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#165 stream2.input infinite loops with streams  ← ↑ →  #167 Infinite Floats Domain

#166 elemnum.input
  
last edited 17 years ago

Edit detail for #166 elemnum.input revision 1 of 1
1
Editor:
Time: 2007/11/17 22:00:57 GMT-8
Note: property change 
changed:
-
20050510 tpd src/interp/vmlisp.lisp define DFLOAT sec, csc, acsc, asec, csch
20050510 tpd src/interp/vmlisp.lisp define DFLOAT coth sech acsch acoth asech

The problem is that DFLOAT calls these lisp functions directly
but they have no definitions. I added the simple case definitions
that use the lisp versions. The proper fix would be to create
an "infinite float package" that could do arbitrary length
floating point computations. A less portable solution is to
use the hardware doublefloat, possibly thru gmp.


---------------------------------------------------------------------
in elemnum.input:
---------------------------------------------------------------------

x := 0.7::DoubleFloat ==>  0.69999999999999996
but should be              0.7

[exp log x] ==>  [0.69999999999999996]
but should be    [0.7]

x := 0.7::DoubleFloat
acsc  x ==>    ACSC is invalid as a function.
but should be  Result is not real

x := 0.7::DoubleFloat
asec  x ==>    A is invalid as a function.
but should be  Result is not real

x := 0.7::DoubleFloat
acoth x ==>    ACOTH is invalid as a function.
but should be  Result is not real

x := 1.1::DoubleFloat ==> 1.1000000000000001
but should be             1.1

[                          tan atan x,  cot acot x, csc acsc x,   sec asec x  ]
                ==> ACSC is invalid as a function
but should be   [1.1,1.1,1.1,1.1]

[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
                ==> CSC is invalid as a function
but should be   [1.1,1.1,1.1,1.1,1.1,1.1]

[sinh asinh x,cosh acosh x,             coth acoth x,csch acsch x             ]
                ==> ACOTH is invalid as a function
but should be   [1.1,1.1,1.1,1.1]

[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
                ==> COTH is invalid as a function
but should be   [1.1,1.1,1.1,1.1,1.1,1.1]

asech x         ==> ASECH is invalid as a function.
but should be   Result is not real

qtest(sa, sb, 1)
 
   Compiling function qtest with type (DoubleFloat,DoubleFloat,
      PositiveInteger) -> List Complex DoubleFloat 

   (28)
   [1.1102230246251565E-16, 2.2204460492503131E-16 - 4.4408920985006262E-16%i,
    1.1102230246251565E-16,
    - 4.4408920985006262E-16 - 2.2204460492503131E-16%i,
    4.4408920985006262E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i, 0.0,
    - 6.6613381477509392E-16%i, - 1.1102230246251565E-16,
    - 3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16,
    - 3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i,
    - 5.5511151231257827E-16, - 2.2204460492503131E-16,
    - 1.1102230246251565E-16, 1.1102230246251565E-16, 0.0,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16]
                                               Type: List Complex DoubleFloat

but should be:

qtest(sa, sb, 1)
 
   Compiling function qtest with type (DoubleFloat,DoubleFloat,
      PositiveInteger) -> List Complex DoubleFloat 

   (35)
   [1.11022302462516e-16, 1.11022302462516e-16 - 2.22044604925031e-16%i,
    1.11022302462516e-16 - 2.22044604925031e-16%i, - 1.11022302462516e-16,
    1.1102230246251565e-16, 1.1102230246251565e-16 + 2.2204460492503131e-16%i,
    2.2204460492503131e-16%i, 1.11022302462516e-16,
    1.11022302462516e-16 - 2.22044604925031e-16%i,
    1.11022302462516e-16 - 2.22044604925031e-16%i, 3.3306690738754696e-16,
    3.3306690738754696e-16 - 2.2204460492503131e-16%i,
    1.1102230246251565e-16 - 2.2204460492503131e-16%i, - 1.11022302462516e-16,
    0.0, 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    1.1102230246251565e-16 - 2.2204460492503131e-16%i,
    - 5.5511151231257827e-16, 1.11022302462516e-16, - 1.11022302462516e-16,
    0.0, 2.2204460492503131e-16 + 2.2204460492503131e-16%i,
    3.3306690738754696e-16,
    - 2.2204460492503131e-16 + 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat


qerr % ==>     1.1899284087167906E-31
but should be  5.6889007588053731e-32


qtest(sa, sb, 2)
 

