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Re: A final word on casting.

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On Friday, December 28, 2018 at 2:10:44 PM UTC-5, Ike Naar wrote:
> On 2018-12-23, Bart <bc@freeuk.com> wrote:
> > On 23/12/2018 17:56, Ben Bacarisse wrote:
> >> Bart <bc@freeuk.com> writes:
> >
> >>> How does "1.999999999999..." in source code end up as /exactly/ 2.0?
> >> 
> >> Because the compiler is giving you the closest double to the number you
> >> wrote.
> >
> > You say that so glibly that anyone reading it would just it take at face 
> > value.
> >
> > What it doesn't explain is how a compiler, presented with a complex set 
> > of lossy calculations to arrive at that result, and armed only with the 
> > same 64-bit set of binary floating point operations, actually achieves it.
> >
> > My own C compiler gets this answer, (exactly 2.0 rather than the next 
> > value below which is, I believe, 
> > 1.9999999999999997779553950749686919152736663818359375), but that is 
> > largely by chance. Generally, floating point constants might differ from 
> > mature compilers like gcc by one least significant bit.
> >
> >> If you are going to do numerical work, you would need to understand
> >> what's happening but it's much simpler, for me, to leave you puzzled.
> >
> > I know what's happening here. What I don't know is the approach needed 
> > to turn a string of decimal digits into the closest possible ieee 64-bit 
> > float value.
> 
> One possible approach is to use strtod().

That would be consistent with the recommended practice "The translation-
time conversion of floating constants should match the execution-time
conversion of character strings by library functions, such as strtod,
given matching inputs suitable for both conversions, the same result
format, and default execution-time rounding." (6.4.4.2p7).
This is also a good idea since, as noted in footnote 76, "The
specification for the library functions recommends more accurate
conversion than required for floating constants (see 7.22.1.3)."

7.22.1.3 says:
>   Recommended Practice
>
> 8 If the subject sequence has the hexadecimal form, FLT_RADIX is not
>   a power of 2, and the result is not exactly representable, the
>   result should be one of the two numbers in the appropriate internal
>   format that are adjacent to the hexadecimal floating source value,
>   with the extra stipulation that the error should have a correct sign
>   for the current rounding direction.
>
> 9 If the subject sequence has the decimal form and at most DECIMAL_DIG
>   (defined in <float.h>) significant digits, the result should be
>   correctly rounded. If the subject sequence D has the decimal form
>   and more than DECIMAL_DIG significant digits, consider the two
>   bounding, adjacent decimal strings L and U, both having DECIMAL_DIG
>   significant digits, such that the values of L, D, and U satisfy
>   L ≤ D ≤ U. The result should be one of the (equal or adjacent)
>   values that would be obtained by correctly rounding L and U
>   according to the current rounding direction, with the extra
>   stipulation that the error with respect to D should have a correct
>   sign for the current rounding direction.

