```      SUBROUTINE ZLARTG( F, G, CS, SN, R )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
DOUBLE PRECISION   CS
COMPLEX*16         F, G, R, SN
*     ..
*
*  Purpose
*  =======
*
*  ZLARTG generates a plane rotation so that
*
*     [  CS  SN  ]     [ F ]     [ R ]
*     [  __      ]  .  [   ]  =  [   ]   where CS**2 + |SN|**2 = 1.
*     [ -SN  CS  ]     [ G ]     [ 0 ]
*
*  This is a faster version of the BLAS1 routine ZROTG, except for
*  the following differences:
*     F and G are unchanged on return.
*     If G=0, then CS=1 and SN=0.
*     If F=0, then CS=0 and SN is chosen so that R is real.
*
*  Arguments
*  =========
*
*  F       (input) COMPLEX*16
*          The first component of vector to be rotated.
*
*  G       (input) COMPLEX*16
*          The second component of vector to be rotated.
*
*  CS      (output) DOUBLE PRECISION
*          The cosine of the rotation.
*
*  SN      (output) COMPLEX*16
*          The sine of the rotation.
*
*  R       (output) COMPLEX*16
*          The nonzero component of the rotated vector.
*
*  Further Details
*  ======= =======
*
*  3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel
*
*  This version has a few statements commented out for thread safety
*  (machine parameters are computed on each entry). 10 feb 03, SJH.
*
*  =====================================================================
*
*     .. Parameters ..
DOUBLE PRECISION   TWO, ONE, ZERO
PARAMETER          ( TWO = 2.0D+0, ONE = 1.0D+0, ZERO = 0.0D+0 )
COMPLEX*16         CZERO
PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ) )
*     ..
*     .. Local Scalars ..
*     LOGICAL            FIRST
INTEGER            COUNT, I
DOUBLE PRECISION   D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
\$                   SAFMN2, SAFMX2, SCALE
COMPLEX*16         FF, FS, GS
*     ..
*     .. External Functions ..
DOUBLE PRECISION   DLAMCH, DLAPY2
EXTERNAL           DLAMCH, DLAPY2
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG,
\$                   MAX, SQRT
*     ..
*     .. Statement Functions ..
DOUBLE PRECISION   ABS1, ABSSQ
*     ..
*     .. Save statement ..
*     SAVE               FIRST, SAFMX2, SAFMIN, SAFMN2
*     ..
*     .. Data statements ..
*     DATA               FIRST / .TRUE. /
*     ..
*     .. Statement Function definitions ..
ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) )
ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2
*     ..
*     .. Executable Statements ..
*
*     IF( FIRST ) THEN
SAFMIN = DLAMCH( 'S' )
EPS = DLAMCH( 'E' )
SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
\$            LOG( DLAMCH( 'B' ) ) / TWO )
SAFMX2 = ONE / SAFMN2
*        FIRST = .FALSE.
*     END IF
SCALE = MAX( ABS1( F ), ABS1( G ) )
FS = F
GS = G
COUNT = 0
IF( SCALE.GE.SAFMX2 ) THEN
10    CONTINUE
COUNT = COUNT + 1
FS = FS*SAFMN2
GS = GS*SAFMN2
SCALE = SCALE*SAFMN2
IF( SCALE.GE.SAFMX2 )
\$      GO TO 10
ELSE IF( SCALE.LE.SAFMN2 ) THEN
IF( G.EQ.CZERO ) THEN
CS = ONE
SN = CZERO
R = F
RETURN
END IF
20    CONTINUE
COUNT = COUNT - 1
FS = FS*SAFMX2
GS = GS*SAFMX2
SCALE = SCALE*SAFMX2
IF( SCALE.LE.SAFMN2 )
\$      GO TO 20
END IF
F2 = ABSSQ( FS )
G2 = ABSSQ( GS )
IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN
*
*        This is a rare case: F is very small.
*
IF( F.EQ.CZERO ) THEN
CS = ZERO
R = DLAPY2( DBLE( G ), DIMAG( G ) )
*           Do complex/real division explicitly with two real divisions
D = DLAPY2( DBLE( GS ), DIMAG( GS ) )
SN = DCMPLX( DBLE( GS ) / D, -DIMAG( GS ) / D )
RETURN
END IF
F2S = DLAPY2( DBLE( FS ), DIMAG( FS ) )
*        G2 and G2S are accurate
*        G2 is at least SAFMIN, and G2S is at least SAFMN2
G2S = SQRT( G2 )
*        Error in CS from underflow in F2S is at most
*        UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
*        If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
*        and so CS .lt. sqrt(SAFMIN)
*        If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
*        and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
*        Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
CS = F2S / G2S
*        Make sure abs(FF) = 1
*        Do complex/real division explicitly with 2 real divisions
IF( ABS1( F ).GT.ONE ) THEN
D = DLAPY2( DBLE( F ), DIMAG( F ) )
FF = DCMPLX( DBLE( F ) / D, DIMAG( F ) / D )
ELSE
DR = SAFMX2*DBLE( F )
DI = SAFMX2*DIMAG( F )
D = DLAPY2( DR, DI )
FF = DCMPLX( DR / D, DI / D )
END IF
SN = FF*DCMPLX( DBLE( GS ) / G2S, -DIMAG( GS ) / G2S )
R = CS*F + SN*G
ELSE
*
*        This is the most common case.
*        Neither F2 nor F2/G2 are less than SAFMIN
*        F2S cannot overflow, and it is accurate
*
F2S = SQRT( ONE+G2 / F2 )
*        Do the F2S(real)*FS(complex) multiply with two real multiplies
R = DCMPLX( F2S*DBLE( FS ), F2S*DIMAG( FS ) )
CS = ONE / F2S
D = F2 + G2
*        Do complex/real division explicitly with two real divisions
SN = DCMPLX( DBLE( R ) / D, DIMAG( R ) / D )
SN = SN*DCONJG( GS )
IF( COUNT.NE.0 ) THEN
IF( COUNT.GT.0 ) THEN
DO 30 I = 1, COUNT
R = R*SAFMX2
30          CONTINUE
ELSE
DO 40 I = 1, -COUNT
R = R*SAFMN2
40          CONTINUE
END IF
END IF
END IF
RETURN
*
*     End of ZLARTG
*
END

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