static
void _fmpz_mod_mat_det(fmpz_t rop, const fmpz *M, slong n, const fmpz_t pN)
{
fmpz *F;
fmpz *a;
fmpz *A;
fmpz_t s;
slong t, i, j, p, k;
F = _fmpz_vec_init(n);
a = _fmpz_vec_init((n-1) * n);
A = _fmpz_vec_init(n);
fmpz_init(s);
fmpz_neg(F + 0, M + 0*n + 0);
for (t = 1; t < n; t++)
{
for (i = 0; i <= t; i++)
fmpz_set(a + 0*n + i, M + i*n + t);
fmpz_set(A + 0, M + t*n + t);
for (p = 1; p < t; p++)
{
for (i = 0; i <= t; i++)
{
fmpz_zero(s);
for (j = 0; j <= t; j++)
fmpz_addmul(s, M + i*n + j, a + (p-1)*n + j);
fmpz_mod(a + p*n + i, s, pN);
}
fmpz_set(A + p, a + p*n + t);
}
fmpz_zero(s);
for (j = 0; j <= t; j++)
fmpz_addmul(s, M + t*n + j, a + (t-1)*n + j);
fmpz_mod(A + t, s, pN);
for (p = 0; p <= t; p++)
{
fmpz_sub(F + p, F + p, A + p);
for (k = 0; k < p; k++)
fmpz_submul(F + p, A + k, F + (p-k-1));
fmpz_mod(F + p, F + p, pN);
}
}
/*
Now [F{n-1}, F{n-2}, ..., F{0}, 1] is the
characteristic polynomial of the matrix M.
*/
if (n % WORD(2) == 0)
{
fmpz_set(rop, F + (n-1));
}
else
{
fmpz_neg(rop, F + (n-1));
fmpz_mod(rop, rop, pN);
}
_fmpz_vec_clear(F, n);
_fmpz_vec_clear(a, (n-1)*n);
_fmpz_vec_clear(A, n);
fmpz_clear(s);
}
int main()
{
fmpz * num1;
fmpz * den1;
fmpz_t num2;
fmpz_t den2;
long n, N;
printf("bernoulli_number....");
fflush(stdout);
N = 4000;
num1 = _fmpz_vec_init(N);
den1 = _fmpz_vec_init(N);
fmpz_init(num2);
fmpz_init(den2);
_bernoulli_number_vec_multi_mod(num1, den1, N);
for (n = 0; n < N; n++)
{
_bernoulli_number(num2, den2, n);
if (!fmpz_equal(num1 + n, num2))
{
printf("FAIL: n = %ld, numerator\n", n);
printf("vec: "); fmpz_print(num1 + n); printf("\n");
printf("single: "); fmpz_print(num2); printf("\n");
abort();
}
if (!fmpz_equal(den1 + n, den2))
{
printf("FAIL: n = %ld, denominator\n", n);
printf("vec: "); fmpz_print(den1 + n); printf("\n");
printf("single: "); fmpz_print(den2); printf("\n");
abort();
}
}
/* Check non underscore versions */
do
{
long N = 100;
fmpq * x;
fmpq_t t;
fmpq_init(t);
x = flint_malloc(sizeof(fmpq) * N);
for (n = 0; n < N; n++)
fmpq_init(x + n);
bernoulli_number_vec(x, N);
for (n = 0; n < N; n++)
{
bernoulli_number(t, n);
if (!fmpq_equal(x + n, t))
{
printf("FAIL!: n = %ld\n", n);
abort();
}
}
for (n = 0; n < N; n++)
fmpq_clear(x + n);
flint_free(x);
fmpq_clear(t);
} while (0);
_fmpz_vec_clear(num1, N);
_fmpz_vec_clear(den1, N);
fmpz_clear(num2);
fmpz_clear(den2);
mpfr_free_cache();
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("scalar_mul_2exp....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing of a and b */
for (i = 0; i < 10000; i++)
{
fmpz *a, *b;
long len = n_randint(state, 100);
ulong exp = n_randint(state, 200);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_scalar_mul_2exp(b, a, len, exp);
_fmpz_vec_scalar_mul_2exp(a, a, len, exp);
result = (_fmpz_vec_equal(a, b, len));
if (!result)
{
printf("FAIL:\n");
printf("exp = %lu\n", exp);
_fmpz_vec_print(a, len), printf("\n\n");
_fmpz_vec_print(b, len), printf("\n\n");
abort();
}
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
}
/* Check aliasing of (a*2^e1)*2^e2 equals a*2^(e1+e2) */
for (i = 0; i < 10000; i++)
{
fmpz *a, *b;
long len = n_randint(state, 100);
ulong e1 = n_randint(state, 200);
ulong e2 = n_randint(state, 200);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_scalar_mul_2exp(b, a, len, e1);
_fmpz_vec_scalar_mul_2exp(b, b, len, e2);
_fmpz_vec_scalar_mul_2exp(a, a, len, e1 + e2);
result = (_fmpz_vec_equal(a, b, len));
if (!result)
{
printf("FAIL:\n");
printf("e1 = %lu, e2 = %lu\n", e1, e2);
_fmpz_vec_print(a, len), printf("\n\n");
_fmpz_vec_print(b, len), printf("\n\n");
abort();
}
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int main()
{
long iter;
flint_rand_t state;
printf("rising2_ui....");
fflush(stdout);
flint_randinit(state);
for (iter = 0; iter < 1000; iter++)
{
arb_t a, u, v, u2, v2;
fmpz *f;
arb_ptr g;
ulong n;
long i, prec;
arb_init(a);
arb_init(u);
arb_init(v);
arb_init(u2);
arb_init(v2);
arb_randtest(a, state, 1 + n_randint(state, 4000), 10);
arb_randtest(u, state, 1 + n_randint(state, 4000), 10);
arb_randtest(v, state, 1 + n_randint(state, 4000), 10);
n = n_randint(state, 120);
f = _fmpz_vec_init(n + 1);
g = _arb_vec_init(n + 1);