   (32)
   [- 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 4.4408920985006262E-16%i,
    - 3.3306690738754696E-16,
    4.4408920985006262E-16 - 2.2204460492503131E-16%i,
    - 4.4408920985006262E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i, 0.0,
    3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    - 1.1102230246251565E-16, 2.2204460492503131E-16,
    3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    - 1.1102230246251565E-16, 8.8817841970012523E-16, 2.2204460492503131E-16,
    1.1102230246251565E-16, 3.3306690738754696E-16,
    - 1.1102230246251565E-16 + 2.2204460492503131E-16%i,
    1.1102230246251565E-16, 2.2204460492503131E-16 - 2.2204460492503131E-16%i]
                                               Type: List Complex DoubleFloat

but should be
qtest(sa, sb, 2)
 

   (39)
   [- 1.11022302462516e-16, - 1.11022302462516e-16 - 2.22044604925031e-16%i,
    - 3.33066907387547e-16 - 2.22044604925031e-16%i, 1.11022302462516e-16,
    - 1.1102230246251565e-16, - 2.2204460492503131e-16, 2.2204460492503131e-16,
    - 1.11022302462516e-16, - 3.33066907387547e-16 - 2.22044604925031e-16%i,
    - 1.11022302462516e-16 - 2.22044604925031e-16%i, - 3.3306690738754696e-16,
    - 2.2204460492503131e-16,
    - 1.1102230246251565e-16 - 2.2204460492503131e-16%i, 0.0, 0.0,
    - 1.11022302462516e-16, - 1.11022302462516e-16, 0.0,
    - 1.1102230246251565e-16 - 2.2204460492503131e-16%i,
    8.8817841970012523e-16, - 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    - 2.2204460492503131e-16 + 2.2204460492503131e-16%i,
    - 3.3306690738754696e-16,
    2.2204460492503131e-16 + 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat


qerr %          ==>  1.355854680848614E-31
but should be        7.7748310370340103e-32

qtest(sa, sb, 3)
 

   (36)
   [- 1.1102230246251565E-16, 0.0,
    - 2.2204460492503131E-16 + 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16, 0.0, - 4.4408920985006262E-16,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16,
    - 2.2204460492503131E-16 + 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 + 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i, 0.0, 0.0,
    - 3.3306690738754696E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16, 0.0,
    - 3.3306690738754696E-16 + 2.2204460492503131E-16%i,
    8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
    3.3306690738754696E-16,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    1.1102230246251565E-16, 2.2204460492503131E-16 + 2.2204460492503131E-16%i]
                                               Type: List Complex DoubleFloat

but should be
qtest(sa, sb, 3)
 

   (43)
   [- 1.11022302462516e-16, - 1.11022302462516e-16 + 2.22044604925031e-16%i,
    - 3.33066907387547e-16 + 2.22044604925031e-16%i, 1.11022302462516e-16,
    - 1.1102230246251565e-16, - 2.2204460492503131e-16, 2.2204460492503131e-16,
    - 1.11022302462516e-16, - 3.33066907387547e-16 + 2.22044604925031e-16%i,
    - 1.11022302462516e-16 + 2.22044604925031e-16%i, - 3.3306690738754696e-16,
    - 2.2204460492503131e-16,
    - 1.1102230246251565e-16 + 2.2204460492503131e-16%i, 0.0, 0.0,
    - 1.11022302462516e-16, - 1.11022302462516e-16, 0.0,
    - 1.1102230246251565e-16 + 2.2204460492503131e-16%i,
    8.8817841970012523e-16, - 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    - 2.2204460492503131e-16 - 2.2204460492503131e-16%i,
    - 3.3306690738754696e-16,
    2.2204460492503131e-16 - 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat


qerr %        ==>  1.0002983834232781E-31
but should be      7.7748310370340103e-32


qtest(sa, sb, 4)
 

