void fmpz_poly_q_scalar_mul_si(fmpz_poly_q_t rop, const fmpz_poly_q_t op, long x)
{
fmpz_t cont, fx, gcd;
if (fmpz_poly_q_is_zero(op) || (x == 0))
{
fmpz_poly_q_zero(rop);
return;
}
if (x == 1)
{
fmpz_poly_q_set(rop, op);
return;
}
fmpz_init(cont);
fmpz_poly_content(cont, op->den);
if (fmpz_is_one(cont))
{
fmpz_poly_scalar_mul_si(rop->num, op->num, x);
fmpz_poly_set(rop->den, op->den);
fmpz_clear(cont);
return;
}
fmpz_init(fx);
fmpz_init(gcd);
fmpz_set_si(fx, x);
fmpz_gcd(gcd, cont, fx);
if (fmpz_is_one(gcd))
{
fmpz_poly_scalar_mul_si(rop->num, op->num, x);
fmpz_poly_set(rop->den, op->den);
}
else
{
fmpz_divexact(fx, fx, gcd);
fmpz_poly_scalar_mul_fmpz(rop->num, op->num, fx);
fmpz_poly_scalar_divexact_fmpz(rop->den, op->den, gcd);
}
fmpz_clear(cont);
fmpz_clear(fx);
fmpz_clear(gcd);
}
void
fmpz_poly_scalar_mul_ui(fmpz_poly_t poly1, const fmpz_poly_t poly2, ulong x)
{
long i;
/* Either scalar or input poly is zero */
if ((x == 0) || (poly2->length == 0))
{
fmpz_poly_zero(poly1);
return;
}
/* Special case, multiply by 1 */
if (x == 1)
{
fmpz_poly_set(poly1, poly2);
return;
}
fmpz_poly_fit_length(poly1, poly2->length);
for (i = 0; i < poly2->length; i++)
fmpz_mul_ui(poly1->coeffs + i, poly2->coeffs + i, x);
_fmpz_poly_set_length(poly1, poly2->length);
}
int dgsl_rot_mp_call_gpv_inlattice(fmpz_poly_t rop, const dgsl_rot_mp_t *self, gmp_randstate_t state) {
assert(rop); assert(self);
const long n = self->n;
mpz_t tmp_z; mpz_init(tmp_z);
fmpz_t tmp; fmpz_init(tmp);
fmpz_poly_zero(rop);
fmpz_poly_t tmp_poly;
fmpz_poly_init(tmp_poly);
fmpz_poly_set(tmp_poly, self->B);
fmpz_poly_realloc(tmp_poly, n);
tmp_poly->length = n;
fmpz_poly_t tmp2;
fmpz_poly_init(tmp2);
for(long i=0; i<n; i++) {
self->D[i]->call(tmp_z, self->D[i], state); fmpz_set_mpz(tmp, tmp_z);
fmpz_poly_scalar_mul_fmpz(tmp2, tmp_poly, tmp);
fmpz_poly_add(rop, rop, tmp2);
_fmpz_vec_rot_left_neg(tmp_poly->coeffs, tmp_poly->coeffs, n);
}
fmpz_poly_clear(tmp_poly);
fmpz_poly_add(rop, rop, self->c_z);
fmpz_poly_clear(tmp2);
mpz_clear(tmp_z);
fmpz_clear(tmp);
return 0;
}
void
poly_starmultiply(fmpz_poly_t c,
const fmpz_poly_t a,
const fmpz_poly_t b,
const ntru_params *params,
uint32_t modulus)
{
fmpz_poly_t a_tmp;
fmpz_t c_coeff_k;
fmpz_poly_init(a_tmp);
fmpz_init(c_coeff_k);
/* avoid side effects */
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(c);
for (int k = params->N - 1; k >= 0; k--) {
int j;
j = k + 1;
fmpz_set_si(c_coeff_k, 0);
for (int i = params->N - 1; i >= 0; i--) {
fmpz *a_tmp_coeff_i,
*b_coeff_j;
if (j == (int)(params->N))
j = 0;
a_tmp_coeff_i = fmpz_poly_get_coeff_ptr(a_tmp, i);
b_coeff_j = fmpz_poly_get_coeff_ptr(b, j);
if (fmpz_cmp_si_n(a_tmp_coeff_i, 0) &&
fmpz_cmp_si_n(b_coeff_j, 0)) {
fmpz_t fmpz_tmp;
fmpz_init(fmpz_tmp);
fmpz_mul(fmpz_tmp, a_tmp_coeff_i, b_coeff_j);
fmpz_add(fmpz_tmp, fmpz_tmp, c_coeff_k);
fmpz_mod_ui(c_coeff_k, fmpz_tmp, modulus);
fmpz_poly_set_coeff_fmpz(c, k, c_coeff_k);
fmpz_clear(fmpz_tmp);
}
j++;
}
fmpz_clear(c_coeff_k);
}
fmpz_poly_clear(a_tmp);
}
int
main(void)
{
int iter;
FLINT_TEST_INIT(state);
flint_printf("sgn_eval_at_half....");
fflush(stdout);
/* Check aliasing */
for (iter = 0; iter < 1000 * flint_test_multiplier(); iter++)
{
fmpz_t a;
fmpz_poly_t f, g;
long i, d;
int s1, s2;
fmpz_init(a);
fmpz_poly_init(f);
fmpz_poly_init(g);
fmpz_poly_randtest(f, state, n_randint(state, 100), 200);
s1 = fmpz_poly_sgn_eval_at_half(f);
fmpz_poly_set(g, f);
d = fmpz_poly_degree(g);
for (i = 0; i <= d; i++)
{
fmpz_mul_2exp(fmpz_poly_get_coeff_ptr(g, i),
fmpz_poly_get_coeff_ptr(g, i), d - i);
}
fmpz_one(a);
fmpz_poly_evaluate_fmpz(a, g, a);
s2 = fmpz_sgn(a);
if (s1 != s2)
{
flint_printf("FAIL:\n");
fmpz_poly_print(f); printf("\n\n");
printf("s1 = %d, s2 = %d\n\n", s1, s2);
abort();
}
fmpz_clear(a);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int dgsl_rot_mp_call_plus_fmpz_poly(fmpz_poly_t rop, const dgsl_rot_mp_t *self, const fmpz_poly_t c, gmp_randstate_t state) {
fmpz_poly_t t; fmpz_poly_init(t);
fmpz_poly_set(t, c);
fmpq_poly_t tq; fmpq_poly_init(tq); // == 0
fmpq_poly_set_fmpz_poly(tq, t);
fmpq_poly_neg(tq, tq);
dgsl_rot_mp_call_recenter_fmpq_poly(rop, self, tq, state);
fmpz_poly_add(rop, rop, t);
fmpq_poly_clear(tq);
fmpz_poly_clear(t);
return 0;
}
void
fmpz_poly_mat_trace(fmpz_poly_t trace, const fmpz_poly_mat_t mat)
{
long i, n = fmpz_poly_mat_nrows(mat);
if (n == 0)
fmpz_poly_zero(trace);
else
{
fmpz_poly_set(trace, fmpz_poly_mat_entry(mat, 0, 0));
for (i = 1; i < n; i++)
fmpz_poly_add(trace, trace, fmpz_poly_mat_entry(mat, i, i));
}
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("swap....");
fflush(stdout);
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, c;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_randtest(a, state, n_randint(state, 100), 200);
fmpz_poly_randtest(b, state, n_randint(state, 100), 200);
fmpz_poly_set(c, b);
fmpz_poly_swap(a, b);
result = (fmpz_poly_equal(a, c));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(a), flint_printf("\n\n");
fmpz_poly_print(b), flint_printf("\n\n");
fmpz_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void
fmpz_poly_pow_multinomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e)
{
const long len = poly->length;
long rlen;
if ((len < 2) | (e < 3UL))
{
if (e == 0UL)
fmpz_poly_set_ui(res, 1);
else if (len == 0)
fmpz_poly_zero(res);
else if (len == 1)
{
fmpz_poly_fit_length(res, 1);
fmpz_pow_ui(res->coeffs, poly->coeffs, e);
_fmpz_poly_set_length(res, 1);
}
else if (e == 1UL)
fmpz_poly_set(res, poly);
else /* e == 2UL */
fmpz_poly_sqr(res, poly);
return;
}
rlen = (long) e * (len - 1) + 1;
if (res != poly)
{
fmpz_poly_fit_length(res, rlen);
_fmpz_poly_pow_multinomial(res->coeffs, poly->coeffs, len, e);
_fmpz_poly_set_length(res, rlen);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, rlen);
_fmpz_poly_pow_multinomial(t->coeffs, poly->coeffs, len, e);
_fmpz_poly_set_length(t, rlen);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}
void
fmpz_poly_pow_binomial(fmpz_poly_t res, const fmpz_poly_t poly, ulong e)
{
const long len = poly->length;
long rlen;
if (len != 2)
{
printf("Exception: poly->length not equal to 2 in fmpz_poly_pow_binomial\n");
abort();
}
if (e < 3UL)
{
if (e == 0UL)
fmpz_poly_set_ui(res, 1UL);
else if (e == 1UL)
fmpz_poly_set(res, poly);
else /* e == 2UL */
fmpz_poly_sqr(res, poly);
return;
}
rlen = (long) e + 1;
if (res != poly)
{
fmpz_poly_fit_length(res, rlen);
_fmpz_poly_set_length(res, rlen);
_fmpz_poly_pow_binomial(res->coeffs, poly->coeffs, e);
}
else
{
fmpz_poly_t t;
fmpz_poly_init2(t, rlen);
_fmpz_poly_set_length(t, rlen);
_fmpz_poly_pow_binomial(t->coeffs, poly->coeffs, e);
fmpz_poly_swap(res, t);
fmpz_poly_clear(t);
}
}
void
fmpz_poly_deflate(fmpz_poly_t result, const fmpz_poly_t input, ulong deflation)
{
slong res_length, i;
if (deflation == 0)
{
flint_printf("Exception (fmpz_poly_deflate). Division by zero.\n");
abort();
}
if (input->length <= 1 || deflation == 1)
{
fmpz_poly_set(result, input);
return;
}
res_length = (input->length - 1) / deflation + 1;
fmpz_poly_fit_length(result, res_length);
for (i = 0; i < res_length; i++)
fmpz_set(result->coeffs + i, input->coeffs + i*deflation);
result->length = res_length;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("set_si_equal....");
fflush(stdout);
/* equal polynomials */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b;
slong n;
fmpz_poly_init(a);
fmpz_poly_init(b);
n = z_randtest(state);
fmpz_poly_set_si(a, n);
fmpz_poly_set(b, a);
result = (fmpz_poly_equal(a, b));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("n = %wd\n\n", n);
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
