result of:  j=0 indicates x too small
            j=100 indicates x too large
   locate       j       xx(j)      xx(j+1) 
  -90.0000      0    lower lim   -72.948730 
  -80.0000      0    lower lim   -72.948730 
  -70.0000     27   -70.142578   -69.944801
  -60.0000     52   -60.536263   -59.845963
  -50.0000     63   -50.663937   -49.467468
  -40.0000     70   -40.884548   -39.186684
  -30.0000     75   -31.478918   -29.298815
  -20.0000     79   -22.064632   -19.401850
  -10.0000     83   -10.566000    -7.313669
    0.0000     86    -0.300206     3.478463
   10.0000     88     7.450869    11.626944
   20.0000     90    16.017132    20.632408
   30.0000     92    25.484316    30.584986
   40.0000     94    35.947174    41.584286
   50.0000     96    47.510418    53.740391
   60.0000     97    53.740391    60.289780
   70.0000     99    67.174965    74.413162
   80.0000    100    74.413162    upper lim
   90.0000    100    74.413162    upper lim