/* $Id: CoinOslFactorization2.cpp 2083 2019-01-06 19:38:09Z unxusr $ */
/*
  Copyright (C) 1987, 2009, International Business Machines
  Corporation and others.  All Rights Reserved.

  This code is licensed under the terms of the Eclipse Public License (EPL).
*/
#if COIN_BIG_INDEX == 0
/*
  CLP_OSL - if defined use osl
  0 - don't unroll 2 and 3 - don't use in Gomory
  1 - don't unroll - do use in Gomory
  2 - unroll - don't use in Gomory
  3 - unroll and use in Gomory
*/
#include "CoinOslFactorization.hpp"
#include "CoinOslC.h"
#include "CoinFinite.hpp"

#ifndef NDEBUG
extern int ets_count;
extern int ets_check;
#endif
#define COIN_REGISTER register
#define COIN_REGISTER2
#define COIN_REGISTER3 register
#ifdef COIN_USE_RESTRICT
#define COIN_RESTRICT2 __restrict
#else
#define COIN_RESTRICT2
#endif
static int c_ekkshfpo_scan2zero(COIN_REGISTER const EKKfactinfo *COIN_RESTRICT2 fact, const int *COIN_RESTRICT mpermu,
  double *COIN_RESTRICT worki, double *COIN_RESTRICT worko, int *COIN_RESTRICT mptr)
{

  /* Local variables */
  int irow;
  double tolerance = fact->zeroTolerance;
  int nin = fact->nrow;
  int *COIN_RESTRICT mptrX = mptr;
  if ((nin & 1) != 0) {
    irow = 1;
    if (fact->packedMode) {
      int irow0 = *mpermu;
      double dval;
      assert(irow0 >= 1 && irow0 <= nin);
      mpermu++;
      dval = worki[irow0];
      if (NOT_ZERO(dval)) {
        worki[irow0] = 0.0;
        if (fabs(dval) >= tolerance) {
          *(worko++) = dval;
          *(mptrX++) = 0;
        }
      }
    } else {
      int irow0 = *mpermu;
      double dval;
      assert(irow0 >= 1 && irow0 <= nin);
      mpermu++;
      dval = worki[irow0];
      if (NOT_ZERO(dval)) {
        worki[irow0] = 0.0;
        if (fabs(dval) >= tolerance) {
          *worko = dval;
          *(mptrX++) = 0;
        }
      }
      worko++;
    }
  } else {
    irow = 0;
  }
  if (fact->packedMode) {
    for (; irow < nin; irow += 2) {
      int irow0, irow1;
      double dval0, dval1;
      irow0 = mpermu[0];
      irow1 = mpermu[1];
      assert(irow0 >= 1 && irow0 <= nin);
      assert(irow1 >= 1 && irow1 <= nin);
      dval0 = worki[irow0];
      dval1 = worki[irow1];
      if (NOT_ZERO(dval0)) {
        worki[irow0] = 0.0;
        if (fabs(dval0) >= tolerance) {
          *(worko++) = dval0;
          *(mptrX++) = irow + 0;
        }
      }
      if (NOT_ZERO(dval1)) {
        worki[irow1] = 0.0;
        if (fabs(dval1) >= tolerance) {
          *(worko++) = dval1;
          *(mptrX++) = irow + 1;
        }
      }
      mpermu += 2;
    }
  } else {
    for (; irow < nin; irow += 2) {
      int irow0, irow1;
      double dval0, dval1;
      irow0 = mpermu[0];
      irow1 = mpermu[1];
      assert(irow0 >= 1 && irow0 <= nin);
      assert(irow1 >= 1 && irow1 <= nin);
      dval0 = worki[irow0];
      dval1 = worki[irow1];
      if (NOT_ZERO(dval0)) {
        worki[irow0] = 0.0;
        if (fabs(dval0) >= tolerance) {
          worko[0] = dval0;
          *(mptrX++) = irow + 0;
        }
      }
      if (NOT_ZERO(dval1)) {
        worki[irow1] = 0.0;
        if (fabs(dval1) >= tolerance) {
          worko[1] = dval1;
          *(mptrX++) = irow + 1;
        }
      }
      mpermu += 2;
      worko += 2;
    }
  }
  return static_cast< int >(mptrX - mptr);
}
/*
 * c_ekkshfpi_list executes the following loop:
 *
 * for (k=nincol, i=1; k; k--, i++) {
 *   int ipt = mptr[i];
 *   int irow = mpermu[ipt]; 
 *   worko[mpermu[irow]] = worki[i];
 *   worki[i] = 0.0;
 * }
 */
static int c_ekkshfpi_list(const int *COIN_RESTRICT mpermu,
  double *COIN_RESTRICT worki,
  double *COIN_RESTRICT worko,
  const int *COIN_RESTRICT mptr, int nincol,
  int *lastNonZero)
{
  int i, k, irow0, irow1;
  int first = COIN_INT_MAX;
  int last = 0;
  /* worko was zeroed out outside */
  k = nincol;
  i = 0;
  if ((k & 1) != 0) {
    int ipt = mptr[i];
    irow0 = mpermu[ipt];
    first = CoinMin(irow0, first);
    last = CoinMax(irow0, last);
    i++;
    worko[irow0] = *worki;
    *worki++ = 0.0;
  }
  k = k >> 1;
  for (; k; k--) {
    int ipt0 = mptr[i];
    int ipt1 = mptr[i + 1];
    irow0 = mpermu[ipt0];
    irow1 = mpermu[ipt1];
    i += 2;
    first = CoinMin(irow0, first);
    last = CoinMax(irow0, last);
    first = CoinMin(irow1, first);
    last = CoinMax(irow1, last);
    worko[irow0] = worki[0];
    worko[irow1] = worki[1];
    worki[0] = 0.0;
    worki[1] = 0.0;
    worki += 2;
  }
  *lastNonZero = last;
  return first;
}
/*
 * c_ekkshfpi_list2 executes the following loop:
 *
 * for (k=nincol, i=1; k; k--, i++) {
 *   int ipt = mptr[i];
 *   int irow = mpermu[ipt]; 
 *   worko[mpermu[irow]] = worki[ipt];
 *   worki[ipt] = 0.0;
 * }
 */
static int c_ekkshfpi_list2(const int *COIN_RESTRICT mpermu, double *COIN_RESTRICT worki, double *COIN_RESTRICT worko,
  const int *COIN_RESTRICT mptr, int nincol,
  int *lastNonZero)
{
#if 1
  int i, k, irow0, irow1;
  int first = COIN_INT_MAX;
  int last = 0;
  /* worko was zeroed out outside */
  k = nincol;
  i = 0;
  if ((k & 1) != 0) {
    int ipt = mptr[i];
    irow0 = mpermu[ipt];
    first = CoinMin(irow0, first);
    last = CoinMax(irow0, last);
    i++;
    worko[irow0] = worki[ipt];
    worki[ipt] = 0.0;
  }
  k = k >> 1;
  for (; k; k--) {
    int ipt0 = mptr[i];
    int ipt1 = mptr[i + 1];
    irow0 = mpermu[ipt0];
    irow1 = mpermu[ipt1];
    i += 2;
    first = CoinMin(irow0, first);
    last = CoinMax(irow0, last);
    first = CoinMin(irow1, first);
    last = CoinMax(irow1, last);
    worko[irow0] = worki[ipt0];
    worko[irow1] = worki[ipt1];
    worki[ipt0] = 0.0;
    worki[ipt1] = 0.0;
  }
#else
  int first = COIN_INT_MAX;
  int last = 0;
  /* worko was zeroed out outside */
  for (int i = 0; i < nincol; i++) {
    int ipt = mptr[i];
    int irow = mpermu[ipt];
    first = CoinMin(irow, first);
    last = CoinMax(irow, last);
    worko[irow] = worki[ipt];
    worki[ipt] = 0.0;
  }
#endif
  *lastNonZero = last;
  return first;
}
/*
 * c_ekkshfpi_list3 executes the following loop:
 *
 * for (k=nincol, i=1; k; k--, i++) {
 *   int ipt  = mptr[i];
 *   int irow = mpermu[ipt];
 *   worko[irow] = worki[i];
 *   worki[i] = 0.0;
 *   mptr[i] = mpermu[ipt];
 * }
 */
static void c_ekkshfpi_list3(const int *COIN_RESTRICT mpermu,
  double *COIN_RESTRICT worki, double *COIN_RESTRICT worko,
  int *COIN_RESTRICT mptr, int nincol)
{
  int i, k, irow0, irow1;
  /* worko was zeroed out outside */
  k = nincol;
  i = 0;
  if ((k & 1) != 0) {
    int ipt = mptr[i];
    irow0 = mpermu[ipt];
    mptr[i] = irow0;
    i++;
    worko[irow0] = *worki;
    *worki++ = 0.0;
  }
  k = k >> 1;
  for (; k; k--) {
    int ipt0 = mptr[i];
    int ipt1 = mptr[i + 1];
    irow0 = mpermu[ipt0];
    irow1 = mpermu[ipt1];
    mptr[i] = irow0;
    mptr[i + 1] = irow1;
    i += 2;
    worko[irow0] = worki[0];
    worko[irow1] = worki[1];
    worki[0] = 0.0;
    worki[1] = 0.0;
    worki += 2;
  }
}
static int c_ekkscmv(COIN_REGISTER const EKKfactinfo *COIN_RESTRICT2 fact, int n, double *COIN_RESTRICT dwork, int *COIN_RESTRICT mptr,
  double *COIN_RESTRICT dwork2)
{
  double tolerance = fact->zeroTolerance;
  int irow;
  const int *COIN_RESTRICT mptrsave = mptr;
  double *COIN_RESTRICT dwhere = dwork + 1;
  if ((n & 1) != 0) {
    if (NOT_ZERO(*dwhere)) {
      if (fabs(*dwhere) >= tolerance) {
        *++dwork2 = *dwhere;
        *++mptr = SHIFT_INDEX(1);
      } else {
        *dwhere = 0.0;
      }
    }
    dwhere++;
    irow = 2;
  } else {
    irow = 1;
  }
  for (n = n >> 1; n; n--) {
    int second = NOT_ZERO(*(dwhere + 1));
    if (NOT_ZERO(*dwhere)) {
      if (fabs(*dwhere) >= tolerance) {
        *++dwork2 = *dwhere;
        *++mptr = SHIFT_INDEX(irow);
      } else {
        *dwhere = 0.0;
      }
    }
    if (second) {
      if (fabs(*(dwhere + 1)) >= tolerance) {
        *++dwork2 = *(dwhere + 1);
        *++mptr = SHIFT_INDEX(irow + 1);
      } else {
        *(dwhere + 1) = 0.0;
      }
    }
    dwhere += 2;
    irow += 2;
  }

