template<class T, class Policies> inline
interval<T, Policies> cos(const interval<T, Policies>& x)
{
if (interval_lib::detail::test_input(x))
return interval<T, Policies>::empty();
typename Policies::rounding rnd;
typedef interval<T, Policies> I;
typedef typename interval_lib::unprotect<I>::type R;
// get lower bound within [0, pi]
const R pi2 = interval_lib::pi_twice<R>();
R tmp = fmod((const R&)x, pi2);
if (width(tmp) >= pi2.lower())
return I(static_cast<T>(-1), static_cast<T>(1), true); // we are covering a full period
if (tmp.lower() >= interval_lib::constants::pi_upper<T>())
return -cos(tmp - interval_lib::pi<R>());
T l = tmp.lower();
T u = tmp.upper();
BOOST_USING_STD_MIN();
// separate into monotone subintervals
if (u <= interval_lib::constants::pi_lower<T>())
return I(rnd.cos_down(u), rnd.cos_up(l), true);
else if (u <= pi2.lower())
return I(static_cast<T>(-1), rnd.cos_up(min BOOST_PREVENT_MACRO_SUBSTITUTION(rnd.sub_down(pi2.lower(), u), l)), true);
else
return I(static_cast<T>(-1), static_cast<T>(1), true);
}
int main()
{
R a(5,4);
a.print(); //µ÷ÓÃvoid print()
const R b(20,52);
b.print(); //µ÷ÓÃvoid print() const
}
/// @brief Makes the inverse relation, mapping codim_to entities
/// to their codim_from neighbours.
///
/// Implementation note: The algorithm has been changed
/// to a three-pass O(n) algorithm.
/// @param inv The OrientedEntityTable
void makeInverseRelation(OrientedEntityTable<codim_to, codim_from>& inv) const
{
// Find the maximum index used. This will give (one less than) the size
// of the table to be created.
int maxind = -1;
for (int i = 0; i < size(); ++i) {
EntityRep<codim_from> from_ent(i, true);
row_type r = operator[](from_ent);
for (int j = 0; j < r.size(); ++j) {
EntityRep<codim_to> to_ent = r[j];
int ind = to_ent.index();
maxind = std::max(ind, maxind);
}
}
// Build the new_sizes vector and compute datacount.
std::vector<int> new_sizes(maxind + 1);
int datacount = 0;
for (int i = 0; i < size(); ++i) {
EntityRep<codim_from> from_ent(i, true);
row_type r = operator[](from_ent);
datacount += r.size();
for (int j = 0; j < r.size(); ++j) {
EntityRep<codim_to> to_ent = r[j];
int ind = to_ent.index();
++new_sizes[ind];
}
}
// Compute the cumulative sizes.
std::vector<int> cumul_sizes(new_sizes.size() + 1);
cumul_sizes[0] = 0;
std::partial_sum(new_sizes.begin(), new_sizes.end(), cumul_sizes.begin() + 1);
// Using the cumulative sizes array as indices, we populate new_data.
// Note that cumul_sizes[ind] is not kept constant, but incremented so that
// it always gives the correct index for new data corresponding to index ind.
std::vector<int> new_data(datacount);
for (int i = 0; i < size(); ++i) {
EntityRep<codim_from> from_ent(i, true);
row_type r = operator[](from_ent);
for (int j = 0; j < r.size(); ++j) {
EntityRep<codim_to> to_ent = r[j];
int ind = to_ent.index();
int data_ind = cumul_sizes[ind];
new_data[data_ind] = to_ent.orientation() ? i : ~i;
++cumul_sizes[ind];
}
}
inv = OrientedEntityTable<codim_to, codim_from>(new_data.begin(),
new_data.end(),
new_sizes.begin(),
new_sizes.end());
}
/** @brief Prints the relation matrix corresponding to the table.
Let the entities of codimensions f and t be given by
the sets \f$E^f = { e^f_i } \f$ and \f$E^t = { e^t_j }\f$.
A relation matrix R is defined by
\f{eqnarray*}{
R_{ij} &=& 0 \mbox{ if } e^f_i \mbox{ and } e^t_j \mbox{ are not neighbours }\\
R_{ij} &=& 1 \mbox{ if they are neighbours with same orientation }\\
R_{ij} &=& -1 \mbox{ if they are neighbours with opposite orientation.}
\f}
@param os The output stream.
