void
nmod_poly_compose_series_horner(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, long n)
{
long len1 = poly1->length;
long len2 = poly2->length;
long lenr;
if (len2 != 0 && poly2->coeffs[0] != 0)
{
printf("exception: nmod_poly_compose_series_horner: inner polynomial "
"must have zero constant term\n");
abort();
}
if (len1 == 0 || n == 0)
{
nmod_poly_zero(res);
return;
}
if (len2 == 0 || len1 == 1)
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = poly1->coeffs[0];
res->length = 1;
_nmod_poly_normalise(res);
return;
}
lenr = FLINT_MIN((len1 - 1) * (len2 - 1) + 1, n);
len1 = FLINT_MIN(len1, lenr);
len2 = FLINT_MIN(len2, lenr);
if ((res != poly1) && (res != poly2))
{
nmod_poly_fit_length(res, lenr);
_nmod_poly_compose_series_horner(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, res->mod);
res->length = lenr;
_nmod_poly_normalise(res);
}
else
{
nmod_poly_t t;
nmod_poly_init2_preinv(t, res->mod.n, res->mod.ninv, lenr);
_nmod_poly_compose_series_horner(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, lenr, res->mod);
t->length = lenr;
_nmod_poly_normalise(t);
nmod_poly_swap(res, t);
nmod_poly_clear(t);
}
}
void
nmod_poly_pow(nmod_poly_t res, const nmod_poly_t poly, ulong e)
{
const slong len = poly->length;
slong rlen;
if ((len < 2) | (e < UWORD(3)))
{
if (len == 0)
nmod_poly_zero(res);
else if (len == 1)
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = n_powmod2_ui_preinv(poly->coeffs[0], e,
poly->mod.n, poly->mod.ninv);
res->length = 1;
_nmod_poly_normalise(res);
}
else if (e == UWORD(0))
{
nmod_poly_set_coeff_ui(res, 0, UWORD(1));
res->length = 1;
_nmod_poly_normalise(res);
}
else if (e == UWORD(1))
nmod_poly_set(res, poly);
else /* e == UWORD(2) */
nmod_poly_mul(res, poly, poly);
return;
}
rlen = (slong) e * (len - 1) + 1;
if (res != poly)
{
nmod_poly_fit_length(res, rlen);
_nmod_poly_pow(res->coeffs, poly->coeffs, len, e, poly->mod);
}
else
{
nmod_poly_t t;
nmod_poly_init2(t, poly->mod.n, rlen);
_nmod_poly_pow(t->coeffs, poly->coeffs, len, e, poly->mod);
nmod_poly_swap(res, t);
nmod_poly_clear(t);
}
res->length = rlen;
_nmod_poly_normalise(res);
}
void nmod_poly_integral(nmod_poly_t x_int, const nmod_poly_t x)
{
nmod_poly_fit_length(x_int, x->length + 1);
_nmod_poly_integral(x_int->coeffs, x->coeffs, x->length + 1, x->mod);
x_int->length = x->length + 1;
_nmod_poly_normalise(x_int);
}
void
nmod_poly_randtest(nmod_poly_t poly, flint_rand_t state, slong len)
{
nmod_poly_fit_length(poly, len);
_nmod_vec_randtest(poly->coeffs, state, len, poly->mod);
poly->length = len;
_nmod_poly_normalise(poly);
}
void
nmod_poly_cosh_series(nmod_poly_t g, const nmod_poly_t h, long n)
{
mp_ptr g_coeffs, h_coeffs;
nmod_poly_t t1;
long h_len;
h_len = h->length;
if (h_len > 0 && h->coeffs[0] != 0UL)
{
printf("Exception: nmod_poly_cosh_series: constant term != 0\n");
abort();
}
if (h_len == 1 || n < 2)
{
nmod_poly_zero(g);
if (n > 0)
nmod_poly_set_coeff_ui(g, 0, 1UL);
return;
}
if (h_len < n)
{
h_coeffs = _nmod_vec_init(n);
mpn_copyi(h_coeffs, h->coeffs, h_len);
