accuracy of asinh and atanh

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accuracy of asinh and atanh

Matt Peddie
Hi devs,

I tried to use  asinh :: Double -> Double  and discovered that it's
inaccurate compared to my system library (GNU libm), even returning
-Infinity in place of finite values in the neighborhood of -22 for
large negative arguments.  `atanh` is also inaccurate compared to the
system library.  I wrote up a more detailed description of the problem
including plots in the README file at
https://github.com/peddie/ghc-inverse-hyperbolic -- this repository is
package that can help you examine the error for yourself or generate
the plots, and it also contains accurate pure-Haskell translations of
the system library's implementation for these functions.  What's the
next step to fixing this in GHC?

Cheers

Matt Peddie
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Re: accuracy of asinh and atanh

Edward Kmett-2
Note: From skimming your readme it is worth noting that  log1p _is_ in base now (alongside expm1, log1pexp, and log1mexp). We added them all a couple of years back as a result of the very thread linked in your README.

You need to `import Numeric` to see them, though.

Switching to more accurate functions for doubles and floats for asinh, atanh, etc. to exploit this sort of functionality at least seems to make a lot of sense.

That can be done locally without any user API impact as the current definitions aren't supplied as defaults, merely as pointwise implementations instance by instance. Things will just become more accurate.

In that same spirit, we can probably crib a better version for complex numbers from somewhere as well, as it follows the same general simplistic formula right now, even if it can't be plugged directly into the equations you've given. For that matter, the log1p definition we're using for complex numbers was the best I could come up with, but there may well be a more accurate version you can find down in the mines of libm or another math library written by real analysts.
    log1p x@(a :+ b)
      | abs a < 0.5 && abs b < 0.5
      , u <- 2*a + a*a + b*b = log1p (u/(1 + sqrt(u+1))) :+ atan2 (1 + a) b
      | otherwise = log (1 + x)

So, here's a +1 from the libraries committee side towards improving the situation.

From there, it's a small matter of implementation. 

Here's where I'd usually get Ben involved. Hi Ben!

-Edward

On Sat, Jun 2, 2018 at 1:23 AM, Matt Peddie <[hidden email]> wrote:
Hi devs,

I tried to use  asinh :: Double -> Double  and discovered that it's
inaccurate compared to my system library (GNU libm), even returning
-Infinity in place of finite values in the neighborhood of -22 for
large negative arguments.  `atanh` is also inaccurate compared to the
system library.  I wrote up a more detailed description of the problem
including plots in the README file at
https://github.com/peddie/ghc-inverse-hyperbolic -- this repository is
package that can help you examine the error for yourself or generate
the plots, and it also contains accurate pure-Haskell translations of
the system library's implementation for these functions.  What's the
next step to fixing this in GHC?

Cheers

Matt Peddie
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http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs


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Re: accuracy of asinh and atanh

Ben Gamari-3
Sending again, this time including ghc-devs.

Edward Kmett <[hidden email]> writes:

> Note: From skimming your readme it is worth noting that  log1p _is_ in base
> now (alongside expm1, log1pexp, and log1mexp). We added them all a couple
> of years back as a result of the very thread linked in your README.
>
> You need to `import Numeric` to see them, though.
>
> Switching to more accurate functions for doubles and floats for asinh,
> atanh, etc. to exploit this sort of functionality at least seems to make a
> lot of sense.
>
> That can be done locally without any user API impact as the current
> definitions aren't supplied as defaults, merely as pointwise
> implementations instance by instance. Things will just become more accurate.
>
> In that same spirit, we can probably crib a better version for complex
> numbers from somewhere as well, as it follows the same general simplistic
> formula right now, even if it can't be plugged directly into the equations
> you've given. For that matter, the log1p definition we're using for complex
> numbers was the best I could come up with, but there may well be a more
> accurate version you can find down in the mines of libm or another math
> library written by real analysts.
>
[snip]
>
> So, here's a +1 from the libraries committee side towards improving the
> situation.
>
> From there, it's a small matter of implementation.
>
> Here's where I'd usually get Ben involved. Hi Ben!
>
Hi Edward and Matt!

