void
arb_ui_div(arb_t z, ulong x, const arb_t y, long prec)
{
arb_t t;
arb_init(t);
arb_set_ui(t, x);
arb_div(z, t, y, prec);
arb_clear(t);
}
void arb_twobytwo_diag(arb_t u1, arb_t u2, const arb_t a, const arb_t b, const arb_t d, slong prec) {
// Compute the orthogonal matrix that diagonalizes
//
// A = [a b]
// [b d]
//
// This matrix will have the form
//
// U = [cos x , -sin x]
// [sin x, cos x]
//
// where the diagonal matrix is U^t A U.
// We set u1 = cos x, u2 = -sin x.
if(arb_contains_zero(b)) {
// this is not quite right (doesn't set error intervals)
arb_set_ui(u1, 1);
arb_set_ui(u2, 0);
return;
}
arb_t x; arb_init(x);
arb_mul(u1, b, b, prec); // u1 = b^2
arb_sub(u2, a, d, prec); // u2 = a - d
arb_mul_2exp_si(u2, u2, -1); // u2 = (a - d)/2
arb_mul(u2, u2, u2, prec); // u2 = ( (a - d)/2 )^2
arb_add(u1, u1, u2, prec); // u1 = b^2 + ( (a-d)/2 )^2
arb_sqrt(u1, u1, prec); // u1 = sqrt(above)
arb_mul_2exp_si(u1, u1, 1); // u1 = 2 (sqrt (above) )
arb_add(u1, u1, d, prec); // u1 += d
arb_sub(u1, u1, a, prec); // u1 -= a
arb_mul_2exp_si(u1, u1, -1); // u1 = (d - a)/2 + sqrt(b^2 + ( (a-d)/2 )^2)
arb_mul(x, u1, u1, prec);
arb_addmul(x, b, b, prec); // x = u1^2 + b^2
arb_sqrt(x, x, prec); // x = sqrt(u1^2 + b^2)
arb_div(u2, u1, x, prec);
arb_div(u1, b, x, prec);
arb_neg(u1, u1);
arb_clear(x);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("cauchy_bound....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100; iter++)
{
arb_t b, radius, ans;
acb_t x;
slong r, prec, maxdepth;
arb_init(b);
arb_init(radius);
arb_init(ans);
acb_init(x);
acb_set_ui(x, 5);
r = 1 + n_randint(state, 10);
arb_set_ui(radius, r);
prec = 2 + n_randint(state, 100);
maxdepth = n_randint(state, 10);
acb_calc_cauchy_bound(b, sin_x, NULL, x, radius, maxdepth, prec);
arf_set_d(arb_midref(ans), answers[r-1]);
mag_set_d(arb_radref(ans), 1e-8);
if (!arb_overlaps(b, ans))
{
flint_printf("FAIL\n");
flint_printf("r = %wd, prec = %wd, maxdepth = %wd\n\n", r, prec, maxdepth);
arb_printd(b, 15); flint_printf("\n\n");
arb_printd(ans, 15); flint_printf("\n\n");
abort();
}
arb_clear(b);
arb_clear(radius);
arb_clear(ans);
acb_clear(x);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
acb_modular_is_in_fundamental_domain(const acb_t z, const arf_t tol, long prec)
{
arb_t t;
arb_init(t);
/* require re(w) + 1/2 >= 0 */
arb_set_ui(t, 1);
arb_mul_2exp_si(t, t, -1);
arb_add(t, t, acb_realref(z), prec);
arb_add_arf(t, t, tol, prec);
if (!arb_is_nonnegative(t))
{
arb_clear(t);
return 0;
}
/* require re(w) - 1/2 <= 0 */
arb_set_ui(t, 1);
arb_mul_2exp_si(t, t, -1);
arb_sub(t, acb_realref(z), t, prec);
arb_sub_arf(t, t, tol, prec);
if (!arb_is_nonpositive(t))
{
arb_clear(t);
return 0;
}
/* require |w| >= 1 - tol, i.e. |w| - 1 + tol >= 0 */
acb_abs(t, z, prec);
arb_sub_ui(t, t, 1, prec);
arb_add_arf(t, t, tol, prec);
if (!arb_is_nonnegative(t))
{
arb_clear(t);
return 0;
}
arb_clear(t);
return 1;
}
int main()
{
long iter;
flint_rand_t state;
printf("div_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c, d;
