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FORTRAN Version


Script started on Mon Mar 27 14:01:52 1995
[~]: telnet dalph1
Trying 134.30.15.12...
Connected to dalph1.
Escape character is '^]'.



    Welcome on HMI node DALPH1, a VAX ALPH with VMS V6.1


dalph1_cbu:>set def [.paranoia]

dalph1_cbu:>show cpu

DALPH1, a DEC 3000 Model 400
Multiprocessing is DISABLED. Uniprocessing synchronization image loaded.
Minimum multiprocessing revision levels: CPU = 1

PRIMARY CPU = 00
Active CPUs:      00
Configured CPUs:  00


dalph1_cbu:>run dpara

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:
Subexpressions do not appear to be calculated
 with extra precision.

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 appears to be correctly rounded.
Division appears to be correctly rounded.
Add/subtract appears to be correctly rounded.
checking for sticky bit:
Sticky bit used incorrectly or not at all.

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 appears to be correctly rounded.

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 .
%MTH-F-INVARGMAT, invalid argument to math library
  user PC 80550B1C
%TRACE-F-TRACEBACK, symbolic stack dump follows
 Image Name   Module Name     Routine Name    Line Number  rel PC      abs PC 
                                                        0 80550B1C    80550B1C
                                                        0 80550C10    80550C10
                                                        0 80552DA8    80552DA8
 DPARA        DPARA$MAIN      POWER                   986 00004AD4    00034AD4
 DPARA        DPARA$MAIN      DPARA$MAIN              266 00000B00    00030B00
                                                        0 846B9A50    846B9A50

dalph1_cbu:>run dpara
Is this a program restart after failure (1)
or a start from scratch (0) ?
1
Restarting from milestone    90.

To continue diagnosis, press return.

Diagnosis resumes after milestone  #   90,    ... page     9

Testing powers  z^i  for small integers  z  and  i :
No discrepancies found.

Seeking underflow threshold and min positive number:
Smallest strictly positive number found is  minpos  =  5.56268465-309
Since comparison denies   MINPOS  = 0,
 evaluating  ( MINPOS  +  MINPOS ) /  MINPOS   should be safe;
what the machine gets for  ( MINPOS  +  MINPOS ) /  MINPOS   is
           0.2000000E+01
This is O.K. provided over/underflow has not just been signaled.
FLAW:  x =  0.76486914-308 is unequal to  z =  0.55626846-308 ,
yet  x-z  yields   0.0000000E+00
Should this not signal underflow, this is a SERIOUS
DEFECT that causes confusion when innocent statements like
if (x.eq.z) then ... else ... ( f(x)-f(z) )/(x-z) ...
encounter division by zero although actually  x/z = 1 +   0.37500000E+00
The  underflow threshold is   0.55626846-308 , below which
calculation may suffer larger relative error than merely roundoff.

To continue diagnosis, press return.

Diagnosis resumes after milestone  #  130,    ... page    10

since underflow occurs below the threshold  =
         (  2.00000000E+00)^( -1.02400000E+03) ,
only underflow should afflict the expression
         (  2.00000000E+00)^( -2.04800000E+03) ;
actually calculating it yields   
  0.00000000E+00
This computed value is O.K.
Testing  x^((x+1)/(x-1)) vs. exp(2) =   0.73890561E+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    11

Searching for overflow threshold:
%SYSTEM-F-HPARITH, high performance arithmetic trap, Imask=00000000, Fmask=00000
020, summary=08, PC=000333B8, PS=0000001B
-SYSTEM-F-FLTOVF, arithmetic trap, floating overflow at PC=000333B8, PS=0000001B
%TRACE-F-TRACEBACK, symbolic stack dump follows
 Image Name   Module Name     Routine Name    Line Number  rel PC      abs PC 
 DPARA        DPARA$MAIN      OVERF                  1150 000033B8    000333B8
 DPARA        DPARA$MAIN      DPARA$MAIN              278 00000B50    00030B50
                                                        0 846B9A50    846B9A50

dalph1_cbu:>run dpara
Is this a program restart after failure (1)
or a start from scratch (0) ?
1
Restarting from milestone   161.
Can " z = -y " overflow?  trying it on  y =  -4.49423284+307
Seems O.K.
Overflow threshold is  v =   8.98846567+307
There is no saturation value because
the system traps on overflow.
No overflow should be signaled for  v*1 = 
                                            8.98846567+307
                           nor for  v/1 = 
                                            8.98846567+307
Any overflow signal separating this  *  from one above is a DEFECT.

To continue diagnosis, press return.

Diagnosis resumes after milestone  #  190,    ... page    12


What messages and/or values does division by zero produce?
About to compute 1/0...
%SYSTEM-F-HPARITH, high performance arithmetic trap, Imask=00000000, Fmask=00000
001, summary=04, PC=0003BA58, PS=0000001B
-SYSTEM-F-FLTDIV, arithmetic trap, floating/decimal divide by zero at PC=0003BA5
8, PS=0000001B
%TRACE-F-TRACEBACK, symbolic stack dump follows
 Image Name   Module Name     Routine Name    Line Number  rel PC      abs PC 
 DPARA        DPARA$MAIN      ZEROS                  3343 0000BA58    0003BA58
 DPARA        DPARA$MAIN      DPARA$MAIN              284 00000B74    00030B74
                                                        0 846B9A50    846B9A50

dalph1_cbu:>run dpara
Is this a program restart after failure (1)
or a start from scratch (0) ?
1
Restarting from milestone   211.
About to compute 0/0...
%SYSTEM-F-HPARITH, high performance arithmetic trap, Imask=00000000, Fmask=00000
001, summary=04, PC=0003BAE8, PS=0000001B
-SYSTEM-F-FLTDIV, arithmetic trap, floating/decimal divide by zero at PC=0003BAE
8, PS=0000001B
%TRACE-F-TRACEBACK, symbolic stack dump follows
 Image Name   Module Name     Routine Name    Line Number  rel PC      abs PC 
 DPARA        DPARA$MAIN      ZEROS                  3350 0000BAE8    0003BAE8
 DPARA        DPARA$MAIN      DPARA$MAIN              284 00000B74    00030B74
                                                        0 846B9A50    846B9A50

dalph1_cbu:>run dpara
Is this a program restart after failure (1)
or a start from scratch (0) ?
1
Restarting from milestone   212.

To continue diagnosis, press return.

Diagnosis resumes after milestone  #  220,    ... page    13

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