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Re: [Axiom-developer] regression testing


From: Gabriel Dos Reis
Subject: Re: [Axiom-developer] regression testing
Date: 01 Apr 2007 20:07:25 -0500

address@hidden writes:

| I'm working my way back from the latest version thru the various
| versions in arch. I've come across a difference that can't be
| explained by any change I've made. Can someone please test this
| on their platform and send me the results?
| 
| Attached is a portion of the regression test file. It consists of
| tests delimited by --S (start) and --E (end)... The --R lines show the
| "expected" results, that is, the results in silver. The --G result
| show what comes from gold. The embedded lines are the computed
| lines. They should be identical and clearly they are not. Please let
| me know what your results are so I can guess where this bug might be.
| 
| You should just be able to clip the rest of this file into an input
| file, say foo.input and the start axiom and do 
|  )spool result
|  )read foo
|  )spool 
| 
| and send me the resulting file along with some idea of what
| source tree you used to build it.

It will help me if you can say more about exactly what is being
tested.  I see DoubleFloat computations, from what I discussed two or
three days ago, the underlying representation is Lisp' long-float --
which I think is bogus.  That representation tends to differ from
platform to platform along with the accuracy.  I believe double-float
is more portable with predictable accuracy across platforms.  Also,
there are platform-dependent libm variations to factor in (plus
C compiler optimizations).  Those remarks may or may not be relevant,
but it would help me to understand yoru issue if you could elaborate a
bit.   See below, results with build-improvements, on an
i686-suse-linux.

   % rpm -q glibc
   glibc-2.5-25

-- Gaby

Starts dribbling to foo.txt (2007/4/1, 19:0:47).
(1) -> )r td


)version
 
Value = "Monday March 5, 2007 at 17:21:39 "

---------------------------------------------------------------------
--This is test 15. It sets x for test 18.
---------------------------------------------------------------------
--S 15 of 50
x := 0.7::DoubleFloat
 
   Loading /usr/local/lib/axiom/target/i686-suse-linux/algebra/FLOAT.o 
      for domain Float 

   Loading /usr/local/lib/axiom/target/i686-suse-linux/algebra/DFLOAT.o
      for domain DoubleFloat 
   (1)  0.69999999999999996
                                                            Type: DoubleFloat
--G 
--G
--G   (15)  0.69999999999999996
--G                                                            Type: DoubleFloat
--R 
--R
--R   (15)  0.69999999999999996
--R                                                            Type: DoubleFloat
--E 15


---------------------------------------------------------------------
-- This is test 18. Clearly cos(acos(x)) differs.
---------------------------------------------------------------------
--S 18 of 50
[sin asin x,  cos acos x,  tan atan x,  cot acot x]
 

   (2)
   [0.69999999999999996, 0.70000000000000007, 0.69999999999999996,
    0.69999999999999996]
                                                       Type: List DoubleFloat
--G 
--G
--G   (18)
--G   [0.69999999999999996, 0.69999999999999996, 0.69999999999999996,
--G    0.69999999999999996]
--G                                                       Type: List DoubleFloat
--R 
--R
--R   (18)
--R   [0.69999999999999996, 0.70000000000000007, 0.69999999999999996,
--R    0.69999999999999996]
--R                                                       Type: List DoubleFloat
--E 18

--MISMATCH
--expected:"   [0.69999999999999996, 0.70000000000000007, 0.69999999999999996,"
--     got:"   [0.69999999999999996, 0.69999999999999996, 0.69999999999999996,"
--FAILED elemnum  18 of 50














---------------------------------------------------------------------
-- This is test 22. It sets the value of variable x for later testing
---------------------------------------------------------------------

--S 22 of 50
x := 1.1::DoubleFloat
 

   (3)  1.0999999999999999
                                                            Type: DoubleFloat
--G 
--G
--G   (22)  1.1000000000000001
--G                                                            Type: DoubleFloat
--R 
--R
--R   (22)  1.1000000000000001
--R                                                            Type: DoubleFloat
--E 22

