From: Michael McNamara (mac@verisity.com)
Date: Fri Jun 22 2001 - 15:44:29 PDT
Precedence: bulk
<p>Sorry, Cliff.
The mathematical definition of positive is indeed 'numbers greater
than zero'.
Check out www.dictionary.com
-mac
<p>Ref:
Paul Graham writes:
> Precedence: bulk
>
> Cliff,
>
> > Unfortunately I disagree with the "widely accepted definition"
> > claim. To make sure I was not complete ancient, I looked for
> > "natural" in my Java and even my old college Ada text. No such
> > definition exists in either of these languages that I could
> > find. I believe this is a term that was invented for VHDL.
>
> Must not have been a very good Ada textbook. Ada's package
> standard defines subtypes POSITIVE and NATURAL:
>
> subtype NATURAL is INTEGER range 0..INTEGER'LAST;
> subtype POSITIVE is INTEGER range 1..INTEGER'LAST;
>
> > I equate positive to be >= 0, positive, non-zero to be >0, with similar
> > definitions on the negative side. The Verilog standard has never had a
> > definition for "natural" nor do I see a compelling reason to add one to
> > the IEEE document.
>
> Think about your definitions for a minute. If positive means >= 0, and
> negative means <= 0, then what is 0? What is -0? Positive and negative are
> disjoint sets. Natural and negative are also disjoint sets. There is an
> asymmetry here, because people are not usually interested in the range
> INTEGER'FIRST..0.
>
> You'll also find the definitions of natural and positive in a high school
> algebra textbook, if not earlier. I remember being introduced to them in
> seventh grade :-) My Random House College Dictionary ((c) 1980) defines
> positive (definition 19) as "noting a quantity greater than zero". Knuth
> TAOCP vol. 1 ((c) 1973) defines "Positive: Greater than zero (*not* zero)".
> I'm sure I could find more references in a library.
>
> Anyway, I think anyone who *carefully* reads the text of the LRM will treat
> genvars as being greater than zero, but not zero. But it's also likely that
> implementors will follow the examples instead of reading the text, and make
> genvars either natural (i.e., unsigned) or signed. It's also likely that
> implementors will simply reuse some of their existing code for sequential
> for loops and will treat genvars basically as integers (signed).
>
> Paul
>
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