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#include "cra.hpp"
#include <assert.h>
#include <stddef.h>
#include "error.h"
#include "freemod.hpp"
#include "matrix-con.hpp"
#include "matrix.hpp"
#include "monoid.hpp"
#include "poly.hpp"
#include "ring.hpp"
#include "style.hpp"
void ChineseRemainder::CRA0(mpz_srcptr a,
mpz_srcptr b,
mpz_srcptr um,
mpz_srcptr vn,
mpz_srcptr mn,
mpz_t result)
{
mpz_t mn_half;
mpz_init(mn_half);
mpz_mul(result, um, b);
mpz_addmul(result, vn, a);
mpz_mod(result, result, mn);
mpz_tdiv_q_2exp(mn_half, mn, 1);
// get canonical representative
if (mpz_cmp(result, mn_half) > 0)
{
mpz_sub(result, result, mn);
}
mpz_clear(mn_half);
}
bool ChineseRemainder::computeMultipliers(mpz_srcptr m,
mpz_srcptr n,
mpz_t result_um,
mpz_t result_vn,
mpz_t result_mn)
{
mpz_t g;
mpz_init(g);
mpz_gcdext(g, result_um, result_vn, m, n);
if (0 != mpz_cmp_si(g, 1)) return false;
mpz_mul(result_mn, m, n);
mpz_mul(result_um, result_um, m);
mpz_mul(result_vn, result_vn, n);
mpz_clear(g);
return true;
}
ring_elem ChineseRemainder::CRA(const PolyRing *R,
ring_elem ff,
ring_elem gg,
mpz_srcptr um,
mpz_srcptr vn,
mpz_srcptr mn)
{
mpz_t result_coeff;
mpz_t mn_half;
mpz_init(result_coeff);
mpz_init(mn_half);
Nterm *f = ff;
Nterm *g = gg;
Nterm head;
Nterm *result = &head;
mpz_tdiv_q_2exp(mn_half, mn, 1);
const Monoid *M = R->getMonoid();
const Ring *K = R->getCoefficientRing();
while (1)
{
if (g == nullptr)
{
// mult each term of f by n:
for (; f != nullptr; f = f->next)
{
result->next = R->new_term();
result = result->next;
result->next = nullptr;
M->copy(f->monom, result->monom);
mpz_mul(result_coeff, f->coeff.get_mpz(), vn);
mpz_mod(result_coeff, result_coeff, mn);
if (mpz_cmp(result_coeff, mn_half) > 0)
{
mpz_sub(result_coeff, result_coeff, mn);
}
result->coeff = K->from_int(result_coeff);
}
break;
}
if (f == nullptr)
{
// mult each term of g by n:
for (; g != nullptr; g = g->next)
{
result->next = R->new_term();
result = result->next;
result->next = nullptr;
M->copy(g->monom, result->monom);
mpz_mul(result_coeff, g->coeff.get_mpz(), um);
mpz_mod(result_coeff, result_coeff, mn);
if (mpz_cmp(result_coeff, mn_half) > 0)
{
mpz_sub(result_coeff, result_coeff, mn);
}
result->coeff = K->from_int(result_coeff);
}
break;
}
switch (M->compare(f->monom, g->monom))
{
case -1:
result->next = R->new_term();
result = result->next;
result->next = nullptr;
M->copy(g->monom, result->monom);
mpz_mul(result_coeff, g->coeff.get_mpz(), um);
result->coeff = K->from_int(result_coeff);
g = g->next;
break;
case 1:
result->next = R->new_term();
result = result->next;
result->next = nullptr;
M->copy(f->monom, result->monom);
mpz_mul(result_coeff, f->coeff.get_mpz(), vn);
result->coeff = K->from_int(result_coeff);
f = f->next;
break;
case 0:
Nterm *tmf = f;
Nterm *tmg = g;
f = f->next;
g = g->next;
CRA0(tmf->coeff.get_mpz(),
tmg->coeff.get_mpz(),
um,
vn,
mn,
result_coeff);
Nterm *t = R->new_term();
M->copy(tmf->monom, t->monom);
t->coeff = K->from_int(result_coeff);
t->next = nullptr;
result->next = t;
result = t;
break;
}
}
mpz_clear(result_coeff);
mpz_clear(mn_half);
result->next = nullptr;
return head.next;
}
ring_elem ChineseRemainder::CRA(const PolyRing *R,
ring_elem ff,
ring_elem gg,
mpz_srcptr m,
mpz_srcptr n)
{
// compute the multipliers
mpz_t um, vn, mn;
mpz_init(um);
mpz_init(vn);
mpz_init(mn);
computeMultipliers(m, n, um, vn, mn);
// compute the chinese remainder with precomputed multipliers
ring_elem result = CRA(R, ff, gg, um, vn, mn);
mpz_clear(um);
mpz_clear(vn);
mpz_clear(mn);
return result;
}
vec ChineseRemainder::CRA(const PolyRing *R,
vec f,
vec g,
mpz_srcptr um,
mpz_srcptr vn,
mpz_srcptr mn)
{
vecterm head;
vec result = &head;
while (1)
{
if (g == nullptr)
{
// mult each term of f by n:
for (; f != nullptr; f = f->next)
{
result->next = R->new_vec();
result = result->next;
result->next = nullptr;
result->coeff = CRA(R, f->coeff, nullptr, um, vn, mn);
result->comp = f->comp;
}
break;
}
if (f == NULL)
{
// mult each term of g by n:
for (; g != nullptr; g = g->next)