  return static_cast< int >(mptr - mptrsave);
} /* c_ekkscmv */
double c_ekkputl(const EKKfactinfo *COIN_RESTRICT2 fact,
  const int *COIN_RESTRICT mpt2,
  double *COIN_RESTRICT dwork1,
  double del3,
  int nincol, int nuspik)
{
  double *COIN_RESTRICT dwork3 = fact->xeeadr + fact->nnentu;
  int *COIN_RESTRICT hrowi = fact->xeradr + fact->nnentu;
  int offset = fact->R_etas_start[fact->nR_etas + 1];
  int *COIN_RESTRICT hrowiR = fact->R_etas_index + offset;
  double *COIN_RESTRICT dluval = fact->R_etas_element + offset;
  int i, j;

  /* dwork1 is r', the new R transform
   * dwork3 is the updated incoming column, alpha_p
   * del3 apparently has the pivot of the incoming column (???).
   * Here, we compute the p'th element of R^-1 alpha_p
   * (as described on p. 273), which is just a dot product.
   * I don't know why we subtract.
   */
  for (i = 1; i <= nuspik; ++i) {
    j = UNSHIFT_INDEX(hrowi[i]);
    del3 -= dwork3[i] * dwork1[j];
  }

  /* here we finally copy the r' to where we want it, the end */
  /* also take into account that the p'th row of R^-1 is -(p'th row of R). */
  /* also zero out dwork1 as we go */
  for (i = 0; i < nincol; ++i) {
    j = mpt2[i];
    hrowiR[-i] = SHIFT_INDEX(j);
    dluval[-i] = -dwork1[j];
    dwork1[j] = 0.;
  }

  return del3;
} /* c_ekkputl */
/* making this static seems to slow code down!
   may be being inlined
*/
int c_ekkputl2(const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  double *del3p,
  int nuspik)
{
  double *COIN_RESTRICT dwork3 = fact->xeeadr + fact->nnentu;
  int *COIN_RESTRICT hrowi = fact->xeradr + fact->nnentu;
  int offset = fact->R_etas_start[fact->nR_etas + 1];
  int *COIN_RESTRICT hrowiR = fact->R_etas_index + offset;
  double *COIN_RESTRICT dluval = fact->R_etas_element + offset;
  int i, j;
#if 0
  int nincol=c_ekksczr(fact,fact->nrow,dwork1,hrowiR);
#else
  int nrow = fact->nrow;
  const double tolerance = fact->zeroTolerance;
  int *COIN_RESTRICT mptrX = hrowiR;
  for (i = 1; i <= nrow; ++i) {
    if (dwork1[i] != 0.) {
      if (fabs(dwork1[i]) >= tolerance) {
        *(mptrX--) = SHIFT_INDEX(i);
      } else {
        dwork1[i] = 0.0;
      }
    }
  }
  int nincol = static_cast< int >(hrowiR - mptrX);
#endif
  double del3 = *del3p;
  /* dwork1 is r', the new R transform
   * dwork3 is the updated incoming column, alpha_p
   * del3 apparently has the pivot of the incoming column (???).
   * Here, we compute the p'th element of R^-1 alpha_p
   * (as described on p. 273), which is just a dot product.
   * I don't know why we subtract.
   */
  for (i = 1; i <= nuspik; ++i) {
    j = UNSHIFT_INDEX(hrowi[i]);
    del3 -= dwork3[i] * dwork1[j];
  }

  /* here we finally copy the r' to where we want it, the end */
  /* also take into account that the p'th row of R^-1 is -(p'th row of R). */
  /* also zero out dwork1 as we go */
  for (i = 0; i < nincol; ++i) {
    j = UNSHIFT_INDEX(hrowiR[-i]);
    dluval[-i] = -dwork1[j];
    dwork1[j] = 0.;
  }

  *del3p = del3;
  return nincol;
} /* c_ekkputl */
static void c_ekkbtj4p_no_dense(const int nrow, const double *COIN_RESTRICT dluval,
  const int *COIN_RESTRICT hrowi,
  const int *COIN_RESTRICT mcstrt,
  double *COIN_RESTRICT dwork1, int ndo, int jpiv)
{
  int i;
  double dv1;
  int iel;
  int irow;
  int i1, i2;

  /* count down to first nonzero */
  for (i = nrow; i >= 1; i--) {
    if (dwork1[i]) {
      break;
    }
  }
  i--; /* as pivot is just 1.0 */
  if (i > ndo + jpiv) {
    i = ndo + jpiv;
  }
  mcstrt -= jpiv;
  i2 = mcstrt[i + 1];
  for (; i > jpiv; --i) {
    double dv1b = 0.0;
    int nel;
    i1 = mcstrt[i];
    nel = i1 - i2;
    dv1 = dwork1[i];
    iel = i2;
    if ((nel & 1) != 0) {
      irow = hrowi[iel];
      dv1b = SHIFT_REF(dwork1, irow) * dluval[iel];
      iel++;
    }
    for (; iel < i1; iel += 2) {
      int irow = hrowi[iel];
      int irowb = hrowi[iel + 1];
      dv1 += SHIFT_REF(dwork1, irow) * dluval[iel];
      dv1b += SHIFT_REF(dwork1, irowb) * dluval[iel + 1];
    }
    i2 = i1;
    dwork1[i] = dv1 + dv1b;
  }
} /* c_ekkbtj4 */

static int c_ekkbtj4p_dense(const int nrow, const double *COIN_RESTRICT dluval,
  const int *COIN_RESTRICT hrowi,
  const int *COIN_RESTRICT mcstrt, double *COIN_RESTRICT dwork1,
  int ndenuc,
  int ndo, int jpiv)
{
  int i;
  int i2;

