Re: Radians Or Degrees?

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Sujet : Re: Radians Or Degrees?
De : monnier (at) *nospam* iro.umontreal.ca (Stefan Monnier)
Groupes : comp.lang.c comp.arch
Date : 20. Mar 2024, 18:59:24
Autres entêtes
Organisation : A noiseless patient Spider
Message-ID : <jwvr0g4j1ta.fsf-monnier+comp.arch@gnu.org>
References : 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18
User-Agent : Gnus/5.13 (Gnus v5.13)
The [Rlibm](https://people.cs.rutgers.edu/~sn349/rlibm/) project
claims to get much better performance (basically, in the same
ballpark as not-correctly-rounded implementations).
I had only read the 1st page.
It sounds like they are not particularly interested in IEEE binary64
which appears to be the major point of interest of math libs of
conventional languages.

Indeed, I hoped by now they had attacked the world of 64bit floats, but
it looks like it's not the case yet.  In theory the same idea is
applicable there and should give similar results, but of course it's
harder for two reasons:

- The search space to consider is much larger, making it much more
  costly to do exhaustive testing (and to collect the info they need to
  choose/compute the polynomials).
- You can't cheaply use higher-precision floats for internal computations.

It all depend of what you compare against.
For scalar call for majority of transcendental functions on IEEE-754
list, it's probably very easy to get correctly rounded binary32 results
in approximately the same time as results calculated with max. err of,
say, 0.75 ULP. Especially so if target machine has fast binary64
arithmetic.

IIUC that was not the case before their work: it was "easy" to get the
correct result in 99% of the cases, but covering all 100% of the cases
used to be costly because those few cases needed a lot more
internal precision.

I don't want to pay for correct rounding of transcendental functions.
Neither in speed and especially nor in tables footprint.  Not even a
little.  Because for me there are no advantages.

For that reason, correctly rounded results were nowhere near the menu,
indeed.  But the proposition of Rlibm is that maybe we can have our cake
and eat it too, because (if all goes well) you don't have to pay for it
in speed nor in table size.

I'm hoping that pans out :-)

Now, there are things that I am ready to pay for. E.g. preservation of
mathematical properties of original exact function. I.e. if original is
monotonic on certain interval then I do want at least weak monotonicity
of approximation. If original is even (or odd) I want the same for
approximation. If original never exceed 1, I want the same
for approximation. Etc... But correct rounding is not on the list.

But correct rounding would give you those properties.


        Stefan

Date Sujet#  Auteur
14 Mar 24 * Re: Radians Or Degrees?55Michael S
14 Mar 24 +* Re: Radians Or Degrees?9MitchAlsup1
14 Mar 24 i+* Re: Radians Or Degrees?2MitchAlsup1
15 Mar 24 ii`- Re: Radians Or Degrees?1Terje Mathisen
14 Mar 24 i+* Re: Radians Or Degrees?5Lawrence D'Oliveiro
15 Mar 24 ii+- Re: Radians Or Degrees?1Chris M. Thomasson
15 Mar 24 ii`* Re: Radians Or Degrees?3MitchAlsup1
15 Mar 24 ii `* Re: Radians Or Degrees?2Chris M. Thomasson
15 Mar 24 ii  `- Re: Radians Or Degrees?1Chris M. Thomasson
15 Mar 24 i`- Re: Radians Or Degrees?1Michael S
15 Mar 24 +* Re: Radians Or Degrees?28Terje Mathisen
15 Mar 24 i+* Re: Radians Or Degrees?3Michael S
16 Mar 24 ii`* Re: Radians Or Degrees?2MitchAlsup1
16 Mar 24 ii `- Re: Radians Or Degrees?1Terje Mathisen
15 Mar 24 i`* Re: Radians Or Degrees?24Chris M. Thomasson
15 Mar 24 i +* Re: Radians Or Degrees?2Chris M. Thomasson
16 Mar 24 i i`- Re: Radians Or Degrees?1Chris M. Thomasson
15 Mar 24 i +* Re: Radians Or Degrees?20Keith Thompson
15 Mar 24 i i+* Re: Radians Or Degrees?5Chris M. Thomasson
15 Mar 24 i ii`* Re: Radians Or Degrees?4Chris M. Thomasson
16 Mar 24 i ii `* Re: Radians Or Degrees?3Keith Thompson
17 Mar 24 i ii  `* Re: Radians Or Degrees?2Chris M. Thomasson
18 Mar 24 i ii   `- Re: Radians Or Degrees?1Chris M. Thomasson
16 Mar 24 i i`* Re: Radians Or Degrees?14MitchAlsup1
16 Mar 24 i i `* Re: Radians Or Degrees?13Michael S
16 Mar 24 i i  `* Re: Radians Or Degrees?12MitchAlsup1
16 Mar 24 i i   +- Re: Radians Or Degrees?1Michael S
17 Mar 24 i i   `* Re: Radians Or Degrees?10Keith Thompson
17 Mar 24 i i    +* Re: Radians Or Degrees?5bart
17 Mar 24 i i    i`* Re: Radians Or Degrees?4Keith Thompson
17 Mar 24 i i    i `* Re: Radians Or Degrees?3bart
17 Mar 24 i i    i  `* Re: Radians Or Degrees?2Keith Thompson
17 Mar 24 i i    i   `- Re: Radians Or Degrees?1David Brown
17 Mar 24 i i    `* Re: Radians Or Degrees?4Michael S
17 Mar 24 i i     +- Re: Radians Or Degrees?1Michael S
17 Mar 24 i i     `* Re: Radians Or Degrees?2bart
17 Mar 24 i i      `- Re: Radians Or Degrees?1Michael S
16 Mar 24 i `- Re: Radians Or Degrees?1Chris M. Thomasson
18 Mar 24 `* Re: Radians Or Degrees?17Stefan Monnier
19 Mar 24  `* Re: Radians Or Degrees?16MitchAlsup1
20 Mar 24   `* Re: Radians Or Degrees?15Stefan Monnier
20 Mar 24    +* Re: Radians Or Degrees?11Michael S
20 Mar 24    i+* Re: Radians Or Degrees?6Stefan Monnier
20 Mar 24    ii`* Re: Radians Or Degrees?5MitchAlsup1
21 Mar 24    ii `* Re: Radians Or Degrees?4Terje Mathisen
21 Mar 24    ii  `* Re: Radians Or Degrees?3Michael S
21 Mar 24    ii   +- Re: Radians Or Degrees?1MitchAlsup1
23 Mar 24    ii   `- Re: Radians Or Degrees?1Terje Mathisen
20 Mar 24    i+* Re: Radians Or Degrees?2Steven G. Kargl
20 Mar 24    ii`- Re: Radians Or Degrees?1MitchAlsup1
20 Mar 24    i`* Re: Radians Or Degrees?2MitchAlsup1
21 Mar 24    i `- Re: Radians Or Degrees?1Michael S
20 Mar 24    +* Re: Radians Or Degrees?2MitchAlsup1
20 Mar 24    i`- Re: Radians Or Degrees?1Stefan Monnier
21 Mar 24    `- Re: Radians Or Degrees?1Terje Mathisen

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