Indeed the sinh sinh situation should already be improved in 8.6. See
#14927 and GHC commit 3ea33411d7cbf32c20940cc72ca07df6830eeed7. I
suspect this should fix Matt's issue.

Regarding log1p, I'd happily accept patches improving on the status quo.

Cheers,

- Ben

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Re: accuracy of asinh and atanh

George Colpitts
In reply to this post by Matt Peddie
Hello Mat

Just curious, why the preferred solution isn't to call the system math library? As it says in the README you reference below,
  • One good solution would be to always call the system math library for these functions.

Hope this is isn't a stupid question.

Thanks

George





On Sat, Jun 2, 2018 at 2:23 AM Matt Peddie <[hidden email]> wrote:
Hi devs,

I tried to use  asinh :: Double -> Double  and discovered that it's
inaccurate compared to my system library (GNU libm), even returning
-Infinity in place of finite values in the neighborhood of -22 for
large negative arguments.  `atanh` is also inaccurate compared to the
system library.  I wrote up a more detailed description of the problem
including plots in the README file at
https://github.com/peddie/ghc-inverse-hyperbolic -- this repository is
package that can help you examine the error for yourself or generate
the plots, and it also contains accurate pure-Haskell translations of
the system library's implementation for these functions.  What's the
next step to fixing this in GHC?

Cheers

Matt Peddie
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Re: accuracy of asinh and atanh

Matt Peddie
Hi George,

Not a stupid question.  I don't have a single source at hand, but I
think I read in a few places on the wiki that calling out to the
system math library is not an option due to the variety of system math
libraries on the platforms GHC supports.  It'd be great if I got the
wrong impression and this could just be a call to C.  Can anyone set
me straight on this point?

Matt

On Thu, Aug 2, 2018 at 5:13 AM, George Colpitts
<[hidden email]> wrote:

> Hello Mat
>
> Just curious, why the preferred solution isn't to call the system math
> library? As it says in the README you reference below,
>
> One good solution would be to always call the system math library for these
> functions.
>
> Hope this is isn't a stupid question.
>
> Thanks
>
> George
>
>
>
>
>
> On Sat, Jun 2, 2018 at 2:23 AM Matt Peddie <[hidden email]> wrote:
>>
>> Hi devs,
>>
>> I tried to use  asinh :: Double -> Double  and discovered that it's
>> inaccurate compared to my system library (GNU libm), even returning
>> -Infinity in place of finite values in the neighborhood of -22 for
>> large negative arguments.  `atanh` is also inaccurate compared to the
>> system library.  I wrote up a more detailed description of the problem
>> including plots in the README file at
>> https://github.com/peddie/ghc-inverse-hyperbolic -- this repository is
>> package that can help you examine the error for yourself or generate
>> the plots, and it also contains accurate pure-Haskell translations of
>> the system library's implementation for these functions.  What's the
>> next step to fixing this in GHC?
>>
>> Cheers
>>
>> Matt Peddie
>> _______________________________________________
>> ghc-devs mailing list
>> [hidden email]
>> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
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Re: accuracy of asinh and atanh

Ben Gamari-2
Matt Peddie <[hidden email]> writes:

> Hi George,
>
> Not a stupid question.  I don't have a single source at hand, but I
> think I read in a few places on the wiki that calling out to the
> system math library is not an option due to the variety of system math
> libraries on the platforms GHC supports.  It'd be great if I got the
> wrong impression and this could just be a call to C.  Can anyone set
> me straight on this point?
>
Indeed it's not a stupid question at all. Indeed this is precisely what
we do for the simpler transcendentals (e.g. sin, asin, log). We very
well could move in this direction in the case of asinh/atanh as well. I
believe the reason we don't currently is that atanh was only
standardized in C99, which we only started requiring a few releases ago.
Perhaps this is ultimately the right direction.

