init(l);
arf_init(r);
arb_get_interval_arf(l, r, a, prec);
arb_set_arf(b, l);
_fmpz_poly_evaluate_arb(c, pol->coeffs, pol->length, b, 2*prec);
lsign = arb_sgn2(c);
arb_set_arf(b, r);
_fmpz_poly_evaluate_arb(c, pol->coeffs, pol->length, b, 2*prec);
rsign = arb_sgn2(c);
arb_clear(c);
if (lsign * rsign == -1)
{
der = _fmpz_vec_init(pol->length - 1);
_fmpz_poly_derivative(der, pol->coeffs, pol->length);
_fmpz_poly_evaluate_arb(b, der, pol->length - 1, a, prec);
_fmpz_vec_clear(der, pol->length - 1);
if (!arb_contains_zero(b))
{
arf_clear(l);
arf_clear(r);
arb_clear(b);
return 1;
}
}
else
return 0;
arb_clear(b);
/* 2 - expensive testing */
fmpq_t ql, qr;
fmpq_init(ql);
fmpq_init(qr);
arf_get_fmpq(ql, l);
arf_get_fmpq(qr, r);
fmpz_poly_init(pol2);
fmpz_poly_fit_length(pol2, pol->length);
_fmpz_vec_set(pol2->coeffs, pol->coeffs, pol->length);
pol2->length = pol->length;
_fmpz_poly_scale_0_1_fmpq(pol2->coeffs, pol2->length, ql, qr);
n = fmpz_poly_num_real_roots_0_1(pol2);
fmpz_poly_clear(pol2);
fmpq_clear(ql);
fmpq_clear(qr);
return (n == 1);
}
}
int main()
{
long iter;
flint_rand_t state;
printf("agm....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
fmprb_t a, b, c;
fmpq_t q, r;
mpfr_t t, u;
long prec = 2 + n_randint(state, 200);
fmprb_init(a);
fmprb_init(b);
fmprb_init(c);
fmpq_init(q);
fmpq_init(r);
mpfr_init2(t, prec + 100);
mpfr_init2(u, prec + 100);
fmprb_randtest(a, state, 1 + n_randint(state, 200), 3);
fmprb_randtest(b, state, 1 + n_randint(state, 200), 3);
fmprb_randtest(c, state, 1 + n_randint(state, 200), 3);
fmprb_agm(c, a, b, prec);
if (fmprb_equal(a, b))
{
if (!fmprb_contains(c, a))
{
printf("FAIL: containment (identity)\n\n");
printf("a = ");
fmprb_print(a);
printf("\n\n");
printf("b = ");
fmprb_print(b);
printf("\n\n");
printf("c = ");
fmprb_print(c);
printf("\n\n");
abort();
}
}
else
{
fmprb_get_rand_fmpq(q, state, a, 1 + n_randint(state, 200));
fmprb_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 (!fmprb_contains_mpfr(c, t))
{
printf("FAIL: containment\n\n");
printf("a = ");
fmprb_print(a);
printf("\n\n");
printf("b = ");
fmprb_print(b);
printf("\n\n");
printf("c = ");
fmprb_print(c);
printf("\n\n");
abort();
}
}
fmprb_clear(a);
fmprb_clear(b);
fmprb_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(void)
{
int i, result;
ulong cflags = UWORD(0);
FLINT_TEST_INIT(state);
flint_printf("scalar_mul_fmpq....");
fflush(stdout);
/* Check aliasing of a and b */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b;
fmpq_t z;
fmpq_init(z);
fmpq_randtest(z, state, 100);
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_randtest(a, state, n_randint(state, 100), 200);
fmpq_poly_scalar_mul_fmpq(b, a, z);
fmpq_poly_scalar_mul_fmpq(a, a, z);
