NAG Library Routine Document
S01EAF evaluates the exponential function , for
|COMPLEX (KIND=nag_wp) S01EAF
S01EAF evaluates the exponential function , taking care to avoid machine overflow, and giving a warning if the result cannot be computed to more than half precision. The function is evaluated as , where and are the real and imaginary parts respectively of .
are less than or equal to
in magnitude, it is possible that
may overflow although
does not. In this case the alternative formula
is used for the real part of the result, and
for the imaginary part. If either part of the result still overflows, a warning is returned through parameter IFAIL
is too large, precision may be lost in the evaluation of
. Again, a warning is returned through IFAIL
- 1: Z – COMPLEX (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 real part of the result overflows, and is set to the largest safe number with the correct sign. The imaginary part of the result is meaningful.
The imaginary part of the result overflows, and is set to the largest safe number with the correct sign. The real part of the result is meaningful.
Both real and imaginary parts of the result overflow, and are set to the largest safe number with the correct signs.
The computed result is accurate to less than half precision, due to the size of .
The computed result has no precision, due to the size of , and is set to zero.
Accuracy is limited in general only by the accuracy of the standard functions in the computation of
gets larger, precision will probably be lost due to argument reduction in the evaluation of the sine and cosine functions, until the warning error
gets larger than
is the machine precision
. Note that on some machines, the intrinsic functions SIN and COS will not operate on arguments larger than about
, and so IFAIL
can never return as
In the comparatively rare event that the result is computed by the formulae and , a further small loss of accuracy may be expected due to rounding errors in the logarithmic function.
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 (s01eafe.f90)
9.2 Program Data
Program Data (s01eafe.d)
9.3 Program Results
Program Results (s01eafe.r)