static __inline__ void
fmpcb_inv_mid(fmpcb_t z, const fmpcb_t x, long prec)
{
fmpr_t t;
fmpr_init(t);
#define a fmprb_midref(fmpcb_realref(x))
#define b fmprb_midref(fmpcb_imagref(x))
#define e fmprb_midref(fmpcb_realref(z))
#define f fmprb_midref(fmpcb_imagref(z))
fmpr_mul(t, a, a, prec, FMPR_RND_DOWN);
fmpr_addmul(t, b, b, prec, FMPR_RND_DOWN);
fmpr_div(e, a, t, prec, FMPR_RND_DOWN);
fmpr_div(f, b, t, prec, FMPR_RND_DOWN);
fmpr_neg(f, f);
#undef a
#undef b
#undef e
#undef f
fmpr_clear(t);
}
void
fmprb_mul_main_naive(fmprb_t z, const fmprb_t x, const fmprb_t y, slong prec)
{
if (fmpr_is_pos_inf(fmprb_radref(x)) || fmpr_is_pos_inf(fmprb_radref(y)))
{
fmpr_mul(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN);
fmpr_pos_inf(fmprb_radref(z));
}
else
{
fmpr_t t, u;
slong r;
fmpr_init(t);
fmpr_init(u);
/* (x+a)*(y+b) = x*y + x*b + y*a + a*b*/
fmpr_mul(t, fmprb_midref(x), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_abs(t, t);
fmpr_mul(u, fmprb_midref(y), fmprb_radref(x), FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_abs(u, u);
fmpr_add(t, t, u, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_addmul(t, fmprb_radref(x), fmprb_radref(y), FMPRB_RAD_PREC, FMPR_RND_UP);
r = fmpr_mul(fmprb_midref(z), fmprb_midref(x), fmprb_midref(y), prec, FMPR_RND_DOWN);
fmpr_add_error_result(fmprb_radref(z), t,
fmprb_midref(z), r, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_clear(t);
fmpr_clear(u);
}
}
slong
fmpr_addmul_fmpz(fmpr_t z, const fmpr_t x, const fmpz_t y, slong prec, fmpr_rnd_t rnd)
{
fmpr_t t; slong r;
fmpr_init(t);
fmpr_set_fmpz(t, y);
r = fmpr_addmul(z, x, t, prec, rnd);
fmpr_clear(t);
return r;
}
void
fmprb_vec_get_fmpr_2norm_squared_bound(fmpr_t s, fmprb_srcptr vec, long len, long prec)
{
long i;
fmpr_t t;
fmpr_init(t);
fmpr_zero(s);
for (i = 0; i < len; i++)
{
fmprb_get_abs_ubound_fmpr(t, vec + i, prec);
fmpr_addmul(s, t, t, prec, FMPR_RND_UP);
}
fmpr_clear(t);
}
void _fmprb_poly_mullow_ztrunc(fmprb_ptr C,
fmprb_srcptr A, long lenA,
fmprb_srcptr B, long lenB, long n, long prec)
{
fmpz * Acoeffs, * Bcoeffs, * Ccoeffs;
fmpz_t Aexp, Bexp, Cexp;
fmpr_t Aerr, Berr, Anorm, Bnorm, err;
long i;
int squaring;
lenA = FLINT_MIN(lenA, n);
lenB = FLINT_MIN(lenB, n);
squaring = (A == B) && (lenA == lenB);
/* TODO: make the code below work correctly with out this workaround */
if (_fmprb_vec_rad_has_inf_nan(A, lenA) ||
(!squaring && _fmprb_vec_rad_has_inf_nan(B, lenB)))
{
_fmprb_vec_indeterminate(C, n);
return;
}
fmpz_init(Aexp);
fmpz_init(Bexp);
fmpz_init(Cexp);
Acoeffs = _fmpz_vec_init(lenA);
Bcoeffs = _fmpz_vec_init(lenB);
Ccoeffs = _fmpz_vec_init(n);
fmpr_init(Aerr);
fmpr_init(Berr);
fmpr_init(Anorm);
fmpr_init(Bnorm);
fmpr_init(err);
_fmprb_poly_get_fmpz_poly_2exp(Aerr, Aexp, Acoeffs, A, lenA, prec);
if (squaring)
{
_fmpz_poly_sqrlow(Ccoeffs, Acoeffs, lenA, n);
fmpz_add(Cexp, Aexp, Aexp);
/* cross-multiply error bounds: (A+r)(B+s) = A^2 + 2Ar + r^2 */
_fmpr_fmpz_vec_max_norm(Anorm, Acoeffs, lenA, FMPRB_RAD_PREC);
fmpr_mul_2exp_fmpz(Anorm, Anorm, Aexp);
fmpr_mul(err, Anorm, Aerr, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_mul_2exp_si(err, err, 1);
fmpr_addmul(err, Aerr, Aerr, FMPRB_RAD_PREC, FMPR_RND_UP);
}
else
{
_fmprb_poly_get_fmpz_poly_2exp(Berr, Bexp, Bcoeffs, B, lenB, prec);
/* main multiplication */
if (lenA >= lenB)
_fmpz_poly_mullow(Ccoeffs, Acoeffs, lenA, Bcoeffs, lenB, n);
else
_fmpz_poly_mullow(Ccoeffs, Bcoeffs, lenB, Acoeffs, lenA, n);
fmpz_add(Cexp, Aexp, Bexp);
/* cross-multiply error bounds: (A+r)(B+s) = AB + As + Br + rs */
_fmpr_fmpz_vec_max_norm(Anorm, Acoeffs, lenA, FMPRB_RAD_PREC);
fmpr_mul_2exp_fmpz(Anorm, Anorm, Aexp);
_fmpr_fmpz_vec_max_norm(Bnorm, Bcoeffs, lenB, FMPRB_RAD_PREC);
fmpr_mul_2exp_fmpz(Bnorm, Bnorm, Bexp);
fmpr_mul(err, Aerr, Berr, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_addmul(err, Anorm, Berr, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_addmul(err, Bnorm, Aerr, FMPRB_RAD_PREC, FMPR_RND_UP);
}
for (i = 0; i < n; i++)
{
fmprb_set_round_fmpz_2exp(C + i, Ccoeffs + i, Cexp, prec);
/* there are at most (i+1) error terms for coefficient i */
/* TODO: make this tight */
fmpr_addmul_ui(fmprb_radref(C + i), err, i + 1,
FMPRB_RAD_PREC, FMPR_RND_UP);
}
fmpr_clear(Aerr);
fmpr_clear(Berr);
fmpr_clear(Anorm);
fmpr_clear(Bnorm);
fmpr_clear(err);
_fmpz_vec_clear(Acoeffs, lenA);
_fmpz_vec_clear(Bcoeffs, lenB);
_fmpz_vec_clear(Ccoeffs, n);
fmpz_clear(Aexp);
fmpz_clear(Bexp);
fmpz_clear(Cexp);
}
