!>
!> DROTG constructs a plane rotation
!>    [  c  s ] [ a ] = [ r ]
!>    [ -s  c ] [ b ]   [ 0 ]
!> satisfying c**2 + s**2 = 1.
!>
!> The computation uses the formulas
!>    sigma = sgn(a)    if |a| >  |b|
!>          = sgn(b)    if |b| >= |a|
!>    r = sigma*sqrt( a**2 + b**2 )
!>    c = 1; s = 0      if r = 0
!>    c = a/r; s = b/r  if r != 0
!> The subroutine also computes
!>    z = s    if |a| > |b|,
!>      = 1/c  if |b| >= |a| and c != 0
!>      = 1    if c = 0
!> This allows c and s to be reconstructed from z as follows:
!>    If z = 1, set c = 0, s = 1.
!>    If |z| < 1, set c = sqrt(1 - z**2) and s = z.
!>    If |z| > 1, set c = 1/z and s = sqrt( 1 - c**2).
!>
!> 

lartg: generate plane rotation, more accurate than BLAS rot,

lartgp: generate plane rotation, more accurate than BLAS rot

A

!>          A is DOUBLE PRECISION
!>          On entry, the scalar a.
!>          On exit, the scalar r.
!> 

B

!>          B is DOUBLE PRECISION
!>          On entry, the scalar b.
!>          On exit, the scalar z.
!> 

C

!>          C is DOUBLE PRECISION
!>          The scalar c.
!> 

S

!>          S is DOUBLE PRECISION
!>          The scalar s.
!> 

Edward Anderson, Lockheed Martin

Weslley Pereira, University of Colorado Denver, USA

!>
!>  Anderson E. (2017)
!>  Algorithm 978: Safe Scaling in the Level 1 BLAS
!>  ACM Trans Math Softw 44:1--28
!>  https://doi.org/10.1145/3061665
!>
!>