}
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b;
slong m, n;
fmpz_poly_init(a);
fmpz_poly_init(b);
m = z_randtest(state);
n = z_randtest(state);
while (m == n)
n = z_randtest(state);
fmpz_poly_set_si(a, m);
fmpz_poly_set_si(b, n);
result = (!fmpz_poly_equal(a, b));
if (!result)
{
flint_printf("FAIL:\n");
flint_printf("m = %wd\n\n", m);
flint_printf("n = %wd\n\n", n);
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
bool
poly_inverse_poly_q(fmpz_poly_t Fq,
const fmpz_poly_t a,
const ntru_params *params)
{
bool retval = false;
int k = 0,
j = 0;
fmpz *b_last;
fmpz_poly_t a_tmp,
b,
c,
f,
g;
/* general initialization of temp variables */
fmpz_poly_init(b);
fmpz_poly_set_coeff_ui(b, 0, 1);
fmpz_poly_init(c);
fmpz_poly_init(f);
fmpz_poly_set(f, a);
/* set g(x) = x^N − 1 */
fmpz_poly_init(g);
fmpz_poly_set_coeff_si(g, 0, -1);
fmpz_poly_set_coeff_si(g, params->N, 1);
/* avoid side effects */
fmpz_poly_init(a_tmp);
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(Fq);
while (1) {
while (fmpz_poly_get_coeff_ptr(f, 0) &&
fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
for (uint32_t i = 1; i <= params->N; i++) {
fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i);
/* f(x) = f(x) / x */
fmpz_poly_set_coeff_fmpz_n(f, i - 1,
f_coeff);
/* c(x) = c(x) * x */
fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i,
c_coeff);
}
fmpz_poly_set_coeff_si(f, params->N, 0);
fmpz_poly_set_coeff_si(c, 0, 0);
k++;
if (fmpz_poly_degree(f) == -1)
goto cleanup;
}
if (fmpz_poly_is_zero(g) == 1)
goto cleanup;
if (fmpz_poly_degree(f) == 0)
break;
if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
fmpz_poly_swap(f, g);
fmpz_poly_swap(b, c);
}
fmpz_poly_add(f, g, f);
fmpz_poly_mod_unsigned(f, 2);
fmpz_poly_add(b, c, b);
fmpz_poly_mod_unsigned(b, 2);
}
k = k % params->N;
b_last = fmpz_poly_get_coeff_ptr(b, params->N);
if (fmpz_cmp_si_n(b_last, 0))
goto cleanup;
/* Fq(x) = x^(N-k) * b(x) */
for (int i = params->N - 1; i >= 0; i--) {
fmpz *b_i;
j = i - k;
if (j < 0)
j = j + params->N;
b_i = fmpz_poly_get_coeff_ptr(b, i);
fmpz_poly_set_coeff_fmpz_n(Fq, j, b_i);
}
poly_mod2_to_modq(Fq, a_tmp, params);
/* check if the f * Fq = 1 (mod p) condition holds true */
fmpz_poly_set(a_tmp, a);
poly_starmultiply(a_tmp, a_tmp, Fq, params, params->q);
if (fmpz_poly_is_one(a_tmp))
retval = true;
else
fmpz_poly_zero(Fq);
cleanup:
fmpz_poly_clear(a_tmp);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
return retval;
}
dgsl_rot_mp_t *dgsl_rot_mp_init(const long n, const fmpz_poly_t B, mpfr_t sigma, fmpq_poly_t c, const dgsl_alg_t algorithm, const oz_flag_t flags) {
assert(mpfr_cmp_ui(sigma, 0) > 0);
dgsl_rot_mp_t *self = (dgsl_rot_mp_t*)calloc(1, sizeof(dgsl_rot_mp_t));
if(!self) dgs_die("out of memory");
dgsl_alg_t alg = algorithm;
self->n = n;
self->prec = mpfr_get_prec(sigma);
fmpz_poly_init(self->B);
fmpz_poly_set(self->B, B);
if(fmpz_poly_length(self->B) > n)
dgs_die("polynomial is longer than length n");
else
fmpz_poly_realloc(self->B, n);
fmpz_poly_init(self->c_z);
fmpq_poly_init(self->c);
mpfr_init2(self->sigma, self->prec);
mpfr_set(self->sigma, sigma, MPFR_RNDN);
if (alg == DGSL_DETECT) {
if (fmpz_poly_is_one(self->B) && (c && fmpq_poly_is_zero(c))) {
alg = DGSL_IDENTITY;
} else if (c && fmpq_poly_is_zero(c))
alg = DGSL_INLATTICE;
else
alg = DGSL_COSET; //TODO: we could test for lattice membership here
}
size_t tau = 3;
if (2*ceil(sqrt(log2((double)n))) > tau)
tau = 2*ceil(sqrt(log2((double)n)));
switch(alg) {
case DGSL_IDENTITY: {
self->D = (dgs_disc_gauss_mp_t**)calloc(1, sizeof(dgs_disc_gauss_mp_t*));
mpfr_t c_;
mpfr_init2(c_, self->prec);
mpfr_set_d(c_, 0.0, MPFR_RNDN);
self->D[0] = dgs_disc_gauss_mp_init(self->sigma, c_, tau, DGS_DISC_GAUSS_DEFAULT);
self->call = dgsl_rot_mp_call_identity;
mpfr_clear(c_);
break;
}
case DGSL_GPV_INLATTICE: {
self->D = (dgs_disc_gauss_mp_t**)calloc(n, sizeof(dgs_disc_gauss_mp_t*));
if (c && !fmpq_poly_is_zero(c)) {
fmpq_t c_i;
fmpq_init(c_i);
for(int i=0; i<n; i++) {
fmpq_poly_get_coeff_fmpq(c_i, c, i);
fmpz_poly_set_coeff_fmpz(self->c_z, i, fmpq_numref(c_i));
}
fmpq_clear(c_i);
}
mpfr_mat_t G;
mpfr_mat_init(G, n, n, self->prec);
mpfr_mat_set_fmpz_poly(G, B);
mpfr_mat_gso(G, MPFR_RNDN);
mpfr_t sigma_;
mpfr_init2(sigma_, self->prec);
mpfr_t norm;
mpfr_init2(norm, self->prec);
mpfr_t c_;
mpfr_init2(c_, self->prec);
mpfr_set_d(c_, 0.0, MPFR_RNDN);
for(long i=0; i<n; i++) {
_mpfr_vec_2norm(norm, G->rows[i], n, MPFR_RNDN);
assert(mpfr_cmp_d(norm, 0.0) > 0);
mpfr_div(sigma_, self->sigma, norm, MPFR_RNDN);
assert(mpfr_cmp_d(sigma_, 0.0) > 0);
self->D[i] = dgs_disc_gauss_mp_init(sigma_, c_, tau, DGS_DISC_GAUSS_DEFAULT);
}
mpfr_clear(sigma_);
mpfr_clear(norm);
mpfr_clear(c_);
mpfr_mat_clear(G);
self->call = dgsl_rot_mp_call_gpv_inlattice;
break;
}
case DGSL_INLATTICE: {
fmpq_poly_init(self->sigma_sqrt);
long r= 2*ceil(sqrt(log(n)));
fmpq_poly_t Bq; fmpq_poly_init(Bq);
fmpq_poly_set_fmpz_poly(Bq, self->B);
fmpq_poly_oz_invert_approx(self->B_inv, Bq, n, self->prec, flags);
fmpq_poly_clear(Bq);
_dgsl_rot_mp_sqrt_sigma_2(self->sigma_sqrt, self->B, sigma, r, n, self->prec, flags);
mpfr_init2(self->r_f, self->prec);
mpfr_set_ui(self->r_f, r, MPFR_RNDN);
self->call = dgsl_rot_mp_call_inlattice;
break;
}
case DGSL_COSET:
dgs_die("not implemented");
default:
dgs_die("not implemented");
}
return self;
}
void
fmpz_poly_pseudo_divrem_cohen(fmpz_poly_t Q, fmpz_poly_t R,
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_cohen\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);
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_cohen(q, r, A->coeffs, A->length, B->coeffs, B->length);
for (lenr = B->length - 1; (lenr >= 0) && r[lenr] == 0L; 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);
}
bool
poly_inverse_poly_p(fmpz_poly_t Fp,
const fmpz_poly_t a,
const ntru_params *params)
{
bool retval = false;
int k = 0,
j = 0;
fmpz *b_last;
fmpz_poly_t a_tmp,
b,
c,
f,
g;
/* general initialization of temp variables */
fmpz_poly_init(b);
fmpz_poly_set_coeff_ui(b, 0, 1);
fmpz_poly_init(c);
fmpz_poly_init(f);
fmpz_poly_set(f, a);
/* set g(x) = x^N − 1 */
fmpz_poly_init(g);
fmpz_poly_set_coeff_si(g, 0, -1);
fmpz_poly_set_coeff_si(g, params->N, 1);
/* avoid side effects */
fmpz_poly_init(a_tmp);
fmpz_poly_set(a_tmp, a);
fmpz_poly_zero(Fp);
while (1) {
while (fmpz_poly_get_coeff_ptr(f, 0) &&
fmpz_is_zero(fmpz_poly_get_coeff_ptr(f, 0))) {
for (uint32_t i = 1; i <= params->N; i++) {
fmpz *f_coeff = fmpz_poly_get_coeff_ptr(f, i);
fmpz *c_coeff = fmpz_poly_get_coeff_ptr(c, params->N - i);
/* f(x) = f(x) / x */
fmpz_poly_set_coeff_fmpz_n(f, i - 1,
f_coeff);
/* c(x) = c(x) * x */
fmpz_poly_set_coeff_fmpz_n(c, params->N + 1 - i,
c_coeff);
}
fmpz_poly_set_coeff_si(f, params->N, 0);
fmpz_poly_set_coeff_si(c, 0, 0);
k++;
if (fmpz_poly_degree(f) == -1)
goto cleanup;
}
if (fmpz_poly_is_zero(g) == 1)
goto cleanup;
if (fmpz_poly_degree(f) == 0)
break;
if (fmpz_poly_degree(f) < fmpz_poly_degree(g)) {
/* exchange f and g and exchange b and c */
fmpz_poly_swap(f, g);
fmpz_poly_swap(b, c);
}
{
fmpz_poly_t c_tmp,
g_tmp;
fmpz_t u,
mp_tmp;
fmpz_init(u);
fmpz_zero(u);
fmpz_init_set(mp_tmp, fmpz_poly_get_coeff_ptr(f, 0));
fmpz_poly_init(g_tmp);
fmpz_poly_set(g_tmp, g);
fmpz_poly_init(c_tmp);
fmpz_poly_set(c_tmp, c);
/* u = f[0] * g[0]^(-1) mod p */
/* = (f[0] mod p) * (g[0] inverse mod p) mod p */
fmpz_invmod_ui(u,
fmpz_poly_get_coeff_ptr(g, 0),
params->p);
fmpz_mod_ui(mp_tmp, mp_tmp, params->p);
fmpz_mul(u, mp_tmp, u);
fmpz_mod_ui(u, u, params->p);
/* f = f - u * g mod p */
fmpz_poly_scalar_mul_fmpz(g_tmp, g_tmp, u);
fmpz_poly_sub(f, f, g_tmp);
