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
_fmpz_poly_revert_series_lagrange(fmpz * Qinv, const fmpz * Q, slong n)
{
slong i;
fmpz *R, *S, *T, *tmp;
if (n <= 2)
{
_fmpz_vec_set(Qinv, Q, n);
return;
}
R = _fmpz_vec_init(n - 1);
S = _fmpz_vec_init(n - 1);
T = _fmpz_vec_init(n - 1);
fmpz_zero(Qinv);
fmpz_set(Qinv + 1, Q + 1);
_fmpz_poly_inv_series(R, Q + 1, n - 1);
_fmpz_vec_set(S, R, n - 1);
for (i = 2; i < n; i++)
{
_fmpz_poly_mullow(T, S, n - 1, R, n - 1, n - 1);
fmpz_divexact_ui(Qinv + i, T + i - 1, i);
tmp = S; S = T; T = tmp;
}
_fmpz_vec_clear(R, n - 1);
_fmpz_vec_clear(S, n - 1);
_fmpz_vec_clear(T, n - 1);
}
void
_fmpz_poly_revert_series_newton(fmpz * Qinv, const fmpz * Q, long n)
{
if (n <= 2)
{
_fmpz_vec_set(Qinv, Q, n);
return;
}
else
{
long *a, i, k;
fmpz *T, *U, *V;
T = _fmpz_vec_init(n);
U = _fmpz_vec_init(n);
V = _fmpz_vec_init(n);
k = n;
for (i = 1; (1L << i) < k; i++);
a = (long *) flint_malloc(i * sizeof(long));
a[i = 0] = k;
while (k >= FLINT_REVERSE_NEWTON_CUTOFF)
a[++i] = (k = (k + 1) / 2);
_fmpz_poly_revert_series_lagrange(Qinv, Q, k);
_fmpz_vec_zero(Qinv + k, n - k);
for (i--; i >= 0; i--)
{
k = a[i];
_fmpz_poly_compose_series(T, Q, k, Qinv, k, k);
_fmpz_poly_derivative(U, T, k); fmpz_zero(U + k - 1);
fmpz_zero(T + 1);
_fmpz_poly_div_series(V, T, U, k);
_fmpz_poly_derivative(T, Qinv, k);
_fmpz_poly_mullow(U, V, k, T, k, k);
_fmpz_vec_sub(Qinv, Qinv, U, k);
}
flint_free(a);
_fmpz_vec_clear(T, n);
_fmpz_vec_clear(U, n);
_fmpz_vec_clear(V, n);
}
}
static __inline__ void
_arb_poly_addmullow_rad(arb_ptr z, fmpz * zz,
const fmpz * xz, const double * xdbl, const fmpz * xexps,
const slong * xblocks, slong xlen,
const fmpz * yz, const double * ydbl, const fmpz * yexps,
const slong * yblocks, slong ylen, slong n)
{
slong i, j, k, ii, xp, yp, xl, yl, bn;
fmpz_t zexp;
mag_t t;
fmpz_init(zexp);
mag_init(t);
for (i = 0; (xp = xblocks[i]) != xlen; i++)
{
for (j = 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);
fmpz_add_inline(zexp, xexps + i, yexps + j);
if (xl > 1 && yl > 1 &&
(xl < DOUBLE_BLOCK_MAX_LENGTH || yl < DOUBLE_BLOCK_MAX_LENGTH))
{
fmpz_add_ui(zexp, zexp, 2 * DOUBLE_BLOCK_SHIFT);
for (k = 0; k < bn; k++)
{
/* Classical multiplication (may round down!) */
double ss = 0.0;
for (ii = FLINT_MAX(0, k - yl + 1);
ii <= FLINT_MIN(xl - 1, k); ii++)
{
ss += xdbl[xp + ii] * ydbl[yp + k - ii];
}
/* Compensate for rounding error */
ss *= DOUBLE_ROUNDING_FACTOR;
mag_set_d_2exp_fmpz(t, ss, zexp);
mag_add(arb_radref(z + xp + yp + k),
arb_radref(z + xp + yp + k), t);
}
}
else
{
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);
for (k = 0; k < bn; k++)
{
mag_set_fmpz_2exp_fmpz(t, zz + k, zexp);
mag_add(arb_radref(z + xp + yp + k),
arb_radref(z + xp + yp + k), t);
}
}
}
}
fmpz_clear(zexp);
mag_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);
}
void
_fmpq_poly_inv_series_newton(fmpz * Qinv, fmpz_t Qinvden,
const fmpz * Q, const fmpz_t Qden, long n)
{
if (n == 1)
{
if (fmpz_sgn(Q) > 0)
{
fmpz_set(Qinv, Qden);
fmpz_set(Qinvden, Q);
}
else
{
fmpz_neg(Qinv, Qden);
fmpz_neg(Qinvden, Q);
}
}
else
{
const long alloc = FLINT_MAX(n, 3 * FMPQ_POLY_INV_NEWTON_CUTOFF);
long *a, i, m;
fmpz *W, *Wden;
W = _fmpz_vec_init(alloc + 1);
Wden = W + alloc;
for (i = 1; (1L << i) < n; i++) ;
a = (long *) flint_malloc(i * sizeof(long));
a[i = 0] = n;
while (n >= FMPQ_POLY_INV_NEWTON_CUTOFF)
a[++i] = (n = (n + 1) / 2);
/* Base case */
{
fmpz *rev = W + 2 * FMPQ_POLY_INV_NEWTON_CUTOFF;
_fmpz_poly_reverse(rev, Q, n, n);
_fmpz_vec_zero(W, 2*n - 2);
fmpz_one(W + (2*n - 2));
fmpz_one(Wden);
_fmpq_poly_div(Qinv, Qinvden, W, Wden, 2*n - 1, rev, Qden, n);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
_fmpz_poly_reverse(Qinv, Qinv, n, n);
}
for (i--; i >= 0; i--)
{
m = n;
n = a[i];
_fmpz_poly_mullow(W, Q, n, Qinv, m, n);
fmpz_mul(Wden, Qden, Qinvden);
_fmpz_poly_mullow(Qinv + m, Qinv, m, W + m, n - m, n - m);
fmpz_mul(Qinvden, Qinvden, Wden);
_fmpz_vec_scalar_mul_fmpz(Qinv, Qinv, m, Wden);
_fmpz_vec_neg(Qinv + m, Qinv + m, n - m);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
}
_fmpz_vec_clear(W, alloc + 1);
flint_free(a);
}
}
