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

 *** WARNING ***


 The output below is valid only if the machine constants
 OVLOG, UNLOG, and EPMACH in data statements in MODUL1,
 MODUL2, and the driver have been set properly for this
 machine.  (The values of OVLOG and UNLOG specified in
 the driver for this run are    88.0 and   87.0.)
 Otherwise, disregard the results, replace the data
 statements, recompile, and make the run again.


 *** Remark ***


 In the output we have included a number of outrageously
 large choices of TVALUE to illustrate how the quality of
 results degrades (unavoidable; see reference papers).
 Note that potential breakdown due to overflow and
 underflow is avoided.
  
  

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



 RUN NUMBER  1  *************************************************

   **** THIS IS OUTPUT FROM A RUN OF TESTMODULE ****

 F(s) = 1/(s+0.5)  +  1/s**2  +  1/(1+(s+0.2)**2) 

 THIS IS THE FIRST RUN FOR TRANSFORM FUNCTION F(s).
     SIGMA0 IS SET LARGER TO PREVENT BVALUE DEFAULT.
 THE PRINCIPAL INPUT PARAMETERS TO MODUL1 ARE:

            SIGMA0      SIGMA       BVALUE      EPSTOL      MTOP

          8.0000E-01  1.0000E+00  1.0000E+00  1.0000E-05    1024


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

  
  

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

 THE PRINCIPAL OUTPUT PARAMETERS FROM MODUL1 ARE:

          NSTATE        SIGMA       BVALUE                   MACT

             1        1.0000E+00  1.0000E+00                   16


 (K)                                       ERRVEC(K)          (J)   ACOEF(J)

 (1): TOTAL ERROR ESTIMATE: (2)+(3)+(4)    2.319E-03          (1)  1.2015E+00
 (2):   DISCRETISATION ERROR ESTIMATE      1.150E-03          (2)  1.3417E-01
 (3):   TRUNCATION ERROR ESTIMATE          1.168E-03          (3) -8.5221E-02
 (4):   ROUND-OFF ERROR ESTIMATE           6.604E-07          (4) -1.0208E-01
 (5): K IN K-R ESTIMATE OF ACOEF DECAY     1.634E-01          (5) -7.6018E-02
 (6): R IN K-R ESTIMATE OF ACOEF DECAY     1.463E+00          (6) -4.6856E-02
 (7): ALPHA: log(max(max.abs(acoef),1))    1.836E-01          (7) -2.4335E-02
 (8): BETA:  log(min.non-zero.abs(acoef)) -8.750E+00          (8) -9.7544E-03
                                                             (15)  4.7570E-04
                                                             (16)  1.5854E-04

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

  
  

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

 MODUL2 IS NOW CALLED 40 TIMES. IN EVERY CALL, THE INPUT PARAMETERS MACT,
 ACOEF, SIGMA, BVALUE, ERRVEC ARE AS GIVEN ABOVE.        THE OTHER INPUT
 PARAMETER, TVALUE, IS LISTED IN COLUMN 2 OF THE FOLLOWING TABLE.

     --INPUT--- -----OUTPUT-----   ----EXACT--- -----ERROR  EVALUATION------
       TVALUE   FUN(TVALUE) IFLO    FUN(TVALUE)  RELATIVE    PSEUDO    INDEX

   1 0.0000E+00 1.000003E+00  0    1.000000E+00  3.457E-06  3.457E-06    0
   2 5.0000E-02 1.074645E+00  0    1.074792E+00 -1.365E-04 -1.396E-04    0
   3 1.0000E-01 1.148855E+00  0    1.149086E+00 -2.013E-04 -2.093E-04    0
   4 1.5000E-01 1.222500E+00  0    1.222765E+00 -2.168E-04 -2.282E-04    0
   5 2.0000E-01 1.295456E+00  0    1.295717E+00 -2.015E-04 -2.137E-04    0
   6 2.5000E-01 1.367604E+00  0    1.367835E+00 -1.688E-04 -1.798E-04    0
   7 3.0000E-01 1.438835E+00  0    1.439018E+00 -1.272E-04 -1.356E-04    0
   8 3.5000E-01 1.509047E+00  0    1.509173E+00 -8.302E-05 -8.829E-05    0
   9 4.0000E-01 1.578146E+00  0    1.578209E+00 -4.026E-05 -4.259E-05    0
  10 4.5000E-01 1.646042E+00  0    1.646045E+00 -1.738E-06 -1.824E-06    0
  11 5.0000E-01 1.712657E+00  0    1.712603E+00  3.153E-05  3.275E-05    0
  12 5.5000E-01 1.777916E+00  0    1.777813E+00  5.807E-05  5.956E-05    0
  13 6.0000E-01 1.841756E+00  0    1.841611E+00  7.839E-05  7.923E-05    0
  14 6.5000E-01 1.904115E+00  0    1.903939E+00  9.267E-05  9.210E-05    0
  15 7.0000E-01 1.964942E+00  0    1.964744E+00  1.008E-04  9.833E-05    0
  16 1.0000E+00 2.295630E+00  0    2.295469E+00  7.042E-05  5.947E-05    0
  17 2.0000E+00 2.977874E+00  0    2.977400E+00  1.593E-04  6.418E-05    0
  18 3.0000E+00 3.300706E+00  0    3.300579E+00  3.857E-05  6.339E-06    0
  19 4.0000E+00 3.793647E+00  0    3.795282E+00 -4.309E-04 -2.995E-05    0
  20 5.0000E+00 4.734097E+00  0    4.729317E+00  1.011E-03  3.221E-05    0
  21 6.0000E+00 5.967686E+00  0    5.965629E+00  3.448E-04  5.099E-06    0
  22 7.0000E+00 7.159913E+00  0    7.192208E+00 -4.490E-03 -2.945E-05    0
  23 8.0000E+00 8.204040E+00  0    8.218063E+00 -1.706E-03 -4.704E-06    0
  24 9.0000E+00 9.267796E+00  0    9.079232E+00  2.077E-02  2.327E-05    0
  25 1.0000E+01 1.022466E+01  0    9.933112E+00  2.935E-02  1.324E-05    0
  26 1.1000E+01 1.018060E+01  0    1.089328E+01 -6.542E-02 -1.190E-05    0
  27 1.2000E+01 8.859344E+00  0    1.195380E+01 -2.589E-01 -1.901E-05    0
  28 1.3000E+01 1.079254E+01  0    1.303271E+01 -1.719E-01 -5.064E-06    0
  29 1.4000E+01 2.779893E+01  0    1.406115E+01  9.770E-01  1.142E-05    0
  30 1.5000E+01 6.506510E+01  0    1.503293E+01  3.328E+00  1.530E-05    0
  31 3.0000E+01 1.750932E+07  0    2.999755E+01  5.837E+05  1.638E-06    0
  32 5.0000E+01 1.689199E+16  0    4.999999E+01  3.378E+14  3.258E-06    0
  33 7.0000E+01-4.162269E+24  0    7.000000E+01 -5.946E+22 -1.655E-06    0
  34 9.0000E+01-2.006425E+31  0    9.000000E+01 -2.229E+29 -1.644E-08    0
  35 1.1000E+02 0.000000E+00  2    1.100000E+02
  36 1.3000E+02 0.000000E+00  2    1.300000E+02
  37 1.5000E+02 0.000000E+00  2    1.500000E+02
  38 1.7000E+02 0.000000E+00  2    1.700000E+02
  39 1.9000E+02 0.000000E+00  2    1.900000E+02
  40 2.1000E+02 0.000000E+00  2    2.100000E+02
                                                errvec(1) = 2.319E-03

