result of:   j=0 indicates x too small
               j=100 indicates x too large
     locate:    guess    j       xx(j)       xx(j+1) 
   -90.00000      5      0    lower lim   -72.948730 
   -80.00000     10      0    lower lim   -72.948730 
   -70.00000     15     27   -70.142578   -69.944801 
   -60.00000     20     52   -60.536263   -59.845963 
   -50.00000     25     63   -50.663937   -49.467468 
   -40.00000     30     70   -40.884548   -39.186684 
   -30.00000     35     75   -31.478918   -29.298815 
   -20.00000     40     79   -22.064632   -19.401850 
   -10.00000     45     83   -10.566000    -7.313669 
     0.00000     50     86    -0.300206     3.478463 
    10.00000     55     88     7.450869    11.626944 
    20.00000     60     90    16.017132    20.632408 
    30.00000     65     92    25.484316    30.584986 
    40.00000     70     94    35.947174    41.584286 
    50.00000     75     96    47.510418    53.740391 
    60.00000     80     97    53.740391    60.289780 
    70.00000     85     99    67.174965    74.413162 
    80.00000     90    100    74.413162    upper lim 
    90.00000     95    100    74.413162    upper lim