205 lines
5.4 KiB
Fortran
205 lines
5.4 KiB
Fortran
*> \brief \b DLARTG generates a plane rotation with real cosine and real sine.
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*
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* =========== DOCUMENTATION ===========
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*
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* Online html documentation available at
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* http://www.netlib.org/lapack/explore-html/
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*
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*> \htmlonly
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*> Download DLARTG + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlartg.f">
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*> [TGZ]</a>
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/dlartg.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/dlartg.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 DLARTG( F, G, CS, SN, R )
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION CS, F, G, R, SN
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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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*> DLARTG generate a plane rotation so that
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*>
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*> [ CS SN ] . [ F ] = [ R ] where CS**2 + SN**2 = 1.
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*> [ -SN CS ] [ G ] [ 0 ]
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*>
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*> This is a slower, more accurate version of the BLAS1 routine DROTG,
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*> with the following other differences:
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*> F and G are unchanged on return.
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*> If G=0, then CS=1 and SN=0.
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*> If F=0 and (G .ne. 0), then CS=0 and SN=1 without doing any
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*> floating point operations (saves work in DBDSQR when
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*> there are zeros on the diagonal).
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*>
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*> If F exceeds G in magnitude, CS will be positive.
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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] F
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*> \verbatim
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*> F is DOUBLE PRECISION
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*> The first component of vector to be rotated.
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*> \endverbatim
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*>
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*> \param[in] G
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*> \verbatim
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*> G is DOUBLE PRECISION
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*> The second component of vector to be rotated.
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*> \endverbatim
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*>
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*> \param[out] CS
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*> \verbatim
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*> CS is DOUBLE PRECISION
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*> The cosine of the rotation.
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*> \endverbatim
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*>
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*> \param[out] SN
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*> \verbatim
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*> SN is DOUBLE PRECISION
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*> The sine of the rotation.
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*> \endverbatim
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*>
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*> \param[out] R
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*> \verbatim
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*> R is DOUBLE PRECISION
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*> The nonzero component of the rotated vector.
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*>
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*> This version has a few statements commented out for thread safety
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*> (machine parameters are computed on each entry). 10 feb 03, SJH.
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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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*
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*> \date September 2012
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*
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*> \ingroup auxOTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE DLARTG( F, G, CS, SN, R )
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*
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* -- LAPACK auxiliary routine (version 3.4.2) --
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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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* September 2012
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION CS, F, G, R, SN
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* ..
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*
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* =====================================================================
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*
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* .. Parameters ..
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DOUBLE PRECISION ZERO
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PARAMETER ( ZERO = 0.0D0 )
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DOUBLE PRECISION ONE
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PARAMETER ( ONE = 1.0D0 )
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DOUBLE PRECISION TWO
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PARAMETER ( TWO = 2.0D0 )
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* ..
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* .. Local Scalars ..
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* LOGICAL FIRST
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INTEGER COUNT, I
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DOUBLE PRECISION EPS, F1, G1, SAFMIN, SAFMN2, SAFMX2, SCALE
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* ..
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* .. External Functions ..
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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 ABS, INT, LOG, MAX, SQRT
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* ..
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* .. Save statement ..
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* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2
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* ..
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* .. Data statements ..
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* DATA FIRST / .TRUE. /
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* ..
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* .. Executable Statements ..
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*
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* IF( FIRST ) THEN
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SAFMIN = DLAMCH( 'S' )
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EPS = DLAMCH( 'E' )
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SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
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$ LOG( DLAMCH( 'B' ) ) / TWO )
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SAFMX2 = ONE / SAFMN2
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* FIRST = .FALSE.
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* END IF
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IF( G.EQ.ZERO ) THEN
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CS = ONE
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SN = ZERO
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R = F
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ELSE IF( F.EQ.ZERO ) THEN
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CS = ZERO
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SN = ONE
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R = G
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ELSE
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F1 = F
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G1 = G
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SCALE = MAX( ABS( F1 ), ABS( G1 ) )
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IF( SCALE.GE.SAFMX2 ) THEN
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COUNT = 0
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10 CONTINUE
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COUNT = COUNT + 1
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F1 = F1*SAFMN2
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G1 = G1*SAFMN2
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SCALE = MAX( ABS( F1 ), ABS( G1 ) )
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IF( SCALE.GE.SAFMX2 )
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$ GO TO 10
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R = SQRT( F1**2+G1**2 )
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CS = F1 / R
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SN = G1 / R
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DO 20 I = 1, COUNT
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R = R*SAFMX2
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20 CONTINUE
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ELSE IF( SCALE.LE.SAFMN2 ) THEN
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COUNT = 0
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30 CONTINUE
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COUNT = COUNT + 1
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F1 = F1*SAFMX2
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G1 = G1*SAFMX2
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SCALE = MAX( ABS( F1 ), ABS( G1 ) )
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IF( SCALE.LE.SAFMN2 )
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$ GO TO 30
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R = SQRT( F1**2+G1**2 )
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CS = F1 / R
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SN = G1 / R
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DO 40 I = 1, COUNT
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R = R*SAFMN2
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40 CONTINUE
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ELSE
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R = SQRT( F1**2+G1**2 )
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CS = F1 / R
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SN = G1 / R
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END IF
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IF( ABS( F ).GT.ABS( G ) .AND. CS.LT.ZERO ) THEN
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CS = -CS
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SN = -SN
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R = -R
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END IF
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END IF
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RETURN
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*
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* End of DLARTG
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*
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END
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