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FORTRAN Version (using f2c)



 Diagnosis resumes after milestone  #    7,    ... page     5

 Program is now RUNNING tests on small integers:
 -1, 0, 1/2 , 1, 2, 3, 4, 5, 9, 27, 32 & 240 are O.K.

 Searching for radix and precision...
 Radix =   2.
 Closest relative separation found is   1.11022302E-16
 Recalculating radix and precision 
 confirms closest relative separation .
 Radix confirmed.
 The number of significant digits of radix   2. is  53.00
 Test for extra-precise subexpressions:
 Some subexpressions appear to be calculated extra-precicely
 with about      .1100000E+02 extra base b digits, i.e.
 roughly    .3311330E+01 extra significant decimals.
 That feature is not tested further by this program.

 To continue diagnosis, press return.
 Diagnosis resumes after milestone  #   30,    ... page     6

 Subtraction appears to be normalized as it should.
 Checking for guard digits in multiply divide and subtract.
 These operations appear to have guard digits as they should.

 To continue diagnosis, press return.
 Diagnosis resumes after milestone  #   40,    ... page     7

 Checking for rounding in multiply, divide and add/subtract:
 Multiplication is neither chopped nor correctly rounded.
 Division is neither chopped nor correctly rounded.
 Add/subtract neither chopped nor correctly rounded.
 Sticky bit used incorrectly or not at all.
 FLAW: lack(s) of guard digits or failure(s) to correctly round or chop
 (noted above) count as one flaw in the final tally below.

 Does multiplication commute? Testing if  x*y = y*x  for  20 random pairs:
 No failure found in   20 randomly chosen pairs.

 Running tests of square root...
 Testing if  sqrt(x*x)  =  x  for    20 integers  x.
 Found no discrepancies.
 Sqrt has passed a test for monotonicity.
 Testing whether  sqrt  is rounded or chopped:
 Square root is neither chopped nor correctly rounded.
 Observed errors run from    -.5000000E+00  to     .5000000E+00 ulps.

 To continue diagnosis, press return.
 Diagnosis resumes after milestone  #   90,    ... page     8

 Testing powers  z^i  for small integers  z  and  i :
 Start with 0.**0 .
 No discrepancies found.

 Seeking underflow threshold and min positive number:
 Smallest strictly positive number found is  minpos  =  4.94065646-324
 Since comparison denies   MINPOS  = 0,
  evaluating  ( MINPOS  +  MINPOS ) /  MINPOS   should be safe;
 what the machine gets for  ( MINPOS  +  MINPOS ) /  MINPOS   is
             .2000000E+01
 This is O.K. provided over/underflow has not just been  signaled.
 Underflow is gradual; it incurs  absolute error = 
 (roundoff in underflow threshold) < minpos.
 The  underflow threshold is    .22250739-307 , below which
 calculation may suffer larger relative error than merely roundoff.

 To continue diagnosis, press return.
 Diagnosis resumes after milestone  #  130,    ... page     9

 since underflow occurs below the threshold  =
          (  2.00000000E+00)^( -1.02200000E+03) ,
 only underflow should afflict the expression
          (  2.00000000E+00)^( -2.04400000E+03) ;
 actually calculating it yields   
    .00000000E+01
 This computed value is O.K.
 Testing  x^((x+1)/(x-1)) vs. exp(2) =    .73890561E+01  as  x -> 1.
 Accuracy seems adequate.
 Testing powers  z^q  at four nearly extreme values:
 No discrepancies found.


 To continue diagnosis, press return.
 Diagnosis resumes after milestone  #  160,    ... page    10

 Searching for overflow threshold:
 Is this a program restart after failure (1)
 or a start from scratch (0) ?
 Restarting from milestone   161.
 Can " z = -y " overflow?  trying it on  y =  -8.98846567+307
 Seems O.K.
 Overflow threshold is  v =   1.79769313+308
 There is no saturation value because
 the system traps on overflow.
 No overflow should be signaled for  v*1 = 
                                             1.79769313+308
                            nor for  v/1 = 
                                             1.79769313+308
 Any overflow signal separating this  *  from one above is a DEFECT.

 To continue diagnosis, press return.
 Diagnosis resumes after milestone  #  190,    ... page    11


 What messages and/or values does division by zero produce?
 About to compute 1/0...
 Is this a program restart after failure (1)
 or a start from scratch (0) ?
 Restarting from milestone   211.
 About to compute 0/0...
 Is this a program restart after failure (1)
 or a start from scratch (0) ?
 Restarting from milestone   212.

 To continue diagnosis, press return.
 Diagnosis resumes after milestone  #  220,    ... page    12

 The number of  FLAWs  discovered =              1
 The arithmetic diagnosed seems Satisfactory though flawed.
 End of Test.


peter@physik3.gwdg.de
Tue Aug 8 13:05:00 GMT+0200 1995