void _nmod_poly_mulmod(mp_ptr res, mp_srcptr poly1, long len1,
mp_srcptr poly2, long len2, mp_srcptr f,
long lenf, nmod_t mod)
{
mp_ptr T, Q;
long lenT, lenQ;
lenT = len1 + len2 - 1;
lenQ = lenT - lenf + 1;
T = _nmod_vec_init(lenT + lenQ);
Q = T + lenT;
if (len1 >= len2)
_nmod_poly_mul(T, poly1, len1, poly2, len2, mod);
else
_nmod_poly_mul(T, poly2, len2, poly1, len1, mod);
_nmod_poly_divrem(Q, res, T, lenT, f, lenf, mod);
_nmod_vec_clear(T);
}
void
_nmod_poly_product_roots_nmod_vec(mp_ptr poly, mp_srcptr xs, slong n, nmod_t mod)
{
if (n == 0)
{
poly[0] = UWORD(1);
}
else if (n < 20)
{
slong i, j;
poly[n] = UWORD(1);
poly[n - 1] = nmod_neg(xs[0], mod);
for (i = 1; i < n; i++)
{
poly[n-i-1] = nmod_neg(n_mulmod2_preinv(poly[n-i], xs[i],
mod.n, mod.ninv), mod);
for (j = 0; j < i - 1; j++)
{
poly[n-i+j] = nmod_sub(poly[n-i+j],
n_mulmod2_preinv(poly[n-i+j+1], xs[i], mod.n, mod.ninv),
mod);
}
poly[n-1] = nmod_sub(poly[n-1], xs[i], mod);
}
}
else
{
const slong m = (n + 1) / 2;
mp_ptr tmp;
tmp = _nmod_vec_init(n + 2);
_nmod_poly_product_roots_nmod_vec(tmp, xs, m, mod);
_nmod_poly_product_roots_nmod_vec(tmp + m + 1, xs + m, n - m, mod);
_nmod_poly_mul(poly, tmp, m + 1, tmp + m + 1, n - m + 1, mod);
_nmod_vec_clear(tmp);
}
}
void
_nmod_poly_compose_series_horner(mp_ptr res, mp_srcptr poly1, long len1,
mp_srcptr poly2, long len2, long n, nmod_t mod)
{
if (n == 1)
{
res[0] = poly1[0];
}
else
{
long i = len1 - 1;
long lenr;
mp_ptr t = _nmod_vec_init(n);
lenr = len2;
_nmod_vec_scalar_mul_nmod(res, poly2, len2, poly1[i], mod);
i--;
res[0] = nmod_add(res[0], poly1[i], mod);
while (i > 0)
{
i--;
if (lenr + len2 - 1 < n)
{
_nmod_poly_mul(t, res, lenr, poly2, len2, mod);
lenr = lenr + len2 - 1;
}
else
{
_nmod_poly_mullow(t, res, lenr, poly2, len2, n, mod);
lenr = n;
}
_nmod_poly_add(res, t, lenr, poly1 + i, 1, mod);
}
_nmod_vec_zero(res + lenr, n - lenr);
_nmod_vec_clear(t);
}
}
void _fq_nmod_pow(mp_limb_t *rop, const mp_limb_t *op, slong len, const fmpz_t e,
const fq_nmod_ctx_t ctx)
{
const slong d = fq_nmod_ctx_degree(ctx);
if (fmpz_is_zero(e))
{
rop[0] = WORD(1);
_nmod_vec_zero(rop + 1, 2 * d - 1 - 1);
}
else if (fmpz_is_one(e))
{
_nmod_vec_set(rop, op, len);
_nmod_vec_zero(rop + len, 2 * d - 1 - len);
}
else
{
ulong bit;
mp_limb_t *v = _nmod_vec_init(2 * d - 1);
mp_limb_t *R, *S, *T;
_nmod_vec_zero(v, 2 * d - 1);
_nmod_vec_zero(rop, 2 * d - 1);
/*
Set bits to the bitmask with a 1 one place lower than the msb of e
*/
bit = fmpz_bits(e) - 2;
/*
Trial run without any polynomial arithmetic to determine the parity
of the number of swaps; then set R and S accordingly
*/
{
unsigned int swaps = 0U;
ulong bit2 = bit;
if (fmpz_tstbit(e, bit2))
swaps = ~swaps;
while (bit2--)
if (!fmpz_tstbit(e, bit2))
swaps = ~swaps;
if (swaps == 0U)
{
R = rop;
S = v;
}
else
{
R = v;
S = rop;
}
}
/*
We unroll the first step of the loop, referring to {op, len}
*/
_nmod_poly_mul(R, op, len, op, len, ctx->mod);
_fq_nmod_reduce(R, 2 * len - 1, ctx);
if (fmpz_tstbit(e, bit))
{
_nmod_poly_mul(S, R, d, op, len, ctx->mod);
_fq_nmod_reduce(S, d + len - 1, ctx);
T = R;
R = S;
S = T;
}
while (bit--)
{
if (fmpz_tstbit(e, bit))
{
_nmod_poly_mul(S, R, d, R, d, ctx->mod);
_fq_nmod_reduce(S, 2 * d - 1, ctx);
_nmod_poly_mul(R, S, d, op, len, ctx->mod);
_fq_nmod_reduce(R, d + len - 1, ctx);
}
else
{
_nmod_poly_mul(S, R, d, R, d, ctx->mod);
_fq_nmod_reduce(S, 2 * d - 1, ctx);
T = R;
R = S;
S = T;
}
}
_nmod_vec_clear(v);
}
}
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);
}