  int last = ndo - ndenuc + 1;
  double *COIN_RESTRICT densew = &dwork1[nrow - 1];
  int nincol = 0;
  const double *COIN_RESTRICT dlu1;
  dluval--;
  hrowi--;
  /* count down to first nonzero */
  for (i = nrow; i >= 1; i--) {
    if (dwork1[i]) {
      break;
    }
  }
  if (i < ndo + jpiv) {
    int diff = ndo + jpiv - i;
    ndo -= diff;
    densew -= diff;
    nincol = diff;
  }
  i2 = mcstrt[ndo + 1];
  dlu1 = &dluval[i2 + 1];
  for (i = ndo; i > last; i -= 2) {
    int k;
    double dv1, dv2;
    const double *COIN_RESTRICT dlu2;
    dv1 = densew[1];
    dlu2 = dlu1 + nincol;
    dv2 = densew[0];
    for (k = 0; k < nincol; k++) {
#ifdef DEBUG
      int kk = dlu1 - dluval;
      int jj = (densew + (nincol - k + 1)) - dwork1;
      int ll = hrowi[k + kk];
      if (ll != jj)
        abort();
#endif
      dv1 += densew[nincol - k + 1] * dlu1[k];
      dv2 += densew[nincol - k + 1] * dlu2[k];
    }
    densew[1] = dv1;
    dlu1 = dlu2 + nincol;
    dv2 += dv1 * dlu1[0];
    dlu1++;
    nincol += 2;
    densew[0] = dv2;
    densew -= 2;
  }
  return i;
} /* c_ekkbtj4 */

static void c_ekkbtj4p_after_dense(const double *COIN_RESTRICT dluval,
  const int *COIN_RESTRICT hrowi,
  const int *COIN_RESTRICT mcstrt,
  double *COIN_RESTRICT dwork1, int i, int jpiv)
{
  int iel;
  mcstrt -= jpiv;
  i += jpiv;
  iel = mcstrt[i + 1];
  for (; i > jpiv + 1; i -= 2) {
    int i1 = mcstrt[i];
    double dv1 = dwork1[i];
    double dv2;
    for (; iel < i1; iel++) {
      int irow = hrowi[iel];
      dv1 += SHIFT_REF(dwork1, irow) * dluval[iel];
    }
    i1 = mcstrt[i - 1];
    dv2 = dwork1[i - 1];
    dwork1[i] = dv1;
    for (; iel < i1; iel++) {
      int irow = hrowi[iel];
      dv2 += SHIFT_REF(dwork1, irow) * dluval[iel];
    }
    dwork1[i - 1] = dv2;
  }
  if (i > jpiv) {
    int i1 = mcstrt[i];
    double dv1 = dwork1[i];
    for (; iel < i1; iel++) {
      int irow = hrowi[iel];
      dv1 += SHIFT_REF(dwork1, irow) * dluval[iel];
    }
    dwork1[i] = dv1;
  }
}

static void c_ekkbtj4p(COIN_REGISTER const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1)
{
  int lstart = fact->lstart;
  const int *COIN_RESTRICT hpivco = fact->kcpadr;
  const double *COIN_RESTRICT dluval = fact->xeeadr + 1;
  const int *COIN_RESTRICT hrowi = fact->xeradr + 1;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr + lstart - 1;
  int jpiv = hpivco[lstart] - 1;
  int ndo = fact->xnetalval;
  /*     see if dense enough to unroll */
  if (fact->ndenuc < 5) {
    c_ekkbtj4p_no_dense(fact->nrow, dluval, hrowi, mcstrt, dwork1, ndo, jpiv);
  } else {
    int i = c_ekkbtj4p_dense(fact->nrow, dluval, hrowi, mcstrt, dwork1,
      fact->ndenuc, ndo, jpiv);
    c_ekkbtj4p_after_dense(dluval, hrowi, mcstrt, dwork1, i, jpiv);
  }
} /* c_ekkbtj4p */

static int c_ekkbtj4_sparse(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt, /* C style */
  double *COIN_RESTRICT dworko,
  int nincol, int *COIN_RESTRICT spare)
{
  const int nrow = fact->nrow;
  const int *COIN_RESTRICT hcoli = fact->xecadr;
  const int *COIN_RESTRICT mrstrt = fact->xrsadr + nrow;
  char *COIN_RESTRICT nonzero = fact->nonzero;
  const int *COIN_RESTRICT hpivro = fact->krpadr;
  const double *COIN_RESTRICT de2val = fact->xe2adr - 1;
  double tolerance = fact->zeroTolerance;
  double dv;
  int iel;

  int k, nStack, kx;
  int nList = 0;
  int *COIN_RESTRICT list = spare;
  int *COIN_RESTRICT stack = spare + nrow;
  int *COIN_RESTRICT next = stack + nrow;
  int iPivot, kPivot;
  int iput, nput = 0, kput = nrow;
  int j;
  int firstDoRow = fact->firstDoRow;

  for (k = 0; k < nincol; k++) {
    nStack = 1;
    iPivot = mpt[k];
    if (nonzero[iPivot] != 1 && iPivot >= firstDoRow) {
      stack[0] = iPivot;
      next[0] = mrstrt[iPivot];
      while (nStack) {
        /* take off stack */
        kPivot = stack[--nStack];
        if (nonzero[kPivot] != 1 && kPivot >= firstDoRow) {
          j = next[nStack];
          if (j == mrstrt[kPivot + 1]) {
            /* finished so mark */
            list[nList++] = kPivot;
            nonzero[kPivot] = 1;
          } else {
            kPivot = hcoli[j];
            /* put back on stack */
            next[nStack++]++;
            if (!nonzero[kPivot]) {
              /* and new one */
              stack[nStack] = kPivot;
              nonzero[kPivot] = 2;
              next[nStack++] = mrstrt[kPivot];
            }
          }
        } else if (kPivot < firstDoRow) {
          list[--kput] = kPivot;
          nonzero[kPivot] = 1;
        }
      }
    } else if (nonzero[iPivot] != 1) {
      /* nothing to do (except check size at end) */
      list[--kput] = iPivot;
      nonzero[iPivot] = 1;
    }
  }
  if (fact->packedMode) {
    dworko++;
    for (k = nList - 1; k >= 0; k--) {
      double dv;
      iPivot = list[k];
      dv = dwork1[iPivot];
      dwork1[iPivot] = 0.0;
      nonzero[iPivot] = 0;
      if (fabs(dv) > tolerance) {
        iput = hpivro[iPivot];
        kx = mrstrt[iPivot];
        dworko[nput] = dv;
        for (iel = kx; iel < mrstrt[iPivot + 1]; iel++) {
          double dval;
          int irow = hcoli[iel];
          dval = de2val[iel];
          dwork1[irow] += dv * dval;
        }
        mpt[nput++] = iput - 1;
      } else {
        dwork1[iPivot] = 0.0; /* force to zero, not just near zero */
      }
    }
    /* check remainder */
    for (k = kput; k < nrow; k++) {
      iPivot = list[k];
      nonzero[iPivot] = 0;
      dv = dwork1[iPivot];
      dwork1[iPivot] = 0.0;
      iput = hpivro[iPivot];
      if (fabs(dv) > tolerance) {
        dworko[nput] = dv;
        mpt[nput++] = iput - 1;
      }
    }
  } else {
    /* not packed */
    for (k = nList - 1; k >= 0; k--) {
      double dv;
      iPivot = list[k];
      dv = dwork1[iPivot];
      dwork1[iPivot] = 0.0;
      nonzero[iPivot] = 0;
      if (fabs(dv) > tolerance) {
        iput = hpivro[iPivot];
        kx = mrstrt[iPivot];
        dworko[iput] = dv;
        for (iel = kx; iel < mrstrt[iPivot + 1]; iel++) {
          double dval;
          int irow = hcoli[iel];
          dval = de2val[iel];
          dwork1[irow] += dv * dval;
        }
        mpt[nput++] = iput - 1;
      } else {
        dwork1[iPivot] = 0.0; /* force to zero, not just near zero */
      }
    }
    /* check remainder */
    for (k = kput; k < nrow; k++) {
      iPivot = list[k];
      nonzero[iPivot] = 0;
      dv = dwork1[iPivot];
      dwork1[iPivot] = 0.0;
      iput = hpivro[iPivot];
      if (fabs(dv) > tolerance) {
        dworko[iput] = dv;
        mpt[nput++] = iput - 1;
      }
    }
  }

  return (nput);
} /* c_ekkbtj4 */

static void c_ekkbtjl(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1)
{
  int i, j, k, k1;
  int l1;
  const double *COIN_RESTRICT dluval = fact->R_etas_element;
  const int *COIN_RESTRICT hrowi = fact->R_etas_index;
  const int *COIN_RESTRICT mcstrt = fact->R_etas_start;
  const int *COIN_RESTRICT hpivco = fact->hpivcoR;
  int ndo = fact->nR_etas;
#ifndef UNROLL1
#define UNROLL1 4
#endif
#if UNROLL1 > 2
  int l2;
#endif
  int kn;
  double dv;
  int iel;
  int ipiv;
  int knext;