prec = 2 + n_randint(state, 4000);
arb_rising2_ui(u, v, a, n, prec);
arith_stirling_number_1u_vec(f, n, n + 1);
for (i = 0; i <= n; i++)
arb_set_fmpz(g + i, f + i);
_arb_poly_evaluate(u2, g, n + 1, a, prec);
_arb_poly_derivative(g, g, n + 1, prec);
_arb_poly_evaluate(v2, g, n, a, prec);
if (!arb_overlaps(u, u2) || !arb_overlaps(v, v2))
{
printf("FAIL: overlap\n\n");
printf("n = %lu\n", n);
printf("a = ");
arb_printd(a, 15);
printf("\n\n");
printf("u = ");
arb_printd(u, 15);
printf("\n\n");
printf("u2 = ");
arb_printd(u2, 15);
printf("\n\n");
printf("v = ");
arb_printd(v, 15);
printf("\n\n");
printf("v2 = ");
arb_printd(v2, 15);
printf("\n\n");
abort();
}
arb_set(u2, a);
arb_rising2_ui(u2, v, u2, n, prec);
if (!arb_equal(u2, u))
{
printf("FAIL: aliasing 1\n\n");
printf("a = ");
arb_printd(a, 15);
printf("\n\n");
printf("u = ");
arb_printd(u, 15);
printf("\n\n");
printf("u2 = ");
arb_printd(u2, 15);
printf("\n\n");
printf("n = %lu\n", n);
abort();
}
arb_set(v2, a);
arb_rising2_ui(u, v2, v2, n, prec);
if (!arb_equal(v2, v))
{
printf("FAIL: aliasing 2\n\n");
printf("a = ");
arb_printd(a, 15);
printf("\n\n");
printf("v = ");
arb_printd(v, 15);
printf("\n\n");
printf("v2 = ");
arb_printd(v2, 15);
printf("\n\n");
printf("n = %lu\n", n);
abort();
}
arb_clear(a);
arb_clear(u);
arb_clear(v);
arb_clear(u2);
arb_clear(v2);
_fmpz_vec_clear(f, n + 1);
_arb_vec_clear(g, n + 1);
}
flint_randclear(state);
flint_cleanup();
printf("PASS\n");
return EXIT_SUCCESS;
}
static void
__fmpz_poly_divrem_divconquer(fmpz * Q, fmpz * R,
const fmpz * A, long lenA,
const fmpz * B, long lenB)
{
if (lenA < 2 * lenB - 1)
{
/*
Convert unbalanced division into a 2 n1 - 1 by n1 division
*/
const long n1 = lenA - lenB + 1;
const long n2 = lenB - n1;
const fmpz * p1 = A + n2;
const fmpz * d1 = B + n2;
const fmpz * d2 = B;
fmpz * W = _fmpz_vec_init((2 * n1 - 1) + lenB - 1);
fmpz * d1q1 = R + n2;
fmpz * d2q1 = W + (2 * n1 - 1);
_fmpz_poly_divrem_divconquer_recursive(Q, d1q1, W, p1, d1, n1);
/*
Compute d2q1 = Q d2, of length lenB - 1
*/
if (n1 >= n2)
_fmpz_poly_mul(d2q1, Q, n1, d2, n2);
else
_fmpz_poly_mul(d2q1, d2, n2, Q, n1);
/*
Compute BQ = d1q1 * x^n1 + d2q1, of length lenB - 1;
then compute R = A - BQ
*/
_fmpz_vec_swap(R, d2q1, n2);
_fmpz_vec_add(R + n2, R + n2, d2q1 + n2, n1 - 1);
_fmpz_vec_sub(R, A, R, lenA);
_fmpz_vec_clear(W, (2 * n1 - 1) + lenB - 1);
}
else if (lenA > 2 * lenB - 1)
{
/*
We shift A right until it is of length 2 lenB - 1, call this p1
*/
const long shift = lenA - 2 * lenB + 1;
const fmpz * p1 = A + shift;
fmpz * q1 = Q + shift;
fmpz * q2 = Q;
fmpz * W = R + lenA;
fmpz * d1q1 = W + (2 * lenB - 1);
/*
XXX: In this case, we expect R to be of length
lenA + 2 * (2 * lenB - 1) and A to be modifiable
*/
/*
Set q1 to p1 div B, a 2 lenB - 1 by lenB division, so q1 ends up
being of length lenB; set d1q1 = d1 * q1 of length 2 lenB - 1
*/
_fmpz_poly_divrem_divconquer_recursive(q1, d1q1, W, p1, B, lenB);
/*
We have dq1 = d1 * q1 * x^shift, of length lenA
Compute R = A - dq1; the first lenB coeffs represent remainder
terms (zero if division is exact), leaving lenA - lenB significant
terms which we use in the division
*/
_fmpz_vec_sub((fmpz *) A + shift, A + shift, d1q1, lenB - 1);
/*
Compute q2 = trunc(R) div B; it is a smaller division than the
original since len(trunc(R)) = lenA - lenB
*/
__fmpz_poly_divrem_divconquer(q2, R, A, lenA - lenB, B, lenB);
_fmpz_vec_sub(R + lenA - lenB, A + lenA - lenB, d1q1 + lenB - 1, lenB);
/*
We have Q = q1 * x^shift + q2; Q has length lenB + shift;
note q2 has length shift since the above division is
lenA - lenB by lenB
We've also written the remainder in place
*/
}
else /* lenA = 2 * lenB - 1 */
{
fmpz * W = _fmpz_vec_init(lenA);
_fmpz_poly_divrem_divconquer_recursive(Q, R, W, A, B, lenB);
_fmpz_vec_sub(R, A, R, lenA);
_fmpz_vec_clear(W, lenA);
}
}
void _padic_teichmuller(fmpz_t rop, const fmpz_t op, const fmpz_t p, slong N)
{
if (fmpz_equal_ui(p, 2))
{
fmpz_one(rop);
}
else if (N == 1)
{
fmpz_mod(rop, op, p);
}
else
{
slong *a, i, n;
fmpz *pow, *u;
fmpz_t s, t;
fmpz_t inv;
fmpz_t pm1;
a = _padic_lifts_exps(&n, N);
pow = _fmpz_vec_init(2 * n);
u = pow + n;
_padic_lifts_pows(pow, a, n, p);
fmpz_init(s);
fmpz_init(t);
