[Gcl-devel] Re: m68k gcl/maxima: Minor Floating point errors

[Jakob Eriksson]

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,
>
>
>