void
_fmpz_poly_pseudo_divrem_cohen(fmpz * Q, fmpz * R, const fmpz * A,
long lenA, const fmpz * B, long lenB)
{
const fmpz * leadB = B + (lenB - 1);
long e, lenQ;
fmpz_t pow;
if (lenB == 1)
{
fmpz_init(pow);
fmpz_pow_ui(pow, leadB, lenA - 1);
_fmpz_vec_scalar_mul_fmpz(Q, A, lenA, pow);
_fmpz_vec_zero(R, lenA);
fmpz_clear(pow);
return;
}
lenQ = lenA - lenB + 1;
_fmpz_vec_zero(Q, lenQ);
if (R != A)
_fmpz_vec_set(R, A, lenA);
e = lenA - lenB;
/* Unroll the first run of the while loop */
{
fmpz_set(Q + (lenQ - 1), R + (lenA - 1));
_fmpz_vec_scalar_mul_fmpz(R, R, lenA - 1, leadB);
_fmpz_vec_scalar_submul_fmpz(R + (lenA - lenB), B, lenB - 1, R + (lenA - 1));
fmpz_zero(R + (lenA - 1));
for (lenA -= 2; (lenA >= 0) && (R[lenA] == 0L); lenA--) ;
lenA++;
}
while (lenA >= lenB)
{
_fmpz_vec_scalar_mul_fmpz(Q, Q, lenQ, leadB);
fmpz_add(Q + (lenA - lenB), Q + (lenA - lenB), R + (lenA - 1));
_fmpz_vec_scalar_mul_fmpz(R, R, lenA - 1, leadB);
_fmpz_vec_scalar_submul_fmpz(R + lenA - lenB, B, lenB - 1, R + (lenA - 1));
fmpz_zero(R + (lenA - 1));
for (lenA -= 2; (lenA >= 0) && (R[lenA] == 0L); lenA--) ;
lenA++;
e--;
}
fmpz_init(pow);
fmpz_pow_ui(pow, leadB, e);
_fmpz_vec_scalar_mul_fmpz(Q, Q, lenQ, pow);
_fmpz_vec_scalar_mul_fmpz(R, R, lenA, pow);
fmpz_clear(pow);
}
void _qadic_exp_balanced(fmpz *rop, const fmpz *x, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N, const fmpz_t pN)
{
const slong d = j[lena - 1];
fmpz_t pw;
fmpz *r, *s, *t;
slong i, w;
r = _fmpz_vec_init(d);
s = _fmpz_vec_init(2*d - 1);
t = _fmpz_vec_init(d);
fmpz_init(pw);
fmpz_pow_ui(pw, p, v);
_fmpz_vec_scalar_mul_fmpz(t, x, len, pw);
_fmpz_vec_scalar_mod_fmpz(t, t, len, pN);
_fmpz_vec_zero(t + len, d - len);
fmpz_set(pw, p);
fmpz_one(rop + 0);
_fmpz_vec_zero(rop + 1, d - 1);
w = 1;
while (!_fmpz_vec_is_zero(t, d))
{
fmpz_mul(pw, pw, pw);
for (i = 0; i < d; i++)
{
fmpz_fdiv_r(r + i, t + i, pw);
fmpz_sub(t + i, t + i, r + i);
}
if (!_fmpz_vec_is_zero(r, d))
{
_qadic_exp_bsplit(r, r, w, d, a, j, lena, p, N);
_fmpz_poly_mul(s, rop, d, r, d);
_fmpz_poly_reduce(s, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mod_fmpz(rop, s, d, pN);
}
w *= 2;
}
_fmpz_vec_clear(r, d);
_fmpz_vec_clear(s, 2*d - 1);
_fmpz_vec_clear(t, d);
fmpz_clear(pw);
}
void _fmpz_poly_sqrlow_KS(fmpz * res, const fmpz * poly, long len, long n)
{
int neg;
long bits, limbs, loglen, sign = 0;
mp_limb_t *arr_in, *arr_out;
FMPZ_VEC_NORM(poly, len);
if (len == 0)
{
_fmpz_vec_zero(res, n);
return;
}
neg = (fmpz_sgn(poly + len - 1) > 0) ? 0 : -1;
if (n > 2 * len - 1)
{
_fmpz_vec_zero(res + 2 * len - 1, n - (2 * len - 1));
n = 2 * len - 1;
}
bits = _fmpz_vec_max_bits(poly, len);
if (bits < 0)
{
sign = 1;
bits = - bits;
}
loglen = FLINT_BIT_COUNT(len);
bits = 2 * bits + loglen + sign;
limbs = (bits * len - 1) / FLINT_BITS + 1;
arr_in = flint_calloc(limbs, sizeof(mp_limb_t));
arr_out = flint_malloc((2 * limbs) * sizeof(mp_limb_t));
_fmpz_poly_bit_pack(arr_in, poly, len, bits, neg);
mpn_sqr(arr_out, arr_in, limbs);
if (sign)
_fmpz_poly_bit_unpack(res, n, arr_out, bits, 0);
else
_fmpz_poly_bit_unpack_unsigned(res, n, arr_out, bits);
flint_free(arr_in);
flint_free(arr_out);
}
void _fmpq_poly_scalar_mul_fmpz(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, long len,
const fmpz_t c)
{
fmpz_t gcd; /* GCD( den, c ) */
if (fmpz_is_zero(c))
{
_fmpz_vec_zero(rpoly, len);
fmpz_one(rden);
return;
}
fmpz_init(gcd);
fmpz_one(gcd);
if (*c != 1L)
fmpz_gcd(gcd, c, den);
if (*gcd == 1L)
{
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, c);
fmpz_set(rden, den);
}
else
{
fmpz_t c2;
fmpz_init(c2);
fmpz_divexact(c2, c, gcd);
_fmpz_vec_scalar_mul_fmpz(rpoly, poly, len, c2);
fmpz_divexact(rden, den, gcd);
fmpz_clear(c2);
}
fmpz_clear(gcd);
}
/* Assumes poly1 and poly2 are not length 0 and len1 >= len2. */
void
_fmpz_poly_mul_karatsuba(fmpz * res, const fmpz * poly1,
long len1, const fmpz * poly2, long len2)
{
fmpz *rev1, *rev2, *out, *temp;
long length, loglen = 0;
