[boost] [units] dimensionless specialization

From: Matthias Schabel (boost_at_[hidden])
Date: 2007-04-05 13:00:00

Steven raised some good points about the dimensionless  
specializations of quantities. The crux of the problem is that  
sometimes we would like to be able to specify a formally  
dimensionless quantity as a heterogeneous quantity : e.g.  
1.0*CGS::dyne/SI::newton. If we automatically convert, we lose the  
ability to represent quantities like this and all dimensionless  
quantities become equivalent. However, in some cases you would like  
to preserve the information on the unit system; for trig functions,  
as an example, you would like to have closure so that

acos(cos(quantity<some_angular_unit,Y>))

returns the argument passed to cos. If system information is  
stripped, this becomes impossible without explicitly specifying the  
return type of acos. Furthermore, now we can't represent  
dimensionless quantities for which conversion factors haven't been  
defined. Now, if we preserve this capability, the system resulting  
from a dimensionless unit such as 1.5*CGS::dyne/SI::newton becomes  
ambiguous - should it be an SI dimensionless quantity or a CGS  
dimensionless quantity. So, even though it is a bit ugly, I think  
Steven is right that users will just need to explicitly cast  
heterogeneous dimensionless quantities to homogeneous ones which are  
well-defined and convertible to the underlying value_type...

1.0*CGS::dyne/SI::newton -> quantity< unit<dimensionless_type,[mixed  
CGS/SI system]> >, not convertible to double
quantity<SI::dimensionless>(1.0*CGS::dyne/SI::newton) -> convertible  
to double

At least this is consistent with the treatment of heterogeneous units  
(which will be better documented any time now...) throughout the  
remainder of the library...

Matthias