fmpz_poly_mod_unsigned(f, params->p);
/* b = b - u * c mod p */
fmpz_poly_scalar_mul_fmpz(c_tmp, c_tmp, u);
fmpz_poly_sub(b, b, c_tmp);
fmpz_poly_mod_unsigned(b, params->p);
fmpz_clear(u);
fmpz_poly_clear(g_tmp);
fmpz_poly_clear(c_tmp);
}
}
k = k % params->N;
b_last = fmpz_poly_get_coeff_ptr(b, params->N);
if (fmpz_cmp_si_n(b_last, 0))
goto cleanup;
/* Fp(x) = x^(N-k) * b(x) */
for (int i = params->N - 1; i >= 0; i--) {
fmpz *b_i;
/* b(X) = f[0]^(-1) * b(X) (mod p) */
{
fmpz_t mp_tmp;
fmpz_init(mp_tmp);
fmpz_invmod_ui(mp_tmp,
fmpz_poly_get_coeff_ptr(f, 0),
params->p);
if (fmpz_poly_get_coeff_ptr(b, i)) {
fmpz_mul(fmpz_poly_get_coeff_ptr(b, i),
fmpz_poly_get_coeff_ptr(b, i),
mp_tmp);
fmpz_mod_ui(fmpz_poly_get_coeff_ptr(b, i),
fmpz_poly_get_coeff_ptr(b, i),
params->p);
}
}
j = i - k;
if (j < 0)
j = j + params->N;
b_i = fmpz_poly_get_coeff_ptr(b, i);
fmpz_poly_set_coeff_fmpz_n(Fp, j, b_i);
}
/* check if the f * Fp = 1 (mod p) condition holds true */
fmpz_poly_set(a_tmp, a);
poly_starmultiply(a_tmp, a_tmp, Fp, params, params->p);
if (fmpz_poly_is_one(a_tmp))
retval = true;
else
fmpz_poly_zero(Fp);
cleanup:
fmpz_poly_clear(a_tmp);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(f);
fmpz_poly_clear(g);
return retval;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("mul_KS....");
fflush(stdout);
flint_randinit(state);
/* Check aliasing of a and b */
for (i = 0; i < 2000; i++)
{
fmpz_poly_t a, b, c;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_randtest(b, state, n_randint(state, 50), 200);
fmpz_poly_randtest(c, state, n_randint(state, 50), 200);
fmpz_poly_mul_KS(a, b, c);
fmpz_poly_mul_KS(b, b, c);
result = (fmpz_poly_equal(a, b));
if (!result)
{
printf("FAIL:\n");
fmpz_poly_print(a), printf("\n\n");
fmpz_poly_print(b), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
/* Check aliasing of a and c */
for (i = 0; i < 2000; i++)
{
fmpz_poly_t a, b, c;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_randtest(b, state, n_randint(state, 50), 200);
fmpz_poly_randtest(c, state, n_randint(state, 50), 200);
fmpz_poly_mul_KS(a, b, c);
fmpz_poly_mul_KS(c, b, c);
result = (fmpz_poly_equal(a, c));
if (!result)
{
printf("FAIL:\n");
fmpz_poly_print(a), printf("\n\n");
fmpz_poly_print(c), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
/* Check aliasing of b and c */
for (i = 0; i < 2000; i++)
{
fmpz_poly_t a, b, c;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_randtest(b, state, n_randint(state, 50), 200);
fmpz_poly_set(c, b);
fmpz_poly_mul_KS(a, b, b);
fmpz_poly_mul_KS(c, b, c);
result = (fmpz_poly_equal(a, c));
if (!result)
{
printf("FAIL:\n");
fmpz_poly_print(a), printf("\n\n");
fmpz_poly_print(c), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
/* Compare with mul_classical */
for (i = 0; i < 10000; i++)
{
fmpz_poly_t a, b, c, d;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_init(d);
fmpz_poly_randtest(b, state, n_randint(state, 50), 200);
fmpz_poly_randtest(c, state, n_randint(state, 50), 200);
fmpz_poly_mul_KS(a, b, c);
fmpz_poly_mul_classical(d, b, c);
result = (fmpz_poly_equal(a, d));
if (!result)
{
printf("FAIL:\n");
fmpz_poly_print(a), printf("\n\n");
fmpz_poly_print(d), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(d);
}
/* Compare with mul_classical unsigned */
for (i = 0; i < 10000; i++)
{
fmpz_poly_t a, b, c, d;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_init(d);
fmpz_poly_randtest_unsigned(b, state, n_randint(state, 50), 200);
fmpz_poly_randtest_unsigned(c, state, n_randint(state, 50), 200);
fmpz_poly_mul_KS(a, b, c);
fmpz_poly_mul_classical(d, b, c);
result = (fmpz_poly_equal(a, d));
if (!result)
{
printf("FAIL:\n");
fmpz_poly_print(a), printf("\n\n");
fmpz_poly_print(d), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
fmpz_poly_clear(d);
}
/* Check _fmpz_poly_mul_KS directly */
for (i = 0; i < 2000; i++)
{
long len1, len2;
fmpz_poly_t a, b, out1, out2;
len1 = n_randint(state, 100) + 1;
len2 = n_randint(state, 100) + 1;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(out1);
fmpz_poly_init(out2);
fmpz_poly_randtest(a, state, len1, 200);
fmpz_poly_randtest(b, state, len2, 200);
fmpz_poly_mul_KS(out1, a, b);
fmpz_poly_fit_length(a, a->alloc + n_randint(state, 10));
fmpz_poly_fit_length(b, b->alloc + n_randint(state, 10));
a->length = a->alloc;
b->length = b->alloc;
fmpz_poly_fit_length(out2, a->length + b->length - 1);
_fmpz_poly_mul_KS(out2->coeffs, a->coeffs, a->length,
b->coeffs, b->length);
_fmpz_poly_set_length(out2, a->length + b->length - 1);
_fmpz_poly_normalise(out2);
result = (fmpz_poly_equal(out1, out2));
if (!result)
{
printf("FAIL:\n");
fmpz_poly_print(out1), printf("\n\n");
fmpz_poly_print(out2), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(out1);
fmpz_poly_clear(out2);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
long _fmpz_poly_hensel_start_lift(fmpz_poly_factor_t lifted_fac, long *link,
fmpz_poly_t *v, fmpz_poly_t *w, const fmpz_poly_t f,
const nmod_poly_factor_t local_fac, long N)
{
const long r = local_fac->num;
long i, preve;
fmpz_t p, P;
fmpz_poly_t monic_f;
fmpz_init(p);
fmpz_init(P);
fmpz_poly_init(monic_f);
fmpz_set_ui(p, (local_fac->p + 0)->mod.n);
fmpz_pow_ui(P, p, N);
if (fmpz_is_one(fmpz_poly_lead(f)))
{
fmpz_poly_set(monic_f, f);
}
else if (fmpz_cmp_si(fmpz_poly_lead(f), -1) == 0)
{
fmpz_poly_neg(monic_f, f);
}
else
{
fmpz_t t;
fmpz_init(t);
fmpz_mod(t, fmpz_poly_lead(f), P);
if (fmpz_invmod(t, t, P) == 0)
{
printf("Exception in fmpz_poly_start_hensel_lift.\n");
abort();
}
fmpz_poly_scalar_mul_fmpz(monic_f, f, t);
fmpz_poly_scalar_mod_fmpz(monic_f, monic_f, P);
fmpz_clear(t);
}
fmpz_poly_hensel_build_tree(link, v, w, local_fac);
{
long *e, n = FLINT_CLOG2(N) + 1;
e = flint_malloc(n * sizeof(long));
for (e[i = 0] = N; e[i] > 1; i++)
e[i + 1] = (e[i] + 1) / 2;
for (i--; i > 0; i--)
{
fmpz_poly_hensel_lift_tree(link, v, w, monic_f, r,
p, e[i+1], e[i], 1);
}
if (N > 1)
{
fmpz_poly_hensel_lift_tree(link, v, w, monic_f, r,
p, e[i+1], e[i], 0);
}
preve = e[i+1];
flint_free(e);
}
/*
Now everything is lifted to p^N, we just need to
insert the factors into their correct places in lifted_fac.
*/
fmpz_poly_factor_fit_length(lifted_fac, r);
for (i = 0; i < 2*r - 2; i++)
{
if (link[i] < 0)
{
fmpz_poly_scalar_smod_fmpz(lifted_fac->p + (- link[i] - 1), v[i], P);
lifted_fac->exp[- link[i] - 1] = 1L;
}
}
lifted_fac->num = r;
fmpz_clear(p);
fmpz_clear(P);
fmpz_poly_clear(monic_f);
return preve;
}
int main(int argc, char *argv[]) {
cmdline_params_t cmdline_params;
const char *name = "Jigsaw Puzzles";
parse_cmdline(cmdline_params, argc, argv, name, NULL);
print_header(name, cmdline_params);
aes_randstate_t randstate;
aes_randinit_seed(randstate, cmdline_params->shaseed, NULL);
uint64_t t = ggh_walltime(0);
uint64_t t_total = ggh_walltime(0);
uint64_t t_gen = 0;
gghlite_sk_t self;
gghlite_jigsaw_init(self,
cmdline_params->lambda,
cmdline_params->kappa,
cmdline_params->flags,
randstate);
printf("\n");
gghlite_params_print(self->params);
printf("\n---\n\n");
t_gen = ggh_walltime(t);
printf("1. GGH InstGen wall time: %8.2f s\n", ggh_seconds(t_gen));
t = ggh_walltime(0);
fmpz_t p; fmpz_init(p);
fmpz_poly_oz_ideal_norm(p, self->g, self->params->n, 0);
fmpz_t a[5];
for(long k=0; k<5; k++)
fmpz_init(a[k]);
fmpz_t acc; fmpz_init(acc);
fmpz_set_ui(acc, 1);
// reducing these elements to something small mod g is expensive, for benchmarketing purposes we
// hence avoid this costly step most of the time by doing it only twice and by then computing the
// remaining elements from those two elements using cheap operations. The reported times still
// refer to the expensive step for fairness.