fmpz_init(inv);
fmpz_init(pm1);
fmpz_sub_ui(pm1, p, 1);
/* Compute reduced units for (p-1) */
{
fmpz_mod(u + 0, pm1, pow + 0);
}
for (i = 1; i < n; i++)
{
fmpz_mod(u + i, u + (i - 1), pow + i);
}
/* Run Newton iteration */
i = n - 1;
{
fmpz_mod(rop, op, pow + i);
fmpz_set(inv, pm1);
}
for (i--; i >= 0; i--)
{
/* Lift rop */
fmpz_powm(s, rop, p, pow + i);
fmpz_sub(s, s, rop);
fmpz_mul(t, s, inv);
fmpz_sub(rop, rop, t);
fmpz_mod(rop, rop, pow + i);
/* Lift inv */
if (i > 0)
{
fmpz_mul(s, inv, inv);
fmpz_mul(t, u + i, s);
fmpz_mul_2exp(inv, inv, 1);
fmpz_sub(inv, inv, t);
fmpz_mod(inv, inv, pow + i);
}
}
fmpz_clear(s);
fmpz_clear(t);
fmpz_clear(inv);
fmpz_clear(pm1);
_fmpz_vec_clear(pow, 2 * n);
flint_free(a);
}
}
void
acb_rising2_ui_rs(acb_t u, acb_t v,
const acb_t x, ulong n, ulong m, long prec)
{
if (n == 0)
{
acb_zero(v);
acb_one(u);
}
else if (n == 1)
{
acb_set(u, x);
acb_one(v);
}
else
{
long wp;
ulong i, j, a, b;
acb_ptr xs;
acb_t S, T, U, V;
fmpz *A, *B;
wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
if (m == 0)
{
ulong m1, m2;
m1 = 0.6 * pow(wp, 0.4);
m2 = n_sqrt(n);
m = FLINT_MIN(m1, m2);
}
m = FLINT_MAX(m, 1);
xs = _acb_vec_init(m + 1);
A = _fmpz_vec_init(2 * m + 1);
B = A + (m + 1);
acb_init(S);
acb_init(T);
acb_init(U);
acb_init(V);
_acb_vec_set_powers(xs, x, m + 1, wp);
for (i = 0; i < n; i += m)
{
a = i;
b = FLINT_MIN(n, a + m);
if (a == 0 || b != a + m)
{
_gamma_rf_bsplit(A, a, b);
}
else
{
fmpz tt = m;
_fmpz_poly_taylor_shift(A, &tt, m + 1);
}
_fmpz_poly_derivative(B, A, b - a + 1);
acb_set_fmpz(S, A);
for (j = 1; j <= b - a; j++)
acb_addmul_fmpz(S, xs + j, A + j, wp);
acb_set_fmpz(T, B);
for (j = 1; j < b - a; j++)
acb_addmul_fmpz(T, xs + j, B + j, wp);
if (i == 0)
{
acb_set(U, S);
acb_set(V, T);
}
else
{
acb_mul(V, V, S, wp);
acb_addmul(V, U, T, wp);
acb_mul(U, U, S, wp);
}
}
acb_set(u, U);
acb_set(v, V);
_acb_vec_clear(xs, m + 1);
_fmpz_vec_clear(A, 2 * m + 1);
acb_clear(S);
acb_clear(T);
acb_clear(U);
acb_clear(V);
}
}
void fmpz_mod_poly_radix(fmpz_mod_poly_struct **B,
const fmpz_mod_poly_t F,
const fmpz_mod_poly_radix_t D)
{
const long lenF = F->length;
const long degF = F->length - 1;
const long degR = D->degR;
const long N = degF / degR;
if (N == 0)
{
fmpz_mod_poly_set(B[0], F);
}
else
{
const long k = FLINT_BIT_COUNT(N); /* k := ceil{log{N+1}} */
const long lenG = (1L << k) * degR; /* Padded size */
const long t = (lenG - 1) / degR - N; /* Extra {degR}-blocks */
fmpz *G; /* Padded copy of F */
fmpz *T; /* Additional B[i] */
fmpz **C; /* Enlarged version of B */
fmpz *W; /* Temporary space */
long i;
if (lenF < lenG)
{
G = flint_malloc(lenG * sizeof(fmpz));
for (i = 0; i < lenF; i++)
G[i] = F->coeffs[i];
mpn_zero((mp_ptr) G + lenF, lenG - lenF);
T = t ? _fmpz_vec_init(t * degR) : NULL;
}
else /* lenF == lenG */
{
G = F->coeffs;
T = NULL;
}
C = flint_malloc((N + 1 + t) * sizeof(fmpz *));
for (i = 0; i <= N; i++)
{
fmpz_mod_poly_fit_length(B[i], degR);
C[i] = B[i]->coeffs;
}
for (i = 0; i < t; i++)
{
C[N + 1 + i] = T + i * degR;
}
W = _fmpz_vec_init(lenG);
_fmpz_mod_poly_radix(C, G, D->Rpow, D->Rinv, degR, 0, k-1, W, &(F->p));
_fmpz_vec_clear(W, lenG);
for (i = 0; i <= N; i++)
{
_fmpz_mod_poly_set_length(B[i], degR);
_fmpz_mod_poly_normalise(B[i]);
}
flint_free(C);
if (lenF < lenG)
{
flint_free(G);
}
if (t)
{
_fmpz_vec_clear(T, t * degR);
}
}
}
int
_fmpz_poly_sqrt_classical(fmpz * res, const fmpz * poly, long len)
{
long i, m;
int result;
/* the degree must be even */
if (len % 2 == 0)
return 0;
/* valuation must be even, and then can be reduced to 0 */
while (fmpz_is_zero(poly))
{
if (!fmpz_is_zero(poly + 1))
return 0;
fmpz_zero(res);
poly += 2;
len -= 2;
res++;
}
/* check whether a square root exists modulo 2 */
for (i = 1; i < len; i += 2)
if (!fmpz_is_even(poly + i))
return 0;
/* check endpoints */
if (!fmpz_is_square(poly) || (len > 1 && !fmpz_is_square(poly + len - 1)))
return 0;
/* square root of leading coefficient */
m = (len + 1) / 2;
fmpz_sqrt(res + m - 1, poly + len - 1);
result = 1;
/* do long divison style 'square root with remainder' from top to bottom */
if (len > 1)
{
fmpz_t t, u;
fmpz * r;
fmpz_init(t);
fmpz_init(u);
r = _fmpz_vec_init(len);
_fmpz_vec_set(r, poly, len);