if (len1 == 1)
{
fmpz_mul(res, poly1, poly2);
return;
}
while ((1L << loglen) < len1)
loglen++;
length = (1L << loglen);
rev1 = (fmpz *) flint_calloc(4 * length, sizeof(fmpz *));
rev2 = rev1 + length;
out = rev1 + 2 * length;
temp = _fmpz_vec_init(2 * length);
revbin1(rev1, poly1, len1, loglen);
revbin1(rev2, poly2, len2, loglen);
_fmpz_poly_mul_kara_recursive(out, rev1, rev2, temp, loglen);
_fmpz_vec_zero(res, len1 + len2 - 1);
revbin2(res, out, len1 + len2 - 1, loglen + 1);
_fmpz_vec_clear(temp, 2 * length);
flint_free(rev1);
}
int
fmpq_poly_set_str(fmpq_poly_t poly, const char * str)
{
int ans;
long len;
len = atol(str);
if (len < 0)
return -1;
if (len == 0)
{
fmpq_poly_zero(poly);
return 0;
}
fmpq_poly_fit_length(poly, len);
ans = _fmpq_poly_set_str(poly->coeffs, poly->den, str);
if (ans == 0)
{
_fmpq_poly_set_length(poly, len);
_fmpq_poly_normalise(poly);
}
else
{
_fmpz_vec_zero(poly->coeffs, len);
fmpz_set_ui(poly->den, 1);
_fmpq_poly_set_length(poly, 0);
}
return ans;
}
void _fmpq_poly_scalar_mul_ui(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, slong len,
ulong c)
{
fmpz_t gcd; /* GCD( den, c ) */
if (c == 0)
{
_fmpz_vec_zero(rpoly, len);
fmpz_one(rden);
return;
}
fmpz_init(gcd);
fmpz_set_ui(gcd, c);
fmpz_gcd(gcd, gcd, den);
if (*gcd == WORD(1))
{
_fmpz_vec_scalar_mul_ui(rpoly, poly, len, c);
fmpz_set(rden, den);
}
else
{
ulong gcd2 = fmpz_get_ui(gcd);
ulong c2 = c / gcd2;
_fmpz_vec_scalar_mul_ui(rpoly, poly, len, c2);
fmpz_fdiv_q_ui(rden, den, gcd2);
}
fmpz_clear(gcd);
}
void
_fmpq_poly_compose_series_horner(fmpz * res, fmpz_t den, const fmpz * poly1,
const fmpz_t den1, long len1, const fmpz * poly2,
const fmpz_t den2, long len2, long n)
{
if (fmpz_is_one(den2))
{
_fmpz_poly_compose_series(res, poly1, len1, poly2, len2, n);
fmpz_set(den, den1);
_fmpq_poly_canonicalise(res, den, n);
}
else if (n == 1)
{
fmpz_set(res, poly1);
fmpz_set(den, den1);
_fmpq_poly_canonicalise(res, den, 1);
}
else
{
long i = len1 - 1;
long lenr;
fmpz_t tden;
fmpz * t = _fmpz_vec_init(n);
fmpz_init(tden);
_fmpz_vec_zero(res, n);
lenr = len2;
_fmpq_poly_scalar_mul_fmpz(res, den, poly2, den2, len2, poly1 + i);
_fmpq_poly_scalar_div_fmpz(res, den, res, den, len2, den1);
i--;
_fmpq_poly_add(res, den, res, den, len2, poly1 + i, den1, 1);
_fmpq_poly_canonicalise(res, den, lenr);
while (i > 0)
{
i--;
if (lenr + len2 - 1 < n)
{
_fmpq_poly_mul(t, tden, res, den, lenr, poly2, den2, len2);
lenr = lenr + len2 - 1;
}
else
{
_fmpq_poly_mullow(t, tden, res, den, lenr,
poly2, den2, len2, n);
lenr = n;
}
_fmpq_poly_canonicalise(t, tden, lenr);
_fmpq_poly_add(res, den, t, tden, lenr, poly1 + i, den1, 1);
}
_fmpq_poly_canonicalise(res, den, n);
_fmpz_vec_clear(t, n);
fmpz_clear(tden);
}
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("is_zero....");
fflush(stdout);
flint_randinit(state);
/* Check zero vector */
for (i = 0; i < 10000; i++)
{
fmpz *a;
long len = n_randint(state, 100);
a = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_zero(a, len);
result = (_fmpz_vec_is_zero(a, len));
if (!result)
{
printf("FAIL1:\n");
_fmpz_vec_print(a, len), printf("\n\n");
abort();
}
_fmpz_vec_clear(a, len);
}
/* Check non-zero vector */
for (i = 0; i < 10000; i++)
{
fmpz *a;
long len = n_randint(state, 100) + 1;
a = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
fmpz_set_ui(a + (len - 1), 1UL);
result = (!_fmpz_vec_is_zero(a, len));
if (!result)
{
printf("FAIL2:\n");
_fmpz_vec_print(a, len), printf("\n\n");
abort();
}
_fmpz_vec_clear(a, len);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
void
_fmpq_poly_invsqrt_series(fmpz * rpoly, fmpz_t rden,
const fmpz * poly, const fmpz_t den, long n)
{
long m;
fmpz * t, * u;
fmpz_t tden, uden;
if (n == 1)
{
fmpz_one(rpoly);
fmpz_one(rden);
return;
}
m = (n + 1) / 2;
_fmpq_poly_invsqrt_series(rpoly, rden, poly, den, m);
fmpz_init(tden);
fmpz_init(uden);
t = _fmpz_vec_init(n);
u = _fmpz_vec_init(n);
_fmpz_vec_zero(rpoly + m, n - m);
