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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



     #include <sunperf.h>

     void slae2(float a, float b,  float  c,  float  *rt1,  float
               *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) element of the 2-by-2 matrix.

     B         (input) REAL
               The (1,2) and (2,1) elements 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.

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.

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