static void
_qadic_exp_bsplit_series(fmpz *P, fmpz_t Q, fmpz *T,
const fmpz *x, slong len, slong lo, slong hi,
const fmpz *a, const slong *j, slong lena)
{
const slong d = j[lena - 1];
if (hi - lo == 1)
{
_fmpz_vec_set(P, x, len);
_fmpz_vec_zero(P + len, 2*d - 1 - len);
fmpz_set_si(Q, lo);
_fmpz_vec_set(T, P, 2*d - 1);
}
else if (hi - lo == 2)
{
_fmpz_poly_sqr(P, x, len);
_fmpz_vec_zero(P + (2*len - 1), d - (2*len - 1));
_fmpz_poly_reduce(P, 2*len - 1, a, j, lena);
fmpz_set_si(Q, lo);
fmpz_mul_si(Q, Q, lo + 1);
_fmpz_vec_scalar_mul_si(T, x, len, lo + 1);
_fmpz_vec_zero(T + len, d - len);
_fmpz_vec_add(T, T, P, d);
}
else
{
const slong m = (lo + hi) / 2;
fmpz *PR, *TR, *W;
fmpz_t QR;
PR = _fmpz_vec_init(2*d - 1);
TR = _fmpz_vec_init(2*d - 1);
W = _fmpz_vec_init(2*d - 1);
fmpz_init(QR);
_qadic_exp_bsplit_series(P, Q, T, x, len, lo, m, a, j, lena);
_qadic_exp_bsplit_series(PR, QR, TR, x, len, m, hi, a, j, lena);
_fmpz_poly_mul(W, TR, d, P, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mul_fmpz(T, T, d, QR);
_fmpz_vec_add(T, T, W, d);
_fmpz_poly_mul(W, P, d, PR, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_swap(P, W, d);
fmpz_mul(Q, Q, QR);
_fmpz_vec_clear(PR, 2*d - 1);
_fmpz_vec_clear(TR, 2*d - 1);
_fmpz_vec_clear(W, 2*d - 1);
fmpz_clear(QR);
}
}
static void
__fmpz_poly_divrem_divconquer(fmpz * Q, fmpz * R,
const fmpz * A, long lenA,
const fmpz * B, long lenB)
{
if (lenA < 2 * lenB - 1)
{
/*
Convert unbalanced division into a 2 n1 - 1 by n1 division
*/
const long n1 = lenA - lenB + 1;
const long n2 = lenB - n1;
const fmpz * p1 = A + n2;
const fmpz * d1 = B + n2;
const fmpz * d2 = B;
fmpz * W = _fmpz_vec_init((2 * n1 - 1) + lenB - 1);
fmpz * d1q1 = R + n2;
fmpz * d2q1 = W + (2 * n1 - 1);
_fmpz_poly_divrem_divconquer_recursive(Q, d1q1, W, p1, d1, n1);
/*
Compute d2q1 = Q d2, of length lenB - 1
*/
if (n1 >= n2)
_fmpz_poly_mul(d2q1, Q, n1, d2, n2);
else
_fmpz_poly_mul(d2q1, d2, n2, Q, n1);
/*
Compute BQ = d1q1 * x^n1 + d2q1, of length lenB - 1;
then compute R = A - BQ
*/
_fmpz_vec_swap(R, d2q1, n2);
_fmpz_vec_add(R + n2, R + n2, d2q1 + n2, n1 - 1);
_fmpz_vec_sub(R, A, R, lenA);
_fmpz_vec_clear(W, (2 * n1 - 1) + lenB - 1);
}
else if (lenA > 2 * lenB - 1)
{
/*
We shift A right until it is of length 2 lenB - 1, call this p1
*/
const long shift = lenA - 2 * lenB + 1;
const fmpz * p1 = A + shift;
fmpz * q1 = Q + shift;
fmpz * q2 = Q;
fmpz * W = R + lenA;
fmpz * d1q1 = W + (2 * lenB - 1);
/*
XXX: In this case, we expect R to be of length
lenA + 2 * (2 * lenB - 1) and A to be modifiable
*/
/*
Set q1 to p1 div B, a 2 lenB - 1 by lenB division, so q1 ends up
being of length lenB; set d1q1 = d1 * q1 of length 2 lenB - 1
*/
_fmpz_poly_divrem_divconquer_recursive(q1, d1q1, W, p1, B, lenB);
/*
We have dq1 = d1 * q1 * x^shift, of length lenA
Compute R = A - dq1; the first lenB coeffs represent remainder
terms (zero if division is exact), leaving lenA - lenB significant
terms which we use in the division
*/
_fmpz_vec_sub((fmpz *) A + shift, A + shift, d1q1, lenB - 1);
/*
Compute q2 = trunc(R) div B; it is a smaller division than the
original since len(trunc(R)) = lenA - lenB
*/
__fmpz_poly_divrem_divconquer(q2, R, A, lenA - lenB, B, lenB);
_fmpz_vec_sub(R + lenA - lenB, A + lenA - lenB, d1q1 + lenB - 1, lenB);
/*
We have Q = q1 * x^shift + q2; Q has length lenB + shift;
note q2 has length shift since the above division is
lenA - lenB by lenB
We've also written the remainder in place
*/
}
else /* lenA = 2 * lenB - 1 */
{
fmpz * W = _fmpz_vec_init(lenA);
_fmpz_poly_divrem_divconquer_recursive(Q, R, W, A, B, lenB);
_fmpz_vec_sub(R, A, R, lenA);
_fmpz_vec_clear(W, lenA);
}
}