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A final word on casting. chanrasjid@gmail.com - 2018-12-23 03:02 -0800
  Re: A final word on casting. Bart <bc@freeuk.com> - 2018-12-23 12:11 +0000
    Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2018-12-23 13:08 +0000
      Re: A final word on casting. Bart <bc@freeuk.com> - 2018-12-23 14:43 +0000
        Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2018-12-23 14:56 +0000
          Re: A final word on casting. chanrasjid@gmail.com - 2018-12-23 07:08 -0800
            Re: A final word on casting. Bart <bc@freeuk.com> - 2018-12-23 15:55 +0000
              Re: A final word on casting. Bart <bc@freeuk.com> - 2018-12-23 16:07 +0000
              Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2018-12-23 08:21 -0800
              Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2018-12-23 17:56 +0000
                Re: A final word on casting. Bart <bc@freeuk.com> - 2018-12-23 19:23 +0000
                Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2018-12-23 20:12 +0000
                Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2018-12-23 14:06 -0800
                Re: A final word on casting. Tim Rentsch <txr@alumni.caltech.edu> - 2018-12-28 09:34 -0800
                Re: A final word on casting. Bart <bc@freeuk.com> - 2018-12-28 20:29 +0000
                Re: A final word on casting. Tim Rentsch <txr@alumni.caltech.edu> - 2018-12-28 15:07 -0800
                Re: A final word on casting. Richard Damon <Richard@Damon-Family.org> - 2018-12-28 20:56 -0500
                Re: A final word on casting. Tim Rentsch <txr@alumni.caltech.edu> - 2018-12-29 09:22 -0800
                Re: A final word on casting. Tim Rentsch <txr@alumni.caltech.edu> - 2019-01-01 13:27 -0800
                Re: A final word on casting. Bart <bc@freeuk.com> - 2019-01-02 01:07 +0000
                Re: A final word on casting. Bart <bc@freeuk.com> - 2019-01-03 18:55 +0000
                Re: A final word on casting. Richard Damon <Richard@Damon-Family.org> - 2019-01-03 22:27 -0500
                Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2019-01-04 16:25 -0500
                Re: A final word on casting. Ike Naar <ike@iceland.freeshell.org> - 2018-12-28 19:10 +0000
                Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2018-12-28 12:33 -0800
                Re: A final word on casting. "Chris M. Thomasson" <invalid_chris_thomasson@invalid.invalid> - 2018-12-23 14:11 -0800
                Re: A final word on casting. Malcolm McLean <malcolm.arthur.mclean@gmail.com> - 2018-12-24 02:54 -0800
                Re: A final word on casting. fir <profesor.fir@gmail.com> - 2018-12-24 03:24 -0800
                Re: A final word on casting. fir <profesor.fir@gmail.com> - 2018-12-24 03:29 -0800
                Re: A final word on casting. fir <profesor.fir@gmail.com> - 2018-12-24 03:45 -0800
                Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2018-12-24 13:44 +0000
                Re: A final word on casting. Richard Damon <Richard@Damon-Family.org> - 2018-12-24 08:51 -0500
              Re: A final word on casting. Richard Damon <Richard@Damon-Family.org> - 2018-12-23 14:53 -0500
                Re: A final word on casting. Robert Wessel <robertwessel2@yahoo.com> - 2018-12-24 09:39 -0600
                Re: A final word on casting. Richard Damon <Richard@Damon-Family.org> - 2018-12-24 13:38 -0500
              Re: A final word on casting. Manfred <noname@add.invalid> - 2018-12-23 21:22 +0100
              Re: A final word on casting. Manfred <noname@add.invalid> - 2018-12-23 21:33 +0100
            Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2018-12-23 10:56 -0500
              Re: A final word on casting. Sjouke Burry <burrynulnulfour@ppllaanneett.nnll> - 2018-12-23 17:18 +0100
        Re: A final word on casting. Bart <bc@freeuk.com> - 2018-12-23 20:03 +0000
    Re: A final word on casting. "Rick C. Hodgin" <rick.c.hodgin@gmail.com> - 2018-12-28 14:47 -0500
  Re: A final word on casting. Ben Bacarisse <ben.usenet@bsb.me.uk> - 2018-12-23 12:24 +0000
  Re: A final word on casting. Richard Damon <Richard@Damon-Family.org> - 2018-12-23 07:28 -0500
    Re: A final word on casting. Tim Rentsch <txr@alumni.caltech.edu> - 2018-12-28 07:50 -0800
  Re: A final word on casting. fir <profesor.fir@gmail.com> - 2018-12-23 04:35 -0800
    Re: A final word on casting. fir <profesor.fir@gmail.com> - 2018-12-23 04:42 -0800
      Re: A final word on casting. fir <profesor.fir@gmail.com> - 2018-12-23 04:52 -0800
  Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2018-12-23 10:28 -0500
  Re: A final word on casting. Barry Schwarz <schwarzb@dqel.com> - 2018-12-23 11:39 -0800
    Re: A final word on casting. Ike Naar <ike@iceland.freeshell.org> - 2018-12-24 07:56 +0000
  Re: A final word on casting. chanrasjid@gmail.com - 2018-12-24 14:03 -0800
    Re: A final word on casting. Barry Schwarz <schwarzb@dqel.com> - 2018-12-24 14:39 -0800
      Re: A final word on casting. chanrasjid@gmail.com - 2018-12-24 14:50 -0800
        Re: A final word on casting. Keith Thompson <kst-u@mib.org> - 2018-12-24 15:34 -0800
      Re: A final word on casting. Keith Thompson <kst-u@mib.org> - 2018-12-24 15:23 -0800
        Re: A final word on casting. chanrasjid@gmail.com - 2018-12-24 20:34 -0800
    Re: A final word on casting. Keith Thompson <kst-u@mib.org> - 2018-12-24 14:52 -0800
      Re: A final word on casting. chanrasjid@gmail.com - 2018-12-24 20:25 -0800
    Re: A final word on casting. James Kuyper <jameskuyper@alumni.caltech.edu> - 2018-12-24 17:52 -0500
    Re: A final word on casting. luser droog <luser.droog@gmail.com> - 2018-12-24 21:27 -0800
      Re: A final word on casting. luser droog <luser.droog@gmail.com> - 2018-12-24 21:39 -0800
      Re: A final word on casting. chanrasjid@gmail.com - 2018-12-24 22:36 -0800

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