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Date: Tue, 14 May 2002 14:52:58 -0400
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Preben Randhol wrote:
>>As a chemist I want mol and Kelvin, but how do one deal with
>>constructions like this:
>>
>>Constant = (C1*C2)/(C3^0.5)  = mol�/mol^0.5 = mol^(3/2)

Time for me to bring up my usual post about units in C++,
which can be done with complete type safety and with no
run-time overhead in time or storage, because of C++'s
automatic instantiation rules. Here's the simplified
example involving only mass, distance, and time. The code
allows only like units to be added or subtracted, but
arbitrary units to be multiplied or divided, with the
correctly typed result. Constants are units with all
paremeters set to zero. All the verbiage is for types;
the actual storage for each unit object is just the
value, and all type correctness is checked at compile
time, not run time. The correctly typed operators are
automatically instantiated when used, without manual
intervention.

I first saw this idiom in _Scientific and Engineering C++_
by Bartion & Nackman.

template<typename RepType, int Mass, int Distance, int Time>
struct Unit
{
	RepType value;
	explicit Unit(value) : value(value) { }
	Unit operator+(Unit other)
	{ return Unit(value + other.value); }
	Unit operator-(Unit other)
	{ return Unit(value - other.value); }
};

template<typename RepType,
	 int MassL, int DistanceL, int TimeL,
	 int MassR, int DistanceR, int TimeR>
Unit<RepType,
      MassL + MassR,
      DistanceL + DistanceR,
      TimeL + TimeR>
operator*(Unit<RepType, MassL, DistanceL, TimeL> l,
	  Unit<RepType, MassR, DistanceR, TimeR> r)
{
	return Unit<RepType,
		    MassL + MassR,
		    DistanceL + DistanceR,
		    TimeL + TimeR>(l.value * r.value);
}

template<typename RepType,
	 int MassL, int DistanceL, int TimeL,
	 int MassR, int DistanceR, int TimeR>
Unit<RepType,
      MassL - MassR,
      DistanceL - DistanceR,
      TimeL - TimeR>
operator/(Unit<RepType, MassL, DistanceL, TimeL> l,
	  Unit<RepType, MassR, DistanceR, TimeR> r)
{
	return Unit<RepType,
		    MassL - MassR,
		    DistanceL - DistanceR,
		    TimeL - TimeR>(l.value / r.value);
}

typedef Unit<double, 0, 1, -1> Velocity;
typedef Unit<double, 0, 1, -2> Acceleration;
typedef Unit<double, 1, 2, -2> Energy;
typedef Unit<double, 0, 0, -1> Herz;
// etc.