wsbusup@EUTWS1.WIN.TUE.NL (Jan Stout) (03/01/91)
FE>From: "Frank C. Earl" <S47852EF@etsuacad.bitnet>
FE>Subject: Division... Is both types of division in BASIS arithmatically
FE> wrong???
FE>To: Multiple recipients of list FIGI-L <FIGI-L@scfvm.win.tue.nl>
FE>
FE>To the net:
FE>
FE>This is an emprical proof of the fact that the forms of division used in
FE>most of the current computer languages (Including the two used in the
FE>BASIS...) are incorrect in the results given for the remainder for
FE>operations in the third quadrant (both divisor and dividend are
FE>negative). This is in response to a comment made to me by Mitch
FE>Bradley over a statement that I made about this being a problem in both
FE>types of division.
FE>
FE>
FE>Passed to /MOD is the values minus four and minus three-
FE>
FE>Results:
FE>
FE>F-PC 1 -1
FE>MVP 1 -1
FE>TaskForth 1 -1
FE>
FE>So, you might ask, what is wrong with this?
FE>
FE>The remainder is NEGATIVE.
FE>This is incorrect, as you will soon see...
FE>
FE>
FE>Consider,
FE> -4
FE>-4 -3 /MOD is equivalent to -- in fractional expression terms.
FE> -3
FE>
FE> -4 -1 4 -1
FE>Given this, -- = -- * - . The -- = 1 because the signs cancel.
FE> -3 -1 3 -1
FE>
FE> 4 1
FE>Therefore, our calculation is really with - , which is 1 + - .
FE> 3 3
FE>
FE>This is what /MOD passes back as a result - the whole number resulting
FE>from the division and the dividend of the fraction that's left over.
FE> -1
FE>But, every Forth dialect that I have asked, tells me that it's 1 + -- ,
FE> 3
FE>which, from what I just said is *quite* wrong... (Not only is Forth off
FE>here, but every language dialect I've tried does the same thing (ADA's the
FE>only one I know of that does the right calculation for the remainder
FE>portion)). If you think that this doesn't matter- think again...
FE>
FE> 1 4 -1 3 1 2 4 2
FE>1 + - = - and, 1 + -- = - - - = - and, - does not equal - .
FE> 3 3 3 3 3 3 3 3
FE>
FE>
FE>That's sufficient enough an error to justify re-working it (What if you
FE>don't check to see that this throws off your calculations- it could
FE>prove catastrophic- might cause a horrible accident of some sort if it
FE>was used in a critical application that only very rarely drifted off
FE>into the third quadrant??) and looking at ways of doing it better...
FE>
FE>The next posting from me (time permitting) will be a description of the
FE>algorithm I propose should be considered for standardization (I know it's
FE>too late- but we could start considering it for the next standard...) and
FE>some sample Forth-83 (F-PC) code that does the desired operation...
FE>
FE>Frank
Sorry Frank, but in my opinion you're misinterpreting the meaning of the
modulo result. My schoolbook tells me the definition of division is such
that
x r
- = q + -
y y
because x = q * y + r , in your case -4 = 1 * -3 + -1, which is perfectly
valid. Note that in the above equation the last term r / y is dependant
on y, so it becomes quite questionable wether your step to remove the
minus signs is justifiable...
Jan Stout, wsbusup@eutws1.win.tue.nlS47852EF@ETSUACAD.BITNET ("Frank C. Earl") (03/01/91)
On Thu, 28 Feb 91 14:53:43 EST Jan Stout said: >Sorry Frank, but in my opinion you're misinterpreting the meaning of the >modulo result. My schoolbook tells me the definition of division is such >that > x r > - = q + - > y y > >because x = q * y + r , in your case -4 = 1 * -3 + -1, which is perfectly >valid. Note that in the above equation the last term r / y is dependant >on y, so it becomes quite questionable wether your step to remove the >minus signs is justifiable... > >Jan Stout, wsbusup@eutws1.win.tue.nl Ok, I see some of what you are saying, but it seems strange to operate that way (Why? because you don't know whether or not the divisor is negative or not... you don't know- and therefore, looking at the output, you could get confused.. [My instance, I suppose] Besides, ADA doesn't do it that way- because of symmetry with the 1st quadrant (Why I suggested it in the first place).) In any case, it got people OFF of the subject of FIG bungling/doing ok!! :) Thanks, Frank