  knext = mcstrt[ndo + 1];
#if UNROLL1 > 2
  for (i = ndo; i > 0; --i) {
    k1 = knext;
    knext = mcstrt[i];
    ipiv = hpivco[i];
    dv = dwork1[ipiv];
    /*       fast floating */
    k = knext - k1;
    kn = k >> 2;
    iel = k1 + 1;
    if (dv != 0.) {
      l1 = (k & 1) != 0;
      l2 = (k & 2) != 0;
      for (j = 1; j <= kn; j++) {
        int irow0 = hrowi[iel + 0];
        int irow1 = hrowi[iel + 1];
        int irow2 = hrowi[iel + 2];
        int irow3 = hrowi[iel + 3];
        double dval0 = dv * dluval[iel + 0] + SHIFT_REF(dwork1, irow0);
        double dval1 = dv * dluval[iel + 1] + SHIFT_REF(dwork1, irow1);
        double dval2 = dv * dluval[iel + 2] + SHIFT_REF(dwork1, irow2);
        double dval3 = dv * dluval[iel + 3] + SHIFT_REF(dwork1, irow3);
        SHIFT_REF(dwork1, irow0) = dval0;
        SHIFT_REF(dwork1, irow1) = dval1;
        SHIFT_REF(dwork1, irow2) = dval2;
        SHIFT_REF(dwork1, irow3) = dval3;
        iel += 4;
      }
      if (l1) {
        int irow0 = hrowi[iel];
        SHIFT_REF(dwork1, irow0) += dv * dluval[iel];
        ++iel;
      }
      if (l2) {
        int irow0 = hrowi[iel + 0];
        int irow1 = hrowi[iel + 1];
        SHIFT_REF(dwork1, irow0) += dv * dluval[iel];
        SHIFT_REF(dwork1, irow1) += dv * dluval[iel + 1];
      }
    }
  }
#else
  for (i = ndo; i > 0; --i) {
    k1 = knext;
    knext = mcstrt[i];
    ipiv = hpivco[i];
    dv = dwork1[ipiv];
    k = knext - k1;
    kn = k >> 1;
    iel = k1 + 1;
    if (dv != 0.) {
      l1 = (k & 1) != 0;
      for (j = 1; j <= kn; j++) {
        int irow0 = hrowi[iel + 0];
        int irow1 = hrowi[iel + 1];
        double dval0 = dv * dluval[iel + 0] + SHIFT_REF(dwork1, irow0);
        double dval1 = dv * dluval[iel + 1] + SHIFT_REF(dwork1, irow1);
        SHIFT_REF(dwork1, irow0) = dval0;
        SHIFT_REF(dwork1, irow1) = dval1;
        iel += 2;
      }
      if (l1) {
        int irow0 = hrowi[iel];
        SHIFT_REF(dwork1, irow0) += dv * dluval[iel];
        ++iel;
      }
    }
  }
#endif
} /* c_ekkbtjl */

static int c_ekkbtjl_sparse(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt, int nincol)
{
  const double *COIN_RESTRICT dluval = fact->R_etas_element;
  const int *COIN_RESTRICT hrowi = fact->R_etas_index;
  const int *COIN_RESTRICT mcstrt = fact->R_etas_start;
  const int *COIN_RESTRICT hpivco = fact->hpivcoR;
  char *COIN_RESTRICT nonzero = fact->nonzero;
  int ndo = fact->nR_etas;
  int i, j, k1;
  double dv;
  int ipiv;
  int irow0, irow1;
  int knext;
  int number = nincol;

  /*     ------------------------------------------- */
  /* adjust back */
  hrowi++;
  dluval++;

  /*         DO ANY ROW TRANSFORMATIONS */

  /* Function Body */
  knext = mcstrt[ndo + 1];
  for (i = ndo; i > 0; --i) {
    k1 = knext;
    knext = mcstrt[i];
    ipiv = hpivco[i];
    dv = dwork1[ipiv];
    if (dv) {
      for (j = k1; j < knext - 1; j += 2) {
        irow0 = hrowi[j];
        irow1 = hrowi[j + 1];
        SHIFT_REF(dwork1, irow0) += dv * dluval[j];
        SHIFT_REF(dwork1, irow1) += dv * dluval[j + 1];
        if (!nonzero[irow0]) {
          nonzero[irow0] = 1;
          mpt[++number] = UNSHIFT_INDEX(irow0);
        }
        if (!nonzero[irow1]) {
          nonzero[irow1] = 1;
          mpt[++number] = UNSHIFT_INDEX(irow1);
        }
      }
      if (j < knext) {
        irow0 = hrowi[j];
        SHIFT_REF(dwork1, irow0) += dv * dluval[j];
        if (!nonzero[irow0]) {
          nonzero[irow0] = 1;
          mpt[++number] = UNSHIFT_INDEX(irow0);
        }
      }
    }
  }
  return (number);
} /* c_ekkbtjl */

static void c_ekkbtju_dense(const int nrow,
  const double *COIN_RESTRICT dluval,
  const int *COIN_RESTRICT hrowi,
  const int *COIN_RESTRICT mcstrt,
  int *COIN_RESTRICT hpivco,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT start, int last, int offset,
  double *COIN_RESTRICT densew)
{
  /* Local variables */
  int ipiv1, ipiv2;
  int save = hpivco[last];

  hpivco[last] = nrow + 1;

  ipiv1 = *start;
  ipiv2 = hpivco[ipiv1];
  while (ipiv2 < last) {
    int iel, k;
    const int kx1 = mcstrt[ipiv1];
    const int kx2 = mcstrt[ipiv2];
    const int nel1 = hrowi[kx1 - 1];
    const int nel2 = hrowi[kx2 - 1];
    const double dpiv1 = dluval[kx1 - 1];
    const double dpiv2 = dluval[kx2 - 1];
    const int n1 = offset + ipiv1; /* number in dense part */
    const int nsparse1 = nel1 - n1;
    const int nsparse2 = nel2 - n1 - (ipiv2 - ipiv1);
    const int k1 = kx1 + nsparse1;
    const int k2 = kx2 + nsparse2;
    const double *dlu1 = &dluval[k1];
    const double *dlu2 = &dluval[k2];

    double dv1 = dwork1[ipiv1];
    double dv2 = dwork1[ipiv2];

    for (iel = kx1; iel < k1; ++iel) {
      dv1 -= SHIFT_REF(dwork1, hrowi[iel]) * dluval[iel];
    }
    for (iel = kx2; iel < k2; ++iel) {
      dv2 -= SHIFT_REF(dwork1, hrowi[iel]) * dluval[iel];
    }
    for (k = 0; k < n1; k++) {
      dv1 -= dlu1[k] * densew[k];
      dv2 -= dlu2[k] * densew[k];
    }
    dv1 *= dpiv1;
    dv2 -= dlu2[n1] * dv1;
    dwork1[ipiv1] = dv1;
    dwork1[ipiv2] = dv2 * dpiv2;
    ipiv1 = hpivco[ipiv2];
    ipiv2 = hpivco[ipiv1];
  }
  hpivco[last] = save;

  *start = ipiv1;
  return;
}
/* about 8-10% of execution time is spent in this routine */
static int c_ekkbtju_aux(const double *COIN_RESTRICT dluval,
  const int *COIN_RESTRICT hrowi,
  const int *COIN_RESTRICT mcstrt,
  const int *COIN_RESTRICT hpivco,
  double *COIN_RESTRICT dwork1,
  int ipiv, int loop_end)
{
#define UNROLL2 2
#ifndef UNROLL2
#if CLP_OSL == 2 || CLP_OSL == 3
#define UNROLL2 2
#else
#define UNROLL2 1
#endif
#endif
  while (ipiv <= loop_end) {
    int kx = mcstrt[ipiv];
    const int nel = hrowi[kx - 1];
#if UNROLL2 < 2
    const int kxe = kx + nel;
#endif

    double dv = dwork1[ipiv]; /* rhs */
#if UNROLL2 > 1
    const int *hrowi2 = hrowi + kx;
    const int *hrowi2end = hrowi2 + nel;
    const double *dluval2 = dluval + kx;
#else
    int iel;
#endif
    const double dpiv = dluval[kx - 1]; /* inverse of pivot */