Cheers,

- Ben

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Re: accuracy of asinh and atanh

Matt Peddie
Thanks, Ben, for chiming in.  I think calling out to C for these
functions is the way to go if it's now feasible.  (Calling out to libm
is the workaround I'm using in the application that led me to discover
the inaccuracy.)

Matt

On Thu, Aug 2, 2018 at 11:33 AM, Ben Gamari <[hidden email]> wrote:

> Matt Peddie <[hidden email]> writes:
>
>> Hi George,
>>
>> Not a stupid question.  I don't have a single source at hand, but I
>> think I read in a few places on the wiki that calling out to the
>> system math library is not an option due to the variety of system math
>> libraries on the platforms GHC supports.  It'd be great if I got the
>> wrong impression and this could just be a call to C.  Can anyone set
>> me straight on this point?
>>
> Indeed it's not a stupid question at all. Indeed this is precisely what
> we do for the simpler transcendentals (e.g. sin, asin, log). We very
> well could move in this direction in the case of asinh/atanh as well. I
> believe the reason we don't currently is that atanh was only
> standardized in C99, which we only started requiring a few releases ago.
> Perhaps this is ultimately the right direction.
>
> Cheers,
>
> - Ben
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Re: accuracy of asinh and atanh

Artem Pelenitsyn
I'd be willing to do this.

--
Best wishes,
Artem

On Thu, 2 Aug 2018, 04:38 Matt Peddie, <[hidden email]> wrote:
Thanks, Ben, for chiming in.  I think calling out to C for these
functions is the way to go if it's now feasible.  (Calling out to libm
is the workaround I'm using in the application that led me to discover
the inaccuracy.)

Matt

On Thu, Aug 2, 2018 at 11:33 AM, Ben Gamari <[hidden email]> wrote:
> Matt Peddie <[hidden email]> writes:
>
>> Hi George,
>>
>> Not a stupid question.  I don't have a single source at hand, but I
>> think I read in a few places on the wiki that calling out to the
>> system math library is not an option due to the variety of system math
>> libraries on the platforms GHC supports.  It'd be great if I got the
>> wrong impression and this could just be a call to C.  Can anyone set
>> me straight on this point?
>>
> Indeed it's not a stupid question at all. Indeed this is precisely what
> we do for the simpler transcendentals (e.g. sin, asin, log). We very
> well could move in this direction in the case of asinh/atanh as well. I
> believe the reason we don't currently is that atanh was only
> standardized in C99, which we only started requiring a few releases ago.
> Perhaps this is ultimately the right direction.
>
> Cheers,
>
> - Ben
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Re: accuracy of asinh and atanh

Artem Pelenitsyn

--
Best, Artem

On Thu, 2 Aug 2018 at 06:26 Artem Pelenitsyn <[hidden email]> wrote:
I'd be willing to do this.

--
Best wishes,
Artem


On Thu, 2 Aug 2018, 04:38 Matt Peddie, <[hidden email]> wrote:
Thanks, Ben, for chiming in.  I think calling out to C for these
functions is the way to go if it's now feasible.  (Calling out to libm
is the workaround I'm using in the application that led me to discover
the inaccuracy.)

Matt

On Thu, Aug 2, 2018 at 11:33 AM, Ben Gamari <[hidden email]> wrote:
> Matt Peddie <[hidden email]> writes:
>
>> Hi George,
>>
>> Not a stupid question.  I don't have a single source at hand, but I
>> think I read in a few places on the wiki that calling out to the
>> system math library is not an option due to the variety of system math
>> libraries on the platforms GHC supports.  It'd be great if I got the
>> wrong impression and this could just be a call to C.  Can anyone set
>> me straight on this point?
>>
> Indeed it's not a stupid question at all. Indeed this is precisely what
> we do for the simpler transcendentals (e.g. sin, asin, log). We very
> well could move in this direction in the case of asinh/atanh as well. I
> believe the reason we don't currently is that atanh was only
> standardized in C99, which we only started requiring a few releases ago.
> Perhaps this is ultimately the right direction.
>
> Cheers,
>
> - Ben
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Re: accuracy of asinh and atanh

David Feuer-2
Wasn't there a very recent commit to improve these functions, by leftaroundabout?

