// X_i^p = X_i
void nmod_multi_poly_mod_fermat(mp_ptr f_bar, const mp_ptr f, slong p, slong d, slong m, const slong* P) {
if(p < d) {
slong i, cpt, *pos, coord_p;
_nmod_vec_zero(f_bar,n_pow(p,m));
pos = (slong*)calloc(sizeof(slong),m);
coord_p;
cpt = 0;
while(pos[m-1] != d) {
coord_p = Coord_mod(P,p,pos,m);
f_bar[coord_p] = n_addmod(f_bar[coord_p],f[cpt],p);
pos[0]++;
cpt++;
i = 0;
while( (pos[i] == d) && (i != (m-1)) ) {
pos[i] = 0;
// Le i est incrémenté avant pos++
pos[++i]++;
}
}
free(pos);
}
}
void partition_function_nmod_vec(mp_ptr res, long len, nmod_t mod)
{
mp_ptr tmp;
mp_limb_t r;
long k, n;
r = mod.n - 1UL;
if (len < 1)
return;
tmp = _nmod_vec_init(len);
_nmod_vec_zero(tmp, len);
tmp[0] = 1UL;
for (n = k = 1; n + 4*k + 2 < len; k += 2)
{
tmp[n] = r;
tmp[n + k] = r;
tmp[n + 3*k + 1] = 1UL;
tmp[n + 4*k + 2] = 1UL;
n += 6*k + 5;
}
if (n < len) tmp[n] = r;
if (n + k < len) tmp[n + k] = r;
if (n + 3*k + 1 < len) tmp[n + 3*k + 1] = 1L;
_nmod_poly_inv_series(res, tmp, len, mod);
_nmod_vec_free(tmp);
}
void
nmod_poly_randtest_pentomial(nmod_poly_t poly, flint_rand_t state, slong len)
{
nmod_poly_fit_length(poly, len);
_nmod_vec_zero(poly->coeffs, len);
poly->coeffs[0] = n_randtest(state) % poly->mod.n;
poly->coeffs[1] = n_randtest(state) % poly->mod.n;
poly->coeffs[2] = n_randtest(state) % poly->mod.n;
poly->coeffs[3] = n_randtest(state) % poly->mod.n;
poly->coeffs[len - 1] = 1;
_nmod_poly_set_length(poly, len);
}
void
nmod_poly_randtest_trinomial(nmod_poly_t poly, flint_rand_t state, slong len)
{
ulong k;
nmod_poly_fit_length(poly, len);
_nmod_vec_zero(poly->coeffs, len);
poly->coeffs[0] = n_randtest(state) % poly->mod.n;
poly->coeffs[len - 1] = 1;
k = (n_randtest(state) % (len - 2)) + 1;
poly->coeffs[k] = n_randtest(state) % poly->mod.n;
_nmod_poly_set_length(poly, len);
}
void
__nmod_poly_exp_series_prealloc(mp_ptr f, mp_ptr g, mp_srcptr h,
mp_srcptr hprime, mp_ptr T, mp_ptr U, long n, nmod_t mod, int extend)
{
long m, m2, l;
if (n < NMOD_NEWTON_EXP_CUTOFF)
{
_nmod_poly_exp_series_basecase(f, h, n, n, mod);
_nmod_poly_inv_series_basecase(g, f, extend ? n : (n + 1) / 2, mod);
return;
}
m = (n + 1) / 2;
m2 = (m + 1) / 2;
l = m - 1; /* shifted for derivative */
/* f := exp(h) + O(x^m), g := exp(-h) + O(x^m2) */
__nmod_poly_exp_series_prealloc(f, g, h, hprime, T, U, m, mod, 0);
/* g := exp(-h) + O(x^m) */
_nmod_poly_mullow(T, f, m, g, m2, m, mod);
_nmod_poly_mullow(g + m2, g, m2, T + m2, m - m2, m - m2, mod);
_nmod_vec_neg(g + m2, g + m2, m - m2, mod);
/* U := h' + g (f' - f h') + O(x^(n-1))
Note: should replace h' by h' mod x^(m-1) */
_nmod_vec_zero(f + m, n - m);
_nmod_poly_mullow(T, f, n, hprime, n, n, mod); /* should be mulmid */
_nmod_poly_derivative(U, f, n, mod); /* should skip low terms */
_nmod_vec_sub(U + l, U + l, T + l, n - l, mod);