cflags |= fmpq_poly_is_canonical(a) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(b) ? 0 : 2;
result = (fmpq_poly_equal(a, b) && !cflags);
if (!result)
{
flint_printf("FAIL (aliasing):\n\n");
flint_printf("a = "), fmpq_poly_debug(a), flint_printf("\n\n");
flint_printf("b = "), fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("z = "), fmpq_print(z), flint_printf("\n\n");
gmp_printf("z = %Qd\n\n", z);
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_clear(z);
fmpq_poly_clear(a);
fmpq_poly_clear(b);
}
/* Check that (a * n1) * n2 == a * (n1 * n2) */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, lhs, rhs;
fmpq_t z1, z2, z;
fmpq_init(z1);
fmpq_init(z2);
fmpq_init(z);
fmpq_randtest(z1, state, 100);
fmpq_randtest(z2, state, 100);
fmpq_mul(z, z1, z2);
fmpq_poly_init(a);
fmpq_poly_init(lhs);
fmpq_poly_init(rhs);
fmpq_poly_randtest(a, state, n_randint(state, 100), 200);
fmpq_poly_scalar_mul_fmpq(lhs, a, z1);
fmpq_poly_scalar_mul_fmpq(lhs, lhs, z2);
fmpq_poly_scalar_mul_fmpq(rhs, a, z);
cflags |= fmpq_poly_is_canonical(lhs) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(rhs) ? 0 : 2;
result = (fmpq_poly_equal(lhs, rhs) && !cflags);
if (!result)
{
flint_printf("FAIL (a * n1 * n2):\n");
fmpq_poly_debug(a), flint_printf("\n\n");
flint_printf("z1 = "), fmpq_print(z1), flint_printf("\n\n");
flint_printf("z2 = "), fmpq_print(z2), flint_printf("\n\n");
flint_printf("z = "), fmpq_print(z), flint_printf("\n\n");
fmpq_poly_debug(lhs), flint_printf("\n\n");
fmpq_poly_debug(rhs), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_clear(z1);
fmpq_clear(z2);
fmpq_clear(z);
fmpq_poly_clear(a);
fmpq_poly_clear(lhs);
fmpq_poly_clear(rhs);
}
/* Check that (a + b) * n == a*n + b*n */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpq_poly_t a, b, lhs, rhs;
fmpq_t z;
fmpq_init(z);
fmpq_randtest(z, state, 100);
fmpq_poly_init(a);
fmpq_poly_init(b);
fmpq_poly_init(lhs);
fmpq_poly_init(rhs);
fmpq_poly_randtest(a, state, n_randint(state, 100), 200);
fmpq_poly_randtest(b, state, n_randint(state, 100), 200);
fmpq_poly_scalar_mul_fmpq(lhs, a, z);
fmpq_poly_scalar_mul_fmpq(rhs, b, z);
fmpq_poly_add(rhs, lhs, rhs);
fmpq_poly_add(lhs, a, b);
fmpq_poly_scalar_mul_fmpq(lhs, lhs, z);
cflags |= fmpq_poly_is_canonical(lhs) ? 0 : 1;
cflags |= fmpq_poly_is_canonical(rhs) ? 0 : 2;
result = (fmpq_poly_equal(lhs, rhs) && !cflags);
if (!result)
{
flint_printf("FAIL ((a + b) / n):\n");
fmpq_poly_debug(a), flint_printf("\n\n");
fmpq_poly_debug(b), flint_printf("\n\n");
flint_printf("z = "), fmpq_print(z), flint_printf("\n\n");
fmpq_poly_debug(lhs), flint_printf("\n\n");
fmpq_poly_debug(rhs), flint_printf("\n\n");
flint_printf("cflags = %wu\n\n", cflags);
abort();
}
fmpq_clear(z);
fmpq_poly_clear(a);
fmpq_poly_clear(b);