On Thursday, August 2, 2018 8:16:10 AM EDT Artem Pelenitsyn wrote:

> Here is the patch: https://phabricator.haskell.org/D5034
>
> --
> Best, Artem
>
> On Thu, 2 Aug 2018 at 06:26 Artem Pelenitsyn <[hidden email]> wrote:
>
> > I'd be willing to do this.
> >
> > --
> > Best wishes,
> > Artem
> >
> >
> > On Thu, 2 Aug 2018, 04:38 Matt Peddie, <[hidden email]> wrote:
> >
> >> Thanks, Ben, for chiming in.  I think calling out to C for these
> >> functions is the way to go if it's now feasible.  (Calling out to libm
> >> is the workaround I'm using in the application that led me to discover
> >> the inaccuracy.)
> >>
> >> Matt
> >>
> >> On Thu, Aug 2, 2018 at 11:33 AM, Ben Gamari <[hidden email]> wrote:
> >> > Matt Peddie <[hidden email]> writes:
> >> >
> >> >> Hi George,
> >> >>
> >> >> Not a stupid question.  I don't have a single source at hand, but I
> >> >> think I read in a few places on the wiki that calling out to the
> >> >> system math library is not an option due to the variety of system math
> >> >> libraries on the platforms GHC supports.  It'd be great if I got the
> >> >> wrong impression and this could just be a call to C.  Can anyone set
> >> >> me straight on this point?
> >> >>
> >> > Indeed it's not a stupid question at all. Indeed this is precisely what
> >> > we do for the simpler transcendentals (e.g. sin, asin, log). We very
> >> > well could move in this direction in the case of asinh/atanh as well. I
> >> > believe the reason we don't currently is that atanh was only
> >> > standardized in C99, which we only started requiring a few releases ago.
> >> > Perhaps this is ultimately the right direction.
> >> >
> >> > Cheers,
> >> >
> >> > - Ben
> >> _______________________________________________
> >> ghc-devs mailing list
> >> [hidden email]
> >> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
> >>
> >
>


--
David Feuer
Well-Typed
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Re: accuracy of asinh and atanh

Artem Pelenitsyn
Thanks David! Indeed, here is the commit and ticket:


This concerns only `asinh` though. The implementation is closer to what Matt proposes in his package but simpler. Nevertheless, the original issue about `Infinity` on large negative numbers seems to be fixed with this.

So, I guess, feel free to kill the patch.

--
Best, Artem

On Thu, 2 Aug 2018 at 23:19 David Feuer <[hidden email]> wrote:
Wasn't there a very recent commit to improve these functions, by leftaroundabout?