_fmpq_poly_mul(t, tden, rpoly, rden, m, rpoly, rden, m);
if (2*m - 1 < n)
fmpz_zero(t + n - 1);
_fmpq_poly_mullow(u, uden, t, tden, n, rpoly, rden, n, n);
_fmpq_poly_mullow(t, tden, u, uden, n, poly, den, n, n);
_fmpz_vec_neg(t + m, t + m, n - m);
_fmpz_vec_zero(t, m);
fmpz_mul_ui(tden, tden, 2UL);
_fmpq_poly_canonicalise(t, tden, n);
_fmpq_poly_add(rpoly, rden, rpoly, rden, m, t, tden, n);
fmpz_clear(tden);
fmpz_clear(uden);
_fmpz_vec_clear(t, n);
_fmpz_vec_clear(u, n);
}
void
fmpz_poly_zero_coeffs(fmpz_poly_t poly, long i, long j)
{
if (i < 0)
i = 0;
if (j > poly->length)
j = poly->length;
_fmpz_vec_zero(poly->coeffs, j - i);
if (j == poly->length)
{
_fmpz_poly_set_length(poly, i);
_fmpz_poly_normalise(poly);
}
}
void _qadic_exp(fmpz *rop, const fmpz *op, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N, const fmpz_t pN)
{
if (N < (WORD(1) << 13) / (slong) fmpz_bits(p))
{
_qadic_exp_rectangular(rop, op, v, len, a, j, lena, p, N, pN);
}
else
{
const slong d = j[lena - 1];
_qadic_exp_balanced(rop, op, v, len, a, j, lena, p, N, pN);
_fmpz_vec_zero(rop + d, d - 1);
}
}
void
_fmpz_poly_pow_multinomial(fmpz * res, const fmpz * poly, long len, ulong e)
{
long k, low, rlen;
fmpz_t d, t;
fmpz * P;
rlen = (long) e * (len - 1L) + 1L;
_fmpz_vec_zero(res, rlen);
for (low = 0L; poly[low] == 0L; low++) ;
if (low == 0L)
{
P = (fmpz *) poly;
}
else
{
P = (fmpz *) poly + low;
len -= low;
res += (long) e * low;
rlen -= (long) e * low;
}
fmpz_init(d);
fmpz_init(t);
fmpz_pow_ui(res, P, e);
for (k = 1; k < rlen; k++)
{
long i, u = -k;
for (i = 1; i <= FLINT_MIN(k, len - 1); i++)
{
fmpz_mul(t, P + i, res + (k - i));
u += (long) e + 1;
if (u >= 0)
fmpz_addmul_ui(res + k, t, (ulong) u);
else
fmpz_submul_ui(res + k, t, - ((ulong) u));
}
fmpz_add(d, d, P);
fmpz_divexact(res + k, res + k, d);
}
fmpz_clear(d);
fmpz_clear(t);
}
int dgsl_mp_call_identity(fmpz *rop, const dgsl_mp_t *self, gmp_randstate_t state) {
assert(rop); assert(self);
const long n = fmpz_mat_ncols(self->B);
mpz_t tmp_g; mpz_init(tmp_g);
_fmpz_vec_zero(rop, n);
for(long i=0; i<n; i++) {
self->D[0]->call(tmp_g, self->D[0], state);
fmpz_set_mpz(rop+i, tmp_g);
}
mpz_clear(tmp_g);
return 0;
}
void
_fmpz_poly_revert_series_newton(fmpz * Qinv, const fmpz * Q, long n)
{
if (n <= 2)
{
_fmpz_vec_set(Qinv, Q, n);
return;
}
else
{
long *a, i, k;
fmpz *T, *U, *V;
T = _fmpz_vec_init(n);
U = _fmpz_vec_init(n);
V = _fmpz_vec_init(n);
k = n;
for (i = 1; (1L << i) < k; i++);
a = (long *) flint_malloc(i * sizeof(long));
a[i = 0] = k;
while (k >= FLINT_REVERSE_NEWTON_CUTOFF)
a[++i] = (k = (k + 1) / 2);
_fmpz_poly_revert_series_lagrange(Qinv, Q, k);
_fmpz_vec_zero(Qinv + k, n - k);
for (i--; i >= 0; i--)
{
k = a[i];
_fmpz_poly_compose_series(T, Q, k, Qinv, k, k);
_fmpz_poly_derivative(U, T, k); fmpz_zero(U + k - 1);
fmpz_zero(T + 1);
_fmpz_poly_div_series(V, T, U, k);
_fmpz_poly_derivative(T, Qinv, k);
_fmpz_poly_mullow(U, V, k, T, k, k);
_fmpz_vec_sub(Qinv, Qinv, U, k);
}
flint_free(a);
_fmpz_vec_clear(T, n);
_fmpz_vec_clear(U, n);
_fmpz_vec_clear(V, n);
}
}
static void
_qadic_exp_bsplit(fmpz *y, const fmpz *x, slong v, slong len,
const fmpz *a, const slong *j, slong lena,
const fmpz_t p, slong N)
{
const slong d = j[lena - 1];
const slong n = _padic_exp_bound(v, N, p);
if (n == 1)
{
fmpz_one(y + 0);
_fmpz_vec_zero(y + 1, d - 1);
}
else
{
fmpz *P, *T;
fmpz_t Q, R;
slong f;
P = _fmpz_vec_init(2*d - 1);
T = _fmpz_vec_init(2*d - 1);
fmpz_init(Q);
fmpz_init(R);
_qadic_exp_bsplit_series(P, Q, T, x, len, 1, n, a, j, lena);
fmpz_add(T + 0, T + 0, Q); /* (T,Q) := (T,Q) + 1 */
/* Note exp(x) is a unit so val(T) == val(Q). */
f = fmpz_remove(Q, Q, p);
fmpz_pow_ui(R, p, f);
_fmpz_vec_scalar_divexact_fmpz(T, T, d, R);
_padic_inv(Q, Q, p, N);
_fmpz_vec_scalar_mul_fmpz(y, T, d, Q);
_fmpz_vec_clear(P, 2*d - 1);
_fmpz_vec_clear(T, 2*d - 1);
fmpz_clear(Q);
fmpz_clear(R);
}
}
int dgsl_mp_call_inlattice(fmpz *rop, const dgsl_mp_t *self, gmp_randstate_t state) {