ulong x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
arb_init(d);
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);
x = n_randtest(state);
prec = 2 + n_randint(state, 2000);
arb_set_ui(b, x);
arb_div_ui(c, a, x, prec);
arb_div(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);
}
/* aliasing */
for (iter = 0; iter < 10000; iter++)
{
arb_t a, b, c;
ulong x;
long prec;
arb_init(a);
arb_init(b);
arb_init(c);
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);
x = n_randtest(state);
prec = 2 + n_randint(state, 2000);
arb_set_ui(b, x);
arb_div_ui(c, a, x, prec);
arb_div_ui(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);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("rising_ui_series....");
fflush(stdout);
flint_randinit(state);
/* check rf(f, a) * rf(f + a, b) = rf(f, a + b) */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
slong bits, trunc;
ulong a, b;
arb_poly_t f, g, h1, h2, h1h2, h3;
bits = 2 + n_randint(state, 200);
trunc = 1 + n_randint(state, 20);
a = n_randint(state, 10);
b = n_randint(state, 10);
arb_poly_init(f);
arb_poly_init(g);
arb_poly_init(h1);
arb_poly_init(h2);
arb_poly_init(h1h2);
arb_poly_init(h3);
arb_poly_randtest(f, state, 1 + n_randint(state, 20), bits, 4);
arb_poly_set(g, f);
/* g = f + 1 */
if (g->length == 0)
{
arb_poly_fit_length(g, 1);
arb_set_ui(g->coeffs, a);
_arb_poly_set_length(g, 1);
_arb_poly_normalise(g);
}
else
{
arb_add_ui(g->coeffs, g->coeffs, a, bits);
_arb_poly_normalise(g);
}
arb_poly_rising_ui_series(h1, f, a, trunc, bits);
arb_poly_rising_ui_series(h2, g, b, trunc, bits);
arb_poly_rising_ui_series(h3, f, a + b, trunc, bits);
arb_poly_mullow(h1h2, h1, h2, trunc, bits);
if (!arb_poly_overlaps(h1h2, h3))
{
flint_printf("FAIL\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("trunc = %wd\n", trunc);
flint_printf("a = %wu\n", a);
flint_printf("b = %wu\n", a);
flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("g = "); arb_poly_printd(g, 15); flint_printf("\n\n");
flint_printf("h1 = "); arb_poly_printd(h1, 15); flint_printf("\n\n");
flint_printf("h2 = "); arb_poly_printd(h2, 15); flint_printf("\n\n");
flint_printf("h1h2 = "); arb_poly_printd(h1h2, 15); flint_printf("\n\n");
flint_printf("h3 = "); arb_poly_printd(h3, 15); flint_printf("\n\n");
abort();
}
arb_poly_rising_ui_series(f, f, a, trunc, bits);
if (!arb_poly_equal(f, h1))
{
flint_printf("FAIL (aliasing)\n\n");
flint_printf("bits = %wd\n", bits);
flint_printf("trunc = %wd\n", trunc);
flint_printf("a = %wu\n", a);
flint_printf("b = %wu\n", a);
flint_printf("f = "); arb_poly_printd(f, 15); flint_printf("\n\n");
flint_printf("h1 = "); arb_poly_printd(h1, 15); flint_printf("\n\n");
abort();
}
arb_poly_clear(f);
arb_poly_clear(g);
arb_poly_clear(h1);
arb_poly_clear(h2);
arb_poly_clear(h1h2);
arb_poly_clear(h3);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("zeta_cpx_series....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
acb_t s, a;
acb_ptr z1, z2;
slong i, len, prec1, prec2;
int deflate;
acb_init(s);