   (40)
   [1.1102230246251565E-16, 0.0,
    3.3306690738754696E-16 + 4.4408920985006262E-16%i, 2.2204460492503131E-16,
    0.0, 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i, 1.1102230246251565E-16,
    - 2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    3.3306690738754696E-16 + 2.2204460492503131E-16%i, 0.0,
    6.6613381477509392E-16%i, - 1.1102230246251565E-16, 0.0,
    1.1102230246251565E-16, 1.1102230246251565E-16, 0.0,
    1.1102230246251565E-16, - 6.6613381477509392E-16, - 2.2204460492503131E-16,
    - 1.1102230246251565E-16, 1.1102230246251565E-16, 0.0,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16]
                                               Type: List Complex DoubleFloat

but should be
qtest(sa, sb, 4)
 

   (47)
   [1.11022302462516e-16, 1.11022302462516e-16 + 2.22044604925031e-16%i,
    1.11022302462516e-16 + 2.22044604925031e-16%i, - 1.11022302462516e-16,
    1.1102230246251565e-16, 1.1102230246251565e-16 - 2.2204460492503131e-16%i,
    - 2.2204460492503131e-16%i, 1.11022302462516e-16,
    1.11022302462516e-16 + 2.22044604925031e-16%i,
    1.11022302462516e-16 + 2.22044604925031e-16%i, 3.3306690738754696e-16,
    3.3306690738754696e-16 + 2.2204460492503131e-16%i,
    1.1102230246251565e-16 + 2.2204460492503131e-16%i, - 1.11022302462516e-16,
    0.0, 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    1.1102230246251565e-16 + 2.2204460492503131e-16%i,
    - 5.5511151231257827e-16, 1.11022302462516e-16, - 1.11022302462516e-16,
    0.0, 2.2204460492503131e-16 - 2.2204460492503131e-16%i,
    3.3306690738754696e-16,
    - 2.2204460492503131e-16 - 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat
qerr %       ==>  7.5852010117404986E-32
but should be     5.6889007588053731e-32


x:=0.7::Float
csc x ==> 1.55227
  the Float csc function comes from FLOAT
  which comes from TrigonometricFunctionCategory (TRIGCAT)
  (defun CSC (x) (/ 1 (sin x))) gives a value
x:=0.7::DoubleFloat
csc x ==> CSC is invalid as a function

x:=0.7::Float
acsch x ==> 1.15447
x:=0.7::DoubleFloat
acsch x ==> ACSCH is invalid as a function

x:=0.7::Float
coth x ==> 1.65462
x:=0.7::DoubleFloat
coth x ==> COTH is invalid as a function

x:=0.7::DoubleFloat
asec x ==> A is invalid as a function

x:=1.1::Float
acsc x ==> 1.14109
x:=1.1::DoubleFloat
acsc x ==> ACSC is invalid as a function

x:=1.1::Float
csc x ==> 1.100000
x:=1.1::DoubleFloat
csc x ==> CSC is invalid as a function

x:=1.1::Float
acoth x ==> 1.52226
x:=1.1::DoubleFloat
acoth x ==> ACOTH is invalid as a function

x:=1.1::Float
coth x ==> 1.24922
x:=1.1::DoubleFloat
coth x ==> COTH is invalid as a function

x:=1.1::Float
asech x ==> invalid argument to acosh
x:=1.1::DoubleFloat
asech x ==> ASECH is invalid as a function





From greg Fri Oct 7 12:00:06 -0500 2005
From: greg
Date: Fri, 07 Oct 2005 12:00:06 -0500
Subject: property change
Message-ID: <20051007120006-0500@wiki.axiom-developer.org>

Status: pending (next release) => closed

Submitted by : (unknown) at: 2007-11-17T22:00:57-08:00 (17 years ago)
Name :
Axiom Version :
Category : Severity : Status :
Optional subject :  
Optional comment : 

20050510 tpd src/interp/vmlisp.lisp define DFLOAT sec, csc, acsc, asec, csch
20050510 tpd src/interp/vmlisp.lisp define DFLOAT coth sech acsch acoth asech

The problem is that DFLOAT calls these lisp functions directly
but they have no definitions. I added the simple case definitions
that use the lisp versions. The proper fix would be to create
an "infinite float package" that could do arbitrary length
floating point computations. A less portable solution is to
use the hardware doublefloat, possibly thru gmp.


