Re: Getting the exponent of an x87 float

Date	2026-08-26 22:55 +1000
Subject	Re: Getting the exponent of an x87 float
Newsgroups	comp.lang.forth
References	(7 earlier) <2026Aug24.084259@mips.complang.tuwien.ac.at> <6a8dbb2d$1@news.ausics.net> <2026Aug25.182436@mips.complang.tuwien.ac.at> <6a8e5c71$1@news.ausics.net> <2026Aug26.125504@mips.complang.tuwien.ac.at>
From	dxf <dxforth@gmail.com>
Message-ID	<6a8ee226$1@news.ausics.net> (permalink)
Organization	Ausics - https://newsgroups.ausics.net

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On 26/08/2026 8:55 pm, Anton Ertl wrote:
> dxf <dxforth@gmail.com> writes:
>> E.EXACT is good for fooling people into believing a 64-bit
>> float can hold a 66 digit number.
> 
> Not just that, a 64-bit float can hold a number that takes 757
> characters (751 mantissa digits plus other characters) to represent
> exactly in decimal representation:
> 
> 4.940656458412465441765687928682213723650598026143247644255856825006755072702087518652998363616359923797965646954457177309266567103559397963987747960107818781263007131903114045278458171678489821036887186360569987307230500063874091535649843873124733972731696151400317153853980741262385655911710266585566867681870395603106249319452715914924553293054565444011274801297099995419319894090804165633245247571478690147267801593552386115501348035264934720193790268107107491703332226844753335720832431936092382893458368060106011506169809753078342277318329247904982524730776375927247874656084778203734469699533647017972677717585125660551199131504891101451037862738167250955837389733598993664809941164205702637090279242767544565229087538682506419718265533447265625e-324
> 
> The next number representable as IEEE 64-bit FP number, however, has
> the exact decimal representation
> 
> 9.88131291682493088353137585736442744730119605228649528851171365001351014540417503730599672723271984759593129390891435461853313420711879592797549592021563756252601426380622809055691634335697964207377437272113997461446100012774818307129968774624946794546339230280063430770796148252477131182342053317113373536374079120621249863890543182984910658610913088802254960259419999083863978818160833126649049514295738029453560318710477223100269607052986944038758053621421498340666445368950667144166486387218476578691673612021202301233961950615668455463665849580996504946155275185449574931216955640746893939906729403594535543517025132110239826300978220290207572547633450191167477946719798732961988232841140527418055848553508913045817507736501283943653106689453125e-324
> 
> So most people prefer to print these numbers as "5e-324" and "1e-323",
> which are not the exact values of these numbers, but when you convert
> these strings to FP, they convert back to the FP value the string was
> generated from.
> 
> Similarly, if you print the value of the closest FP number to 1e-6,
> the exact value would be
> 
> 9.99999999999999954748111825886258685613938723690807819366455078125e-7
> 
> but most people prefer the output to be
> 
> 1e-6

I want to see digits that I can reasonably engage with - which for a binary-64
float corresponds to approx 16 decimal digits which gives the answer 1e-6.
I assumed IEEE was on the same page but based on what I'm seeing here I've no
idea what it is about any more.

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

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