IE and IEEE 754

From	Dr J R Stockton <reply1400@merlyn.demon.co.uk.invalid>
Newsgroups	comp.lang.javascript
Subject	IE and IEEE 754
Date	2014-09-01 23:05 +0100
Organization	Home
Message-ID	<kX9fedgC3OBUFwmP@invalid.uk.co.demon.merlyn.invalid> (permalink)
References	(5 earlier) <87sikgzz71.fsf@bsb.me.uk> <3souv99slp2vt6nktr48gadd2e4r8th8o4@4ax.com> <871ts0md0v.fsf@bsb.me.uk> <KzbU3UAebiAUFwoS@invalid.uk.co.demon.merlyn.invalid> <8761h9le2k.fsf@bsb.me.uk>

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In comp.lang.javascript message <8761h9le2k.fsf@bsb.me.uk>, Sun, 31 Aug
2014 01:04:19, Ben Bacarisse <ben.usenet@bsb.me.uk> posted:

>Dr J R Stockton <reply1400@merlyn.demon.co.uk.invalid> writes:
>
>> In comp.lang.javascript message <871ts0md0v.fsf@bsb.me.uk>, Fri, 29 Aug
>> 2014 00:04:48, Ben Bacarisse <ben.usenet@bsb.me.uk> posted:
>>
>>>Gene Wirchenko <genew@telus.net> writes:
>>>
>>>> On Thu, 28 Aug 2014 11:27:30 +0100, Ben Bacarisse
>>>> <ben.usenet@bsb.me.uk> wrote:
>>>>
>>>> [snip]
>>>>
>>>>>I think it must.  The ECMAScript specification imports IEEE 754's strict
>>>>>rounding and representation rules.  The IEEE FP value closest to 123.45,
>>>>>when multiplies by 100 must yield 12345 according to those rules.
>>>>
>>>>      Why?  What if the value that you have (and want) happens to be
>>>> the value closest to 123.45?  When you multiply that value by 100,
>>>> wouldn't you want 100 times the value instead of 12345?
>>>
>>>Yes, but you won't get it.  You'll get the nearest floating point
>>>number, which is 12345.  Am I missing your point?
>>
>> With FF31, or IE8, or Opera 12.17, or Chrome 36.0, in WinXP sp3, FWIW,
>> try
>>
>>         S = ""
>>         for (J=1 ; J<111 ; J+=2) S += "\n" + J + "\t" +(1/J)*J
>>         alert(S)
>>
>> And, in FF31 and Chrome 37.0,
>>         (123.45/100)*100 - 123.45    ->    -1.4210854715202004e-14
>>
>> Two nominally-inverse arithmetic operations on IEEE Doubles do not
>> always yield the exact input.
>
>Of course not (I hope I never suggested otherwise).  I am happy to see
>that the result you report is the one expected from IEEE 745's rules, so
>I am not surprised that it's what you get in a wide range of browsers.
>(In fact those that did not give this result are the ones I'd won't to
>know about.)

My aim was to reinforce what you said, not to argue with it.  BTW, the
36.0 & 37.0 do not show a typo; I was "upgrading" while writing.


AIUI, all ordinary numerical operations in IEEE 754 will give the exact
result when the exact result can be expressed exactly in an IEEE Double;
and for that it is necessary that the exact result is within range and
has no more than 54 significant bits in the binary mantissa.  I don't
recall whether that holds for expressions involving exp, log, or trig-
type functions.

Of course, one can achieve an arbitrary degree of accuracy in ECMA-
262-3, Mar 2000, JavaScript : one just needs to abandon the idea of
storing a high-accuracy variable in a single IEEE Double.

-- 
 (c) John Stockton, nr London, UK.  For Mail, see Home Page.  Turnpike, WinXP.
 Web  <http://www.merlyn.demon.co.uk/> - FAQ-type topics, acronyms, and links.
 Command-prompt MiniTrue is useful for viewing/searching/altering files. Free,
 DOS/Win/UNIX now 2.0.6;  see my <http://www.merlyn.demon.co.uk/pc-links.htm>.