---------------------------------------------------------------------
-- This is test 26. asin(sin(x)) is different.
---------------------------------------------------------------------
--S 26 of 50
[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
 

   (4)
   [1.0999999999999999, 1.0999999999999999, 1.0999999999999999,
    1.0999999999999999, 1.0999999999999999, 1.0999999999999999]
                                                       Type: List DoubleFloat
--G 
--G
--G   (26)
--G   [1.1000000000000001, 1.1000000000000001, 1.1000000000000001,
--G    1.1000000000000001, 1.0999999999999999, 1.1000000000000001]
--G                                                       Type: List DoubleFloat
--R 
--R
--R   (26)
--R   [1.1000000000000003, 1.1000000000000001, 1.1000000000000001,
--R    1.1000000000000001, 1.0999999999999999, 1.1000000000000001]
--R                                                       Type: List DoubleFloat
--E 26


--MISMATCH
--expected:"   [1.1000000000000003, 1.1000000000000001, 1.1000000000000001,"
--     got:"   [1.1000000000000001, 1.1000000000000001, 1.1000000000000001,"
--FAILED elemnum  26 of 50












---------------------------------------------------------------------
-- This is test 29. It constructs the function used in later tests.
---------------------------------------------------------------------

--S 29 of 50
qtest(a,b,n) ==
   m1 := if n = 1 or n = 4 then 0 else  1
   s1 := if n = 1 or n = 4 then 1 else -1
   s2 := if n = 1 or n = 2 then 1 else -1
   x := complex(s1*a, s2*b)
   [x- exp   log x, _
    x- sin   asin  x, x-    cos   acos  x, x- tan   atan  x , _
    x- csc   acsc  x, x-    sec   asec  x, x- cot   acot  x , _
    x- sinh  asinh x, x-    cosh  acosh x, x- tanh  atanh x , _
    x- csch  acsch x, x-    sech  asech x, x- coth  acoth x , _
    x- log   exp   x, _
    x- asin  sin   x, x- s1*acos  cos   x, x- atan  tan  x , _
    x- acsc  csc   x, x- s1*asec  sec   x, x- acot  cot  x + m1*%pi, _
    x- asinh sinh  x, x- s1*acosh cosh  x, x- atanh tanh x , _
    x- acsch csch  x, x- s1*asech sech  x, x- acoth coth x ]
 
                                                                   Type: Void
--G 
--G                                                                   Type: Void
--R 
--R                                                                   Type: Void
--E 29


---------------------------------------------------------------------
-- This is test 31 that sets the variable sa used below.
---------------------------------------------------------------------

--S 31 of 50
sa := 0.7::DoubleFloat
 

   (6)  0.69999999999999996
                                                            Type: DoubleFloat
--G 
--G
--G   (31)  0.69999999999999996
--G                                                            Type: DoubleFloat
--R 
--R
--R   (31)  0.69999999999999996
--R                                                            Type: DoubleFloat
--E 31

---------------------------------------------------------------------
-- This is test 32 that sets the variable sb used below.
---------------------------------------------------------------------
--S 32 of 50
sb := 1.1::DoubleFloat
 

   (7)  1.0999999999999999
                                                            Type: DoubleFloat
--G 
--G
--G   (32)  1.1000000000000001
--G                                                            Type: DoubleFloat
--R 
--R
--R   (32)  1.1000000000000001
--R                                                            Type: DoubleFloat
--E 32



---------------------------------------------------------------------
-- This is test 35. There are various mismatches that follow.
---------------------------------------------------------------------