fmpq_poly_clear(lhs);
fmpq_poly_clear(rhs);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i;
flint_rand_t state;
flint_randinit(state);
printf("bsplit_sum_abpq....");
fflush(stdout);
for (i = 0; i < 10000; i++)
{
fmpq *ab, *pq;
fmpq_t s1, s2, t, pqp;
fmpq_bsplit_t sum;
long k, n;
n = n_randint(state, 40);
ab = _fmpq_vec_init(n);
pq = _fmpq_vec_init(n);
fmpq_init(s1);
fmpq_init(s2);
fmpq_init(pqp);
fmpq_init(t);
for (k = 0; k < n; k++) fmpq_randtest(ab + k, state, 10);
for (k = 0; k < n; k++) fmpq_randtest(pq + k, state, 10);
fmpq_bsplit_init(sum);
fmpq_bsplit_sum_abpq(sum, ab, pq, 0, n);
fmpq_bsplit_get_fmpq(s1, sum);
fmpq_zero(s2);
fmpq_one(pqp);
for (k = 0; k < n; k++)
{
fmpq_mul(pqp, pqp, pq + k);
fmpq_mul(t, pqp, ab + k);
fmpq_add(s2, s2, t);
}
if (!fmpq_is_canonical(s1) || !fmpq_equal(s1, s2))
{
printf("FAIL\n");
printf("(a/b) = ");
for (k = 0; k < n; k++) fmpq_print(ab+k), printf(" ");
printf("\n");
printf("(p/q) = ");
for (k = 0; k < n; k++) fmpq_print(pq+k), printf(" ");
printf("\n");
printf("s1: ");
fmpq_print(s1);
printf("\n");
printf("s2: ");
fmpq_print(s2);
printf("\n");
abort();
}
/* Check numerical evaluation */
{
mpfr_t f1, f2;
mpfr_prec_t prec;
prec = 5 + n_randint(state, 1000);
mpfr_init2(f1, prec);
mpfr_init2(f2, prec);
fmpq_bsplit_get_mpfr(f1, sum);
fmpq_get_mpfr(f2, s1, MPFR_RNDN);
mpfr_sub(f1, f1, f2, MPFR_RNDN);
if (!mpfr_zero_p(f1) &&
!(mpfr_get_exp(f1) <= mpfr_get_exp(f2) - prec + 3))
{
printf("FAIL: numerical evaluation\n");
printf("%ld, %ld, %ld\n", prec, mpfr_get_exp(f1),
mpfr_get_exp(f2) - prec + 3);
abort();
}
mpfr_clear(f1);
mpfr_clear(f2);
}
fmpq_bsplit_clear(sum);
fmpq_clear(s1);
fmpq_clear(s2);
fmpq_clear(pqp);
fmpq_clear(t);
_fmpq_vec_clear(ab, n);
_fmpq_vec_clear(pq, n);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i;
FLINT_TEST_INIT(state);
flint_printf("add....");
fflush(stdout);
/* x = y + z */
for (i = 0; i < 10000; i++)
{
fmpq_t x, y, z;
mpq_t X, Y, Z;
fmpq_init(x);
fmpq_init(y);
fmpq_init(z);
mpq_init(X);
mpq_init(Y);
mpq_init(Z);
fmpq_randtest(x, state, 200);
fmpq_randtest(y, state, 200);
fmpq_randtest(z, state, 200);
fmpq_get_mpq(X, x);
fmpq_get_mpq(Y, y);
fmpq_get_mpq(Z, z);
fmpq_add(x, y, z);
if (!fmpq_is_canonical(x))
{
flint_printf("FAIL: result not canonical!\n");
abort();
}
mpq_add(X, Y, Z);
fmpq_get_mpq(Y, x);
if (!mpq_equal(X, Y))
{
flint_printf("FAIL: fmpq_add(x,y,z) != mpq_add(X,Y,Z)\n");
flint_printf("x = ");
fmpq_print(x);
flint_printf("\ny = ");
fmpq_print(y);
flint_printf("\nz = ");
fmpq_print(z);
flint_printf("\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
fmpq_clear(z);
mpq_clear(X);
mpq_clear(Y);
mpq_clear(Z);
}
/* x = x + y */
for (i = 0; i < 10000; i++)
{
fmpq_t x, y;
mpq_t X, Y;
fmpq_init(x);
fmpq_init(y);
