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Re: Taking hypot(3) To The Edge

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Michael S <already5chosen@yahoo.com> posted:

> On Wed, 14 Oct 2026 22:13:04 GMT
> MitchAlsup <user5857@newsgrouper.org.invalid> wrote:
> 
> > Michael S <already5chosen@yahoo.com> posted:
> > 
> > > On Tue, 13 Oct 2026 21:33:23 GMT
> > > MitchAlsup <user5857@newsgrouper.org.invalid> wrote:
> > >   
> > > > 
> > > > For example, I have eXcel from 2003, and on AMD machines I get
> > > > 80-bit precision (when real careful in eXcel math)--but those
> > > > same programs on Intel and Arm display 64-bit precision.
> > > >   
> > > 
> > > Are you sure that you use exactly the same version of Excel on AMD
> > > and Intel? Also, what OS do you have on each machine?
> > > 
> > > Also, how exactly do you detect that precision is higher than IEEE
> > > binary64? By forcing mantisa to hold more than 53 bits
> > > (incl.hidden) or by forcing exponent to hold more than 11 bits?  
> > 
> > Very carefully crafted arithmetic. I calculated the Chebyshev points
> > on a 128-bit FP machine and then transported the ASCII data back and
> > gained 1.2ULP instead of calculating them using COS( point/k ) which
> > is the standard formula.
> > 
> > Also, instead of calculating a bunch of terms in multiple cells, I use
> > SUMPRODUCT() which I found to be ~0.3ULP better than writing the 
> > equations out by hand.
> > 
> > I have no idea why, just that I can measure {LOG(ABS(value),2)} as the
> > number of bits of precision--where value is the {AMD,Intel} builtin
> > minus my Chebyshev polynomial evaluated at the same point. Given 1,000
> > evaluations points between [a, b] with random dither at each point
> > the shape of the graph shows the accuracy while the noise on the graph
> > shows the arithmetic noise.
> > > 
> > > 
> > > 
> 
> All that sounds non-trivial. The difference can be easily related to
> something else, e.g. to results of evaluation of trigs. Which do differ
> a little between AMD and Intel.
> 
> What about trivial tests? 
> A = 1; B = A + 1e-18; C = B - 1;

It is really something which is a lot easier to see in graphical form--
like the difference between a multimeter and an oscilloscope.

And yes, there is a lot more numerical noise when I compare EXPM1 with
EXP-1 or LNP1 with Ln+1. But mostly the noise stays down near 52.3-bits
of precision {after all the careful attention to "things"; whereas it
started near 51-bits of precision before care was applied.

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Re: Taking hypot(3) To The Edge Michael S <already5chosen@yahoo.com> - 2026-10-01 14:12 +0300
  Re: Taking hypot(3) To The Edge David Brown <david.brown@hesbynett.no> - 2026-10-01 13:47 +0200
    Re: Taking hypot(3) To The Edge Terje Mathisen <terje.mathisen@tmsw.no> - 2026-10-02 20:35 +0200
      Re: Taking hypot(3) To The Edge BGB <cr88192@gmail.com> - 2026-10-02 17:13 -0500
        Re: Taking hypot(3) To The Edge Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-10-03 02:17 +0000
          Re: Taking hypot(3) To The Edge BGB <cr88192@gmail.com> - 2026-10-03 15:20 -0500
            Re: Taking hypot(3) To The Edge Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-10-03 21:46 +0000
              Re: Taking hypot(3) To The Edge BGB <cr88192@gmail.com> - 2026-10-03 20:35 -0500
                Re: Taking hypot(3) To The Edge Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-10-04 23:54 +0000
      Re: Taking hypot(3) To The Edge Michael S <already5chosen@yahoo.com> - 2026-10-03 21:06 +0300
        Re: Taking hypot(3) To The Edge Terje Mathisen <terje.mathisen@tmsw.no> - 2026-10-03 20:22 +0200
          Re: Taking hypot(3) To The Edge Michael S <already5chosen@yahoo.com> - 2026-10-03 22:01 +0300
            Re: Taking hypot(3) To The Edge Terje Mathisen <terje.mathisen@tmsw.no> - 2026-10-03 23:20 +0200
            Re: Taking hypot(3) To The Edge MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-10-04 17:49 +0000
          Re: Taking hypot(3) To The Edge Thomas Koenig <tkoenig@netcologne.de> - 2026-10-03 19:47 +0000
  Re: Taking hypot(3) To The Edge MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-10-13 21:33 +0000
    Re: Taking hypot(3) To The Edge Lawrence D’Oliveiro <ldo@nz.invalid> - 2026-10-13 21:51 +0000
    Re: Taking hypot(3) To The Edge anton@mips.complang.tuwien.ac.at (Anton Ertl) - 2026-10-13 21:54 +0000
    Re: Taking hypot(3) To The Edge Michael S <already5chosen@yahoo.com> - 2026-10-14 22:45 +0300
      Re: Taking hypot(3) To The Edge MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-10-14 22:13 +0000
        Re: Taking hypot(3) To The Edge Michael S <already5chosen@yahoo.com> - 2026-10-15 22:03 +0300
          Re: Taking hypot(3) To The Edge MitchAlsup <user5857@newsgrouper.org.invalid> - 2026-10-15 19:19 +0000

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