sici

Sine and cosine integrals.

SYNOPSIS:

double x, Ci, Si, sici();
sici(x, &Si, &Ci);

DESCRIPTION:

Evaluates the integrals:

                          x
                          -
                         | cos t - 1
   Ci(x) = eul + ln x + | --------- dt,
                         |      t
                        -
                         0
             x
             -
            | sin t
   Si(x) = | ----- dt
            |    t
           -
            0

where eul = 0.57721566490153286061 is Euler's constant. The integrals are approximated by rational functions. For x > 8 auxiliary functions f(x) and g(x) are employed such that

Ci(x) = f(x) sin(x) - g(x) cos(x)
Si(x) = pi/2 - f(x) cos(x) - g(x) sin(x)

ACCURACY:

Test interval = [0,50].
Absolute error, except relative when > 1:

arithmetic   function   # trials      peak         rms
    IEEE        Si        30000       4.4e-16     7.3e-17
    IEEE        Ci        30000       6.9e-16     5.1e-17
    DEC         Si         5000       4.4e-17     9.0e-18
    DEC         Ci         5300       7.9e-17     5.2e-18