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spence

Dilogarithm.

SYNOPSIS:

double x, y, spence();
y = spence(x);

DESCRIPTION:

Computes the integral:

                    x
                    -
                   | | log t
spence(x)  =  -   |   ----- dt
                 | |   t - 1
                  -
                  1

for x >= 0.  A rational approximation gives the integral in the interval (0.5, 1.5).  Transformation formulas for 1/x and 1-x are employed outside the basic expansion range.

ACCURACY:

                      Relative error:
arithmetic   domain     # trials      peak         rms
    IEEE      0,4         30000       3.9e-15     5.4e-16
    DEC       0,4          3000       2.5e-16     4.5e-17