mpn_zero(h_coeffs + h_len, n - h_len);
}
else
h_coeffs = h->coeffs;
if (h == g && h_len >= n)
{
nmod_poly_init2(t1, h->mod.n, n);
g_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(g, n);
g_coeffs = g->coeffs;
}
_nmod_poly_cosh_series(g_coeffs, h_coeffs, n, h->mod);
if (h == g && h_len >= n)
{
nmod_poly_swap(g, t1);
nmod_poly_clear(t1);
}
g->length = n;
if (h_len < n)
_nmod_vec_free(h_coeffs);
_nmod_poly_normalise(g);
}
void nmod_poly_divrem_newton(nmod_poly_t Q, nmod_poly_t R,
const nmod_poly_t A, const nmod_poly_t B)
{
const long lenA = A->length, lenB = B->length;
mp_ptr q, r;
if (lenB == 0)
{
printf("Exception: division by zero in nmod_poly_divrem_newton\n");
abort();
}
if (lenA < lenB)
{
nmod_poly_set(R, A);
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
q = _nmod_vec_init(lenA - lenB + 1);
}
else
{
nmod_poly_fit_length(Q, lenA - lenB + 1);
q = Q->coeffs;
}
if (R == A || R == B)
{
r = _nmod_vec_init(lenB - 1);
}
else
{
nmod_poly_fit_length(R, lenB - 1);
r = R->coeffs;
}
_nmod_poly_divrem_newton(q, r, A->coeffs, lenA,
B->coeffs, lenB, B->mod);
if (Q == A || Q == B)
{
_nmod_vec_clear(Q->coeffs);
Q->coeffs = q;
Q->alloc = lenA - lenB + 1;
}
if (R == A || R == B)
{
_nmod_vec_clear(R->coeffs);
R->coeffs = r;
R->alloc = lenB - 1;
}
Q->length = lenA - lenB + 1;
R->length = lenB - 1;
_nmod_poly_normalise(R);
}
void nmod_poly_reverse(nmod_poly_t output, const nmod_poly_t input, long m)
{
nmod_poly_fit_length(output, m);
_nmod_poly_reverse(output->coeffs, input->coeffs, input->length, m);
output->length = m;
_nmod_poly_normalise(output);
}
void
nmod_poly_div_basecase(nmod_poly_t Q, const nmod_poly_t A,
const nmod_poly_t B)
{
mp_ptr Q_coeffs, W;
nmod_poly_t t1;
long Alen, Blen;
Blen = B->length;
if (Blen == 0)
{
printf("Exception: division by zero in nmod_poly_div_basecase\n");
abort();
}
Alen = A->length;
if (Alen < Blen)
{
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
nmod_poly_init2_preinv(t1, B->mod.n, B->mod.ninv,
Alen - Blen + 1);
Q_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Q, Alen - Blen + 1);
Q_coeffs = Q->coeffs;
}
W = _nmod_vec_init(NMOD_DIV_BC_ITCH(Alen, Blen, A->mod));
_nmod_poly_div_basecase(Q_coeffs, W, A->coeffs, Alen,
B->coeffs, Blen, B->mod);
if (Q == A || Q == B)
{
nmod_poly_swap(Q, t1);
nmod_poly_clear(t1);
}
Q->length = Alen - Blen + 1;
_nmod_vec_clear(W);
_nmod_poly_normalise(Q);
}
void
nmod_poly_revert_series_lagrange(nmod_poly_t Qinv,
const nmod_poly_t Q, long n)
{
mp_ptr Qinv_coeffs, Q_coeffs;
nmod_poly_t t1;
long Qlen;
Qlen = Q->length;
if (Qlen < 2 || Q->coeffs[0] != 0 || Q->coeffs[1] == 0)
{
printf("exception: nmod_poly_revert_series_lagrange: input must have "
"zero constant and an invertible coefficient of x^1");
abort();
}
if (Qlen < n)
{
Q_coeffs = _nmod_vec_init(n);
mpn_copyi(Q_coeffs, Q->coeffs, Qlen);
mpn_zero(Q_coeffs + Qlen, n - Qlen);
}
else
Q_coeffs = Q->coeffs;
if (Q == Qinv && Qlen >= n)
{
nmod_poly_init2(t1, Q->mod.n, n);
Qinv_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Qinv, n);
Qinv_coeffs = Qinv->coeffs;
}
