root / src / lapack / double / dlasq6.f @ 10
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SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, |
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$ DNM1, DNM2 ) |
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* |
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* -- LAPACK routine (version 3.2) -- |
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* |
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* -- Contributed by Osni Marques of the Lawrence Berkeley National -- |
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* -- Laboratory and Beresford Parlett of the Univ. of California at -- |
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* -- Berkeley -- |
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* -- November 2008 -- |
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* |
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* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
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* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* |
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* .. Scalar Arguments .. |
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INTEGER I0, N0, PP |
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DOUBLE PRECISION DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 |
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* .. |
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* .. Array Arguments .. |
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DOUBLE PRECISION Z( * ) |
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* .. |
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* |
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* Purpose |
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* ======= |
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* |
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* DLASQ6 computes one dqd (shift equal to zero) transform in |
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* ping-pong form, with protection against underflow and overflow. |
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* |
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* Arguments |
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* ========= |
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* |
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* I0 (input) INTEGER |
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* First index. |
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* |
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* N0 (input) INTEGER |
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* Last index. |
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* |
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* Z (input) DOUBLE PRECISION array, dimension ( 4*N ) |
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* Z holds the qd array. EMIN is stored in Z(4*N0) to avoid |
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* an extra argument. |
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* |
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* PP (input) INTEGER |
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* PP=0 for ping, PP=1 for pong. |
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* |
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* DMIN (output) DOUBLE PRECISION |
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* Minimum value of d. |
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* |
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* DMIN1 (output) DOUBLE PRECISION |
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* Minimum value of d, excluding D( N0 ). |
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* |
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* DMIN2 (output) DOUBLE PRECISION |
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* Minimum value of d, excluding D( N0 ) and D( N0-1 ). |
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* |
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* DN (output) DOUBLE PRECISION |
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* d(N0), the last value of d. |
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* |
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* DNM1 (output) DOUBLE PRECISION |
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* d(N0-1). |
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* |
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* DNM2 (output) DOUBLE PRECISION |
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* d(N0-2). |
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* |
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* ===================================================================== |
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* |
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* .. Parameter .. |
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DOUBLE PRECISION ZERO |
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PARAMETER ( ZERO = 0.0D0 ) |
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* .. |
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* .. Local Scalars .. |
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INTEGER J4, J4P2 |
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DOUBLE PRECISION D, EMIN, SAFMIN, TEMP |
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* .. |
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* .. External Function .. |
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DOUBLE PRECISION DLAMCH |
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EXTERNAL DLAMCH |
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* .. |
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* .. Intrinsic Functions .. |
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INTRINSIC MIN |
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* .. |
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* .. Executable Statements .. |
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* |
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IF( ( N0-I0-1 ).LE.0 ) |
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$ RETURN |
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* |
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SAFMIN = DLAMCH( 'Safe minimum' ) |
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J4 = 4*I0 + PP - 3 |
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EMIN = Z( J4+4 ) |
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D = Z( J4 ) |
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DMIN = D |
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* |
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IF( PP.EQ.0 ) THEN |
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DO 10 J4 = 4*I0, 4*( N0-3 ), 4 |
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Z( J4-2 ) = D + Z( J4-1 ) |
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IF( Z( J4-2 ).EQ.ZERO ) THEN |
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Z( J4 ) = ZERO |
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D = Z( J4+1 ) |
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DMIN = D |
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EMIN = ZERO |
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ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND. |
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$ SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN |
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TEMP = Z( J4+1 ) / Z( J4-2 ) |
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Z( J4 ) = Z( J4-1 )*TEMP |
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D = D*TEMP |
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ELSE |
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Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) |
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D = Z( J4+1 )*( D / Z( J4-2 ) ) |
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END IF |
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DMIN = MIN( DMIN, D ) |
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EMIN = MIN( EMIN, Z( J4 ) ) |
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10 CONTINUE |
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ELSE |
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DO 20 J4 = 4*I0, 4*( N0-3 ), 4 |
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Z( J4-3 ) = D + Z( J4 ) |
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IF( Z( J4-3 ).EQ.ZERO ) THEN |
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Z( J4-1 ) = ZERO |
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D = Z( J4+2 ) |
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DMIN = D |
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EMIN = ZERO |
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ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND. |
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$ SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN |
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TEMP = Z( J4+2 ) / Z( J4-3 ) |
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Z( J4-1 ) = Z( J4 )*TEMP |
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D = D*TEMP |
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ELSE |
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Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) |
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D = Z( J4+2 )*( D / Z( J4-3 ) ) |
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END IF |
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DMIN = MIN( DMIN, D ) |
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EMIN = MIN( EMIN, Z( J4-1 ) ) |
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20 CONTINUE |
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END IF |
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* |
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* Unroll last two steps. |
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* |
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DNM2 = D |
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DMIN2 = DMIN |
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J4 = 4*( N0-2 ) - PP |
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J4P2 = J4 + 2*PP - 1 |
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Z( J4-2 ) = DNM2 + Z( J4P2 ) |
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IF( Z( J4-2 ).EQ.ZERO ) THEN |
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Z( J4 ) = ZERO |
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DNM1 = Z( J4P2+2 ) |
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DMIN = DNM1 |
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EMIN = ZERO |
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ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. |
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$ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN |
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TEMP = Z( J4P2+2 ) / Z( J4-2 ) |
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Z( J4 ) = Z( J4P2 )*TEMP |
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DNM1 = DNM2*TEMP |
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ELSE |
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Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) |
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DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) |
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END IF |
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DMIN = MIN( DMIN, DNM1 ) |
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* |
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DMIN1 = DMIN |
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J4 = J4 + 4 |
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J4P2 = J4 + 2*PP - 1 |
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Z( J4-2 ) = DNM1 + Z( J4P2 ) |
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IF( Z( J4-2 ).EQ.ZERO ) THEN |
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Z( J4 ) = ZERO |
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DN = Z( J4P2+2 ) |
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DMIN = DN |
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EMIN = ZERO |
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ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. |
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$ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN |
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TEMP = Z( J4P2+2 ) / Z( J4-2 ) |
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Z( J4 ) = Z( J4P2 )*TEMP |
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DN = DNM1*TEMP |
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ELSE |
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Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) |
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DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) |
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END IF |
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DMIN = MIN( DMIN, DN ) |
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* |
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Z( J4+2 ) = DN |
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Z( 4*N0-PP ) = EMIN |
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RETURN |
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* |
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* End of DLASQ6 |
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* |
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END |