mpq_init(X);
mpq_init(Y);
fmpq_randtest(x, state, 200);
fmpq_randtest(y, state, 200);
fmpq_get_mpq(X, x);
fmpq_get_mpq(Y, y);
fmpq_add(x, x, y);
if (!fmpq_is_canonical(x))
{
flint_printf("FAIL: result not canonical!\n");
abort();
}
mpq_add(X, X, Y);
fmpq_get_mpq(Y, x);
if (!mpq_equal(X, Y))
{
flint_printf("FAIL: fmpq_add(x,x,y) != mpq_add(X,X,Y)\n");
flint_printf("x = ");
fmpq_print(x);
flint_printf("\ny = ");
fmpq_print(y);
flint_printf("\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
mpq_clear(X);
mpq_clear(Y);
}
/* x = y + x */
for (i = 0; i < 10000; i++)
{
fmpq_t x, y;
mpq_t X, Y;
fmpq_init(x);
fmpq_init(y);
mpq_init(X);
mpq_init(Y);
fmpq_randtest(x, state, 200);
fmpq_randtest(y, state, 200);
fmpq_get_mpq(X, x);
fmpq_get_mpq(Y, y);
fmpq_add(x, y, x);
if (!fmpq_is_canonical(x))
{
flint_printf("FAIL: result not canonical!\n");
abort();
}
mpq_add(X, Y, X);
fmpq_get_mpq(Y, x);
if (!mpq_equal(X, Y))
{
flint_printf("FAIL: fmpq_add(x,y,x) != mpq_add(X,Y,X)\n");
flint_printf("x = ");
fmpq_print(x);
flint_printf("\ny = ");
fmpq_print(y);
flint_printf("\n");
abort();
}
fmpq_clear(x);
fmpq_clear(y);
mpq_clear(X);
mpq_clear(Y);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int main()
{
slong iter;
flint_rand_t state;
flint_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;
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_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))
{
flint_printf("FAIL: containment\n\n");
flint_printf("a = "); arb_print(a); flint_printf("\n\n");
flint_printf("b = "); arb_print(b); flint_printf("\n\n");
flint_printf("c = "); arb_print(c); flint_printf("\n\n");
abort();
}
arb_clear(a);
arb_clear(b);
arb_clear(c);
fmpq_clear(q);
fmpq_clear(r);
mpfr_clear(t);
mpfr_clear(u);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("trace....");
fflush(stdout);
flint_randinit(state);
/* check that the acb trace contains the fmpq trace */
for (iter = 0; iter < 10000; iter++)
{
fmpq_mat_t Q;
fmpq_t Qtrace;
acb_mat_t A;
acb_t Atrace;
slong n, qbits, prec;
n = n_randint(state, 8);
qbits = 1 + n_randint(state, 100);
prec = 2 + n_randint(state, 200);
fmpq_mat_init(Q, n, n);
fmpq_init(Qtrace);
acb_mat_init(A, n, n);
acb_init(Atrace);
fmpq_mat_randtest(Q, state, qbits);
fmpq_mat_trace(Qtrace, Q);
acb_mat_set_fmpq_mat(A, Q, prec);
acb_mat_trace(Atrace, A, prec);
if (!acb_contains_fmpq(Atrace, Qtrace))
{
flint_printf("FAIL (containment, iter = %wd)\n", iter);
flint_printf("n = %wd, prec = %wd\n", n, prec);
flint_printf("\n");
flint_printf("Q = \n"); fmpq_mat_print(Q); flint_printf("\n\n");
flint_printf("Qtrace = \n"); fmpq_print(Qtrace); flint_printf("\n\n");
flint_printf("A = \n"); acb_mat_printd(A, 15); flint_printf("\n\n");
flint_printf("Atrace = \n"); acb_printd(Atrace, 15); flint_printf("\n\n");