fmpz_mul_ui(u, res + m - 1, 2);
for (i = 1; i < m; i++)
{
fmpz_fdiv_qr(res + m - i - 1, t, r + len - i - 1, u);
if (!fmpz_is_zero(t))
{
result = 0;
break;
}
fmpz_mul_si(t, res + m - i - 1, -2);
_fmpz_vec_scalar_addmul_fmpz(r + len - 2*i, res + m - i, i - 1, t);
fmpz_submul(r + len - 2*i - 1, res + m - i - 1, res + m - i - 1);
}
for (i = m; i < len && result; i++)
if (!fmpz_is_zero(r + len - 1 - i))
result = 0;
_fmpz_vec_clear(r, len);
fmpz_clear(t);
fmpz_clear(u);
}
return result;
}
void
acb_rising_ui_rs(acb_t y, const acb_t x, ulong n, ulong m, slong prec)
{
acb_ptr xs;
acb_t t, u, v;
ulong i, k, rem;
fmpz_t c, h;
fmpz *s, *d;
slong wp;
if (n == 0)
{
acb_one(y);
return;
}
if (n == 1)
{
acb_set_round(y, x, prec);
return;
}
wp = ARF_PREC_ADD(prec, FLINT_BIT_COUNT(n));
acb_init(t);
acb_init(u);
acb_init(v);
fmpz_init(c);
fmpz_init(h);
if (m == 0)
{
ulong m1, m2;
m1 = 0.2 * pow(2.0 * wp, 0.4);
m2 = n_sqrt(n);
m = FLINT_MIN(m1, m2);
}
m = FLINT_MIN(m, n);
m = FLINT_MAX(m, 1);
xs = _acb_vec_init(m + 1);
d = _fmpz_vec_init(m * m);
s = _fmpz_vec_init(m + 1);
_acb_vec_set_powers(xs, x, m + 1, wp);
rising_difference_polynomial(s, d, m);
/* tail */
rem = m;
while (rem + m <= n)
rem += m;
acb_one(y);
for (k = rem; k < n; k++)
{
acb_add_ui(t, xs + 1, k, wp);
acb_mul(y, y, t, wp);
}
/* initial rising factorial */
acb_zero(t);
for (i = 1; i <= m; i++)
acb_addmul_fmpz(t, xs + i, s + i, wp);
acb_mul(y, y, t, wp);
/* the leading coefficient is always the same */
acb_mul_fmpz(xs + m - 1, xs + m - 1, d + m - 1 + 0, wp);
for (k = 0; k + 2 * m <= n; k += m)
{
for (i = 0; i < m - 1; i++)
{
fmpz_set_ui(h, k);
_fmpz_poly_evaluate_horner_fmpz(c, d + i * m, m - i, h);
if (i == 0)
acb_add_fmpz(t, t, c, wp);
else
acb_addmul_fmpz(t, xs + i, c, wp);
}
acb_add(t, t, xs + m - 1, wp);
acb_mul(y, y, t, wp);
}
acb_set_round(y, y, prec);
acb_clear(t);
acb_clear(u);
acb_clear(v);
_acb_vec_clear(xs, m + 1);
_fmpz_vec_clear(d, m * m);
_fmpz_vec_clear(s, m + 1);
fmpz_clear(c);
fmpz_clear(h);
}
void
bernoulli_rev_init(bernoulli_rev_t iter, ulong nmax)
{
long j;
fmpz_t t;
arb_t x;
arf_t u;
int round1, round2;
long wp;
nmax -= (nmax % 2);
iter->n = nmax;
iter->alloc = 0;
if (nmax < BERNOULLI_REV_MIN)
return;
iter->prec = wp = bernoulli_global_prec(nmax);
iter->max_power = bernoulli_zeta_terms(nmax, iter->prec);
iter->alloc = iter->max_power + 1;
iter->powers = _fmpz_vec_init(iter->alloc);
fmpz_init(iter->pow_error);
arb_init(iter->prefactor);
arb_init(iter->two_pi_squared);
arb_init(x);
fmpz_init(t);
arf_init(u);
/* precompute powers */
for (j = 3; j <= iter->max_power; j += 2)
{
arb_ui_pow_ui(x, j, nmax, bernoulli_power_prec(j, nmax, wp));
arb_inv(x, x, bernoulli_power_prec(j, nmax, wp));
round1 = arf_get_fmpz_fixed_si(t, arb_midref(x), -wp);
fmpz_set(iter->powers + j, t);
/* error: the radius, plus two roundings */
arf_set_mag(u, arb_radref(x));
round2 = arf_get_fmpz_fixed_si(t, u, -wp);
fmpz_add_ui(t, t, (round1 != 0) + (round2 != 0));
if (fmpz_cmp(iter->pow_error, t) < 0)
fmpz_set(iter->pow_error, t);
}
/* precompute (2pi)^2 and 2*(n!)/(2pi)^n */
arb_fac_ui(iter->prefactor, nmax, wp);
arb_mul_2exp_si(iter->prefactor, iter->prefactor, 1);
arb_const_pi(x, wp);
arb_mul_2exp_si(x, x, 1);
arb_mul(iter->two_pi_squared, x, x, wp);
arb_pow_ui(x, iter->two_pi_squared, nmax / 2, wp);
arb_div(iter->prefactor, iter->prefactor, x, wp);
fmpz_clear(t);
arb_clear(x);
arf_clear(u);
}
int fmpq_poly_check_unique_real_root(const fmpq_poly_t pol, const arb_t a, slong prec)
{
if (pol->length < 2)
return 0;
else if (pol->length == 2)
{
/* linear polynomial */
fmpq_t root;
int ans;
fmpq_init(root);
fmpq_set_fmpz_frac(root, fmpq_poly_numref(pol), fmpq_poly_numref(pol) + 1);
fmpq_neg(root, root);
ans = arb_contains_fmpq(a, root);
fmpq_clear(root);
return ans;
}
else
{
arb_t b, c;
arf_t l, r;
fmpz * der;
int lsign, rsign;
fmpz_poly_t pol2;
slong n;
/* 1 - cheap test: */
/* - sign(left) * sign(right) = -1 */
/* - no zero of the derivative */
arb_init(b);
arb_init(c);
arf_init(l);
arf_init(r);
arb_get_interval_arf(l, r, a, prec);
arb_set_arf(b, l);
_fmpz_poly_evaluate_arb(c, pol->coeffs, pol->length, b, 2*prec);
lsign = arb_sgn2(c);
arb_set_arf(b, r);
