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

Subject: Re: [boost] [Boost.FixedPoint] Choose notation
From: Vicente J. Botet Escriba (vicente.botet_at_[hidden])
Date: 2013-04-30 02:13:12

Le 29/04/13 20:56, Michael Marcin a écrit :
> 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>
>
IIUC, your design is there to solve the usual case of having 2 
arguments, but IMO don't works when there are multiple arguments as you 
can loss information here.
Why do you find it is safe to do that?
Why this is better and how it solves the issue?

> Then do the scaling down only at the end.
> fixed<16,16> b = a*a*a*a;
This would not compile on my prototype with open arithmetic and on C++1y 
proposal as there is a possible loss of information. An explicit 
downcast is needed.
> Unfortunately auto no longer does the intuitive thing here, but there 
> is precedence for that in the language.
>
Could you  give us some examples?

Best,
Vicente