static slong _fmpr_add_special(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
if (fmpr_is_zero(x))
{
if (fmpr_is_zero(y))
{
fmpr_zero(z);
return FMPR_RESULT_EXACT;
}
else
return fmpr_set_round(z, y, prec, rnd);
}
else if (fmpr_is_zero(y))
{
return fmpr_set_round(z, x, prec, rnd);
}
else if (fmpr_is_nan(x) || fmpr_is_nan(y)
|| (fmpr_is_pos_inf(x) && fmpr_is_neg_inf(y))
|| (fmpr_is_neg_inf(x) && fmpr_is_pos_inf(y)))
{
fmpr_nan(z);
return FMPR_RESULT_EXACT;
}
else if (fmpr_is_special(x))
{
fmpr_set(z, x);
return FMPR_RESULT_EXACT;
}
else
{
fmpr_set(z, y);
return FMPR_RESULT_EXACT;
}
}
void
_fmpcb_poly_refine_roots_durand_kerner(fmpcb_ptr roots,
fmpcb_srcptr poly, long len, long prec)
{
long i, j;
fmpcb_t x, y, t;
fmpcb_init(x);
fmpcb_init(y);
fmpcb_init(t);
for (i = 0; i < len - 1; i++)
{
_fmpcb_poly_evaluate_mid(x, poly, len, roots + i, prec);
fmpcb_set(y, poly + len - 1);
for (j = 0; j < len - 1; j++)
{
if (i != j)
{
fmpcb_sub_mid(t, roots + i, roots + j, prec);
fmpcb_mul_mid(y, y, t, prec);
}
}
fmpr_zero(fmprb_radref(fmpcb_realref(y)));
fmpr_zero(fmprb_radref(fmpcb_imagref(y)));
fmpcb_inv_mid(t, y, prec);
fmpcb_mul_mid(t, t, x, prec);
fmpcb_sub_mid(roots + i, roots + i, t, prec);
fmpr_set_round(fmprb_radref(fmpcb_realref(roots + i)),
fmprb_midref(fmpcb_realref(t)), FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_set_round(fmprb_radref(fmpcb_imagref(roots + i)),
fmprb_midref(fmpcb_imagref(t)), FMPRB_RAD_PREC, FMPR_RND_UP);
}
fmpcb_clear(x);
fmpcb_clear(y);
fmpcb_clear(t);
}
slong
fmpr_rsqrt(fmpr_t y, const fmpr_t x, slong prec, fmpr_rnd_t rnd)
{
slong r;
if (fmpr_is_special(x))
{
if (fmpr_is_zero(x))
fmpr_pos_inf(y);
else if (fmpr_is_pos_inf(x))
fmpr_zero(y);
else
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
if (fmpr_sgn(x) < 0)
{
fmpr_nan(y);
return FMPR_RESULT_EXACT;
}
/* special case: 4^n */
if (fmpz_is_one(fmpr_manref(x)) && fmpz_is_even(fmpr_expref(x)))
{
r = fmpr_set_round(y, x, prec, rnd);
fmpz_tdiv_q_2exp(fmpr_expref(y), fmpr_expref(y), 1);
fmpz_neg(fmpr_expref(y), fmpr_expref(y));
return r;
}
{
fmpr_t t;
fmpz_t e;
fmpr_init(t);
fmpz_init(e);
fmpz_neg(e, fmpr_expref(x));
if (fmpz_is_odd(e))
fmpz_add_ui(e, e, 1);
fmpr_mul_2exp_fmpz(t, x, e);
CALL_MPFR_FUNC(r, mpfr_rec_sqrt, y, t, prec, rnd);
fmpz_tdiv_q_2exp(e, e, 1);
fmpr_mul_2exp_fmpz(y, y, e);
fmpr_clear(t);
fmpz_clear(e);
return r;
}
}
void _fmpr_fmpz_vec_max_norm(fmpr_t norm, const fmpz * vec, long len, long prec)
{
fmpr_set_fmpz(norm, vec + _fmpz_vec_height_index(vec, len));
fmpr_set_round(norm, norm, prec, FMPR_RND_UP);
fmpr_abs(norm, norm);
}
int main()
{
long iter;
flint_rand_t state;
printf("set_round_ui_2exp_fmpz....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 100000; iter++)
{
long prec, ret1, ret2;
fmpz_t man, exp;
fmpr_t x, y;
mp_limb_t lo;
fmpr_rnd_t rnd;
int negative;
fmpz_init(man);
fmpz_init(exp);
fmpr_init(x);
fmpr_init(y);
prec = 2 + n_randint(state, 1000);
if (n_randint(state, 10) == 0)
prec = FMPR_PREC_EXACT;
negative = n_randint(state, 2);
lo = n_randtest(state);
fmpz_randtest(exp, state, 1 + n_randint(state, 100));
if (negative)
fmpz_neg_ui(man, lo);
else
fmpz_set_ui(man, lo);
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
