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      DOUBLE PRECISION FUNCTION QQ(V)


C     Returns the square of Q(V); this is done for numerical purposes,
C     so that appropriate action (necessary because of roundoff error)
C     can be taken if QQ=Q**2 is negative.

C     Code written by Phillip Helbig, Hamburg Observatory, Sep 1995.


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C     Declarations


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C     input variables from the calling routine (parameter list)


C     (1 + z)

      DOUBLE PRECISION V



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C     variables in common block


C     cosmological variables

      DOUBLE PRECISION LAMBDA, OMEGA, ETA, K

      COMMON /COSMOL/ LAMBDA, OMEGA, ETA, K

C     save until the next call

      SAVE /COSMOL/



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C     calculations


C     Calculates the square of fuction Q(v) needed by the ANGSIZ routine
C     itself and by ASDRHS; in addition, INICOS uses QQ to make sure
C     that ZMAX isn't too large due to roundoff error.

      QQ  = OMEGA*V**3 - K*V**2 + LAMBDA



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      END