void fmpz_poly_sqrlow(fmpz_poly_t res, const fmpz_poly_t poly, long n)
{
const long len = poly->length;
if (len == 0 || n == 0)
{
fmpz_poly_zero(res);
return;
}
if (res == poly)
{
fmpz_poly_t t;
fmpz_poly_init2(t, n);
fmpz_poly_sqrlow(t, poly, n);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
return;
}
n = FLINT_MIN(2 * len - 1, n);
fmpz_poly_fit_length(res, n);
_fmpz_poly_sqrlow(res->coeffs, poly->coeffs, len, n);
_fmpz_poly_set_length(res, n);
_fmpz_poly_normalise(res);
}
static __inline__ void
_arb_poly_addmullow_block(arb_ptr z, fmpz * zz,
const fmpz * xz, const fmpz * xexps, const slong * xblocks, slong xlen,
const fmpz * yz, const fmpz * yexps, const slong * yblocks, slong ylen,
slong n, slong prec, int squaring)
{
slong i, j, k, xp, yp, xl, yl, bn;
fmpz_t zexp;
fmpz_init(zexp);
if (squaring)
{
for (i = 0; (xp = xblocks[i]) != xlen; i++)
{
if (2 * xp >= n)
continue;
xl = xblocks[i + 1] - xp;
bn = FLINT_MIN(2 * xl - 1, n - 2 * xp);
xl = FLINT_MIN(xl, bn);
_fmpz_poly_sqrlow(zz, xz + xp, xl, bn);
_fmpz_add2_fast(zexp, xexps + i, xexps + i, 0);
for (k = 0; k < bn; k++)
arb_add_fmpz_2exp(z + 2 * xp + k, z + 2 * xp + k, zz + k, zexp, prec);
}
}
for (i = 0; (xp = xblocks[i]) != xlen; i++)
{
for (j = squaring ? i + 1 : 0; (yp = yblocks[j]) != ylen; j++)
{
if (xp + yp >= n)
continue;
xl = xblocks[i + 1] - xp;
yl = yblocks[j + 1] - yp;
bn = FLINT_MIN(xl + yl - 1, n - xp - yp);
xl = FLINT_MIN(xl, bn);
yl = FLINT_MIN(yl, bn);
if (xl >= yl)
_fmpz_poly_mullow(zz, xz + xp, xl, yz + yp, yl, bn);
else
_fmpz_poly_mullow(zz, yz + yp, yl, xz + xp, xl, bn);
_fmpz_add2_fast(zexp, xexps + i, yexps + j, squaring);
for (k = 0; k < bn; k++)
arb_add_fmpz_2exp(z + xp + yp + k, z + xp + yp + k, zz + k, zexp, prec);
}
}
fmpz_clear(zexp);
}
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);
}