/* Assumes poly1 and poly2 are not length 0 and 0 < trunc <= len1 + len2 - 1 */
void
_nmod_poly_mullow_classical(mp_ptr res, mp_srcptr poly1, slong len1,
mp_srcptr poly2, slong len2, slong trunc, nmod_t mod)
{
if (len1 == 1 || trunc == 1) /* Special case if the length of output is 1 */
{
res[0] = n_mulmod2_preinv(poly1[0], poly2[0], mod.n, mod.ninv);
}
else /* Ordinary case */
{
slong i;
slong bits = FLINT_BITS - (slong) mod.norm;
slong log_len = FLINT_BIT_COUNT(len2);
if (2 * bits + log_len <= FLINT_BITS)
{
/* Set res[i] = poly1[i]*poly2[0] */
mpn_mul_1(res, poly1, FLINT_MIN(len1, trunc), poly2[0]);
if (len2 != 1)
{
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
if (trunc > len1)
mpn_mul_1(res + len1, poly2 + 1, trunc - len1,
poly1[len1 - 1]);
/* out[i+j] += in1[i]*in2[j] */
for (i = 0; i < FLINT_MIN(len1, trunc) - 1; i++)
mpn_addmul_1(res + i + 1, poly2 + 1,
FLINT_MIN(len2, trunc - i) - 1, poly1[i]);
}
_nmod_vec_reduce(res, res, trunc, mod);
}
else
{
/* Set res[i] = poly1[i]*poly2[0] */
_nmod_vec_scalar_mul_nmod(res, poly1, FLINT_MIN(len1, trunc),
poly2[0], mod);
if (len2 == 1)
return;
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
if (trunc > len1)
_nmod_vec_scalar_mul_nmod(res + len1, poly2 + 1, trunc - len1,
poly1[len1 - 1], mod);
/* out[i+j] += in1[i]*in2[j] */
for (i = 0; i < FLINT_MIN(len1, trunc) - 1; i++)
_nmod_vec_scalar_addmul_nmod(res + i + 1, poly2 + 1,
FLINT_MIN(len2, trunc - i) - 1,
poly1[i], mod);
}
}
}
void _nmod_poly_divrem_q1(mp_ptr Q, mp_ptr R,
mp_srcptr A, long lenA, mp_srcptr B, long lenB,
nmod_t mod)
{
const mp_limb_t invL = (B[lenB-1] == 1) ? 1 : n_invmod(B[lenB-1], mod.n);
if (lenB == 1)
{
_nmod_vec_scalar_mul_nmod(Q, A, lenA, invL, mod);
}
else
{
mp_limb_t t;
Q[1] = n_mulmod2_preinv(A[lenA-1], invL, mod.n, mod.ninv);
t = n_mulmod2_preinv(Q[1], B[lenB-2], mod.n, mod.ninv);
t = n_submod(A[lenA-2], t, mod.n);
Q[0] = n_mulmod2_preinv(t, invL, mod.n, mod.ninv);
if (FLINT_BITS + 2 <= 2 * mod.norm)
{
mpn_mul_1(R, B, lenB - 1, Q[0]);
if (lenB > 2)
mpn_addmul_1(R + 1, B, lenB - 2, Q[1]);
_nmod_vec_reduce(R, R, lenB - 1, mod);
}
else
{
_nmod_vec_scalar_mul_nmod(R, B, lenB - 1, Q[0], mod);
if (lenB > 2)
_nmod_vec_scalar_addmul_nmod(R + 1, B, lenB - 2, Q[1], mod);
}
_nmod_vec_sub(R, A, R, lenB - 1, mod);
}
}
void
_nmod_poly_cosh_series(mp_ptr f, mp_srcptr h, long n, nmod_t mod)
{
mp_ptr g, T, U, hprime;
g = _nmod_vec_init(n);
T = _nmod_vec_init(n);
U = _nmod_vec_init(n);
hprime = _nmod_vec_init(n);
_nmod_poly_derivative(hprime, h, n, mod); hprime[n-1] = 0UL;
__nmod_poly_exp_series_prealloc(f, g, h, hprime, T, U, n, mod, 1);
_nmod_vec_add(f, f, g, n, mod);
_nmod_vec_scalar_mul_nmod(f, f, n, n_invmod(2UL, mod.n), mod);
_nmod_vec_free(hprime);
_nmod_vec_free(g);
_nmod_vec_free(T);
_nmod_vec_free(U);
}
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_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
_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);
}