assert(rop); assert(self);
const long m = fmpz_mat_nrows(self->B);
const long n = fmpz_mat_ncols(self->B);
mpz_t tmp_g; mpz_init(tmp_g);
fmpz_t tmp_f; fmpz_init(tmp_f);
_fmpz_vec_zero(rop, n);
for(long i=0; i<m; i++) {
self->D[i]->call(tmp_g, self->D[i], state);
fmpz_set_mpz(tmp_f, tmp_g);
_fmpz_vec_scalar_addmul_fmpz(rop, self->B->rows[i], n, tmp_f);
}
_fmpz_vec_add(rop, rop, self->c_z, n);
mpz_clear(tmp_g);
fmpz_clear(tmp_f);
return 0;
}
void
_fmpz_poly_pseudo_divrem_basecase(fmpz * Q, fmpz * R, ulong * d,
const fmpz * A, long lenA, const fmpz * B,
long lenB)
{
const fmpz * leadB = B + (lenB - 1);
long iQ = lenA - lenB, iR = lenA - 1;
fmpz_t rem;
fmpz_init(rem);
*d = 0;
_fmpz_vec_zero(Q, lenA - lenB + 1);
if (R != A)
_fmpz_vec_set(R, A, lenA);
while (iR >= lenB - 1)
{
fmpz_fdiv_qr(Q + iQ, rem, R + iR, leadB);
if (!fmpz_is_zero(rem))
{
_fmpz_vec_scalar_mul_fmpz(Q, Q, lenA - lenB + 1, leadB);
fmpz_set(Q + iQ, R + iR);
_fmpz_vec_scalar_mul_fmpz(R, R, lenA, leadB);
(*d)++;
}
if (lenB > 1)
_fmpz_vec_scalar_submul_fmpz(R + (iR - lenB + 1), B, lenB - 1, Q + iQ);
fmpz_zero(R + iR);
iR--;
iQ--;
}
fmpz_clear(rem);
}
void fmpz_poly_ramanujan_tau(fmpz_poly_t res, long n)
{
long j, k, jv, kv;
fmpz_t tmp;
fmpz_poly_fit_length(res, n);
_fmpz_vec_zero(res->coeffs, n);
_fmpz_poly_set_length(res, n);
fmpz_init(tmp);
for (j = jv = 0; jv < n; jv += ++j)
{
fmpz_set_ui(tmp, 2*j+1);
for (k = kv = 0; jv + kv < n; kv += ++k)
{
if ((j+k) & 1)
fmpz_submul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
else
fmpz_addmul_ui(res->coeffs + jv+kv, tmp, 2*k+1);
}
}
fmpz_poly_mullow(res, res, res, n-1);
fmpz_poly_mullow(res, res, res, n-1);
fmpz_poly_shift_left(res, res, 1);
fmpz_clear(tmp);
}
void
_fmpq_poly_exp_series(fmpz * g, fmpz_t gden,
const fmpz * h, const fmpz_t hden, long n)
{
long m;
fmpz * t, * u;
fmpz_t tden, uden;
if (n < 2)
{
fmpz_one(g);
fmpz_one(gden);
return;
}
m = (n + 1) / 2;
_fmpq_poly_exp_series(g, gden, h, hden, m);
_fmpz_vec_zero(g + m, n - m);
t = _fmpz_vec_init(n);
u = _fmpz_vec_init(n);
fmpz_init(tden);
fmpz_init(uden);
_fmpq_poly_log_series(t, tden, g, gden, n);
_fmpq_poly_sub(t, tden, t, tden, n, h, hden, n);
/* TODO: half of product is redundant! */
_fmpq_poly_mullow(u, uden, g, gden, n, t, tden, n, n);
_fmpq_poly_sub(g, gden, g, gden, n, u, uden, n);
_fmpq_poly_canonicalise(g, gden, n);
fmpz_clear(tden);
fmpz_clear(uden);
_fmpz_vec_clear(t, n);
_fmpz_vec_clear(u, n);
}
/* Assumes poly1 and poly2 are not length 0. */
void
_fmpz_poly_mulhigh_classical(fmpz * res, const fmpz * poly1,
long len1, const fmpz * poly2, long len2,
long start)
{
_fmpz_vec_zero(res, start);
if (len1 == 1 && len2 == 1) /* Special case if the length of both inputs is 1 */
{
if (start == 0)
fmpz_mul(res, poly1, poly2);
}
else /* Ordinary case */
{
long i, m, n;
/* Set res[i] = poly1[i]*poly2[0] */
if (start < len1)
_fmpz_vec_scalar_mul_fmpz(res + start, poly1 + start, len1 - start,
poly2);
/* Set res[i+len1-1] = in1[len1-1]*in2[i] */
m = FLINT_MAX(len1 - 1, start);
_fmpz_vec_scalar_mul_fmpz(res + m, poly2 + m - len1 + 1,
len2 - 1 + len1 - m, poly1 + len1 - 1);
/* out[i+j] += in1[i]*in2[j] */
m = FLINT_MAX(start, len2 - 1);
for (i = m - len2 + 1; i < len1 - 1; i++)
{
n = FLINT_MAX(i + 1, start);
_fmpz_vec_scalar_addmul_fmpz(res + n, poly2 + n - i, len2 + i - n,
poly1 + i);
}
}
}
int dgsl_mp_call_coset(fmpz *rop, const dgsl_mp_t *self, gmp_randstate_t state) {
assert(rop); assert(self);
const long n = fmpz_mat_ncols(self->B);
_fmpz_vec_zero(rop, n);
mpfr_t *c = _mpfr_vec_init(n, mpfr_get_prec(self->sigma));
_mpfr_vec_set(c, self->c, n, MPFR_RNDN);
mpfr_t c_prime;
mpfr_init2(c_prime, mpfr_get_prec(self->sigma));
mpfr_t tmp;
mpfr_init2(tmp, mpfr_get_prec(self->sigma));
mpfr_t sigma_prime;
mpfr_init2(sigma_prime, mpfr_get_prec(self->sigma));
mpz_t z;
mpz_init(z);
mpfr_t z_mpfr;
mpfr_init2(z_mpfr, mpfr_get_prec(self->sigma));
fmpz_t z_fmpz;
fmpz_init(z_fmpz);
