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SUBROUTINE SLASQ6( I0, N0, Z, PP, DMIN, DMIN1, DMIN2, DN,
$ DNM1, DNM2 ) * * -- LAPACK routine (version 3.2) -- * * -- Contributed by Osni Marques of the Lawrence Berkeley National -- * -- Laboratory and Beresford Parlett of the Univ. of California at -- * -- Berkeley -- * -- November 2008 -- * * -- LAPACK is a software package provided by Univ. of Tennessee, -- * -- Univ. of California Berkeley, Univ. of Colorado Denver and NAG Ltd..-- * * .. Scalar Arguments .. INTEGER I0, N0, PP REAL DMIN, DMIN1, DMIN2, DN, DNM1, DNM2 * .. * .. Array Arguments .. REAL Z( * ) * .. * * Purpose * ======= * * SLASQ6 computes one dqd (shift equal to zero) transform in * ping-pong form, with protection against underflow and overflow. * * Arguments * ========= * * I0 (input) INTEGER * First index. * * N0 (input) INTEGER * Last index. * * Z (input) REAL array, dimension ( 4*N ) * Z holds the qd array. EMIN is stored in Z(4*N0) to avoid * an extra argument. * * PP (input) INTEGER * PP=0 for ping, PP=1 for pong. * * DMIN (output) REAL * Minimum value of d. * * DMIN1 (output) REAL * Minimum value of d, excluding D( N0 ). * * DMIN2 (output) REAL * Minimum value of d, excluding D( N0 ) and D( N0-1 ). * * DN (output) REAL * d(N0), the last value of d. * * DNM1 (output) REAL * d(N0-1). * * DNM2 (output) REAL * d(N0-2). * * ===================================================================== * * .. Parameter .. REAL ZERO PARAMETER ( ZERO = 0.0E0 ) * .. * .. Local Scalars .. INTEGER J4, J4P2 REAL D, EMIN, SAFMIN, TEMP * .. * .. External Function .. REAL SLAMCH EXTERNAL SLAMCH * .. * .. Intrinsic Functions .. INTRINSIC MIN * .. * .. Executable Statements .. * IF( ( N0-I0-1 ).LE.0 ) $ RETURN * SAFMIN = SLAMCH( 'Safe minimum' ) J4 = 4*I0 + PP - 3 EMIN = Z( J4+4 ) D = Z( J4 ) DMIN = D * IF( PP.EQ.0 ) THEN DO 10 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-2 ) = D + Z( J4-1 ) IF( Z( J4-2 ).EQ.ZERO ) THEN Z( J4 ) = ZERO D = Z( J4+1 ) DMIN = D EMIN = ZERO ELSE IF( SAFMIN*Z( J4+1 ).LT.Z( J4-2 ) .AND. $ SAFMIN*Z( J4-2 ).LT.Z( J4+1 ) ) THEN TEMP = Z( J4+1 ) / Z( J4-2 ) Z( J4 ) = Z( J4-1 )*TEMP D = D*TEMP ELSE Z( J4 ) = Z( J4+1 )*( Z( J4-1 ) / Z( J4-2 ) ) D = Z( J4+1 )*( D / Z( J4-2 ) ) END IF DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4 ) ) 10 CONTINUE ELSE DO 20 J4 = 4*I0, 4*( N0-3 ), 4 Z( J4-3 ) = D + Z( J4 ) IF( Z( J4-3 ).EQ.ZERO ) THEN Z( J4-1 ) = ZERO D = Z( J4+2 ) DMIN = D EMIN = ZERO ELSE IF( SAFMIN*Z( J4+2 ).LT.Z( J4-3 ) .AND. $ SAFMIN*Z( J4-3 ).LT.Z( J4+2 ) ) THEN TEMP = Z( J4+2 ) / Z( J4-3 ) Z( J4-1 ) = Z( J4 )*TEMP D = D*TEMP ELSE Z( J4-1 ) = Z( J4+2 )*( Z( J4 ) / Z( J4-3 ) ) D = Z( J4+2 )*( D / Z( J4-3 ) ) END IF DMIN = MIN( DMIN, D ) EMIN = MIN( EMIN, Z( J4-1 ) ) 20 CONTINUE END IF * * Unroll last two steps. * DNM2 = D DMIN2 = DMIN J4 = 4*( N0-2 ) - PP J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM2 + Z( J4P2 ) IF( Z( J4-2 ).EQ.ZERO ) THEN Z( J4 ) = ZERO DNM1 = Z( J4P2+2 ) DMIN = DNM1 EMIN = ZERO ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN TEMP = Z( J4P2+2 ) / Z( J4-2 ) Z( J4 ) = Z( J4P2 )*TEMP DNM1 = DNM2*TEMP ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DNM1 = Z( J4P2+2 )*( DNM2 / Z( J4-2 ) ) END IF DMIN = MIN( DMIN, DNM1 ) * DMIN1 = DMIN J4 = J4 + 4 J4P2 = J4 + 2*PP - 1 Z( J4-2 ) = DNM1 + Z( J4P2 ) IF( Z( J4-2 ).EQ.ZERO ) THEN Z( J4 ) = ZERO DN = Z( J4P2+2 ) DMIN = DN EMIN = ZERO ELSE IF( SAFMIN*Z( J4P2+2 ).LT.Z( J4-2 ) .AND. $ SAFMIN*Z( J4-2 ).LT.Z( J4P2+2 ) ) THEN TEMP = Z( J4P2+2 ) / Z( J4-2 ) Z( J4 ) = Z( J4P2 )*TEMP DN = DNM1*TEMP ELSE Z( J4 ) = Z( J4P2+2 )*( Z( J4P2 ) / Z( J4-2 ) ) DN = Z( J4P2+2 )*( DNM1 / Z( J4-2 ) ) END IF DMIN = MIN( DMIN, DN ) * Z( J4+2 ) = DN Z( 4*N0-PP ) = EMIN RETURN * * End of SLASQ6 * END |