--S 35 of 50
qtest(sa, sb, 1)
 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/COMPLEX.o for
      domain Complex 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/COMPCAT-.o 
      for domain ComplexCategory& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/MONOGEN-.o 
      for domain MonogenicAlgebra& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/FRAMALG-.o 
      for domain FramedAlgebra& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/FINRALG-.o 
      for domain FiniteRankAlgebra& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/FEVALAB-.o 
      for domain FullyEvalableOver& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/FRETRCT-.o 
      for domain FullyRetractableTo& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/TRANFUN-.o 
      for domain TranscendentalFunctionCategory& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/BASTYPE-.o 
      for domain BasicType& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/RADCAT-.o for
      domain RadicalCategory& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/TRIGCAT-.o 
      for domain TrigonometricFunctionCategory& 
   Loading /usr/local/lib/axiom/target/i686-suse-linux/algebra/ATRIG-.o
      for domain ArcTrigonometricFunctionCategory& 
   Loading 
      /usr/local/lib/axiom/target/i686-suse-linux/algebra/HYPCAT-.o for
      domain HyperbolicFunctionCategory& 
   Loading /usr/local/lib/axiom/target/i686-suse-linux/algebra/HACKPI.o
      for domain Pi 
   Loading /usr/local/lib/axiom/target/i686-suse-linux/algebra/UPMP.o 
      for package UnivariatePolynomialMultiplicationPackage 
   Compiling function qtest with type (DoubleFloat,DoubleFloat,
      PositiveInteger) -> List Complex DoubleFloat 
   Loading /usr/local/lib/axiom/target/i686-suse-linux/algebra/FPS-.o 
      for domain FloatingPointSystem& 
   Loading /usr/local/lib/axiom/target/i686-suse-linux/algebra/RNS-.o 
      for domain RealNumberSystem& 

   (8)
   [-1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
    -2.2204460492503131E-16 %i, -1.1102230246251565E-16,
    1.1102230246251565E-16, 2.2204460492503131E-16,
    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
    -2.2204460492503131E-16 %i,
    -2.2204460492503131E-16 + -4.4408920985006262E-16 %i,
    2.2204460492503131E-16, -1.1102230246251565E-16,
    1.1102230246251565E-16 + 4.4408920985006262E-16 %i,
    1.1102230246251565E-16 + 2.2204460492503131E-16 %i,
    -1.1102230246251565E-16,
    3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
    -2.2204460492503131E-16, -3.3306690738754696E-16,
    3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
    3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
    1.1102230246251565E-16, -1.1102230246251565E-16, -3.3306690738754696E-16,
    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
    -2.2204460492503131E-16, -3.3306690738754696E-16,
    -1.1102230246251565E-16 + 2.2204460492503131E-16 %i]
                                               Type: List Complex DoubleFloat
--G 
--G   Compiling function qtest with type (DoubleFloat,DoubleFloat,
--G      PositiveInteger) -> List Complex DoubleFloat 
--G
--G   (35)
--G   [1.1102230246251565E-16,
--G    2.2204460492503131E-16 + -4.4408920985006262E-16 %i,
--G    1.1102230246251565E-16,
--G    -4.4408920985006262E-16 + -2.2204460492503131E-16 %i,
--G    4.4408920985006262E-16 + 2.2204460492503131E-16 %i,
--G    -1.1102230246251565E-16,
--G    -2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
--G    1.1102230246251565E-16,
--G    -2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
--G    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--G    3.3306690738754696E-16 + -2.2204460492503131E-16 %i, 0.,
--G    -6.6613381477509392E-16 %i, -1.1102230246251565E-16,
--G    -3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
--G    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,
--G    -2.2204460492503131E-16,
--G    -3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
--G    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,
--G    -5.5511151231257827E-16, -2.2204460492503131E-16, 
-1.1102230246251565E-16,
--G    1.1102230246251565E-16, 0., -1.1102230246251565E-16,
--G    -1.1102230246251565E-16]
--G                                               Type: List Complex DoubleFloat
--R 
--R   Compiling function qtest with type (DoubleFloat,DoubleFloat,
--R      PositiveInteger) -> List Complex DoubleFloat 
--R
--R   (35)
--R   [1.1102230246251565E-16,
--R    2.2204460492503131E-16 + -4.4408920985006262E-16 %i,
--R    -2.2204460492503131E-16,
--R    -4.4408920985006262E-16 + -2.2204460492503131E-16 %i,
--R    4.4408920985006262E-16, -1.1102230246251565E-16,
--R    -2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16,
--R    -2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    1.1102230246251565E-16 + -2.2204460492503131E-16 %i, 0.,
--R    -6.6613381477509392E-16 %i, -1.1102230246251565E-16,
--R    -4.4408920985006262E-16 + -4.4408920985006262E-16 %i,
--R    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,
--R    -3.3306690738754696E-16,
--R    -4.4408920985006262E-16 + -4.4408920985006262E-16 %i,
--R    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,
--R    -5.5511151231257827E-16, -2.2204460492503131E-16, 
-1.1102230246251565E-16,
--R    1.1102230246251565E-16, 0., -1.1102230246251565E-16,
--R    -1.1102230246251565E-16]
--R                                               Type: List Complex DoubleFloat
--E 35

