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Re: Getting the exponent of an x87 float

Date 2026-08-18 03:47 +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>
From dxf <dxforth@gmail.com>
Message-ID <6a834928$1@news.ausics.net> (permalink)
Organization Ausics - https://newsgroups.ausics.net

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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.

> One way to implement exp# so it always produces the result you expect
> would be to have a table of the 1e-N values, and use (binary) search
> to find the exponent.
> 
> - anton

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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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