size_t tau = 3;
if (ceil(sqrt(log2((double)n))) > tau)
tau = ceil(sqrt(log2((double)n)));
mpfr_t *b = _mpfr_vec_init(n, mpfr_get_prec(self->sigma));
const long m = fmpz_mat_nrows(self->B);
for(long j=0; j<m; j++) {
long i = m-j-1;
_mpfr_vec_dot_product(c_prime, c, self->G->rows[i], n, MPFR_RNDN);
_mpfr_vec_dot_product(tmp, self->G->rows[i], self->G->rows[i], n, MPFR_RNDN);
mpfr_div(c_prime, c_prime, tmp, MPFR_RNDN);
mpfr_sqrt(tmp, tmp, MPFR_RNDN);
mpfr_div(sigma_prime, self->sigma, tmp, MPFR_RNDN);
assert(mpfr_cmp_d(sigma_prime, 0.0) > 0);
dgs_disc_gauss_mp_t *D = dgs_disc_gauss_mp_init(sigma_prime, c_prime, tau, DGS_DISC_GAUSS_UNIFORM_ONLINE);
D->call(z, D, state);
dgs_disc_gauss_mp_clear(D);
mpfr_set_z(z_mpfr, z, MPFR_RNDN);
mpfr_neg(z_mpfr, z_mpfr, MPFR_RNDN);
_mpfr_vec_set_fmpz_vec(b, self->B->rows[i], n, MPFR_RNDN);
_mpfr_vec_scalar_addmul_mpfr(c, b, n, z_mpfr, MPFR_RNDN);
fmpz_set_mpz(z_fmpz, z);
_fmpz_vec_scalar_addmul_fmpz(rop, self->B->rows[i], n, z_fmpz);
}
fmpz_clear(z_fmpz);
mpfr_clear(z_mpfr);
mpfr_clear(sigma_prime);
mpfr_clear(tmp);
mpfr_clear(c_prime);
_mpfr_vec_clear(c, n);
_mpfr_vec_clear(b, n);
return 0;
}
void
_fmpq_poly_interpolate_fmpz_vec(fmpz * poly, fmpz_t den,
const fmpz * xs, const fmpz * ys, long n)
{
fmpz *P, *Q, *w;
fmpz_t t;
long i, j;
/* Constant */
if (n == 1)
{
fmpz_set(poly, ys);
fmpz_one(den);
return;
}
/* Linear */
if (n == 2)
{
fmpz_sub(den, xs, xs + 1);
fmpz_sub(poly + 1, ys, ys + 1);
fmpz_mul(poly, xs, ys + 1);
fmpz_submul(poly, xs + 1, ys);
return;
}
fmpz_init(t);
P = _fmpz_vec_init(n + 1);
Q = _fmpz_vec_init(n);
w = _fmpz_vec_init(n);
/* P = (x-x[0])*(x-x[1])*...*(x-x[n-1]) */
_fmpz_poly_product_roots_fmpz_vec(P, xs, n);
/* Weights */
for (i = 0; i < n; i++)
{
fmpz_one(w + i);
for (j = 0; j < n; j++)
{
if (i != j)
{
fmpz_sub(t, xs + i, xs + j);
fmpz_mul(w + i, w + i, t);
}
}
}
_fmpz_vec_zero(poly, n);
_fmpz_vec_lcm(den, w, n);
for (i = 0; i < n; i++)
{
/* Q = P / (x - x[i]) */
_fmpz_poly_div_root(Q, P, n + 1, xs + i);
/* result += Q * weight(i) */
fmpz_divexact(t, den, w + i);
fmpz_mul(t, t, ys + i);
_fmpz_vec_scalar_addmul_fmpz(poly, Q, n, t);
}
_fmpz_vec_clear(P, n + 1);
_fmpz_vec_clear(Q, n);
_fmpz_vec_clear(w, n);
fmpz_clear(t);
}
/* convert to an fmpz poly with a common exponent and coefficients
at most prec bits, also bounding input error plus rounding error */
void _fmprb_poly_get_fmpz_poly_2exp(fmpr_t error, fmpz_t exp, fmpz * coeffs,
fmprb_srcptr A, long lenA, long prec)
{
fmpz_t top_exp, bot_exp;
long shift;
long i;
int rounding;
fmpz_init(top_exp);
fmpz_init(bot_exp);
if (!_fmprb_poly_mid_get_hull(bot_exp, top_exp, A, lenA))
{
fmpz_zero(exp);
_fmpz_vec_zero(coeffs, lenA);
fmpr_zero(error);
for (i = 0; i < lenA; i++)
{
if (fmpr_cmp(fmprb_radref(A + i), error) > 0)
fmpr_set(error, fmprb_radref(A + i));
}
return; /* no need to clear fmpzs */
}
/* only take as much precision as necessary */
shift = _fmpz_sub_small(top_exp, bot_exp);
prec = FLINT_MIN(prec, shift);
fmpz_sub_ui(exp, top_exp, prec);
/* extract integer polynomial */
rounding = 0;
for (i = 0; i < lenA; i++)
rounding |= fmpr_get_fmpz_fixed_fmpz(coeffs + i,
fmprb_midref(A + i), exp);
fmpr_zero(error);
/* compute maximum of input errors */
for (i = 0; i < lenA; i++)
{
if (fmpr_cmp(fmprb_radref(A + i), error) > 0)
fmpr_set(error, fmprb_radref(A + i));
}
/* add rounding error */
if (rounding)
{
fmpr_t t;
fmpr_init(t);
fmpz_set_ui(fmpr_manref(t), 1UL);
fmpz_set(fmpr_expref(t), exp);
fmpr_add(error, error, t, FMPRB_RAD_PREC, FMPR_RND_UP);
fmpr_clear(t);
}
fmpz_clear(top_exp);
}
void _padic_poly_sub(fmpz *rop, slong *val, slong N,
const fmpz *op1, slong val1, slong len1, slong N1,
const fmpz *op2, slong val2, slong len2, slong N2,
const padic_ctx_t ctx)
{
const slong len = FLINT_MAX(len1, len2);
*val = FLINT_MIN(val1, val2);
if (val1 == val2)
{
_fmpz_poly_sub(rop, op1, len1, op2, len2);
_padic_poly_canonicalise(rop, val, len, ctx->p);
}
else
{