acb_init(a);
if (n_randint(state, 2))
{
acb_randtest(s, state, 1 + n_randint(state, 300), 3);
}
else
{
arb_set_ui(acb_realref(s), 1);
arb_mul_2exp_si(acb_realref(s), acb_realref(s), -1);
arb_randtest(acb_imagref(s), state, 1 + n_randint(state, 300), 4);
}
switch (n_randint(state, 3))
{
case 0:
acb_randtest(a, state, 1 + n_randint(state, 300), 3);
break;
case 1:
arb_randtest(acb_realref(a), state, 1 + n_randint(state, 300), 3);
break;
case 2:
acb_one(a);
break;
}
prec1 = 2 + n_randint(state, 300);
prec2 = prec1 + 30;
len = 1 + n_randint(state, 20);
deflate = n_randint(state, 2);
z1 = _acb_vec_init(len);
z2 = _acb_vec_init(len);
_acb_poly_zeta_cpx_series(z1, s, a, deflate, len, prec1);
_acb_poly_zeta_cpx_series(z2, s, a, deflate, len, prec2);
for (i = 0; i < len; i++)
{
if (!acb_overlaps(z1 + i, z2 + i))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("iter = %wd\n", iter);
flint_printf("deflate = %d, len = %wd, i = %wd\n\n", deflate, len, i);
flint_printf("s = "); acb_printd(s, prec1 / 3.33); flint_printf("\n\n");
flint_printf("a = "); acb_printd(a, prec1 / 3.33); flint_printf("\n\n");
flint_printf("z1 = "); acb_printd(z1 + i, prec1 / 3.33); flint_printf("\n\n");
flint_printf("z2 = "); acb_printd(z2 + i, prec2 / 3.33); flint_printf("\n\n");
abort();
}
}
acb_clear(a);
acb_clear(s);
_acb_vec_clear(z1, len);
_acb_vec_clear(z2, len);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("solve_tril....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 2000 * arb_test_multiplier(); iter++)
{
arb_mat_t A, X, B, Y;
slong rows, cols, prec, i, j;
int unit;
prec = 2 + n_randint(state, 200);
if (n_randint(state, 10) == 0)
{
rows = n_randint(state, 60);
cols = n_randint(state, 60);
}
else
{
rows = n_randint(state, 10);
cols = n_randint(state, 10);
}
unit = n_randint(state, 2);
arb_mat_init(A, rows, rows);
arb_mat_init(B, rows, cols);
arb_mat_init(X, rows, cols);
arb_mat_init(Y, rows, cols);
arb_mat_randtest(A, state, prec, 10);
arb_mat_randtest(X, state, prec, 10);
arb_mat_randtest(Y, state, prec, 10);
for (i = 0; i < rows; i++)
{
if (unit)
arb_one(arb_mat_entry(A, i, i));
else
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
for (j = i + 1; j < rows; j++)
arb_zero(arb_mat_entry(A, i, j));
}
arb_mat_mul(B, A, X, prec);
if (unit) /* check that diagonal entries are ignored */
{
for (i = 0; i < rows; i++)
arb_set_ui(arb_mat_entry(A, i, i), 1 + n_randint(state, 100));
}
/* Check Y = A^(-1) * (A * X) = X */
arb_mat_solve_tril(Y, A, B, unit, prec);
if (!arb_mat_overlaps(Y, X))
{
flint_printf("FAIL\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
/* Check aliasing */
arb_mat_solve_tril(B, A, B, unit, prec);
if (!arb_mat_equal(B, Y))
{
flint_printf("FAIL (aliasing)\n");
flint_printf("A = \n"); arb_mat_printd(A, 10); flint_printf("\n\n");
flint_printf("B = \n"); arb_mat_printd(B, 10); flint_printf("\n\n");
flint_printf("X = \n"); arb_mat_printd(X, 10); flint_printf("\n\n");
flint_printf("Y = \n"); arb_mat_printd(Y, 10); flint_printf("\n\n");
flint_abort();
