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Re: Getting the exponent of an x87 float

From anton@mips.complang.tuwien.ac.at (Anton Ertl)
Newsgroups comp.lang.forth
Subject Re: Getting the exponent of an x87 float
Date 2026-08-26 10:55 +0000
Organization Institut fuer Computersprachen, Technische Universitaet Wien
Message-ID <2026Aug26.125504@mips.complang.tuwien.ac.at> (permalink)
References (6 earlier) <6a8bca85$1@news.ausics.net> <2026Aug24.084259@mips.complang.tuwien.ac.at> <6a8dbb2d$1@news.ausics.net> <2026Aug25.182436@mips.complang.tuwien.ac.at> <6a8e5c71$1@news.ausics.net>

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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

- 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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