On Thursday, August 2, 2018 8:16:10 AM EDT Artem Pelenitsyn wrote:
> Here is the patch: https://phabricator.haskell.org/D5034
>
> --
> Best, Artem
>
> On Thu, 2 Aug 2018 at 06:26 Artem Pelenitsyn <[hidden email]> wrote:
>
> > I'd be willing to do this.
> >
> > --
> > Best wishes,
> > Artem
> >
> >
> > On Thu, 2 Aug 2018, 04:38 Matt Peddie, <[hidden email]> wrote:
> >
> >> Thanks, Ben, for chiming in.  I think calling out to C for these
> >> functions is the way to go if it's now feasible.  (Calling out to libm
> >> is the workaround I'm using in the application that led me to discover
> >> the inaccuracy.)
> >>
> >> Matt
> >>
> >> On Thu, Aug 2, 2018 at 11:33 AM, Ben Gamari <[hidden email]> wrote:
> >> > Matt Peddie <[hidden email]> writes:
> >> >
> >> >> Hi George,
> >> >>
> >> >> Not a stupid question.  I don't have a single source at hand, but I
> >> >> think I read in a few places on the wiki that calling out to the
> >> >> system math library is not an option due to the variety of system math
> >> >> libraries on the platforms GHC supports.  It'd be great if I got the
> >> >> wrong impression and this could just be a call to C.  Can anyone set
> >> >> me straight on this point?
> >> >>
> >> > Indeed it's not a stupid question at all. Indeed this is precisely what
> >> > we do for the simpler transcendentals (e.g. sin, asin, log). We very
> >> > well could move in this direction in the case of asinh/atanh as well. I
> >> > believe the reason we don't currently is that atanh was only
> >> > standardized in C99, which we only started requiring a few releases ago.
> >> > Perhaps this is ultimately the right direction.
> >> >
> >> > Cheers,
> >> >
> >> > - Ben
> >> _______________________________________________
> >> ghc-devs mailing list
> >> [hidden email]
> >> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
> >>
> >
>


--
David Feuer
Well-Typed

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Re: accuracy of asinh and atanh

George Colpitts
In reply to this post by David Feuer-2
I believe there was but IMHO calling the libm library function is the better solution, as discussed in the previous emails below. Less maintenance, less testing, and possibly better performance, e.g. as explained here:  the C compiler used to produce libm may generate appropriate 128 and 256-bit Intel AVX VEX-encoded instructions,  generating multiple, processor-specific, auto-dispatched code paths when there is a performance benefit. The most appropriate code would be executed at run time.

Cheers
George

On Thu, Aug 2, 2018 at 5:19 PM David Feuer <[hidden email]> wrote:
Wasn't there a very recent commit to improve these functions, by leftaroundabout?

On Thursday, August 2, 2018 8:16:10 AM EDT Artem Pelenitsyn wrote:
> Here is the patch: https://phabricator.haskell.org/D5034
>
> --
> Best, Artem
>
> On Thu, 2 Aug 2018 at 06:26 Artem Pelenitsyn <[hidden email]> wrote:
>
> > I'd be willing to do this.
> >
> > --
> > Best wishes,
> > Artem
> >
> >
> > On Thu, 2 Aug 2018, 04:38 Matt Peddie, <[hidden email]> wrote:
> >
> >> Thanks, Ben, for chiming in.  I think calling out to C for these
> >> functions is the way to go if it's now feasible.  (Calling out to libm
> >> is the workaround I'm using in the application that led me to discover
> >> the inaccuracy.)
> >>
> >> Matt
> >>
> >> On Thu, Aug 2, 2018 at 11:33 AM, Ben Gamari <[hidden email]> wrote:
> >> > Matt Peddie <[hidden email]> writes:
> >> >
> >> >> Hi George,
> >> >>
> >> >> Not a stupid question.  I don't have a single source at hand, but I
> >> >> think I read in a few places on the wiki that calling out to the
> >> >> system math library is not an option due to the variety of system math
> >> >> libraries on the platforms GHC supports.  It'd be great if I got the
> >> >> wrong impression and this could just be a call to C.  Can anyone set
> >> >> me straight on this point?
> >> >>
> >> > Indeed it's not a stupid question at all. Indeed this is precisely what
> >> > we do for the simpler transcendentals (e.g. sin, asin, log). We very
> >> > well could move in this direction in the case of asinh/atanh as well. I
> >> > believe the reason we don't currently is that atanh was only
> >> > standardized in C99, which we only started requiring a few releases ago.
> >> > Perhaps this is ultimately the right direction.
> >> >
> >> > Cheers,
> >> >
> >> > - Ben
> >> _______________________________________________
> >> ghc-devs mailing list
> >> [hidden email]
> >> http://mail.haskell.org/cgi-bin/mailman/listinfo/ghc-devs
> >>
> >
>


--
David Feuer
Well-Typed
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