Re: Trigonometric operations on x86 and x64 CPUs

[already5chosen@yahoo.com]

On Tuesday, December 20, 2016 at 1:11:26 AM UTC+2, Randy Brukardt wrote:
> <already5chosen@yahoo.com> wrote in message 
> news:a6734b29-5ffc-4938-bbc2-453f7ae92325@googlegroups.com...
> ...
> >> Creating a package which does the range reduction right, and passes
> >> small values through to the hardware instructions is not all that hard.
> >
> >Such implementations are common, due the hype created by sensationalists.
> 
> Yeah, like the people at Intel who document how to use these instructions. 
> :-) 
> They recommend (at least in the documents I have seen) to do argument 
> reduction before using the instructions.
> 

I don't know what documents you had seen.
In "Intel 64 and IA-32 Architectures Software Developer’s Manual" Intel recommend to use argument reduction when the argument is out of supported range [-2**63..+2**63].
Of course trigs with double precision argument outside of range [-2**54..+2**54] are no more than equivalents of bad PRNG, so Intel's advice does not have a lot of practical significance.
IMHO, for x outside of [-2**63..+2**63] it would be o.k. for sin(x) and cos(x) to return any value in range [-1..1]. They are all equally meaningless.

> There's also the little matter of meeting the Ada language requirements. The 
> people who put accuracy requirements on Ada numeric libraries might have 
> been "sensationalists"", but those of us implementing Ada have to abide by 
> those requirements. 

Unfortunately, I don't know where to look for Ada language requirement.
Can you tell me what are requirements for sin/cos in Ada numeric library?

> (Argubly, one of the advantages of Ada is that there are 
> requirements, so you have some asssurance out of the box that the numerics 
> will work predicably, no matter what target you use.)
> 
>                                  Randy.

Yes, before IEEE-754 that was a significant advantage*.
Today - less so.

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* - I wonder what happened in real world on machines with bad arithmetic, like CRAY-1? Did not it lead to situation where significant parts of Ada numeric library were so slow that users concerned with speed were rolling their own alternatives.