_nmod_poly_revert_series_lagrange(Qinv_coeffs, Q_coeffs, n, Q->mod);
if (Q == Qinv && Qlen >= n)
{
nmod_poly_swap(Qinv, t1);
nmod_poly_clear(t1);
}
Qinv->length = n;
if (Qlen < n)
_nmod_vec_clear(Q_coeffs);
_nmod_poly_normalise(Qinv);
}
void fq_nmod_pow(fq_nmod_t rop, const fq_nmod_t op, const fmpz_t e, const fq_nmod_ctx_t ctx)
{
if (fmpz_sgn(e) < 0)
{
flint_printf("Exception (fq_nmod_pow). e < 0.\n");
abort();
}
if (fmpz_is_zero(e))
{
fq_nmod_one(rop, ctx);
}
else if (fq_nmod_is_zero(op, ctx))
{
fq_nmod_zero(rop, ctx);
}
else if (fmpz_is_one(e))
{
fq_nmod_set(rop, op, ctx);
}
else
{
const slong d = fq_nmod_ctx_degree(ctx);
mp_limb_t *t;
if (rop == op)
{
t = _nmod_vec_init(2 * d - 1);
}
else
{
nmod_poly_fit_length(rop, 2 * d - 1);
t = rop->coeffs;
}
_fq_nmod_pow(t, op->coeffs, op->length, e, ctx);
if (rop == op)
{
_nmod_vec_clear(rop->coeffs);
rop->coeffs = t;
rop->alloc = 2 * d - 1;
rop->length = d;
}
else
{
_nmod_poly_set_length(rop, d);
}
_nmod_poly_normalise(rop);
}
}
void
nmod_poly_inv_series_basecase(nmod_poly_t Qinv,
const nmod_poly_t Q, long n)
{
mp_ptr Qinv_coeffs, Q_coeffs;
nmod_poly_t t1;
long Qlen;
Qlen = Q->length;
if (n == 0 || Q->length == 0 || Q->coeffs[0] == 0)
{
printf("Exception: division by zero in nmod_poly_inv_series_basecase\n");
abort();
}
if (Qlen < n)
{
Q_coeffs = _nmod_vec_init(n);
mpn_copyi(Q_coeffs, Q->coeffs, Qlen);
mpn_zero(Q_coeffs + Qlen, n - Qlen);
}
else
Q_coeffs = Q->coeffs;
if (Q == Qinv && Qlen >= n)
{
nmod_poly_init2(t1, Q->mod.n, n);
Qinv_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Qinv, n);
Qinv_coeffs = Qinv->coeffs;
}
_nmod_poly_inv_series_basecase(Qinv_coeffs, Q_coeffs, n, Q->mod);
if (Q == Qinv && Qlen >= n)
{
nmod_poly_swap(Qinv, t1);
nmod_poly_clear(t1);
}
Qinv->length = n;
if (Qlen < n)
_nmod_vec_free(Q_coeffs);
_nmod_poly_normalise(Qinv);
}
void
nmod_poly_mulmod(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, const nmod_poly_t f)
{
long len1, len2, lenf;
mp_ptr fcoeffs;
lenf = f->length;
len1 = poly1->length;
len2 = poly2->length;
if (lenf == 0)
{
printf("Exception: nmod_poly_mulmod: divide by zero\n");
abort();
}
if (lenf == 1 || len1 == 0 || len2 == 0)
{
nmod_poly_zero(res);
return;
}
if (len1 + len2 - lenf > 0)
{
if (f == res)
{
fcoeffs = flint_malloc(sizeof(mp_limb_t) * lenf);
_nmod_vec_set(fcoeffs, f->coeffs, lenf);
}
else
fcoeffs = f->coeffs;
nmod_poly_fit_length(res, lenf - 1);
_nmod_poly_mulmod(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2,
fcoeffs, lenf,
res->mod);
if (f == res)
flint_free(fcoeffs);
res->length = lenf - 1;
_nmod_poly_normalise(res);
}
else
{
nmod_poly_mul(res, poly1, poly2);
}
}
void nmod_poly_mulhigh(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2, long n)
{
long len1, len2, len_out;
len1 = poly1->length;
len2 = poly2->length;
len_out = poly1->length + poly2->length - 1;
if (n > len_out)
n = len_out;
if (len1 == 0 || len2 == 0 || n == 0)
{
nmod_poly_zero(res);
return;
}
if (res == poly1 || res == poly2)
{
nmod_poly_t temp;
nmod_poly_init2(temp, poly1->mod.n, len_out);
if (len1 >= len2)