fmpz_t x;
fmpz_init(x);
if (val1 < val2) /* F := p^g (G - p^{h-g} H) */
{
fmpz_pow_ui(x, ctx->p, val2 - val1);
if (rop == op1)
{
_fmpz_vec_zero(rop + len1, len2 - len1);
_fmpz_vec_scalar_submul_fmpz(rop, op2, len2, x);
}
else
{
_fmpz_vec_scalar_mul_fmpz(rop, op2, len2, x);
_fmpz_vec_neg(rop, rop, len2);
_fmpz_poly_add(rop, op1, len1, rop, len2);
}
}
else /* F := p^h (p^(g-h) G - H) */
{
fmpz_pow_ui(x, ctx->p, val1 - val2);
if (rop == op2)
{
_fmpz_vec_neg(rop, op2, len2);
_fmpz_vec_zero(rop + len2, len1 - len2);
_fmpz_vec_scalar_addmul_fmpz(rop, op1, len1, x);
}
else
{
_fmpz_vec_scalar_mul_fmpz(rop, op1, len1, x);
_fmpz_poly_sub(rop, rop, len1, op2, len2);
}
}
fmpz_clear(x);
}
/* Reduce */
if (N - *val > 0)
{
fmpz_t pow;
int alloc;
alloc = _padic_ctx_pow_ui(pow, N - *val, ctx);
if (N >= N1 && N >= N2)
{
slong i;
for (i = 0; i < len; i++)
if (fmpz_sgn(rop + i) < 0)
fmpz_add(rop + i, rop + i, pow);
}
else
{
_fmpz_vec_scalar_mod_fmpz(rop, rop, len, pow);
}
if (alloc)
fmpz_clear(pow);
}
else
{
_fmpz_vec_zero(rop, len);
*val = 0;
}
}
/* Assumes len1 != 0 != len2 */
int
_fmpz_poly_gcd_heuristic(fmpz * res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2)
{
ulong bits1, bits2, max_bits, pack_bits, bound_bits, bits_G, bits_Q;
ulong limbs1, limbs2, limbsg, pack_limbs, qlimbs;
ulong log_glen, log_length;
long sign1, sign2, glen, qlen;
fmpz_t ac, bc, d, gc;
fmpz * A, * B, * G, * Q, * t;
mp_ptr array1, array2, arrayg, q, temp;
int divides;
fmpz_init(ac);
fmpz_init(bc);
fmpz_init(d);
/* compute gcd of content of poly1 and poly2 */
_fmpz_poly_content(ac, poly1, len1);
_fmpz_poly_content(bc, poly2, len2);
fmpz_gcd(d, ac, bc);
/* special case, one of the polys is a constant */
if (len2 == 1) /* if len1 == 1 then so does len2 */
{
fmpz_set(res, d);
fmpz_clear(ac);
fmpz_clear(bc);
fmpz_clear(d);
return 1;
}
/* divide poly1 and poly2 by their content */
A = _fmpz_vec_init(len1);
B = _fmpz_vec_init(len2);
_fmpz_vec_scalar_divexact_fmpz(A, poly1, len1, ac);
_fmpz_vec_scalar_divexact_fmpz(B, poly2, len2, bc);
fmpz_clear(ac);
fmpz_clear(bc);
/* special case, one of the polys is length 2 */
if (len2 == 2) /* if len1 == 2 then so does len2 */
{
Q = _fmpz_vec_init(len1 - len2 + 1);
if (_fmpz_poly_divides(Q, A, len1, B, 2))
{
_fmpz_vec_scalar_mul_fmpz(res, B, 2, d);
if (fmpz_sgn(res + 1) < 0)
_fmpz_vec_neg(res, res, 2);
}
else
{
fmpz_set(res, d);
fmpz_zero(res + 1);
}
fmpz_clear(d);
_fmpz_vec_clear(A, len1);
_fmpz_vec_clear(B, len2);
_fmpz_vec_clear(Q, len1 - len2 + 1);
return 1;
}
/*
Determine how many bits (pack_bits) to pack into. The bound
bound_bits ensures that if G | A and G | B with G primitive
then G is the gcd of A and B. The bound is taken from
http://arxiv.org/abs/cs/0206032v1
*/
bits1 = FLINT_ABS(_fmpz_vec_max_bits(A, len1));
bits2 = FLINT_ABS(_fmpz_vec_max_bits(B, len2));
max_bits = FLINT_MAX(bits1, bits2);
bound_bits = FLINT_MIN(bits1, bits2) + 6;
pack_bits = FLINT_MAX(bound_bits, max_bits); /* need to pack original polys */
pack_limbs = (pack_bits - 1)/FLINT_BITS + 1;
if (pack_bits >= 32) /* pack into multiples of limbs if >= 32 bits */
pack_bits = FLINT_BITS*pack_limbs;
/* allocate space to pack into */
limbs1 = (pack_bits*len1 - 1)/FLINT_BITS + 1;
limbs2 = (pack_bits*len2 - 1)/FLINT_BITS + 1;
array1 = flint_calloc(limbs1, sizeof(mp_limb_t));
array2 = flint_calloc(limbs2, sizeof(mp_limb_t));
arrayg = flint_calloc(limbs2, sizeof(mp_limb_t));
/* pack first poly and normalise */
sign1 = (long) fmpz_sgn(A + len1 - 1);
_fmpz_poly_bit_pack(array1, A, len1, pack_bits, sign1);
while (array1[limbs1 - 1] == 0) limbs1--;
/* pack second poly and normalise */
sign2 = (long) fmpz_sgn(B + len2 - 1);
_fmpz_poly_bit_pack(array2, B, len2, pack_bits, sign2);
while (array2[limbs2 - 1] == 0) limbs2--;
/* compute integer GCD */
limbsg = mpn_gcd_full(arrayg, array1, limbs1, array2, limbs2);
/*
Make space for unpacked gcd. May have one extra coeff due to
1 0 -x being packed as 0 -1 -x.
