 *********************************************************************
 Sample results showing the relative error in the real and imaginary parts
 from the "Original 680 code" and the "Revised 680 code" for points scattered
 over the region in which the Original 680 code loses its accuracy
 *********************************************************************
                                                            Original 680                   Revised 680
           x                      y                    Error V        Error L        Error V        Error L
 1.830000000000000E+000 9.999999999999999E-021        0.00000E+00    2.89886E-16    0.00000E+00    8.69658E-16
 1.840000000000000E+000 9.999999999999999E-021        1.12720E-14   -5.83921E-16    0.00000E+00    5.83921E-16
 2.300000000000000E+000 9.999999999999999E-021       -7.74160E-15   -3.95060E-16    0.00000E+00   -3.95060E-16
 2.500000000000000E+000 9.999999999999999E-021       -1.44676E-13    1.32315E-15    0.00000E+00    2.20525E-16
 3.900000000000000E+000 9.999999999999999E-021       -2.00899E-10   -1.11028E-15    0.00000E+00    0.00000E+00
 4.300000000000000E+000 9.999999999999999E-021        2.66195E-09    1.23274E-15    0.00000E+00    2.87640E-15
 4.500000000000000E+000 9.999999999999999E-021       -3.84836E-09    2.15602E-16    0.00000E+00   -2.15602E-16
 9.999999999999999E-021 6.300000000000000E+000        1.56872E-16    5.48782E-15    4.70615E-16    6.00230E-15
 6.300000000000000E+000 2.000000000000000E-001       -4.84381E-15    6.27816E-15   -4.40346E-15    6.58441E-15
 6.300000000000000E+000 3.000000000000000E-004       -1.32244E-12    5.50659E-15    9.73644E-15    6.11844E-15
 6.300000000000000E+000 4.500000000000000E-006       -8.70515E-11    5.96548E-15    9.94326E-15    6.88324E-15
 6.300000000000000E+000 5.000000000000000E-011       -7.83303E-06    5.81252E-15    9.96807E-15    6.73028E-15
 6.300000000000000E+000-9.999999999999999E-021        1.00003E+00    5.81252E-15    0.00000E+00    6.73028E-15
-6.300000000000000E+000 1.000000000000000E-018       -9.97453E-01    5.81252E-15    0.00000E+00    6.73028E-15
 5.300000000000000E+000 1.000000000000000E-016       -1.12426E-05    2.68708E-15   -1.59787E-16    2.68708E-15
 5.300000000000000E+000 1.000000000000000E-014       -9.88603E-06    3.07095E-15    0.00000E+00    2.68708E-15
 5.300000000000000E+000 1.000000000000000E-012       -1.64937E-05    2.04730E-15    3.09170E-16    2.68708E-15
 5.300000000000000E+000 1.000000000000000E-010       -4.51950E-07    2.30321E-15    3.51385E-15    2.68708E-15
 5.300000000000000E+000 1.000000000000000E-008       -1.77503E-08    2.81504E-15    4.48384E-15    2.68708E-15
 5.300000000000000E+000 1.000000000000000E-006       -7.05761E-10    3.71073E-15    3.88932E-15    3.07095E-15
 5.300000000000000E+000 1.000000000000000E-004       -4.58319E-12    2.17526E-15    4.77934E-15    3.32686E-15
 5.300000000000000E+000 1.000000000000000E-002       -9.94107E-15    2.68709E-15    4.20584E-15    3.32688E-15
 5.300000000000000E+000 1.000000000000000E-001        1.02001E-15    2.17611E-15    1.42802E-15    2.56013E-15
 7.300000000000000E+000 9.999999999999999E-021       -6.18430E-02   -7.11382E-16    7.68913E-15   -3.55691E-16
 7.300000000000000E+000 1.000000000000000E-018       -6.58762E-04   -7.11382E-16    8.41476E-15   -3.55691E-16
 7.300000000000000E+000 1.000000000000000E-016       -6.59192E-06   -7.11382E-16    8.48099E-15   -3.55691E-16
 7.300000000000000E+000 1.000000000000000E-014       -6.59196E-08   -7.11382E-16    8.36796E-15   -3.55691E-16
 7.300000000000000E+000 1.000000000000000E-012       -6.59197E-10   -7.11382E-16    8.25036E-15   -3.55691E-16
 7.300000000000000E+000 1.000000000000000E-010       -6.59325E-12   -7.11382E-16    8.15193E-15   -3.55691E-16
 1.730000000000000E+001 9.999999999999999E-021        2.10949E-14    2.08166E-14   -2.48175E-14    2.12414E-14
 2.130000000000000E+001 9.999999999999999E-021        7.76084E-14    7.71946E-14    7.80795E-14    7.75871E-14
 2.230000000000000E+001 0.000000000000000E+000        0.00000E+00    2.10971E-14    0.00000E+00    2.15081E-14
 2.700000000000000E+001 0.000000000000000E+000       -9.99999E-01    3.31841E-16   -9.99999E-01    6.63683E-16
 7.300000000000000E+000 1.000000000000000E-001       -1.98974E-16   -1.06728E-15    0.00000E+00   -5.33642E-16
 7.300000000000000E+000 0.000000000000000E+000        0.00000E+00   -7.11382E-16    0.00000E+00   -3.55691E-16
 5.300000000000000E+000 0.000000000000000E+000        0.00000E+00    2.68708E-15    0.00000E+00    2.68708E-15
 6.400000000000000E+000 9.999999999999999E-021       -9.99912E-01    5.12997E-15    0.00000E+00    5.59634E-15
    
