On 07/29/2012 07:08 AM, Bruce Evans wrote:
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/28/2012 09:31 PM, Bruce Evans wrote:
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/28/2012 09:31 PM, Bruce Evans wrote:
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due to the implemen
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Bruce Evans
To: Stephen Montgomery-Smith
Cc: Bruce Evans , freebsd-bugs@FreeBSD.org,
freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/28/2012 11:15 AM, Stephen Montgomery-Smith wrote:
On 07/28/2012 10:46 AM, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due
On 07/28/2012 09:31 PM, Bruce Evans wrote:
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due to the implementation of log1p. The ULP of the
final answer seems to
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due to the implementation of log1p. The ULP of the
final answer seems to be never bigger than a little over 2.
I re
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
On 07/28/2012 04:46 PM, Stephen Montgomery-Smith wrote:
Here are some diffs to catrig.c so that it completely passes Peter
Jeremy's program www.rulingia.com/~peter/ctest.c. That is, it seems to
get all the infs and nans correct.
And I think I messed up these diffs as well. Can we try this ins
On 07/28/2012 06:12 PM, Stephen Montgomery-Smith wrote:
On 07/28/2012 11:15 AM, Stephen Montgomery-Smith wrote:
On 07/28/2012 10:46 AM, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be du
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Bruce Evans
To: Stephen Montgomery-Smith
Cc: Bruce Evans , freebsd-bugs@FreeBSD.org,
freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/28/2012 10:46 AM, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due to the implementation of log1p. The ULP of the
final ans
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
On 07/28/2012 11:15 AM, Stephen Montgomery-Smith wrote:
On 07/28/2012 10:46 AM, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due to the implementation of log1p. The ULP of the
final a
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
Here are some diffs to catrig.c so that it completely passes Peter
Jeremy's program www.rulingia.com/~peter/ctest.c. That is, it seems to
get all the infs and nans correct.
--- catrig.c-old1 2012-07-28 15:00:46.0 -0500
+++ catrig.c 2012-07-28 16:39:24.0 -0500
@@ -89,7 +89,7 @@
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
On 07/28/2012 10:46 AM, Stephen Montgomery-Smith wrote:
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due to the implementation of log1p. The ULP of the
final answer seems to be never bigger than a little over 2.
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: freebsd-bugs@freebsd.org, freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
OK. This clog really seems to work.
x*x + y*y - 1 is computed with a ULP less than 0.8. The rest of the
errors seem to be due to the implementation of log1p. The ULP of the
final answer seems to be never bigger than a little over 2.
___
freebsd-
On 07/28/2012 02:35 AM, Bruce Evans wrote:
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/28/2012 12:25 AM, Bruce Evans wrote:
#defineDEDBL_EPSILON// for clarity
(1) 1 + DE/2= 1 (half way case rounded down to even)
(2) 1 + DE/2 + DE/2 = 1
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
Yes, everywhere I said "double precision" I meant "doubled precision."
I think the papers by Hull et al were perfectly happy with a ULP of
around 4.
I have been trying to do a little better, but like you I am noticing
that log1p isn't that g
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Bruce Evans
To: Stephen Montgomery-Smith
Cc: Bruce Evans , freebsd-bugs@freebsd.org,
freebsd-gnats-sub...@freebsd.org,
Stephen Montgomery-Smith
Subject: Re: bin/170206: complex arcsinh, log, etc
On Sat, 28 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/28/2012 12:25 AM, Bruce Evans wrote:
#defineDEDBL_EPSILON// for clarity
(1) 1 + DE/2= 1 (half way case rounded down to even)
(2) 1 + DE/2 + DE/2 = 1 (double rounding)
(3) DE/2 + DE/2 + 1 =
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: Stephen Montgomery-Smith ,
freebsd-gnats-sub...@freebsd.org, freebsd-bugs@freebsd.org
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
On 07/28/2012 12:25 AM, Bruce Evans wrote:
On Fri, 27 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/27/2012 09:26 AM, Bruce Evans wrote:
% hm1 = -1;
% for (i=0;i<12;i++) hm1 += val[i];
% return (cpack(0.5 * log1p(hm1), atan2(y, x)));
It is the trailing terms that I think don't
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: Stephen Montgomery-Smith ,
freebsd-gnats-sub...@freebsd.org, freebsd-bugs@FreeBSD.org
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012
Yes, everywhere I said "double precision" I meant "doubled precision."