    /* subtract terms whose unknowns have been solved for */

    /* a significant proportion of these loops may not modify dv at all.
     * However, it seems to be just as expensive to check if the loop
     * would modify dv as it is to just do it.
     * The only difference would be that dluval wouldn't be referenced
     * for those loops, would might save some cache paging,
     * but unfortunately the code generated to search for zeros (on AIX)
     * is *worse* than code that just multiplies by dval.
     */
#if UNROLL2 < 2
    for (iel = kx; iel < kxe; ++iel) {
      const int irow = hrowi[iel];
      const double dval = dluval[iel];
      dv -= SHIFT_REF(dwork1, irow) * dval;
    }

    dwork1[ipiv] = dv * dpiv; /* divide by the pivot */
#else
    if ((nel & 1) != 0) {
      int irow = *hrowi2;
      double dval = *dluval2;
      dv -= SHIFT_REF(dwork1, irow) * dval;
      hrowi2++;
      dluval2++;
    }
    for (; hrowi2 < hrowi2end; hrowi2 += 2, dluval2 += 2) {
      int irow0 = hrowi2[0];
      int irow1 = hrowi2[1];
      double dval0 = dluval2[0];
      double dval1 = dluval2[1];
      double d0 = SHIFT_REF(dwork1, irow0);
      double d1 = SHIFT_REF(dwork1, irow1);
      dv -= d0 * dval0;
      dv -= d1 * dval1;
    }
    dwork1[ipiv] = dv * dpiv; /* divide by the pivot */
#endif

    ipiv = hpivco[ipiv];
  }

  return (ipiv);
}

/*
 * We are given the upper diagonal matrix U from the LU factorization
 * and a rhs dwork1.
 * This solves the system U x = dwork1
 * by back substitution, overwriting dwork1 with the solution x.
 *
 * It does this in textbook style by solving the equations "bottom" up,
 * so for each equation one new unknown is solved for by subtracting
 * from the rhs the sum of the terms whose unknowns have been solved for,
 * then dividing by the coefficient of the new unknown.
 *
 * Since we update the U matrix using F-T, the order of the columns
 * changes slightly each iteration.  Initially, hpivco[i] == i+1,
 * and each iteration (generally) introduces one element where this
 * is no longer true.  However, because we periodically refactorize,
 * it is much more common for hpivco[i] == i+1 than not.
 *
 * The one quirk is that value referred to as the pivot is actually
 * the reciprocal of the pivot, to avoid a division.
 *
 * Solving in this fashion is inappropriate if there are frequently
 * cases where all unknowns in an equation have value zero.
 * This seems to happen frequently if the sparsity of the rhs is, say, 10%.
 */
static void c_ekkbtju(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int ipiv)
{
  const int nrow = fact->nrow;
  double *COIN_RESTRICT dluval = fact->xeeadr;
  int *COIN_RESTRICT hrowi = fact->xeradr;
  int *COIN_RESTRICT mcstrt = fact->xcsadr;
  int *COIN_RESTRICT hpivco_new = fact->kcpadr + 1;
  int ndenuc = fact->ndenuc;
  int first_dense = fact->first_dense;
  int last_dense = fact->last_dense;

  const int has_dense = (first_dense < last_dense && mcstrt[ipiv] <= mcstrt[last_dense]);

  /* Parameter adjustments */
  /* dluval and hrowi were NOT decremented here.
     I believe that they are used as C-style arrays below.
     At this point, I am going to convert them from Fortran- to C-style
     here by incrementing them; at some later time, I will convert their
     uses in this file to Fortran-style.
  */
  dluval++;
  hrowi++;

  if (has_dense)
    ipiv = c_ekkbtju_aux(dluval, hrowi, mcstrt, hpivco_new, dwork1, ipiv,
      first_dense - 1);

  if (has_dense) {
    int n = 0;
    int firstDense = nrow - ndenuc + 1;
    double *densew = &dwork1[firstDense];

    /* check first dense to see where in triangle it is */
    int last = first_dense;
    int j = mcstrt[last] - 1;
    int k1 = j;
    int k2 = j + hrowi[j];

    for (j = k2; j > k1; j--) {
      int irow = UNSHIFT_INDEX(hrowi[j]);
      if (irow < firstDense) {
        break;
      } else {
#ifdef DEBUG
        if (irow != last - 1) {
          abort();
        }
#endif
        last = irow;
        n++;
      }
    }
    c_ekkbtju_dense(nrow, dluval, hrowi, mcstrt, const_cast< int * >(hpivco_new),
      dwork1, &ipiv, last_dense, n - first_dense, densew);
  }

  (void)c_ekkbtju_aux(dluval, hrowi, mcstrt, hpivco_new, dwork1, ipiv, nrow);
} /* c_ekkbtju */

/*
 * mpt / *nincolp contain the indices of nonzeros in dwork1.
 * nonzero contains the same information as a byte-mask.
 *
 * currently, erase_nonzero is true iff this is called from c_ekketsj.
 */
static int c_ekkbtju_sparse(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt, int nincol,
  int *COIN_RESTRICT spare)
{
  const double *COIN_RESTRICT dluval = fact->xeeadr + 1;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr;
  char *COIN_RESTRICT nonzero = fact->nonzero;
  const int *COIN_RESTRICT hcoli = fact->xecadr;
  const int *COIN_RESTRICT mrstrt = fact->xrsadr;
  const int *COIN_RESTRICT hinrow = fact->xrnadr;
  const double *COIN_RESTRICT de2val = fact->xe2adr - 1;
  int i;
  int iPivot;
  int nList = 0;
  int nStack, k, kx;
  const int nrow = fact->nrow;
  const double tolerance = fact->zeroTolerance;
  int *COIN_RESTRICT list = spare;
  int *COIN_RESTRICT stack = spare + nrow;
  int *COIN_RESTRICT next = stack + nrow;
  /*
   * Examine all nonzero elements and determine which elements may be
   * nonzero in the result.
   * Any row in U that contains terms that may have nonzero variable values
   * may produce a nonzero value.
   */
  for (k = 0; k < nincol; k++) {
    nStack = 1;
    iPivot = mpt[k];
    stack[0] = iPivot;
    next[0] = 0;
    while (nStack) {
      int kPivot, ninrow, j;
      /* take off stack */
      kPivot = stack[--nStack];
      /*printf("nStack %d kPivot %d, ninrow %d, j %d, nList %d\n",
	nStack,kPivot,hinrow[kPivot],
	next[nStack],nList);*/
      if (nonzero[kPivot] != 1) {
        ninrow = hinrow[kPivot];
        j = next[nStack];
        if (j != ninrow) {
          kx = mrstrt[kPivot];
          kPivot = hcoli[kx + j];
          /* put back on stack */
          next[nStack++]++;
          if (!nonzero[kPivot]) {
            /* and new one */
            stack[nStack] = kPivot;
            nonzero[kPivot] = 2;
            next[nStack++] = 0;
          }
        } else {
          /* finished so mark */
          list[nList++] = kPivot;
          nonzero[kPivot] = 1;
        }
      }
    }
  }

  i = nList - 1;
  nList = 0;
  for (; i >= 0; i--) {
    double dpiv;
    double dv;
    iPivot = list[i];
    kx = mcstrt[iPivot];
    dpiv = dluval[kx - 1];
    dv = dpiv * dwork1[iPivot];
    nonzero[iPivot] = 0;
    if (fabs(dv) >= tolerance) {
      int iel;
      int krx = mrstrt[iPivot];
      int krxe = krx + hinrow[iPivot];
      dwork1[iPivot] = dv;
      mpt[nList++] = iPivot;
      for (iel = krx; iel < krxe; iel++) {
        int irow0 = hcoli[iel];
        double dval = de2val[iel];
        dwork1[irow0] -= dv * dval;
      }
    } else {
      dwork1[iPivot] = 0.0;
    }
  }

  return (nList);
} /* c_ekkbtjuRow */

/*
 * dpermu is supposed to be zeroed on entry to this routine.
 * It is used as a working buffer.
 * The input vector dwork1 is permuted into dpermu, operated on,
 * and the answer is permuted back into dwork1, zeroing dpermu in
 * the process.
 */
/*
 * nincol > 0 ==> mpt contains indices of non-zeros in dpermu
 *
 * first_nonzero contains index of first (last??)nonzero;
 * only used if nincol==0.
 *
 * dpermu contains permuted input; dwork1 is now zero
 */
int c_ekkbtrn(COIN_REGISTER3 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt, int first_nonzero)
{
  double *COIN_RESTRICT dpermu = fact->kadrpm;
  const int *COIN_RESTRICT mpermu = fact->mpermu;
  const int *COIN_RESTRICT hpivco_new = fact->kcpadr + 1;

  const int nrow = fact->nrow;
  int i;
  int nincol;
  /* find the first non-zero input */
  int ipiv;
  if (first_nonzero) {
    ipiv = first_nonzero;
#if 1
    if (c_ekk_IsSet(fact->bitArray, ipiv)) {
      /* slack */
      int lastSlack = fact->lastSlack;
      int firstDo = hpivco_new[lastSlack];
      assert(dpermu[ipiv]);
      while (ipiv != firstDo) {
        assert(c_ekk_IsSet(fact->bitArray, ipiv));
        if (dpermu[ipiv])
          dpermu[ipiv] = -dpermu[ipiv];
        ipiv = hpivco_new[ipiv];
      }
    }
#endif
  } else {
    int lastSlack = fact->numberSlacks;
    ipiv = hpivco_new[0];
    for (i = 0; i < lastSlack; i++) {
      int next_piv = hpivco_new[ipiv];
      assert(c_ekk_IsSet(fact->bitArray, ipiv));
      if (dpermu[ipiv]) {
        break;
      } else {
        ipiv = next_piv;
      }
    }

