/*-------------------------------------------------------------------------*/
void
poly_rootopt_run(poly_rootopt_t *data, mpz_t * alg_coeffs,
mpz_t * rat_coeffs, double sizeopt_norm,
double projective_alpha)
{
uint32 i;
stage2_curr_data_t *s = (stage2_curr_data_t *)(data->internal);
curr_poly_t *c = &s->curr_poly;
dd_precision_t precision = 0;
uint32 precision_changed = 0;
if (!dd_precision_is_ieee()) {
precision_changed = 1;
precision = dd_set_precision_ieee();
}
mpz_set(c->gmp_lina[0], rat_coeffs[0]);
mpz_set(c->gmp_lina[1], rat_coeffs[1]);
mpz_neg(c->gmp_d, rat_coeffs[0]);
mpz_set(c->gmp_p, rat_coeffs[1]);
for (i = 0; i <= data->degree; i++)
mpz_set(c->gmp_a[i], alg_coeffs[i]);
if (sizeopt_norm == 0) {
/* size optimization possibly did not run
previously; check poly and get the norm */
if (check_poly(c, c->gmp_a, c->gmp_lina[0],
data->gmp_N, data->degree) != 1) {
goto finished;
}
optimize_initial(c, data->degree, &sizeopt_norm, 1);
stage2_root_score(data->degree, c->gmp_a, 100,
&projective_alpha, 1);
}
if (sizeopt_norm * exp(projective_alpha) <= data->max_sizeopt_norm)
root_sieve_run(data, sizeopt_norm, projective_alpha);
finished:
if (precision_changed)
dd_clear_precision(precision);
}
bool SchreyerFrame::debugCheckOrder(int lev) const
{
if (lev == 0) return true;
bool result = true;
auto& mylevel = level(lev);
auto& myorder = schreyerOrder(lev-1);
int which = 0;
for (auto i = mylevel.cbegin(); i != mylevel.cend(); ++i, ++which)
{
if (!check_poly(ring(), i->mSyzygy, myorder))
{
std::cout << "Error: terms of polynomial at level " << lev << " location " << which << " not in order" << std::endl;
std::cout << " poly = ";
display_poly(stdin, ring(), i->mSyzygy);
std::cout << std::endl;
result = false;
}
}
return result;
}
bool SchreyerFrame::insertLevelOne(res_packed_monomial monom, int deg, poly& syzygy)
{
insertBasic(1, monom, deg); // deg is the actual degree of this element.
long comp = monoid().get_component(monom);
auto last = level(1).size();
auto& p = level(0)[comp];
if (p.mBegin == -1)
p.mBegin = last-1;
p.mEnd = last;
if (!check_poly(ring(), syzygy, schreyerOrder(0)))
{
if (M2_gbTrace >= 1)
{
std::cout << "Error: expected terms of polynomial to be in order, in poly#" << last << ": ";
display_poly(stdout, ring(), syzygy);
std::cout << std::endl;
}
return false;
}
std::swap(level(1)[level(1).size()-1].mSyzygy, syzygy);
return true;
}
/**
* Run step 5 of the AKS algorithm.
*/
int check_polys(mpz_t r, mpz_t n) {
mpz_t a, lim;
mpz_init(a);
mpz_init(lim);
int status = PRIME;
if (aks_debug) gmp_printf("computing upper limit\n");
compute_upper_limit(lim, r, n);
if (aks_debug) gmp_printf("lim=%Zd\n", lim);
// For values of a from 1 to sqrt(totient(r)) * log(n)
for (mpz_set_ui(a, 1); mpz_cmp(a, lim) <= 0; mpz_add_ui(a, a, 1)) {
if (!check_poly(n, a, r)) {
status = COMPOSITE;
break;
}
}
mpz_clear(a);
mpz_clear(lim);
return status;
}
static int
pol_expand(curr_poly_t *c, mpz_t gmp_N, mpz_t high_coeff,
mpz_t gmp_p, mpz_t gmp_d,
double coeff_bound, uint32 degree)
{
uint32 i, j;
if (mpz_cmp_ui(c->gmp_p, (mp_limb_t)1) == 0)
mpz_set_ui(c->gmp_help1, (mp_limb_t)1);
