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