# NAG Library Routine Document

## 1Purpose

f06baf generates a real Givens plane rotation and the tangent of that rotation.

## 2Specification

Fortran Interface
 Subroutine f06baf ( a, b, c, s)
 Real (Kind=nag_wp), Intent (Inout) :: a, b Real (Kind=nag_wp), Intent (Out) :: c, s
#include nagmk26.h
 void f06baf_ (double *a, double *b, double *c, double *s)

## 3Description

f06baf generates a real Givens plane rotation with parameters $c$ ($\text{}\ge 0$) and $s$, such that, given real $a$ and $b$:
 $c s -s c a b = d 0 .$
On exit, $b$ is overwritten by $t$, the tangent of the rotation; $c$ and $s$ can be reconstructed from the single stored value $t$, by a subsequent call to f06bcf.
If $\left|b\right|<\sqrt{\epsilon }\left|a\right|$, where $\epsilon$ is the machine precision, the routine sets $c=1$ and $s=0$; if $\left|a\right|<\sqrt{\epsilon }\left|b\right|$, the routine sets $c=0$ and $s=\mathrm{sign}b/a$.
Note that $t$ is always set to $b/a$, unless this would overflow, in which case the value $\mathit{flmax}×\mathrm{sign}b/a$ is returned, where $\mathit{flmax}$ is the value given by $1/\left({\mathbf{x02amf}}\right)$.
To apply the plane rotation to a pair of real vectors, call f06epf (drot); to apply it to a pair of complex vectors, call f06kpf (zdrot).
None.

## 5Arguments

1:     $\mathbf{a}$ – Real (Kind=nag_wp)Input/Output
On entry: the value $a$, the first element of the vector which determines the rotation.
On exit: the value $d$.
2:     $\mathbf{b}$ – Real (Kind=nag_wp)Input/Output
On entry: the value $b$, the second element of the vector which determines the rotation.
On exit: the value $t$, the tangent of the rotation.
3:     $\mathbf{c}$ – Real (Kind=nag_wp)Output
On exit: the value $c$, the cosine of the rotation.
4:     $\mathbf{s}$ – Real (Kind=nag_wp)Output
On exit: the value $s$, the sine of the rotation.

None.

Not applicable.

## 8Parallelism and Performance

f06baf is not threaded in any implementation.