--MISMATCH
--expected:"    -4.4408920985006262E-16 + -4.4408920985006262E-16 %i,"
--     got:"    -3.3306690738754696E-16 + -4.4408920985006262E-16 %i,"
--MISMATCH
--expected:"    -3.3306690738754696E-16,"
--     got:"    -2.2204460492503131E-16,"
--MISMATCH
--expected:"    -4.4408920985006262E-16 + -4.4408920985006262E-16 %i,"
--     got:"    -3.3306690738754696E-16 + -4.4408920985006262E-16 %i,"
--MISMATCH
--expected:"    1.1102230246251565E-16 + -2.2204460492503131E-16 %i, 0.,"
--     got:"    3.3306690738754696E-16 + -2.2204460492503131E-16 %i, 0.,"
--MISMATCH
--expected:"    4.4408920985006262E-16, -1.1102230246251565E-16,"
--     got:"    -1.1102230246251565E-16,"
--MISMATCH
--expected:"    -4.4408920985006262E-16 + -2.2204460492503131E-16 %i,"
--     got:"    4.4408920985006262E-16 + 2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    -2.2204460492503131E-16,"
--     got:"    -4.4408920985006262E-16 + -2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    2.2204460492503131E-16 + -4.4408920985006262E-16 %i,"
--     got:"    1.1102230246251565E-16,"
--MISMATCH
--expected:"   [1.1102230246251565E-16,"
--     got:"    2.2204460492503131E-16 + -4.4408920985006262E-16 %i,"
--MISMATCH
--expected:"   (35)"
--     got:"   [1.1102230246251565E-16,"
--MISMATCH
--expected:""
--     got:"   (35)"
--MISMATCH
--expected:"      PositiveInteger) -> List Complex DoubleFloat "
--     got:""
--MISMATCH
--expected:"   Compiling function qtest with type (DoubleFloat,DoubleFloat,"
--     got:"      PositiveInteger) -> List Complex DoubleFloat "
--MISMATCH
--expected:" "
--     got:"   Compiling function qtest with type (DoubleFloat,DoubleFloat,"
--FAILED elemnum  35 of 50

















---------------------------------------------------------------------
-- This is test 39. It fails in various ways. Check the attached mismatches
---------------------------------------------------------------------

--S 39 of 50
qtest(sa, sb, 2)
 

