Subject: Re: m68k gcl/maxima: Minor Floating point errors
From: Jakob Eriksson
Date: Thu, 19 Sep 2002 17:40:05 +0200
does your machine have a math coprocessor? a 68020 or 68020 with a 68881
or a 68882?
is it a 68040? if it is, is it a 680LC40?
if it hos no coprocessor, there probably is a small fault in the
floating point emulator.
which is no big deal IMHO, we should be happy to have any FP emulation
at all on m68k.
Camm Maguire wrote:
>Greetings! I have one Debian machine (m68k) which is producing very
>small numerical discrepancies on the results of the two floating point
>intensive tests in rtest8.mac:
>
>=============================================================================
>/* ********************** Problem 8. *************** */
>%Input is
>SORT(ALLROOTS(%))
>
>
>The result is
>[X = - 1.015754699707032, X = 0.8296747207641602, X = 1.0,
>
>X = - 0.9659624099731445 %I - 0.4069597721099853,
>
>X = 0.9659624099731445 %I - 0.4069597721099853]
>
>This differed from the expected result:
>[X = - 1.015755543828121, X = 0.8296749902129361, X = 1.0,
>
>X = - 0.4069597231924075 - 0.9659625152196368 %I,
>
>X = 0.9659625152196368 %I - 0.4069597231924075]
>
>/* ********************** Problem 24. *************** */
>%Input is
>SOLVE(%, [X, Y])
>
>
>The result is
>[[X = 2, Y = 2], [X = 0.5202593803405762 %I - 0.1331241130828857,
>
>Y = 0.07678413391113277 - 3.608001708984376 %I],
>
>[X = - 0.5202593803405762 %I - 0.1331241130828857,
>
>Y = 3.608001708984376 %I + 0.07678413391113277],
>
>[X = - 1.733751425313569, Y = - 0.1535679052943111]]
>
>This differed from the expected result:
>[[X = 2, Y = 2], [X = 0.5202594388652008 %I - 0.1331240357358706,
>
>Y = 0.07678378523787777 - 3.608003221870287 %I],
>
>[X = - 0.1331240357358706 - 0.5202594388652008 %I,
>
>Y = 0.07678378523787777 + 3.608003221870287 %I],
>
>[X = - 1.733751846381093, Y = - 0.1535675710019696]]
>
>=============================================================================
>
>I notice that these are the two tests which also have commented
>variable results on different machines in the rtest8.mac file:
>
>=============================================================================
>sort(ALLROOTS(%));
>[X = -1.0157555438281209,X = 0.82967499021293611,X = 1.0,
> X = -0.96596251521963683*%I-0.40695972319240747,
> X = 0.96596251521963683*%I-0.40695972319240747];
>/* lispm
>[X = 0.829675,X = -1.0157557,X = 0.9659626*%I-0.4069597,
> X = -0.9659626*%I-0.4069597,X = 1.0000001]; */
>/* result tops20 [X = 0.82967498,X = -1.01575564,X = 0.96596261*%I-0.406959705,
> X = -0.96596261*%I-0.406959705,X = 1.00000006]$ */
>SOLVE(%,[X,Y]);
>[[X = 2,Y = 2],
> [X = 0.5202594388652008*%I-0.1331240357358706,
> Y = 0.07678378523787777-3.608003221870287*%I],
> [X = -0.5202594388652008*%I-0.1331240357358706,
> Y = 3.608003221870287*%I+0.07678378523787777],
> [X = -1.733751846381093,Y = -0.1535675710019696]];
>/* lispm
>[[X = 2,Y = 2],[X = 0.52025807*%I-0.13312346,Y = 0.07678269-3.6080136*%I],
> [X = -0.52025807*%I-0.13312346,Y = 3.6080136*%I+0.07678269],
> [X = -1.7337531,Y = -0.1535668]]$ */
>/* tops 20 :[[X = 2,Y = 2],[X = 0.52025944*%I-0.133124037,Y = 0.076783786-3.6080032*%I],
> [X = -0.52025944*%I-0.133124037,Y = 3.6080032*%I+0.076783786],
> [X = -1.73375185,Y = -0.153567577]]$ */
>=============================================================================
>
>Questions:
>
>1) I take it this is still (likely a gcl) error, as all IEEE floating
> point machines should produce an identical result, no? Should
> these results vary somewhat in "correct" operation?
>
>2) I'd like to debug this at the lisp level. I've read the info pages
> on the dbl mode, and can run the example cited. But when I try to
> :br any function in the maxima source .lisp files, I'm told there
> is no line info. What's the best way to see where this result is
> varying in a maxima/lisp debugger?
>
>3) Any m68k cognoscenti care to suggest a likely explanation?
>
>Take care,
>
>
>
>