NAG CL Interface
s15adc returns the value of the complementary error function, .
The function may be called by the names: s15adc, nag_specfun_erfc_real or nag_erfc.
calculates an approximate value for the complement of the error function
| |Unless stated otherwise in the Users' Note, s15adc calls the complementary error function supplied by the compiler used for your implementation; as such, details of the underlying algorithm should be obtained from the documentation supplied by the compiler vendor. The following discussion only applies if the Users' Note for your implementation indicates that the compiler's supplied function was not available.
be the root of the equation
the value of
is based on the following rational Chebyshev expansion for
denotes a rational function of degree
in the numerator and
in the denominator.
the value of
is based on a rational Chebyshev expansion for
the value is based on the expansion
it is based on the expansion
For each expansion, the specific values of
are selected to be minimal such that the maximum relative error in the expansion is of the order
is the maximum number of decimal digits that can be accurately represented for the particular implementation (see X02BEC
there is a danger of setting underflow in
(the value of
is given in the Users' Note
for your implementation).. For
Cody W J (1969) Rational Chebyshev approximations for the error function Math.Comp. 23 631–637
On entry: the argument of the function.
Error Indicators and Warnings
Unless stated otherwise in the Users' Note, s15adc calls the complementary error function supplied by the compiler used for your implementation. The following discussion only applies if the Users' Note for your implementation indicates that the compiler's supplied function was not available.
are relative errors in the argument and result, respectively, then in principle
That is, the relative error in the argument,
, is amplified by a factor
in the result.
The behaviour of this factor is shown in Figure 1
It should be noted that near
this factor behaves as
and hence the accuracy is largely determined by the machine precision
. Also, for large negative
, where the factor is
, accuracy is mainly limited by machine precision
. However, for large positive
, the factor becomes
and to an extent relative accuracy is necessarily lost. The absolute accuracy
is given by
so absolute accuracy is guaranteed for all
Parallelism and Performance
s15adc is not threaded in any implementation.
Internal changes have been made to this function as follows:
For details of all known issues which have been reported for the NAG Library please refer to the Known Issues
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.