Re: Getting the exponent of an x87 float

Date	2026-08-19 13:48 +1000
Subject	Re: Getting the exponent of an x87 float
Newsgroups	comp.lang.forth
References	<115qthh$3pnrg$1@dont-email.me> <2026Aug17.171145@mips.complang.tuwien.ac.at> <6a834928$1@news.ausics.net> <11626b8$v1c9$3@paganini.bofh.team>
From	dxf <dxforth@gmail.com>
Message-ID	<6a852781$1@news.ausics.net> (permalink)
Organization	Ausics - https://newsgroups.ausics.net

Show all headers | View raw

On 19/08/2026 3:55 am, Waldek Hebisch wrote:
> dxf <dxforth@gmail.com> wrote:
>> On 18/08/2026 1:11 am, Anton Ertl wrote:
>>> dxf <dxforth@gmail.com> writes:
>>>> Implementers of floating point output have likely encountered the exponent
>>>> function which returns the exponent of a given fp number.  It's typically
>>>> defined:
>>>>
>>>> : exp# ( f -- exp )
>>>>  fdup f0= if fdrop 0 exit then
>>>>  fabs flog
>>>>  floor f>s ;
>>>>
>>>> It works well enough until applied to the x87 FPU where the FLOG FLOOR
>>>> calculation is done at 80-bit precision:
>>>>
>>>> 1e-1 exp# . -1  ok
>>>> 1e-2 exp# . -2  ok
>>>> 1e-3 exp# . -4  ok
>>>> 1e-4 exp# . -4  ok
>>>> 1e-5 exp# . -5  ok
>>>>
>>>> In the third case -3 was expected but -4 was produced.  Needless to say this
>>>> can/has resulted in problems down the track.  Testing over the full range of
>>>> exponents (0..4932) 235 such duplicated exponents were found.  Below is the
>>>> test program used, along with a potential fix.
>>>
>>> Given that 1/5 cannot be represented exactly in binary floating point
>>> (whether binary64, binary32, binary128 or Intels 80-bit format), the
>>> numbers you get when you type in 1e-1 etc. can be either above or
>>> below the value you would like (typically half of the numbers are
>>> above and half of them are below the value).  Next, you check by using
>>> FLOG, which also performs some rounding.  With luck, the result will
>>> be what you would like to see, but without either proper numerical
>>> analysis or (in this case possible) exhaustive testing I would not
>>> rely on it.  Your exhaustive testing has shown that mistrust is
>>> justified.
>>>
>>>> create aa  8 allot
>>>>
>>>> : exp# ( f -- exp )
>>>>  fdup f0= if fdrop 0 exit then
>>>>  fabs flog
>>>> \  aa df! aa df@  \ fix
>>>>  floor f>s ;
>>>
>>> That's interesting.  Your fix is to introduce additional rounding
>>> after the FLOG step (the rounding happens implicitly in the DF!).
>>> Yes, this will help for 1e-3 and friends, but it also means that
>>>
>>> 0.999999999999999999e-4 exp# .
>>>
>>> prints -4 instead of -5.
>>
>> The output routine using it doesn't seem affected.  My problem was
>> output wasn't switching to sci notation when input fell below 0.001.
>> I'd seen the patch years ago in another forth.  Only now did I realize
>> what it was for.
> 
> If your goal is printing, then natural approach is to produce a
> pair of integers m and k so that m*10^k is good approximation to
> f.  Modern libraries aim for "correctly rounded" result, that
> is pair (m, k) should represent decimal floating point number
> closest to f.  That requires increased precision in intermediate
> calculations.  If you are satified with close but possibly not
> closest number than needed calculation can be done in normal
> floating point.
> 
> Once you have m and k as above you can produce digits of m and
> _after_ that decide if number should be printed in scientific
> notation.  The only tricky case there is if you are requested
> to produce number in traditional notation and exponent is
> large and you want all printed digits to be correct.  Then you
> need intermediate calculations with high precion (proportional
> to the number of printed digits).
> 
> One more thing: when printing it is typically expected that
> result will be rounded.  Directly using floor in such case
> is problematic.  One possible work around is to add a fuzz
> factor bigger than possible error and apply floor after
> that.

I'm satisfied with 'close' as anything else becomes prohibitive.  It's
nevertheless interesting how most (all?) REPRESENTs can start out with
the wrong exponent for 1E-3 and produce the correct result with basic
math.  It's doubtful implementers knew 1E-3 etc were problematic, let
alone planned for it.  Consequently there seems to be a good deal of
'luck' involved in fp.  Since IEEE however, there's been the perception
floating point can, should be, 'foolproof'.  A good deal of effort has
been thrown into it.  I can't but help feel it's misguided.  In my case
I took Anton's advice and used REPRESENT to calculate the exponent of
1E-3.  I don't like it - it's clumsy - but everything else has proven
worse.

Thread

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

csiph-web