fmpz_randm_aes(a[0], randstate, p);
fmpz_mul(acc, acc, a[0]);
fmpz_mod(acc, acc, p);
fmpz_randm_aes(a[1], randstate, p);
fmpz_mul(acc, acc, a[1]);
fmpz_mod(acc, acc, p);
fmpz_set(a[3], a[0]);
fmpz_set(a[4], a[1]);
for(long k=2; k<cmdline_params->kappa; k++) {
fmpz_mul(a[2], a[0], a[1]);
fmpz_add_ui(a[2], a[2], k);
fmpz_mod(a[2], a[2], p);
fmpz_mul(acc, acc, a[2]);
fmpz_mod(acc, acc, p);
fmpz_set(a[1], a[0]);
fmpz_set(a[0], a[2]);
}
printf("2. Sampling from U(Z_p) wall time: %8.2f s\n", ggh_seconds(ggh_walltime(t)));
gghlite_clr_t e[3];
gghlite_clr_init(e[0]);
gghlite_clr_init(e[1]);
gghlite_clr_init(e[2]);
gghlite_enc_t u_k;
gghlite_enc_init(u_k, self->params);
gghlite_enc_t left;
gghlite_enc_init(left, self->params);
gghlite_enc_set_ui0(left, 1, self->params);
fmpz_poly_set_coeff_fmpz(e[0], 0, a[3]);
int GAMMA = 20;
uint64_t t_enc = ggh_walltime(0);
int group0[GAMMA];
memset(group0, 0, GAMMA * sizeof(int));
group0[0] = 1;
gghlite_enc_set_gghlite_clr(u_k, self, e[0], 1, group0, 1, randstate);
t_enc = ggh_walltime(t_enc);
printf("3. Encoding wall time: %8.2f s (per elem)\n", ggh_seconds(t_enc));
fflush(0);
uint64_t t_mul = 0;
t = ggh_walltime(0);
gghlite_enc_mul(left, self->params, left, u_k);
t_mul += ggh_walltime(t);
fmpz_poly_set_coeff_fmpz(e[1], 0, a[4]);
int group1[GAMMA];
memset(group1, 0, GAMMA * sizeof(int));
group1[1] = 1;
gghlite_enc_set_gghlite_clr(u_k, self, e[1], 1, group1, 1, randstate);
t = ggh_walltime(0);
gghlite_enc_mul(left, self->params, left, u_k);
t_mul += ggh_walltime(t);
const mp_bitcnt_t prec = (self->params->n/4 < 8192) ? 8192 : self->params->n/4;
const oz_flag_t flags = (self->params->flags & GGHLITE_FLAGS_VERBOSE) ? OZ_VERBOSE : 0;
_fmpz_poly_oz_rem_small_iter(e[0], e[0], self->g, self->params->n, self->g_inv, prec, flags);
_fmpz_poly_oz_rem_small_iter(e[1], e[1], self->g, self->params->n, self->g_inv, prec, flags);
for(long k=2; k<cmdline_params->kappa; k++) {
fmpz_poly_oz_mul(e[2], e[0], e[1], self->params->n);
assert(fmpz_poly_degree(e[2])>=0);
fmpz_add_ui(e[2]->coeffs, e[2]->coeffs, k);
_fmpz_poly_oz_rem_small_iter(e[2], e[2], self->g, self->params->n, self->g_inv, prec, flags);
int groupk[GAMMA];
memset(groupk, 0, GAMMA * sizeof(int));
groupk[k] = 1;
gghlite_enc_set_gghlite_clr(u_k, self, e[2], 1, groupk, 1, randstate);
t = ggh_walltime(0);
gghlite_enc_mul(left, self->params, left, u_k);
t_mul += ggh_walltime(t);
fmpz_poly_set(e[1], e[0]);
fmpz_poly_set(e[0], e[2]);
}
printf("4. Multiplication wall time: %8.4f s\n", ggh_seconds(t_mul));
fflush(0);
t = ggh_walltime(0);
gghlite_enc_t rght;
gghlite_enc_init(rght, self->params);
gghlite_enc_set_ui0(rght, 1, self->params);
fmpz_poly_t tmp; fmpz_poly_init(tmp);
fmpz_poly_set_coeff_fmpz(tmp, 0, acc);
gghlite_enc_set_gghlite_clr0(rght, self, tmp, randstate);
for(long k=0; k<cmdline_params->kappa; k++) {
gghlite_enc_mul(rght, self->params, rght, self->z_inv[k]);
}
printf("5. RHS generation wall time: %8.2f s\n", ggh_seconds(ggh_walltime(t)));
t = ggh_walltime(0);
gghlite_enc_sub(rght, self->params, rght, left);
int status = 1 - gghlite_enc_is_zero(self->params, rght);
gghlite_clr_t clr; gghlite_clr_init(clr);
gghlite_enc_extract(clr, self->params, rght);
double size = fmpz_poly_2norm_log2(clr);
gghlite_clr_clear(clr);
printf("6. Checking correctness wall time: %8.2f s\n", ggh_seconds(ggh_walltime(t)));
printf(" Correct: %8s (%8.2f)\n\n", (status == 0) ? "TRUE" : "FALSE", size);
for(long i=0; i<5; i++) {
fmpz_clear(a[i]);
}
gghlite_clr_clear(e[0]);
gghlite_clr_clear(e[1]);
gghlite_clr_clear(e[2]);
gghlite_enc_clear(u_k);
fmpz_clear(acc);
gghlite_enc_clear(left);
gghlite_enc_clear(rght);
gghlite_clr_clear(tmp);
fmpz_clear(p);
gghlite_sk_clear(self, 1);
t_total = ggh_walltime(t_total);
printf("λ: %3ld, κ: %2ld, n: %6ld, seed: 0x%08lx, success: %d, gen: %10.2fs, enc: %8.2fs, mul: %8.4fs, time: %10.2fs\n",
cmdline_params->lambda, cmdline_params->kappa, self->params->n, cmdline_params->seed,
status==0,
ggh_seconds(t_gen), ggh_seconds(t_enc), ggh_seconds(t_mul), ggh_seconds(t_total));
aes_randclear(randstate);
mpfr_free_cache();
flint_cleanup();
return status;
}
int
main(void)
{
int i, result;
flint_rand_t state;
printf("set_ui_equal....");
fflush(stdout);
flint_randinit(state);
/* equal polynomials */
for (i = 0; i < 10000; i++)
{
fmpz_poly_t a, b;
ulong n;
fmpz_poly_init(a);
fmpz_poly_init(b);
n = n_randtest(state);
fmpz_poly_set_ui(a, n);
fmpz_poly_set(b, a);
result = (fmpz_poly_equal(a, b));
if (!result)
{
printf("FAIL:\n");
printf("n = %lu\n\n", n);
printf("a = "), fmpz_poly_print(a), printf("\n\n");
printf("b = "), fmpz_poly_print(b), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
}
for (i = 0; i < 10000; i++)
{
fmpz_poly_t a, b;
ulong m, n;
fmpz_poly_init(a);
fmpz_poly_init(b);
m = n_randtest(state);
n = n_randtest(state);
while (m == n)
n = n_randtest(state);
fmpz_poly_set_ui(a, m);
fmpz_poly_set_ui(b, n);
result = (!fmpz_poly_equal(a, b));
if (!result)
{
printf("FAIL:\n");
printf("m = %lu\n\n", m);
printf("n = %lu\n\n", n);
printf("a = "), fmpz_poly_print(a), printf("\n\n");
printf("b = "), fmpz_poly_print(b), printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
}
flint_randclear(state);
_fmpz_cleanup();
printf("PASS\n");
return 0;
}
int
fmpz_poly_mat_inv(fmpz_poly_mat_t Ainv, fmpz_poly_t den,
const fmpz_poly_mat_t A)
{
long n = fmpz_poly_mat_nrows(A);
if (n == 0)
{
fmpz_poly_one(den);
return 1;
}
else if (n == 1)
{
fmpz_poly_set(den, E(A, 0, 0));
fmpz_poly_one(E(Ainv, 0, 0));
return !fmpz_poly_is_zero(den);
}
else if (n == 2)
{
fmpz_poly_mat_det(den, A);
if (fmpz_poly_is_zero(den))
{
return 0;
}
else if (Ainv == A)
{
fmpz_poly_swap(E(A, 0, 0), E(A, 1, 1));
fmpz_poly_neg(E(A, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(A, 1, 0), E(A, 1, 0));
return 1;
}
else
{
fmpz_poly_set(E(Ainv, 0, 0), E(A, 1, 1));
fmpz_poly_set(E(Ainv, 1, 1), E(A, 0, 0));
fmpz_poly_neg(E(Ainv, 0, 1), E(A, 0, 1));
fmpz_poly_neg(E(Ainv, 1, 0), E(A, 1, 0));
return 1;
}
}
else
{
fmpz_poly_mat_t LU, I;
long * perm;
int result;
perm = _perm_init(n);
fmpz_poly_mat_init_set(LU, A);
result = (fmpz_poly_mat_fflu(LU, den, perm, LU, 1) == n);
if (result)
{
fmpz_poly_mat_init(I, n, n);
fmpz_poly_mat_one(I);
fmpz_poly_mat_solve_fflu_precomp(Ainv, perm, LU, I);
fmpz_poly_mat_clear(I);
}
else
fmpz_poly_zero(den);
if (_perm_parity(perm, n))
{
fmpz_poly_mat_neg(Ainv, Ainv);
fmpz_poly_neg(den, den);
}
_perm_clear(perm);
fmpz_poly_mat_clear(LU);
return result;
}
}
int main(int argc, char *argv[])
{
int ans;
char *str, *strout;
fmpz_poly_t zpoly;
fmpz_poly_q_t qpoly1;
mpz_t mpzzero, mpzone, mpztwo;
mpq_t mpqzero, mpqone, mpqtwo, mpqtwoinv;
FLINT_TEST_INIT(state);
flint_printf("all... ");
fflush(stdout);
/* Accessing numerator and denominator ***********************************/
fmpz_poly_q_init(qpoly1);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
str = "2 -1 1";
strout = fmpz_poly_get_str(fmpz_poly_q_numref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_numref: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
flint_printf(" qpoly1 = \""), fmpz_poly_q_print(qpoly1), flint_printf("\"\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
str = "2 0 1";
strout = fmpz_poly_get_str(fmpz_poly_q_denref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_denref: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
fmpz_poly_set(zpoly, fmpz_poly_q_numref(qpoly1));
str = "2 -1 1";
strout = fmpz_poly_get_str(zpoly);
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_get_num: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "2 -1 1/2 0 1");
fmpz_poly_set(zpoly, fmpz_poly_q_denref(qpoly1));
str = "2 0 1";
strout = fmpz_poly_get_str(zpoly);
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_get_den: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "1 1/1 1");