 (1)    (2)          (3)     (4)        (5)         (6)        (7)     (8)

 COLUMN(3) CONTAINS THE RESULT FOR FUN(TVALUE) RETURNED BY MODUL2.
 COLUMN(4) CONTAINS IFLO FROM MODUL2, NORMALLY 0.
     IFLO IS NONZERO IF THE RESULT IN COLUMN 3 WOULD
     EXCEED THE OVERFLOW/UNDERFLOW LIMIT.
 COLUMN(5) CONTAINS THE EXACT RESULT FOR FUN(TVALUE).
 COLUMN(6) CONTAINS RELATIVE ERROR: ( COLUMN(3) - COLUMN(5) ) / COLUMN(5).
 COLUMN(7) CONTAINS PSEUDO-ERROR: ( COLUMN(3) - COLUMN(5) ) / EXP(SIGMA*TVALUE).
 COLUMN(8) CONTAINS INDEX, NORMALLY 0.
     IF COLUMN(7) IS GREATER THAN ERRVEC(1), INDEX = -1.
 ENTRIES (6-8) AFFECTED BY OVERFLOW/UNDERFLOW ARE BLANK.

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

  
  

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



 RUN NUMBER  2  *************************************************

   **** THIS IS OUTPUT FROM A RUN OF TESTMODULE ****

 F(s) = 1/(s+0.5)  +  1/s**2  +  1/(1+(s+0.2)**2) 

 NOTE NEW VALUE OF PARAMETER BVALUE.          bvalue = 3.000E+00

 THE PRINCIPAL INPUT PARAMETERS TO MODUL1 ARE:

            SIGMA0      SIGMA       BVALUE      EPSTOL      MTOP

          0.0000E+00  1.0000E+00  3.0000E+00  1.0000E-05    1024


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

  
  

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

 THE PRINCIPAL OUTPUT PARAMETERS FROM MODUL1 ARE:

          NSTATE        SIGMA       BVALUE                   MACT

             0        1.0000E+00  3.0000E+00                   16


 (K)                                       ERRVEC(K)          (J)   ACOEF(J)

 (1): TOTAL ERROR ESTIMATE: (2)+(3)+(4)    1.369E-06          (1)  1.8419E+00
 (2):   DISCRETISATION ERROR ESTIMATE      1.353E-07          (2) -1.0173E+00
 (3):   TRUNCATION ERROR ESTIMATE          1.374E-07          (3)  1.8619E-01
 (4):   ROUND-OFF ERROR ESTIMATE           1.096E-06          (4) -3.0466E-02
 (5): K IN K-R ESTIMATE OF ACOEF DECAY     1.003E+00          (5)  2.9485E-02
 (6): R IN K-R ESTIMATE OF ACOEF DECAY     2.762E+00          (6) -9.8774E-03
 (7): ALPHA: log(max(max.abs(acoef),1))    6.108E-01          (7) -4.5017E-04
 (8): BETA:  log(min.non-zero.abs(acoef)) -1.525E+01          (8)  3.3572E-04
                                                             (15) -6.6845E-07
                                                             (16)  1.0348E-07

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

  
  

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

 MODUL2 IS NOW CALLED 40 TIMES. IN EVERY CALL, THE INPUT PARAMETERS MACT,
 ACOEF, SIGMA, BVALUE, ERRVEC ARE AS GIVEN ABOVE.        THE OTHER INPUT
 PARAMETER, TVALUE, IS LISTED IN COLUMN 2 OF THE FOLLOWING TABLE.

     --INPUT--- -----OUTPUT-----   ----EXACT--- -----ERROR  EVALUATION------
       TVALUE   FUN(TVALUE) IFLO    FUN(TVALUE)  RELATIVE    PSEUDO    INDEX

   1 0.0000E+00 1.000000E+00  0    1.000000E+00  0.000E+00  0.000E+00    0
   2 5.0000E-02 1.074791E+00  0    1.074792E+00 -3.327E-07 -3.402E-07    0
   3 1.0000E-01 1.149086E+00  0    1.149086E+00 -3.112E-07 -3.236E-07    0
   4 1.5000E-01 1.222765E+00  0    1.222765E+00 -9.749E-08 -1.026E-07    0
   5 2.0000E-01 1.295717E+00  0    1.295717E+00 -9.200E-08 -9.760E-08    0
   6 2.5000E-01 1.367835E+00  0    1.367835E+00 -1.743E-07 -1.857E-07    0
   7 3.0000E-01 1.439018E+00  0    1.439018E+00  0.000E+00  0.000E+00    0
   8 3.5000E-01 1.509173E+00  0    1.509173E+00  2.370E-07  2.520E-07    0
   9 4.0000E-01 1.578209E+00  0    1.578209E+00  1.511E-07  1.598E-07    0
  10 4.5000E-01 1.646045E+00  0    1.646045E+00 -1.448E-07 -1.520E-07    0
  11 5.0000E-01 1.712603E+00  0    1.712603E+00 -6.961E-08 -7.230E-08    0
  12 5.5000E-01 1.777813E+00  0    1.777813E+00  0.000E+00  0.000E+00    0
  13 6.0000E-01 1.841611E+00  0    1.841611E+00  6.473E-08  6.542E-08    0
  14 6.5000E-01 1.903939E+00  0    1.903939E+00  1.878E-07  1.867E-07    0
  15 7.0000E-01 1.964744E+00  0    1.964744E+00 -1.820E-07 -1.776E-07    0
  16 1.0000E+00 2.295468E+00  0    2.295469E+00 -2.077E-07 -1.754E-07    0
  17 2.0000E+00 2.977399E+00  0    2.977400E+00 -2.402E-07 -9.680E-08    0
  18 3.0000E+00 3.300577E+00  0    3.300579E+00 -5.779E-07 -9.496E-08    0
  19 4.0000E+00 3.795281E+00  0    3.795282E+00 -1.885E-07 -1.310E-08    0
  20 5.0000E+00 4.729321E+00  0    4.729317E+00  8.066E-07  2.570E-08    0
  21 6.0000E+00 5.965626E+00  0    5.965629E+00 -3.997E-07 -5.910E-09    0
  22 7.0000E+00 7.192214E+00  0    7.192208E+00  8.619E-07  5.653E-09    0
  23 8.0000E+00 8.218052E+00  0    8.218063E+00 -1.393E-06 -3.839E-09    0
  24 9.0000E+00 9.079308E+00  0    9.079232E+00  8.298E-06  9.298E-09    0
  25 1.0000E+01 9.934024E+00  0    9.933112E+00  9.179E-05  4.139E-08    0
  26 1.1000E+01 1.089593E+01  0    1.089328E+01  2.425E-04  4.412E-08    0
  27 1.2000E+01 1.195851E+01  0    1.195380E+01  3.941E-04  2.895E-08    0
  28 1.3000E+01 1.304533E+01  0    1.303271E+01  9.680E-04  2.852E-08    0
  29 1.4000E+01 1.410972E+01  0    1.406115E+01  3.454E-03  4.039E-08    0
  30 1.5000E+01 1.517472E+01  0    1.503293E+01  9.432E-03  4.338E-08    0
  31 3.0000E+01-4.206549E+02  0    2.999755E+01 -1.502E+01 -4.217E-11    0
  32 5.0000E+01-1.479451E+02  0    4.999999E+01 -3.959E+00 -3.818E-20    0
  33 7.0000E+01-1.573707E+00  0    7.000000E+01 -1.022E+00 -2.845E-29    0
  34 9.0000E+01-3.785562E-03  0    9.000000E+01 -1.000E+00 -7.375E-38    0
  35 1.1000E+02 0.000000E+00  2    1.100000E+02
  36 1.3000E+02 0.000000E+00  2    1.300000E+02
  37 1.5000E+02 0.000000E+00  2    1.500000E+02
  38 1.7000E+02 0.000000E+00  2    1.700000E+02
  39 1.9000E+02 0.000000E+00  2    1.900000E+02
  40 2.1000E+02 0.000000E+00  2    2.100000E+02
                                                errvec(1) = 1.369E-06