I think the papers by Hull et al were perfectly happy with a ULP of
around 4.
I have been trying to do a little better, but like you I am noticing
that log1p isn't that good either.
I have tried some other things. I am
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Bruce Evans
To: Stephen Montgomery-Smith
Cc: Bruce Evans ,
Stephen Montgomery-Smith ,
freebsd-gnats-sub...@freebsd.org, freebsd-bugs@freebsd.org
Subject: Re: bin/170206: complex arcsinh, log, etc
On Fri, 27 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/27/2012 09:26 AM, Bruce Evans wrote:
% hm1 = -1;
% for (i=0;i<12;i++) hm1 += val[i];
% return (cpack(0.5 * log1p(hm1), atan2(y, x)));
It is the trailing terms that I think don't work right here. You sort
them and add from
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Bruce Evans
To: Stephen Montgomery-Smith
Cc: Bruce Evans ,
Stephen Montgomery-Smith ,
freebsd-gnats-sub...@freebsd.org, freebsd-bugs@FreeBSD.org
Subject: Re: bin/170206: complex arcsinh, log, etc
On Fri, 27 Jul 2012, Stephen Montgomery-Smith wrote:
On 07/27/2012 09:26 AM, Bruce Evans wrote:
VC> > For clog, the worst case that I've found so far has x^2+y^2-1 ~=
1e-47:
VC> >
VC> > x =
0.9995559107901499373838305473327636718750
VC> > y =
VC> > 0.000298023
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: Stephen Montgomery-Smith ,
freebsd-gnats-sub...@freebsd.org, freebsd-bugs@freebsd.org
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Fri, 27 Jul 2012
On 07/27/2012 09:26 AM, Bruce Evans wrote:
VC> > For clog, the worst case that I've found so far has x^2+y^2-1 ~=
1e-47:
VC> >
VC> > x =
0.9995559107901499373838305473327636718750
VC> > y =
VC> > 0.000298023223876953091912775497878893005143652317201485857367516
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: Stephen Montgomery-Smith ,
freebsd-gnats-sub...@freebsd.org, freebsd-bugs@freebsd.org
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Fri, 27 Jul 2012
On 07/27/2012 09:26 AM, Bruce Evans wrote:
% hm1 = -1;
% for (i=0;i<12;i++) hm1 += val[i];
% return (cpack(0.5 * log1p(hm1), atan2(y, x)));
It is the trailing terms that I think don't work right here. You sort
them and add from high to low, but normally it is necessary to add
from
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: Bruce Evans
Cc: Stephen Montgomery-Smith ,
freebsd-gnats-sub...@freebsd.org, freebsd-bugs@freebsd.org
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Fri, 27 Jul 2012
On 07/27/2012 09:26 AM, Bruce Evans wrote:
On Wed, 25 Jul 2012, Stephen Montgomery-Smith wrote:
This function seems to be able to compute clog with a worst case
relative error of 4 or 5 ULP.
...
I lost your previous reply about this after reading just the first part.
Please resend if interest
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Bruce Evans
To: Stephen Montgomery-Smith
Cc: freebsd-gnats-sub...@freebsd.org, freebsd-bugs@freebsd.org
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Sat, 28 Jul 2012 00:26:56 +1000 (EST)
On Wed, 25
On Wed, 25 Jul 2012, Stephen Montgomery-Smith wrote:
This function seems to be able to compute clog with a worst case relative
error of 4 or 5 ULP.
...
I lost your previous reply about this after reading just the first part.
Please resend if interested.
First part recovered by vidcontrol:
V
The following reply was made to PR bin/170206; it has been noted by GNATS.
From: Stephen Montgomery-Smith
To: bug-follo...@freebsd.org, step...@freebsd.org
Cc:
Subject: Re: bin/170206: complex arcsinh, log, etc.
Date: Thu, 26 Jul 2012 23:50:03 -0500
Oops - error in the comments for catanh
>Number: 170206
>Category: bin
>Synopsis: complex arcsinh, log, etc.
>Confidential: no
>Severity: non-critical
>Priority: low
>Responsible:freebsd-bugs
>State: open
>Quarter:
>Keywords:
>Date-Required:
>Class: change-request
>S
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