476 lines
13 KiB
C++
476 lines
13 KiB
C++
/* fortran/dlasq3.f -- translated by f2c (version 20200916).
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You must link the resulting object file with libf2c:
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on Microsoft Windows system, link with libf2c.lib;
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on Linux or Unix systems, link with .../path/to/libf2c.a -lm
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or, if you install libf2c.a in a standard place, with -lf2c -lm
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-- in that order, at the end of the command line, as in
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cc *.o -lf2c -lm
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Source for libf2c is in /netlib/f2c/libf2c.zip, e.g.,
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http://www.netlib.org/f2c/libf2c.zip
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*/
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#ifdef __cplusplus
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extern "C" {
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#endif
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#include "lmp_f2c.h"
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/* > \brief \b DLASQ3 checks for deflation, computes a shift and calls dqds. Used by sbdsqr. */
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/* =========== DOCUMENTATION =========== */
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/* Online html documentation available at */
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/* http://www.netlib.org/lapack/explore-html/ */
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/* > \htmlonly */
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/* > Download DLASQ3 + dependencies */
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/* > <a href="http://www.netlib.org/cgi-bin/netlibfiles.tgz?format=tgz&filename=/lapack/lapack_routine/dlasq3.
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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/dlasq3.
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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/dlasq3.
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f"> */
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/* > [TXT]</a> */
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/* > \endhtmlonly */
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/* Definition: */
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/* =========== */
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/* SUBROUTINE DLASQ3( I0, N0, Z, PP, DMIN, SIGMA, DESIG, QMAX, NFAIL, */
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/* ITER, NDIV, IEEE, TTYPE, DMIN1, DMIN2, DN, DN1, */
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/* DN2, G, TAU ) */
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/* .. Scalar Arguments .. */
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/* LOGICAL IEEE */
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/* INTEGER I0, ITER, N0, NDIV, NFAIL, PP */
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/* DOUBLE PRECISION DESIG, DMIN, DMIN1, DMIN2, DN, DN1, DN2, G, */
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/* $ QMAX, SIGMA, TAU */
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/* .. */
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/* .. Array Arguments .. */
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/* DOUBLE PRECISION Z( * ) */
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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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/* > DLASQ3 checks for deflation, computes a shift (TAU) and calls dqds. */
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/* > In case of failure it changes shifts, and tries again until output */
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/* > is positive. */
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/* > \endverbatim */
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/* Arguments: */
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/* ========== */
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/* > \param[in] I0 */
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/* > \verbatim */
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/* > I0 is INTEGER */
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/* > First index. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] N0 */
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/* > \verbatim */
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/* > N0 is INTEGER */
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/* > Last index. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] Z */
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/* > \verbatim */
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/* > Z is DOUBLE PRECISION array, dimension ( 4*N0 ) */
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/* > Z holds the qd array. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] PP */
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/* > \verbatim */
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/* > PP is INTEGER */
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/* > PP=0 for ping, PP=1 for pong. */
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/* > PP=2 indicates that flipping was applied to the Z array */
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/* > and that the initial tests for deflation should not be */
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/* > performed. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] DMIN */
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/* > \verbatim */
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/* > DMIN is DOUBLE PRECISION */
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/* > Minimum value of d. */
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/* > \endverbatim */
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/* > */
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/* > \param[out] SIGMA */
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/* > \verbatim */
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/* > SIGMA is DOUBLE PRECISION */
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/* > Sum of shifts used in current segment. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DESIG */
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/* > \verbatim */
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/* > DESIG is DOUBLE PRECISION */
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/* > Lower order part of SIGMA */
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/* > \endverbatim */
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/* > */
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/* > \param[in] QMAX */
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/* > \verbatim */
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/* > QMAX is DOUBLE PRECISION */
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/* > Maximum value of q. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] NFAIL */
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/* > \verbatim */
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/* > NFAIL is INTEGER */
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/* > Increment NFAIL by 1 each time the shift was too big. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] ITER */
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/* > \verbatim */
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/* > ITER is INTEGER */
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/* > Increment ITER by 1 for each iteration. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] NDIV */
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/* > \verbatim */
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/* > NDIV is INTEGER */
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/* > Increment NDIV by 1 for each division. */
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/* > \endverbatim */
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/* > */
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/* > \param[in] IEEE */
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/* > \verbatim */
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/* > IEEE is LOGICAL */
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/* > Flag for IEEE or non IEEE arithmetic (passed to DLASQ5). */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] TTYPE */
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/* > \verbatim */
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/* > TTYPE is INTEGER */
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/* > Shift type. */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DMIN1 */
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/* > \verbatim */
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/* > DMIN1 is DOUBLE PRECISION */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DMIN2 */
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/* > \verbatim */
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/* > DMIN2 is DOUBLE PRECISION */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DN */
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/* > \verbatim */