_nmod_poly_mullow(T + l, g, n - m, U + l, n - m, n - m, mod);
_nmod_vec_add(U + l, hprime + l, T + l, n - m, mod);
/* f := f + f * (h - int U) + O(x^n) = exp(h) + O(x^n) */
_nmod_poly_integral(U, U, n, mod); /* should skip low terms */
_nmod_vec_sub(U + m, h + m, U + m, n - m, mod);
_nmod_poly_mullow(f + m, f, n - m, U + m, n - m, n - m, mod);
/* g := exp(-h) + O(x^n) */
if (extend)
{
_nmod_poly_mullow(T, f, n, g, m, n, mod);
_nmod_poly_mullow(g + m, g, m, T + m, n - m, n - m, mod);
_nmod_vec_neg(g + m, g + m, n - m, mod);
}
}
void _fq_nmod_trace(fmpz_t rop2, const mp_limb_t *op, slong len,
const fq_nmod_ctx_t ctx)
{
const slong d = fq_nmod_ctx_degree(ctx);
ulong i, l;
mp_limb_t *t, rop;
t = _nmod_vec_init(d);
_nmod_vec_zero(t, d);
t[0] = n_mod2_preinv(d, ctx->mod.n, ctx->mod.ninv);
for (i = 1; i < d; i++)
{
for (l = ctx->len - 2; l >= 0 && ctx->j[l] >= d - (i - 1); l--)
{
t[i] = n_addmod(t[i],
n_mulmod2_preinv(t[ctx->j[l] + i - d], ctx->a[l], ctx->mod.n, ctx->mod.ninv),
ctx->mod.n);
}
if (l >= 0 && ctx->j[l] == d - i)
{
t[i] = n_addmod(t[i],
n_mulmod2_preinv(ctx->a[l], i, ctx->mod.n, ctx->mod.ninv),
ctx->mod.n);
}
t[i] = n_negmod(t[i], ctx->mod.n);
}
rop = WORD(0);
for (i = 0; i < d; i++)
{
rop = n_addmod(rop,
n_mulmod2_preinv(op[i], t[i], ctx->mod.n, ctx->mod.ninv),
ctx->mod.n);
}
_nmod_vec_clear(t);
fmpz_set_ui(rop2, rop);
}
void
_nmod_poly_exp_series_monomial_ui(mp_ptr res, mp_limb_t coeff, ulong power,
slong n, nmod_t mod)
{
slong k, r;
mp_limb_t rfac;
mp_limb_t a;
r = (n - 1) / power;
rfac = n_factorial_mod2_preinv(r, mod.n, mod.ninv);
rfac = n_invmod(rfac, mod.n);
if (power > 1)
_nmod_vec_zero(res, n);
res[0] = UWORD(1);
if (coeff == UWORD(1))
{
a = rfac;
for (k = r; k >= 1; k--)
{
res[k * power] = a;
a = n_mulmod2_preinv(a, k, mod.n, mod.ninv);
}
}
else
{
a = coeff;
for (k = power; k < n; k += power)
{
res[k] = a;
a = n_mulmod2_preinv(a, coeff, mod.n, mod.ninv);
}
a = rfac;
for (k = r; k >= 1; k--)
{
res[k * power] = n_mulmod2_preinv(res[k * power],
a, mod.n, mod.ninv);
a = n_mulmod2_preinv(a, k, mod.n, mod.ninv);
}
}
}
void
_nmod_poly_interpolate_nmod_vec_barycentric(mp_ptr poly,
mp_srcptr xs, mp_srcptr ys, slong n, nmod_t mod)
{
mp_ptr P, Q, w;
slong i, j;
if (n == 1)
{
poly[0] = ys[0];
return;
}
P = _nmod_vec_init(n + 1);
Q = _nmod_vec_init(n);
w = _nmod_vec_init(n);
_nmod_poly_product_roots_nmod_vec(P, xs, n, mod);
for (i = 0; i < n; i++)
{
w[i] = UWORD(1);
for (j = 0; j < n; j++)
{
if (i != j)
w[i] = nmod_mul(w[i], nmod_sub(xs[i], xs[j], mod), mod);
}
w[i] = n_invmod(w[i], mod.n);
}
_nmod_vec_zero(poly, n);
for (i = 0; i < n; i++)
{
_nmod_poly_div_root(Q, P, n + 1, xs[i], mod);
_nmod_vec_scalar_addmul_nmod(poly, Q, n,
nmod_mul(w[i], ys[i], mod), mod);
}
_nmod_vec_clear(P);
_nmod_vec_clear(Q);
_nmod_vec_clear(w);
}
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);
}
}
