!>
!> DLARTG generates a plane rotation so that
!>
!>    [  C  S  ]  .  [ F ]  =  [ R ]
!>    [ -S  C  ]     [ G ]     [ 0 ]
!>
!> where C**2 + S**2 = 1.
!>
!> The mathematical formulas used for C and S are
!>    R = sign(F) * sqrt(F**2 + G**2)
!>    C = F / R
!>    S = G / R
!> Hence C >= 0. The algorithm used to compute these quantities
!> incorporates scaling to avoid overflow or underflow in computing the
!> square root of the sum of squares.
!>
!> This version is discontinuous in R at F = 0 but it returns the same
!> C and S as ZLARTG for complex inputs (F,0) and (G,0).
!>
!> This is a more accurate version of the BLAS1 routine DROTG,
!> with the following other differences:
!>    F and G are unchanged on return.
!>    If G=0, then C=1 and S=0.
!>    If F=0 and (G .ne. 0), then C=0 and S=sign(1,G) without doing any
!>       floating point operations (saves work in DBDSQR when
!>       there are zeros on the diagonal).
!>
!> Below, wp=>dp stands for double precision from LA_CONSTANTS module.
!> 

F

!>          F is REAL(wp)
!>          The first component of vector to be rotated.
!> 

G

!>          G is REAL(wp)
!>          The second component of vector to be rotated.
!> 

C

!>          C is REAL(wp)
!>          The cosine of the rotation.
!> 

S

!>          S is REAL(wp)
!>          The sine of the rotation.
!> 

R

!>          R is REAL(wp)
!>          The nonzero component of the rotated vector.
!> 

Edward Anderson, Lockheed Martin

July 2016

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
!>
!>