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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