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From: dxf <dxforth@gmail.com>
Newsgroups: comp.lang.forth
Subject: Re: "The Best Programming Language for the End of the World"
Date: Sat, 12 Apr 2025 00:46:00 +1000
Organization: i2pn2 (i2pn.org)
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On 11/04/2025 11:39 pm, sjack wrote:
> dxf <dxforth@gmail.com> wrote:
>>
>> With REPRESENT we're dealing with full-precision numbers being displayed
>> in lesser precision.  Would 'significant digits plus one' even apply?
>>
> Unsure what is meant by "full-precision numbers" so the following
> reasoning my be off in that respect:
> 
> Floating-point has _potential_ to express a number with _maximum_ of u
> significant digits plus one rounded digit.  However, in application a
> result may have less than the maximum potential significant digits and
> should be returned (displayed) with all digits _after the first 
> non-significant digit_ chopped (or padded with zero's).
> 
> For sure I'm no authority on floating-point numbers. The only thing 
> I know is what I recall from remedial math in the olden days of light
> that one wants a result of u significant digits plus the one rounded
> digit. Such form of number is then useful for other floating-point 
> calculations.

I recall IEEE-754 talking about 'correctly rounded' numbers when
converting to external representation.  This is likely to have
been a factor in Intel's decision to use 80-bits internally.