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*> \brief \b SLADIV performs complex division in real arithmetic, avoiding unnecessary overflow.
*
* =========== DOCUMENTATION ===========
*
* Online html documentation available at
* http://www.netlib.org/lapack/explore-html/
*
*> \htmlonly
*> Download SLADIV + dependencies
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/sladiv.f">
*> [TGZ]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.zip?format=zip&filename=/lapack/lapack_routine/sladiv.f">
*> [ZIP]</a>
*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.txt?format=txt&filename=/lapack/lapack_routine/sladiv.f">
*> [TXT]</a>
*> \endhtmlonly
*
* Definition:
* ===========
*
* SUBROUTINE SLADIV( A, B, C, D, P, Q )
*
* .. Scalar Arguments ..
* REAL A, B, C, D, P, Q
* ..
*
*
*> \par Purpose:
* =============
*>
*> \verbatim
*>
*> SLADIV performs complex division in real arithmetic
*>
*> a + i*b
*> p + i*q = ---------
*> c + i*d
*>
*> The algorithm is due to Michael Baudin and Robert L. Smith
*> and can be found in the paper
*> "A Robust Complex Division in Scilab"
*> \endverbatim
*
* Arguments:
* ==========
*
*> \param[in] A
*> \verbatim
*> A is REAL
*> \endverbatim
*>
*> \param[in] B
*> \verbatim
*> B is REAL
*> \endverbatim
*>
*> \param[in] C
*> \verbatim
*> C is REAL
*> \endverbatim
*>
*> \param[in] D
*> \verbatim
*> D is REAL
*> The scalars a, b, c, and d in the above expression.
*> \endverbatim
*>
*> \param[out] P
*> \verbatim
*> P is REAL
*> \endverbatim
*>
*> \param[out] Q
*> \verbatim
*> Q is REAL
*> The scalars p and q in the above expression.
*> \endverbatim
*
* Authors:
* ========
*
*> \author Univ. of Tennessee
*> \author Univ. of California Berkeley
*> \author Univ. of Colorado Denver
*> \author NAG Ltd.
*
*> \ingroup ladiv
*
* =====================================================================
SUBROUTINE SLADIV( A, B, C, D, P, Q )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
REAL A, B, C, D, P, Q
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL BS
PARAMETER ( BS = 2.0E0 )
REAL HALF
PARAMETER ( HALF = 0.5E0 )
REAL TWO
PARAMETER ( TWO = 2.0E0 )
*
* .. Local Scalars ..
REAL AA, BB, CC, DD, AB, CD, S, OV, UN, BE, EPS
* ..
* .. External Functions ..
REAL SLAMCH
EXTERNAL SLAMCH
* ..
* .. External Subroutines ..
EXTERNAL SLADIV1
* ..
* .. Intrinsic Functions ..
INTRINSIC ABS, MAX
* ..
* .. Executable Statements ..
*
AA = A
BB = B
CC = C
DD = D
AB = MAX( ABS(A), ABS(B) )
CD = MAX( ABS(C), ABS(D) )
S = 1.0E0
OV = SLAMCH( 'Overflow threshold' )
UN = SLAMCH( 'Safe minimum' )
EPS = SLAMCH( 'Epsilon' )
BE = BS / (EPS*EPS)
IF( AB >= HALF*OV ) THEN
AA = HALF * AA
BB = HALF * BB
S = TWO * S
END IF
IF( CD >= HALF*OV ) THEN
CC = HALF * CC
DD = HALF * DD
S = HALF * S
END IF
IF( AB <= UN*BS/EPS ) THEN
AA = AA * BE
BB = BB * BE
S = S / BE
END IF
IF( CD <= UN*BS/EPS ) THEN
CC = CC * BE
DD = DD * BE
S = S * BE
END IF
IF( ABS( D ).LE.ABS( C ) ) THEN
CALL SLADIV1(AA, BB, CC, DD, P, Q)
ELSE
CALL SLADIV1(BB, AA, DD, CC, P, Q)
Q = -Q
END IF
P = P * S
Q = Q * S
*
RETURN
*
* End of SLADIV
*
END
*> \ingroup ladiv
SUBROUTINE SLADIV1( A, B, C, D, P, Q )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
REAL A, B, C, D, P, Q
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ONE
PARAMETER ( ONE = 1.0E0 )
*
* .. Local Scalars ..
REAL R, T
* ..
* .. External Functions ..
REAL SLADIV2
EXTERNAL SLADIV2
* ..
* .. Executable Statements ..
*
R = D / C
T = ONE / (C + D * R)
P = SLADIV2(A, B, C, D, R, T)
A = -A
Q = SLADIV2(B, A, C, D, R, T)
*
RETURN
*
* End of SLADIV1
*
END
*> \ingroup ladiv
REAL FUNCTION SLADIV2( A, B, C, D, R, T )
*
* -- LAPACK auxiliary routine --
* -- LAPACK is a software package provided by Univ. of Tennessee, --
* -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
*
* .. Scalar Arguments ..
REAL A, B, C, D, R, T
* ..
*
* =====================================================================
*
* .. Parameters ..
REAL ZERO
PARAMETER ( ZERO = 0.0E0 )
*
* .. Local Scalars ..
REAL BR
* ..
* .. Executable Statements ..
*
IF( R.NE.ZERO ) THEN
BR = B * R
if( BR.NE.ZERO ) THEN
SLADIV2 = (A + BR) * T
ELSE
SLADIV2 = A * T + (B * T) * R
END IF
ELSE
SLADIV2 = (A + D * (B / C)) * T
END IF
*
RETURN
*
* End of SLADIV2
*
END
|