fmpz_poly_set_str(zpoly, "2 0 1");
fmpz_poly_set(fmpz_poly_q_numref(qpoly1), zpoly);
str = "2 0 1";
strout = fmpz_poly_get_str(fmpz_poly_q_numref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_set_num: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
fmpz_poly_init(zpoly);
fmpz_poly_q_set_str(qpoly1, "1 1/1 1");
fmpz_poly_set_str(zpoly, "2 0 1");
fmpz_poly_set(fmpz_poly_q_denref(qpoly1), zpoly);
str = "2 0 1";
strout = fmpz_poly_get_str(fmpz_poly_q_denref(qpoly1));
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_set_den: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_clear(zpoly);
flint_free(strout);
/* Canonicalise **********************************************************/
fmpz_poly_q_init(qpoly1);
str = "2 -1 1/2 0 1";
fmpz_poly_q_set_str(qpoly1, str);
strout = fmpz_poly_q_get_str(qpoly1);
ans = !strcmp(str, strout);
if (!ans)
{
flint_printf("test_canonicalize: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
fmpz_poly_q_clear(qpoly1);
flint_free(strout);
fmpz_poly_q_init(qpoly1);
str = "2 -1 -1/2 0 1";
fmpz_poly_q_set_str(qpoly1, "2 1 1/2 0 -1");
strout = fmpz_poly_q_get_str(qpoly1);
ans = !strcmp("2 -1 -1/2 0 1", strout);
if (!ans)
{
flint_printf("test_canonicalize: failed\n");
flint_printf(" Expected \"%s\", got \"%s\"\n", str, strout);
abort();
}
flint_free(strout);
fmpz_poly_q_clear(qpoly1);
/* Initialization, memory management and basic operations ****************/
test_set("0", "0");
test_set("0/1 1", "0");
test_set("3 -1 0 1/2 0 1", "3 -1 0 1/2 0 1");
test_set("3 -1 0 1/2 1 1", "2 -1 1");
test_set_si(-1, "1 -1");
test_set_si(13, "1 13");
test_set_si(0, "0");
test_swap("3 -1 0 1/2 0 1", "1 2/1 3", "1 2/1 3", "3 -1 0 1/2 0 1");
test_zero("0", "0");
test_zero("0/1 1", "0");
test_zero("3 -1 0 1/2 0 1", "0");
test_neg("0", "0");
test_neg("1 1/1 2", "1 -1/1 2");
test_neg("3 -1 0 1/2 0 1", "3 1 0 -1/2 0 1");
test_inv("1 1/1 2", "1 2");
test_inv("3 -1 0 1/2 0 1", "2 0 1/3 -1 0 1");
test_inv("3 -1 0 -1/2 0 1", "2 0 -1/3 1 0 1");
test_inv_inplace("1 1/1 2", "1 2");
test_inv_inplace("3 -1 0 1/2 0 1", "2 0 1/3 -1 0 1");
test_inv_inplace("3 -1 0 -1/2 0 1", "2 0 -1/3 1 0 1");
test_is_zero("0", 1);
test_is_zero("0/1 1", 1);
test_is_zero("3 -1 0 1/2 0 1", 0);
test_is_zero("3 -1 0 1/2 1 1", 0);
test_is_one("0", 0);
test_is_one("0/1 1", 0);
test_is_one("1 1/1 1", 1);
test_is_one("2 1 1/2 1 1", 1);
test_is_one("3 -1 0 1/2 0 1", 0);
test_equal("1 1/1 2", "1 1/1 2", 1);
test_equal("1 1/1 2", "1 1/1 2", 1);
test_equal("3 -1 0 1/2 1 1", "2 -1 1", 1);
test_equal("3 -1 0 1/2 -1 1", "2 -1 1", 0);
/* Addition and subtraction **********************************************/
test_add("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 1 0 1/4 0 1 0 1");
test_add("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 3 -2 1/2 -1 1");
test_add("0/2 1 1", "1 2/1 1", "1 2");
test_add("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_add("2 1 1/1 1", "2 -1 1/1 1", "2 0 2");
test_add("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 -1 2 2/3 0 -1 1");
test_add("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 7 12 7 1/3 2 3 1");
test_add("2 1 1/2 -1 1", "2 1 1", "3 0 1 1/2 -1 1");
test_add("1 1/2 1 1", "2 0 1/2 1 1", "1 1");
test_add("2 1 1/3 4 -4 1", "1 1/2 -2 1", "2 -1 2/3 4 -4 1");
test_add("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "0");
test_add("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2");
test_add("1 1/3 3 5 2", "1 1/3 6 7 2", "1 1/3 2 3 1");
test_add_in_place1("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 1 0 1/4 0 1 0 1");
test_add_in_place1("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 3 -2 1/2 -1 1");
test_add_in_place1("0/2 1 1", "1 2/1 1", "1 2");
test_add_in_place1("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_add_in_place1("2 1 1/1 1", "2 -1 1/1 1", "2 0 2");
test_add_in_place1("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 -1 2 2/3 0 -1 1");
test_add_in_place1("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 7 12 7 1/3 2 3 1");
test_add_in_place1("2 1 1/2 -1 1", "2 1 1", "3 0 1 1/2 -1 1");
test_add_in_place1("1 1/2 1 1", "2 0 1/2 1 1", "1 1");
test_add_in_place1("2 1 1/3 4 -4 1", "1 1/2 -2 1", "2 -1 2/3 4 -4 1");
test_add_in_place1("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "0");
test_add_in_place1("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2");
test_add_in_place2("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 1 0 1/4 0 1 0 1");
test_add_in_place2("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 3 -2 1/2 -1 1");
test_add_in_place2("0/2 1 1", "1 2/1 1", "1 2");
test_add_in_place2("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_add_in_place2("2 1 1/1 1", "2 -1 1/1 1", "2 0 2");
test_add_in_place2("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 -1 2 2/3 0 -1 1");
test_add_in_place2("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 7 12 7 1/3 2 3 1");
test_add_in_place2("2 1 1/2 -1 1", "2 1 1", "3 0 1 1/2 -1 1");
test_add_in_place2("1 1/2 1 1", "2 0 1/2 1 1", "1 1");
test_add_in_place2("2 1 1/3 4 -4 1", "1 1/2 -2 1", "2 -1 2/3 4 -4 1");
test_add_in_place2("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "0");
test_add_in_place2("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2");
test_add_in_place3("2 1 1", "2 2 2");
test_add_in_place3("2 1 1/1 2", "2 1 1");
test_sub("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub("0/2 1 1", "1 2/1 1", "1 -2");
test_sub("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub("2 -1 1/2 0 1", "1 1", "1 -1/2 0 1");
test_sub("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub("0/2 1 1", "1 2/1 1", "1 -2");
test_sub("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub("2 1 1/2 -1 1", "2 1 1", "3 2 1 -1/2 -1 1");
test_sub("1 1/2 1 1", "2 0 1/2 1 1", "2 1 -1/2 1 1");
test_sub("2 1 1/3 4 -4 1", "1 1/2 -2 1", "1 3/3 4 -4 1");
test_sub("3 0 1 1/3 1 2 1", "2 0 -1/2 1 1", "2 0 2/2 1 1");
test_sub("2 1 1/2 0 1", "2 -1 1/2 0 1", "1 2/2 0 1");
test_sub("1 1/3 3 5 2", "1 1/3 6 7 2", "1 1/4 6 13 9 2");
test_sub("2 1 1/2 0 2", "2 1 1/2 0 2", "0");
test_sub("2 -1 2/2 0 1", "2 -1 1/2 0 1", "1 1");
test_sub_in_place1("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub_in_place1("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub_in_place1("0/2 1 1", "1 2/1 1", "1 -2");
test_sub_in_place1("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub_in_place1("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub_in_place1("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub_in_place1("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub_in_place2("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "5 1 0 3 0 1/4 0 1 0 1");
test_sub_in_place2("3 -1 0 1/2 1 1", "1 2/2 -1 1", "3 -1 -2 1/2 -1 1");
test_sub_in_place2("0/2 1 1", "1 2/1 1", "1 -2");
test_sub_in_place2("1 -3/1 4", "0/3 1 0 1", "1 -3/1 4");
test_sub_in_place2("2 1 1/1 1", "2 -1 1/1 1", "1 2");
test_sub_in_place2("2 1 1/2 0 1", "2 2 1/2 -1 1", "2 -1 -2/3 0 -1 1");
test_sub_in_place2("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "4 -9 -12 -5 -1/3 2 3 1");
test_sub_in_place3("2 -1 1/2 2 1", "0");
test_addmul("1 1/2 0 2", "2 3 1/1 4", "3 1 0 1/4 -2 0 0 1", "5 -4 3 1 5 1/5 0 -8 0 0 4");
test_submul("1 1/2 0 2", "2 3 1/1 4", "3 1 0 1/4 -2 0 0 1", "5 -4 -3 -1 -1 -1/5 0 -8 0 0 4");
/* Scalar multiplication and devision ************************************/
flint_mpz_init_set_si(mpzzero, 0);
flint_mpz_init_set_si(mpzone, 1);
flint_mpz_init_set_si(mpztwo, 2);
mpq_init(mpqzero); flint_mpq_set_si(mpqzero, 0, 1);
mpq_init(mpqone); flint_mpq_set_si(mpqone, 1, 1);
mpq_init(mpqtwo); flint_mpq_set_si(mpqtwo, 2, 1);
mpq_init(mpqtwoinv); flint_mpq_set_si(mpqtwoinv, 1, 2);
test_scalar_mul_si("0", 1, "0");
