Jose wrote:
> 0 ((-: ; ;)& (3!:3)) _0
This is not surprising; except for rationals and extended ints, J ignores any
symbols in constants which do not effect the value. So 0.0 is boolean, as is
0j0 as is 0x0.0j_0e_1 , etc (A).
> 0 ((-: ; ;)& (3!:3)) -0
The result of -0 isn't negative, it's merely integer. One way to tell if
you've generated a true negative zero is to look at its reciprocal. The
reciprocal of regular 0 is positive infinity, the reciprocal of negative zero
is negative infinity. Thus:
%0
_
%_0
_
%-0
_
% 0%_1
__
Note that negative zeros must be floating or complex. No other numeric type
can represent a negative zero.
>Then again, the function 3!:3 can distinguish between 0 and -0,
Right. A nice insight here is that 3!:3 can be used to __generate__ a
negative zero. Henry Rich once posed a challenge to find ways to generate
negative zero (B). Here was one of my submissions (C):
i_1 =. }:0 1 _1 2.5
bin =. #: @: (a.&i.) @: (3!:1"1) @: (,. :. {.)
] Z =. ~:/ &.: bin i_1
0
%Z
__
Basically it finds the difference in the binary representations of 1 and _1
and applies that patch to 0 (all numbers are floating point).
So, if ever Roger "fixes" % (such that 0 -:&:(3!:3) 0%_1 ) and any other
primitives which can name the beast, J will still have a negative zero (because
the IEEE floating point standard calls for it).
-Dan
(A) http://www.jsoftware.com/jwiki/Guides/Constants#simplest
(2nd bullet in notes)
http://www.jsoftware.com/pipermail/general/2004-July/017905.html
(3rd long paragraph, begins with "J constants are created")
(B) http://www.jsoftware.com/pipermail/programming/2005-December/000540.html
(C) http://www.jsoftware.com/pipermail/programming/2005-December/000545.html
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