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slae2

 NAME
      SLAE2 - compute the eigenvalues of a 2-by-2 symmetric matrix
      [ A B ]  [ B C ]

 SYNOPSIS
      SUBROUTINE SLAE2( A, B, C, RT1, RT2 )

          REAL          A, B, C, RT1, RT2

 PURPOSE
      SLAE2  computes the eigenvalues of a 2-by-2 symmetric matrix
         [  A   B  ]
         [  B   C  ].  On return, RT1 is the eigenvalue of larger
      absolute value, and RT2 is the eigenvalue of smaller abso-
      lute value.

 ARGUMENTS
      A       (input) REAL
              The (1,1) entry of the 2-by-2 matrix.

      B       (input) REAL
              The (1,2) and (2,1) entries of the 2-by-2 matrix.

      C       (input) REAL
              The (2,2) entry of the 2-by-2 matrix.

      RT1     (output) REAL
              The eigenvalue of larger absolute value.

      RT2     (output) REAL
              The eigenvalue of smaller absolute value.

 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.

      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.