NAG Library Function Document
nag_erfc (s15adc) returns the value of the complementary error function, .
||nag_erfc (double x)
calculates an approximate value for the complement of the error function
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 nag_decimal_digits (X02BEC)
there is a danger of setting underflow in
(the value of
is given in the Users' Note
for your implementation). For
, nag_erfc (s15adc)
Abramowitz M and Stegun I A (1972) Handbook of Mathematical Functions (3rd Edition) Dover Publications
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
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
nag_erfc (s15adc) is not threaded in any implementation.
This example reads values of the argument from a file, evaluates the function at each value of and prints the results.
Program Text (s15adce.c)
Program Data (s15adce.d)
Program Results (s15adce.r)