SLARTG 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 CLARTG for complex inputs (F,0) and (G,0).


 This is a more accurate version of the BLAS1 routine SROTG,


 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 SBDSQR when


       there are zeros on the diagonal).


 Below, wp=>sp stands for single 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