else {
if (!mpz_invert(c->gmp_help1, gmp_d, gmp_p))
return 0;
}
mpz_set(c->gmp_b[1], c->gmp_help1);
for (i = 2; i < degree; i++)
mpz_mul(c->gmp_b[i], c->gmp_b[i-1], c->gmp_help1);
mpz_set(c->gmp_c[1], gmp_d);
for (i = 2; i <= degree; i++)
mpz_mul(c->gmp_c[i], c->gmp_c[i-1], gmp_d);
mpz_set(c->gmp_a[degree], high_coeff);
mpz_set(c->gmp_help2, gmp_N);
for (i = degree - 1; (int32)i >= 0; i--) {
mpz_mul(c->gmp_help3, c->gmp_a[i+1], c->gmp_c[i+1]);
mpz_sub(c->gmp_help3, c->gmp_help2, c->gmp_help3);
mpz_tdiv_q(c->gmp_help2, c->gmp_help3, gmp_p);
if (i > 0) {
mpz_tdiv_q(c->gmp_a[i], c->gmp_help2, c->gmp_c[i]);
mpz_mul(c->gmp_help3, c->gmp_help2, c->gmp_b[i]);
mpz_sub(c->gmp_help3, c->gmp_help3, c->gmp_a[i]);
mpz_tdiv_r(c->gmp_help4, c->gmp_help3, gmp_p);
if (mpz_sgn(c->gmp_help4) < 0)
mpz_add(c->gmp_help4, c->gmp_help4, gmp_p);
mpz_add(c->gmp_a[i], c->gmp_a[i], c->gmp_help4);
}
}
mpz_set(c->gmp_a[0], c->gmp_help2);
mpz_tdiv_q_2exp(c->gmp_help1, gmp_d, (mp_limb_t)1);
for (i = 0; i < degree; i++) {
for (j = 0; j < MAX_CORRECT_STEPS &&
mpz_cmpabs(c->gmp_a[i], c->gmp_help1) > 0; j++) {
if (mpz_sgn(c->gmp_a[i]) < 0) {
mpz_add(c->gmp_a[i], c->gmp_a[i], gmp_d);
mpz_sub(c->gmp_a[i+1], c->gmp_a[i+1], gmp_p);
}
else {
mpz_sub(c->gmp_a[i], c->gmp_a[i], gmp_d);
mpz_add(c->gmp_a[i+1], c->gmp_a[i+1], gmp_p);
}
}
if (j == MAX_CORRECT_STEPS)
return 0;
}
#if 0
gmp_printf("%+Zd\n", c->gmp_lina[0]);
gmp_printf("%+Zd\n", c->gmp_lina[1]);
for (i = 0; i <= degree; i++)
gmp_printf("%+Zd\n", c->gmp_a[i]);
printf("coeff ratio = %.5lf\n",
fabs(mpz_get_d(c->gmp_a[degree-2])) / coeff_bound);
#endif
if (check_poly(c, c->gmp_a,
c->gmp_lina[0], gmp_N, degree) != 1) {
return 0;
}
if (mpz_cmpabs_d(c->gmp_a[degree - 2], coeff_bound) > 0) {
return 1;
}
return 2;
}
static void BSPTreeCreateRecursive(BSPTreeNode *tree,
PolyListNode *pllist,
#if BSPTREE_STATS
int depth,
#endif
struct obstack *scratch)
{
PolyListNode *plnode, *front, *back;
EdgeIntersection edges[2];
tree->front = tree->back = NULL;
ListPop(pllist, plnode);
tree->polylist = plnode;
check_poly(plnode->poly);
PolyPlane(plnode, &tree->plane);
front = back = NULL;
while (pllist) {
ListPop(pllist, plnode);
check_poly(plnode->poly);
switch (ClassifyPoly(&tree->plane, plnode->poly, edges)) {
case BACKOF:
check_poly(plnode->poly);
ListPush(back, plnode);
break;
case COPLANAR:
check_poly(plnode->poly);
ListPush(tree->polylist, plnode);
break;
case INFRONTOF:
check_poly(plnode->poly);
ListPush(front, plnode);
break;
case BOTH_SIDES:
check_poly(plnode->poly);
SplitPolyNode(plnode, &front, &back, edges, scratch);
break;
}
}
if (front) {
tree->front = obstack_alloc(scratch, sizeof(*tree->front));
BSPTreeCreateRecursive(tree->front, front,
#if BSPTREE_STATS
depth+1,
#endif
scratch);
}
if (back) {
tree->back = obstack_alloc(scratch, sizeof(*tree->back));
BSPTreeCreateRecursive(tree->back, back,
#if BSPTREE_STATS
depth+1,
#endif
scratch);
}
#if BSPTREE_STATS
if (depth > tree_depth) {
tree_depth = depth;
}
#endif
}
/* Split plnode along plane. We know that plane really intersects
* plnode->poly. We also know that plnode->poly is planar and convex.