    /* usually, there is a non-zero slack entry... */
    if (i == lastSlack) {
      /* but if there isn't... */
      for (; i < nrow; i++) {
        if (!dpermu[ipiv]) {
          ipiv = hpivco_new[ipiv];
        } else {
          break;
        }
      }
    } else {
      /* reverse signs for slacks */
      for (; i < lastSlack; i++) {
        assert(c_ekk_IsSet(fact->bitArray, ipiv));
        if (dpermu[ipiv])
          dpermu[ipiv] = -dpermu[ipiv];
        ipiv = hpivco_new[ipiv];
      }
      assert(!c_ekk_IsSet(fact->bitArray, ipiv) || ipiv > fact->nrow);

      /* this is presumably the first non-zero non slack */
      /*ipiv=firstDo;*/
    }
  }
  if (ipiv <= fact->nrow) {
    /* skipBtju is always (?) 0 first the first call,
     * ipiv tends to be >nrow for the second */

    /*       DO U */
    c_ekkbtju(fact, dpermu,
      ipiv);
  }

  /*       DO ROW ETAS IN L */
  c_ekkbtjl(fact, dpermu);
  c_ekkbtj4p(fact, dpermu);

  /* dwork1[mpermu] = dpermu; dpermu = 0; mpt = indices of non-zeros */
  nincol = c_ekkshfpo_scan2zero(fact, &mpermu[1], dpermu, &dwork1[1], &mpt[1]);

  /* dpermu should be zero now */
#ifdef DEBUG
  for (i = 1; i <= nrow; i++) {
    if (dpermu[i]) {
      abort();
    } /* endif */
  } /* endfor */
#endif
  return (nincol);
} /* c_ekkbtrn */

static int c_ekkbtrn0_new(COIN_REGISTER3 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt, int nincol,
  int *COIN_RESTRICT spare)
{
  double *COIN_RESTRICT dpermu = fact->kadrpm;
  const int *COIN_RESTRICT mpermu = fact->mpermu;
  const int *COIN_RESTRICT hpivro = fact->krpadr;

  const int nrow = fact->nrow;

  int i;
  char *nonzero = fact->nonzero;
  int doSparse = 1;

  /* so:  dpermu must contain room for:
   * nrow doubles, followed by
   * nrow ints (mpermu), followed by
   * nrow ints (the inverse permutation), followed by
   * an unused area (?) of nrow ints, followed by
   * nrow chars (this non-zero array).
   *
   * and apparently the first nrow elements of nonzero are expected
   * to already be zero.
   */
#ifdef DEBUG
  for (i = 1; i <= nrow; i++) {
    if (nonzero[i]) {
      abort();
    } /* endif */
  } /* endfor */
#endif
  /* now nonzero[i]==1 iff there is an entry for i in mpt */

  nincol = c_ekkbtju_sparse(fact, dpermu,
    &mpt[1], nincol,
    spare);

  /* the vector may have more nonzero elements now */
  /*       DO ROW ETAS IN L */
#define DENSE_THRESHOLD (nincol * 10 + 100)
  if (DENSE_THRESHOLD > nrow) {
    doSparse = 0;
    c_ekkbtjl(fact, dpermu);
  } else {
    /* set nonzero */
    for (i = 0; i < nincol; i++) {
      int j = mpt[i + 1];
      nonzero[j] = 1;
    }
    nincol = c_ekkbtjl_sparse(fact,
      dpermu,
      mpt,
      nincol);
    for (i = 0; i < nincol; i++) {
      int j = mpt[i + 1];
      nonzero[j] = 0;
    }
    if (DENSE_THRESHOLD > nrow) {
      doSparse = 0;
#ifdef DEBUG
      for (i = 1; i <= nrow; i++) {
        if (nonzero[i]) {
          abort();
        }
      }
#endif
    }
  }
  if (!doSparse) {
    c_ekkbtj4p(fact, dpermu);
    /* dwork1[mpermu] = dpermu; dpermu = 0; mpt = indices of non-zeros */
    nincol = c_ekkshfpo_scan2zero(fact, &mpermu[1], dpermu, &dwork1[1], &mpt[1]);

    /* dpermu should be zero now */
#ifdef DEBUG
    for (i = 1; i <= nrow; i++) {
      if (dpermu[i]) {
        abort();
      } /* endif */
    } /* endfor */
#endif
  } else {
    /* still sparse */
    if (fact->nnentl) {
      nincol = c_ekkbtj4_sparse(fact,
        dpermu,
        &mpt[1],
        dwork1,
        nincol, spare);
    } else {
      double tolerance = fact->zeroTolerance;
      int irow;
      int nput = 0;
      if (fact->packedMode) {
        for (i = 0; i < nincol; i++) {
          int irow0;
          double dval;
          irow = mpt[i + 1];
          dval = dpermu[irow];
          if (NOT_ZERO(dval)) {
            if (fabs(dval) >= tolerance) {
              irow0 = hpivro[irow];
              dwork1[1 + nput] = dval;
              mpt[1 + nput++] = irow0 - 1;
            }
            dpermu[irow] = 0.0;
          }
        }
      } else {
        for (i = 0; i < nincol; i++) {
          int irow0;
          double dval;
          irow = mpt[i + 1];
          dval = dpermu[irow];
          if (NOT_ZERO(dval)) {
            if (fabs(dval) >= tolerance) {
              irow0 = hpivro[irow];
              dwork1[irow0] = dval;
              mpt[1 + nput++] = irow0 - 1;
            }
            dpermu[irow] = 0.0;
          }
        }
      }
      nincol = nput;
    }
  }

  return (nincol);
} /* c_ekkbtrn */

/* returns c_ekkbtrn(fact, dwork1, mpt)
 *
 * but since mpt[1..nincol] contains the indices of non-zeros in dwork1,
 * we can do faster.
 */
static int c_ekkbtrn_mpt(COIN_REGISTER3 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt, int nincol, int *COIN_RESTRICT spare)
{
  double *COIN_RESTRICT dpermu = fact->kadrpm;
  const int nrow = fact->nrow;

  const int *COIN_RESTRICT mpermu = fact->mpermu;
  /*const int *mrstrt	= fact->xrsadr;*/

#ifdef DEBUG
  int i;
  memset(spare, 'A', 3 * nrow * sizeof(int));
  {

    for (i = 1; i <= nrow; i++) {
      if (dpermu[i]) {
        abort();
      }
    }
  }
#endif

  int i;
#ifdef DEBUG
  for (i = 1; i <= nrow; i++) {
    if (fact->nonzero[i] || dpermu[i]) {
      abort();
    }
  }
#endif
  assert(fact->if_sparse_update > 0 && mpt && fact->rows_ok);

  /* read the input vector from mpt/dwork1;
   * permute it into dpermu;
   * construct a nonzero mask in nonzero;
   * overwrite mpt with the permuted indices;
   * clear the dwork1 vector.
   */
  for (i = 0; i < nincol; i++) {
    int irow = mpt[i + 1];
    int jrow = mpermu[irow];
    dpermu[jrow] = dwork1[irow];
    /*nonzero[jrow-1]=1; this is done in btrn0 */
    mpt[i + 1] = jrow;
    dwork1[irow] = 0.0;
  }

  if (DENSE_THRESHOLD < nrow) {
    nincol = c_ekkbtrn0_new(fact, dwork1, mpt, nincol, spare);
  } else {
    nincol = c_ekkbtrn(fact, dwork1, mpt, 0);
  }
#ifdef DEBUG
  {

    for (i = 1; i <= nrow; i++) {
      if (dpermu[i]) {
        abort();
      }
    }
    if (fact->if_sparse_update > 0) {
      for (i = 1; i <= nrow; i++) {
        if (fact->nonzero[i]) {
          abort();
        }
      }
    }
  }
#endif
  return nincol;
}