*/
void printRelationMatrix(std::ostream& os) const
{
int columns = numberOfColumns();
for (int i = 0; i < size(); ++i) {
FromType from_ent(i);
row_type r = operator[](from_ent);
int cur_col = 0;
int next_ent = 0;
ToType to_ent = r[next_ent];
int next_print = to_ent.index();
while (cur_col < columns) {
if (cur_col == next_print) {
if (to_ent.orientation()) {
os << " 1";
} else {
os << " -1";
}
++next_ent;
if (next_ent >= r.size()) {
next_print = columns;
} else {
to_ent = r[next_ent];
next_print = to_ent.index();
}
} else {
os << " 0";
}
++cur_col;
}
os << '\n';
}
}
int numberOfColumns() const
{
int maxind = 0;
for (int i = 0; i < size(); ++i) {
FromType from_ent(i);
row_type r = operator[](from_ent);
for (int j = 0; j < r.size(); ++j) {
maxind = std::max(maxind, r[j].index());
}
}
return maxind + 1;
}
inline void storeDataImpl(Contents<D> & cont) const
{
r_.storeData(cont);
}
virtual bool empty() const { return r.empty(); }
void append(S*& dest) const
{
left.append(dest);
right.append(dest);
}
int size() const
{
return left.size() + right.size();
}
void run(const P& p0,
const P& p1,
const bool* blocked,
int* flood_buffer,
const P& map_dims,
std::vector<P>& out,
const bool allow_diagonal,
const bool randomize_steps)
{
out.clear();
if (p0 == p1)
{
// Origin and target is same cell
return;
}
floodfill::run(p0,
blocked,
flood_buffer,
map_dims,
-1,
p1,
allow_diagonal);
if (flood_buffer[idx2(p1, map_dims.y)] == 0)
{
// No path exists
return;
}
const std::vector<P>& dirs = allow_diagonal ?
dir_utils::dir_list :
dir_utils::cardinal_list;
const size_t nr_dirs = dirs.size();
// Corresponds to the elements in "dirs"
std::vector<bool> valid_offsets(nr_dirs, false);
// The path length will be equal to the flood value at the target cell, so
// we can reserve that many elements beforehand.
out.reserve(flood_buffer[idx2(p1, map_dims.y)]);
P p(p1);
out.push_back(p);
const R map_r(P(0, 0), map_dims - 1);
while (true)
{
const int val = flood_buffer[idx2(p, map_dims.y)];
P adj_p;
// Find valid offsets, and check if origin is reached
for (size_t i = 0; i < nr_dirs; ++i)
{
const P& d(dirs[i]);
adj_p = p + d;
if (adj_p == p0)
{
// Origin reached
return;
}
// TODO: What is the purpose of this check? If the current value is
// zero, doesn't that mean this cell is the target? Only the target
// cell and unreachable cells should have values of zero(?)
// Try removing the check and verify if the algorithm still works
if (val != 0)
{
const bool is_inside_map = map_r.is_p_inside(adj_p);
const int adj_val = is_inside_map ?
flood_buffer[idx2(adj_p, map_dims.y)] : 0;
// Mark this as a valid travel direction if it's fewer steps
// from the target than the current cell
valid_offsets[i] = adj_val < val;
}
}
// Set the next position to one of the valid offsets - either pick one
// randomly, or iterate over the list and pick the first valid choice.
if (randomize_steps)
{
std::vector<P> adj_p_bucket;
for (size_t i = 0; i < nr_dirs; ++i)
{
if (valid_offsets[i])
{
adj_p_bucket.push_back(p + dirs[i]);
}
}
ASSERT(!adj_p_bucket.empty());
adj_p = rnd::element(adj_p_bucket);
}
else // Do not randomize step choices - iterate over offset list
{
for (size_t i = 0; i < nr_dirs; ++i)
{
if (valid_offsets[i])
{
adj_p = P(p + dirs[i]);
break;
}
}
}
out.push_back(adj_p);
p = adj_p;
} //while
}
void run(const P& p0,
const bool* blocked,
int* out,
const P& map_dims,
int travel_lmt,
const P& p1,
const bool allow_diagonal)
{
std::fill_n(out, map_dims.x * map_dims.y, 0);
// List of positions to travel to
std::vector<P> positions;
// In the worst case we need to visit every position, reserve the elements
positions.reserve(map_dims.x * map_dims.y);
// Instead of removing evaluated positions from the vector, we track which
// index to try next (cheaper than erasing front elements).
size_t next_p_idx = 0;
int val = 0;
bool path_exists = true;
bool is_at_tgt = false;
bool is_stopping_at_tgt = p1.x != -1;
const R bounds(P(1, 1), map_dims - 2);
P p(p0);
const auto& dirs = allow_diagonal ?
dir_utils::dir_list :
dir_utils::cardinal_list;
bool done = false;
while (!done)
{
// "Flood" around the current position, and add those to the list of
// positions to travel to.
