SUBROUTINE R7RPLY(UU, VV, NZ, P, QP, K, QK, SVK)
C VARIABLE-SHIFT K-POLYNOMIAL ITERATION FOR A
C QUADRATIC FACTOR CONVERGES ONLY IF THE ZEROS ARE
C EQUIMODULAR OR NEARLY SO.
C UU,VV - COEFFICIENTS OF STARTING QUADRATIC
C NZ - NUMBER OF ZERO FOUND
C
      COMMON /P66PLY/ SR, SI, U,
     1 V, A, B, C, D, A1, A2, A3, A6, A7, E, F, G,
     2 H, SZR, SZI, LZR, LZI, ETA, ARE, MRE, N, NN
C
      INTEGER N, NN
      INTEGER NZ, TYPE, I, J
C
      REAL ETA, ARE, MRE
      REAL MP, OMP, EE, RELSTP, T, ZM
C
      REAL P(1), QP(1), K(1),
     1   QK(1), SVK(1), SR, SI, U, V, A, B, C, D,
     2   A1, A2, A3, A6, A7, E, F, G, H, SZR, SZI,
     3   LZR, LZI
C
      REAL UI, VI, UU, VV, ABS
      LOGICAL TRIED
C
      NZ = 0
      TRIED = .FALSE.
      U = UU
      V = VV
      J = 0
C MAIN LOOP
   10 CALL R6RPLY(1.E0, U, V, SZR, SZI, LZR, LZI)
C RETURN IF ROOTS OF THE QUADRATIC ARE REAL AND NOT
C CLOSE TO MULTIPLE OR NEARLY EQUAL AND  OF OPPOSITE
C SIGN
      IF (ABS(ABS(SZR)-ABS(LZR)).GT..01E0*
     1   ABS(LZR)) RETURN
C EVALUATE POLYNOMIAL BY QUADRATIC SYNTHETIC DIVISION
      CALL R8RPLY(NN, U, V, P, QP, A, B)
      MP = ABS(A-SZR*B) + ABS(SZI*B)
C COMPUTE A RIGOROUS  BOUND ON THE ROUNDING ERROR IN
C EVALUTING P
      ZM = SQRT(ABS((V)))
      EE = 2.*ABS((QP(1)))
      T = -SZR*B
      DO 20 I=2,N
        EE = EE*ZM + ABS((QP(I)))
   20 CONTINUE
      EE = EE*ZM + ABS((A)+T)
      EE = (5.*MRE+4.*ARE)*EE - (5.*MRE+2.*ARE)*
     2   (ABS((A)+T)+ABS((B))*ZM) +
     3   2.*ARE*ABS(T)
C ITERATION HAS CONVERGED SUFFICIENTLY IF THE
C POLYNOMIAL VALUE IS LESS THAN 20 TIMES THIS BOUND
      IF (MP.GT.20.*EE) GO TO 30
      NZ = 2
      RETURN
   30 J = J + 1
C STOP ITERATION AFTER 20 STEPS
      IF (J.GT.20) RETURN
      IF (J.LT.2) GO TO 50
      IF (RELSTP.GT..01 .OR. MP.LT.OMP .OR. TRIED)
     1   GO TO 50
C A CLUSTER APPEARS TO BE STALLING THE CONVERGENCE.
C FIVE FIXED SHIFT STEPS ARE TAKEN WITH A U,V CLOSE
C TO THE CLUSTER
      IF (RELSTP.LT.ETA) RELSTP = ETA
      RELSTP = SQRT(RELSTP)
      U = U - U*RELSTP
      V = V + V*RELSTP
      CALL R8RPLY(NN, U, V, P, QP, A, B)
      DO 40 I=1,5
        CALL R2RPLY(TYPE, K, QK)
        CALL R5RPLY(TYPE, P, QP, K, QK)
   40 CONTINUE
      TRIED = .TRUE.
      J = 0
   50 OMP = MP
C CALCULATE NEXT K POLYNOMIAL AND NEW U AND V
      CALL R2RPLY(TYPE, K, QK)
      CALL R5RPLY(TYPE, P, QP, K, QK)
      CALL R2RPLY(TYPE, K, QK)
      CALL R4RPLY(TYPE, UI, VI, P, K)
C IF VI IS ZERO THE ITERATION IS NOT CONVERGING
      IF (VI.EQ.0.E0) RETURN
      RELSTP = ABS((VI-V)/VI)
      U = UI
      V = VI
      GO TO 10
      END

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