/* returns c_ekkbtrn(fact, dwork1, mpt)
 *
 * but since (dwork1[i]!=0) == (i==ipivrw),
 * we can do faster.
 */
int c_ekkbtrn_ipivrw(COIN_REGISTER3 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt, int ipivrw, int *COIN_RESTRICT spare)
{
  double *COIN_RESTRICT dpermu = fact->kadrpm;
  const int nrow = fact->nrow;

  const int *COIN_RESTRICT mpermu = fact->mpermu;
  const double *COIN_RESTRICT dluval = fact->xeeadr;
  const int *COIN_RESTRICT mrstrt = fact->xrsadr;
  const int *COIN_RESTRICT hinrow = fact->xrnadr;
  const int *COIN_RESTRICT hcoli = fact->xecadr;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr;

  int nincol;

#ifdef DEBUG
  int i;
  for (i = 1; i <= nrow; i++) {
    if (dpermu[i]) {
      abort();
    } /* endif */
  } /* endfor */
#endif

  if (fact->if_sparse_update > 0 && mpt && fact->rows_ok) {
    mpt[1] = ipivrw;
    nincol = c_ekkbtrn_mpt(fact, dwork1, mpt, 1, spare);
  } else {
    int ipiv;
    int kpivrw = mpermu[ipivrw];
    dpermu[kpivrw] = dwork1[ipivrw];
    dwork1[ipivrw] = 0.0;

    if (fact->rows_ok) {
      /* !fact->if_sparse_update
       * but we still have rowwise info,
       * so we may as well use it to do the slack row
       */
      int iipivrw = nrow + 1;
      int itest = fact->nnentu + 1;
      int k = mrstrt[kpivrw];
      int lastInRow = k + hinrow[kpivrw];
      double dpiv, dv;
      for (; k < lastInRow; k++) {
        int icol = hcoli[k];
        int start = mcstrt[icol];
        if (start < itest) {
          iipivrw = icol;
          itest = start;
        }
      }
      /* do missed pivot */
      itest = mcstrt[kpivrw];
      dpiv = dluval[itest];
      dv = dpermu[kpivrw];
      dv *= dpiv;
      dpermu[kpivrw] = dv;
      ipiv = iipivrw;
    } else {
      /* no luck - c_ekkbtju will slog through slacks (?) */
      ipiv = kpivrw;
    }
    /* nincol not read */
    /* not sparse */
    /* do slacks */
    if (ipiv <= fact->nrow) {
      if (c_ekk_IsSet(fact->bitArray, ipiv)) {
        const int *hpivco_new = fact->kcpadr + 1;
        int lastSlack = fact->lastSlack;
        int firstDo = hpivco_new[lastSlack];
        /* slack */
        /* need pivot row of first nonslack */
        dpermu[ipiv] = -dpermu[ipiv];
#ifndef NDEBUG
        while (1) {
          assert(c_ekk_IsSet(fact->bitArray, ipiv));
          ipiv = hpivco_new[ipiv];
          if (ipiv > fact->nrow || ipiv == firstDo)
            break;
        }
        assert(!c_ekk_IsSet(fact->bitArray, ipiv) || ipiv > fact->nrow);
        assert(ipiv == firstDo);
#endif
        ipiv = firstDo;
      }
    }
    nincol = c_ekkbtrn(fact, dwork1, mpt, ipiv);
  }

  return nincol;
}
/*
 * Does work associated with eq. 3.7:
 *	r' = u' U^-1
 *
 * where u' (can't write the overbar) is the p'th row of U, without
 * the entry for column p.  (here, jpivrw is p).
 * We solve this as for btju.  We know
 *	r' U = u'
 *
 * so we solve from low index to hi, determining the next value u_i'
 * by doing the dot-product of r' and the i'th column of U (excluding
 * element i itself), subtracting that from u'_i, and dividing by
 * U_ii (we store the reciprocal, so here we multiply).
 *
 * Now, in principle dwork1 should be initialized to the p'th row of U.
 * Instead, it is initially zeroed and filled in as we go along.
 * Of the entries in u' that we reference during a dot product with
 * a column of U, either
 *	the entry is 0 by definition, since it is < p, or
 *	it has already been set by a previous iteration, or
 *	it is p.
 *
 * Because of this, we know that all elements < p will be zero;
 * that's why we start with p (kpivrw).
 
 * While we do this product, we also zero out the p'th row.
 */
static void c_ekketju_aux(COIN_REGISTER2 EKKfactinfo *COIN_RESTRICT2 fact, int sparse,
  double *COIN_RESTRICT dluval, int *COIN_RESTRICT hrowi,
  const int *COIN_RESTRICT mcstrt, const int *COIN_RESTRICT hpivco,
  double *COIN_RESTRICT dwork1,
  int *ipivp, int jpivrw, int stop_col)
{
  int ipiv = *ipivp;
  if (1 && ipiv < stop_col && c_ekk_IsSet(fact->bitArray, ipiv)) {
    /* slack */
    int lastSlack = fact->lastSlack;
    int firstDo = hpivco[lastSlack];
    while (1) {
      assert(c_ekk_IsSet(fact->bitArray, ipiv));
      dwork1[ipiv] = -dwork1[ipiv];
      ipiv = hpivco[ipiv]; /* next column - generally ipiv+1 */
      if (ipiv == firstDo || ipiv >= stop_col)
        break;
    }
  }

  while (ipiv < stop_col) {
    double dv = dwork1[ipiv];
    int kx = mcstrt[ipiv];
    int nel = hrowi[kx];
    double dpiv = dluval[kx];
    int kcs = kx + 1;
    int kce = kx + nel;
    int iel;

    for (iel = kcs; iel <= kce; ++iel) {
      int irow = hrowi[iel];
      irow = UNSHIFT_INDEX(irow);
      dv -= dwork1[irow] * dluval[iel];
      if (irow == jpivrw) {
        break;
      }
    }

    /* assuming the p'th row is sparse,
     * this branch will be infrequently taken */
    if (iel <= kce) {
      int irow = hrowi[iel];
      /* irow == jpivrw */
      dv += dluval[iel];

      if (sparse) {
        /* delete this entry by overwriting it with the last */
        --nel;
        hrowi[kx] = nel;
        hrowi[iel] = hrowi[kce];
#ifdef CLP_REUSE_ETAS
        double temp = dluval[iel];
        dluval[iel] = dluval[kce];
        hrowi[kce] = jpivrw;
        dluval[kce] = temp;
#else
        dluval[iel] = dluval[kce];
#endif
        kce--;
      } else {
        /* we can't delete an entry from a dense column,
	 * so we just zero it out */
        dluval[iel] = 0.0;
        iel++;
      }

      /* finish up the remaining entries; same as above loop, but no check */
      for (; iel <= kce; ++iel) {
        irow = UNSHIFT_INDEX(hrowi[iel]);
        dv -= dwork1[irow] * dluval[iel];
      }
    }
    dwork1[ipiv] = dv * dpiv; /* divide by pivot */
    ipiv = hpivco[ipiv]; /* next column - generally ipiv+1 */
  }

  /* ? is it guaranteed that ipiv==stop_col at this point?? */
  *ipivp = ipiv;
}

/* dwork1 is assumed to be zeroed on entry */
static void c_ekketju(COIN_REGISTER EKKfactinfo *COIN_RESTRICT2 fact, double *dluval, int *hrowi,
  const int *COIN_RESTRICT mcstrt, const int *COIN_RESTRICT hpivco,
  double *COIN_RESTRICT dwork1,
  int kpivrw, int first_dense, int last_dense)
{
  int ipiv = hpivco[kpivrw];
  int jpivrw = SHIFT_INDEX(kpivrw);

  const int nrow = fact->nrow;

  if (first_dense < last_dense && mcstrt[ipiv] <= mcstrt[last_dense]) {
    /* There are dense columns, and
     * some dense columns precede the pivot column */

    /* first do any sparse columns "on the left" */
    c_ekketju_aux(fact, true, dluval, hrowi, mcstrt, hpivco, dwork1,
      &ipiv, jpivrw, first_dense);

