🚀 go-pugleaf

In article <1996Mar21.113301.2622@sq.com>, msb@sq.com (Mark Brader) writes:
#  The function shall return an integer less than, equal to, or greater
#  than zero if the first argument is considered to be respectively
#  less than, equal to, or greater than the second.

>In other words, it must yield an ordering of the possible data values.
>This is only the case if
>
>1. It is a pure function:
>   repeated calls to compar(x,y) yield a result having the
>       same sign each time
>
>2. It is antisymmetric (I think that's the right word):
>   if compar(x,y) <  0, then compar(y,x) >  0
>   if compar(x,y) == 0, then compar(y,x) == 0
>   if compar(x,y) >  0, then compar(y,x) <  0
>
>3. If is transitive:
>   if compar(x,y) > 0 && compar(y,z) > 0, then compar(x,z) > 0

You have given an intuitively and logically reasonable definition of a
comparison system, but the standard does not.  The standard has trouble
defining a pure binary numeration system and even has trouble refering
to a document which did it.  Until the standard finds a definition of a
comparison system, it is defective.

>>>On tracking down a bug in some old code I noticed that we had the
>>>compare function returning something like "a > b" instead of "b - a".

>>Just one sentence earlier, you gave the exact reason why
>>it doesn't matter if you do "a > b" instead of "a - b".

>Of course it matters.  With this function, if compar(x,y) > 0, then
>compar(y,x) == 0.  This is not antisymmetric.

Argh!  I was remembering what the hardware usually does for comparison
instructions, and forgot that C operators lose part of that information.
I must be getting Cnile.

>(a > b)? 1: (a < b)? -1: 0

Yup.  Incidentally, do you think the average implementation's
interprocedural optimization phase will change this user function into
one machine instruction in the library's qsort() function :-?
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