for (const P& d : dirs)
{
const P new_p(p + d);
if (
!blocked[idx2(new_p, map_dims.y)] &&
bounds.is_p_inside(new_p) &&
out[idx2(new_p, map_dims.y)] == 0 &&
new_p != p0)
{
val = out[idx2(p, map_dims.y)];
if (travel_lmt == -1 || val < travel_lmt)
{
out[idx2(new_p, map_dims.y)] = val + 1;
}
if (is_stopping_at_tgt && new_p == p1)
{
is_at_tgt = true;
break;
}
if (!is_stopping_at_tgt || !is_at_tgt)
{
positions.push_back(new_p);
}
}
} // Offset loop
if (is_stopping_at_tgt)
{
if (positions.size() == next_p_idx)
{
path_exists = false;
}
if (is_at_tgt || !path_exists)
{
done = true;
}
}
else if (positions.size() == next_p_idx)
{
done = true;
}
if (val == travel_lmt)
{
done = true;
}
if (!is_stopping_at_tgt || !is_at_tgt)
{
if (positions.size() == next_p_idx)
{
// No more positions to evaluate
path_exists = false;
}
else // There are more positions to evaluate
{
p = positions[next_p_idx];
++next_p_idx;
}
}
} // while
}
virtual value_type front() const { return std::make_pair(l.front(), r.front()); }
virtual void popFront() {
do {
r.popFront();
} while (!r.empty() && !p(r.front()));
}
RangeFilter(const R &_r, const P &_p) : r(_r), p(_p) {
if (!r.empty() && !p(r.front())) {
this->popFront();
}
}
virtual void popFront() {
if (!l.empty())
l.popFront();
else
r.popFront();
}
virtual value_type front() const {
if (!l.empty())
return l.front();
else
return r.front();
}
virtual bool empty() const { return l.empty() && r.empty(); }
virtual void popFront() {
l.popFront();
r.popFront();
}
inline void storeLinkImpl(Links<A> & cont) const
{
cont.push_back(ConditionJumpLink<A, true>(pred_, r_.getContentsSize(), r_.getLinksSize() + 1));
r_.storeLink(cont);
cont.push_back(JumpLink(-r_.getContentsSize(), -r_.getLinksSize() - 2));
}
void run(const P& p0,
const P& p1,
const bool blocked[map_w][map_h],
std::vector<P>& out,
const bool allow_diagonal,
const bool randomize_steps)
{
out.clear();
if (p0 == p1)
{
// Origin and target is same cell
return;
}
int flood_buffer[map_w][map_h];
floodfill::run(p0,
blocked,
flood_buffer,
-1,
p1,
allow_diagonal);
if (flood_buffer[p1.x][p1.y] == 0)
{
// No path exists
return;
}
const std::vector<P>& dirs = allow_diagonal ?
dir_utils::dir_list :
dir_utils::cardinal_list;
const size_t nr_dirs = dirs.size();
// Corresponds to the elements in "dirs"
std::vector<bool> valid_offsets(nr_dirs, false);
// The path length will be equal to the flood value at the target cell, so
// we can reserve that many elements beforehand.
out.reserve(flood_buffer[p1.x][p1.y]);
// We start at the target cell
P p(p1);
out.push_back(p);
const R map_r(P(0, 0), P(map_w, map_h) - 1);
while (true)
{
const int current_val = flood_buffer[p.x][p.y];
P adj_p;
// Find valid offsets, and check if origin is reached
for (size_t i = 0; i < nr_dirs; ++i)
{
const P& d(dirs[i]);
adj_p = p + d;
if (adj_p == p0)
{
// Origin reached
return;
}
if (map_r.is_p_inside(adj_p))
{
const int adj_val = flood_buffer[adj_p.x][adj_p.y];
// Mark this as a valid travel direction if it is not blocked,
// and is fewer steps from the target than the current cell.
valid_offsets[i] =
(adj_val != 0) &&
(adj_val < current_val);
}
}
// Set the next position to one of the valid offsets - either pick one
// randomly, or iterate over the list and pick the first valid choice.
if (randomize_steps)
{
std::vector<P> adj_p_bucket;
for (size_t i = 0; i < nr_dirs; ++i)
{
if (valid_offsets[i])
{
adj_p_bucket.push_back(p + dirs[i]);
}
}
ASSERT(!adj_p_bucket.empty());
adj_p = rnd::element(adj_p_bucket);
}
else // Do not randomize step choices - iterate over offset list
{
for (size_t i = 0; i < nr_dirs; ++i)
{
if (valid_offsets[i])
{
adj_p = P(p + dirs[i]);
break;
}
}
}
out.push_back(adj_p);
p = adj_p;
} // while
}
virtual value_type front() const {
return r.front();
}