   (9)
   [-1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
    -2.2204460492503131E-16 %i, -4.4408920985006262E-16,
    -1.1102230246251565E-16, -2.2204460492503131E-16,
    1.1102230246251565E-16 + -4.4408920985006262E-16 %i,
    6.6613381477509392E-16 %i,
    2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
    4.4408920985006262E-16 + -4.4408920985006262E-16 %i,
    -2.2204460492503131E-16,
    5.5511151231257827E-16 + -6.6613381477509392E-16 %i,
    -1.1102230246251565E-16 + -4.4408920985006262E-16 %i,
    -2.2204460492503131E-16, 0.,
    -3.3306690738754696E-16 + -4.4408920985006262E-16 %i, 0.,
    3.3306690738754696E-16,
    -3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
    -2.2204460492503131E-16 %i, 0., 0., 3.3306690738754696E-16,
    -4.4408920985006262E-16 %i,
    2.2204460492503131E-16 + 2.2204460492503131E-16 %i, 3.3306690738754696E-16,
    2.2204460492503131E-16]
                                               Type: List Complex DoubleFloat
--G 
--G
--G   (39)
--G   [-1.1102230246251565E-16,
--G    -2.2204460492503131E-16 + -4.4408920985006262E-16 %i,
--G    -3.3306690738754696E-16,
--G    4.4408920985006262E-16 + -2.2204460492503131E-16 %i,
--G    -4.4408920985006262E-16 + 2.2204460492503131E-16 %i,
--G    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
--G    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,
--G    -1.1102230246251565E-16,
--G    -2.2204460492503131E-16 + -4.4408920985006262E-16 %i,
--G    -2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--G    2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
--G    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
--G    2.2204460492503131E-16 + -2.2204460492503131E-16 %i, 0.,
--G    3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
--G    -1.1102230246251565E-16, 2.2204460492503131E-16,
--G    3.3306690738754696E-16 + -4.4408920985006262E-16 %i,
--G    -1.1102230246251565E-16, 8.8817841970012523E-16, 2.2204460492503131E-16,
--G    1.1102230246251565E-16, 3.3306690738754696E-16,
--G    -1.1102230246251565E-16 + 2.2204460492503131E-16 %i,
--G    1.1102230246251565E-16,
--G    2.2204460492503131E-16 + -2.2204460492503131E-16 %i]
--G                                               Type: List Complex DoubleFloat
--R 
--R
--R   (39)
--R   [-1.1102230246251565E-16,
--R    -2.2204460492503131E-16 + -4.4408920985006262E-16 %i,
--R    -3.3306690738754696E-16,
--R    4.4408920985006262E-16 + -2.2204460492503131E-16 %i,
--R    -4.4408920985006262E-16,
--R    1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
--R    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,
--R    -1.1102230246251565E-16,
--R    4.4408920985006262E-16 + -2.2204460492503131E-16 %i,
--R    -2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
--R    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,
--R    2.2204460492503131E-16 + -2.2204460492503131E-16 %i, 0.,
--R    4.4408920985006262E-16 + -4.4408920985006262E-16 %i, 0.,
--R    3.3306690738754696E-16,
--R    4.4408920985006262E-16 + -4.4408920985006262E-16 %i, 0.,
--R    8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
--R    3.3306690738754696E-16, -1.1102230246251565E-16, 1.1102230246251565E-16,
--R    2.2204460492503131E-16 + -2.2204460492503131E-16 %i]
--R                                               Type: List Complex DoubleFloat
--E 39