}
arb_mat_clear(A);
arb_mat_clear(B);
arb_mat_clear(X);
arb_mat_clear(Y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("bernoulli_poly_ui....");
fflush(stdout);
flint_randinit(state);
/* test multiplication theorem */
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
arb_t x, t, res1, res2;
ulong n, m, k;
slong prec;
n = n_randint(state, 50);
m = 1 + n_randint(state, 5);
prec = 2 + n_randint(state, 200);
arb_init(x);
arb_init(t);
arb_init(res1);
arb_init(res2);
arb_randtest(x, state, 2 + n_randint(state, 200), 20);
arb_randtest(res1, state, 2 + n_randint(state, 200), 20);
arb_mul_ui(t, x, m, prec);
arb_bernoulli_poly_ui(res1, n, t, prec);
arb_zero(res2);
for (k = 0; k < m; k++)
{
arb_set_ui(t, k);
arb_div_ui(t, t, m, prec);
arb_add(t, t, x, prec);
arb_bernoulli_poly_ui(t, n, t, prec);
arb_add(res2, res2, t, prec);
}
if (n > 0)
{
arb_ui_pow_ui(t, m, n - 1, prec);
arb_mul(res2, res2, t, prec);
}
else
{
arb_div_ui(res2, res2, m, prec);
}
if (!arb_overlaps(res1, res2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu, m = %wu\n\n", n, m);
flint_printf("x = "); arb_printd(x, 15); flint_printf("\n\n");
flint_printf("res1 = "); arb_printd(res1, 15); flint_printf("\n\n");
flint_printf("res2 = "); arb_printd(res2, 15); flint_printf("\n\n");
abort();
}
arb_clear(x);
arb_clear(t);
arb_clear(res1);
arb_clear(res2);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
void arb_fib_fmpz(arb_t f, const fmpz_t n, slong prec)
{
arb_t t, u;
slong wp, sign, i;
if (fmpz_sgn(n) < 0)
{
fmpz_t m;
fmpz_init(m);
fmpz_neg(m, n);
arb_fib_fmpz(f, m, prec);
if (fmpz_is_even(m))
arb_neg(f, f);
fmpz_clear(m);
return;
}
if (fmpz_cmp_ui(n, 4) <= 0)
{
ulong x = fmpz_get_ui(n);
arb_set_ui(f, x - (x > 1));
return;
}
wp = ARF_PREC_ADD(prec, 3 * fmpz_bits(n));
arb_init(u);
arb_init(t);
arb_set_ui(f, UWORD(1));
arb_set_ui(u, UWORD(1));
sign = -1;
for (i = fmpz_flog_ui(n, UWORD(2)) - 1; i > 0; i--)
{
arb_mul(t, f, f, wp);
arb_add(f, f, u, wp);
arb_mul_2exp_si(f, f, -1);
arb_mul(f, f, f, wp);
arb_mul_2exp_si(f, f, 1);
arb_submul_ui(f, t, 3, wp);
arb_sub_si(f, f, 2 * sign, wp);
arb_mul_ui(u, t, 5, wp);
arb_add_si(u, u, 2 * sign, wp);
sign = 1;
if (fmpz_tstbit(n, i))
{
arb_set(t, f);
arb_add(f, f, u, wp);
arb_mul_2exp_si(f, f, -1);
arb_mul_2exp_si(t, t, 1);
arb_add(u, f, t, wp);
sign = -1;
}
}
if (fmpz_tstbit(n, 0))
{
arb_add(f, f, u, wp);
arb_mul_2exp_si(f, f, -1);
arb_mul(f, f, u, wp);
arb_sub_si(f, f, sign, prec);
}
else
{
arb_mul(f, f, u, prec);
}
arb_clear(u);
arb_clear(t);
}
static int
arb_set_float_str(arb_t res, const char * inp, slong prec)
{
char * emarker;
char * buf;
int error;
slong i;
fmpz_t exp;
fmpz_t man;
slong num_int, num_frac;
int after_radix;
if (inp[0] == '+')
{
return arb_set_float_str(res, inp + 1, prec);
}
if (inp[0] == '-')
{
error = arb_set_float_str(res, inp + 1, prec);
arb_neg(res, res);
return error;
}
if (strcmp(inp, "inf") == 0)
{
arb_pos_inf(res);
return 0;
}
if (strcmp(inp, "nan") == 0)
{
arb_indeterminate(res);
return 0;
}
error = 0;
fmpz_init(exp);
