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Re: Document libm accuracy goals

On Thu, 28 Nov 2013, Carlos O'Donell wrote:

> Could you please add an entry to the FAQ for the libm goals and
> specifically call out monotonicity?

> > +@item
> > +For the IBM @code{long double} format, as used on PowerPC GNU/Linux,
> Is it sufficient to say "PowerPC GNU/Linux" when we mean both the 32-bit
> and 64-bit runtimes?

I think so.  If a future update to ELFv2 moves 64-bit LE away from IBM 
long double, this text could always be changed then.

> > +@item
> > +@Theglibc{} does not aim for functions to satisfy other properties of
> > +the underlying mathematical function, such as monotonicity, where not
> > +implied by the above goals.
> Aside from montonicity what other properties might we call out explicitly
> here as things we don't plan to satisfy?

I don't think there are other properties to call out.  For IBM long double 
you have e.g. properties such as sin^2 + cos^2 = 1 - where we don't 
guarantee that sin and cos will do the range reduction the same, and for 
cases that don't fit in 106 bits the range reduction may not be accurate 
(it's not that accurate range reduction for discontiguous mantissas is 
hard, but the code doesn't attempt it).  But I expect that in fact the 
range reduction will be done compatibly for both functions, so that sin^2 
+ cos^2 = 1 to high precision even if the sin and cos values relate to 
some argument other than the exact input.

Joseph S. Myers

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