test_scalar_mul_si("0", 0, "0");
test_scalar_mul_si("1 2", 0, "0");
test_scalar_mul_si("1 1/1 2", -2, "1 -1");
test_scalar_mul_si("2 1 1/2 -2 3", 5, "2 5 5/2 -2 3");
test_scalar_mul_si("2 1 1/2 -2 2", 3, "2 3 3/2 -2 2");
test_scalar_mul_mpz("0", mpzone, "0");
test_scalar_mul_mpz("0", mpzzero, "0");
test_scalar_mul_mpz("1 2", mpzzero, "0");
test_scalar_mul_mpz("1 1/1 2", mpztwo, "1 1");
test_scalar_mul_mpq("0", mpqone, "0");
test_scalar_mul_mpq("0", mpqzero, "0");
test_scalar_mul_mpq("1 2", mpqzero, "0");
test_scalar_mul_mpq("1 1/1 2", mpqtwo, "1 1");
test_scalar_mul_mpq("1 -2/1 1", mpqtwoinv, "1 -1");
test_scalar_div_si("0", 1, "0");
test_scalar_div_si("1 2", 2, "1 1");
test_scalar_div_si("1 1/1 2", -2, "1 -1/1 4");
test_scalar_div_si("3 -5 0 3/2 1 1", 2, "3 -5 0 3/2 2 2");
test_scalar_div_si("3 2 8 4/2 0 1", 3, "3 2 8 4/2 0 3");
test_scalar_div_si("3 2 8 4/2 0 1", -3, "3 -2 -8 -4/2 0 3");
test_scalar_div_si("3 -27 0 9/2 0 1", -3, "3 9 0 -3/2 0 1");
test_scalar_div_mpz("0", mpzone, "0");
test_scalar_div_mpz("1 2", mpztwo, "1 1");
test_scalar_div_mpz("1 1/1 2", mpztwo, "1 1/1 4");
test_scalar_div_mpq("0", mpqone, "0");
test_scalar_div_mpq("1 2", mpqone, "1 2");
test_scalar_div_mpq("1 1/1 2", mpqtwo, "1 1/1 4");
test_scalar_div_mpq("1 -2/1 1", mpqtwoinv, "1 -4");
mpz_clear(mpzzero);
mpz_clear(mpzone);
mpz_clear(mpztwo);
mpq_clear(mpqzero);
mpq_clear(mpqone);
mpq_clear(mpqtwo);
mpq_clear(mpqtwoinv);
/* Multiplication, division and powing *********************************/
test_mul("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "1 -1");
test_mul("3 -1 0 1/2 1 1", "1 2/2 -1 1", "1 2");
test_mul("0/2 1 1", "1 2/1 1", "0");
test_mul("1 -3/1 4", "0/3 1 0 1", "0");
test_mul("2 1 1/1 1", "2 -1 1/1 1", "3 -1 0 1");
test_mul("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 2 3 1/3 0 -1 1");
test_mul("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "3 -2 1 1/2 1 1");
test_mul_in_place1("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "1 -1");
test_mul_in_place1("3 -1 0 1/2 1 1", "1 2/2 -1 1", "1 2");
test_mul_in_place1("0/2 1 1", "1 2/1 1", "0");
test_mul_in_place1("1 -3/1 4", "0/3 1 0 1", "0");
test_mul_in_place1("2 1 1/1 1", "2 -1 1/1 1", "3 -1 0 1");
test_mul_in_place1("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 2 3 1/3 0 -1 1");
test_mul_in_place1("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "3 -2 1 1/2 1 1");
test_mul_in_place2("3 1 0 1/2 0 1", "2 0 -1/3 1 0 1", "1 -1");
test_mul_in_place2("3 -1 0 1/2 1 1", "1 2/2 -1 1", "1 2");
test_mul_in_place2("0/2 1 1", "1 2/1 1", "0");
test_mul_in_place2("1 -3/1 4", "0/3 1 0 1", "0");
test_mul_in_place2("2 1 1/1 1", "2 -1 1/1 1", "3 -1 0 1");
test_mul_in_place2("2 1 1/2 0 1", "2 2 1/2 -1 1", "3 2 3 1/3 0 -1 1");
test_mul_in_place2("2 -1 1/2 2 1", "3 4 4 1/2 1 1", "3 -2 1 1/2 1 1");
test_mul_in_place3("2 0 1/2 1 1", "3 0 0 1/3 1 2 1");
test_div("3 -1 0 1/1 2", "2 1 1/1 1", "2 -1 1/1 2");
test_div("0/2 1 1", "2 1 1/1 1", "0");
test_div("3 -1 0 1/1 4", "2 -1 -1/1 2", "2 1 -1/1 2");
test_div("2 1 1", "2 1 -1/2 1 -1", "2 1 1");
test_div("2 1 1/3 4 4 1", "2 -1 1/3 6 5 1", "3 3 4 1/3 -2 1 1");
test_div_in_place1("3 -1 0 1/1 2", "2 1 1/1 1", "2 -1 1/1 2");
test_div_in_place1("0/2 1 1", "2 1 1/1 1", "0");
test_div_in_place1("3 -1 0 1/1 4", "2 -1 -1/1 2", "2 1 -1/1 2");
test_div_in_place1("2 1 1", "2 1 -1/2 1 -1", "2 1 1");
test_div_in_place1("2 1 1/3 4 4 1", "2 -1 1/3 6 5 1", "3 3 4 1/3 -2 1 1");
test_div_in_place1("0", "1 2/2 3 5", "0");
test_div_in_place2("3 -1 0 1/1 2", "2 1 1/1 1", "2 -1 1/1 2");
test_div_in_place2("0/2 1 1", "2 1 1/1 1", "0");
test_div_in_place2("3 -1 0 1/1 4", "2 -1 -1/1 2", "2 1 -1/1 2");
test_div_in_place2("2 1 1", "2 1 -1/2 1 -1", "2 1 1");
test_div_in_place2("2 1 1/3 4 4 1", "2 -1 1/3 6 5 1", "3 3 4 1/3 -2 1 1");
test_div_in_place3("3 -1 0 1/1 2", "1 1");
test_pow("2 0 -1/1 2", 3, "4 0 0 0 -1/1 8");
test_pow("0", 0, "1 1");
test_pow("2 1 -1", 0, "1 1");
test_pow("2 1 1/2 0 1", 0, "1 1");
/* Derivative ************************************************************/
test_derivative("0", "0");
test_derivative("1 2", "0");
test_derivative("1 -1/1 2", "0");
test_derivative("2 0 1", "1 1");
test_derivative("3 1 0 1", "2 0 2");
test_derivative("1 1/2 0 1", "1 -1/3 0 0 1");
test_derivative("2 2 1/2 -1 1", "1 -3/3 1 -2 1");
test_derivative("2 0 1/3 1 2 1", "2 1 -1/4 1 3 3 1");
/* Bug which allowed constant factors */
test_derivative("3 5 1 -2/2 10 2", "3 0 -10 -1/3 25 10 1");
/* Evaluation ************************************************************/
test_evaluate("1 1/1 2", -2, 3, "1/2");
test_evaluate("3 1 0 1/2 0 1", -1, 2, "-5/2");
test_evaluate("2 3 1/2 -1 1", 1, 1, "P");
test_evaluate("2 3 1/2 -1 1", 2, 3, "-11");
test_evaluate("2 3 1/2 -1 2", 1, 2, "P");
test_evaluate("2 1 1/2 -1 1", 2, 1, "3");
/* String methods ********************************************************/
fmpz_poly_q_init(qpoly1);
ans = fmpz_poly_q_set_str(qpoly1, "1 3/xyz");
if ((ans == 0) || !fmpz_poly_q_is_zero(qpoly1))
{
flint_printf("test_set_str: failed\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_q_init(qpoly1);
ans = fmpz_poly_q_set_str(qpoly1, "abc/1 3");
if ((ans == 0) || !fmpz_poly_q_is_zero(qpoly1))
{
flint_printf("test_set_str: failed\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
fmpz_poly_q_init(qpoly1);
ans = fmpz_poly_q_set_str(qpoly1, "abc/xyz");
if ((ans == 0) || !fmpz_poly_q_is_zero(qpoly1))
{
flint_printf("test_set_str: failed\n");
abort();
}
fmpz_poly_q_clear(qpoly1);
test_get_str_pretty("1 -3", "-3");
test_get_str_pretty("3 1 2 1", "t^2+2*t+1");
test_get_str_pretty("1 -2/2 1 1", "-2/(t+1)");
test_get_str_pretty("2 1 1/2 -1 1", "(t+1)/(t-1)");
test_get_str_pretty("2 1 1/1 2", "(t+1)/2");
test_get_str_pretty("1 1/1 2", "1/2");
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return EXIT_SUCCESS;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("sqr_karatsuba....");
fflush(stdout);
/* Check aliasing of a and b */
for (i = 0; i < 200 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, c;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_randtest(a, state, n_randint(state, 50), 200);
fmpz_poly_set(b, a);
fmpz_poly_sqr_karatsuba(c, b);
fmpz_poly_sqr_karatsuba(b, b);
result = (fmpz_poly_equal(b, c));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(a), flint_printf("\n\n");
fmpz_poly_print(b), flint_printf("\n\n");
fmpz_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
/* Compare with mul_karatsuba */
for (i = 0; i < 200 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, c;
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_poly_randtest(a, state, n_randint(state, 50), 200);
fmpz_poly_sqr_karatsuba(b, a);
fmpz_poly_mul_karatsuba(c, a, a);
result = (fmpz_poly_equal(b, c));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(a), flint_printf("\n\n");
fmpz_poly_print(b), flint_printf("\n\n");
fmpz_poly_print(c), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
/* Check _fmpz_poly_sqr_karatsuba directly */
for (i = 0; i < 200 * flint_test_multiplier(); i++)
{
slong len;
fmpz_poly_t a, out1, out2;
len = n_randint(state, 100) + 1;
fmpz_poly_init(a);
fmpz_poly_init(out1);
fmpz_poly_init(out2);
fmpz_poly_randtest(a, state, len, 200);
fmpz_poly_sqr_karatsuba(out1, a);
fmpz_poly_fit_length(a, a->alloc + n_randint(state, 10));
a->length = a->alloc;
fmpz_poly_fit_length(out2, 2 * a->length - 1);
_fmpz_poly_sqr_karatsuba(out2->coeffs, a->coeffs, a->length);
_fmpz_poly_set_length(out2, 2 * a->length - 1);
_fmpz_poly_normalise(out2);
result = (fmpz_poly_equal(out1, out2));
if (!result)
{
flint_printf("FAIL:\n");
fmpz_poly_print(out1), flint_printf("\n\n");
fmpz_poly_print(out2), flint_printf("\n\n");
abort();
}
fmpz_poly_clear(a);
fmpz_poly_clear(out1);
