generation of interpolation tables
 ... sin(x)    0<x<PI
 ... exp(x)    0<x<1 
how many entries go in these tables?

sine function from 0 to PI

        x          f(x)     interpolated         error
    0.157080     0.156434     0.156435         0.000050
    0.471239     0.453990     0.453990        -0.000003
    0.785398     0.707107     0.707107         0.000001
    1.099557     0.891007     0.891006         0.000000
    1.413717     0.987688     0.987688         0.000000
    1.727876     0.987688     0.987688         0.000000
    2.042035     0.891007     0.891007         0.000000
    2.356194     0.707107     0.707107         0.000001
    2.670354     0.453991     0.453991        -0.000003
    2.984513     0.156434     0.156434        -0.000003

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press RETURN

exponential function from 0 to 1

        x          f(x)     interpolated         error
    0.050000     1.051271     1.051273         0.000001
    0.150000     1.161834     1.161834         0.000000
    0.250000     1.284025     1.284026         0.000000
    0.350000     1.419068     1.419067         0.000000
    0.450000     1.568312     1.568312         0.000000
    0.550000     1.733253     1.733253         0.000000
    0.650000     1.915541     1.915541         0.000000
    0.750000     2.117000     2.117000         0.000000
    0.850000     2.339647     2.339647         0.000000
    0.950000     2.585710     2.585710         0.000000

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press RETURN