---------------------------------------------------------------------
in elemnum.input:
---------------------------------------------------------------------

x := 0.7::DoubleFloat ==>  0.69999999999999996
but should be              0.7

[exp log x] ==>  [0.69999999999999996]
but should be    [0.7]

x := 0.7::DoubleFloat
acsc  x ==>    ACSC is invalid as a function.
but should be  Result is not real

x := 0.7::DoubleFloat
asec  x ==>    A is invalid as a function.
but should be  Result is not real

x := 0.7::DoubleFloat
acoth x ==>    ACOTH is invalid as a function.
but should be  Result is not real

x := 1.1::DoubleFloat ==> 1.1000000000000001
but should be             1.1

[                          tan atan x,  cot acot x, csc acsc x,   sec asec x  ]
                ==> ACSC is invalid as a function
but should be   [1.1,1.1,1.1,1.1]

[asin sin x,  acos cos x,  atan tan x,  acot cot x, acsc csc x,   asec sec x  ]
                ==> CSC is invalid as a function
but should be   [1.1,1.1,1.1,1.1,1.1,1.1]

[sinh asinh x,cosh acosh x,             coth acoth x,csch acsch x             ]
                ==> ACOTH is invalid as a function
but should be   [1.1,1.1,1.1,1.1]

[asinh sinh x,acosh cosh x,atanh tanh x,acoth coth x,acsch csch x,asech sech x]
                ==> COTH is invalid as a function
but should be   [1.1,1.1,1.1,1.1,1.1,1.1]

asech x         ==> ASECH is invalid as a function.
but should be   Result is not real

qtest(sa, sb, 1)
 
   Compiling function qtest with type (DoubleFloat,DoubleFloat,
      PositiveInteger) -> List Complex DoubleFloat 

   (28)
   [1.1102230246251565E-16, 2.2204460492503131E-16 - 4.4408920985006262E-16%i,
    1.1102230246251565E-16,
    - 4.4408920985006262E-16 - 2.2204460492503131E-16%i,
    4.4408920985006262E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i, 0.0,
    - 6.6613381477509392E-16%i, - 1.1102230246251565E-16,
    - 3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i,
    - 2.2204460492503131E-16,
    - 3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i,
    - 5.5511151231257827E-16, - 2.2204460492503131E-16,
    - 1.1102230246251565E-16, 1.1102230246251565E-16, 0.0,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16]
                                               Type: List Complex DoubleFloat

but should be:

qtest(sa, sb, 1)
 
   Compiling function qtest with type (DoubleFloat,DoubleFloat,
      PositiveInteger) -> List Complex DoubleFloat 

   (35)
   [1.11022302462516e-16, 1.11022302462516e-16 - 2.22044604925031e-16%i,
    1.11022302462516e-16 - 2.22044604925031e-16%i, - 1.11022302462516e-16,
    1.1102230246251565e-16, 1.1102230246251565e-16 + 2.2204460492503131e-16%i,
    2.2204460492503131e-16%i, 1.11022302462516e-16,
    1.11022302462516e-16 - 2.22044604925031e-16%i,
    1.11022302462516e-16 - 2.22044604925031e-16%i, 3.3306690738754696e-16,
    3.3306690738754696e-16 - 2.2204460492503131e-16%i,
    1.1102230246251565e-16 - 2.2204460492503131e-16%i, - 1.11022302462516e-16,
    0.0, 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    1.1102230246251565e-16 - 2.2204460492503131e-16%i,
    - 5.5511151231257827e-16, 1.11022302462516e-16, - 1.11022302462516e-16,
    0.0, 2.2204460492503131e-16 + 2.2204460492503131e-16%i,
    3.3306690738754696e-16,
    - 2.2204460492503131e-16 + 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat


qerr % ==>     1.1899284087167906E-31
but should be  5.6889007588053731e-32


qtest(sa, sb, 2)
 

