# NAG Library Routine Document

## 1Purpose

x02ahf returns the largest positive argument for which the Fortran intrinsic functions SIN and COS return a result with some meaningful accuracy.

## 2Specification

Fortran Interface
 Function x02ahf ( x)
 Real (Kind=nag_wp) :: x02ahf Real (Kind=nag_wp), Intent (In) :: x
#include nagmk26.h
 double x02ahf_ (double *x)

## 3Description

The trigonometric functions $\mathrm{sin}$ and $\mathrm{cos}$ supplied in some compiler run-time libraries do not return accurate results when their argument is large. Often the related accuracy of a result gets progressively worse as the argument gets larger. x02ahf gives a value beyond which the compiler run-time library returns results with no relative accuracy at all. Note that some run-time libraries do return accurate results for all arguments to $\mathrm{sin}$ and $\mathrm{cos}$.

None.

## 5Arguments

1:     $\mathbf{x}$ – Real (Kind=nag_wp)Dummy

None.

None.

## 8Parallelism and Performance

x02ahf is not threaded in any implementation.