 (1)    (2)          (3)     (4)        (5)         (6)        (7)     (8)

 COLUMN(3) CONTAINS THE RESULT FOR FUN(TVALUE) RETURNED BY MODUL2.
 COLUMN(4) CONTAINS IFLO FROM MODUL2, NORMALLY 0.
     IFLO IS NONZERO IF THE RESULT IN COLUMN 3 WOULD
     EXCEED THE OVERFLOW/UNDERFLOW LIMIT.
 COLUMN(5) CONTAINS THE EXACT RESULT FOR FUN(TVALUE).
 COLUMN(6) CONTAINS RELATIVE ERROR: ( COLUMN(3) - COLUMN(5) ) / COLUMN(5).
 COLUMN(7) CONTAINS PSEUDO-ERROR: ( COLUMN(3) - COLUMN(5) ) / EXP(SIGMA*TVALUE).
 COLUMN(8) CONTAINS INDEX, NORMALLY 0.
     IF COLUMN(7) IS GREATER THAN ERRVEC(1), INDEX = -1.
 ENTRIES (6-8) AFFECTED BY OVERFLOW/UNDERFLOW ARE BLANK.

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

  
  

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



 RUN NUMBER  3  *************************************************

   **** THIS IS OUTPUT FROM A RUN OF TESTMODULE ****

 F(s) = 1/(s+0.5)  +  1/s**2  +  1/(1+(s+0.2)**2) 

 NOTE NEW VALUE OF PARAMETER BVALUE.          bvalue = 9.000E+00

 THE PRINCIPAL INPUT PARAMETERS TO MODUL1 ARE:

            SIGMA0      SIGMA       BVALUE      EPSTOL      MTOP

          0.0000E+00  1.0000E+00  9.0000E+00  1.0000E-05    1024


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

  
  

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

 THE PRINCIPAL OUTPUT PARAMETERS FROM MODUL1 ARE:

          NSTATE        SIGMA       BVALUE                   MACT

             2        1.0000E+00  9.0000E+00                   32


 (K)                                       ERRVEC(K)          (J)   ACOEF(J)

 (1): TOTAL ERROR ESTIMATE: (2)+(3)+(4)    8.131E-05          (1)  2.0663E+00
 (2):   DISCRETISATION ERROR ESTIMATE      3.891E-05          (2) -1.9808E+00
 (3):   TRUNCATION ERROR ESTIMATE          4.014E-05          (3)  1.6095E+00
 (4):   ROUND-OFF ERROR ESTIMATE           2.262E-06          (4) -1.1846E+00
 (5): K IN K-R ESTIMATE OF ACOEF DECAY     6.883E+00          (5)  8.1876E-01
 (6): R IN K-R ESTIMATE OF ACOEF DECAY     1.508E+00          (6) -5.4579E-01
 (7): ALPHA: log(max(max.abs(acoef),1))    7.257E-01          (7)  3.5916E-01
 (8): BETA:  log(min.non-zero.abs(acoef)) -1.082E+01          (8) -2.3807E-01
                                                             (15)  2.0224E-02
                                                             (16) -1.3946E-02
                                                             (31)  3.0435E-05
                                                             (32) -1.9978E-05

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

 NOTE VALUE OF NSTATE.
  
  

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

 MODUL2 IS NOW CALLED 40 TIMES. IN EVERY CALL, THE INPUT PARAMETERS MACT,
 ACOEF, SIGMA, BVALUE, ERRVEC ARE AS GIVEN ABOVE.        THE OTHER INPUT
 PARAMETER, TVALUE, IS LISTED IN COLUMN 2 OF THE FOLLOWING TABLE.

     --INPUT--- -----OUTPUT-----   ----EXACT--- -----ERROR  EVALUATION------
       TVALUE   FUN(TVALUE) IFLO    FUN(TVALUE)  RELATIVE    PSEUDO    INDEX

   1 0.0000E+00 1.000000E+00  0    1.000000E+00  0.000E+00  0.000E+00    0
   2 5.0000E-02 1.074798E+00  0    1.074792E+00  5.324E-06  5.443E-06    0
   3 1.0000E-01 1.149095E+00  0    1.149086E+00  8.196E-06  8.521E-06    0
   4 1.5000E-01 1.222771E+00  0    1.222765E+00  4.582E-06  4.822E-06    0
   5 2.0000E-01 1.295725E+00  0    1.295717E+00  5.980E-06  6.344E-06    0
   6 2.5000E-01 1.367844E+00  0    1.367835E+00  6.624E-06  7.056E-06    0
   7 3.0000E-01 1.439026E+00  0    1.439018E+00  5.053E-06  5.387E-06    0
   8 3.5000E-01 1.509179E+00  0    1.509173E+00  4.107E-06  4.368E-06    0
   9 4.0000E-01 1.578218E+00  0    1.578209E+00  5.665E-06  5.993E-06    0
  10 4.5000E-01 1.646055E+00  0    1.646045E+00  6.011E-06  6.309E-06    0
  11 5.0000E-01 1.712612E+00  0    1.712603E+00  5.569E-06  5.784E-06    0
  12 5.5000E-01 1.777820E+00  0    1.777813E+00  3.755E-06  3.852E-06    0
  13 6.0000E-01 1.841617E+00  0    1.841611E+00  3.172E-06  3.206E-06    0
  14 6.5000E-01 1.903946E+00  0    1.903939E+00  4.007E-06  3.983E-06    0
  15 7.0000E-01 1.964754E+00  0    1.964744E+00  5.036E-06  4.913E-06    0
  16 1.0000E+00 2.295476E+00  0    2.295469E+00  3.012E-06  2.544E-06    0
  17 2.0000E+00 2.977413E+00  0    2.977400E+00  4.564E-06  1.839E-06    0
  18 3.0000E+00 3.300574E+00  0    3.300579E+00 -1.300E-06 -2.137E-07    0
  19 4.0000E+00 3.795270E+00  0    3.795282E+00 -3.267E-06 -2.271E-07    0
  20 5.0000E+00 4.729302E+00  0    4.729317E+00 -3.025E-06 -9.639E-08    0
  21 6.0000E+00 5.965345E+00  0    5.965629E+00 -4.756E-05 -7.033E-07    0
  22 7.0000E+00 7.191133E+00  0    7.192208E+00 -1.494E-04 -9.796E-07    0
  23 8.0000E+00 8.221043E+00  0    8.218063E+00  3.625E-04  9.994E-07    0
  24 9.0000E+00 9.076845E+00  0    9.079232E+00 -2.629E-04 -2.946E-07    0
  25 1.0000E+01 9.940937E+00  0    9.933112E+00  7.878E-04  3.552E-07    0
  26 1.1000E+01 1.083744E+01  0    1.089328E+01 -5.126E-03 -9.327E-07    0
  27 1.2000E+01 1.226147E+01  0    1.195380E+01  2.574E-02  1.890E-06    0
  28 1.3000E+01 1.264529E+01  0    1.303271E+01 -2.973E-02 -8.757E-07    0
  29 1.4000E+01 1.011287E+01  0    1.406115E+01 -2.808E-01 -3.283E-06    0
  30 1.5000E+01 6.049758E+00  0    1.503293E+01 -5.976E-01 -2.748E-06    0
  31 3.0000E+01 3.202149E-11  0    2.999755E+01 -1.000E+00 -2.807E-12    0
  32 5.0000E+01 4.911846E-34  0    4.999999E+01 -1.000E+00 -9.644E-21    0
  33 7.0000E+01 0.000000E+00 -1    7.000000E+01
  34 9.0000E+01 0.000000E+00 -1    9.000000E+01
  35 1.1000E+02 0.000000E+00  2    1.100000E+02
  36 1.3000E+02 0.000000E+00  2    1.300000E+02
  37 1.5000E+02 0.000000E+00  2    1.500000E+02
  38 1.7000E+02 0.000000E+00  2    1.700000E+02
  39 1.9000E+02 0.000000E+00  2    1.900000E+02
  40 2.1000E+02 0.000000E+00  2    2.100000E+02
                                                errvec(1) = 8.131E-05