   (32)
   [- 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 4.4408920985006262E-16%i,
    - 3.3306690738754696E-16,
    4.4408920985006262E-16 - 2.2204460492503131E-16%i,
    - 4.4408920985006262E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    3.3306690738754696E-16 - 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16,
    - 2.2204460492503131E-16 - 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i, 0.0,
    3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    - 1.1102230246251565E-16, 2.2204460492503131E-16,
    3.3306690738754696E-16 - 4.4408920985006262E-16%i,
    - 1.1102230246251565E-16, 8.8817841970012523E-16, 2.2204460492503131E-16,
    1.1102230246251565E-16, 3.3306690738754696E-16,
    - 1.1102230246251565E-16 + 2.2204460492503131E-16%i,
    1.1102230246251565E-16, 2.2204460492503131E-16 - 2.2204460492503131E-16%i]
                                               Type: List Complex DoubleFloat

but should be
qtest(sa, sb, 2)
 

   (39)
   [- 1.11022302462516e-16, - 1.11022302462516e-16 - 2.22044604925031e-16%i,
    - 3.33066907387547e-16 - 2.22044604925031e-16%i, 1.11022302462516e-16,
    - 1.1102230246251565e-16, - 2.2204460492503131e-16, 2.2204460492503131e-16,
    - 1.11022302462516e-16, - 3.33066907387547e-16 - 2.22044604925031e-16%i,
    - 1.11022302462516e-16 - 2.22044604925031e-16%i, - 3.3306690738754696e-16,
    - 2.2204460492503131e-16,
    - 1.1102230246251565e-16 - 2.2204460492503131e-16%i, 0.0, 0.0,
    - 1.11022302462516e-16, - 1.11022302462516e-16, 0.0,
    - 1.1102230246251565e-16 - 2.2204460492503131e-16%i,
    8.8817841970012523e-16, - 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    - 2.2204460492503131e-16 + 2.2204460492503131e-16%i,
    - 3.3306690738754696e-16,
    2.2204460492503131e-16 + 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat


qerr %          ==>  1.355854680848614E-31
but should be        7.7748310370340103e-32

qtest(sa, sb, 3)
 

   (36)
   [- 1.1102230246251565E-16, 0.0,
    - 2.2204460492503131E-16 + 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16, 0.0, - 4.4408920985006262E-16,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16,
    - 2.2204460492503131E-16 + 4.4408920985006262E-16%i,
    - 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16 + 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i, 0.0, 0.0,
    - 3.3306690738754696E-16 + 2.2204460492503131E-16%i,
    - 1.1102230246251565E-16, 0.0,
    - 3.3306690738754696E-16 + 2.2204460492503131E-16%i,
    8.8817841970012523E-16, 2.2204460492503131E-16, 1.1102230246251565E-16,
    3.3306690738754696E-16,
    - 1.1102230246251565E-16 - 2.2204460492503131E-16%i,
    1.1102230246251565E-16, 2.2204460492503131E-16 + 2.2204460492503131E-16%i]
                                               Type: List Complex DoubleFloat

but should be
qtest(sa, sb, 3)
 

   (43)
   [- 1.11022302462516e-16, - 1.11022302462516e-16 + 2.22044604925031e-16%i,
    - 3.33066907387547e-16 + 2.22044604925031e-16%i, 1.11022302462516e-16,
    - 1.1102230246251565e-16, - 2.2204460492503131e-16, 2.2204460492503131e-16,
    - 1.11022302462516e-16, - 3.33066907387547e-16 + 2.22044604925031e-16%i,
    - 1.11022302462516e-16 + 2.22044604925031e-16%i, - 3.3306690738754696e-16,
    - 2.2204460492503131e-16,
    - 1.1102230246251565e-16 + 2.2204460492503131e-16%i, 0.0, 0.0,
    - 1.11022302462516e-16, - 1.11022302462516e-16, 0.0,
    - 1.1102230246251565e-16 + 2.2204460492503131e-16%i,
    8.8817841970012523e-16, - 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    - 2.2204460492503131e-16 - 2.2204460492503131e-16%i,
    - 3.3306690738754696e-16,
    2.2204460492503131e-16 - 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat


qerr %        ==>  1.0002983834232781E-31
but should be      7.7748310370340103e-32


qtest(sa, sb, 4)
 

