Re: A final word on casting.

From	Tim Rentsch <tr.17687@z991.linuxsc.com>
Newsgroups	comp.lang.c
Subject	Re: A final word on casting.
Date	2019-03-06 09:33 -0800
Organization	A noiseless patient Spider
Message-ID	<86k1hbucvh.fsf@mailhub.linuxsc.com> (permalink)
References	(16 earlier) <tUsXD.1964$gy2.1241@fx21.am4> <3pAXD.199851$e%3.151775@fx42.iad> <q0oj0b$khc$1@dont-email.me> <86mumjau3t.fsf@mailhub.linuxsc.com> <q58l4p$q2g$1@dont-email.me>

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James Kuyper <jameskuyper@alumni.caltech.edu> writes:

> On 2/26/19 08:41, James Kuyper wrote:
> ...
>
>> Thinking about it some more in response to your question, I suspect that
>> a number slightly less than 1.0 might require slightly more significant
>> digits than one slightly higher than 1.0.  However, I don't have time to
>> confirm that right now.
>
> I was on the right track, I just had to go down one order of magnitude.
> The following are a consecutive pair of exactly representable double values:
>
> 0.100000000000000005551115123125782702118158340454101562500 ==
> 0x1.999999999999ap-4
> 0.100000000000000019428902930940239457413554191589355468750
> == 0x1.999999999999bp-4
>
> The value exactly half way between them is:
> 0.100000000000000012490009027033011079765856266021728515625
> == 0x1.999999999999a8p-4
>
> Therefore,
> 0.100000000000000012490009027033011079765856266021728515624 should round
> to 0x1.999999999999ap-4, while
> 0.100000000000000012490009027033011079765856266021728515626 should round
> to 0x1.999999999999bp-4
>
> Therefore, an implementation needs to read 57 significant digits before
> it can determine which way to round either of those constants.  For a
> constant starting with
> "0.100000000000000012490009027033011079765856266021728515625", it can
> switch over to testing whether any of the subsequent digits is non-0,
> but only after reading the first 57 significant digits.

The number 2**300, which is

  2037035976334486086268445688409378161051468393665936250636140449354381299763336706183397376

is exactly reprsentable.  The next representable number is
2**300 + 2**248, so halfway between those is 2**300 + 2**247,
which is

  2037035976334486312424869980042572347713548488759506276554079249433607939328930471638728704

This gets us up to 91 digits.  Can we do better?

Thread

Re: A final word on casting. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-02-25 23:26 -0800
  Re: A final word on casting. "I Set My Girlfriend's Pantyhose on Fire" <cdalten@gmail.com> - 2019-02-26 03:12 -0800
  Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-02-26 05:41 -0800
    Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-02-26 19:00 -0800
      Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-02-27 06:37 -0800
  Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-02-28 07:45 -0500
    Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-02-28 08:20 -0500
    Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-02-28 15:16 +0000
      Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-03-01 01:16 +0000
        Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-03-02 01:10 +0000
    Re: A final word on casting. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-03-06 08:36 -0800
      Re: A final word on casting. Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2019-03-06 09:04 -0800
        Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2019-03-21 11:19 +0000
    Re: A final word on casting. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-03-06 09:33 -0800
      Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-03-06 11:19 -0800
        Re: A final word on casting. Tim Rentsch <tr.17687@z991.linuxsc.com> - 2019-03-23 10:49 -0700
          Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-03-25 12:06 -0700

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