_nmod_poly_mulhigh(temp->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, n, poly1->mod);
else
_nmod_poly_mulhigh(temp->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1, n, poly1->mod);
nmod_poly_swap(temp, res);
nmod_poly_clear(temp);
} else
{
nmod_poly_fit_length(res, len_out);
if (len1 >= len2)
_nmod_poly_mulhigh(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, n, poly1->mod);
else
_nmod_poly_mulhigh(res->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1, n, poly1->mod);
}
res->length = len_out;
_nmod_poly_normalise(res);
}
void
nmod_poly_mullow_classical(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
slong trunc)
{
slong len_out;
if (poly1->length == 0 || poly2->length == 0 || trunc == 0)
{
nmod_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
if (trunc > len_out)
trunc = len_out;
if (res == poly1 || res == poly2)
{
nmod_poly_t temp;
nmod_poly_init2_preinv(temp, poly1->mod.n, poly1->mod.ninv, trunc);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_classical(temp->coeffs, poly1->coeffs,
poly1->length, poly2->coeffs,
poly2->length, trunc, poly1->mod);
else
_nmod_poly_mullow_classical(temp->coeffs, poly2->coeffs,
poly2->length, poly1->coeffs,
poly1->length, trunc, poly1->mod);
nmod_poly_swap(res, temp);
nmod_poly_clear(temp);
}
else
{
nmod_poly_fit_length(res, trunc);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_classical(res->coeffs, poly1->coeffs,
poly1->length, poly2->coeffs,
poly2->length, trunc, poly1->mod);
else
_nmod_poly_mullow_classical(res->coeffs, poly2->coeffs,
poly2->length, poly1->coeffs,
poly1->length, trunc, poly1->mod);
}
res->length = trunc;
_nmod_poly_normalise(res);
}
void
nmod_poly_mullow_KS(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
mp_bitcnt_t bits, long n)
{
long len_out;
if ((poly1->length == 0) || (poly2->length == 0))
{
nmod_poly_zero(res);
return;
}
len_out = poly1->length + poly2->length - 1;
if (n > len_out)
n = len_out;
if (res == poly1 || res == poly2)
{
nmod_poly_t temp;
nmod_poly_init2_preinv(temp, poly1->mod.n, poly1->mod.ninv, len_out);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_KS(temp->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, bits,
n, poly1->mod);
else
_nmod_poly_mullow_KS(temp->coeffs, poly2->coeffs, poly2->length,
poly1->coeffs, poly1->length, bits,
n, poly1->mod);
nmod_poly_swap(res, temp);
nmod_poly_clear(temp);
}
else
{
nmod_poly_fit_length(res, len_out);
if (poly1->length >= poly2->length)
_nmod_poly_mullow_KS(res->coeffs, poly1->coeffs, poly1->length,
poly2->coeffs, poly2->length, bits,
n, poly1->mod);
else
_nmod_poly_mullow_KS(res->coeffs, poly2->coeffs, poly2->length,
poly1->coeffs, poly1->length, bits,
n, poly1->mod);
}
res->length = n;
_nmod_poly_normalise(res);
}
void
_fmpz_vec_get_nmod_poly(nmod_poly_t res, const fmpz * coeffs, slong len)
{
if (len == 0)
{
nmod_poly_zero(res);
}
else
{
slong i;
nmod_poly_fit_length(res, len);
for (i = 0; i < len; i++)
res->coeffs[i] = fmpz_fdiv_ui(coeffs + i, res->mod.n);
_nmod_poly_set_length(res, len);
