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Groups > comp.lang.forth > #135407
| From | anton@mips.complang.tuwien.ac.at (Anton Ertl) |
|---|---|
| Newsgroups | comp.lang.forth |
| Subject | Re: Getting the exponent of an x87 float |
| Date | 2026-08-24 06:42 +0000 |
| Organization | Institut fuer Computersprachen, Technische Universitaet Wien |
| Message-ID | <2026Aug24.084259@mips.complang.tuwien.ac.at> (permalink) |
| References | (2 earlier) <6a8ab39b$1@news.ausics.net> <116fhve$26f3o$1@dont-email.me> <6a8ba185$1@news.ausics.net> <116gcoo$2dtuf$1@dont-email.me> <6a8bca85$1@news.ausics.net> |
dxf <dxforth@gmail.com> writes:
>On 24/08/2026 1:11 pm, Krishna Myneni wrote:
>> There is example code for correct binary to ascii decimal conversion, such as David Gay's dtoa.c. From his paper, the aim is to show that it can be done fast for most cases. It appears that much of the complexity in his code is a result of optimizations for speed. If one throws away the idea of efficiency and special values, the algorithm for the conversion is fairly easy to express using big integer arithmetic. I posted partially complete Forth code, using big integer arithmetic, elsewhere for the conversion.
>> ...
>
>Would you have done any of that had IEEE not required it?
Does IEEE 754 require it? Since when?
>I don't regret being
>caught out by 1E-3 #EXP at 80-bits giving me an answer I wasn't expecting. I
>got to see reality as opposed to what IEEE wants me to see.
What is it that IEEE supposedly wants you to see?
>The result is I'm
>more suspicious of IEEE than without. Most (all?) forths using the x87 are using
>native precision. Apparently forthers prefer higher precision with the ugliness
>of fp exposed, than an air-brushed lower precision.
Intels 80-bit format can represent more values than binary64 (IEEE 754
DP FP), but, like any binary formats, it cannot represent 1/5, powers
of 1/5, and integer multiples of such numbers, while decimal
respresentation can: 1/5=0.2. In particular, neither the 80-bit
format nor binary64 can represent 1e-3. The closest binary64 number
to 1e-3 is (represented in decimal):
.001000000000000000020816681711721685132943093776702880859375e
So when you compute the decimal exponent exactly, you get -3.
However, for 1e-6 the closest binary64 number is:
9.99999999999999954748111825886258685613938723690807819366455078125e-7
And when I use PAD 100 REPRESENT on this number (with a REPRESENT that
produces the exact result, given a big-enough buffer), REPRESENT
returns an exponent of -6 (while the naively expected value is -5, for
"0.1e-5").
Concerning the method using FLOG, the rounding involved in that may
compensate the necessary conversion error in the conversion to binary
FP, but I would not rely on it without numerical analysis (moreover,
AFAIK 1/2 ulp error is not required by IEEE 754 for transcendental
functions like FLOG). For the number close to 1e-6 above, FLOG in
Gforth (using glibc's log10() implementation) gives me -6e, however,
so in this case the rounding does compensate the conversion error.
Concerning 80387 80-bit numbers, how accurate is the FLOG computation?
And how accurate is your string->FP conversion? The "reality" you see
may be due to inherent limitations of binary FP (with binary64 dodging
them just by luck), or it may be due to inaccuracies coming from the
implementation of these functions.
Just to check whether FLOG really works for binary64, I wrote:
: foo
324 1 do
cr i 0 <<# #s s" 1e-" holds #> 2dup type >float drop flog space e. #>>
loop ;
This shows the naively expected FLOG result for i=1 to i=311, whith
last lines of the output being:
1e-308 -308e
1e-309 -309e
1e-310 -310e
1e-311 -311e
1e-312 -312.0000000000007e
1e-313 -312.9999999999942e
1e-314 -314.0000000000157e
1e-315 -315.0000000006594e
1e-316 -316.0000000070965e
1e-317 -316.99999989981154e
1e-318 -318.0000005435218e
1e-319 -319.000004834948e
1e-320 -320.000004834948e
1e-321 -321.0008639736692e
1e-322 -322.0051853474518e
1e-323 -323.0051853474518e
The subnormal numbers start around 1e-308, and with subnormal numbers
fewer and fewer mantissa bits are significant the smaller they get.