_fmpz_poly_evaluate_arb(c, pol->coeffs, pol->length, b, 2*prec);
rsign = arb_sgn2(c);
arb_clear(c);
if (lsign * rsign == -1)
{
der = _fmpz_vec_init(pol->length - 1);
_fmpz_poly_derivative(der, pol->coeffs, pol->length);
_fmpz_poly_evaluate_arb(b, der, pol->length - 1, a, prec);
_fmpz_vec_clear(der, pol->length - 1);
if (!arb_contains_zero(b))
{
arf_clear(l);
arf_clear(r);
arb_clear(b);
return 1;
}
}
else
return 0;
arb_clear(b);
/* 2 - expensive testing */
fmpq_t ql, qr;
fmpq_init(ql);
fmpq_init(qr);
arf_get_fmpq(ql, l);
arf_get_fmpq(qr, r);
fmpz_poly_init(pol2);
fmpz_poly_fit_length(pol2, pol->length);
_fmpz_vec_set(pol2->coeffs, pol->coeffs, pol->length);
pol2->length = pol->length;
_fmpz_poly_scale_0_1_fmpq(pol2->coeffs, pol2->length, ql, qr);
n = fmpz_poly_num_real_roots_0_1(pol2);
fmpz_poly_clear(pol2);
fmpq_clear(ql);
fmpq_clear(qr);
return (n == 1);
}
}
void _fmpq_poly_resultant(fmpz_t rnum, fmpz_t rden,
const fmpz *poly1, const fmpz_t den1, long len1,
const fmpz *poly2, const fmpz_t den2, long len2)
{
if (len2 == 1)
{
if (len1 == 1)
{
fmpz_one(rnum);
fmpz_one(rden);
}
else if (len1 == 2)
{
fmpz_set(rnum, poly2);
fmpz_set(rden, den2);
}
else
{
fmpz_pow_ui(rnum, poly2, len1 - 1);
if (fmpz_is_one(den2))
{
fmpz_one(rden);
}
else
{
fmpz_pow_ui(rden, den2, len1 - 1);
}
}
}
else /* len1 >= len2 >= 2 */
{
fmpz_t c1, c2;
fmpz *prim1, *prim2, *g;
long lenG = len2;
fmpz_init(c1);
fmpz_init(c2);
_fmpz_vec_content(c1, poly1, len1);
_fmpz_vec_content(c2, poly2, len2);
prim1 = _fmpz_vec_init(len1);
prim2 = _fmpz_vec_init(len2);
g = _fmpz_vec_init(len2);
_fmpz_vec_scalar_divexact_fmpz(prim1, poly1, len1, c1);
_fmpz_vec_scalar_divexact_fmpz(prim2, poly2, len2, c2);
_fmpz_poly_gcd(g, prim1, len1, prim2, len2);
FMPZ_VEC_NORM(g, lenG);
if (lenG > 1)
{
fmpz_zero(rnum);
fmpz_one(rden);
}
else /* prim1, prim2 are coprime */
{
fmpz_t t;
fmpz_init(t);
_fmpz_poly_resultant(rnum, prim1, len1, prim2, len2);
if (!fmpz_is_one(c1))
{
fmpz_pow_ui(t, c1, len2 - 1);
fmpz_mul(rnum, rnum, t);
}
if (!fmpz_is_one(c2))
{
fmpz_pow_ui(t, c2, len1 - 1);
fmpz_mul(rnum, rnum, t);
}
if (fmpz_is_one(den1))
{
if (fmpz_is_one(den2))
fmpz_one(rden);
else
fmpz_pow_ui(rden, den2, len1 - 1);
}
else
{
if (fmpz_is_one(den2))
fmpz_pow_ui(rden, den1, len2 - 1);
else
{
fmpz_pow_ui(rden, den1, len2 - 1);
fmpz_pow_ui(t, den2, len1 - 1);
fmpz_mul(rden, rden, t);
}
}
_fmpq_canonicalise(rnum, rden);
fmpz_clear(t);
}
fmpz_clear(c1);
fmpz_clear(c2);
_fmpz_vec_clear(prim1, len1);
_fmpz_vec_clear(prim2, len2);
_fmpz_vec_clear(g, len2);
}
}
#include <stdlib.h>
#include <mpir.h>
#include "flint.h"
#include "fmpz.h"
#include "fmpz_vec.h"
#include "fmpz_poly.h"
#include "fmpz_mod_poly.h"
void _fmpz_mod_poly_pow(fmpz *res, const fmpz *poly, long len, ulong e,
const fmpz_t p)
{
ulong bit = ~((~0UL) >> 1);
long rlen;
long alloc = (long) e * (len - 1) + 1;
fmpz *v = _fmpz_vec_init(alloc);
fmpz *R, *S, *T;
/*
Set bits to the bitmask with a 1 one place lower than the msb of e
*/
while ((bit & e) == 0UL)
bit >>= 1;
bit >>= 1;
/*
Trial run without any polynomial arithmetic to determine the parity
of the number of swaps; then set R and S accordingly
*/
int fmpq_mat_inv(fmpq_mat_t B, const fmpq_mat_t A)
{
long n = A->r;
if (n == 0)
{
return 1;
}
else if (n == 1)
{
if (fmpq_is_zero(fmpq_mat_entry(A, 0, 0)))
return 0;
fmpq_inv(fmpq_mat_entry(B, 0, 0), fmpq_mat_entry(A, 0, 0));
return 1;
}
else if (n == 2)
{
fmpq_t d;
int success;
fmpq_init(d);
fmpq_mul(d, fmpq_mat_entry(A, 0, 0), fmpq_mat_entry(A, 1, 1));
fmpq_submul(d, fmpq_mat_entry(A, 0, 1), fmpq_mat_entry(A, 1, 0));
success = !fmpq_is_zero(d);
if (success)
{
fmpq_t t00, t01, t10, t11;
fmpq_inv(d, d);
fmpq_init(t00);
fmpq_init(t01);
fmpq_init(t10);
fmpq_init(t11);
fmpq_mul(t00, fmpq_mat_entry(A, 1, 1), d);
fmpq_mul(t01, fmpq_mat_entry(A, 0, 1), d);
fmpq_mul(t10, fmpq_mat_entry(A, 1, 0), d);
fmpq_mul(t11, fmpq_mat_entry(A, 0, 0), d);
fmpq_set(fmpq_mat_entry(B, 0, 0), t00);
fmpq_neg(fmpq_mat_entry(B, 0, 1), t01);
fmpq_neg(fmpq_mat_entry(B, 1, 0), t10);
fmpq_set(fmpq_mat_entry(B, 1, 1), t11);
fmpq_clear(t00);
fmpq_clear(t01);
fmpq_clear(t10);
fmpq_clear(t11);
}
fmpq_clear(d);
return success;
}
else
{
fmpz_mat_t Aclear, Bclear, I;
fmpz * den;
