NAG Library Function Document
nag_fresnel_s (s20acc) returns a value for the Fresnel Integral .
||nag_fresnel_s (double x)
nag_fresnel_s (s20acc) evaluates an approximation to the Fresnel Integral
The function is based on Chebyshev expansions.
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
x – doubleInput
On entry: the argument of the function.
6 Error Indicators and Warnings
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 hence there is only moderate amplification of relative error. Of course for very small where the correct result would underflow and exact zero is returned, relative error-control is lost.
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.
The following program reads values of the argument from a file, evaluates the function at each value of and prints the results.
9.1 Program Text
Program Text (s20acce.c)
9.2 Program Data
Program Data (s20acce.d)
9.3 Program Results
Program Results (s20acce.r)