void
arb_pow(arb_t z, const arb_t x, const arb_t y, slong prec)
{
if (arb_is_zero(y))
{
arb_one(z);
return;
}
if (arb_is_zero(x))
{
if (arb_is_positive(y))
arb_zero(z);
else
arb_indeterminate(z);
return;
}
if (arb_is_exact(y) && !arf_is_special(arb_midref(x)))
{
const arf_struct * ymid = arb_midref(y);
/* small half-integer or integer */
if (arf_cmpabs_2exp_si(ymid, BINEXP_LIMIT) < 0 &&
arf_is_int_2exp_si(ymid, -1))
{
fmpz_t e;
fmpz_init(e);
if (arf_is_int(ymid))
{
arf_get_fmpz_fixed_si(e, ymid, 0);
arb_pow_fmpz_binexp(z, x, e, prec);
}
else
{
arf_get_fmpz_fixed_si(e, ymid, -1);
arb_sqrt(z, x, prec + fmpz_bits(e));
arb_pow_fmpz_binexp(z, z, e, prec);
}
fmpz_clear(e);
return;
}
else if (arf_is_int(ymid) && arf_sgn(arb_midref(x)) < 0)
{
/* use (-x)^n = (-1)^n * x^n to avoid NaNs
at least at high enough precision */
int odd = !arf_is_int_2exp_si(ymid, 1);
_arb_pow_exp(z, x, 1, y, prec);
if (odd)
arb_neg(z, z);
return;
}
}
_arb_pow_exp(z, x, 0, y, prec);
}
void
arf_ceil(arf_t z, const arf_t x)
{
if (arf_is_special(x) || arf_is_int(x))
{
arf_set(z, x);
}
else
{
slong exp = ARF_EXP(x);
/* now exp cannot be too large, as we would have
caught this in arf_is_int() */
if (COEFF_IS_MPZ(exp) || exp <= 0)
{
if (ARF_SGNBIT(x))
arf_zero(z);
else
arf_one(z);
}
else if (exp == 1)
{
arf_set_si(z, ARF_SGNBIT(x) ? -1 : 2);
}
else
{
arf_set_round(z, x, exp, ARF_RND_CEIL);
}
}
}
void
acb_pow_arb(acb_t z, const acb_t x, const arb_t y, long prec)
{
const arf_struct * ymid = arb_midref(y);
const mag_struct * yrad = arb_radref(y);
if (arb_is_zero(y))
{
acb_one(z);
return;
}
if (mag_is_zero(yrad))
{
/* small half-integer or integer */
if (arf_cmpabs_2exp_si(ymid, BINEXP_LIMIT) < 0 &&
arf_is_int_2exp_si(ymid, -1))
{
fmpz_t e;
fmpz_init(e);
if (arf_is_int(ymid))
{
arf_get_fmpz_fixed_si(e, ymid, 0);
acb_pow_fmpz_binexp(z, x, e, prec);
}
else
{
/* hack: give something finite here (should fix sqrt/rsqrt etc) */
if (arb_contains_zero(acb_imagref(x)) && arb_contains_nonpositive(acb_realref(x)))
{
_acb_pow_arb_exp(z, x, y, prec);
fmpz_clear(e);
return;
}
arf_get_fmpz_fixed_si(e, ymid, -1);
acb_sqrt(z, x, prec + fmpz_bits(e));
acb_pow_fmpz_binexp(z, z, e, prec);
}
fmpz_clear(e);
return;
}
}
_acb_pow_arb_exp(z, x, y, prec);
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("is_int_2exp_si....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000 * arb_test_multiplier(); iter++)
{
arf_t x, y;
fmpz_t t;
slong e;
int res1, res2;
arf_init(x);
arf_init(y);
fmpz_init(t);
arf_randtest_special(x, state, 2000, 100);
e = n_randtest(state);
arf_mul_2exp_si(y, x, e);
res1 = arf_is_int(x);
res2 = arf_is_int_2exp_si(y, e);
if (res1 != res2)
{
flint_printf("FAIL! (1)\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("res1 = %d, res2 = %d\n\n", res1, res2);
abort();
}
if (res1)
{
if (n_randint(state, 2))
arf_floor(y, x);
else
arf_ceil(y, x);
if (!arf_equal(x, y) || !arf_is_finite(x))
{
flint_printf("FAIL! (2)\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("res1 = %d\n\n", res1);
