[libre-riscv-dev] [isa-dev] Re: FP transcendentals (trigonometry, root/exp/log) proposal

[Luke Kenneth Casson Leighton]

On Thursday, January 16, 2020, Jacob Lifshay <programmerjake at gmail.com>
wrote:

> On Thu, Jan 16, 2020, 01:22 Luke Kenneth Casson Leighton <lkcl at lkcl.net>
> wrote:
>
> > On Thursday, January 16, 2020, <whygee at f-cpu.org> wrote:
> >
> > > On 2020-01-16 04:04, lkcl . wrote:
> >
> >
> >
> > > the time (let alone rounding).  how do you *know* when the rounding (or
> > the
> > >> last bit of the mantissa) is wrong?
> > >>
> > >
> > > That was my reaction :
> > > if you *know* your LSB is wrong then you can correct it...
> >
> >
> > ... or can you? this is what i'm fascinated to hear about, mitch.
> >
> > is there some mathematical way in which the accuracy can be computed yet
> > the effort not known?
> >
>
> Yes. you just compute the output to a few more bits where the output is
> known to always be within a certain distance of the correct output,


sorry to be sounding dumb: the question thus becomes, "how do you know when
the output is always within a cer... etc etc " :)


Newton Raphson is basically useless for functions like sin or cos, since
> you have to compute the inverse function (asin or acos) to a higher
> accuracy which takes even more work than just computing the function to
> enough accuracy in the first place.


oh whoops. oh yes.

l.



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