{
result->next = R->new_vec();
result = result->next;
result->next = nullptr;
result->coeff = CRA(R, nullptr, g->coeff, um, vn, mn);
result->comp = g->comp;
}
break;
}
if (f->comp < g->comp)
{
result->next = R->new_vec();
result = result->next;
result->next = nullptr;
result->coeff = CRA(R, nullptr, g->coeff, um, vn, mn);
result->comp = g->comp;
g = g->next;
}
else if (f->comp > g->comp)
{
result->next = R->new_vec();
result = result->next;
result->next = nullptr;
result->coeff = CRA(R, f->coeff, nullptr, um, vn, mn);
result->comp = f->comp;
f = f->next;
}
else
{
result->next = R->new_vec();
result = result->next;
result->next = nullptr;
result->coeff = CRA(R, f->coeff, g->coeff, um, vn, mn);
result->comp = f->comp;
f = f->next;
g = g->next;
}
}
result->next = nullptr;
return head.next;
}
Matrix *ChineseRemainder::CRA(const Matrix *f,
const Matrix *g,
mpz_srcptr um,
mpz_srcptr vn,
mpz_srcptr mn)
{
if (f->get_ring() != g->get_ring())
{
ERROR("matrices have different base rings");
return nullptr;
}
if (f->rows()->rank() != g->rows()->rank() ||
f->cols()->rank() != g->cols()->rank())
{
ERROR("matrices have different shapes");
return nullptr;
}
const PolyRing *R = f->get_ring()->cast_to_PolyRing();
if (R == nullptr)
{
ERROR("expected polynomial ring over ZZ");
return nullptr;
}
const FreeModule *F = f->rows();
const FreeModule *G = f->cols();
const int *deg;
if (!f->rows()->is_equal(g->rows())) F = R->make_FreeModule(f->n_rows());
if (!f->cols()->is_equal(g->cols())) G = R->make_FreeModule(f->n_cols());
if (EQ == f->degree_monoid()->compare(f->degree_shift(), g->degree_shift()))
deg = f->degree_shift();
else
deg = f->degree_monoid()->make_one();
MatrixConstructor mat(F, G, deg);
for (int i = 0; i < f->n_cols(); i++)
{
vec u = CRA(R, f->elem(i), g->elem(i), um, vn, mn);
mat.set_column(i, u);
}
return mat.to_matrix();
}
bool ChineseRemainder::ratConversion(mpz_srcptr c, mpz_srcptr m, mpq_t result)
{
mpz_t a1, a2, u1, u2, q, h, mhalf, u2sqr, a2sqr;
bool retVal = true;
mpz_init_set(a1, m);
mpz_init_set(a2, c);
mpz_init_set_si(u1, 0);
mpz_init_set_si(u2, 1);
mpz_init_set_si(q, 0);
mpz_init_set_si(h, 0);
mpz_init(u2sqr);
mpz_init(a2sqr);
mpz_init(mhalf);
mpz_tdiv_q_2exp(mhalf, m, 1);
for (;;)
{
mpz_mul(u2sqr, u2, u2);
if (mpz_cmp(u2sqr, mhalf) >= 0) // u2sqr >= mhalf
{
retVal = false;
mpq_set_z(result, c);
break;
}
mpz_mul(a2sqr, a2, a2);
if (mpz_cmp(a2sqr, mhalf) < 0) // a2sqr < half
{
retVal = true;
mpq_set_num(result, a2);
mpq_set_den(result, u2);
mpq_canonicalize(result);
break;
}
mpz_fdiv_q(q, a1, a2);
mpz_submul(a1, q, a2);
mpz_submul(u1, q, u2);
mpz_swap(a1, a2);
mpz_swap(u1, u2);
}
// clean up
// mpz_clears(a1,a2,u1,u2,q,h,mhalf,u2sqr,a2sqr,(void *)0);
mpz_clear(a1);
mpz_clear(a2);
mpz_clear(u1);
mpz_clear(u2);
mpz_clear(q);
mpz_clear(h);
mpz_clear(mhalf);
mpz_clear(u2sqr);
mpz_clear(a2sqr);
return retVal;
}
ring_elem ChineseRemainder::ratConversion(const ring_elem ff,
mpz_srcptr m,
const PolyRing *RQ)
{
mpq_t result_coeff;
mpq_init(result_coeff);
Nterm *f = ff;
Nterm head;
Nterm *result = &head;
const Monoid *M = RQ->getMonoid();
const Ring *K = RQ->getCoefficientRing();
for (; f != nullptr; f = f->next)
{
result->next = RQ->new_term();
result = result->next;
result->next = nullptr;
M->copy(f->monom, result->monom);
ratConversion(f->coeff.get_mpz(), m, result_coeff);
bool ok1 = K->from_rational(result_coeff, result->coeff);
(void)ok1;
assert(ok1); // K is supposed to contain (or be) the rationals, so this
// should not fail.
}
mpq_clear(result_coeff);
result->next = nullptr;
return head.next;
}
vec ChineseRemainder::ratConversion(vec f, mpz_srcptr m, const PolyRing *RQ)
{
vecterm head;
vec result = &head;
for (; f != nullptr; f = f->next)
{
result->next = RQ->new_vec();
result = result->next;
result->next = nullptr;
result->comp = f->comp;
result->coeff = ratConversion(f->coeff, m, RQ);
}
result->next = nullptr;
return head.next;
}
// Local Variables:
// indent-tabs-mode: nil
// End:
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