s15ad returns the value of the complementary error function, erfcx.


public static double s15ad(
	double x
Visual Basic
Public Shared Function s15ad ( _
	x As Double _
) As Double
Visual C++
static double s15ad(
	double x
static member s15ad : 
        x : float -> float 


Type: System..::..Double
On entry: the argument x of the function.

Return Value

s15ad returns the value of the complementary error function, erfcx.


s15ad calculates an approximate value for the complement of the error function
Let x^ be the root of the equation erfcx-erfx=0 (then x^0.46875). For xx^ the value of erfcx is based on the following rational Chebyshev expansion for erfx:
where R,m denotes a rational function of degree  in the numerator and m in the denominator.
For x>x^ the value of erfcx is based on a rational Chebyshev expansion for erfcx: for x^<x4 the value is based on the expansion
and for x>4 it is based on the expansion
For each expansion, the specific values of  and m are selected to be minimal such that the maximum relative error in the expansion is of the order 10-d, where d is the maximum number of decimal digits that can be accurately represented for the particular implementation (see x02be).
For xxhi there is a danger of setting underflow in erfcx (the value of xhi is given in the Users' Note for your implementation). For xxhi, s15ad returns erfcx=0; for x-xhi it returns erfcx=2.


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

Error Indicators and Warnings

There are no failure exits from s15ad. The parameter _ifail has been included for consistency with other methods in this chapter.


If δ and ε are relative errors in the argument and result, respectively, then in principle
That is, the relative error in the argument, x, is amplified by a factor 2xe-x2πerfcx in the result.
The behaviour of this factor is shown in Figure 1.
Figure 1
Figure 1
It should be noted that near x=0 this factor behaves as 2xπ and hence the accuracy is largely determined by the machine precision. Also for large negative x, where the factor is xe-x2π, accuracy is mainly limited by machine precision. However, for large positive x, the factor becomes 2x2 and to an extent relative accuracy is necessarily lost. The absolute accuracy E is given by
so absolute accuracy is guaranteed for all x.

Parallelism and Performance


Further Comments



This example reads values of the argument x from a file, evaluates the function at each value of x and prints the results.

Example program (C#): s15ade.cs

Example program data: s15ade.d

Example program results: s15ade.r

See Also