C++ class to represent real numbers in the log domain

logval.h

#ifndef LOGVAL_H_
#define LOGVAL_H_

// represent values internally in the log domain (much larger effective range than float,
// double, or long double). useful for very small probabilities or very large unnormalized
// probabilities while avoiding underflows/overflows.
//
// this should be used as if it were a double or float, i.e. for doubles a and b:
//     a * b = LogVal(a) * LogVal(b)
//     a + b = LogVal(a) + LogVal(b)
//
// Placed by Chris Dyer <[email protected]> in the public domain on April 16, 2012.
//

#include <iostream>
#include <cstdlib>
#include <cmath>
#include <limits>
#include <cassert>

template <class T>
class LogVal {
 public:
  typedef LogVal<T> Self;

  LogVal() : s_(), v_(std::log(T())) {}
  LogVal(double x) : s_(std::signbit(x)), v_(s_ ? std::log(-x) : std::log(x)) {}
  const Self& operator=(double x) { s_ = std::signbit(x); v_ = s_ ? std::log(-x) : std::log(x); return *this; }
  LogVal(double lnx,bool sign) : s_(sign),v_(lnx) {}
  static Self exp(T lnx) { return Self(lnx,false); }

  static Self One() { return Self(1); }
  static Self Zero() { return Self(); }
  static Self e() { return Self(1,false); }
  void logeq(const T& v) { s_ = false; v_ = v; }

  // true is negative, false is positive
  bool signbit() const {
    return s_;
  }

  Self& operator+=(const Self& a) {
    if (a == Zero()) 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& operator*=(const Self& a) {
    s_ = (s_ != a.s_);
    v_ += a.v_;
    return *this;
  }

  Self& operator/=(const Self& a) {
    s_ = (s_ != a.s_);
    v_ -= a.v_;
    return *this;
  }

  Self& operator-=(const Self& a) {
    Self b = a;
    b.negate();
    return *this += b;
  }

  friend Self abslog(Self x) {
    if (x.v_<0) x.v_=-x.v_;
    return x;
  }

  Self& poweq(const T& power) {
    if (s_) {
      std::cerr << "poweq(T) not implemented when s_ is true\n";
      std::abort();
    } else
      v_ *= power;
    return *this;
  }

  //remember, s_ means negative.
  inline bool lt(Self const& o) const {
    return s_==o.s_ ? v_ < o.v_ : s_ > o.s_;
  }
  inline bool gt(Self const& o) const {
    return s_==o.s_ ? o.v_ < v_ : s_ < o.s_;
  }

  Self operator-() const {
    return Self(v_,!s_);
  }
  void negate() { s_ = !s_; }

  Self inverse() const { return Self(-v_,s_); }

  Self pow(const T& power) const {
    Self res = *this;
    res.poweq(power);
    return res;
  }

  Self root(const T& root) const {
    return pow(1/root);
  }

  T as_float() const {
    if (s_) return -std::exp(v_); else return std::exp(v_);
  }

  bool s_;
  T v_;
};

template <class T>
inline std::ostream& operator<<(std::ostream& os, const LogVal<T>& v) {
  if (v.s_) os<<"(-)";
  return os<<v.v_;
}

template<class T>
LogVal<T> operator+(LogVal<T> o1, const LogVal<T>& o2) {
  o1 += o2;
  return o1;
}

template<class T>
LogVal<T> operator*(LogVal<T> o1, const LogVal<T>& o2) {
  o1 *= o2;
  return o1;
}

template<class T>
LogVal<T> operator/(LogVal<T> o1, const LogVal<T>& o2) {
  o1 /= o2;
  return o1;
}

template<class T>
LogVal<T> operator-(LogVal<T> o1, const LogVal<T>& o2) {
  o1 -= o2;
  return o1;
}

template<class T>
T log(const LogVal<T>& o) {
  if (o.s_) return log(-1.0);
  return o.v_;
}

template<class T>
inline bool signbit(const LogVal<T>& x) { return x.signbit(); }

template<class T>
inline LogVal<T> abs(const LogVal<T>& o) {
  if (o.s_) {
    LogVal<T> res = o;
    res.s_ = false;
    return res;
  } else { return o; }
}

template <class T>
inline LogVal<T> pow(const LogVal<T>& b, const T& e) {
  return b.pow(e);
}

template <class T>
bool operator==(const LogVal<T>& lhs, const LogVal<T>& rhs) {
  return (lhs.v_ == rhs.v_) && (lhs.s_ == rhs.s_);
}

template <class T>
bool operator!=(const LogVal<T>& lhs, const LogVal<T>& rhs) {
  return !(lhs == rhs);
}

template <class T>
bool operator<(const LogVal<T>& lhs, const LogVal<T>& rhs) {
  if (lhs.s_ == rhs.s_) {
    return (lhs.v_ < rhs.v_);
  } else {
    return lhs.s_ > rhs.s_;
  }
}

template <class T>
bool operator<=(const LogVal<T>& lhs, const LogVal<T>& rhs) {
  return (lhs < rhs) || (lhs == rhs);
}

template <class T>
bool operator>(const LogVal<T>& lhs, const LogVal<T>& rhs) {
  return !(lhs <= rhs);
}

template <class T>
bool operator>=(const LogVal<T>& lhs, const LogVal<T>& rhs) {
  return !(lhs < rhs);
}

#endif