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/* > DN is DOUBLE PRECISION */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DN1 */
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/* > \verbatim */
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/* > DN1 is DOUBLE PRECISION */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] DN2 */
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/* > \verbatim */
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/* > DN2 is DOUBLE PRECISION */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] G */
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/* > \verbatim */
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/* > G is DOUBLE PRECISION */
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/* > \endverbatim */
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/* > */
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/* > \param[in,out] TAU */
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/* > \verbatim */
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/* > TAU is DOUBLE PRECISION */
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/* > */
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/* > These are passed as arguments in order to save their values */
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/* > between calls to DLASQ3. */
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/* > \endverbatim */
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/* Authors: */
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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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/* > \ingroup auxOTHERcomputational */
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/* ===================================================================== */
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/* Subroutine */ int dlasq3_(integer *i0, integer *n0, doublereal *z__,
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integer *pp, doublereal *dmin__, doublereal *sigma, doublereal *desig,
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doublereal *qmax, integer *nfail, integer *iter, integer *ndiv,
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logical *ieee, integer *ttype, doublereal *dmin1, doublereal *dmin2,
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doublereal *dn, doublereal *dn1, doublereal *dn2, doublereal *g,
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doublereal *tau)
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{
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/* System generated locals */
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integer i__1;
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doublereal d__1, d__2;
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/* Builtin functions */
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double sqrt(doublereal);
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/* Local variables */
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doublereal s, t;
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integer j4, nn;
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doublereal eps, tol;
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integer n0in, ipn4;
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doublereal tol2, temp;
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extern /* Subroutine */ int dlasq4_(integer *, integer *, doublereal *,
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integer *, integer *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *, integer *,
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doublereal *), dlasq5_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *, doublereal *, doublereal *, logical *
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, doublereal *), dlasq6_(integer *, integer *, doublereal *,
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integer *, doublereal *, doublereal *, doublereal *, doublereal *,
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doublereal *, doublereal *);
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extern doublereal dlamch_(char *, ftnlen);
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extern logical disnan_(doublereal *);
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/* -- LAPACK computational routine -- */
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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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/* .. Scalar Arguments .. */
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/* .. */
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/* .. Array Arguments .. */
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/* .. */
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/* ===================================================================== */
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/* .. Parameters .. */
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/* .. */
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/* .. Local Scalars .. */
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/* .. */
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/* .. External Subroutines .. */
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/* .. */
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/* .. External Function .. */
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/* .. */
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/* .. Intrinsic Functions .. */
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/* .. */
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/* .. Executable Statements .. */
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/* Parameter adjustments */
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--z__;
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/* Function Body */
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n0in = *n0;
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eps = dlamch_((char *)"Precision", (ftnlen)9);
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tol = eps * 100.;
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/* Computing 2nd power */
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d__1 = tol;
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tol2 = d__1 * d__1;
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/* Check for deflation. */
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L10:
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if (*n0 < *i0) {
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return 0;
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}
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if (*n0 == *i0) {
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goto L20;
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}
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nn = (*n0 << 2) + *pp;
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if (*n0 == *i0 + 1) {
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goto L40;
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}
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/* Check whether E(N0-1) is negligible, 1 eigenvalue. */
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if (z__[nn - 5] > tol2 * (*sigma + z__[nn - 3]) && z__[nn - (*pp << 1) -
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4] > tol2 * z__[nn - 7]) {
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goto L30;
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}
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L20:
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z__[(*n0 << 2) - 3] = z__[(*n0 << 2) + *pp - 3] + *sigma;
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--(*n0);
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goto L10;
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/* Check whether E(N0-2) is negligible, 2 eigenvalues. */
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L30:
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if (z__[nn - 9] > tol2 * *sigma && z__[nn - (*pp << 1) - 8] > tol2 * z__[
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nn - 11]) {
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goto L50;
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}
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L40:
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if (z__[nn - 3] > z__[nn - 7]) {
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s = z__[nn - 3];
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z__[nn - 3] = z__[nn - 7];
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z__[nn - 7] = s;
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}
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t = (z__[nn - 7] - z__[nn - 3] + z__[nn - 5]) * .5;
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if (z__[nn - 5] > z__[nn - 3] * tol2 && t != 0.) {
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s = z__[nn - 3] * (z__[nn - 5] / t);
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if (s <= t) {
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s = z__[nn - 3] * (z__[nn - 5] / (t * (sqrt(s / t + 1.) + 1.)));
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} else {
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s = z__[nn - 3] * (z__[nn - 5] / (t + sqrt(t) * sqrt(t + s)));
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}
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t = z__[nn - 7] + (s + z__[nn - 5]);