long i;
int success;
fmpz_mat_init(Aclear, n, n);
fmpz_mat_init(Bclear, n, n);
fmpz_mat_init(I, n, n);
den = _fmpz_vec_init(n);
fmpq_mat_get_fmpz_mat_rowwise(Aclear, den, A);
for (i = 0; i < n; i++)
fmpz_set(fmpz_mat_entry(I, i, i), den + i);
success = fmpz_mat_solve(Bclear, den, Aclear, I);
if (success)
fmpq_mat_set_fmpz_mat_div_fmpz(B, Bclear, den);
fmpz_mat_clear(Aclear);
fmpz_mat_clear(Bclear);
fmpz_mat_clear(I);
_fmpz_vec_clear(den, A->r);
return success;
}
}
void precompute_muex(fmpz **mu, long M,
const long **C, const long *lenC,
const fmpz *a, long n, long p, long N)
{
const long ve = (p == 2) ? M / 4 + 1 : M / (p * (p - 1)) + 1;
fmpz_t P, pNe, pe;
fmpz_t apow, f, g, h;
fmpz *nu;
long *v;
long i, j;
fmpz_init_set_ui(P, p);
fmpz_init(pNe);
fmpz_init(pe);
fmpz_pow_ui(pNe, P, N + ve);
fmpz_pow_ui(pe, P, ve);
fmpz_init(apow);
fmpz_init(f);
fmpz_init(g);
fmpz_init(h);
/* Precompute $(l!)^{-1}$ */
nu = _fmpz_vec_init(M + 1);
v = malloc((M + 1) * sizeof(long));
{
long *D, lenD = 0, k = 0;
for (i = 0; i <= n; i++)
lenD += lenC[i];
D = malloc(lenD * sizeof(long));
for (i = 0; i <= n; i++)
for (j = 0; j < lenC[i]; j++)
D[k++] = C[i][j];
_remove_duplicates(D, &lenD);
_sort(D, lenD);
precompute_nu(nu, v, M, D, lenD, p, N + ve);
free(D);
}
for (i = 0; i <= n; i++)
{
long m = -1, quo, idx, w;
fmpz *z;
/* Set apow = a[i]^{-(p-1)} mod p^N */
fmpz_invmod(apow, a + i, pNe);
fmpz_powm_ui(apow, apow, p - 1, pNe);
/*
Run over all relevant m in [0, M].
Note that lenC[i] > 0 for all i.
*/
for (quo = 0; m <= M; quo++)
{
for (idx = 0; idx < lenC[i]; idx++)
{
m = quo * p + C[i][idx];
if (m > M)
break;
/*
Note that $\mu_m$ is equal to
$\sum_{k=0}^{\floor{m/p}} p^{\floor{m/p}-k}\nu_{m-pk}\nu_k$
where $\nu_i$ denotes the number with unit part nu[i]
and valuation v[i].
*/
w = (p == 2) ? (3 * m) / 4 - (m == 3 || m == 7) : m / p;
z = mu[i] + lenC[i] * quo + idx;
fmpz_zero(z);
fmpz_one(h);
for (j = 0; j <= m / p; j++)
{
fmpz_pow_ui(f, P, ve + w - j + v[m - p*j] + v[j]);
fmpz_mul(g, nu + (m - p*j), nu + j);
fmpz_mul(f, f, g);
fmpz_mul(f, f, h);
fmpz_add(z, z, f);
fmpz_mod(z, z, pNe);
/* Set h = a[i]^{- (j+1)(p-1)} mod p^{N+e} */
fmpz_mul(h, h, apow);
fmpz_mod(h, h, pNe);
}
fmpz_divexact(z, z, pe);
}
}
}
fmpz_clear(P);
fmpz_clear(pNe);
fmpz_clear(pe);
fmpz_clear(apow);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(h);
_fmpz_vec_clear(nu, M + 1);
free(v);
}
/* 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 diagfrob(padic_mat_t F, const fmpz *a, long n, long d, long N,
const padic_ctx_t ctx, const int verbose)
{
const fmpz *P = ctx->p;
const long p = fmpz_get_si(P);
const long delta = diagfrob_delta(n, P);
const long N2 = N - n + 2 * (padic_val_fac_ui(n - 1, P) + n + delta);
const long M = (p * p * (N2 + n_clog(N2 + 3, p) + 4) + (p - 2))
/ (p - 1) - 1;
mon_t *B;
long *iB, lenB, lo, hi;
long i, j, k, *u, *v;
long **C, *lenC;
fmpz *dinv, **mu;
clock_t t0 = 0, t1 = 0;
double t;
gmc_basis_sets(&B, &iB, &lenB, &lo, &hi, n, d);
if (verbose)
{
printf("Frobenius on the diagonal fibre\n");
printf("N = %ld\n", N);
printf("N2 = %ld\n", N2);
printf("M = %ld\n", M);
}
if (verbose)
{
printf("Basis for H_{dR}^%ld(U)\n", n);
gmc_basis_print(B, iB, lenB, n, d);
printf("\n");
}
C = malloc((n + 1) * sizeof(long *));
C[0] = malloc((n + 1) * lenB * sizeof(long));
for (i = 1; i <= n; i++)
{
C[i] = C[i-1] + lenB;
}
lenC = malloc((n + 1) * sizeof(long));
for (i = 0; i <= n; i++)
{
_congruence_class(C[i], &lenC[i], i, B, lenB, n, d, p);
}
dinv = _fmpz_vec_init(M/p + 1);
mu = malloc((n + 1) * sizeof(fmpz *));
for (i = 0; i <= n; i++)
{
mu[i] = _fmpz_vec_init(((M + 1 + p - 1) / p) * lenC[i]);
}
u = malloc((n + 1) * sizeof(long));
v = malloc((n + 1) * sizeof(long));
if (verbose)
{
printf("Sequence d^{-r}\n");
t0 = clock();
}
precompute_dinv(dinv, M, d, p, N2);
if (verbose)
{
t1 = clock();
t = (double) (t1 - t0) / CLOCKS_PER_SEC;
printf("T = %f\n", t);
}
if (verbose)
{
printf("Sequence mu_{m}\n");
t0 = clock();
}
precompute_muex(mu, M, (const long **) C, lenC, a, n, p, N2); /* XXX */
if (verbose)
{
t1 = clock();
t = (double) (t1 - t0) / CLOCKS_PER_SEC;
printf("T = %f\n", t);
}
if (verbose)
{
printf("Matrix F\n");
t0 = clock();
}
for (i = 0; i < lenB; i++)