 (1)    (2)          (3)     (4)        (5)         (6)        (7)     (8)

 COLUMN(3) CONTAINS THE RESULT FOR FUN(TVALUE) RETURNED BY MODUL2.
 COLUMN(4) CONTAINS IFLO FROM MODUL2, NORMALLY 0.
     IFLO IS NONZERO IF THE RESULT IN COLUMN 3 WOULD
     EXCEED THE OVERFLOW/UNDERFLOW LIMIT.
 COLUMN(5) CONTAINS THE EXACT RESULT FOR FUN(TVALUE).
 COLUMN(6) CONTAINS RELATIVE ERROR: ( COLUMN(3) - COLUMN(5) ) / COLUMN(5).
 COLUMN(7) CONTAINS PSEUDO-ERROR: ( COLUMN(3) - COLUMN(5) ) / EXP(SIGMA*TVALUE).
 COLUMN(8) CONTAINS INDEX, NORMALLY 0.
     IF COLUMN(7) IS GREATER THAN ERRVEC(1), INDEX = -1.
 ENTRIES (6-8) AFFECTED BY OVERFLOW/UNDERFLOW ARE BLANK.

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

  
  

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



 RUN NUMBER  4  *************************************************

   **** THIS IS OUTPUT FROM A RUN OF TESTMODULE ****

 F(s) = 1/(s+0.5)  +  1/s**2  +  1/(1+(s+0.2)**2) 

 NOTE NEW VALUE OF PARAMETER BVALUE.          bvalue = 0.000E+00

 THE PRINCIPAL INPUT PARAMETERS TO MODUL1 ARE:

            SIGMA0      SIGMA       BVALUE      EPSTOL      MTOP

          0.0000E+00  1.0000E+00  0.0000E+00  1.0000E-05    1024


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

  
  

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

 THE PRINCIPAL OUTPUT PARAMETERS FROM MODUL1 ARE:

          NSTATE        SIGMA       BVALUE                   MACT

             0        1.0000E+00  2.5000E+00                   16


 (K)                                       ERRVEC(K)          (J)   ACOEF(J)

 (1): TOTAL ERROR ESTIMATE: (2)+(3)+(4)    1.516E-06          (1)  1.7599E+00
 (2):   DISCRETISATION ERROR ESTIMATE      2.470E-07          (2) -7.8846E-01
 (3):   TRUNCATION ERROR ESTIMATE          2.509E-07          (3)  1.7379E-02
 (4):   ROUND-OFF ERROR ESTIMATE           1.018E-06          (4) -1.1629E-02
 (5): K IN K-R ESTIMATE OF ACOEF DECAY     9.811E-01          (5)  2.2242E-02
 (6): R IN K-R ESTIMATE OF ACOEF DECAY     2.660E+00          (6)  3.1208E-03
 (7): ALPHA: log(max(max.abs(acoef),1))    5.653E-01          (7) -1.7887E-03
 (8): BETA:  log(min.non-zero.abs(acoef)) -1.525E+01          (8) -9.7697E-04
                                                             (15)  1.0820E-06
                                                             (16)  3.5605E-07

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

  
  

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

 MODUL2 IS NOW CALLED 40 TIMES. IN EVERY CALL, THE INPUT PARAMETERS MACT,
 ACOEF, SIGMA, BVALUE, ERRVEC ARE AS GIVEN ABOVE.        THE OTHER INPUT
 PARAMETER, TVALUE, IS LISTED IN COLUMN 2 OF THE FOLLOWING TABLE.

     --INPUT--- -----OUTPUT-----   ----EXACT--- -----ERROR  EVALUATION------
       TVALUE   FUN(TVALUE) IFLO    FUN(TVALUE)  RELATIVE    PSEUDO    INDEX