abort();
}
}
if (arf_is_finite(x) && !arf_is_zero(x))
{
arf_bot(t, x);
fmpz_neg(t, t);
arf_mul_2exp_fmpz(x, x, t);
res1 = arf_is_int(x);
arf_mul_2exp_si(y, x, -1);
res2 = arf_is_int(y);
if (!arf_is_int(x) || arf_is_int(y))
{
flint_printf("FAIL! (3)\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
flint_printf("res1 = %d, res2 = %d\n\n", res1, res2);
abort();
}
}
arf_clear(x);
arf_clear(y);
fmpz_clear(t);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
arb_get_unique_fmpz(fmpz_t z, const arb_t x)
{
if (!arb_is_finite(x))
{
return 0;
}
else if (arb_is_exact(x))
{
/* x = b*2^e, e >= 0 */
if (arf_is_int(arb_midref(x)))
{
/* arf_get_fmpz aborts on overflow */
arf_get_fmpz(z, arb_midref(x), ARF_RND_DOWN);
return 1;
}
else
{
return 0;
}
}
/* if the radius is >= 1, there are at least two integers */
else if (mag_cmp_2exp_si(arb_radref(x), 0) >= 0)
{
return 0;
}
/* there are 0 or 1 integers if the radius is < 1 */
else
{
fmpz_t a, b, exp;
int res;
/* if the midpoint is exactly an integer, it is what we want */
if (arf_is_int(arb_midref(x)))
{
/* arf_get_fmpz aborts on overflow */
arf_get_fmpz(z, arb_midref(x), ARF_RND_DOWN);
return 1;
}
fmpz_init(a);
fmpz_init(b);
fmpz_init(exp);
/* if the radius is tiny, it can't be an integer */
arf_bot(a, arb_midref(x));
if (fmpz_cmp(a, MAG_EXPREF(arb_radref(x))) > 0)
{
res = 0;
}
else
{
arb_get_interval_fmpz_2exp(a, b, exp, x);
if (COEFF_IS_MPZ(*exp))
{
flint_printf("arb_get_unique_fmpz: input too large\n");
abort();
}
if (*exp >= 0)
{
res = fmpz_equal(a, b);
if (res)
{
fmpz_mul_2exp(a, a, *exp);
fmpz_mul_2exp(b, b, *exp);
}
}
else
{
fmpz_cdiv_q_2exp(a, a, -(*exp));
fmpz_fdiv_q_2exp(b, b, -(*exp));
res = fmpz_equal(a, b);
}
if (res)
fmpz_set(z, a);
}
fmpz_clear(a);
fmpz_clear(b);
fmpz_clear(exp);
return res;
}
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("floor....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 10000; iter++)
{
arf_t x, y;
int result;
arf_init(x);
arf_init(y);
arf_randtest_special(x, state, 2000, 100);
arf_randtest_special(y, state, 2000, 100);
arf_floor(y, x);
result = 1;
if (arf_is_int(x) || !arf_is_finite(x))
{
result = arf_equal(y, x);
}
else if (!arf_is_int(y))
{
result = 0;
}
else if (arf_cmp(y, x) >= 0)
{
result = 0;
}
else
{
arf_t s, t[3];
/* check floor(x) - x + 1 > 0 */
arf_init(s);
arf_init(t[0]);
arf_init(t[1]);
arf_init(t[2]);
arf_set(t[0], y);
arf_neg(t[1], x);
arf_one(t[2]);
arf_sum(s, (arf_ptr) t, 3, 32, ARF_RND_DOWN);
result = arf_sgn(s) > 0;
arf_clear(s);
arf_clear(t[0]);
arf_clear(t[1]);
arf_clear(t[2]);
}
if (!result)
{
flint_printf("FAIL!\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
abort();
}
arf_floor(x, x);
if (!arf_equal(x, y))
{
flint_printf("FAIL (aliasing)!\n");
flint_printf("x = "); arf_print(x); flint_printf("\n\n");
flint_printf("y = "); arf_print(y); flint_printf("\n\n");
abort();
}
arf_clear(x);
arf_clear(y);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
