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Re: Are Floating Point Numbers still a Can of Worms?

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John Harris <niam@jghnorth.org.uk.invalid> writes:

> On 15/10/2022 15:31, R.Wieser wrote:
>
>   <snip>
>> P.s.
>> I've got some numbers for you :
>> -- 1889*1889*1889*1889*1889* etc. calculated thru the FPU
>> 53A891D176398773 - 1.0250068783051204e+095
>   <snip>
>
> For what it's worth, the correct value of 1889**29 is :
>
> 102500687830512064253064716070601123218909116358654017979384519544555980744900395407329380298209
>
> so the ...206 value is most accurate and ...207 is only slightly less
> accurate.

True.  But neither 1.0250068783051206e95 nor 1.0250068783051207e95 can
be represented in binary floating point.  The two representable
numbers closest to 1889**29 are

  1025006878305120[5]6620692472528153354473784341513556365963141787204703693721957646169653433597952

and

  1025006878305120[7]1442079894904626368690870422625608571181699824406695890772528399182534027509760

So the larger of the two is, in fact, the more accurate.  There are two
kinds of accuracy at this level: (1) what binary floating point number
is the closest and, (2) what decimal is the closest representation to
/that/ binary number?

-- 
Ben.

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Thread

Are Floating Point Numbers still a Can of Worms? Mostowski Collapse <bursejan@gmail.com> - 2022-10-14 15:52 -0700
  Re: Are Floating Point Numbers still a Can of Worms? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-10-15 01:52 +0100
  Re: Are Floating Point Numbers still a Can of Worms? "R.Wieser" <address@not.available> - 2022-10-15 09:33 +0200
    Re: Are Floating Point Numbers still a Can of Worms? "R.Wieser" <address@not.available> - 2022-10-15 10:00 +0200
    Re: Are Floating Point Numbers still a Can of Worms? John Harris <niam@jghnorth.org.uk.invalid> - 2022-10-15 11:13 +0100
      Re: Are Floating Point Numbers still a Can of Worms? "R.Wieser" <address@not.available> - 2022-10-15 13:43 +0200
        Re: Are Floating Point Numbers still a Can of Worms? John Harris <niam@jghnorth.org.uk.invalid> - 2022-10-15 15:56 +0100
          Re: Are Floating Point Numbers still a Can of Worms? "R.Wieser" <address@not.available> - 2022-10-15 17:44 +0200
  Re: Are Floating Point Numbers still a Can of Worms? Mostowski Collapse <janburse@fastmail.fm> - 2022-10-15 14:25 +0200
    Re: Are Floating Point Numbers still a Can of Worms? "R.Wieser" <address@not.available> - 2022-10-15 16:31 +0200
      Re: Are Floating Point Numbers still a Can of Worms? John Harris <niam@jghnorth.org.uk.invalid> - 2022-10-15 16:22 +0100
        Re: Are Floating Point Numbers still a Can of Worms? Ben Bacarisse <ben.usenet@bsb.me.uk> - 2022-10-15 17:04 +0100
          Re: Are Floating Point Numbers still a Can of Worms? Mostowski Collapse <bursejan@gmail.com> - 2022-10-15 09:47 -0700
            Re: Are Floating Point Numbers still a Can of Worms? Mostowski Collapse <janburse@fastmail.fm> - 2022-10-15 18:51 +0200
              Re: Are Floating Point Numbers still a Can of Worms? Mostowski Collapse <bursejan@gmail.com> - 2022-10-22 14:35 -0700
                Re: Are Floating Point Numbers still a Can of Worms? Mostowski Collapse <bursejan@gmail.com> - 2022-11-21 09:02 -0800
  Re: Are Floating Point Numbers still a Can of Worms? Julio Di Egidio <julio@diegidio.name> - 2022-10-17 02:00 -0700
    Re: Are Floating Point Numbers still a Can of Worms? Mostowski Collapse <bursejan@gmail.com> - 2022-10-18 07:40 -0700

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