LAPACK  3.10.0
LAPACK: Linear Algebra PACKage

◆ dladiv()

subroutine dladiv ( double precision  A,
double precision  B,
double precision  C,
double precision  D,
double precision  P,
double precision  Q 
)

DLADIV performs complex division in real arithmetic, avoiding unnecessary overflow.

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Purpose:
 DLADIV 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"
Parameters
[in]A
          A is DOUBLE PRECISION
[in]B
          B is DOUBLE PRECISION
[in]C
          C is DOUBLE PRECISION
[in]D
          D is DOUBLE PRECISION
          The scalars a, b, c, and d in the above expression.
[out]P
          P is DOUBLE PRECISION
[out]Q
          Q is DOUBLE PRECISION
          The scalars p and q in the above expression.
Author
Univ. of Tennessee
Univ. of California Berkeley
Univ. of Colorado Denver
NAG Ltd.

Definition at line 90 of file dladiv.f.

91 *
92 * -- LAPACK auxiliary routine --
93 * -- LAPACK is a software package provided by Univ. of Tennessee, --
94 * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
95 *
96 * .. Scalar Arguments ..
97  DOUBLE PRECISION A, B, C, D, P, Q
98 * ..
99 *
100 * =====================================================================
101 *
102 * .. Parameters ..
103  DOUBLE PRECISION BS
104  parameter( bs = 2.0d0 )
105  DOUBLE PRECISION HALF
106  parameter( half = 0.5d0 )
107  DOUBLE PRECISION TWO
108  parameter( two = 2.0d0 )
109 *
110 * .. Local Scalars ..
111  DOUBLE PRECISION AA, BB, CC, DD, AB, CD, S, OV, UN, BE, EPS
112 * ..
113 * .. External Functions ..
114  DOUBLE PRECISION DLAMCH
115  EXTERNAL dlamch
116 * ..
117 * .. External Subroutines ..
118  EXTERNAL dladiv1
119 * ..
120 * .. Intrinsic Functions ..
121  INTRINSIC abs, max
122 * ..
123 * .. Executable Statements ..
124 *
125  aa = a
126  bb = b
127  cc = c
128  dd = d
129  ab = max( abs(a), abs(b) )
130  cd = max( abs(c), abs(d) )
131  s = 1.0d0
132 
133  ov = dlamch( 'Overflow threshold' )
134  un = dlamch( 'Safe minimum' )
135  eps = dlamch( 'Epsilon' )
136  be = bs / (eps*eps)
137 
138  IF( ab >= half*ov ) THEN
139  aa = half * aa
140  bb = half * bb
141  s = two * s
142  END IF
143  IF( cd >= half*ov ) THEN
144  cc = half * cc
145  dd = half * dd
146  s = half * s
147  END IF
148  IF( ab <= un*bs/eps ) THEN
149  aa = aa * be
150  bb = bb * be
151  s = s / be
152  END IF
153  IF( cd <= un*bs/eps ) THEN
154  cc = cc * be
155  dd = dd * be
156  s = s * be
157  END IF
158  IF( abs( d ).LE.abs( c ) ) THEN
159  CALL dladiv1(aa, bb, cc, dd, p, q)
160  ELSE
161  CALL dladiv1(bb, aa, dd, cc, p, q)
162  q = -q
163  END IF
164  p = p * s
165  q = q * s
166 *
167  RETURN
168 *
169 * End of DLADIV
170 *
double precision function dlamch(CMACH)
DLAMCH
Definition: dlamch.f:69
subroutine dladiv1(A, B, C, D, P, Q)
Definition: dladiv.f:177
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