fmpz_poly_clear(out2);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
int
fmpz_poly_gcd_heuristic(fmpz_poly_t res,
const fmpz_poly_t poly1, const fmpz_poly_t poly2)
{
const long len1 = poly1->length;
const long len2 = poly2->length;
long rlen;
int done = 0;
if (len1 == 0)
{
if (len2 == 0)
fmpz_poly_zero(res);
else
{
if (fmpz_sgn(poly2->coeffs + (len2 - 1)) > 0)
fmpz_poly_set(res, poly2);
else
fmpz_poly_neg(res, poly2);
}
return 1;
}
else
{
if (len2 == 0)
{
if (fmpz_sgn(poly1->coeffs + (len1 - 1)) > 0)
fmpz_poly_set(res, poly1);
else
fmpz_poly_neg(res, poly1);
return 1;
}
}
rlen = FLINT_MIN(len1, len2);
if (res == poly1 || res == poly2)
{
fmpz_poly_t temp;
fmpz_poly_init2(temp, rlen);
if (len1 >= len2)
done = _fmpz_poly_gcd_heuristic(temp->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2);
else
done = _fmpz_poly_gcd_heuristic(temp->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1);
fmpz_poly_swap(temp, res);
fmpz_poly_clear(temp);
}
else
{
fmpz_poly_fit_length(res, rlen);
if (len1 >= len2)
done = _fmpz_poly_gcd_heuristic(res->coeffs, poly1->coeffs, len1,
poly2->coeffs, len2);
else
done = _fmpz_poly_gcd_heuristic(res->coeffs, poly2->coeffs, len2,
poly1->coeffs, len1);
}
if (done)
{
_fmpz_poly_set_length(res, rlen);
_fmpz_poly_normalise(res);
}
return done;
}
int
main(void)
{
int i, result;
FLINT_TEST_INIT(state);
flint_printf("scalar_addmul_fmpz....");
fflush(stdout);
/* Check aliasing of a and b */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, c;
fmpz_t x;
fmpz_init(x);
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_randtest(x, state, n_randint(state, 100));
fmpz_poly_randtest(a, state, n_randint(state, 100), 200);
fmpz_poly_set(b, a);
fmpz_poly_set(c, a);
fmpz_poly_scalar_addmul_fmpz(b, a, x);
fmpz_poly_scalar_addmul_fmpz(a, a, x);
result = (fmpz_poly_equal(a, b));
if (!result)
{
flint_printf("FAIL (1):\n");
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
flint_printf("c = "), fmpz_poly_print(c), flint_printf("\n\n");
flint_printf("x = "), fmpz_print(x), flint_printf("\n\n");
abort();
}
fmpz_clear(x);
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
/* Check that b += x*a is the same as c = b + x*a */
for (i = 0; i < 1000 * flint_test_multiplier(); i++)
{
fmpz_poly_t a, b, c;
fmpz_t x;
fmpz_init(x);
fmpz_poly_init(a);
fmpz_poly_init(b);
fmpz_poly_init(c);
fmpz_randtest(x, state, n_randint(state, 100));
fmpz_poly_randtest(a, state, n_randint(state, 100), 200);
fmpz_poly_randtest(b, state, n_randint(state, 100), 200);
fmpz_poly_scalar_mul_fmpz(c, a, x);
fmpz_poly_add(c, b, c);
fmpz_poly_scalar_addmul_fmpz(b, a, x);
result = (fmpz_poly_equal(b, c));
if (!result)
{
flint_printf("FAIL (2):\n");
flint_printf("a = "), fmpz_poly_print(a), flint_printf("\n\n");
flint_printf("b = "), fmpz_poly_print(b), flint_printf("\n\n");
flint_printf("c = "), fmpz_poly_print(c), flint_printf("\n\n");
flint_printf("x = "), fmpz_print(x), flint_printf("\n\n");
abort();
}
fmpz_clear(x);
fmpz_poly_clear(a);
fmpz_poly_clear(b);
fmpz_poly_clear(c);
}
FLINT_TEST_CLEANUP(state);
flint_printf("PASS\n");
return 0;
}
void frob(const mpoly_t P, const ctx_t ctxFracQt,
const qadic_t t1, const qadic_ctx_t Qq,
prec_t *prec, const prec_t *prec_in,
int verbose)
{
const padic_ctx_struct *Qp = &Qq->pctx;
const fmpz *p = Qp->p;
const long a = qadic_ctx_degree(Qq);
const long n = P->n - 1;
const long d = mpoly_degree(P, -1, ctxFracQt);
const long b = gmc_basis_size(n, d);
long i, j, k;
/* Diagonal fibre */
padic_mat_t F0;
/* Gauss--Manin Connection */
mat_t M;
mon_t *bR, *bC;
fmpz_poly_t r;
/* Local solution */
fmpz_poly_mat_t C, Cinv;
long vC, vCinv;
/* Frobenius */
fmpz_poly_mat_t F;
long vF;
fmpz_poly_mat_t F1;
long vF1;
fmpz_poly_t cp;
clock_t c0, c1;
double c;
if (verbose)
{
printf("Input:\n");
printf(" P = "), mpoly_print(P, ctxFracQt), printf("\n");
printf(" p = "), fmpz_print(p), printf("\n");
printf(" t1 = "), qadic_print_pretty(t1, Qq), printf("\n");
printf("\n");
fflush(stdout);
}
/* Step 1 {M, r} *********************************************************/
c0 = clock();
mat_init(M, b, b, ctxFracQt);
fmpz_poly_init(r);
gmc_compute(M, &bR, &bC, P, ctxFracQt);
{
fmpz_poly_t t;
fmpz_poly_init(t);
fmpz_poly_set_ui(r, 1);
for (i = 0; i < M->m; i++)
for (j = 0; j < M->n; j++)
{
fmpz_poly_lcm(t, r, fmpz_poly_q_denref(
(fmpz_poly_q_struct *) mat_entry(M, i, j, ctxFracQt)));
fmpz_poly_swap(r, t);
}
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Gauss-Manin connection:\n");
printf(" r(t) = "), fmpz_poly_print_pretty(r, "t"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
{
qadic_t t;
qadic_init2(t, 1);
fmpz_poly_evaluate_qadic(t, r, t1, Qq);
if (qadic_is_zero(t))
{
printf("Exception (deformation_frob).\n");
printf("The resultant r evaluates to zero (mod p) at t1.\n");
abort();
}
qadic_clear(t);
}
/* Precisions ************************************************************/
if (prec_in != NULL)
{
*prec = *prec_in;
}
else
{
deformation_precisions(prec, p, a, n, d, fmpz_poly_degree(r));
}
if (verbose)
{
printf("Precisions:\n");
printf(" N0 = %ld\n", prec->N0);
printf(" N1 = %ld\n", prec->N1);
printf(" N2 = %ld\n", prec->N2);
printf(" N3 = %ld\n", prec->N3);
printf(" N3i = %ld\n", prec->N3i);
printf(" N3w = %ld\n", prec->N3w);
printf(" N3iw = %ld\n", prec->N3iw);
printf(" N4 = %ld\n", prec->N4);
printf(" m = %ld\n", prec->m);
printf(" K = %ld\n", prec->K);
printf(" r = %ld\n", prec->r);
printf(" s = %ld\n", prec->s);
printf("\n");
fflush(stdout);
}
/* Initialisation ********************************************************/
padic_mat_init2(F0, b, b, prec->N4);
fmpz_poly_mat_init(C, b, b);
fmpz_poly_mat_init(Cinv, b, b);
fmpz_poly_mat_init(F, b, b);
vF = 0;
fmpz_poly_mat_init(F1, b, b);
vF1 = 0;
fmpz_poly_init(cp);
/* Step 2 {F0} ***********************************************************/
{
padic_ctx_t pctx_F0;
fmpz *t;
padic_ctx_init(pctx_F0, p, FLINT_MIN(prec->N4 - 10, 0), prec->N4, PADIC_VAL_UNIT);
t = _fmpz_vec_init(n + 1);
c0 = clock();
mpoly_diagonal_fibre(t, P, ctxFracQt);
diagfrob(F0, t, n, d, prec->N4, pctx_F0, 0);
padic_mat_transpose(F0, F0);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Diagonal fibre:\n");
printf(" P(0) = {"), _fmpz_vec_print(t, n + 1), printf("}\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
_fmpz_vec_clear(t, n + 1);
padic_ctx_clear(pctx_F0);
}
/* Step 3 {C, Cinv} ******************************************************/
/*
Compute C as a matrix over Z_p[[t]]. A is the same but as a series
of matrices over Z_p. Mt is the matrix -M^t, and Cinv is C^{-1}^t,
the local solution of the differential equation replacing M by Mt.
*/
c0 = clock();
{
const long K = prec->K;
padic_mat_struct *A;
gmde_solve(&A, K, p, prec->N3, prec->N3w, M, ctxFracQt);
gmde_convert_soln(C, &vC, A, K, p);
for(i = 0; i < K; i++)
padic_mat_clear(A + i);
free(A);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Local solution:\n");
printf(" Time for C = %f\n", c);
fflush(stdout);
}
c0 = clock();
{
const long K = (prec->K + (*p) - 1) / (*p);
mat_t Mt;
padic_mat_struct *Ainv;
mat_init(Mt, b, b, ctxFracQt);
mat_transpose(Mt, M, ctxFracQt);
mat_neg(Mt, Mt, ctxFracQt);
gmde_solve(&Ainv, K, p, prec->N3i, prec->N3iw, Mt, ctxFracQt);
gmde_convert_soln(Cinv, &vCinv, Ainv, K, p);
fmpz_poly_mat_transpose(Cinv, Cinv);
fmpz_poly_mat_compose_pow(Cinv, Cinv, *p);
for(i = 0; i < K; i++)
padic_mat_clear(Ainv + i);
free(Ainv);
mat_clear(Mt, ctxFracQt);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf(" Time for C^{-1} = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 4 {F(t) := C(t) F(0) C(t^p)^{-1}} ********************************/
/*
Computes the product C(t) F(0) C(t^p)^{-1} modulo (p^{N_2}, t^K).
This is done by first computing the unit part of the product
exactly over the integers modulo t^K.