ret1 = fmpr_set_round_ui_2exp_fmpz(x, lo, exp, negative, prec, rnd);
fmpr_set_fmpz_2exp(y, man, exp);
ret2 = fmpr_set_round(y, y, prec, rnd);
if (!fmpr_equal(x, y) || ret1 != ret2 ||
!fmpr_check_ulp(x, ret1, prec) || !fmpr_check_ulp(y, ret2, prec))
{
printf("FAIL\n\n");
printf("prec: %ld\n", prec);
printf("man = "); fmpz_print(man); printf("\n\n");
printf("exp = "); fmpz_print(exp); printf("\n\n");
printf("x = "); fmpr_print(x); printf("\n\n");
printf("y = "); fmpr_print(y); printf("\n\n");
printf("ret1 = %ld, ret2 = %ld\n\n", ret1, ret2);
abort();
}
fmpz_clear(man);
fmpz_clear(exp);
fmpr_clear(x);
fmpr_clear(y);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
int main()
{
slong iter;
flint_rand_t state;
flint_printf("sum....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000000 * arb_test_multiplier(); iter++)
{
slong i, len, prec, bits, expbits, res1, res2;
fmpr_t s1, s2, s3, err, err_bound;
fmpr_struct terms[20];
fmpr_rnd_t rnd;
len = n_randint(state, 20);
bits = 2 + n_randint(state, 1000);
prec = 2 + n_randint(state, 1000);
expbits = n_randint(state, 14);
fmpr_init(s1);
fmpr_init(s2);
fmpr_init(s3);
fmpr_init(err);
fmpr_init(err_bound);
for (i = 0; i < len; i++)
{
fmpr_init(terms + i);
fmpr_randtest_special(terms + i, state, bits, expbits);
}
switch (n_randint(state, 4))
{
case 0: rnd = FMPR_RND_DOWN; break;
case 1: rnd = FMPR_RND_UP; break;
case 2: rnd = FMPR_RND_FLOOR; break;
default: rnd = FMPR_RND_CEIL; break;
}
res1 = fmpr_sum(s1, terms, len, prec, rnd);
fmpr_zero(s2);
for (i = 0; i < len; i++)
fmpr_add(s2, s2, terms + i, FMPR_PREC_EXACT, FMPR_RND_DOWN);
res2 = fmpr_set_round(s3, s2, prec, rnd);
if (!fmpr_equal(s1, s3) || res1 != res2 ||
!fmpr_check_ulp(s1, res1, prec) || !fmpr_check_ulp(s3, res2, prec))
{
flint_printf("FAIL (%wd)\n\n", iter);
flint_printf("prec = %wd\n\n", prec);
for (i = 0; i < len; i++)
{
flint_printf("terms[%wd] = ", i); fmpr_print(terms + i); flint_printf("\n\n");
}
flint_printf("s1 = "); fmpr_print(s1); flint_printf("\n\n");
flint_printf("s2 = "); fmpr_print(s2); flint_printf("\n\n");
flint_printf("s3 = "); fmpr_print(s3); flint_printf("\n\n");
flint_printf("res1 = %wd, res2 = %wd\n\n", res1, res2);
abort();
}
fmpr_sub(err, s1, s2, FMPR_PREC_EXACT, FMPR_RND_DOWN);
fmpr_abs(err, err);
fmpr_set_error_result(err_bound, s1, res1);
if (fmpr_cmp(err, err_bound) > 0)
{
flint_printf("FAIL (error bound)!\n");
flint_printf("prec = %wd\n\n", prec);
for (i = 0; i < len; i++)
{
flint_printf("terms[%wd] = ", i); fmpr_print(terms + i); flint_printf("\n\n");
}
flint_printf("s1 = "); fmpr_print(s1); flint_printf("\n\n");
flint_printf("s2 = "); fmpr_print(s2); flint_printf("\n\n");
flint_printf("s3 = "); fmpr_print(s3); flint_printf("\n\n");
flint_printf("error: "); fmpr_print(err); flint_printf("\n\n");
flint_printf("error bound: "); fmpr_print(err_bound); flint_printf("\n\n");
flint_printf("res1 = %wd, res2 = %wd\n\n", res1, res2);
abort();
}
fmpr_clear(s1);
fmpr_clear(s2);
fmpr_clear(s3);
fmpr_clear(err);
fmpr_clear(err_bound);
for (i = 0; i < len; i++)
fmpr_clear(terms + i);
}
flint_randclear(state);
flint_cleanup();
flint_printf("PASS\n");
return EXIT_SUCCESS;
}