    

Summary of execution time and accuracyin computing 2,840,071 input valuesfor z with 71 values for y and 40001 values for x.
 ___________________________
 ________

case    1

y uniformly spaced on the logarithmic scale between 1e-5 and 1e5 and x uniformly spaced on the linear scale between -500 and 500

Original 680:

Total execution time  =  11.8478     processor dependent units
Average time per call = 0.417166E-06 processor dependent units
   
max_rel_err_Re    = 0.151590E-09
max_rel_err_Im    = 0.168783E-12
   
   

Revised 680:

Total execution time  =  12.1358     processor dependent units
Average time per call = 0.427308E-06 processor dependent units
   
max_rel_err_Re    = 0.169079E-12
max_rel_err_Im    = 0.169250E-12
   
   
 ________

case    2

y uniformly spaced on the logarithmic scale between 1e-20 and 1e4 and x uniformly spaced on the linear scale between -200 and 200

Original 680:

Total execution time  =  15.0530     processor dependent units
Average time per call = 0.530020E-06 processor dependent units
   
max_rel_err_Re    = 0.999974    
max_rel_err_Im    = 0.168162E-12
   
   

Revised 680:

Total execution time  =  14.1075     processor dependent units
Average time per call = 0.496729E-06 processor dependent units
   
max_rel_err_Re    = 0.168755E-12
max_rel_err_Im    = 0.168645E-12
   
   
 ________

case    3

y uniformly spaced on the logarithmic scale between 1e-5 and 1e5 and x uniformly spaced on the linear scale between -10 and 10

Original 680:

Total execution time  =  29.1227     processor dependent units
Average time per call = 0.102542E-05 processor dependent units
   
max_rel_err_Re    = 0.183968E-09
max_rel_err_Im    = 0.294583E-13
   
   

Revised 680:

Total execution time  =  21.2668     processor dependent units
Average time per call = 0.748814E-06 processor dependent units
   
max_rel_err_Re    = 0.816743E-13
max_rel_err_Im    = 0.298873E-13
   
   
 ________

case    4

y uniformly spaced on the logarithmic scale between 1e-20 and 1e6 and x randomly generated to satisfy |z|<=6

Original 680:

Total execution time  =  54.7299     processor dependent units
Average time per call = 0.192706E-05 processor dependent units
   
max_rel_err_Re    = 0.386064E-01
max_rel_err_Im    = 0.228232E-13
   
   

Revised 680:

Total execution time  =  22.9890     processor dependent units
Average time per call = 0.809452E-06 processor dependent units
   
max_rel_err_Re    = 0.593688E-13
max_rel_err_Im    = 0.232236E-13
   
   
   