_nmod_poly_normalise(res);
}
}
void
nmod_poly_interpolate_nmod_vec_barycentric(nmod_poly_t poly,
mp_srcptr xs, mp_srcptr ys, slong n)
{
if (n == 0)
{
nmod_poly_zero(poly);
}
else
{
nmod_poly_fit_length(poly, n);
poly->length = n;
_nmod_poly_interpolate_nmod_vec_barycentric(poly->coeffs,
xs, ys, n, poly->mod);
_nmod_poly_normalise(poly);
}
}
void
nmod_poly_rem_basecase(nmod_poly_t R, const nmod_poly_t A, const nmod_poly_t B)
{
const long lenA = A->length, lenB = B->length;
mp_ptr r, W;
nmod_poly_t t;
if (lenB == 0)
{
printf("Exception: division by zero in nmod_poly_rem_basecase\n");
abort();
}
if (lenA < lenB)
{
nmod_poly_set(R, A);
return;
}
if (R == A || R == B)
{
nmod_poly_init2_preinv(t, B->mod.n, B->mod.ninv, lenB - 1);
r = t->coeffs;
}
else
{
nmod_poly_fit_length(R, lenB - 1);
r = R->coeffs;
}
W = _nmod_vec_init(NMOD_DIVREM_BC_ITCH(lenA, lenB, A->mod));
_nmod_poly_rem_basecase(r, W, A->coeffs, lenA,
B->coeffs, lenB, B->mod);
if (R == A || R == B)
{
nmod_poly_swap(R, t);
nmod_poly_clear(t);
}
R->length = lenB - 1;
_nmod_vec_clear(W);
_nmod_poly_normalise(R);
}
void
nmod_poly_compose_divconquer(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
long lenr;
if (len1 == 0)
{
nmod_poly_zero(res);
return;
}
if (len1 == 1 || len2 == 0)
{
nmod_poly_set_coeff_ui(res, 0, poly1->coeffs[0]);
nmod_poly_truncate(res, 1);
return;
}
lenr = (len1 - 1) * (len2 - 1) + 1;
if (res != poly1 && res != poly2)
{
nmod_poly_fit_length(res, lenr);
_nmod_poly_compose_divconquer(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, poly1->mod);
}
else
{
nmod_poly_t t;
nmod_poly_init2(t, poly1->mod.n, lenr);
_nmod_poly_compose_divconquer(t->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2, poly1->mod);
nmod_poly_swap(res, t);
nmod_poly_clear(t);
}
res->length = lenr;
_nmod_poly_normalise(res);
}
void
nmod_poly_exp_series_monomial_ui(nmod_poly_t res, mp_limb_t coeff,
ulong power, slong n)
{
if (n == 0)
{
nmod_poly_zero(res);
return;
}
if (coeff == UWORD(0))
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = UWORD(1);
res->length = 1;
return;
}
if (power == 0)
{
flint_printf("Exception (nmod_poly_exp_series_monomial_ui). \n"
"Constant term != 0.\n");
abort();
}
if (coeff != UWORD(1))
coeff = n_mod2_preinv(coeff, res->mod.n, res->mod.ninv);
if (n == 1 || power >= n)
{
nmod_poly_fit_length(res, 1);
res->coeffs[0] = UWORD(1);
res->length = 1;
}
nmod_poly_fit_length(res, n);
_nmod_poly_exp_series_monomial_ui(res->coeffs, coeff, power, n, res->mod);
res->length = n;
_nmod_poly_normalise(res);
}
void embeddings_isomorphism(nmod_poly_t G, mp_srcptr F,
const embeddings_t FP, const embeddings_t FQ, const embeddings_t FR){
long m = nmod_poly_degree(FP->P);
long n = nmod_poly_degree(FQ->P);
long i;
nmod_poly_t tmpF, tmpG, S, X;
nmod_t mod = FP->P->mod;
nmod_poly_init(tmpF, mod.n);
nmod_poly_init(tmpG, mod.n);
nmod_poly_init(S, mod.n);
nmod_poly_init(X, mod.n);
nmod_poly_zero(G);
nmod_poly_zero(X);
nmod_poly_set_coeff_ui(X, 1, 1);
embeddings_embed(S, X, FP, FQ, FR);
for (i = m-1; i >= 0; i--){
nmod_poly_fit_length(tmpF, n);
