static slong _fmpr_sub_special(fmpr_t z, const fmpr_t x, const fmpr_t y, slong prec, fmpr_rnd_t rnd)
{
if (fmpr_is_zero(x))
{
return fmpr_neg_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_pos_inf(y))
|| (fmpr_is_neg_inf(x) && fmpr_is_neg_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_neg(z, y);
return FMPR_RESULT_EXACT;
}
}
int
fmpr_get_mpfr(mpfr_t x, const fmpr_t y, mpfr_rnd_t rnd)
{
int r;
if (fmpr_is_special(y))
{
if (fmpr_is_zero(y)) mpfr_set_zero(x, 0);
else if (fmpr_is_pos_inf(y)) mpfr_set_inf(x, 1);
else if (fmpr_is_neg_inf(y)) mpfr_set_inf(x, -1);
else mpfr_set_nan(x);
r = 0;
}
else if (COEFF_IS_MPZ(*fmpr_expref(y)))
{
flint_printf("exception: exponent too large to convert to mpfr");
abort();
}
else
{
if (!COEFF_IS_MPZ(*fmpr_manref(y)))
#if defined(__MINGW64__)
r = mpfr_set_sj_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd);
#else
r = mpfr_set_si_2exp(x, *fmpr_manref(y), *fmpr_expref(y), rnd);
#endif
else
r = mpfr_set_z_2exp(x, COEFF_TO_PTR(*fmpr_manref(y)), *fmpr_expref(y), rnd);
if (!mpfr_regular_p(x))
{
flint_printf("exception: exponent too large to convert to mpfr");
abort();
}
}
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
fmpr_cmp(const fmpr_t x, const fmpr_t y)
{
int res, xsign, ysign;
fmpr_t t;
if (fmpr_equal(x, y))
return 0;
if (fmpr_is_special(x) || fmpr_is_special(y))
{
if (fmpr_is_nan(x) || fmpr_is_nan(y))
return 0;
if (fmpr_is_zero(y)) return fmpr_sgn(x);
if (fmpr_is_zero(x)) return -fmpr_sgn(y);
if (fmpr_is_pos_inf(x)) return 1;
if (fmpr_is_neg_inf(y)) return 1;
return -1;
}
xsign = fmpr_sgn(x);
ysign = fmpr_sgn(y);
if (xsign != ysign)
return (xsign < 0) ? -1 : 1;
/* Reduces to integer comparison if bottom exponents are the same */
if (fmpz_equal(fmpr_expref(x), fmpr_expref(y)))
return fmpz_cmp(fmpr_manref(x), fmpr_manref(y)) < 0 ? -1 : 1;
/* TODO: compare position of top exponents to avoid subtraction */
fmpr_init(t);
fmpr_sub(t, x, y, 2, FMPR_RND_DOWN);
res = fmpr_sgn(t);
fmpr_clear(t);
return res;
}
static void
_fmprb_gamma(fmprb_t y, const fmprb_t x, long prec, int inverse)
{
int reflect;
long r, n, wp;
fmprb_t t, u, v;
if (fmprb_is_exact(x))
{
const fmpr_struct * mid = fmprb_midref(x);
if (fmpr_is_special(mid))
{
if (!inverse && fmpr_is_pos_inf(mid))
{
fmprb_set(y, x);
}
else if (fmpr_is_nan(mid) || fmpr_is_neg_inf(mid) || !inverse)
{
fmpr_nan(fmprb_midref(y));
fmpr_pos_inf(fmprb_radref(y));
}
else
{
fmprb_zero(y);
}
return;
}
else
{
const fmpz exp = *fmpr_expref(mid);
const fmpz man = *fmpr_manref(mid);
/* fast gamma(n), gamma(n/2) or gamma(n/4) */
if (!COEFF_IS_MPZ(exp) && (exp >= -2) &&
((double) fmpz_bits(&man) + exp < prec))
{
fmpq_t a;
fmpq_init(a);
fmpr_get_fmpq(a, mid);
fmprb_gamma_fmpq(y, a, prec + 2 * inverse);
if (inverse)
fmprb_ui_div(y, 1, y, prec);
fmpq_clear(a);
return;
}
}
}
wp = prec + FLINT_BIT_COUNT(prec);
gamma_stirling_choose_param_fmprb(&reflect, &r, &n, x, 1, 0, wp);
fmprb_init(t);
fmprb_init(u);
fmprb_init(v);
if (reflect)
{
/* gamma(x) = (rf(1-x, r) * pi) / (gamma(1-x+r) sin(pi x)) */
fmprb_sub_ui(t, x, 1, wp);
fmprb_neg(t, t);
gamma_rising_fmprb_ui_bsplit(u, t, r, wp);
fmprb_const_pi(v, wp);
fmprb_mul(u, u, v, wp);
fmprb_add_ui(t, t, r, wp);
gamma_stirling_eval_fmprb(v, t, n, 0, wp);
fmprb_exp(v, v, wp);
fmprb_sin_pi(t, x, wp);
fmprb_mul(v, v, t, wp);
}
else
{
/* gamma(x) = gamma(x+r) / rf(x,r) */
fmprb_add_ui(t, x, r, wp);
gamma_stirling_eval_fmprb(u, t, n, 0, wp);
fmprb_exp(u, u, prec);
gamma_rising_fmprb_ui_bsplit(v, x, r, wp);
}
if (inverse)
fmprb_div(y, v, u, prec);
else
fmprb_div(y, u, v, prec);
fmprb_clear(t);
fmprb_clear(u);
fmprb_clear(v);
}
