          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