   1 0.0000E+00 1.000000E+00  0    1.000000E+00  0.000E+00  0.000E+00    0
   2 5.0000E-02 1.074792E+00  0    1.074792E+00  0.000E+00  0.000E+00    0
   3 1.0000E-01 1.149086E+00  0    1.149086E+00  0.000E+00  0.000E+00    0
   4 1.5000E-01 1.222765E+00  0    1.222765E+00 -9.749E-08 -1.026E-07    0
   5 2.0000E-01 1.295717E+00  0    1.295717E+00 -9.200E-08 -9.760E-08    0
   6 2.5000E-01 1.367835E+00  0    1.367835E+00 -8.715E-08 -9.284E-08    0
   7 3.0000E-01 1.439018E+00  0    1.439018E+00  8.284E-08  8.831E-08    0
   8 3.5000E-01 1.509173E+00  0    1.509173E+00 -7.899E-08 -8.401E-08    0
   9 4.0000E-01 1.578209E+00  0    1.578209E+00 -1.511E-07 -1.598E-07    0
  10 4.5000E-01 1.646045E+00  0    1.646045E+00 -7.242E-08 -7.601E-08    0
  11 5.0000E-01 1.712603E+00  0    1.712603E+00  6.961E-08  7.230E-08    0
  12 5.5000E-01 1.777813E+00  0    1.777813E+00 -1.341E-07 -1.376E-07    0
  13 6.0000E-01 1.841611E+00  0    1.841611E+00 -1.942E-07 -1.963E-07    0
  14 6.5000E-01 1.903939E+00  0    1.903939E+00  6.261E-08  6.223E-08    0
  15 7.0000E-01 1.964744E+00  0    1.964744E+00 -1.820E-07 -1.776E-07    0
  16 1.0000E+00 2.295469E+00  0    2.295469E+00 -1.039E-07 -8.771E-08    0
  17 2.0000E+00 2.977400E+00  0    2.977400E+00  0.000E+00  0.000E+00    0
  18 3.0000E+00 3.300577E+00  0    3.300579E+00 -4.334E-07 -7.122E-08    0
  19 4.0000E+00 3.795281E+00  0    3.795282E+00 -1.885E-07 -1.310E-08    0
  20 5.0000E+00 4.729314E+00  0    4.729317E+00 -6.050E-07 -1.928E-08    0
  21 6.0000E+00 5.965621E+00  0    5.965629E+00 -1.359E-06 -2.009E-08    0
  22 7.0000E+00 7.192207E+00  0    7.192208E+00 -1.326E-07 -8.696E-10    0
  23 8.0000E+00 8.217942E+00  0    8.218063E+00 -1.474E-05 -4.063E-08    0
  24 9.0000E+00 9.078961E+00  0    9.079232E+00 -2.983E-05 -3.342E-08    0
  25 1.0000E+01 9.933285E+00  0    9.933112E+00  1.738E-05  7.837E-09    0
  26 1.1000E+01 1.089437E+01  0    1.089328E+01  9.945E-05  1.809E-08    0
  27 1.2000E+01 1.195532E+01  0    1.195380E+01  1.270E-04  9.328E-09    0
  28 1.3000E+01 1.303686E+01  0    1.303271E+01  3.182E-04  9.373E-09    0
  29 1.4000E+01 1.407975E+01  0    1.406115E+01  1.323E-03  1.547E-08    0
  30 1.5000E+01 1.508405E+01  0    1.503293E+01  3.400E-03  1.564E-08    0
  31 3.0000E+01-8.822815E+03  0    2.999755E+01 -2.951E+02 -8.284E-10    0
  32 5.0000E+01-2.031506E+06  0    4.999999E+01 -4.063E+04 -3.918E-16    0
  33 7.0000E+01-5.132537E+06  0    7.000000E+01 -7.332E+04 -2.040E-24    0
  34 9.0000E+01-2.327686E+06  0    9.000000E+01 -2.586E+04 -1.907E-33    0
  35 1.1000E+02 0.000000E+00  2    1.100000E+02
  36 1.3000E+02 0.000000E+00  2    1.300000E+02
  37 1.5000E+02 0.000000E+00  2    1.500000E+02
  38 1.7000E+02 0.000000E+00  2    1.700000E+02
  39 1.9000E+02 0.000000E+00  2    1.900000E+02
  40 2.1000E+02 0.000000E+00  2    2.100000E+02
                                                errvec(1) = 1.516E-06

 (1)    (2)          (3)     (4)        (5)         (6)        (7)     (8)

 COLUMN(3) CONTAINS THE RESULT FOR FUN(TVALUE) RETURNED BY MODUL2.
 COLUMN(4) CONTAINS IFLO FROM MODUL2, NORMALLY 0.
     IFLO IS NONZERO IF THE RESULT IN COLUMN 3 WOULD
     EXCEED THE OVERFLOW/UNDERFLOW LIMIT.
 COLUMN(5) CONTAINS THE EXACT RESULT FOR FUN(TVALUE).
 COLUMN(6) CONTAINS RELATIVE ERROR: ( COLUMN(3) - COLUMN(5) ) / COLUMN(5).
 COLUMN(7) CONTAINS PSEUDO-ERROR: ( COLUMN(3) - COLUMN(5) ) / EXP(SIGMA*TVALUE).
 COLUMN(8) CONTAINS INDEX, NORMALLY 0.
     IF COLUMN(7) IS GREATER THAN ERRVEC(1), INDEX = -1.
 ENTRIES (6-8) AFFECTED BY OVERFLOW/UNDERFLOW ARE BLANK.

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

  
  

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



 RUN NUMBER  5  *************************************************

   **** THIS IS OUTPUT FROM A RUN OF TESTMODULE ****

 F(s) = (s**2-1)/(s**2+1)**2  +exp(-4*s**0.5)  +  (-i/2)*ln((s+i)/(s-i))        
                                                    where i = sqrt(-1)          
 THIS IS THE FIRST RUN FOR TRANSFORM FUNCTION F(s).
 THE PRINCIPAL INPUT PARAMETERS TO MODUL1 ARE:

            SIGMA0      SIGMA       BVALUE      EPSTOL      MTOP

          0.0000E+00  2.5000E-01  0.0000E+00  1.0000E-05    1024


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

  
  

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

 THE PRINCIPAL OUTPUT PARAMETERS FROM MODUL1 ARE:

          NSTATE        SIGMA       BVALUE                   MACT

             2        2.5000E-01  6.2500E-01                  128


 (K)                                       ERRVEC(K)          (J)   ACOEF(J)

 (1): TOTAL ERROR ESTIMATE: (2)+(3)+(4)    1.456E-04          (1)  4.4607E-01
 (2):   DISCRETISATION ERROR ESTIMATE      6.736E-05          (2)  6.1444E-01
 (3):   TRUNCATION ERROR ESTIMATE          7.633E-05          (3)  7.2497E-01
 (4):   ROUND-OFF ERROR ESTIMATE           1.928E-06          (4)  5.5463E-01
 (5): K IN K-R ESTIMATE OF ACOEF DECAY     1.312E+00          (5)  1.2899E-01
 (6): R IN K-R ESTIMATE OF ACOEF DECAY     1.100E+00          (6) -3.8006E-01
 (7): ALPHA: log(max(max.abs(acoef),1))    0.000E+00          (7) -7.6109E-01
 (8): BETA:  log(min.non-zero.abs(acoef)) -1.525E+01          (8) -8.6463E-01
                                                             (15)  3.1684E-01
                                                             (16) -3.6931E-02
                                                             (31) -9.8527E-02
                                                             (32) -1.6489E-02
                                                             (63) -3.6792E-03
                                                             (64) -1.8672E-03
                                                            (127) -5.0620E-06
                                                            (128) -4.6458E-06

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

 NOTE VALUE OF NSTATE.
  
  

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

 MODUL2 IS NOW CALLED 40 TIMES. IN EVERY CALL, THE INPUT PARAMETERS MACT,
 ACOEF, SIGMA, BVALUE, ERRVEC ARE AS GIVEN ABOVE.        THE OTHER INPUT
 PARAMETER, TVALUE, IS LISTED IN COLUMN 2 OF THE FOLLOWING TABLE.