long j;
long offset = i*n;
for (j = 0; j < n; j++)
tmpF->coeffs[j] = F[offset+j];
tmpF->length = n;
_nmod_poly_normalise(tmpF);
embeddings_embed(tmpG, tmpF, FQ, FP, FR);
nmod_poly_mulmod(G, G, S, FR->P);
nmod_poly_add(G, G, tmpG);
}
nmod_poly_clear(tmpF);
nmod_poly_clear(tmpG);
nmod_poly_clear(X);
nmod_poly_clear(S);
}
void
nmod_poly_asin_series(nmod_poly_t g, const nmod_poly_t h, slong n)
{
mp_ptr h_coeffs;
slong h_len = h->length;
if (h_len > 0 && h->coeffs[0] != UWORD(0))
{
flint_printf("Exception (nmod_poly_asin_series). Constant term != 0.\n");
abort();
}
if (h_len == 1 || n < 2)
{
nmod_poly_zero(g);
return;
}
nmod_poly_fit_length(g, n);
if (h_len < n)
{
h_coeffs = _nmod_vec_init(n);
flint_mpn_copyi(h_coeffs, h->coeffs, h_len);
flint_mpn_zero(h_coeffs + h_len, n - h_len);
}
else
h_coeffs = h->coeffs;
_nmod_poly_asin_series(g->coeffs, h_coeffs, n, h->mod);
if (h_len < n)
_nmod_vec_clear(h_coeffs);
g->length = n;
_nmod_poly_normalise(g);
}
void
nmod_poly_tanh_series(nmod_poly_t g, const nmod_poly_t h, long n)
{
mp_ptr h_coeffs;
long h_len = h->length;
if (h_len > 0 && h->coeffs[0] != 0UL)
{
printf("Exception: nmod_poly_tanh_series: constant term != 0\n");
abort();
}
if (h_len == 1 || n < 2)
{
nmod_poly_zero(g);
return;
}
nmod_poly_fit_length(g, n);
if (h_len < n)
{
h_coeffs = _nmod_vec_init(n);
mpn_copyi(h_coeffs, h->coeffs, h_len);
mpn_zero(h_coeffs + h_len, n - h_len);
}
else
h_coeffs = h->coeffs;
_nmod_poly_tanh_series(g->coeffs, h_coeffs, n, h->mod);
if (h_len < n)
_nmod_vec_free(h_coeffs);
g->length = n;
_nmod_poly_normalise(g);
}
/*------------------------------------------------------------*/
void check(int opt){
mp_limb_t n = 12345;
nmod_t Zn;
nmod_init(&Zn, n);
sage_output_init(Zn);
nmod_poly_t a;
nmod_poly_init2(a, n, 10);
long i;
for (i = 0; i < 10; i++)
a->coeffs[i] = i;
a->length = 10;
_nmod_poly_normalise(a);
sage_output_print_poly(a);
printf("\n");
nmod_poly_zero(a);
sage_output_print_poly(a);
printf("\n");
nmod_poly_clear(a);
}
void
nmod_poly_exp_series(nmod_poly_t f, const nmod_poly_t h, long n)
{
mp_ptr f_coeffs, h_coeffs;
nmod_poly_t t1;
long hlen, k;
nmod_poly_fit_length(f, n);
hlen = h->length;
if (hlen > 0 && h->coeffs[0] != 0UL)
{
printf("Exception: nmod_poly_exp_series: constant term != 0\n");
abort();
}
if (n <= 1 || hlen == 0)
{
if (n == 0)
{
nmod_poly_zero(f);
}
else
{
f->coeffs[0] = 1UL;
f->length = 1;
}
return;
}
/* Handle monomials */
for (k = 0; h->coeffs[k] == 0UL && k < n - 1; k++);
if (k == hlen - 1 || k == n - 1)
{
hlen = FLINT_MIN(hlen, n);
_nmod_poly_exp_series_monomial_ui(f->coeffs,
h->coeffs[hlen-1], hlen - 1, n, f->mod);
f->length = n;
_nmod_poly_normalise(f);
return;
}
if (n < NMOD_NEWTON_EXP_CUTOFF2)
{
_nmod_poly_exp_series_basecase(f->coeffs, h->coeffs, hlen, n, f->mod);
f->length = n;
_nmod_poly_normalise(f);
return;
}
if (hlen < n)
{
h_coeffs = _nmod_vec_init(n);
mpn_copyi(h_coeffs, h->coeffs, hlen);
mpn_zero(h_coeffs + hlen, n - hlen);
}
else
h_coeffs = h->coeffs;
if (h == f && hlen >= n)
{
nmod_poly_init2(t1, h->mod.n, n);
