Re: [boost] Re: new compile-time dimensional analysis and unitlibrary

From: Walter Landry (wlandry_at_[hidden])
Date: 2003-12-10 17:59:38

Matthias Schabel <boost_at_[hidden]> wrote:
> >>> Two questions:
> >>> 1) What about something like Radians? I.e.: not strictly a physical
> >>> dimension, yet which under normal circumstances should not be used
> >>> like
> >>>  x = 5 radians;
> >>>  y = sin(x) + x; //>:-0
> >
> > Maybe it is just me, but radians and steradians are really just
> > numbers.  The example above is a completely reasonable thing to do.
> > The equation (y=sin(x) + x ) is a textbook example for minimization
> > problems
> 
> I guess I'd consider them to be dimensionless quantities, which are a  
> slightly
> different animal - they are actually dimensionless ratios of  
> length/length and
> area/area, respectively.  You're completely right that the example  
> equation Dan
> came up is well posed, but I can envision wanting to be able to track  
> angular
> units in trig/inverse trig functions (as well as other places - :
> 
> template<class Y,
>           class Model>
> DimensionedQuantity<Y,DimensionedUnit<Model,dimensionless_type> >
> sin(const DimensionedQuantity<Y,DimensionedUnit<Model,angle_type> >&  
> theta)
> {
>      return  
> std::sin(DimensionedQuantity<Y,DimensionedUnit<SIModel,angle_type>  
>  >(theta).value());
> }
> 
> template<class Y,
>           class Model>
> DimensionedQuantity<Y,DimensionedUnit<Model,angle_type> >
> asin(const  
> DimensionedQuantity<Y,DimensionedUnit<Model,dimensionless_type> >& val)
> {
>      const DimensionedQuantity<Y,DimensionedUnit<SIModel,angle_type> >    
> ret(std::asin(val.value()));
> 
>      return DimensionedQuantity<Y,DimensionedUnit<Model,angle_type>  
>  >(ret);
> }
> 
> and then call it as you'd expect, getting the benefits of dimension  
> verification :
> 
>      // test some trig stuff
>      SI<double>::Angle                   theta = 0.375*_radians;
>      SI<double>::Dimensionless   sin_theta = sin(theta);
>      SI<double>::Angle                   thetap = asin(sin_theta);
> 
>      double  tmp = sin_theta;
> 
>      std::cout << theta << std::endl
>                << sin_theta << std::endl
>                << thetap << std::endl;

You want to redefine the trig functions to only take SI<double>::Angle
units?  The trig functions don't take things with units, they take
numbers.  It is completely reasonable and common to take sin(A/B),
where A and B both have the same units.  You would require people to
write sin(radians *A/B), which is just wrong.

> > Degrees and gradians, on the other hand, definitly have units.
> 
> Of what?  They're just alternative ways of measuring the same thing :  
> distance along an arc of a
> circle relative to that circle's perimeter.  Degrees just define the  
> unit circle to have a circumferance of
> 360 instead of 2 pi...

You don't normally put degrees or gradians into a Taylor series.  You
do that all the time with radians.  It is true that you can convert a
degree to a radian, but you can also convert a centimeter to a second
using the rather common conversion factor of the speed of light.

Regards,
Walter Landry
wlandry_at_[hidden]