NAG Library Routine Document
S15AFF returns a value for Dawson's Integral, , via the function name.
|REAL (KIND=nag_wp) S15AFF
S15AFF evaluates an approximation for Dawson's Integral
The routine is based on two Chebyshev expansions:
, and for
. These approximations are used for those values of
for which the result is correct to machine precision
. For very large
on some machines,
may underflow and then the result is set exactly to zero (see the Users' Note
for your implementation for details).
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
- 1: X – REAL (KIND=nag_wp)Input
On entry: the argument of the function.
- 2: IFAIL – INTEGERInput/Output
must be set to
. If you are unfamiliar with this parameter you should refer to Section 3.3
in the Essential Introduction for details.
For environments where it might be inappropriate to halt program execution when an error is detected, the value
is recommended. If the output of error messages is undesirable, then the value
is recommended. Otherwise, if you are not familiar with this parameter, the recommended value is
. When the value is used it is essential to test the value of IFAIL on exit.
unless the routine detects an error or a warning has been flagged (see Section 6
6 Error Indicators and Warnings
There are no failure exits from this routine.
Let and be the relative errors in the argument and result respectively.
is considerably greater than the machine precision
is due to data errors etc.), then
are approximately related by:
The following graph shows the behaviour of the error amplification factor
is of the same order as machine precision
, then rounding errors could make
somewhat larger than the above relation indicates. In fact
will be largely independent of
, but will be of the order of a few times the machine precision
This example 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 (s15affe.f90)
9.2 Program Data
Program Data (s15affe.d)
9.3 Program Results
Program Results (s15affe.r)