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Commit acbbe6fb authored by Rasmus Villemoes's avatar Rasmus Villemoes Committed by Linus Torvalds
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kcmp: fix standard comparison bug

The C operator <= defines a perfectly fine total ordering on the set of
values representable in a long.  However, unlike its namesake in the
integers, it is not translation invariant, meaning that we do not have
"b <= c" iff "a+b <= a+c" for all a,b,c.

This means that it is always wrong to try to boil down the relationship
between two longs to a question about the sign of their difference,
because the resulting relation [a LEQ b iff a-b <= 0] is neither
anti-symmetric or transitive.  The former is due to -LONG_MIN==LONG_MIN
(take any two a,b with a-b = LONG_MIN; then a LEQ b and b LEQ a, but a !=
b).  The latter can either be seen observing that x LEQ x+1 for all x,
implying x LEQ x+1 LEQ x+2 ...  LEQ x-1 LEQ x; or more directly with the
simple example a=LONG_MIN, b=0, c=1, for which a-b < 0, b-c < 0, but a-c >
0.

Note that it makes absolutely no difference that a transmogrying bijection
has been applied before the comparison is done.  In fact, had the
obfuscation not b...
parent 8542bdfc
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