for (j = 0; j < lenB; j++)
{
for (k = 0; k <= n; k++)
{
u[k] = mon_get_exp(B[i], k);
v[k] = mon_get_exp(B[j], k);
if ((p * (u[k] + 1) - (v[k] + 1)) % d != 0)
{
break;
}
}
if (k <= n)
{
fmpz_zero(padic_mat_entry(F, i, j));
}
else
{
long o;
entry(padic_mat_entry(F, i, j), &o,
u, v, a, dinv, (const fmpz **) mu, M, (const long **) C, lenC, n, d, p, N, N2);
if (o != - delta)
{
fmpz_t w;
fmpz_init(w);
fmpz_pow_ui(w, P, o + delta);
fmpz_mul(padic_mat_entry(F, i, j),
padic_mat_entry(F, i, j), w);
fmpz_clear(w);
}
}
}
padic_mat_val(F) = - delta;
_padic_mat_canonicalise(F, ctx);
if (verbose)
{
t1 = clock();
t = (double) (t1 - t0) / CLOCKS_PER_SEC;
printf("T = %f\n", t);
}
_fmpz_vec_clear(dinv, M/p + 1);
for (i = 0; i <= n; i++)
{
_fmpz_vec_clear(mu[i], ((M + 1 + p - 1) / p) * lenC[i]);
}
free(mu);
free(C[0]);
free(C);
free(lenC);
free(u);
free(v);
free(B);
free(iB);
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("scalar_submul_fmpz....");
fflush(stdout);
flint_randinit(state);
/* Compare with fmpz_vec_scalar_submul_si */
for (i = 0; i < 10000; i++)
{
fmpz *a, *b, *c;
long len, n;
fmpz_t n1;
len = n_randint(state, 100);
n = (long) n_randbits(state, FLINT_BITS - 1);
if (n_randint(state, 2))
n = -n;
fmpz_init(n1);
fmpz_set_si(n1, n);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
c = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_randtest(b, state, len, 200);
_fmpz_vec_set(c, b, len);
_fmpz_vec_scalar_submul_fmpz(b, a, len, n1);
_fmpz_vec_scalar_submul_si(c, a, len, n);
result = (_fmpz_vec_equal(c, b, len));
if (!result)
{
printf("FAIL:\n");
_fmpz_vec_print(c, len), printf("\n\n");
_fmpz_vec_print(b, len), printf("\n\n");
abort();
}
fmpz_clear(n1);
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
_fmpz_vec_clear(c, len);
}
/* Compute a different way */
for (i = 0; i < 10000; i++)
{
fmpz *a, *b, *c, *d;
long len = n_randint(state, 100);
fmpz_t n1;
fmpz_init(n1);
fmpz_randtest(n1, state, 200);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
c = _fmpz_vec_init(len);
d = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_randtest(b, state, len, 200);
_fmpz_vec_set(c, b, len);
_fmpz_vec_scalar_submul_fmpz(b, a, len, n1);
_fmpz_vec_scalar_mul_fmpz(d, a, len, n1);
_fmpz_vec_sub(c, c, d, len);
result = (_fmpz_vec_equal(c, b, len));
if (!result)
{
printf("FAIL:\n");
_fmpz_vec_print(c, len), printf("\n\n");
_fmpz_vec_print(b, len), printf("\n\n");
abort();
}
fmpz_clear(n1);
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
_fmpz_vec_clear(c, len);
_fmpz_vec_clear(d, len);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\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);
}
void
fmpz_poly_pseudo_divrem_basecase(fmpz_poly_t Q, fmpz_poly_t R,
ulong * d, const fmpz_poly_t A,
const fmpz_poly_t B)
{
long lenq, lenr;
fmpz *q, *r;
if (B->length == 0)
{
printf("Exception: division by zero in fmpz_poly_pseudo_divrem_basecase\n");
abort();
}
if (Q == R)
{
printf("Exception: output arguments Q and R may not be aliased\n");
abort();
}
if (A->length < B->length)
{
fmpz_poly_zero(Q);
fmpz_poly_set(R, A);
*d = 0;
return;
}
lenq = A->length - B->length + 1;
lenr = A->length;
if (Q == A || Q == B)
q = _fmpz_vec_init(lenq);
else
{
fmpz_poly_fit_length(Q, lenq);
q = Q->coeffs;
}
if (R == B)
r = _fmpz_vec_init(lenr);
else
{
fmpz_poly_fit_length(R, lenr);
r = R->coeffs;
}
_fmpz_poly_pseudo_divrem_basecase(q, r, d, A->coeffs, A->length,
B->coeffs, B->length);
for (lenr = B->length - 2; (lenr >= 0) && !r[lenr]; lenr--) ;
lenr++;
if (Q == A || Q == B)
{
_fmpz_vec_clear(Q->coeffs, Q->alloc);
Q->coeffs = q;
Q->alloc = lenq;
Q->length = lenq;
}
else
_fmpz_poly_set_length(Q, lenq);
if (R == B)
{
_fmpz_vec_clear(R->coeffs, R->alloc);
R->coeffs = r;
R->alloc = A->length;
R->length = lenr;
}
else
_fmpz_poly_set_length(R, lenr);
}
void _fmpz_poly_signature(long * r1, long * r2, fmpz * poly, long len)
{
fmpz *A, *B, *f, *g, *h, *w;
long lenA, lenB;
int s, t;
if (len <= 2)
{
*r1 = (len == 2);
*r2 = 0;
return;
}
w = _fmpz_vec_init(2 * len + 2);
A = w;
B = w + len;
lenA = len;
lenB = lenA - 1;
f = w + 2 * len - 1;
g = w + 2 * len;
h = w + 2 * len + 1;
_fmpz_poly_primitive_part(A, poly, lenA);
_fmpz_poly_derivative(B, A, lenA);
