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

[Camm Maguire]

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,


-- 
Camm Maguire                                            address@hidden
==========================================================================
"The earth is but one country, and mankind its citizens."  --  Baha'u'llah