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z__[nn - 3] *= z__[nn - 7] / t;
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z__[nn - 7] = t;
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}
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z__[(*n0 << 2) - 7] = z__[nn - 7] + *sigma;
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z__[(*n0 << 2) - 3] = z__[nn - 3] + *sigma;
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*n0 += -2;
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goto L10;
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L50:
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if (*pp == 2) {
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*pp = 0;
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}
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/* Reverse the qd-array, if warranted. */
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if (*dmin__ <= 0. || *n0 < n0in) {
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if (z__[(*i0 << 2) + *pp - 3] * 1.5 < z__[(*n0 << 2) + *pp - 3]) {
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ipn4 = *i0 + *n0 << 2;
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i__1 = *i0 + *n0 - 1 << 1;
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for (j4 = *i0 << 2; j4 <= i__1; j4 += 4) {
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temp = z__[j4 - 3];
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z__[j4 - 3] = z__[ipn4 - j4 - 3];
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z__[ipn4 - j4 - 3] = temp;
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temp = z__[j4 - 2];
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z__[j4 - 2] = z__[ipn4 - j4 - 2];
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z__[ipn4 - j4 - 2] = temp;
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temp = z__[j4 - 1];
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z__[j4 - 1] = z__[ipn4 - j4 - 5];
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z__[ipn4 - j4 - 5] = temp;
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temp = z__[j4];
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z__[j4] = z__[ipn4 - j4 - 4];
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z__[ipn4 - j4 - 4] = temp;
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/* L60: */
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}
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if (*n0 - *i0 <= 4) {
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z__[(*n0 << 2) + *pp - 1] = z__[(*i0 << 2) + *pp - 1];
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z__[(*n0 << 2) - *pp] = z__[(*i0 << 2) - *pp];
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}
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/* Computing MIN */
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d__1 = *dmin2, d__2 = z__[(*n0 << 2) + *pp - 1];
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*dmin2 = min(d__1,d__2);
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/* Computing MIN */
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d__1 = z__[(*n0 << 2) + *pp - 1], d__2 = z__[(*i0 << 2) + *pp - 1]
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, d__1 = min(d__1,d__2), d__2 = z__[(*i0 << 2) + *pp + 3];
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z__[(*n0 << 2) + *pp - 1] = min(d__1,d__2);
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/* Computing MIN */
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d__1 = z__[(*n0 << 2) - *pp], d__2 = z__[(*i0 << 2) - *pp], d__1 =
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min(d__1,d__2), d__2 = z__[(*i0 << 2) - *pp + 4];
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z__[(*n0 << 2) - *pp] = min(d__1,d__2);
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/* Computing MAX */
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d__1 = *qmax, d__2 = z__[(*i0 << 2) + *pp - 3], d__1 = max(d__1,
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d__2), d__2 = z__[(*i0 << 2) + *pp + 1];
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*qmax = max(d__1,d__2);
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*dmin__ = -0.;
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}
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}
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/* Choose a shift. */
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dlasq4_(i0, n0, &z__[1], pp, &n0in, dmin__, dmin1, dmin2, dn, dn1, dn2,
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tau, ttype, g);
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/* Call dqds until DMIN > 0. */
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L70:
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dlasq5_(i0, n0, &z__[1], pp, tau, sigma, dmin__, dmin1, dmin2, dn, dn1,
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dn2, ieee, &eps);
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*ndiv += *n0 - *i0 + 2;
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++(*iter);
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/* Check status. */
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if (*dmin__ >= 0. && *dmin1 >= 0.) {
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/* Success. */
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goto L90;
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} else if (*dmin__ < 0. && *dmin1 > 0. && z__[(*n0 - 1 << 2) - *pp] < tol
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* (*sigma + *dn1) && abs(*dn) < tol * *sigma) {
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/* Convergence hidden by negative DN. */
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z__[(*n0 - 1 << 2) - *pp + 2] = 0.;
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*dmin__ = 0.;
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goto L90;
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} else if (*dmin__ < 0.) {
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/* TAU too big. Select new TAU and try again. */
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++(*nfail);
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if (*ttype < -22) {
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/* Failed twice. Play it safe. */
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*tau = 0.;
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} else if (*dmin1 > 0.) {
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/* Late failure. Gives excellent shift. */
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*tau = (*tau + *dmin__) * (1. - eps * 2.);
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*ttype += -11;
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} else {
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/* Early failure. Divide by 4. */
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*tau *= .25;
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*ttype += -12;
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}
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goto L70;
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} else if (disnan_(dmin__)) {
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/* NaN. */
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if (*tau == 0.) {
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goto L80;
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} else {
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*tau = 0.;
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goto L70;
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}
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} else {
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/* Possible underflow. Play it safe. */
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goto L80;
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}
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/* Risk of underflow. */
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L80:
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dlasq6_(i0, n0, &z__[1], pp, dmin__, dmin1, dmin2, dn, dn1, dn2);
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*ndiv += *n0 - *i0 + 2;
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++(*iter);
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*tau = 0.;
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L90:
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if (*tau < *sigma) {
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*desig += *tau;
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t = *sigma + *desig;
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*desig -= t - *sigma;
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} else {
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t = *sigma + *tau;
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*desig = *sigma - (t - *tau) + *desig;
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}
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*sigma = t;
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return 0;
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/* End of DLASQ3 */
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} /* dlasq3_ */
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#ifdef __cplusplus
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}
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#endif
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