It is interesting that even for 1e-311 we still get the expected
result, and the inaccuracies from subnormality only become apparent
with 1e-312. Given that, I would expect that accurate string->FP
conversion and an accurate FLOG would also produce the expected
results for normal numbers in the 80387 80-bit format.
- anton
--
M. Anton Ertl http://www.complang.tuwien.ac.at/anton/home.html
comp.lang.forth FAQs: http://www.complang.tuwien.ac.at/forth/faq/toc.html
New standard: https://forth-standard.org/
EuroForth 2026 CFP: http://www.euroforth.org/ef26/cfp.html
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Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-16 09:42 +1000
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-17 15:11 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-18 03:47 +1000
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-17 21:18 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-18 12:15 +1000
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-18 09:01 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-18 20:04 +1000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-19 02:30 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-18 09:16 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-23 06:06 -0500
Re: Getting the exponent of an x87 float antispam@fricas.org (Waldek Hebisch) - 2026-08-18 17:55 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-19 13:48 +1000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-19 17:14 +1000
Re: Getting the exponent of an x87 float peter <peter.noreply@tin.it> - 2026-08-19 09:58 +0200
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-19 19:14 +1000
Re: Getting the exponent of an x87 float peter <peter.noreply@tin.it> - 2026-08-19 15:36 +0200
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-20 12:36 +1000
Floating point (was: Getting the exponent of an x87 float) anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-19 08:38 +0000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-19 18:44 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-20 12:35 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-20 03:40 -0500
Re: Getting the exponent of an x87 float albert@spenarnc.xs4all.nl - 2026-08-22 18:43 +0200
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-23 18:47 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-23 14:34 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-24 11:42 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-23 22:11 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-24 14:37 +1000
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-24 06:42 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-26 01:56 +1000
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-25 16:24 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-26 13:24 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-25 23:26 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-26 18:57 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-27 09:24 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-28 11:14 +1000
Re: Getting the exponent of an x87 float Stephen Pelc <stephen@vfxforth.com> - 2026-08-28 10:23 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-28 21:28 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 09:04 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 09:10 -0500
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-28 14:17 +0000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 09:41 -0500
Re: Getting the exponent of an x87 float albert@spenarnc.xs4all.nl - 2026-08-28 19:40 +0200
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 14:00 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 14:25 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 14:40 -0500
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-08-29 12:17 +0200
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-29 10:35 +0000
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-08-29 15:02 +0200
Re: Getting the exponent of an x87 float albert@spenarnc.xs4all.nl - 2026-08-29 15:51 +0200
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-29 14:45 +0000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-29 14:50 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-29 15:01 -0500
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-08-29 23:26 +0200
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-29 17:16 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-03 10:56 +1000
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-09-03 11:52 +0200
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-03 21:00 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-03 06:49 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-03 22:56 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-03 09:02 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-04 11:31 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-04 13:50 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-05 12:22 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-05 08:59 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-06 02:49 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-05 18:20 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-06 12:40 +1000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-06 18:57 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-06 07:36 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-06 07:42 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-07 11:00 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-06 21:16 -0500
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-09-07 08:45 +0200
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-07 21:11 +1000
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-09-07 21:30 +0200
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-07 19:09 -0500
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-09-08 14:06 +0200
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-08 12:14 -0500
Re: Getting the exponent of an x87 float marcel hendrix <mhx@iae.nl> - 2026-09-09 02:15 +0200
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-08 14:41 +1000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-08 19:31 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-08 05:30 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-08 05:44 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-08 23:10 +1000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-09 01:03 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-08 20:49 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-09 13:31 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-09 20:02 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-09-10 12:46 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-07 17:21 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-07 22:13 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-05 21:27 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-09-05 21:55 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-29 07:38 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-30 11:12 +1000
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-29 13:18 -0500
Re: Getting the exponent of an x87 float Krishna Myneni <krishna.myneni@ccreweb.org> - 2026-08-28 07:25 -0500
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-28 23:43 +1000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-28 23:56 +1000
Re: Getting the exponent of an x87 float albert@spenarnc.xs4all.nl - 2026-08-27 12:38 +0200
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-26 10:55 +0000
Re: Getting the exponent of an x87 float dxf <dxforth@gmail.com> - 2026-08-26 22:55 +1000
Re: Getting the exponent of an x87 float anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-08-26 14:29 +0000
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