f_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(f, n);
f_coeffs = f->coeffs;
}
_nmod_poly_exp_series(f_coeffs, h_coeffs, n, f->mod);
if (h == f && hlen >= n)
{
nmod_poly_swap(f, t1);
nmod_poly_clear(t1);
}
f->length = n;
if (hlen < n)
_nmod_vec_free(h_coeffs);
_nmod_poly_normalise(f);
}
void
nmod_poly_compose_mod_brent_kung(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
const nmod_poly_t poly3)
{
long len1 = poly1->length;
long len2 = poly2->length;
long len3 = poly3->length;
long len = len3 - 1;
mp_ptr ptr2;
if (len3 == 0)
{
printf("exception: division by zero in "
"nmod_poly_compose_mod_brent_kung\n");
abort();
}
if (len1 >= len3)
{
printf("exception: nmod_poly_compose_brent_kung: the degree of the"
" first polynomial must be smaller than that of the modulus\n");
abort();
}
if (len1 == 0 || len3 == 1)
{
nmod_poly_zero(res);
return;
}
if (len1 == 1)
{
nmod_poly_set(res, poly1);
return;
}
if (res == poly3 || res == poly1)
{
nmod_poly_t tmp;
nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv);
nmod_poly_compose_mod_brent_kung(tmp, poly1, poly2, poly3);
nmod_poly_swap(tmp, res);
nmod_poly_clear(tmp);
return;
}
ptr2 = _nmod_vec_init(len);
if (len2 <= len)
{
mpn_copyi(ptr2, poly2->coeffs, len2);
mpn_zero(ptr2 + len2, len - len2);
}
else
{
_nmod_poly_rem(ptr2, poly2->coeffs, len2,
poly3->coeffs, len3, res->mod);
}
nmod_poly_fit_length(res, len);
_nmod_poly_compose_mod_brent_kung(res->coeffs,
poly1->coeffs, len1, ptr2, poly3->coeffs, len3, res->mod);
res->length = len;
_nmod_poly_normalise(res);
_nmod_vec_clear(ptr2);
}
void
nmod_poly_compose_mod_horner(nmod_poly_t res,
const nmod_poly_t poly1, const nmod_poly_t poly2,
const nmod_poly_t poly3)
{
long len1 = poly1->length;
long len2 = poly2->length;
long len3 = poly3->length;
long len = len3 - 1;
mp_ptr ptr2;
if (len3 == 0)
{
printf("exception: division by zero in nmod_poly_compose_mod_horner\n");
abort();
}
if (len1 == 0 || len3 == 1)
{
nmod_poly_zero(res);
return;
}
if (len1 == 1)
{
nmod_poly_set(res, poly1);
return;
}
if (res == poly3 || res == poly1)
{
nmod_poly_t tmp;
nmod_poly_init_preinv(tmp, res->mod.n, res->mod.ninv);
nmod_poly_compose_mod_horner(tmp, poly1, poly2, poly3);
nmod_poly_swap(tmp, res);
nmod_poly_clear(tmp);
return;
}
ptr2 = _nmod_vec_init(len);
if (len2 <= len)
{
mpn_copyi(ptr2, poly2->coeffs, len2);
mpn_zero(ptr2 + len2, len - len2);
}
else
{
_nmod_poly_rem(ptr2, poly2->coeffs, len2,
poly3->coeffs, len3, res->mod);
}
nmod_poly_fit_length(res, len);
_nmod_poly_compose_mod_horner(res->coeffs,
poly1->coeffs, len1, ptr2, poly3->coeffs, len3, res->mod);
res->length = len;
_nmod_poly_normalise(res);
_nmod_vec_clear(ptr2);
}
int
main(void)
{
int i;
flint_rand_t state;
printf("sqrt... ");
fflush(stdout);
flint_randinit(state);
/* Test aliasing */
for (i = 0; i < 2000; i++)
{
nmod_poly_t a, b;
int square1, square2;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
nmod_poly_init(a, mod);
nmod_poly_init(b, mod);
nmod_poly_randtest(a, state, 1 + n_randint(state, 50));
if (n_randint(state, 2))
