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    1:       SUBROUTINE ZLARGV( N, X, INCX, Y, INCY, C, INCC )
    2: *
    3: *  -- LAPACK auxiliary routine (version 3.2) --
    4: *  -- LAPACK is a software package provided by Univ. of Tennessee,    --
    5: *  -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..--
    6: *     November 2006
    7: *
    8: *     .. Scalar Arguments ..
    9:       INTEGER            INCC, INCX, INCY, N
   10: *     ..
   11: *     .. Array Arguments ..
   12:       DOUBLE PRECISION   C( * )
   13:       COMPLEX*16         X( * ), Y( * )
   14: *     ..
   15: *
   16: *  Purpose
   17: *  =======
   18: *
   19: *  ZLARGV generates a vector of complex plane rotations with real
   20: *  cosines, determined by elements of the complex vectors x and y.
   21: *  For i = 1,2,...,n
   22: *
   23: *     (        c(i)   s(i) ) ( x(i) ) = ( r(i) )
   24: *     ( -conjg(s(i))  c(i) ) ( y(i) ) = (   0  )
   25: *
   26: *     where c(i)**2 + ABS(s(i))**2 = 1
   27: *
   28: *  The following conventions are used (these are the same as in ZLARTG,
   29: *  but differ from the BLAS1 routine ZROTG):
   30: *     If y(i)=0, then c(i)=1 and s(i)=0.
   31: *     If x(i)=0, then c(i)=0 and s(i) is chosen so that r(i) is real.
   32: *
   33: *  Arguments
   34: *  =========
   35: *
   36: *  N       (input) INTEGER
   37: *          The number of plane rotations to be generated.
   38: *
   39: *  X       (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCX)
   40: *          On entry, the vector x.
   41: *          On exit, x(i) is overwritten by r(i), for i = 1,...,n.
   42: *
   43: *  INCX    (input) INTEGER
   44: *          The increment between elements of X. INCX > 0.
   45: *
   46: *  Y       (input/output) COMPLEX*16 array, dimension (1+(N-1)*INCY)
   47: *          On entry, the vector y.
   48: *          On exit, the sines of the plane rotations.
   49: *
   50: *  INCY    (input) INTEGER
   51: *          The increment between elements of Y. INCY > 0.
   52: *
   53: *  C       (output) DOUBLE PRECISION array, dimension (1+(N-1)*INCC)
   54: *          The cosines of the plane rotations.
   55: *
   56: *  INCC    (input) INTEGER
   57: *          The increment between elements of C. INCC > 0.
   58: *
   59: *  Further Details
   60: *  ======= =======
   61: *
   62: *  6-6-96 - Modified with a new algorithm by W. Kahan and J. Demmel
   63: *
   64: *  This version has a few statements commented out for thread safety
   65: *  (machine parameters are computed on each entry). 10 feb 03, SJH.
   66: *
   67: *  =====================================================================
   68: *
   69: *     .. Parameters ..
   70:       DOUBLE PRECISION   TWO, ONE, ZERO
   71:       PARAMETER          ( TWO = 2.0D+0, ONE = 1.0D+0, ZERO = 0.0D+0 )
   72:       COMPLEX*16         CZERO
   73:       PARAMETER          ( CZERO = ( 0.0D+0, 0.0D+0 ) )
   74: *     ..
   75: *     .. Local Scalars ..
   76: *     LOGICAL            FIRST
   77: 
   78:       INTEGER            COUNT, I, IC, IX, IY, J
   79:       DOUBLE PRECISION   CS, D, DI, DR, EPS, F2, F2S, G2, G2S, SAFMIN,
   80:      $                   SAFMN2, SAFMX2, SCALE
   81:       COMPLEX*16         F, FF, FS, G, GS, R, SN
   82: *     ..
   83: *     .. External Functions ..
   84:       DOUBLE PRECISION   DLAMCH, DLAPY2
   85:       EXTERNAL           DLAMCH, DLAPY2
   86: *     ..
   87: *     .. Intrinsic Functions ..
   88:       INTRINSIC          ABS, DBLE, DCMPLX, DCONJG, DIMAG, INT, LOG,
   89:      $                   MAX, SQRT
   90: *     ..
   91: *     .. Statement Functions ..
   92:       DOUBLE PRECISION   ABS1, ABSSQ
   93: *     ..
   94: *     .. Save statement ..
   95: *     SAVE               FIRST, SAFMX2, SAFMIN, SAFMN2
   96: *     ..
   97: *     .. Data statements ..
   98: *     DATA               FIRST / .TRUE. /
   99: *     ..
  100: *     .. Statement Function definitions ..
  101:       ABS1( FF ) = MAX( ABS( DBLE( FF ) ), ABS( DIMAG( FF ) ) )
  102:       ABSSQ( FF ) = DBLE( FF )**2 + DIMAG( FF )**2
  103: *     ..
  104: *     .. Executable Statements ..
  105: *
  106: *     IF( FIRST ) THEN
  107: *        FIRST = .FALSE.
