  This work is an extension of previous work by Alazah et al. [M. Alazah, S. N.
Chandler-Wilde, and S. La Porte, Numerische Mathematik, 128(4):635-661, 2014].
We split the computation of the Fresnel Integrals into 3 cases: a truncated
Taylor series, modified trapezoid rule and an asymptotic expansion for small,
medium and large arguments respectively. These special functions can be
computed accurately and efficiently up to an arbitrary precision. Error
estimates are provided and we give a systematic method in choosing the various
parameters for a desired precision. We illustrate this method and verify
numerically using double precision.