     --INPUT--- -----OUTPUT-----   ----EXACT--- -----ERROR  EVALUATION------
       TVALUE   FUN(TVALUE) IFLO    FUN(TVALUE)  RELATIVE    PSEUDO    INDEX

   1 0.0000E+00 9.999961E-01  0    1.000000E+00 -3.934E-06 -3.934E-06    0
   2 5.0000E-02 1.049516E+00  0    1.049521E+00 -4.771E-06 -4.945E-06    0
   3 1.0000E-01 1.097784E+00  0    1.097835E+00 -4.637E-05 -4.965E-05    0
   4 1.5000E-01 1.144532E+00  0    1.144570E+00 -3.343E-05 -3.686E-05    0
   5 2.0000E-01 1.189353E+00  0    1.189360E+00 -6.314E-06 -7.144E-06    0
   6 2.5000E-01 1.231852E+00  0    1.231845E+00  5.323E-06  6.159E-06    0
   7 3.0000E-01 1.271678E+00  0    1.271679E+00 -1.406E-06 -1.659E-06    0
   8 3.5000E-01 1.308534E+00  0    1.308548E+00 -1.084E-05 -1.300E-05    0
   9 4.0000E-01 1.342158E+00  0    1.342173E+00 -1.137E-05 -1.381E-05    0
  10 4.5000E-01 1.372301E+00  0    1.372307E+00 -4.604E-06 -5.646E-06    0
  11 5.0000E-01 1.398720E+00  0    1.398713E+00  4.773E-06  5.891E-06    0
  12 5.5000E-01 1.421165E+00  0    1.421149E+00  1.107E-05  1.371E-05    0
  13 6.0000E-01 1.439379E+00  0    1.439362E+00  1.184E-05  1.467E-05    0
  14 6.5000E-01 1.453097E+00  0    1.453087E+00  7.466E-06  9.221E-06    0
  15 7.0000E-01 1.462056E+00  0    1.462056E+00  4.077E-07  5.004E-07    0
  16 1.0000E+00 1.402440E+00  0    1.402440E+00 -8.500E-08 -9.284E-08    0
  17 2.0000E+00-3.236455E-01  0   -3.236540E-01 -2.606E-05  5.116E-06    0
  18 3.0000E+00-2.865687E+00  0   -2.865695E+00 -3.078E-06  4.167E-06    0
  19 4.0000E+00-2.751886E+00  0   -2.751887E+00 -2.599E-07  2.631E-07    0
  20 5.0000E+00 1.271868E+00  0    1.271875E+00 -5.342E-06 -1.947E-06    0
  21 6.0000E+00 5.753878E+00  0    5.753870E+00  1.326E-06  1.702E-06    0
  22 7.0000E+00 5.405565E+00  0    5.405578E+00 -2.382E-06 -2.237E-06    0
  23 8.0000E+00-1.010074E+00  0   -1.010084E+00 -9.796E-06  1.339E-06    0
  24 9.0000E+00-8.127598E+00  0   -8.127585E+00  1.525E-06 -1.307E-06    0
  25 1.0000E+01-8.421177E+00  0   -8.421198E+00 -2.491E-06  1.722E-06    0
  26 1.1000E+01-2.074468E-02  0   -2.072541E-02  9.300E-04 -1.232E-06    0
  27 1.2000E+01 1.010100E+01  0    1.010098E+01  1.983E-06  9.971E-07    0
  28 1.3000E+01 1.184680E+01  0    1.184683E+01 -2.254E-06 -1.035E-06    0
  29 1.4000E+01 2.001236E+00  0    2.001266E+00 -1.513E-05 -9.144E-07    0
  30 1.5000E+01-1.133704E+01  0   -1.133709E+01 -4.206E-06  1.121E-06    0
  31 3.0000E+01 4.599131E+00  0    4.600619E+00 -3.235E-04 -8.231E-07    0
  32 5.0000E+01 4.836720E+01  0    4.824600E+01  2.512E-03  4.517E-07    0
  33 7.0000E+01 1.776022E+01  0    4.434522E+01 -5.995E-01 -6.675E-07    0
  34 9.0000E+01-2.719626E+03  0   -4.031543E+01  6.646E+01 -4.533E-07    0
  35 1.1000E+02 3.189203E+04  0   -1.098917E+02 -2.912E+02  3.648E-08    0
  36 1.3000E+02-2.224673E+07  0   -4.775429E+01  4.659E+05 -1.709E-07    0
  37 1.5000E+02 3.583689E+09  0    1.048834E+02  3.417E+07  1.855E-07    0
  38 1.7000E+02 6.091731E+11  0    1.594617E+02  3.820E+09  2.124E-07    0
  39 1.9000E+02 1.007926E+13  0    1.260398E+01  7.997E+11  2.368E-08    0
  40 2.1000E+02-1.522168E+16  0   -1.856117E+02  8.201E+13 -2.410E-07    0
                                                errvec(1) = 1.456E-04

 (1)    (2)          (3)     (4)        (5)         (6)        (7)     (8)

 COLUMN(3) CONTAINS THE RESULT FOR FUN(TVALUE) RETURNED BY MODUL2.
 COLUMN(4) CONTAINS IFLO FROM MODUL2, NORMALLY 0.
     IFLO IS NONZERO IF THE RESULT IN COLUMN 3 WOULD
     EXCEED THE OVERFLOW/UNDERFLOW LIMIT.
 COLUMN(5) CONTAINS THE EXACT RESULT FOR FUN(TVALUE).
 COLUMN(6) CONTAINS RELATIVE ERROR: ( COLUMN(3) - COLUMN(5) ) / COLUMN(5).
 COLUMN(7) CONTAINS PSEUDO-ERROR: ( COLUMN(3) - COLUMN(5) ) / EXP(SIGMA*TVALUE).
 COLUMN(8) CONTAINS INDEX, NORMALLY 0.
     IF COLUMN(7) IS GREATER THAN ERRVEC(1), INDEX = -1.
 ENTRIES (6-8) AFFECTED BY OVERFLOW/UNDERFLOW ARE BLANK.

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

  
  

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



 RUN NUMBER  6  *************************************************

   **** THIS IS OUTPUT FROM A RUN OF TESTMODULE ****

 F(s) = (s**2-1)/(s**2+1)**2  +exp(-4*s**0.5)  +  (-i/2)*ln((s+i)/(s-i))        
                                                    where i = sqrt(-1)          
 NOTE NEW VALUE OF PARAMETER SIGMA.          sigma = 1.000E+00

 THE PRINCIPAL INPUT PARAMETERS TO MODUL1 ARE:

            SIGMA0      SIGMA       BVALUE      EPSTOL      MTOP

          0.0000E+00  1.0000E+00  0.0000E+00  1.0000E-05    1024


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

  
  

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

 THE PRINCIPAL OUTPUT PARAMETERS FROM MODUL1 ARE:

          NSTATE        SIGMA       BVALUE                   MACT

             0        1.0000E+00  2.5000E+00                   64


 (K)                                       ERRVEC(K)          (J)   ACOEF(J)

 (1): TOTAL ERROR ESTIMATE: (2)+(3)+(4)    9.698E-06          (1)  1.3281E+00
 (2):   DISCRETISATION ERROR ESTIMATE      3.953E-06          (2)  1.6170E-02
 (3):   TRUNCATION ERROR ESTIMATE          4.208E-06          (3) -4.2904E-01
 (4):   ROUND-OFF ERROR ESTIMATE           1.537E-06          (4) -3.8786E-02
 (5): K IN K-R ESTIMATE OF ACOEF DECAY     1.402E-03          (5)  1.2798E-01
 (6): R IN K-R ESTIMATE OF ACOEF DECAY     1.132E+00          (6)  3.0187E-02
 (7): ALPHA: log(max(max.abs(acoef),1))    2.837E-01          (7) -2.8210E-02
 (8): BETA:  log(min.non-zero.abs(acoef)) -1.525E+01          (8) -1.2401E-02
                                                             (15)  1.8021E-04
                                                             (16)  1.2236E-04
                                                             (31) -1.8906E-05
                                                             (32) -1.5820E-05
                                                             (63) -3.9336E-07
                                                             (64) -4.9857E-07

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

  
  

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

 MODUL2 IS NOW CALLED 40 TIMES. IN EVERY CALL, THE INPUT PARAMETERS MACT,
 ACOEF, SIGMA, BVALUE, ERRVEC ARE AS GIVEN ABOVE.        THE OTHER INPUT
 PARAMETER, TVALUE, IS LISTED IN COLUMN 2 OF THE FOLLOWING TABLE.