fmpz_init(man);
buf = flint_malloc(strlen(inp) + 1);
emarker = strchr(inp, 'e');
/* parse exponent (0 by default) */
if (emarker != NULL)
{
/* allow e+42 as well as e42 */
if (emarker[1] == '+')
{
if (!(emarker[2] >= '0' && emarker[2] <= '9'))
error = 1;
else
error = fmpz_set_str(exp, emarker + 2, 10);
}
else
error = fmpz_set_str(exp, emarker + 1, 10);
if (error)
goto cleanup;
}
/* parse floating-point part */
{
num_int = 0;
num_frac = 0;
after_radix = 0;
for (i = 0; inp + i != emarker && inp[i] != '\0'; i++)
{
if (inp[i] == '.' && !after_radix)
{
after_radix = 1;
}
else if (inp[i] >= '0' && inp[i] <= '9')
{
buf[num_int + num_frac] = inp[i];
num_frac += after_radix;
num_int += !after_radix;
}
else
{
error = 1;
goto cleanup;
}
}
buf[num_int + num_frac] = '\0';
/* put trailing zeros into the exponent */
while (num_int + num_frac > 1 && buf[num_int + num_frac - 1] == '0')
{
buf[num_int + num_frac - 1] = '\0';
num_frac--;
}
fmpz_sub_si(exp, exp, num_frac);
error = fmpz_set_str(man, buf, 10);
if (error)
goto cleanup;
}
if (fmpz_is_zero(man))
{
arb_zero(res);
}
else if (fmpz_is_zero(exp))
{
arb_set_round_fmpz(res, man, prec);
}
else
{
arb_t t;
arb_init(t);
arb_set_ui(t, 10);
arb_set_fmpz(res, man);
if (fmpz_sgn(exp) > 0)
{
arb_pow_fmpz_binexp(t, t, exp, prec + 4);
arb_mul(res, res, t, prec);
}
else
{
fmpz_neg(exp, exp);
arb_pow_fmpz_binexp(t, t, exp, prec + 4);
arb_div(res, res, t, prec);
}
arb_clear(t);
}
cleanup:
fmpz_clear(exp);
fmpz_clear(man);
flint_free(buf);
if (error)
arb_indeterminate(res);
return error;
}
void Lib_Arb_Set_Ui(ArbPtr x, uint32_t a)
{
arb_set_ui( (arb_ptr) x, a);
}
void Lib_Arb_Mat_Set_Ui(ArbMatPtr A, int32_t i, int32_t j, int32_t u)
{
arb_set_ui ( arb_mat_entry ((arb_mat_struct*)A, i, j), u);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("central_bin_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000 * arb_test_multiplier(); iter++)
{
arb_t b1, b2, t;
ulong n;
slong prec1, prec2, acc1;
n = n_randtest(state);
prec1 = 2 + n_randint(state, 1000);
prec2 = prec1 + 30;
arb_init(b1);
arb_init(b2);
arb_init(t);
arb_hypgeom_central_bin_ui(b1, n, prec1);
arb_set_ui(t, n);
arb_add_ui(t, t, n, prec2);
arb_add_ui(t, t, 1, prec2);
arb_gamma(t, t, prec2);
arb_set_ui(b2, n);
arb_add_ui(b2, b2, 1, prec2);
arb_rgamma(b2, b2, prec2);
arb_mul(b2, b2, b2, prec2);
arb_mul(b2, b2, t, prec2);
if (!arb_overlaps(b1, b2))
{
flint_printf("FAIL: overlap\n\n");
flint_printf("n = %wu\n\n", n);
flint_printf("b1 = "); arb_printn(b1, 50, 0); flint_printf("\n\n");
flint_printf("b2 = "); arb_printn(b2, 50, 0); flint_printf("\n\n");
flint_abort();
}
acc1 = arb_rel_accuracy_bits(b1);
if (acc1 < prec1 - 2)
{
flint_printf("FAIL: poor accuracy\n\n");
flint_printf("prec1 = %wd, acc1 = %wd\n", prec1, acc1);
flint_printf("b1 = "); arb_printn(b1, prec1 / 3.33, 0); flint_printf("\n\n");
flint_printf("b2 = "); arb_printn(b2, prec2 / 3.33, 0); flint_printf("\n\n");
flint_abort();
}
arb_clear(b1);
arb_clear(b2);
arb_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}