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Re: Taking hypot(3) To The Edge

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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.
> 
> 
> 

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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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