     --INPUT--- -----OUTPUT-----   ----EXACT--- -----ERROR  EVALUATION------
       TVALUE   FUN(TVALUE) IFLO    FUN(TVALUE)  RELATIVE    PSEUDO    INDEX

   1 0.0000E+00 1.000001E+00  0    1.000000E+00  7.153E-07  7.153E-07    0
   2 5.0000E-02 1.049518E+00  0    1.049521E+00 -2.726E-06 -2.721E-06    0
   3 1.0000E-01 1.097836E+00  0    1.097835E+00  1.412E-06  1.402E-06    0
   4 1.5000E-01 1.144568E+00  0    1.144570E+00 -1.354E-06 -1.334E-06    0
   5 2.0000E-01 1.189362E+00  0    1.189360E+00  1.303E-06  1.269E-06    0
   6 2.5000E-01 1.231848E+00  0    1.231845E+00  2.323E-06  2.228E-06    0
   7 3.0000E-01 1.271680E+00  0    1.271679E+00  5.624E-07  5.299E-07    0
   8 3.5000E-01 1.308546E+00  0    1.308548E+00 -1.549E-06 -1.428E-06    0
   9 4.0000E-01 1.342170E+00  0    1.342173E+00 -2.043E-06 -1.838E-06    0
  10 4.5000E-01 1.372307E+00  0    1.372307E+00  1.737E-07  1.520E-07    0
  11 5.0000E-01 1.398715E+00  0    1.398713E+00  1.534E-06  1.301E-06    0
  12 5.5000E-01 1.421151E+00  0    1.421149E+00  1.174E-06  9.629E-07    0
  13 6.0000E-01 1.439363E+00  0    1.439362E+00  4.969E-07  3.925E-07    0
  14 6.5000E-01 1.453085E+00  0    1.453087E+00 -1.231E-06 -9.335E-07    0
  15 7.0000E-01 1.462053E+00  0    1.462056E+00 -1.631E-06 -1.184E-06    0
  16 1.0000E+00 1.402442E+00  0    1.402440E+00  1.190E-06  6.140E-07    0
  17 2.0000E+00-3.236524E-01  0   -3.236540E-01 -4.972E-06  2.178E-07    0
  18 3.0000E+00-2.865691E+00  0   -2.865695E+00 -1.664E-06  2.374E-07    0
  19 4.0000E+00-2.751883E+00  0   -2.751887E+00 -1.473E-06  7.424E-08    0
  20 5.0000E+00 1.271895E+00  0    1.271875E+00  1.593E-05  1.365E-07    0
  21 6.0000E+00 5.753915E+00  0    5.753870E+00  7.790E-06  1.111E-07    0
  22 7.0000E+00 5.405581E+00  0    5.405578E+00  7.057E-07  3.479E-09    0
  23 8.0000E+00-1.010353E+00  0   -1.010084E+00  2.665E-04 -9.030E-08    0
  24 9.0000E+00-8.127125E+00  0   -8.127585E+00 -5.667E-05  5.685E-08    0
  25 1.0000E+01-8.422092E+00  0   -8.421198E+00  1.062E-04 -4.061E-08    0
  26 1.1000E+01-1.926995E-02  0   -2.072541E-02 -7.023E-02  2.431E-08    0
  27 1.2000E+01 1.010220E+01  0    1.010098E+01  1.208E-04  7.494E-09    0
  28 1.3000E+01 1.182786E+01  0    1.184683E+01 -1.601E-03 -4.286E-08    0
  29 1.4000E+01 2.072429E+00  0    2.001266E+00  3.556E-02  5.917E-08    0
  30 1.5000E+01-1.147915E+01  0   -1.133709E+01  1.253E-02 -4.346E-08    0
  31 3.0000E+01 1.245046E+05  0    4.600619E+00  2.706E+04  1.165E-08    0
  32 5.0000E+01 2.365975E+14  0    4.824600E+01  4.904E+12  4.563E-08    0
  33 7.0000E+01-3.927292E+22  0    4.434522E+01 -8.856E+20 -1.561E-08    0
  34 9.0000E+01-3.001883E+31  0   -4.031543E+01  7.446E+29 -2.460E-08    0
  35 1.1000E+02 0.000000E+00  2   -1.098917E+02
  36 1.3000E+02 0.000000E+00  2   -4.775429E+01
  37 1.5000E+02 0.000000E+00  2    1.048834E+02
  38 1.7000E+02 0.000000E+00  2    1.594617E+02
  39 1.9000E+02 0.000000E+00  2    1.260398E+01
  40 2.1000E+02 0.000000E+00  2   -1.856117E+02
                                                errvec(1) = 9.698E-06

 (1)    (2)          (3)     (4)        (5)         (6)        (7)     (8)

 COLUMN(3) CONTAINS THE RESULT FOR FUN(TVALUE) RETURNED BY MODUL2.
 COLUMN(4) CONTAINS IFLO FROM MODUL2, NORMALLY 0.
     IFLO IS NONZERO IF THE RESULT IN COLUMN 3 WOULD
     EXCEED THE OVERFLOW/UNDERFLOW LIMIT.
 COLUMN(5) CONTAINS THE EXACT RESULT FOR FUN(TVALUE).
 COLUMN(6) CONTAINS RELATIVE ERROR: ( COLUMN(3) - COLUMN(5) ) / COLUMN(5).
 COLUMN(7) CONTAINS PSEUDO-ERROR: ( COLUMN(3) - COLUMN(5) ) / EXP(SIGMA*TVALUE).
 COLUMN(8) CONTAINS INDEX, NORMALLY 0.
     IF COLUMN(7) IS GREATER THAN ERRVEC(1), INDEX = -1.
 ENTRIES (6-8) AFFECTED BY OVERFLOW/UNDERFLOW ARE BLANK.

