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