*/
glen = FLINT_MIN((limbsg*FLINT_BITS)/pack_bits + 1, len2);
G = _fmpz_vec_init(glen);
/* unpack gcd */
_fmpz_poly_bit_unpack(G, glen, arrayg, pack_bits, 0);
while (G[glen - 1] == 0) glen--;
/* divide by any content */
fmpz_init(gc);
_fmpz_poly_content(gc, G, glen);
if (!fmpz_is_one(gc))
limbsg = mpn_tdiv_q_fmpz_inplace(arrayg, limbsg, gc);
/* make space for quotient and remainder of first poly by gcd */
qlimbs = limbs1 - limbsg + 1;
qlen = FLINT_MIN(len1, (qlimbs*FLINT_BITS)/pack_bits + 1);
qlimbs = (qlen*pack_bits - 1)/FLINT_BITS + 1;
q = flint_calloc(qlimbs, sizeof(mp_limb_t));
temp = flint_malloc(limbsg*sizeof(mp_limb_t));
divides = 0;
if (mpn_divides(q, array1, limbs1, arrayg, limbsg, temp))
{
/* unpack quotient of first poly by gcd */
Q = _fmpz_vec_init(len1);
t = _fmpz_vec_init(len1 + glen);
_fmpz_poly_bit_unpack(Q, qlen, q, pack_bits, 0);
while (Q[qlen - 1] == 0) qlen--;
/* divide by content */
_fmpz_vec_scalar_divexact_fmpz(G, G, glen, gc);
/* check if we really need to multiply out to check for exact quotient */
bits_G = FLINT_ABS(_fmpz_vec_max_bits(G, glen));
bits_Q = FLINT_ABS(_fmpz_vec_max_bits(Q, qlen));
log_glen = FLINT_BIT_COUNT(glen);
log_length = FLINT_MIN(log_glen, FLINT_BIT_COUNT(qlen));
divides = (bits_G + bits_Q + log_length < pack_bits);
if (!divides) /* need to multiply out to check exact quotient */
divides = multiplies_out(A, len1, Q, qlen, G, glen, sign1, t);
if (divides) /* quotient really was exact */
{
mpn_zero(q, qlimbs);
if (mpn_divides(q, array2, limbs2, arrayg, limbsg, temp))
{
/* unpack quotient of second poly by gcd */
qlimbs = limbs2 - limbsg + 1;
qlen = FLINT_MIN(len2, (qlimbs*FLINT_BITS - 1)/pack_bits + 1);
_fmpz_poly_bit_unpack(Q, qlen, q, pack_bits, 0);
while (Q[qlen - 1] == 0) qlen--;
/* check if we really need to multiply out to check for exact quotient */
bits_Q = FLINT_ABS(_fmpz_vec_max_bits(Q, qlen));
log_length = FLINT_MIN(log_glen, FLINT_BIT_COUNT(qlen));
divides = (bits_G + bits_Q + log_length < pack_bits);
if (!divides) /* we need to multiply out */
divides = multiplies_out(B, len2, Q, qlen, G, glen, sign1, t);
}
}
_fmpz_vec_clear(t, len1 + glen);
_fmpz_vec_clear(Q, len1);
}
flint_free(q);
flint_free(temp);
flint_free(arrayg);
flint_free(array1);
flint_free(array2);
fmpz_clear(gc);
_fmpz_vec_clear(A, len1);
_fmpz_vec_clear(B, len2);
/* we found the gcd, so multiply by content */
if (divides)
{
_fmpz_vec_zero(res + glen, len2 - glen);
_fmpz_vec_scalar_mul_fmpz(res, G, glen, d);
}
fmpz_clear(d);
_fmpz_vec_clear(G, glen);
return divides;
}
void
_fmpz_poly_mullow_KS(fmpz * res, const fmpz * poly1, long len1,
const fmpz * poly2, long len2, long n)
{
int neg1, neg2;
long limbs1, limbs2, loglen;
long bits1, bits2, bits;
mp_limb_t *arr1, *arr2, *arr3;
long sign = 0;
FMPZ_VEC_NORM(poly1, len1);
FMPZ_VEC_NORM(poly2, len2);
if (!len1 | !len2)
{
_fmpz_vec_zero(res, n);
return;
}
neg1 = (fmpz_sgn(poly1 + len1 - 1) > 0) ? 0 : -1;
neg2 = (fmpz_sgn(poly2 + len2 - 1) > 0) ? 0 : -1;
if (n > len1 + len2 - 1)
{
_fmpz_vec_zero(res + len1 + len2 - 1, n - (len1 + len2 - 1));
n = len1 + len2 - 1;
}
bits1 = _fmpz_vec_max_bits(poly1, len1);
if (bits1 < 0)
{
sign = 1;
bits1 = -bits1;
}
if (poly1 != poly2)
{
bits2 = _fmpz_vec_max_bits(poly2, len2);
if (bits2 < 0)
{
sign = 1;
bits2 = -bits2;
}
}
else
bits2 = bits1;
loglen = FLINT_BIT_COUNT(FLINT_MIN(len1, len2));
bits = bits1 + bits2 + loglen + sign;
