[Cuis-dev] Documentation for the different kinds of divisions

[Andres Valloud]

Theoretically it should be possible to reduce the argument of cos to an 
argument to sin between +/- pi / 4 (but it gets more complicated than 
that), then adjusting things via symmetries.  But really it should be a 
primitive.

On 5/25/20 16:35, Andres Valloud via Cuis-dev wrote:
> Hi,
> 
>> It is also the implementation in Cuis :( . I guess we need a new 
>> primitive right? Maybe some simple math trick could give us the 
>> correct result?
> 
> OMG :facepalm:.  Yeah, that's bad.  The only correct way is to write a 
> primitive (other than implementing the C library in Smalltalk).
> 
> Not only you lose ulps that way, also some results will become zero when 
> they shouldn't.  Plus, there is the issue of argument reduction.
> 
>> Still, it is not obvious to me. How far is this from the correct result?
> 
> Without properly massaging the arguments given to trigonometric 
> transcendentals, and without knowing what is really going on, you can 
> get a mantissa consisting of 15 leading non-zero bits, followed by 38 
> zero bits.
> 
> This is why *nobody* should be using the x87 anymore, and for the sake 
> of compatibility the best way is to delegate to some base math library 
> that everybody else uses (because then you get the optimized numerical 
> algorithm that will cause your answers to match their answers, and then 
> you have sanity).  Unless of course you want to reimplement all of that 
> from scratch, and then Gilad's arguments start rising over the horizon 
> unless you have very good reasons.
> 
> Andres.