Tropical algebra overloading: Difference between revisions
C++ implementation
(Corrected error in distribution computation. Added borrowed operator `==`.) |
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5 (X) ( 8 (+) 7 ) = 5 (X) 8 (+) 5 (X) 7 is TRUE
</pre>
=={{header|C++}}==
<lang cpp>#include <iostream>
#include <optional>
using namespace std;
class TropicalAlgebra
{
// use an unset std::optional to represent -infinity
optional<double> m_value;
public:
friend std::ostream& operator<<(std::ostream&, const TropicalAlgebra&);
friend TropicalAlgebra pow(const TropicalAlgebra& base, unsigned int exponent) noexcept;
// create a point that is initialized to -infinity
TropicalAlgebra() = default;
// construct with a value
explicit TropicalAlgebra(double value) noexcept
: m_value{value} {}
// add a value to this one ( p+=q ). it is common to also overload
// the += operator when overloading +
TropicalAlgebra& operator+=(const TropicalAlgebra& rhs) noexcept
{
if(!m_value)
{
// this point is -infinity so the other point is max
*this = rhs;
}
else if (!rhs.m_value)
{
// since rhs is -infinity this point is max
}
else
{
// both values are valid, find the max
*m_value = max(*rhs.m_value, *m_value);
}
return *this;
}
// multiply this value by another (p *= q)
TropicalAlgebra& operator*=(const TropicalAlgebra& rhs) noexcept
{
if(!m_value)
{
// since this value is -infinity this point does not need to be
// modified
}
else if (!rhs.m_value)
{
// the other point is -infinity, make this -infinity too
*this = rhs;
}
else
{
*m_value += *rhs.m_value;
}
return *this;
}
};
// add values (p + q)
inline TropicalAlgebra operator+(TropicalAlgebra lhs, const TropicalAlgebra& rhs) noexcept
{
// implemented using the += operator defined above
lhs += rhs;
return lhs;
}
// multiply values (p * q)
inline TropicalAlgebra operator*(TropicalAlgebra lhs, const TropicalAlgebra& rhs) noexcept
{
lhs *= rhs;
return lhs;
}
// pow is the idomatic way for exponentiation in C++
inline TropicalAlgebra pow(const TropicalAlgebra& base, unsigned int exponent) noexcept
{
auto result = base;
for(unsigned int i = 1; i < exponent; i++)
{
// compute the power by successive multiplication
result *= base;
}
return result;
}
// print the point
ostream& operator<<(ostream& os, const TropicalAlgebra& pt)
{
if(!pt.m_value) cout << "-Inf\n";
else cout << *pt.m_value << "\n";
return os;
}
int main(void) {
const TropicalAlgebra a(-2);
const TropicalAlgebra b(-1);
const TropicalAlgebra c(-0.5);
const TropicalAlgebra d(-0.001);
const TropicalAlgebra e(0);
const TropicalAlgebra h(1.5);
const TropicalAlgebra i(2);
const TropicalAlgebra j(5);
const TropicalAlgebra k(7);
const TropicalAlgebra l(8);
const TropicalAlgebra m; // -Inf
cout << "2 * -2 == " << i * a;
cout << "-0.001 + -Inf == " << d + m;
cout << "0 * -Inf == " << e * m;
cout << "1.5 + -1 == " << h + b;
cout << "-0.5 * 0 == " << c * e;
cout << "pow(5, 7) == " << pow(j, 7);
cout << "5 * (8 + 7)) == " << j * (l + k);
cout << "5 * 8 + 5 * 7 == " << j * l + j * k;
}
</lang>
{{out}}
<pre>
2 * -2 == 0
-0.001 + -Inf == -0.001
0 * -Inf == -Inf
1.5 + -1 == 1.5
-0.5 * 0 == -0.5
pow(5, 7) == 35
5 * (8 + 7)) == 13
5 * 8 + 5 * 7 == 13
</pre>
=={{header|Factor}}==
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