_fmpz_poly_primitive_part(B, B, lenB);
fmpz_one(g);
fmpz_one(h);
s = 1;
t = (lenA & 1L) ? -s : s;
*r1 = 1;
while (1)
{
long delta = lenA - lenB;
int sgnA;
_fmpz_poly_pseudo_rem_cohen(A, A, lenA, B, lenB);
lenA = lenB;
FMPZ_VEC_NORM(A, lenA);
if (lenA == 0)
{
printf("Exception: non-squarefree polynomial detected in fmpz_poly_signature\n");
_fmpz_vec_clear(w, 2 * len + 2);
abort();
}
if ((fmpz_sgn(B + (lenB - 1)) > 0) || (delta & 1L))
_fmpz_vec_neg(A, A, lenA);
sgnA = fmpz_sgn(A + (lenA - 1));
if (sgnA != s)
{
s = -s;
(*r1)--;
}
if (sgnA != ((lenA & 1L) ? t : -t))
{
t = -t;
(*r1)++;
}
if (lenA == 1)
{
*r2 = ((len - 1) - *r1) / 2;
_fmpz_vec_clear(w, 2 * len + 2);
return;
}
else
{
{
fmpz * temp = A;
A = B;
B = temp;
}
{
long temp = lenA;
lenA = lenB;
lenB = temp;
}
if (delta == 1)
{
fmpz_mul(f, g, h);
_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, f);
fmpz_set(g, A + (lenA - 1));
fmpz_set(h, g);
}
else
{
fmpz_pow_ui(f, h, delta);
fmpz_mul(f, f, g);
_fmpz_vec_scalar_divexact_fmpz(B, B, lenB, f);
fmpz_pow_ui(f, h, delta - 1);
fmpz_pow_ui(g, A + (lenA - 1), delta);
fmpz_divexact(h, g, f);
fmpz_set(g, A + (lenA - 1));
}
}
}
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("scalar_divexact_ui....");
fflush(stdout);
/* Check aliasing of a and b */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz *a, *b;
ulong n = n_randtest_not_zero(state);
slong len = n_randint(state, 100);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_scalar_mul_ui(a, a, len, n);
_fmpz_vec_scalar_divexact_ui(b, a, len, n);
_fmpz_vec_scalar_divexact_ui(a, a, len, n);
result = (_fmpz_vec_equal(a, b, len));
if (!result)
{
flint_printf("FAIL:\n");
_fmpz_vec_print(a, len), flint_printf("\n\n");
_fmpz_vec_print(b, len), flint_printf("\n\n");
abort();
}
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
}
/* Check that a * n / n == a */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz *a, *b;
ulong n = n_randtest_not_zero(state);
slong len = n_randint(state, 100);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_set(b, a, len);
_fmpz_vec_scalar_mul_ui(a, a, len, n);
_fmpz_vec_scalar_divexact_ui(a, a, len, n);
result = (_fmpz_vec_equal(a, b, len));
if (!result)
{
flint_printf("FAIL:\n");
_fmpz_vec_print(a, len), flint_printf("\n\n");
_fmpz_vec_print(b, len), flint_printf("\n\n");
abort();
}
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("scalar_fdiv_q_fmpz....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz *a, *b, *c;
fmpz_t n;
mpz_t d, e, f, m;
slong i;
slong len = n_randint(state, 100);
fmpz_init(n);
fmpz_randtest_not_zero(n, state, 100);
if (n_randint(state, 2))
fmpz_neg(n, n);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
c = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_set(b, a, len);
_fmpz_vec_scalar_fdiv_q_fmpz(c, a, len, n);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(m);
for (i = 0; i < len; i++)
{
fmpz_get_mpz(m, n);
fmpz_get_mpz(d, b + i);
mpz_fdiv_q(e, d, m);
fmpz_get_mpz(f, c + i);
result = (mpz_cmp(f, e) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, m = %Zd, e = %Zd, f = %Zd\n", d, m, e, f);
abort();
}
}
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
_fmpz_vec_clear(c, len);
fmpz_clear(n);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(m);
}
/* Test aliasing of a and c */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz *a, *b;
fmpz_t n;
mpz_t d, e, f, m;
slong i;
slong len = n_randint(state, 100);
fmpz_init(n);
fmpz_randtest_not_zero(n, state, 100);
if (n_randint(state, 2))
fmpz_neg(n, n);
a = _fmpz_vec_init(len);
b = _fmpz_vec_init(len);
_fmpz_vec_randtest(a, state, len, 200);
_fmpz_vec_set(b, a, len);
_fmpz_vec_scalar_fdiv_q_fmpz(a, a, len, n);
mpz_init(d);
mpz_init(e);
mpz_init(f);
mpz_init(m);
for (i = 0; i < len; i++)
{
fmpz_get_mpz(m, n);
fmpz_get_mpz(d, b + i);
mpz_fdiv_q(e, d, m);
fmpz_get_mpz(f, a + i);
result = (mpz_cmp(f, e) == 0);
if (!result)
{
flint_printf("FAIL:\n");
gmp_printf("d = %Zd, m = %Zd, e = %Zd, f = %Zd\n", d, m, e, f);
abort();
}
}
_fmpz_vec_clear(a, len);
_fmpz_vec_clear(b, len);
fmpz_clear(n);
mpz_clear(d);
mpz_clear(e);
mpz_clear(f);
mpz_clear(m);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
