NAG Library Routine Document
S13ACF returns the value of the cosine integral
via the routine name where
denotes Euler's constant.
|REAL (KIND=nag_wp) S13ACF
S13ACF calculates an approximate value for .
it is based on the Chebyshev expansion
where the value of
is given in the Users' Note
for your implementation,
to within the accuracy possible (see Section 7
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
If on entry
, explanatory error messages are output on the current error message unit (as defined by X04AAF
Errors or warnings detected by the routine:
The routine has been called with an argument less than or equal to zero for which the function is not defined. The result returned is zero.
are the absolute and relative errors in the result and
is the relative error in the argument then in principle these are related by
That is accuracy will be limited by machine precision
near the origin and near the zeros of
, but near the zeros of
only absolute accuracy can be maintained.
The behaviour of this amplification is shown in Figure 1
For large values of
is limited by the finite precision of the machine it becomes impossible to return results which have any relative accuracy. That is, when
we have that
and hence is not significantly different from zero.
Hence is chosen such that for values of , in principle would have values less than the machine precision and so is essentially zero.
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 (s13acfe.f90)
9.2 Program Data
Program Data (s13acfe.d)
9.3 Program Results
Program Results (s13acfe.r)