Thread

IE and IEE 754 RobG <rgqld@iinet.net.au> - 2014-08-27 22:44 +1000
  Re: IE and IEEE 754 John Harris <niam@jghnorth.org.uk.invalid> - 2014-08-27 15:23 +0100
  IE and IEEE 754 (was: IE and IEE 754) Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2014-08-27 20:59 +0200
  Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-27 22:04 +0200
    Re: IE and IEE 754 "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-27 22:35 +0200
      Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-28 00:07 +0200
        Re: IE and IEE 754 "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-28 00:47 +0200
          Re: IE and IEE 754 Gene Wirchenko <genew@telus.net> - 2014-08-28 10:13 -0700
            Re: IE and IEE 754 "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-28 22:15 +0200
              Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-28 23:24 +0200
                Re: IE and IEE 754 "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-29 01:16 +0200
                Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-29 09:32 +0200
      Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-27 23:59 +0100
        Re: IE and IEE 754 "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-28 02:55 +0200
          Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-28 09:50 +0200
            Re: IE and IEE 754 Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2014-08-28 12:21 +0200
              Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-28 13:42 +0200
          Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-28 11:27 +0100
            Re: IE and IEE 754 Gene Wirchenko <genew@telus.net> - 2014-08-28 10:16 -0700
              Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-29 00:04 +0100
                Re: IE and IEE 754 Gene Wirchenko <genew@telus.net> - 2014-08-29 11:15 -0700
                IEEE 754 (was: IE and IEE 754) "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-29 21:30 +0200
                Re: IEEE 754 (was: IE and IEE 754) Gene Wirchenko <genew@telus.net> - 2014-09-02 11:22 -0700
                Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-29 20:42 +0100
                IEEE 754 (was: IE and IEE 754) "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-29 23:29 +0200
                Re: IEEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-29 23:27 +0100
                Re: IE and IEE 754 Dr J R Stockton <reply1400@merlyn.demon.co.uk.invalid> - 2014-08-30 20:32 +0100
                Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-31 01:04 +0100
                IE and IEEE 754 Dr J R Stockton <reply1400@merlyn.demon.co.uk.invalid> - 2014-09-01 23:05 +0100
    Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-28 00:05 +0100
      Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-28 08:56 +0200
        Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-28 09:51 +0200
          Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-28 11:16 +0100
            Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-28 13:34 +0200
              Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-28 23:41 +0100
                Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-29 09:09 +0200
                Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-29 12:39 +0100
                Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-29 16:55 +0200
                Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-29 18:28 +0100
                Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-30 00:37 +0200
                Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-29 23:53 +0100
                Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-30 01:08 +0200
                Re: IE and IEE 754 Ben Bacarisse <ben.usenet@bsb.me.uk> - 2014-08-30 00:40 +0100
                Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-30 09:32 +0200
                Re: IE and IEE 754 Gene Wirchenko <genew@telus.net> - 2014-08-29 11:22 -0700
                Re: IE and IEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-30 00:14 +0200
  IE and IEEE 754 (was: IE and IEE 754) "Christoph M. Becker" <cmbecker69@arcor.de> - 2014-08-27 22:08 +0200
    Re: IE and IEEE 754 RobG <rgqld@iinet.net.au> - 2014-08-28 22:50 +1000
    Re: IE and IEEE 754 RobG <rgqld@iinet.net.au> - 2014-08-28 22:55 +1000
    Re: IE and IEEE 754 (was: IE and IEE 754) Dr J R Stockton <reply1400@merlyn.demon.co.uk.invalid> - 2014-08-28 21:50 +0100
      Re: IE and IEEE 754 (was: IE and IEE 754) "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-29 09:43 +0200
        Re: IE and IEEE 754 (was: IE and IEE 754) Denis McMahon <denismfmcmahon@gmail.com> - 2014-08-29 08:42 +0000
        Re: IE and IEEE 754 Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2014-08-30 16:24 +0200
          Re: IE and IEEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-30 17:08 +0200
            Re: IE and IEEE 754 Thomas 'PointedEars' Lahn <PointedEars@web.de> - 2014-08-30 18:12 +0200
              Re: IE and IEEE 754 "Evertjan." <exxjxw.hannivoort@inter.nl.net> - 2014-08-30 18:32 +0200

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