257 lines
5.9 KiB
Fortran
257 lines
5.9 KiB
Fortran
*> \brief \b DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow.
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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 DLADIV + dependencies
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*> <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dladiv.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/dladiv.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/dladiv.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 DLADIV( A, B, C, D, P, Q )
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*
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* .. Scalar Arguments ..
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* DOUBLE PRECISION A, B, C, D, P, Q
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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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*> DLADIV performs complex division in real arithmetic
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*>
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*> a + i*b
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*> p + i*q = ---------
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*> c + i*d
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*>
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*> The algorithm is due to Michael Baudin and Robert L. Smith
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*> and can be found in the paper
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*> "A Robust Complex Division in Scilab"
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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] A
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*> \verbatim
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*> A is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in] B
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*> \verbatim
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*> B is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in] C
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*> \verbatim
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*> C is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[in] D
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*> \verbatim
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*> D is DOUBLE PRECISION
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*> The scalars a, b, c, and d in the above expression.
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*> \endverbatim
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*>
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*> \param[out] P
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*> \verbatim
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*> P is DOUBLE PRECISION
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*> \endverbatim
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*>
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*> \param[out] Q
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*> \verbatim
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*> Q is DOUBLE PRECISION
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*> The scalars p and q in the above expression.
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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 January 2013
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*
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*> \ingroup doubleOTHERauxiliary
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*
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* =====================================================================
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SUBROUTINE DLADIV( A, B, C, D, P, Q )
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*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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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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* January 2013
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION A, B, C, D, P, Q
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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 BS
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PARAMETER ( BS = 2.0D0 )
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DOUBLE PRECISION HALF
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PARAMETER ( HALF = 0.5D0 )
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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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DOUBLE PRECISION AA, BB, CC, DD, AB, CD, S, OV, UN, BE, EPS
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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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* .. External Subroutines ..
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EXTERNAL DLADIV1
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* ..
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* .. Intrinsic Functions ..
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INTRINSIC ABS, MAX
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* ..
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* .. Executable Statements ..
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*
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AA = A
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BB = B
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CC = C
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DD = D
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AB = MAX( ABS(A), ABS(B) )
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CD = MAX( ABS(C), ABS(D) )
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S = 1.0D0
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OV = DLAMCH( 'Overflow threshold' )
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UN = DLAMCH( 'Safe minimum' )
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EPS = DLAMCH( 'Epsilon' )
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BE = BS / (EPS*EPS)
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IF( AB >= HALF*OV ) THEN
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AA = HALF * AA
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BB = HALF * BB
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S = TWO * S
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END IF
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IF( CD >= HALF*OV ) THEN
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CC = HALF * CC
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DD = HALF * DD
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S = HALF * S
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END IF
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IF( AB <= UN*BS/EPS ) THEN
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AA = AA * BE
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BB = BB * BE
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S = S / BE
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END IF
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IF( CD <= UN*BS/EPS ) THEN
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CC = CC * BE
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DD = DD * BE
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S = S * BE
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END IF
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IF( ABS( D ).LE.ABS( C ) ) THEN
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CALL DLADIV1(AA, BB, CC, DD, P, Q)
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ELSE
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CALL DLADIV1(BB, AA, DD, CC, P, Q)
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Q = -Q
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END IF
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P = P * S
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Q = Q * S
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*
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RETURN
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*
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* End of DLADIV
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*
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END
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*> \ingroup doubleOTHERauxiliary
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SUBROUTINE DLADIV1( A, B, C, D, P, Q )
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*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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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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* January 2013
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION A, B, C, D, P, Q
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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 ONE
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PARAMETER ( ONE = 1.0D0 )
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*
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* .. Local Scalars ..
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DOUBLE PRECISION R, T
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* ..
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* .. External Functions ..
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DOUBLE PRECISION DLADIV2
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EXTERNAL DLADIV2
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* ..
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* .. Executable Statements ..
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*
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R = D / C
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T = ONE / (C + D * R)
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P = DLADIV2(A, B, C, D, R, T)
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A = -A
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Q = DLADIV2(B, A, C, D, R, T)
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*
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RETURN
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*
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* End of DLADIV1
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*
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END
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*> \ingroup doubleOTHERauxiliary
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DOUBLE PRECISION FUNCTION DLADIV2( A, B, C, D, R, T )
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*
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* -- LAPACK auxiliary routine (version 3.7.0) --
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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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* January 2013
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*
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* .. Scalar Arguments ..
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DOUBLE PRECISION A, B, C, D, R, T
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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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*
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* .. Local Scalars ..
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DOUBLE PRECISION BR
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* ..
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* .. Executable Statements ..
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*
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IF( R.NE.ZERO ) THEN
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BR = B * R
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IF( BR.NE.ZERO ) THEN
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DLADIV2 = (A + BR) * T
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ELSE
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DLADIV2 = A * T + (B * T) * R
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END IF
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ELSE
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DLADIV2 = (A + D * (B / C)) * T
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END IF
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*
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RETURN
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*
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* End of DLADIV12
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*
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END
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