*
* Given this assumptions we know that plnode->poly has to be split
* into exactly two pieces.
*/
static inline void SplitPolyNode(PolyListNode *plnode,
PolyListNode **front, PolyListNode **back,
EdgeIntersection edges[2],
struct obstack *scratch)
{
const void **tagged_app = plnode->tagged_app;
Poly *poly = plnode->poly, savedp;
VARARRAY(savedv, Vertex *, poly->n_vertices);
Vertex *v0, *v1, **vpos;
int istart[2], iend[2], i, nv[2];
Vertex *vstart[2], *vend[2];
#if BSPTREE_STATS
++n_tree_polys;
#endif
vstart[0] = vstart[1] = vend[0] = vend[1] = NULL;
istart[0] = istart[1] = iend[0] = iend[1] = -1;
/* first point of intersection */
if (fzero(edges[0].scp[0])) {
v0 = poly->v[edges[0].v[0]];
if (fpos(edges[0].scp[1])) {
istart[0] = edges[0].v[0];
iend[1] = edges[0].v[0];
} else {
istart[1] = edges[0].v[0];
iend[0] = edges[0].v[0];
}
} else if (fzero(edges[0].scp[1])) {
v0 = poly->v[edges[0].v[1]];
if (fpos(edges[0].scp[0])) {
istart[1] = edges[0].v[1];
iend[0] = edges[0].v[1];
} else {
istart[0] = edges[0].v[1];
iend[1] = edges[0].v[1];
}
} else {
HPt3Coord mu0, mu1;
Vertex *V0 = poly->v[edges[0].v[0]];
Vertex *V1 = poly->v[edges[0].v[1]];
v0 = obstack_alloc(scratch, sizeof(Vertex));
mu0 = edges[0].scp[1]/(edges[0].scp[1]-edges[0].scp[0]);
#if 0
mu1 = edges[0].scp[0]/(edges[0].scp[0]-edges[0].scp[1]);
#else
mu1 = 1.0 - mu0;
#endif
/* Use denormalized variant; otherwise textures may come out wrong
* because the homogeneous divisor is used for perspective
* corrections.
*/
if (poly->flags & VERT_ST) {
v0->st.s = mu0 * V0->st.s + mu1 * V1->st.s;
v0->st.t = mu0 * V0->st.t + mu1 * V1->st.t;
HPt3LinSumDenorm(mu0, &V0->pt, mu1, &V1->pt, &v0->pt);
} else {
HPt3LinSum(mu0, &V0->pt, mu1, &V1->pt, &v0->pt);
}
if (!finite(v0->pt.x + v0->pt.y + v0->pt.z)){
abort();
}
if (poly->flags & VERT_C) {
CoLinSum(mu0, &V0->vcol, mu1, &V1->vcol, &v0->vcol);
}
if (true || (poly->flags & VERT_N)) {
/* The averaged vertex normals do not have an orientation, so
* try to orient them w.r.t. the polygon normal before computing
* the linear combination.
*/
if (Pt3Dot(&V0->vn, &poly->pn)*Pt3Dot(&V1->vn, &poly->pn) < 0) {
Pt3Comb(-mu0, &V0->vn, mu1, &V1->vn, &v0->vn);
} else {
Pt3Comb(mu0, &V0->vn, mu1, &V1->vn, &v0->vn);
}
Pt3Unit(&v0->vn);
}
if (fpos(edges[0].scp[0])) {
vstart[1] = vend[0] = v0;
istart[1] = edges[0].v[1];
iend[0] = edges[0].v[0];
} else {
vstart[0] = vend[1] = v0;
istart[0] = edges[0].v[1];
iend[1] = edges[0].v[0];
}
}
/* second point of intersection */
if (fzero(edges[1].scp[0])) {
v1 = poly->v[edges[1].v[0]];
if (fpos(edges[1].scp[1])) {
istart[0] = edges[1].v[0];
iend[1] = edges[1].v[0];
} else {
istart[1] = edges[1].v[0];
iend[0] = edges[1].v[0];
}
} else if (fzero(edges[1].scp[1])) {
v1 = poly->v[edges[1].v[1]];
if (fpos(edges[1].scp[0])) {
istart[1] = edges[1].v[1];
iend[0] = edges[1].v[1];
} else {
istart[0] = edges[1].v[1];
iend[1] = edges[1].v[1];
}
} else {
HPt3Coord mu0, mu1;
Vertex *V0 = poly->v[edges[1].v[0]];