*/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
for (i = 0; i < b; i++)
{
/* Find the unique k s.t. F0(i,k) is non-zero */
for (k = 0; k < b; k++)
if (!fmpz_is_zero(padic_mat_entry(F0, i, k)))
break;
if (k == b)
{
printf("Exception (frob). F0 is singular.\n\n");
abort();
}
for (j = 0; j < b; j++)
{
fmpz_poly_scalar_mul_fmpz(fmpz_poly_mat_entry(T, i, j),
fmpz_poly_mat_entry(Cinv, k, j),
padic_mat_entry(F0, i, k));
}
}
fmpz_poly_mat_mul(F, C, T);
fmpz_poly_mat_truncate(F, prec->K);
vF = vC + padic_mat_val(F0) + vCinv;
/* Canonicalise (F, vF) */
{
long v = fmpz_poly_mat_ord_p(F, p);
if (v == LONG_MAX)
{
printf("ERROR (deformation_frob). F(t) == 0.\n");
abort();
}
else if (v > 0)
{
fmpz_pow_ui(pN, p, v);
fmpz_poly_mat_scalar_divexact_fmpz(F, F, pN);
vF = vF + v;
}
}
/* Reduce (F, vF) modulo p^{N2} */
fmpz_pow_ui(pN, p, prec->N2 - vF);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Matrix for F(t):\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 5 {G = r(t)^m F(t)} **********************************************/
c0 = clock();
{
fmpz_t pN;
fmpz_poly_t t;
fmpz_init(pN);
fmpz_poly_init(t);
fmpz_pow_ui(pN, p, prec->N2 - vF);
/* Compute r(t)^m mod p^{N2-vF} */
if (prec->denR == NULL)
{
fmpz_mod_poly_t _t;
fmpz_mod_poly_init(_t, pN);
fmpz_mod_poly_set_fmpz_poly(_t, r);
fmpz_mod_poly_pow(_t, _t, prec->m);
fmpz_mod_poly_get_fmpz_poly(t, _t);
fmpz_mod_poly_clear(_t);
}
else
{
/* TODO: We don't really need a copy */
fmpz_poly_set(t, prec->denR);
}
fmpz_poly_mat_scalar_mul_fmpz_poly(F, F, t);
fmpz_poly_mat_scalar_mod_fmpz(F, F, pN);
/* TODO: This should not be necessary? */
fmpz_poly_mat_truncate(F, prec->K);
fmpz_clear(pN);
fmpz_poly_clear(t);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Analytic continuation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Steps 6 and 7 *********************************************************/
if (a == 1)
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t f, g, t, pN;
fmpz_init(f);
fmpz_init(g);
fmpz_init(t);
fmpz_init(pN);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_padic_teichmuller(f, t1->coeffs + 0, p, N);
if (prec->denR == NULL)
{
_fmpz_mod_poly_evaluate_fmpz(g, r->coeffs, r->length, f, pN);
fmpz_powm_ui(t, g, prec->m, pN);
}
else
{
_fmpz_mod_poly_evaluate_fmpz(t, prec->denR->coeffs, prec->denR->length, f, pN);
}
_padic_inv(g, t, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
if (len == 0)
{
fmpz_poly_zero(fmpz_poly_mat_entry(F1, i, j));
}
else
{
fmpz_poly_fit_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_mod_poly_evaluate_fmpz(t, poly->coeffs, len, f, pN);
fmpz_mul(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, g, t);
fmpz_mod(fmpz_poly_mat_entry(F1, i, j)->coeffs + 0,
fmpz_poly_mat_entry(F1, i, j)->coeffs + 0, pN);
_fmpz_poly_set_length(fmpz_poly_mat_entry(F1, i, j), 1);
_fmpz_poly_normalise(fmpz_poly_mat_entry(F1, i, j));
}
}
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(f);
fmpz_clear(g);
fmpz_clear(t);
fmpz_clear(pN);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
else
{
/* Step 6 {F(1) = r(t_1)^{-m} G(t_1)} ********************************/
c0 = clock();
{
const long N = prec->N2 - vF;
fmpz_t pN;
fmpz *f, *g, *t;
fmpz_init(pN);
f = _fmpz_vec_init(a);
g = _fmpz_vec_init(2 * a - 1);
t = _fmpz_vec_init(2 * a - 1);
fmpz_pow_ui(pN, p, N);
/* f := \hat{t_1}, g := r(\hat{t_1})^{-m} */
_qadic_teichmuller(f, t1->coeffs, t1->length, Qq->a, Qq->j, Qq->len, p, N);
if (prec->denR == NULL)
{
fmpz_t e;
fmpz_init_set_ui(e, prec->m);
_fmpz_mod_poly_compose_smod(g, r->coeffs, r->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
_qadic_pow(t, g, a, e, Qq->a, Qq->j, Qq->len, pN);
fmpz_clear(e);
}
else
{
_fmpz_mod_poly_reduce(prec->denR->coeffs, prec->denR->length, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_normalise(prec->denR);
_fmpz_mod_poly_compose_smod(t, prec->denR->coeffs, prec->denR->length, f, a,
Qq->a, Qq->j, Qq->len, pN);
}
_qadic_inv(g, t, a, Qq->a, Qq->j, Qq->len, p, N);
/* F1 := g G(\hat{t_1}) */
for (i = 0; i < b; i++)
for (j = 0; j < b; j++)
{
const fmpz_poly_struct *poly = fmpz_poly_mat_entry(F, i, j);
const long len = poly->length;
fmpz_poly_struct *poly2 = fmpz_poly_mat_entry(F1, i, j);
if (len == 0)
{
fmpz_poly_zero(poly2);
}
else
{
_fmpz_mod_poly_compose_smod(t, poly->coeffs, len, f, a,
Qq->a, Qq->j, Qq->len, pN);
fmpz_poly_fit_length(poly2, 2 * a - 1);
_fmpz_poly_mul(poly2->coeffs, g, a, t, a);
_fmpz_mod_poly_reduce(poly2->coeffs, 2 * a - 1, Qq->a, Qq->j, Qq->len, pN);
_fmpz_poly_set_length(poly2, a);
_fmpz_poly_normalise(poly2);
}
}
/* Now the matrix for p^{-1} F_p at t=t_1 is (F1, vF1). */
vF1 = vF;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
_fmpz_vec_clear(f, a);
_fmpz_vec_clear(g, 2 * a - 1);
_fmpz_vec_clear(t, 2 * a - 1);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Evaluation:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Step 7 {Norm} *****************************************************/
/*
Computes the matrix for $q^{-1} F_q$ at $t = t_1$ as the
product $F \sigma(F) \dotsm \sigma^{a-1}(F)$ up appropriate
transpositions because our convention of columns vs rows is
the opposite of that used by Gerkmann.
Note that, in any case, transpositions do not affect
the characteristic polynomial.
*/
c0 = clock();
{
const long N = prec->N1 - a * vF1;
fmpz_t pN;
fmpz_poly_mat_t T;
fmpz_init(pN);
fmpz_poly_mat_init(T, b, b);
fmpz_pow_ui(pN, p, N);
fmpz_poly_mat_frobenius(T, F1, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
for (i = 2; i < a; i++)
{
fmpz_poly_mat_frobenius(T, T, 1, p, N, Qq);
_qadic_mat_mul(F1, F1, T, pN, Qq);
}
vF1 = a * vF1;
fmpz_poly_mat_canonicalise(F1, &vF1, p);
fmpz_clear(pN);
fmpz_poly_mat_clear(T);
}
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Norm:\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
}
/* Step 8 {Reverse characteristic polynomial} ****************************/
c0 = clock();
deformation_revcharpoly(cp, F1, vF1, n, d, prec->N0, prec->r, prec->s, Qq);
c1 = clock();
c = (double) (c1 - c0) / CLOCKS_PER_SEC;
if (verbose)
{
printf("Reverse characteristic polynomial:\n");
printf(" p(T) = "), fmpz_poly_print_pretty(cp, "T"), printf("\n");
printf(" Time = %f\n", c);
printf("\n");
fflush(stdout);
}
/* Clean up **************************************************************/
padic_mat_clear(F0);
mat_clear(M, ctxFracQt);
free(bR);
free(bC);
fmpz_poly_clear(r);
fmpz_poly_mat_clear(C);
fmpz_poly_mat_clear(Cinv);
fmpz_poly_mat_clear(F);
fmpz_poly_mat_clear(F1);
fmpz_poly_clear(cp);
}
void
fmpz_poly_divrem_divconquer(fmpz_poly_t Q, fmpz_poly_t R,
const fmpz_poly_t A, const fmpz_poly_t B)
{
const long lenA = A->length;
const long lenB = B->length;
fmpz_poly_t tQ, tR;
fmpz *q, *r;
if (lenB == 0)
{
printf("Exception: division by zero in fmpz_poly_divrem_divconquer\n");
abort();
}
if (lenA < lenB)
{
fmpz_poly_set(R, A);
fmpz_poly_zero(Q);
return;
}
if (Q == A || Q == B)
{
fmpz_poly_init2(tQ, lenA - lenB + 1);
q = tQ->coeffs;
}
else
{
fmpz_poly_fit_length(Q, lenA - lenB + 1);
q = Q->coeffs;
}
if (R == A || R == B)
{
fmpz_poly_init2(tR, lenA);
r = tR->coeffs;
}
else
{
fmpz_poly_fit_length(R, lenA);
r = R->coeffs;
}
_fmpz_poly_divrem_divconquer(q, r, A->coeffs, lenA, B->coeffs, lenB);
if (Q == A || Q == B)
{
_fmpz_poly_set_length(tQ, lenA - lenB + 1);
fmpz_poly_swap(tQ, Q);
fmpz_poly_clear(tQ);
}
else
_fmpz_poly_set_length(Q, lenA - lenB + 1);
if (R == A || R == B)
{
_fmpz_poly_set_length(tR, lenA);
fmpz_poly_swap(tR, R);
fmpz_poly_clear(tR);
}
else
_fmpz_poly_set_length(R, lenA);
_fmpz_poly_normalise(Q);
_fmpz_poly_normalise(R);
}
void
fmpz_poly_complex_roots_squarefree(const fmpz_poly_t poly,
slong initial_prec,
slong target_prec,
slong print_digits)
{
slong i, j, prec, deg, deg_deflated, isolated, maxiter, deflation;
acb_poly_t cpoly, cpoly_deflated;
fmpz_poly_t poly_deflated;
acb_ptr roots, roots_deflated;
int removed_zero;
if (fmpz_poly_degree(poly) < 1)
return;
fmpz_poly_init(poly_deflated);
acb_poly_init(cpoly);
acb_poly_init(cpoly_deflated);
/* try to write poly as poly_deflated(x^deflation), possibly multiplied by x */
removed_zero = fmpz_is_zero(poly->coeffs);
if (removed_zero)
fmpz_poly_shift_right(poly_deflated, poly, 1);
else
fmpz_poly_set(poly_deflated, poly);
deflation = fmpz_poly_deflation(poly_deflated);
fmpz_poly_deflate(poly_deflated, poly_deflated, deflation);
deg = fmpz_poly_degree(poly);
deg_deflated = fmpz_poly_degree(poly_deflated);
flint_printf("searching for %wd roots, %wd deflated\n", deg, deg_deflated);
roots = _acb_vec_init(deg);
roots_deflated = _acb_vec_init(deg_deflated);
for (prec = initial_prec; ; prec *= 2)
{
acb_poly_set_fmpz_poly(cpoly_deflated, poly_deflated, prec);
maxiter = FLINT_MIN(FLINT_MAX(deg_deflated, 32), prec);
TIMEIT_ONCE_START
flint_printf("prec=%wd: ", prec);
isolated = acb_poly_find_roots(roots_deflated, cpoly_deflated,
prec == initial_prec ? NULL : roots_deflated, maxiter, prec);
flint_printf("%wd isolated roots | ", isolated);
TIMEIT_ONCE_STOP
if (isolated == deg_deflated)
{
if (!check_accuracy(roots_deflated, deg_deflated, target_prec))
continue;
if (deflation == 1)
{
_acb_vec_set(roots, roots_deflated, deg_deflated);
}
else /* compute all nth roots */
{
acb_t w, w2;
acb_init(w);
acb_init(w2);
acb_unit_root(w, deflation, prec);
acb_unit_root(w2, 2 * deflation, prec);
for (i = 0; i < deg_deflated; i++)
{
if (arf_sgn(arb_midref(acb_realref(roots_deflated + i))) > 0)
{
acb_root_ui(roots + i * deflation,
roots_deflated + i, deflation, prec);
}
else
{
acb_neg(roots + i * deflation, roots_deflated + i);
acb_root_ui(roots + i * deflation,
roots + i * deflation, deflation, prec);
acb_mul(roots + i * deflation,
roots + i * deflation, w2, prec);
}
for (j = 1; j < deflation; j++)
{
acb_mul(roots + i * deflation + j,
roots + i * deflation + j - 1, w, prec);
}
}
acb_clear(w);
acb_clear(w2);
}
/* by assumption that poly is squarefree, must be just one */
if (removed_zero)
acb_zero(roots + deg_deflated * deflation);
if (!check_accuracy(roots, deg, target_prec))
continue;
acb_poly_set_fmpz_poly(cpoly, poly, prec);
if (!acb_poly_validate_real_roots(roots, cpoly, prec))
continue;
for (i = 0; i < deg; i++)
{
if (arb_contains_zero(acb_imagref(roots + i)))
arb_zero(acb_imagref(roots + i));
}
flint_printf("done!\n");
break;
}
}
if (print_digits != 0)
{
_acb_vec_sort_pretty(roots, deg);
for (i = 0; i < deg; i++)
{
acb_printn(roots + i, print_digits, 0);
flint_printf("\n");
}
}
fmpz_poly_clear(poly_deflated);
acb_poly_clear(cpoly);
acb_poly_clear(cpoly_deflated);
_acb_vec_clear(roots, deg);
_acb_vec_clear(roots_deflated, deg_deflated);
}