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From: Ben Bacarisse <ben.usenet@bsb.me.uk>
Newsgroups: comp.lang.javascript
Subject: Re: Are Floating Point Numbers still a Can of Worms?
Date: Sat, 15 Oct 2022 17:04:16 +0100
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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.