Fast trigonometric integration

A fast approximation of sinint or Si(x) and cosint or Ci(x) to ~machine precision using Padé approximants.

This function approximates the integral of sinc(t)=sin(t)/t for the range of 0 to x, as well as the integral of cos(t)/t for the range x to infinity. The resulting functions are often called Si(x) and Ci(x), as e.g. found at https://en.wikipedia.org/wiki/Trigonometric_integral . The function uses Padé approximants to approximate the form of functions, and is accurate to within machine precision for the entire range of computation. The resulting functions are orders of magnitude faster than the native MATLAB implementation.

The result only applies to real-valued numbers. The Ci(x) has been continued into negative range through a mirroring procedure.