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

  
  

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



 RUN NUMBER  7  *************************************************

   **** THIS IS OUTPUT FROM A RUN OF TESTMODULE ****

 F(s) = (s**2-1)/(s**2+1)**2  +exp(-4*s**0.5)  +  (-i/2)*ln((s+i)/(s-i))        
                                                    where i = sqrt(-1)          
 NOTE NEW VALUE OF PARAMETER SIGMA.          sigma = 4.000E+00

 THE PRINCIPAL INPUT PARAMETERS TO MODUL1 ARE:

            SIGMA0      SIGMA       BVALUE      EPSTOL      MTOP

          0.0000E+00  4.0000E+00  0.0000E+00  1.0000E-05    1024


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

  
  

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

 THE PRINCIPAL OUTPUT PARAMETERS FROM MODUL1 ARE:

          NSTATE        SIGMA       BVALUE                   MACT

             0        4.0000E+00  1.0000E+01                   16


 (K)                                       ERRVEC(K)          (J)   ACOEF(J)

 (1): TOTAL ERROR ESTIMATE: (2)+(3)+(4)    2.776E-06          (1)  1.2256E+00
 (2):   DISCRETISATION ERROR ESTIMATE      1.037E-06          (2) -2.4895E-01
 (3):   TRUNCATION ERROR ESTIMATE          1.053E-06          (3)  1.9621E-02
 (4):   ROUND-OFF ERROR ESTIMATE           6.864E-07          (4)  5.5186E-03
 (5): K IN K-R ESTIMATE OF ACOEF DECAY     2.250E-03          (5) -2.2264E-03
 (6): R IN K-R ESTIMATE OF ACOEF DECAY     1.706E+00          (6)  4.1844E-04
 (7): ALPHA: log(max(max.abs(acoef),1))    2.034E-01          (7)  5.8116E-05
 (8): BETA:  log(min.non-zero.abs(acoef)) -1.452E+01          (8) -1.6980E-05
                                                             (15)  3.4929E-06
                                                             (16)  2.2452E-06

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

  
  

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

 MODUL2 IS NOW CALLED 40 TIMES. IN EVERY CALL, THE INPUT PARAMETERS MACT,
 ACOEF, SIGMA, BVALUE, ERRVEC ARE AS GIVEN ABOVE.        THE OTHER INPUT
 PARAMETER, TVALUE, IS LISTED IN COLUMN 2 OF THE FOLLOWING TABLE.

     --INPUT--- -----OUTPUT-----   ----EXACT--- -----ERROR  EVALUATION------
       TVALUE   FUN(TVALUE) IFLO    FUN(TVALUE)  RELATIVE    PSEUDO    INDEX

   1 0.0000E+00 1.000000E+00  0    1.000000E+00  0.000E+00  0.000E+00    0
   2 5.0000E-02 1.049523E+00  0    1.049521E+00  1.817E-06  1.562E-06    0
   3 1.0000E-01 1.097836E+00  0    1.097835E+00  1.629E-06  1.199E-06    0
   4 1.5000E-01 1.144571E+00  0    1.144570E+00  7.291E-07  4.580E-07    0
   5 2.0000E-01 1.189362E+00  0    1.189360E+00  1.403E-06  7.499E-07    0
   6 2.5000E-01 1.231846E+00  0    1.231845E+00  4.839E-07  2.193E-07    0
   7 3.0000E-01 1.271677E+00  0    1.271679E+00 -1.875E-06 -7.181E-07    0
   8 3.5000E-01 1.308545E+00  0    1.308548E+00 -1.822E-06 -5.879E-07    0
   9 4.0000E-01 1.342174E+00  0    1.342173E+00  7.994E-07  2.166E-07    0
  10 4.5000E-01 1.372312E+00  0    1.372307E+00  3.475E-06  7.882E-07    0
  11 5.0000E-01 1.398717E+00  0    1.398713E+00  2.813E-06  5.324E-07    0
  12 5.5000E-01 1.421148E+00  0    1.421149E+00 -7.549E-07 -1.189E-07    0
  13 6.0000E-01 1.439356E+00  0    1.439362E+00 -4.224E-06 -5.515E-07    0
  14 6.5000E-01 1.453078E+00  0    1.453087E+00 -5.825E-06 -6.286E-07    0
  15 7.0000E-01 1.462051E+00  0    1.462056E+00 -3.343E-06 -2.972E-07    0
  16 1.0000E+00 1.402432E+00  0    1.402440E+00 -5.525E-06 -1.419E-07    0
  17 2.0000E+00-3.231656E-01  0   -3.236540E-01 -1.509E-03  1.638E-07    0
  18 3.0000E+00-2.837928E+00  0   -2.865695E+00 -9.690E-03  1.706E-07    0
  19 4.0000E+00-3.021195E+00  0   -2.751887E+00  9.786E-02 -3.031E-08    0
  20 5.0000E+00 4.668805E+00  0    1.271875E+00  2.671E+00  7.002E-09    0
  21 6.0000E+00-3.817619E+03  0    5.753870E+00 -6.645E+02 -1.443E-07    0
  22 7.0000E+00-5.782086E+04  0    5.405578E+00 -1.070E+04 -3.998E-08    0
  23 8.0000E+00-3.666862E+05  0   -1.010084E+00  3.630E+05 -4.644E-09    0
  24 9.0000E+00-1.411164E+06  0   -8.127585E+00  1.736E+05 -3.273E-10    0
  25 1.0000E+01-3.871088E+06  0   -8.421198E+00  4.597E+05 -1.645E-11    0
  26 1.1000E+01-8.282860E+06  0   -2.072541E-02  3.996E+08 -6.445E-13    0
  27 1.2000E+01-1.463360E+07  0    1.010098E+01 -1.449E+06 -2.086E-14    0
  28 1.3000E+01-2.219130E+07  0    1.184683E+01 -1.873E+06 -5.793E-16    0
  29 1.4000E+01-2.969926E+07  0    2.001266E+00 -1.484E+07 -1.420E-17    0
  30 1.5000E+01-3.581137E+07  0   -1.133709E+01  3.159E+06 -3.136E-19    0
  31 3.0000E+01 0.000000E+00  2    4.600619E+00
  32 5.0000E+01 0.000000E+00  2    4.824600E+01
  33 7.0000E+01 0.000000E+00  2    4.434522E+01
  34 9.0000E+01 0.000000E+00  2   -4.031543E+01
  35 1.1000E+02 0.000000E+00  2   -1.098917E+02
  36 1.3000E+02 0.000000E+00  2   -4.775429E+01
  37 1.5000E+02 0.000000E+00  2    1.048834E+02
  38 1.7000E+02 0.000000E+00  2    1.594617E+02
  39 1.9000E+02 0.000000E+00  2    1.260398E+01
  40 2.1000E+02 0.000000E+00  2   -1.856117E+02
                                                errvec(1) = 2.776E-06

 (1)    (2)          (3)     (4)        (5)         (6)        (7)     (8)

 COLUMN(3) CONTAINS THE RESULT FOR FUN(TVALUE) RETURNED BY MODUL2.
 COLUMN(4) CONTAINS IFLO FROM MODUL2, NORMALLY 0.
     IFLO IS NONZERO IF THE RESULT IN COLUMN 3 WOULD
     EXCEED THE OVERFLOW/UNDERFLOW LIMIT.
 COLUMN(5) CONTAINS THE EXACT RESULT FOR FUN(TVALUE).
 COLUMN(6) CONTAINS RELATIVE ERROR: ( COLUMN(3) - COLUMN(5) ) / COLUMN(5).
 COLUMN(7) CONTAINS PSEUDO-ERROR: ( COLUMN(3) - COLUMN(5) ) / EXP(SIGMA*TVALUE).
 COLUMN(8) CONTAINS INDEX, NORMALLY 0.
     IF COLUMN(7) IS GREATER THAN ERRVEC(1), INDEX = -1.
 ENTRIES (6-8) AFFECTED BY OVERFLOW/UNDERFLOW ARE BLANK.