nmod_poly_mul(a, a, a);
square1 = nmod_poly_sqrt(b, a);
square2 = nmod_poly_sqrt(a, a);
if ((square1 != square2) || (square1 && !nmod_poly_equal(a, b)))
{
printf("FAIL: aliasing:\n");
printf("square1 = %d, square2 = %d\n\n", square1, square2);
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
}
/* Test random squares */
for (i = 0; i < 2000; i++)
{
nmod_poly_t a, b, c;
int square;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
nmod_poly_init(a, mod);
nmod_poly_init(b, mod);
nmod_poly_init(c, mod);
nmod_poly_randtest(a, state, 1 + n_randint(state, 50));
nmod_poly_mul(b, a, a);
square = nmod_poly_sqrt(c, b);
if (!square)
{
printf("FAIL: square reported nonsquare:\n");
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
printf("c: "); nmod_poly_print(c); printf("\n\n");
abort();
}
nmod_poly_mul(c, c, c);
if (!nmod_poly_equal(c, b))
{
printf("FAIL: sqrt(b)^2 != b:\n");
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
printf("c: "); nmod_poly_print(c); printf("\n\n");
abort();
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(c);
}
/* Test "almost" squares */
for (i = 0; i < 2000; i++)
{
nmod_poly_t a, b, c;
long j;
int square;
mp_limb_t mod;
mod = n_randtest_prime(state, 0);
nmod_poly_init(a, mod);
nmod_poly_init(b, mod);
nmod_poly_init(c, mod);
nmod_poly_randtest_not_zero(a, state, 1 + n_randint(state, 50));
nmod_poly_mul(b, a, a);
j = n_randint(state, nmod_poly_length(b));
b->coeffs[j] = n_randint(state, mod);
_nmod_poly_normalise(b);
square = nmod_poly_sqrt(c, b);
if (square)
{
nmod_poly_mul(c, c, c);
if (!nmod_poly_equal(c, b))
{
printf("FAIL: sqrt(b)^2 != b:\n");
printf("a: "); nmod_poly_print(a); printf("\n\n");
printf("b: "); nmod_poly_print(b); printf("\n\n");
printf("c: "); nmod_poly_print(c); printf("\n\n");
abort();
}
}
nmod_poly_clear(a);
nmod_poly_clear(b);
nmod_poly_clear(c);
}
flint_randclear(state);
printf("PASS\n");
return 0;
}
void
nmod_poly_divrem_basecase(nmod_poly_t Q, nmod_poly_t R, const nmod_poly_t A,
const nmod_poly_t B)
{
const slong lenA = A->length, lenB = B->length;
mp_ptr Q_coeffs, R_coeffs, W;
nmod_poly_t t1, t2;
TMP_INIT;
if (lenB == 0)
{
flint_printf("Exception (nmod_poly_divrem). Division by zero.\n");
abort();
}
if (lenA < lenB)
{
nmod_poly_set(R, A);
nmod_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
nmod_poly_init2_preinv(t1, B->mod.n, B->mod.ninv, lenA - lenB + 1);
Q_coeffs = t1->coeffs;
}
else
{
nmod_poly_fit_length(Q, lenA - lenB + 1);
Q_coeffs = Q->coeffs;
}
if (R == A || R == B)
{
nmod_poly_init2_preinv(t2, B->mod.n, B->mod.ninv, lenB - 1);
R_coeffs = t2->coeffs;
}
else
{
nmod_poly_fit_length(R, lenB - 1);
R_coeffs = R->coeffs;
}
TMP_START;
W = TMP_ALLOC(NMOD_DIVREM_BC_ITCH(lenA, lenB, A->mod)*sizeof(mp_limb_t));
_nmod_poly_divrem_basecase(Q_coeffs, R_coeffs, W, A->coeffs, lenA,
B->coeffs, lenB, B->mod);
if (Q == A || Q == B)
{
nmod_poly_swap(Q, t1);
nmod_poly_clear(t1);
}
if (R == A || R == B)
{
nmod_poly_swap(R, t2);
nmod_poly_clear(t2);
}
Q->length = lenA - lenB + 1;
R->length = lenB - 1;
TMP_END;
_nmod_poly_normalise(R);
}