limbs1 = (bits * len1 - 1) / FLINT_BITS + 1;
limbs2 = (bits * len2 - 1) / FLINT_BITS + 1;
if (poly1 == poly2)
{
arr1 = (mp_ptr) flint_calloc(limbs1, sizeof(mp_limb_t));
arr2 = arr1;
_fmpz_poly_bit_pack(arr1, poly1, len1, bits, neg1);
}
else
{
arr1 = (mp_ptr) flint_calloc(limbs1 + limbs2, sizeof(mp_limb_t));
arr2 = arr1 + limbs1;
_fmpz_poly_bit_pack(arr1, poly1, len1, bits, neg1);
_fmpz_poly_bit_pack(arr2, poly2, len2, bits, neg2);
}
arr3 = (mp_ptr) flint_malloc((limbs1 + limbs2) * sizeof(mp_limb_t));
if (limbs1 == limbs2)
mpn_mul_n(arr3, arr1, arr2, limbs1);
else if (limbs1 > limbs2)
mpn_mul(arr3, arr1, limbs1, arr2, limbs2);
else
mpn_mul(arr3, arr2, limbs2, arr1, limbs1);
if (sign)
_fmpz_poly_bit_unpack(res, n, arr3, bits, neg1 ^ neg2);
else
_fmpz_poly_bit_unpack_unsigned(res, n, arr3, bits);
flint_free(arr1);
flint_free(arr3);
}
void
_fmpq_poly_inv_series_newton(fmpz * Qinv, fmpz_t Qinvden,
const fmpz * Q, const fmpz_t Qden, long n)
{
if (n == 1)
{
if (fmpz_sgn(Q) > 0)
{
fmpz_set(Qinv, Qden);
fmpz_set(Qinvden, Q);
}
else
{
fmpz_neg(Qinv, Qden);
fmpz_neg(Qinvden, Q);
}
}
else
{
const long alloc = FLINT_MAX(n, 3 * FMPQ_POLY_INV_NEWTON_CUTOFF);
long *a, i, m;
fmpz *W, *Wden;
W = _fmpz_vec_init(alloc + 1);
Wden = W + alloc;
for (i = 1; (1L << i) < n; i++) ;
a = (long *) flint_malloc(i * sizeof(long));
a[i = 0] = n;
while (n >= FMPQ_POLY_INV_NEWTON_CUTOFF)
a[++i] = (n = (n + 1) / 2);
/* Base case */
{
fmpz *rev = W + 2 * FMPQ_POLY_INV_NEWTON_CUTOFF;
_fmpz_poly_reverse(rev, Q, n, n);
_fmpz_vec_zero(W, 2*n - 2);
fmpz_one(W + (2*n - 2));
fmpz_one(Wden);
_fmpq_poly_div(Qinv, Qinvden, W, Wden, 2*n - 1, rev, Qden, n);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
_fmpz_poly_reverse(Qinv, Qinv, n, n);
}
for (i--; i >= 0; i--)
{
m = n;
n = a[i];
_fmpz_poly_mullow(W, Q, n, Qinv, m, n);
fmpz_mul(Wden, Qden, Qinvden);
_fmpz_poly_mullow(Qinv + m, Qinv, m, W + m, n - m, n - m);
fmpz_mul(Qinvden, Qinvden, Wden);
_fmpz_vec_scalar_mul_fmpz(Qinv, Qinv, m, Wden);
_fmpz_vec_neg(Qinv + m, Qinv + m, n - m);
_fmpq_poly_canonicalise(Qinv, Qinvden, n);
}
_fmpz_vec_clear(W, alloc + 1);
flint_free(a);
}
}
static void
_qadic_exp_bsplit_series(fmpz *P, fmpz_t Q, fmpz *T,
const fmpz *x, slong len, slong lo, slong hi,
const fmpz *a, const slong *j, slong lena)
{
const slong d = j[lena - 1];
if (hi - lo == 1)
{
_fmpz_vec_set(P, x, len);
_fmpz_vec_zero(P + len, 2*d - 1 - len);
fmpz_set_si(Q, lo);
_fmpz_vec_set(T, P, 2*d - 1);
}
else if (hi - lo == 2)
{
_fmpz_poly_sqr(P, x, len);
_fmpz_vec_zero(P + (2*len - 1), d - (2*len - 1));
_fmpz_poly_reduce(P, 2*len - 1, a, j, lena);
fmpz_set_si(Q, lo);
fmpz_mul_si(Q, Q, lo + 1);
_fmpz_vec_scalar_mul_si(T, x, len, lo + 1);
_fmpz_vec_zero(T + len, d - len);
_fmpz_vec_add(T, T, P, d);
}
else
{
const slong m = (lo + hi) / 2;
fmpz *PR, *TR, *W;
fmpz_t QR;
PR = _fmpz_vec_init(2*d - 1);
TR = _fmpz_vec_init(2*d - 1);
W = _fmpz_vec_init(2*d - 1);
fmpz_init(QR);
_qadic_exp_bsplit_series(P, Q, T, x, len, lo, m, a, j, lena);
_qadic_exp_bsplit_series(PR, QR, TR, x, len, m, hi, a, j, lena);
_fmpz_poly_mul(W, TR, d, P, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_scalar_mul_fmpz(T, T, d, QR);
_fmpz_vec_add(T, T, W, d);
_fmpz_poly_mul(W, P, d, PR, d);
_fmpz_poly_reduce(W, 2*d - 1, a, j, lena);
_fmpz_vec_swap(P, W, d);
fmpz_mul(Q, Q, QR);
_fmpz_vec_clear(PR, 2*d - 1);
_fmpz_vec_clear(TR, 2*d - 1);
_fmpz_vec_clear(W, 2*d - 1);
fmpz_clear(QR);
}
}
