```      SUBROUTINE SLAEV2( A, B, C, RT1, RT2, CS1, SN1 )
*
*  -- LAPACK auxiliary routine (version 3.1) --
*     Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
*     November 2006
*
*     .. Scalar Arguments ..
REAL               A, B, C, CS1, RT1, RT2, SN1
*     ..
*
*  Purpose
*  =======
*
*  SLAEV2 computes the eigendecomposition of a 2-by-2 symmetric matrix
*     [  A   B  ]
*     [  B   C  ].
*  On return, RT1 is the eigenvalue of larger absolute value, RT2 is the
*  eigenvalue of smaller absolute value, and (CS1,SN1) is the unit right
*  eigenvector for RT1, giving the decomposition
*
*     [ CS1  SN1 ] [  A   B  ] [ CS1 -SN1 ]  =  [ RT1  0  ]
*     [-SN1  CS1 ] [  B   C  ] [ SN1  CS1 ]     [  0  RT2 ].
*
*  Arguments
*  =========
*
*  A       (input) REAL
*          The (1,1) element of the 2-by-2 matrix.
*
*  B       (input) REAL
*          The (1,2) element and the conjugate of the (2,1) element of
*          the 2-by-2 matrix.
*
*  C       (input) REAL
*          The (2,2) element of the 2-by-2 matrix.
*
*  RT1     (output) REAL
*          The eigenvalue of larger absolute value.
*
*  RT2     (output) REAL
*          The eigenvalue of smaller absolute value.
*
*  CS1     (output) REAL
*  SN1     (output) REAL
*          The vector (CS1, SN1) is a unit right eigenvector for RT1.
*
*  Further Details
*  ===============
*
*  RT1 is accurate to a few ulps barring over/underflow.
*
*  RT2 may be inaccurate if there is massive cancellation in the
*  determinant A*C-B*B; higher precision or correctly rounded or
*  correctly truncated arithmetic would be needed to compute RT2
*  accurately in all cases.
*
*  CS1 and SN1 are accurate to a few ulps barring over/underflow.
*
*  Overflow is possible only if RT1 is within a factor of 5 of overflow.
*  Underflow is harmless if the input data is 0 or exceeds
*     underflow_threshold / macheps.
*
* =====================================================================
*
*     .. Parameters ..
REAL               ONE
PARAMETER          ( ONE = 1.0E0 )
REAL               TWO
PARAMETER          ( TWO = 2.0E0 )
REAL               ZERO
PARAMETER          ( ZERO = 0.0E0 )
REAL               HALF
PARAMETER          ( HALF = 0.5E0 )
*     ..
*     .. Local Scalars ..
INTEGER            SGN1, SGN2
REAL               AB, ACMN, ACMX, ACS, ADF, CS, CT, DF, RT, SM,
\$                   TB, TN
*     ..
*     .. Intrinsic Functions ..
INTRINSIC          ABS, SQRT
*     ..
*     .. Executable Statements ..
*
*     Compute the eigenvalues
*
SM = A + C
DF = A - C
ADF = ABS( DF )
TB = B + B
AB = ABS( TB )
IF( ABS( A ).GT.ABS( C ) ) THEN
ACMX = A
ACMN = C
ELSE
ACMX = C
ACMN = A
END IF
IF( ADF.GT.AB ) THEN
RT = ADF*SQRT( ONE+( AB / ADF )**2 )
ELSE IF( ADF.LT.AB ) THEN
RT = AB*SQRT( ONE+( ADF / AB )**2 )
ELSE
*
*        Includes case AB=ADF=0
*
RT = AB*SQRT( TWO )
END IF
IF( SM.LT.ZERO ) THEN
RT1 = HALF*( SM-RT )
SGN1 = -1
*
*        Order of execution important.
*        To get fully accurate smaller eigenvalue,
*        next line needs to be executed in higher precision.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE IF( SM.GT.ZERO ) THEN
RT1 = HALF*( SM+RT )
SGN1 = 1
*
*        Order of execution important.
*        To get fully accurate smaller eigenvalue,
*        next line needs to be executed in higher precision.
*
RT2 = ( ACMX / RT1 )*ACMN - ( B / RT1 )*B
ELSE
*
*        Includes case RT1 = RT2 = 0
*
RT1 = HALF*RT
RT2 = -HALF*RT
SGN1 = 1
END IF
*
*     Compute the eigenvector
*
IF( DF.GE.ZERO ) THEN
CS = DF + RT
SGN2 = 1
ELSE
CS = DF - RT
SGN2 = -1
END IF
ACS = ABS( CS )
IF( ACS.GT.AB ) THEN
CT = -TB / CS
SN1 = ONE / SQRT( ONE+CT*CT )
CS1 = CT*SN1
ELSE
IF( AB.EQ.ZERO ) THEN
CS1 = ONE
SN1 = ZERO
ELSE
TN = -CS / TB
CS1 = ONE / SQRT( ONE+TN*TN )
SN1 = TN*CS1
END IF
END IF
IF( SGN1.EQ.SGN2 ) THEN
TN = CS1
CS1 = -SN1
SN1 = TN
END IF
RETURN
*
*     End of SLAEV2
*
END

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