How to represent a mathematical domain in IR? - c++

Question

I would like to define an object representing a mathematical domain from a list of constraints, but I don't have a clear idea on how to do that.
For example, I start from IR and I have the following constraints :
x > 0
x is not in ]3,5]
x is not in [7,12[
Then, my domain is ]0,3] U ]5,7[ U [12,+oo .
How can I nicely store that in a C++ structure ? Have you ever did that before ? Moreover, I want to be able to check easilly if the domain is empty.

Answer 1

Unless you want to use "3rd party" tools like mentioned in the coments, you'll have to write your own Interval class.
To do this, you can do something like this:
class Interval{
struct Range{
bool leftInclusive, rightInclusive;
double left, right;
bool operator<(Range other){return left<other.left;}
}
std::Set<Range> trueRanges;
void addTrueRange(Range r){
//check for overlaps
//merge if overlapping
//otherwise add to trueRanges
}
bool trueAt(double at){
//find the range with the highest left-bound lower than at
auto candidate = truethRanges.upper_bound(at);
if(candidate == trueRanged.end()) return false; // no range found
//on-point checking here
if(at <= candidate->left) return false;
if(at >= candidate->right) return false;
return true;
}
}
The on-point checking is left out here because you cannot simply say doubleOne == doubleTwo because this mitght result in false negatives. So you have to say ABS(doubleOne-doubleTwo) < tinyValue.
For looking for overlaps you can have a look at this.

Answer 2

Answering my own question.
Actually, I followed the idea of sbabbi using a list of intervals coming from boost/numeric/interval, representing the union of intervals.
Here is an example :
typedef boost::numeric::interval_lib::rounded_math<double> RoundedPolicy;
typedef boost::numeric::interval_lib::checking_base<double> CheckingPolicy;
typedef boost::numeric::interval_lib::policies<RoundedPolicy,CheckingPolicy> IntervalPolicies;
typedef boost::numeric::interval<double,IntervalPolicies> interval;
//...
bool is_interval_empty(const interval& inter)
{
return boost::numeric::empty(inter);
}
void restrict(interval& domain, const interval& inter)
{
for(std::list<interval>::iterator it = domain.begin(); it != domain.end(); ++it)
*it = boost::numeric::intersect(*it, inter);
domain.remove_if(is_interval_empty);
}
void restrict(interval& domain, const interval& inter1, const interval& inter2)
{
for(std::list<interval>::iterator it = domain.begin(); it != domain.end(); ++it)
{
domain.push_front(boost::numeric::intersect(*it, inter1));
*it = boost::numeric::intersect(*it, inter2);
}
domain.remove_if(is_interval_empty);
}
//...
std::list<interval> domain;
for(unsigned long int i = 0; i < constraints.size(); ++i)
{
if(constraints[i].is_lower_bound())
{
interval restriction(constraints[i].get_lower_bound(), std::numeric_limits<double>::infinity());
restrict(domain, restriction);
}
else if(constraints[i].is_upper_bound())
{
interval restriction(-std::numeric_limits<double>::infinity(), constraints[i].get_upper_bound());
restrict(domain, restriction);
}
else if(constraints[i].is_forbidden_range())
{
interval restriction1(-std::numeric_limits<double>::infinity(), constraints[i].get_lower_bound());
interval restriction2(constraints[i].get_upper_bound(), std::numeric_limits<double>::infinity());
restrict(domain, restriction1, restriction2);
}
}
if(domain.size() == 0)
std::cout << "empty domain" << std::endl;
else
std::cout << "the domain exists" << std::endl;