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SUBROUTINE ZLARTG( F, G, CS, SN, R )
*
* -- LAPACK auxiliary routine (version 3.1) --
* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd..
* November 2006
*
* .. Scalar Arguments ..
DOUBLE PRECISION CS
COMPLEX*16 F, G, R, SN
* ..
*
* Purpose
* =======
*
* ZLARTG generates a plane rotation so that
*
* [ CS SN ] [ F ] [ R ]
* [ __ ] . [ ] = [ ] where CS**2 + |SN|**2 = 1.
* [ -SN CS ] [ G ] [ 0 ]
*
* This is a faster version of the BLAS1 routine ZROTG, except for
* the following differences:
* F and G are unchanged on return.
* If G=0, then CS=1 and SN=0.
* If F=0, then CS=0 and SN is chosen so that R is real.
*
* Arguments
* =========
*
* F (input) COMPLEX*16
* The first component of vector to be rotated.
*
* G (input) COMPLEX*16
* The second component of vector to be rotated.
*
* CS (output) DOUBLE PRECISION
* The cosine of the rotation.
*
* SN (output) COMPLEX*16
* The sine of the rotation.
*
* R (output) COMPLEX*16
* The nonzero component of the rotated vector.
*
* Further Details
* ======= =======
*
* 3-5-96 - Modified with a new algorithm by W. Kahan and J. Demmel
*
* This version has a few statements commented out for thread safety
* (machine parameters are computed on each entry). 10 feb 03, SJH.
*
* =====================================================================
*
* .. Parameters ..
DOUBLE PRECISION TWO, ONE, ZERO
PARAMETER ( TWO = 2.0D+0, ONE = 1.0D+0, ZERO = 0.0D+0 )
COMPLEX*16 CZERO
PARAMETER ( CZERO = ( 0.0D+0, 0.0D+0 ) )
* ..
* .. Local Scalars ..
* LOGICAL FIRST
INTEGER COUNT, I
DOUBLE PRECISION D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
$ SAFMN2, SAFMX2, SCALE
COMPLEX*16 FF, FS, GS
* ..
* .. External Functions ..
DOUBLE PRECISION DLAMCH, DLAPY2
EXTERNAL DLAMCH, DLAPY2
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG,
$ MAX, SQRT
* ..
* .. Statement Functions ..
DOUBLE PRECISION ABS1, ABSSQ
* ..
* .. Save statement ..
* SAVE FIRST, SAFMX2, SAFMIN, SAFMN2
* ..
* .. Data statements ..
* DATA FIRST / .TRUE. /
* ..
* .. Statement Function definitions ..
ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) )
ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2
* ..
* .. Executable Statements ..
*
* IF( FIRST ) THEN
SAFMIN = DLAMCH( 'S' )
EPS = DLAMCH( 'E' )
SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
$ LOG( DLAMCH( 'B' ) ) / TWO )
SAFMX2 = ONE / SAFMN2
* FIRST = .FALSE.
* END IF
SCALE = MAX( ABS1( F ), ABS1( G ) )
FS = F
GS = G
COUNT = 0
IF( SCALE.GE.SAFMX2 ) THEN
10 CONTINUE
COUNT = COUNT + 1
FS = FS*SAFMN2
GS = GS*SAFMN2
SCALE = SCALE*SAFMN2
IF( SCALE.GE.SAFMX2 )
$ GO TO 10
ELSE IF( SCALE.LE.SAFMN2 ) THEN
IF( G.EQ.CZERO ) THEN
CS = ONE
SN = CZERO
R = F
RETURN
END IF
20 CONTINUE
COUNT = COUNT - 1
FS = FS*SAFMX2
GS = GS*SAFMX2
SCALE = SCALE*SAFMX2
IF( SCALE.LE.SAFMN2 )
$ GO TO 20
END IF
F2 = ABSSQ( FS )
G2 = ABSSQ( GS )
IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN
*
* This is a rare case: F is very small.
*
IF( F.EQ.CZERO ) THEN
CS = ZERO
R = DLAPY2( DBLE( G ), DIMAG( G ) )
* Do complex/real division explicitly with two real divisions
D = DLAPY2( DBLE( GS ), DIMAG( GS ) )
SN = DCMPLX( DBLE( GS ) / D, -DIMAG( GS ) / D )
RETURN
END IF
F2S = DLAPY2( DBLE( FS ), DIMAG( FS ) )
* G2 and G2S are accurate
* G2 is at least SAFMIN, and G2S is at least SAFMN2
G2S = SQRT( G2 )
* Error in CS from underflow in F2S is at most
* UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
* If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
* and so CS .lt. sqrt(SAFMIN)
* If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
* and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
* Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
CS = F2S / G2S
* Make sure abs(FF) = 1
* Do complex/real division explicitly with 2 real divisions
IF( ABS1( F ).GT.ONE ) THEN
D = DLAPY2( DBLE( F ), DIMAG( F ) )
FF = DCMPLX( DBLE( F ) / D, DIMAG( F ) / D )
ELSE
DR = SAFMX2*DBLE( F )
DI = SAFMX2*DIMAG( F )
D = DLAPY2( DR, DI )
FF = DCMPLX( DR / D, DI / D )
END IF
SN = FF*DCMPLX( DBLE( GS ) / G2S, -DIMAG( GS ) / G2S )
R = CS*F + SN*G
ELSE
*
* This is the most common case.
* Neither F2 nor F2/G2 are less than SAFMIN
* F2S cannot overflow, and it is accurate
*
F2S = SQRT( ONE+G2 / F2 )
* Do the F2S(real)*FS(complex) multiply with two real multiplies
R = DCMPLX( F2S*DBLE( FS ), F2S*DIMAG( FS ) )
CS = ONE / F2S
D = F2 + G2
* Do complex/real division explicitly with two real divisions
SN = DCMPLX( DBLE( R ) / D, DIMAG( R ) / D )
SN = SN*DCONJG( GS )
IF( COUNT.NE.0 ) THEN
IF( COUNT.GT.0 ) THEN
DO 30 I = 1, COUNT
R = R*SAFMX2
30 CONTINUE
ELSE
DO 40 I = 1, -COUNT
R = R*SAFMN2
40 CONTINUE
END IF
END IF
END IF
RETURN
*
* End of ZLARTG
*
END
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