  108:          SAFMIN = DLAMCH( 'S' )
  109:          EPS = DLAMCH( 'E' )
  110:          SAFMN2 = DLAMCH( 'B' )**INT( LOG( SAFMIN / EPS ) /
  111:      $            LOG( DLAMCH( 'B' ) ) / TWO )
  112:          SAFMX2 = ONE / SAFMN2
  113: *     END IF
  114:       IX = 1
  115:       IY = 1
  116:       IC = 1
  117:       DO 60 I = 1, N
  118:          F = X( IX )
  119:          G = Y( IY )
  120: *
  121: *        Use identical algorithm as in ZLARTG
  122: *
  123:          SCALE = MAX( ABS1( F ), ABS1( G ) )
  124:          FS = F
  125:          GS = G
  126:          COUNT = 0
  127:          IF( SCALE.GE.SAFMX2 ) THEN
  128:    10       CONTINUE
  129:             COUNT = COUNT + 1
  130:             FS = FS*SAFMN2
  131:             GS = GS*SAFMN2
  132:             SCALE = SCALE*SAFMN2
  133:             IF( SCALE.GE.SAFMX2 )
  134:      $         GO TO 10
  135:          ELSE IF( SCALE.LE.SAFMN2 ) THEN
  136:             IF( G.EQ.CZERO ) THEN
  137:                CS = ONE
  138:                SN = CZERO
  139:                R = F
  140:                GO TO 50
  141:             END IF
  142:    20       CONTINUE
  143:             COUNT = COUNT - 1
  144:             FS = FS*SAFMX2
  145:             GS = GS*SAFMX2
  146:             SCALE = SCALE*SAFMX2
  147:             IF( SCALE.LE.SAFMN2 )
  148:      $         GO TO 20
  149:          END IF
  150:          F2 = ABSSQ( FS )
  151:          G2 = ABSSQ( GS )
  152:          IF( F2.LE.MAX( G2, ONE )*SAFMIN ) THEN
  153: *
  154: *           This is a rare case: F is very small.
  155: *
  156:             IF( F.EQ.CZERO ) THEN
  157:                CS = ZERO
  158:                R = DLAPY2( DBLE( G ), DIMAG( G ) )
  159: *              Do complex/real division explicitly with two real
  160: *              divisions
  161:                D = DLAPY2( DBLE( GS ), DIMAG( GS ) )
  162:                SN = DCMPLX( DBLE( GS ) / D, -DIMAG( GS ) / D )
  163:                GO TO 50
  164:             END IF
  165:             F2S = DLAPY2( DBLE( FS ), DIMAG( FS ) )
  166: *           G2 and G2S are accurate
  167: *           G2 is at least SAFMIN, and G2S is at least SAFMN2
  168:             G2S = SQRT( G2 )
  169: *           Error in CS from underflow in F2S is at most
  170: *           UNFL / SAFMN2 .lt. sqrt(UNFL*EPS) .lt. EPS
  171: *           If MAX(G2,ONE)=G2, then F2 .lt. G2*SAFMIN,
  172: *           and so CS .lt. sqrt(SAFMIN)
  173: *           If MAX(G2,ONE)=ONE, then F2 .lt. SAFMIN
  174: *           and so CS .lt. sqrt(SAFMIN)/SAFMN2 = sqrt(EPS)
  175: *           Therefore, CS = F2S/G2S / sqrt( 1 + (F2S/G2S)**2 ) = F2S/G2S
  176:             CS = F2S / G2S
  177: *           Make sure abs(FF) = 1
  178: *           Do complex/real division explicitly with 2 real divisions
  179:             IF( ABS1( F ).GT.ONE ) THEN
  180:                D = DLAPY2( DBLE( F ), DIMAG( F ) )
  181:                FF = DCMPLX( DBLE( F ) / D, DIMAG( F ) / D )
  182:             ELSE
  183:                DR = SAFMX2*DBLE( F )
  184:                DI = SAFMX2*DIMAG( F )
  185:                D = DLAPY2( DR, DI )
  186:                FF = DCMPLX( DR / D, DI / D )
  187:             END IF
  188:             SN = FF*DCMPLX( DBLE( GS ) / G2S, -DIMAG( GS ) / G2S )
  189:             R = CS*F + SN*G
  190:          ELSE
  191: *
  192: *           This is the most common case.
  193: *           Neither F2 nor F2/G2 are less than SAFMIN
  194: *           F2S cannot overflow, and it is accurate
  195: *
  196:             F2S = SQRT( ONE+G2 / F2 )
  197: *           Do the F2S(real)*FS(complex) multiply with two real
  198: *           multiplies
  199:             R = DCMPLX( F2S*DBLE( FS ), F2S*DIMAG( FS ) )
  200:             CS = ONE / F2S
  201:             D = F2 + G2
  202: *           Do complex/real division explicitly with two real divisions
  203:             SN = DCMPLX( DBLE( R ) / D, DIMAG( R ) / D )
  204:             SN = SN*DCONJG( GS )
  205:             IF( COUNT.NE.0 ) THEN
  206:                IF( COUNT.GT.0 ) THEN
  207:                   DO 30 J = 1, COUNT
  208:                      R = R*SAFMX2
  209:    30             CONTINUE
  210:                ELSE
  211:                   DO 40 J = 1, -COUNT
  212:                      R = R*SAFMN2
  213:    40             CONTINUE
  214:                END IF
  215:             END IF
  216:          END IF
  217:    50    CONTINUE
  218:          C( IC ) = CS
  219:          Y( IY ) = SN
  220:          X( IX ) = R
  221:          IC = IC + INCC
  222:          IY = IY + INCY
  223:          IX = IX + INCX
  224:    60 CONTINUE
  225:       RETURN
  226: *
  227: *     End of ZLARGV
  228: *
  229:       END