flint_printf("Atrace = \n"); acb_print(Atrace); flint_printf("\n\n");
abort();
}
fmpq_mat_clear(Q);
fmpq_clear(Qtrace);
acb_mat_clear(A);
acb_clear(Atrace);
}
/* check trace(A*B) = trace(B*A) */
for (iter = 0; iter < 10000; iter++)
{
slong m, n, prec;
acb_mat_t a, b, ab, ba;
acb_t trab, trba;
prec = 2 + n_randint(state, 200);
m = n_randint(state, 10);
n = n_randint(state, 10);
acb_mat_init(a, m, n);
acb_mat_init(b, n, m);
acb_mat_init(ab, m, m);
acb_mat_init(ba, n, n);
acb_init(trab);
acb_init(trba);
acb_mat_randtest(a, state, 2 + n_randint(state, 100), 10);
acb_mat_randtest(b, state, 2 + n_randint(state, 100), 10);
acb_mat_mul(ab, a, b, prec);
acb_mat_mul(ba, b, a, prec);
acb_mat_trace(trab, ab, prec);
acb_mat_trace(trba, ba, prec);
if (!acb_overlaps(trab, trba))
{
flint_printf("FAIL (overlap, iter = %wd)\n", iter);
flint_printf("m = %wd, n = %wd, prec = %wd\n", m, n, prec);
flint_printf("\n");
flint_printf("a = \n"); acb_mat_printd(a, 15); flint_printf("\n\n");
flint_printf("b = \n"); acb_mat_printd(b, 15); flint_printf("\n\n");
flint_printf("ab = \n"); acb_mat_printd(ab, 15); flint_printf("\n\n");
flint_printf("ba = \n"); acb_mat_printd(ba, 15); flint_printf("\n\n");
flint_printf("trace(ab) = \n"); acb_printd(trab, 15); flint_printf("\n\n");
flint_printf("trace(ba) = \n"); acb_printd(trba, 15); flint_printf("\n\n");
}
acb_clear(trab);
acb_clear(trba);
acb_mat_clear(a);
acb_mat_clear(b);
acb_mat_clear(ab);
acb_mat_clear(ba);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void init_set(ElementType& result, const ElementType& a) const {
fmpq_init(&result);
fmpq_set(&result, &a);
}
int
main(void)
{
long i;
flint_rand_t state;
printf("trace....");
fflush(stdout);
flint_randinit(state);
/* Test trace(AB) = trace(BA) */
for (i = 0; i < 1000; i++)
{
fmpq_mat_t A, B, AB, BA;
fmpq_t trab, trba;
long m, n;
m = n_randint(state, 10);
n = n_randint(state, 10);
fmpq_mat_init(A, m, n);
fmpq_mat_init(B, n, m);
fmpq_mat_init(AB, m, m);
fmpq_mat_init(BA, n, n);
fmpq_init(trab);
fmpq_init(trba);
fmpq_mat_randtest(A, state, 1 + n_randint(state, 100));
fmpq_mat_randtest(B, state, 1 + n_randint(state, 100));
fmpq_mat_mul(AB, A, B);
fmpq_mat_mul(BA, B, A);
fmpq_mat_trace(trab, AB);
fmpq_mat_trace(trba, BA);
if (!fmpq_equal(trab, trba))
{
printf("FAIL:\n");
fmpq_mat_print(A), printf("\n");
fmpq_mat_print(B), printf("\n");
fmpq_mat_print(AB), printf("\n");
fmpq_mat_print(BA), printf("\n");
printf("tr(AB): "), fmpq_print(trab), printf("\n");
printf("tr(BA): "), fmpq_print(trba), printf("\n");
abort();
}
fmpq_mat_clear(A);
fmpq_mat_clear(B);
fmpq_mat_clear(AB);
fmpq_mat_clear(BA);
fmpq_clear(trab);
fmpq_clear(trba);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