Vertex *V1 = poly->v[edges[1].v[1]];
v1 = obstack_alloc(scratch, sizeof(Vertex));
mu0 = edges[1].scp[1]/(edges[1].scp[1]-edges[1].scp[0]);
#if 0
mu1 = edges[1].scp[0]/(edges[1].scp[0]-edges[1].scp[1]);
#else
mu1 = 1.0 - mu0;
#endif
if (poly->flags & VERT_ST) {
v1->st.s = mu0 * V0->st.s + mu1 * V1->st.s;
v1->st.t = mu0 * V0->st.t + mu1 * V1->st.t;
HPt3LinSumDenorm(mu0, &V0->pt, mu1, &V1->pt, &v1->pt);
} else {
HPt3LinSum(mu0, &V0->pt, mu1, &V1->pt, &v1->pt);
}
if (!finite(v1->pt.x + v1->pt.y + v1->pt.z))
abort();
if (poly->flags & VERT_C) {
CoLinSum(mu0, &V0->vcol, mu1, &V1->vcol, &v1->vcol);
}
if (true || (poly->flags & VERT_N)) {
if (Pt3Dot(&V0->vn, &poly->pn)*Pt3Dot(&V1->vn, &poly->pn) < 0) {
Pt3Comb(-mu0, &V0->vn, mu1, &V1->vn, &v1->vn);
} else {
Pt3Comb(mu0, &V0->vn, mu1, &V1->vn, &v1->vn);
}
Pt3Unit(&v1->vn);
}
if (fpos(edges[1].scp[0])) {
vstart[1] = vend[0] = v1;
istart[1] = edges[1].v[1];
iend[0] = edges[1].v[0];
} else {
vstart[0] = vend[1] = v1;
istart[0] = edges[1].v[1];
iend[1] = edges[1].v[0];
}
}
ListPush(*front, plnode);
ListPush(*back, new_poly_list_node(tagged_app, scratch));
if ((poly->flags & POLY_NONFLAT)) {
if (!(*front)->pn) {
/* Compute the normal on the parent element to avoid numerical
* instabilities on increasingly degenerated polygons.
*/
(*front)->pn = obstack_alloc(scratch, sizeof(Point3));
PolyNormal(poly, (*front)->pn,
true /* 4d */, false /* evert */, NULL, NULL);
}
(*back)->pn = (*front)->pn;
}
for (i = 0; i < 2; i++) {
nv[i] = iend[i] - istart[i] + 1;
if (nv[i] < 0) {
nv[i] += poly->n_vertices;
}
nv[i] += (vstart[i] != NULL) + (vend[i] != NULL);
}
if (poly->flags & POLY_SCRATCH) {
savedp = *poly;
memcpy(savedv, poly->v, poly->n_vertices*sizeof(Vertex *));
if (nv[0] <= poly->n_vertices) {
poly->n_vertices = nv[0];
(*front)->poly = poly;
(*back)->poly = new_poly(nv[1], NULL, scratch);
} else {
if (nv[1] > poly->n_vertices) {
abort();
}
poly->n_vertices = nv[1];
(*back)->poly = poly;
(*front)->poly = new_poly(nv[0], NULL, scratch);
}
/* Attention: gcc had problems with this code snippet with
* -fstrict-aliasing, the "#if 1" stuff seems to work. In the
* "#else" version gcc somehow lost the "savedp.v = savedv"
* assignment. I think this is a compiler bug.
*/
poly = &savedp;
#if 1
poly->v = savedv;
#else
savedp.v = savedv;
#endif
} else {
(*front)->poly = new_poly(nv[0], NULL, scratch);
(*back)->poly = new_poly(nv[1], NULL, scratch);
}
for (i = 0; i < 2; i++) {
PolyListNode *half = (i == 0) ? *front : *back;
int j;
vpos = half->poly->v;
if (vstart[i] != NULL) {
*vpos++ = vstart[i];
}
if (istart[i] <= iend[i]) {
for (j = istart[i]; j <= iend[i] && j < poly->n_vertices; j++) {
*vpos++ = poly->v[j];
}
} else {
for (j = istart[i]; j < poly->n_vertices; j++) {
*vpos++ = poly->v[j];
}
for (j = 0; j <= iend[i]; j++) {
*vpos++ = poly->v[j];
}
}
if (vend[i] != NULL) {
*vpos++ = vend[i];
}
half->poly->pcol = poly->pcol;
half->poly->pn = poly->pn;
half->poly->flags = poly->flags|POLY_SCRATCH;
check_poly(half->poly);
}
}