SLAIC1 applies one step of incremental condition estimation in
 its simplest version:

 Let x, twonorm(x) = 1, be an approximate singular vector of an j-by-j
 lower triangular matrix L, such that
          twonorm(L*x) = sest
 Then SLAIC1 computes sestpr, s, c such that
 the vector
                 [ s*x ]
          xhat = [  c  ]
 is an approximate singular vector of
                 [ L      0  ]
          Lhat = [ w**T gamma ]
 in the sense that
          twonorm(Lhat*xhat) = sestpr.

 Depending on JOB, an estimate for the largest or smallest singular
 value is computed.

 Note that [s c]**T and sestpr**2 is an eigenpair of the system

     diag(sest*sest, 0) + [alpha  gamma] * [ alpha ]
                                           [ gamma ]

 where  alpha =  x**T*w.

          JOB is INTEGER
          = 1: an estimate for the largest singular value is computed.
          = 2: an estimate for the smallest singular value is computed.

          J is INTEGER
          Length of X and W

          X is REAL array, dimension (J)
          The j-vector x.

          SEST is REAL
          Estimated singular value of j by j matrix L

          W is REAL array, dimension (J)
          The j-vector w.

          GAMMA is REAL
          The diagonal element gamma.

          SESTPR is REAL
          Estimated singular value of (j+1) by (j+1) matrix Lhat.

          S is REAL
          Sine needed in forming xhat.

          C is REAL
          Cosine needed in forming xhat.