version 1.2, 2010/04/21 13:45:20
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version 1.16, 2017/06/17 11:06:27
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SUBROUTINE DLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN, |
*> \brief \b DLASQ6 computes one dqd transform in ping-pong form. Used by sbdsqr and sstegr. |
$ DNM1, DNM2 ) |
* |
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* =========== DOCUMENTATION =========== |
* |
* |
* -- LAPACK routine (version 3.2) -- |
* Online html documentation available at |
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* http://www.netlib.org/lapack/explore-html/ |
* |
* |
* -- Contributed by Osni Marques of the Lawrence Berkeley National -- |
*> \htmlonly |
* -- Laboratory and Beresford Parlett of the Univ. of California at -- |
*> Download DLASQ6 + dependencies |
* -- Berkeley -- |
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq6.f"> |
* -- November 2008 -- |
*> [TGZ]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlasq6.f"> |
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*> [ZIP]</a> |
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/dlasq6.f"> |
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*> [TXT]</a> |
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*> \endhtmlonly |
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* |
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* Definition: |
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* =========== |
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* |
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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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* .. 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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* |
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*> \par Purpose: |
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* ============= |
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*> |
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*> \verbatim |
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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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*> \endverbatim |
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* |
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* Arguments: |
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* ========== |
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* |
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*> \param[in] I0 |
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*> \verbatim |
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*> I0 is INTEGER |
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*> First index. |
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*> \endverbatim |
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*> |
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*> \param[in] N0 |
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*> \verbatim |
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*> N0 is INTEGER |
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*> Last index. |
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*> \endverbatim |
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*> |
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*> \param[in] Z |
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*> \verbatim |
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*> Z is 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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*> \endverbatim |
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*> |
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*> \param[in] PP |
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*> \verbatim |
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*> PP is INTEGER |
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*> PP=0 for ping, PP=1 for pong. |
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*> \endverbatim |
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*> |
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*> \param[out] DMIN |
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*> \verbatim |
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*> DMIN is DOUBLE PRECISION |
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*> Minimum value of d. |
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*> \endverbatim |
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*> |
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*> \param[out] DMIN1 |
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*> \verbatim |
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*> DMIN1 is DOUBLE PRECISION |
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*> Minimum value of d, excluding D( N0 ). |
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*> \endverbatim |
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*> |
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*> \param[out] DMIN2 |
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*> \verbatim |
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*> DMIN2 is DOUBLE PRECISION |
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*> Minimum value of d, excluding D( N0 ) and D( N0-1 ). |
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*> \endverbatim |
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*> |
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*> \param[out] DN |
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*> \verbatim |
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*> DN is DOUBLE PRECISION |
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*> d(N0), the last value of d. |
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*> \endverbatim |
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*> |
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*> \param[out] DNM1 |
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*> \verbatim |
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*> DNM1 is DOUBLE PRECISION |
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*> d(N0-1). |
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*> \endverbatim |
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*> |
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*> \param[out] DNM2 |
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*> \verbatim |
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*> DNM2 is DOUBLE PRECISION |
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*> d(N0-2). |
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*> \endverbatim |
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* |
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* Authors: |
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* ======== |
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* |
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*> \author Univ. of Tennessee |
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*> \author Univ. of California Berkeley |
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*> \author Univ. of Colorado Denver |
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*> \author NAG Ltd. |
* |
* |
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*> \date December 2016 |
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* |
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*> \ingroup auxOTHERcomputational |
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* |
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* ===================================================================== |
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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 computational routine (version 3.7.0) -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- LAPACK is a software package provided by Univ. of Tennessee, -- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- |
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* December 2016 |
* |
* |
* .. Scalar Arguments .. |
* .. Scalar Arguments .. |
INTEGER I0, N0, PP |
INTEGER I0, N0, PP |
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DOUBLE PRECISION Z( * ) |
DOUBLE PRECISION Z( * ) |
* .. |
* .. |
* |
* |
* 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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* ===================================================================== |
* ===================================================================== |
* |
* |
* .. Parameter .. |
* .. Parameter .. |
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* |
* |
SAFMIN = DLAMCH( 'Safe minimum' ) |
SAFMIN = DLAMCH( 'Safe minimum' ) |
J4 = 4*I0 + PP - 3 |
J4 = 4*I0 + PP - 3 |
EMIN = Z( J4+4 ) |
EMIN = Z( J4+4 ) |
D = Z( J4 ) |
D = Z( J4 ) |
DMIN = D |
DMIN = D |
* |
* |
IF( PP.EQ.0 ) THEN |
IF( PP.EQ.0 ) THEN |
DO 10 J4 = 4*I0, 4*( N0-3 ), 4 |
DO 10 J4 = 4*I0, 4*( N0-3 ), 4 |
Z( J4-2 ) = D + Z( J4-1 ) |
Z( J4-2 ) = D + Z( J4-1 ) |
IF( Z( J4-2 ).EQ.ZERO ) THEN |
IF( Z( J4-2 ).EQ.ZERO ) THEN |
Z( J4 ) = ZERO |
Z( J4 ) = ZERO |
D = Z( J4+1 ) |
D = Z( J4+1 ) |
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TEMP = Z( J4+1 ) / Z( J4-2 ) |
TEMP = Z( J4+1 ) / Z( J4-2 ) |
Z( J4 ) = Z( J4-1 )*TEMP |
Z( J4 ) = Z( J4-1 )*TEMP |
D = D*TEMP |
D = D*TEMP |
ELSE |
ELSE |
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) |
Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) |
D = Z( J4+1 )*( D / Z( J4-2 ) ) |
D = Z( J4+1 )*( D / Z( J4-2 ) ) |
END IF |
END IF |
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10 CONTINUE |
10 CONTINUE |
ELSE |
ELSE |
DO 20 J4 = 4*I0, 4*( N0-3 ), 4 |
DO 20 J4 = 4*I0, 4*( N0-3 ), 4 |
Z( J4-3 ) = D + Z( J4 ) |
Z( J4-3 ) = D + Z( J4 ) |
IF( Z( J4-3 ).EQ.ZERO ) THEN |
IF( Z( J4-3 ).EQ.ZERO ) THEN |
Z( J4-1 ) = ZERO |
Z( J4-1 ) = ZERO |
D = Z( J4+2 ) |
D = Z( J4+2 ) |
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TEMP = Z( J4+2 ) / Z( J4-3 ) |
TEMP = Z( J4+2 ) / Z( J4-3 ) |
Z( J4-1 ) = Z( J4 )*TEMP |
Z( J4-1 ) = Z( J4 )*TEMP |
D = D*TEMP |
D = D*TEMP |
ELSE |
ELSE |
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) |
Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) |
D = Z( J4+2 )*( D / Z( J4-3 ) ) |
D = Z( J4+2 )*( D / Z( J4-3 ) ) |
END IF |
END IF |
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20 CONTINUE |
20 CONTINUE |
END IF |
END IF |
* |
* |
* Unroll last two steps. |
* Unroll last two steps. |
* |
* |
DNM2 = D |
DNM2 = D |
DMIN2 = DMIN |
DMIN2 = DMIN |