--MISMATCH
--expected:"    3.3306690738754696E-16, -1.1102230246251565E-16, 
1.1102230246251565E-16,"
--     got:"    1.1102230246251565E-16,"
--MISMATCH
--expected:"    8.8817841970012523E-16, 2.2204460492503131E-16, 
1.1102230246251565E-16,"
--     got:"    -1.1102230246251565E-16 + 2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    4.4408920985006262E-16 + -4.4408920985006262E-16 %i, 0.,"
--     got:"    1.1102230246251565E-16, 3.3306690738754696E-16,"
--MISMATCH
--expected:"    3.3306690738754696E-16,"
--     got:"    -1.1102230246251565E-16, 8.8817841970012523E-16, 
2.2204460492503131E-16,"
--MISMATCH
--expected:"    4.4408920985006262E-16 + -4.4408920985006262E-16 %i, 0.,"
--     got:"    3.3306690738754696E-16 + -4.4408920985006262E-16 %i,"
--MISMATCH
--expected:"    2.2204460492503131E-16 + -2.2204460492503131E-16 %i, 0.,"
--     got:"    -1.1102230246251565E-16, 2.2204460492503131E-16,"
--MISMATCH
--expected:"    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,"
--     got:"    3.3306690738754696E-16 + -4.4408920985006262E-16 %i,"
--MISMATCH
--expected:"    2.2204460492503131E-16 + -2.2204460492503131E-16 %i,"
--     got:"    2.2204460492503131E-16 + -2.2204460492503131E-16 %i, 0.,"
--MISMATCH
--expected:"    -2.2204460492503131E-16 + 2.2204460492503131E-16 %i,"
--     got:"    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    4.4408920985006262E-16 + -2.2204460492503131E-16 %i,"
--     got:"    2.2204460492503131E-16 + -2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    -1.1102230246251565E-16,"
--     got:"    -2.2204460492503131E-16 + 2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,"
--     got:"    -2.2204460492503131E-16 + -4.4408920985006262E-16 %i,"
--MISMATCH
--expected:"    1.1102230246251565E-16 + -2.2204460492503131E-16 %i,"
--     got:"    -1.1102230246251565E-16,"
--MISMATCH
--expected:"    -4.4408920985006262E-16,"
--     got:"    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    4.4408920985006262E-16 + -2.2204460492503131E-16 %i,"
--     got:"    -1.1102230246251565E-16 + -2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    -3.3306690738754696E-16,"
--     got:"    -4.4408920985006262E-16 + 2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"    -2.2204460492503131E-16 + -4.4408920985006262E-16 %i,"
--     got:"    4.4408920985006262E-16 + -2.2204460492503131E-16 %i,"
--MISMATCH
--expected:"   [-1.1102230246251565E-16,"
--     got:"    -3.3306690738754696E-16,"
--MISMATCH
--expected:"   (39)"
--     got:"    -2.2204460492503131E-16 + -4.4408920985006262E-16 %i,"
--MISMATCH
--expected:""
--     got:"   [-1.1102230246251565E-16,"
--MISMATCH
--expected:" "
--     got:"   (39)"
--FAILED elemnum  39 of 50
--





---------------------------------------------------------------------
-- This is test 43 which fails. See the mismatch report attached.
---------------------------------------------------------------------
--S 43 of 50
qtest(sa, sb, 3)
 

   (10)
   [-1.1102230246251565E-16 + 2.2204460492503131E-16 %i, 0.,
    -3.3306690738754696E-16 + 2.2204460492503131E-16 %i,
    4.4408920985006262E-16, 2.2204460492503131E-16,
    -4.4408920985006262E-16 + 2.2204460492503131E-16 %i,
    3.3306690738754696E-16 + -2.2204460492503131E-16 %i,
    2.2204460492503131E-16 + 2.2204460492503131E-16 %i,
    4.4408920985006262E-16 + 4.4408920985006262E-16 %i,
    -2.2204460492503131E-16,
    5.5511151231257827E-16 + 6.6613381477509392E-16 %i,
    -1.1102230246251565E-16 + 4.4408920985006262E-16 %i,
    -2.2204460492503131E-16, 0., 0., 2.2204460492503131E-16,
    -2.2204460492503131E-16, 0.,
    -3.3306690738754696E-16 + 4.4408920985006262E-16 %i,
    -2.2204460492503131E-16 %i, 0., 3.3306690738754696E-16,
    4.4408920985006262E-16 %i,
    2.2204460492503131E-16 + -2.2204460492503131E-16 %i,
    3.3306690738754696E-16, 2.2204460492503131E-16]
                                               Type: List Complex DoubleFloat
(11) -> )quit
   Please enter y or yes if you really want to leave the interactive 
      environment and return to the operating system:
y




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