int
arf_sub_special(arf_t z, const arf_t x, const arf_t y, slong prec, arf_rnd_t rnd)
{
if (arf_is_zero(x))
{
if (arf_is_zero(y))
{
arf_zero(z);
return 0;
}
else
return arf_neg_round(z, y, prec, rnd);
}
else if (arf_is_zero(y))
{
return arf_set_round(z, x, prec, rnd);
}
else if (arf_is_nan(x) || arf_is_nan(y)
|| (arf_is_pos_inf(x) && arf_is_pos_inf(y))
|| (arf_is_neg_inf(x) && arf_is_neg_inf(y)))
{
arf_nan(z);
return 0;
}
else if (arf_is_special(x))
{
arf_set(z, x);
return 0;
}
else
{
arf_neg(z, y);
return 0;
}
}
static void
arb_infimum(arf_t res, const arb_t x)
{
if (arf_is_nan(arb_midref(x)))
{
arf_nan(res);
}
else if (mag_is_inf(arb_radref(x)))
{
arf_neg_inf(res);
}
else
{
arf_set_mag(res, arb_radref(x));
arf_sub(res, arb_midref(x), res, ARF_PREC_EXACT, ARF_RND_FLOOR);
}
}
static void
arb_supremum(arf_t res, const arb_t x)
{
if (arf_is_nan(arb_midref(x)))
{
arf_nan(res);
}
else if (mag_is_inf(arb_radref(x)))
{
arf_pos_inf(res);
}
else
{
arf_set_mag(res, arb_radref(x));
arf_add(res, res, arb_midref(x), ARF_PREC_EXACT, ARF_RND_CEIL);
}
}
void
arf_set_fmpr(arf_t y, const fmpr_t x)
{
if (fmpr_is_special(x))
{
if (fmpr_is_zero(x))
arf_zero(y);
else if (fmpr_is_pos_inf(x))
arf_pos_inf(y);
else if (fmpr_is_neg_inf(x))
arf_neg_inf(y);
else
arf_nan(y);
}
else
{
arf_set_fmpz(y, fmpr_manref(x));
fmpz_add_inline(ARF_EXPREF(y), ARF_EXPREF(y), fmpr_expref(x));
}
}
int
arf_root(arf_ptr z, arf_srcptr x, ulong k, slong prec, arf_rnd_t rnd)
{
mp_size_t xn, zn, val;
mp_srcptr xptr;
mp_ptr tmp, zptr;
mpfr_t xf, zf;
fmpz_t q, r;
int inexact;
if (k == 0)
{
arf_nan(z);
return 0;
}
if (k == 1)
return arf_set_round(z, x, prec, rnd);
if (k == 2)
return arf_sqrt(z, x, prec, rnd);
if (arf_is_special(x))
{
if (arf_is_neg_inf(x))
arf_nan(z);
else
arf_set(z, x);
return 0;
}
if (ARF_SGNBIT(x))
{
arf_nan(z);
return 0;
}
fmpz_init(q);
fmpz_init(r);
/* x = m * 2^e where e = qk + r */
/* x^(1/k) = (m * 2^(qk+r))^(1/k) */
/* x^(1/k) = (m * 2^r)^(1/k) * 2^q */
fmpz_set_ui(r, k);
fmpz_fdiv_qr(q, r, ARF_EXPREF(x), r);
ARF_GET_MPN_READONLY(xptr, xn, x);
zn = (prec + FLINT_BITS - 1) / FLINT_BITS;
zf->_mpfr_d = tmp = flint_malloc(zn * sizeof(mp_limb_t));
zf->_mpfr_prec = prec;
zf->_mpfr_sign = 1;
zf->_mpfr_exp = 0;
xf->_mpfr_d = (mp_ptr) xptr;
xf->_mpfr_prec = xn * FLINT_BITS;
xf->_mpfr_sign = 1;
xf->_mpfr_exp = fmpz_get_ui(r);
inexact = mpfr_root(zf, xf, k, arf_rnd_to_mpfr(rnd));
inexact = (inexact != 0);
val = 0;
while (tmp[val] == 0)
val++;
ARF_GET_MPN_WRITE(zptr, zn - val, z);
flint_mpn_copyi(zptr, tmp + val, zn - val);
fmpz_add_si(ARF_EXPREF(z), q, zf->_mpfr_exp);
flint_free(tmp);
fmpz_clear(q);
fmpz_clear(r);
return inexact;
}
int
arf_sum(arf_t s, arf_srcptr terms, long len, long prec, arf_rnd_t rnd)
{
arf_ptr blocks;
long i, j, used;
int have_merged, res;
/* first check if the result is inf or nan */
{
int have_pos_inf = 0;
int have_neg_inf = 0;
for (i = 0; i < len; i++)
{
if (arf_is_pos_inf(terms + i))
{
if (have_neg_inf)
{
arf_nan(s);
return 0;
}
have_pos_inf = 1;
}
else if (arf_is_neg_inf(terms + i))
{
if (have_pos_inf)
{
arf_nan(s);
return 0;
}
have_neg_inf = 1;
}
else if (arf_is_nan(terms + i))
{
arf_nan(s);
return 0;
}
}
if (have_pos_inf)
{
arf_pos_inf(s);
return 0;
}
if (have_neg_inf)
{
arf_neg_inf(s);
return 0;
}
}
blocks = flint_malloc(sizeof(arf_struct) * len);
for (i = 0; i < len; i++)
arf_init(blocks + i);
/* put all terms into blocks */
used = 0;
for (i = 0; i < len; i++)
{
if (!arf_is_zero(terms + i))
{
arf_set(blocks + used, terms + i);
used++;
}
}
/* merge blocks until all are well separated */
have_merged = 1;
while (used >= 2 && have_merged)
{
have_merged = 0;
for (i = 0; i < used && !have_merged; i++)
{
for (j = i + 1; j < used && !have_merged; j++)
{
if (_arf_are_close(blocks + i, blocks + j, prec))
{
arf_add(blocks + i, blocks + i, blocks + j,
ARF_PREC_EXACT, ARF_RND_DOWN);
/* remove the merged block */
arf_swap(blocks + j, blocks + used - 1);
used--;
/* remove the updated block if the sum is zero */
if (arf_is_zero(blocks + i))
{
arf_swap(blocks + i, blocks + used - 1);
used--;
}
have_merged = 1;
}
}
}
}
if (used == 0)
{
arf_zero(s);
res = 0;
}
else if (used == 1)
{
res = arf_set_round(s, blocks + 0, prec, rnd);
}
else
{
/* find the two largest blocks */
for (i = 1; i < used; i++)
if (arf_cmpabs(blocks + 0, blocks + i) < 0)
arf_swap(blocks + 0, blocks + i);
for (i = 2; i < used; i++)
if (arf_cmpabs(blocks + 1, blocks + i) < 0)
arf_swap(blocks + 1, blocks + i);
res = _arf_add_eps(s, blocks + 0, arf_sgn(blocks + 1), prec, rnd);
}
for (i = 0; i < len; i++)
arf_clear(blocks + i);
flint_free(blocks);
return res;
}