   (40)
   [1.1102230246251565E-16, 0.0,
    3.3306690738754696E-16 + 4.4408920985006262E-16%i, 2.2204460492503131E-16,
    0.0, 2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    2.2204460492503131E-16 + 2.2204460492503131E-16%i, 1.1102230246251565E-16,
    - 2.2204460492503131E-16 + 2.2204460492503131E-16%i,
    2.2204460492503131E-16 - 2.2204460492503131E-16%i,
    3.3306690738754696E-16 + 2.2204460492503131E-16%i, 0.0,
    6.6613381477509392E-16%i, - 1.1102230246251565E-16, 0.0,
    1.1102230246251565E-16, 1.1102230246251565E-16, 0.0,
    1.1102230246251565E-16, - 6.6613381477509392E-16, - 2.2204460492503131E-16,
    - 1.1102230246251565E-16, 1.1102230246251565E-16, 0.0,
    - 1.1102230246251565E-16, - 1.1102230246251565E-16]
                                               Type: List Complex DoubleFloat

but should be
qtest(sa, sb, 4)
 

   (47)
   [1.11022302462516e-16, 1.11022302462516e-16 + 2.22044604925031e-16%i,
    1.11022302462516e-16 + 2.22044604925031e-16%i, - 1.11022302462516e-16,
    1.1102230246251565e-16, 1.1102230246251565e-16 - 2.2204460492503131e-16%i,
    - 2.2204460492503131e-16%i, 1.11022302462516e-16,
    1.11022302462516e-16 + 2.22044604925031e-16%i,
    1.11022302462516e-16 + 2.22044604925031e-16%i, 3.3306690738754696e-16,
    3.3306690738754696e-16 + 2.2204460492503131e-16%i,
    1.1102230246251565e-16 + 2.2204460492503131e-16%i, - 1.11022302462516e-16,
    0.0, 1.11022302462516e-16, 1.11022302462516e-16, 0.0,
    1.1102230246251565e-16 + 2.2204460492503131e-16%i,
    - 5.5511151231257827e-16, 1.11022302462516e-16, - 1.11022302462516e-16,
    0.0, 2.2204460492503131e-16 - 2.2204460492503131e-16%i,
    3.3306690738754696e-16,
    - 2.2204460492503131e-16 - 2.2204460492503131e-16%i]
                                               Type: List Complex DoubleFloat
qerr %       ==>  7.5852010117404986E-32
but should be     5.6889007588053731e-32


x:=0.7::Float
csc x ==> 1.55227
  the Float csc function comes from FLOAT
  which comes from TrigonometricFunctionCategory (TRIGCAT)
  (defun CSC (x) (/ 1 (sin x))) gives a value
x:=0.7::DoubleFloat
csc x ==> CSC is invalid as a function

x:=0.7::Float
acsch x ==> 1.15447
x:=0.7::DoubleFloat
acsch x ==> ACSCH is invalid as a function

x:=0.7::Float
coth x ==> 1.65462
x:=0.7::DoubleFloat
coth x ==> COTH is invalid as a function

x:=0.7::DoubleFloat
asec x ==> A is invalid as a function

x:=1.1::Float
acsc x ==> 1.14109
x:=1.1::DoubleFloat
acsc x ==> ACSC is invalid as a function

x:=1.1::Float
csc x ==> 1.100000
x:=1.1::DoubleFloat
csc x ==> CSC is invalid as a function

x:=1.1::Float
acoth x ==> 1.52226
x:=1.1::DoubleFloat
acoth x ==> ACOTH is invalid as a function

x:=1.1::Float
coth x ==> 1.24922
x:=1.1::DoubleFloat
coth x ==> COTH is invalid as a function

x:=1.1::Float
asech x ==> invalid argument to acosh
x:=1.1::DoubleFloat
asech x ==> ASECH is invalid as a function





------------------------------------------------------------


property change --greg, Fri, 07 Oct 2005 12:00:06 -0500

Status: pending (next release) => closed