nag_fresnel_c (s20adc) returns a value for the Fresnel Integral .

nag_fresnel_c (s20adc) evaluates an approximation to the Fresnel Integral

The function is based on Chebyshev expansions.

Let  and  be the relative errors in the argument and result respectively.

If  is somewhat larger than the machine precision (i.e., if  is due to data errors etc.), then  and  are approximately related by .

However, if  is of the same order as the machine precision, then rounding errors could make  slightly larger than the above relation predicts.

For small ,  and there is no amplification of relative error.

For moderately large values of ,  and the result will be subject to increasingly large amplification of errors. However, the above relation breaks down for large values of  (i.e., when  is of the order of the machine precision); in this region the relative error in the result is essentially bounded by .

Hence the effects of error amplification are limited and at worst the relative error loss should not exceed half the possible number of significant figures.

None.