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#ifndef MAX_PLUS_H_
#define MAX_PLUS_H_
#include
// max-plus algebra. ordering a > b really means that (i.e. default a<b sorting will do worst (closest to 0) first. so get used to passing predicates like std::greater<MaxPlus<T> > around
// x+y := max{x,y}
// x*y := x+y
// 0 := -inf
// 1 := 0
// additive inverse does not, but mult. does. (inverse()) and x/y := x-y = x+y.inverse()
//WARNING: default order is reversed, on purpose, i.e. a<b means a "better than" b, i.e. log(p_a)>log(p_b). sorry. defaults in libs are to order ascending, but we want best first.
#include <boost/functional/hash.hpp>
#include <iostream>
#include <cstdlib>
#include <cmath>
#include <limits>
#include "semiring.h"
#define TROPICAL_DEBUG(x)
#undef LOGVAL_LOG0
#define LOGVAL_LOG0 -std::numeric_limits<T>::infinity()
template <class T>
class MaxPlus {
public:
typedef MaxPlus<T> Self;
MaxPlus() : v_(LOGVAL_LOG0) {}
explicit MaxPlus(double x) : v_(std::log(x)) {}
MaxPlus(init_1) : v_(0) { }
MaxPlus(init_0) : v_(LOGVAL_LOG0) { }
MaxPlus(int x) : v_(std::log(x)) {}
MaxPlus(unsigned x) : v_(std::log(x)) { }
MaxPlus(double lnx,bool sign) : v_(lnx) { TROPICAL_DEBUG(assert(!sign)); }
MaxPlus(double lnx,init_lnx) : v_(lnx) {}
static Self exp(T lnx) { return MaxPlus(lnx,false); }
// maybe the below are faster than == 1 and == 0. i don't know.
bool is_1() const { return v_==0; }
bool is_0() const { return v_==LOGVAL_LOG0; }
static Self One() { return Self(init_1()); }
static Self Zero() { return Self(init_0()); }
static Self e() { return Self(1,false); }
void logeq(const T& v) { v_ = v; }
bool signbit() const { return false; }
std::size_t hash_impl() const {
using namespace boost;
return hash_value(v_);
}
Self& logpluseq(const Self& a) {
if (a.is_0()) return *this;
if (a.s_ == s_) {
if (a.v_ < v_) {
v_ = v_ + log1p(std::exp(a.v_ - v_));
} else {
v_ = a.v_ + log1p(std::exp(v_ - a.v_));
}
} else {
if (a.v_ < v_) {
v_ = v_ + log1p(-std::exp(a.v_ - v_));
} else {
v_ = a.v_ + log1p(-std::exp(v_ - a.v_));
s_ = !s_;
}
}
return *this;
}
Self& besteq(const Self& a) {
if (a.v_ < v_)
v_=a.v_;
return *this;
}
Self& operator+=(const Self& a) {
if (a.v_ < v_)
v_=a.v_;
return *this;
}
Self& operator*=(const Self& a) {
v_ += a.v_;
return *this;
}
Self& operator/=(const Self& a) {
v_ -= a.v_;
return *this;
}
// Self(fabs(log(x)),x.s_)
friend Self abslog(Self x) {
if (x.v_<0) x.v_=-x.v_;
return x;
}
Self& poweq(const T& power) {
v_ *= power;
return *this;
}
Self inverse() const {
return Self(-v_,false);
}
Self pow(const T& power) const {
Self res = *this;
res.poweq(power);
return res;
}
Self root(const T& root) const {
return pow(1/root);
}
// copy elision - as opposed to explicit copy of Self const& o1, we should be able to construct Logval r=a+(b+c) as a single result in place in r. todo: return std::move(o1) - C++0x
friend inline operator+(Self a,Self const& b) {
a+=b;
return a;
}
friend inline operator*(Self a,Self const& b) {
a*=b;
return a;
}
friend inline operator/(Self a,Self const& b) {
a/=b;
return a;
}
friend inline T log(Self const& a) {
return a.v_;
}
friend inline T pow(Self const& a,T const& e) {
return a.pow(e);
}
// intentionally not defining an operator < or operator > - because you may want to default (for library convenience) a<b means a better than b (i.e. gt)
inline bool lt(Self const& o) const {
return v_<o.v_;
}
inline bool gt(Self const& o) const {
return o.v_<v_;
}
friend inline bool operator==(Self const& lhs, Self const&rhs) {
return lhs.v_ == rhs.v_;
}
friend inline bool operator!=(Self const& lhs, Self const&rhs) {
return lhs.v_ != rhs.v_;
}
/*
operator T() const {
return std::exp(v_);
}
*/
T as_float() const {
return std::exp(v_);
}
T v_;
};
template <class T>
struct semiring_traits<MaxPlus<T> > : default_semiring_traits<MaxPlus<T> > {
static const bool has_logplus=true;
static const bool has_besteq=true;
};
template <class T>
#if 0
template <class T>
bool operator<=(const MaxPlus<T>& lhs, const MaxPlus<T>& rhs) {
return (lhs.v_ <= rhs.v_);
}
template <class T>
bool operator>(const MaxPlus<T>& lhs, const MaxPlus<T>& rhs) {
return (lhs.v_ > rhs.v_);
}
template <class T>
bool operator>=(const MaxPlus<T>& lhs, const MaxPlus<T>& rhs) {
return (lhs.v_ >= rhs.v_);
}
#endif
template <class T>
std::size_t hash_value(const MaxPlus<T>& x) { return x.hash_impl(); }
template <class T>
bool operator==(const MaxPlus<T>& lhs, const MaxPlus<T>& rhs) {
return (lhs.v_ == rhs.v_) && (lhs.s_ == rhs.s_);
}
template <class T>
bool operator!=(const MaxPlus<T>& lhs, const MaxPlus<T>& rhs) {
return !(lhs == rhs);
}
#endif
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