Re: [boost] [Boost.FixedPoint] Choose notation

Subject: Re: [boost] [Boost.FixedPoint] Choose notation
From: Michael Marcin (mike.marcin_at_[hidden])
Date: 2013-04-29 14:56:21

On 4/29/2013 12:18 PM, Vicente Botet wrote:
> No, this is not solved by implicit/explicit conversion, but using closed
> arithmetic. That is
>
> fixed<8>* fixed<8>-> fixed<8>
>
> The C++1y proposal uses open arithmetic and
>
> fixed<8>* fixed<8>-> fixed<16>
>
> Using closed arithmetic the user must explicitly convert to the desired
> result
>
> fixed<8> a;
> fixed<16> b = fixed<16>(a) * fixed<16>(a);

Whenever possible fixed-point multiply is done in a larger temporary 
then scaled back down. If you can't use a larger internal type it 
becomes much more complicated and takes many more instructions to do the 
operation.

I don't see how this explicit conversion of the operands helps. You've 
gone from needing a 32bit internal type to a 64bit internal type.

If you promote on multiply things get out of hand pretty quickly when 
you chain operations writing natural code.

fixed<16,16> a;
auto b = a*a*a*a;

b is a 128bit fixed<64,64>

There is a middle ground solution whereby:
a*a -> promoted_fixed<32,32>

so a*a*a*a would be:
fixed<16,16> * fixed<16,16> -> promoted_fixed<32,32>
promoted_fixed<32,32> * fixed<16,16> -> promoted_fixed<32,32>
promoted_fixed<32,32> * fixed<16,16> -> promoted_fixed<32,32>

Then do the scaling down only at the end.
fixed<16,16> b = a*a*a*a;
Unfortunately auto no longer does the intuitive thing here, but there is 
precedence for that in the language.

This is what I've chosen in the past.