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dlas2

 NAME
      DLAS2 - compute the singular values of the 2-by-2 matrix  [
      F G ]  [ 0 H ]

 SYNOPSIS
      SUBROUTINE DLAS2( F, G, H, SSMIN, SSMAX )

          DOUBLE        PRECISION F, G, H, SSMAX, SSMIN

 PURPOSE
      DLAS2  computes the singular values of the 2-by-2 matrix
         [  F   G  ]
         [  0   H  ].  On return, SSMIN is the smaller singular
      value and SSMAX is the larger singular value.

 ARGUMENTS
      F       (input) DOUBLE PRECISION
              The (1,1) entry of the 2-by-2 matrix.

      G       (input) DOUBLE PRECISION
              The (1,2) entry of the 2-by-2 matrix.

      H       (input) DOUBLE PRECISION
              The (2,2) entry of the 2-by-2 matrix.

      SSMIN   (output) DOUBLE PRECISION
              The smaller singular value.

      SSMAX   (output) DOUBLE PRECISION
              The larger singular value.

 FURTHER DETAILS
      Barring over/underflow, all output quantities are correct to
      within a few units in the last place (ulps), even in the
      absence of a guard digit in addition/subtraction.

      In IEEE arithmetic, the code works correctly if one matrix
      entry is infinite.

      Overflow will not occur unless the largest singular value
      itself overflows, or is within a few ulps of overflow. (On
      machines with partial overflow, like the Cray, overflow may
      occur if the largest singular value is within a factor of 2
      of overflow.)

      Underflow is harmless if underflow is gradual. Otherwise,
      results may correspond to a matrix modified by perturbations
      of size near the underflow threshold.