void
_nmod_poly_compose_mod_horner(mp_ptr res,
mp_srcptr f, long lenf, mp_srcptr g, mp_srcptr h, long lenh, nmod_t mod)
{
long i, len;
mp_ptr t;
if (lenh == 1)
return;
if (lenf == 1)
{
res[0] = f[0];
return;
}
if (lenh == 2)
{
res[0] = _nmod_poly_evaluate_nmod(f, lenf, g[0], mod);
return;
}
len = lenh - 1;
i = lenf - 1;
t = _nmod_vec_init(len);
_nmod_vec_scalar_mul_nmod(res, g, len, f[i], mod);
i--;
if (i >= 0)
res[0] = nmod_add(res[0], f[i], mod);
while (i > 0)
{
i--;
_nmod_poly_mulmod(t, res, len, g, len, h, lenh, mod);
_nmod_poly_add(res, t, len, f + i, 1, mod);
}
_nmod_vec_clear(t);
}
void
_nmod_poly_compose_divconquer(mp_ptr res, mp_srcptr poly1, long len1,
mp_srcptr poly2, long len2, nmod_t mod)
{
long i, j, k, n;
long * hlen, alloc, powlen;
mp_ptr v, * h, pow, temp;
if (len1 == 1)
{
res[0] = poly1[0];
return;
}
if (len2 == 1)
{
res[0] = _nmod_poly_evaluate_nmod(poly1, len1, poly2[0], mod);
return;
}
if (len1 == 2)
{
_nmod_poly_compose_horner(res, poly1, len1, poly2, len2, mod);
return;
}
/* Initialisation */
hlen = (long *) flint_malloc(((len1 + 1) / 2) * sizeof(long));
for (k = 1; (2 << k) < len1; k++) ;
hlen[0] = hlen[1] = ((1 << k) - 1) * (len2 - 1) + 1;
for (i = k - 1; i > 0; i--)
{
long hi = (len1 + (1 << i) - 1) / (1 << i);
for (n = (hi + 1) / 2; n < hi; n++)
hlen[n] = ((1 << i) - 1) * (len2 - 1) + 1;
}
powlen = (1 << k) * (len2 - 1) + 1;
alloc = 0;
for (i = 0; i < (len1 + 1) / 2; i++)
alloc += hlen[i];
v = _nmod_vec_init(alloc + 2 * powlen);
h = (mp_ptr *) flint_malloc(((len1 + 1) / 2) * sizeof(mp_ptr));
h[0] = v;
for (i = 0; i < (len1 - 1) / 2; i++)
{
h[i + 1] = h[i] + hlen[i];
hlen[i] = 0;
}
hlen[(len1 - 1) / 2] = 0;
pow = v + alloc;
temp = pow + powlen;
/* Let's start the actual work */
for (i = 0, j = 0; i < len1 / 2; i++, j += 2)
{
if (poly1[j + 1] != 0L)
{
_nmod_vec_scalar_mul_nmod(h[i], poly2, len2, poly1[j + 1], mod);
h[i][0] = n_addmod(h[i][0], poly1[j], mod.n);
hlen[i] = len2;
}
else if (poly1[j] != 0L)
{
h[i][0] = poly1[j];
hlen[i] = 1;
}
}
if ((len1 & 1L))
{
if (poly1[j] != 0L)
{
h[i][0] = poly1[j];
hlen[i] = 1;
}
}
_nmod_poly_mul(pow, poly2, len2, poly2, len2, mod);
powlen = 2 * len2 - 1;
for (n = (len1 + 1) / 2; n > 2; n = (n + 1) / 2)
{
if (hlen[1] > 0)
{
long templen = powlen + hlen[1] - 1;
_nmod_poly_mul(temp, pow, powlen, h[1], hlen[1], mod);
_nmod_poly_add(h[0], temp, templen, h[0], hlen[0], mod);
hlen[0] = FLINT_MAX(hlen[0], templen);
}
for (i = 1; i < n / 2; i++)
{
if (hlen[2*i + 1] > 0)
{
_nmod_poly_mul(h[i], pow, powlen, h[2*i + 1], hlen[2*i + 1], mod);
hlen[i] = hlen[2*i + 1] + powlen - 1;
} else
hlen[i] = 0;
_nmod_poly_add(h[i], h[i], hlen[i], h[2*i], hlen[2*i], mod);
hlen[i] = FLINT_MAX(hlen[i], hlen[2*i]);
}
if ((n & 1L))
{
mpn_copyi(h[i], h[2*i], hlen[2*i]);
hlen[i] = hlen[2*i];
}
_nmod_poly_mul(temp, pow, powlen, pow, powlen, mod);
powlen += powlen - 1;
{
mp_ptr t = pow;
pow = temp;
temp = t;
}
}
_nmod_poly_mul(res, pow, powlen, h[1], hlen[1], mod);
_nmod_vec_add(res, res, h[0], hlen[0], mod);
_nmod_vec_clear(v);
flint_free(h);
flint_free(hlen);
}
mp_limb_t
nmod_poly_evaluate_nmod(const nmod_poly_t poly, mp_limb_t c)
{
return _nmod_poly_evaluate_nmod(poly->coeffs, poly->length, c, poly->mod);
}
void
_nmod_poly_compose_mod_brent_kung(mp_ptr res, mp_srcptr poly1, long len1,
mp_srcptr poly2,
mp_srcptr poly3, long len3, nmod_t mod)
{
nmod_mat_t A, B, C;
mp_ptr t, h;
long i, n, m;
n = len3 - 1;
if (len3 == 1)
return;
if (len1 == 1)
{
res[0] = poly1[0];
return;
}
if (len3 == 2)
{
res[0] = _nmod_poly_evaluate_nmod(poly1, len1, poly2[0], mod);
return;
}
m = n_sqrt(n) + 1;
nmod_mat_init(A, m, n, mod.n);
nmod_mat_init(B, m, m, mod.n);
nmod_mat_init(C, m, n, mod.n);
h = _nmod_vec_init(n);
t = _nmod_vec_init(n);
/* Set rows of B to the segments of poly1 */
for (i = 0; i < len1 / m; i++)
_nmod_vec_set(B->rows[i], poly1 + i*m, m);
_nmod_vec_set(B->rows[i], poly1 + i*m, len1 % m);
/* Set rows of A to powers of poly2 */
A->rows[0][0] = 1UL;
_nmod_vec_set(A->rows[1], poly2, n);
for (i = 2; i < m; i++)
_nmod_poly_mulmod(A->rows[i], A->rows[i-1],
n, poly2, n, poly3, len3, mod);
nmod_mat_mul(C, B, A);
/* Evaluate block composition using the Horner scheme */
_nmod_vec_set(res, C->rows[m - 1], n);
_nmod_poly_mulmod(h, A->rows[m - 1], n, poly2, n, poly3, len3, mod);
for (i = m - 2; i >= 0; i--)
{
_nmod_poly_mulmod(t, res, n, h, n, poly3, len3, mod);
_nmod_poly_add(res, t, n, C->rows[i], n, mod);
}
_nmod_vec_clear(h);
_nmod_vec_clear(t);
nmod_mat_clear(A);
nmod_mat_clear(B);
nmod_mat_clear(C);
}