    /* then do dense columns */
    c_ekketju_aux(fact, false, dluval, hrowi, mcstrt, hpivco, dwork1,
      &ipiv, jpivrw, last_dense + 1);

    /* final sparse columns "on the right" ...*/
  }
  /* ...are the same as sparse columns if there are no dense */
  c_ekketju_aux(fact, true, dluval, hrowi, mcstrt, hpivco, dwork1,
    &ipiv, jpivrw, nrow + 1);
} /* c_ekketju */

/*#define PRINT_DEBUG*/
/* dwork1 is assumed to be zeroed on entry */
int c_ekketsj(COIN_REGISTER2 /*const*/ EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt2, double dalpha, int orig_nincol,
  int npivot, int *nuspikp,
  const int ipivrw, int *spare)
{
  int nuspik = *nuspikp;

  int *COIN_RESTRICT mpermu = fact->mpermu;

  int *COIN_RESTRICT hcoli = fact->xecadr;
  double *COIN_RESTRICT dluval = fact->xeeadr;
  int *COIN_RESTRICT mrstrt = fact->xrsadr;
  int *COIN_RESTRICT hrowi = fact->xeradr;
  int *COIN_RESTRICT mcstrt = fact->xcsadr;
  int *COIN_RESTRICT hinrow = fact->xrnadr;
  /*int *hincol	= fact->xcnadr;
    int *hpivro	= fact->krpadr;*/
  int *COIN_RESTRICT hpivco = fact->kcpadr;
  double *COIN_RESTRICT de2val = fact->xe2adr;

  const int nrow = fact->nrow;
  const int ifRowCopy = fact->rows_ok;

  int i, j = -1, k, i1, i2, k1;
  int kc, iel;
  double del3;
  int nroom;
  bool ifrows = (mrstrt[1] != 0);
  int kpivrw, jpivrw;
  int first_dense_mcstrt, last_dense_mcstrt;
  int nnentl; /* includes row stuff */
  int doSparse = (fact->if_sparse_update > 0);
#ifdef MORE_DEBUG
  {
    const int *COIN_RESTRICT hrowi = fact->R_etas_index;
    const int *COIN_RESTRICT mcstrt = fact->R_etas_start;
    int ndo = fact->nR_etas;
    int knext;

    knext = mcstrt[ndo + 1];
    for (int i = ndo; i > 0; --i) {
      int k1 = knext;
      knext = mcstrt[i];
      for (int j = k1 + 1; j < knext; j++) {
        assert(hrowi[j] > 0 && hrowi[j] < 100000);
      }
    }
  }
#endif

  int mcstrt_piv;
  int nincol = 0;
  int *COIN_RESTRICT hpivco_new = fact->kcpadr + 1;
  int *COIN_RESTRICT back = fact->back;
  int irtcod = 0;

  /* Parameter adjustments */
  de2val--;

  /* Function Body */
  if (!ifRowCopy) {
    doSparse = 0;
    fact->if_sparse_update = -abs(fact->if_sparse_update);
  }
  if (npivot == 1) {
    fact->num_resets = 0;
  }
  kpivrw = mpermu[ipivrw];
#if 0 //ndef NDEBUG
  ets_count++;
  if (ets_check>=0&&ets_count>=ets_check) {
    printf("trouble\n");
  }
#endif
  mcstrt_piv = mcstrt[kpivrw];
  /* ndenuc - top has number deleted */
  if (fact->ndenuc) {
    first_dense_mcstrt = mcstrt[fact->first_dense];
    last_dense_mcstrt = mcstrt[fact->last_dense];
  } else {
    first_dense_mcstrt = 0;
    last_dense_mcstrt = 0;
  }
  {
    int kdnspt = fact->nnetas - fact->nnentl;

    i1 = ((kdnspt - 1) + fact->R_etas_start[fact->nR_etas + 1]);
    /*i1 = -99999999;*/

    /* fact->R_etas_start[fact->nR_etas + 1] is -(the number of els in R) */
    nnentl = fact->nnetas - ((kdnspt - 1) + fact->R_etas_start[fact->nR_etas + 1]);
  }
  fact->demark = fact->nnentu + nnentl;
  jpivrw = SHIFT_INDEX(kpivrw);

#ifdef CLP_REUSE_ETAS
  double del3Orig = 0.0;
#endif
  if (nuspik < 0) {
    goto L7000;
  } else if (nuspik == 0) {
    del3 = 0.;
  } else {
    del3 = 0.;
    i1 = fact->nnentu + 1;
    i2 = fact->nnentu + nuspik;
    if (fact->sortedEta) {
      /* binary search */
      if (hrowi[i2] == jpivrw) {
        /* sitting right on the end - easy */
        del3 = dluval[i2];
        --nuspik;
      } else {
        bool foundit = true;

        /* binary search - sort of implies hrowi is sorted */
        i = i1;
        if (hrowi[i] != jpivrw) {
          while (1) {
            i = (i1 + i2) >> 1;
            if (i == i1) {
              foundit = false;
              break;
            }
            if (hrowi[i] < jpivrw) {
              i1 = i;
            } else if (hrowi[i] > jpivrw) {
              i2 = i;
            } else
              break;
          }
        }
        /* ??? what if we didn't find it? */

        if (foundit) {
          del3 = dluval[i];
          --nuspik;
          /* remove it and move the last element into its place */
          hrowi[i] = hrowi[nuspik + fact->nnentu + 1];
          dluval[i] = dluval[nuspik + fact->nnentu + 1];
        }
      }
    } else {
      /* search */
      for (i = i1; i <= i2; i++) {
        if (hrowi[i] == jpivrw) {
          del3 = dluval[i];
          --nuspik;
          /* remove it and move the last element into its place */
          hrowi[i] = hrowi[i2];
          dluval[i] = dluval[i2];
          break;
        }
      }
    }
  }
#ifdef CLP_REUSE_ETAS
  del3Orig = del3;
#endif

  /*      OLD COLUMN POINTERS */
  /* **************************************************************** */
  if (!ifRowCopy) {
    /*       old method */
    /*       DO U */
    c_ekketju(fact, dluval, hrowi, mcstrt, hpivco_new,
      dwork1, kpivrw, fact->first_dense,
      fact->last_dense);
  } else {

    /*       could take out of old column but lets try being crude */
    /*       try taking out */
    if (fact->xe2adr != 0 && doSparse) {

      /*
       * There is both a column and row representation of U.
       * For each row in the kpivrw'th column of the col U rep,
       * find its position in the U row rep and remove it
       * by overwriting it with the last element.
       */
      int k1x = mcstrt[kpivrw];
      int nel = hrowi[k1x]; /* yes, this is the nel, for the pivot */
      int k2x = k1x + nel;

      for (k = k1x + 1; k <= k2x; ++k) {
        int irow = UNSHIFT_INDEX(hrowi[k]);
        int kx = mrstrt[irow];
        int nel = hinrow[irow] - 1;
        hinrow[irow] = nel;

        int jlast = kx + nel;
        for (int iel = kx; iel < jlast; iel++) {
          if (kpivrw == hcoli[iel]) {
            hcoli[iel] = hcoli[jlast];
            de2val[iel] = de2val[jlast];
            break;
          }
        }
      }
    } else if (ifRowCopy) {
      /* still take out */
      int k1x = mcstrt[kpivrw];
      int nel = hrowi[k1x]; /* yes, this is the nel, for the pivot */
      int k2x = k1x + nel;

      for (k = k1x + 1; k <= k2x; ++k) {
        int irow = UNSHIFT_INDEX(hrowi[k]);
        int kx = mrstrt[irow];
        int nel = hinrow[irow] - 1;
        hinrow[irow] = nel;
        int jlast = kx + nel;
        for (; kx < jlast; kx++) {
          if (kpivrw == hcoli[kx]) {
            hcoli[kx] = hcoli[jlast];
            break;
          }
        }
      }
    }

    /*       add to row version */
    /* the updated column (alpha_p) was written to entries
     * nnentu+1..nnentu+nuspik by routine c_ekkftrn_ft.
     * That was just an intermediate value of the usual ftrn.
     */
    i1 = fact->nnentu + 1;
    i2 = fact->nnentu + nuspik;
    int *COIN_RESTRICT eta_last = mpermu + nrow * 2 + 3;
    int *COIN_RESTRICT eta_next = eta_last + nrow + 2;
    if (fact->xe2adr == 0 || !doSparse) {
      /* we have column indices by row, but not the actual values */
      for (iel = i1; iel <= i2; ++iel) {
        int irow = UNSHIFT_INDEX(hrowi[iel]);
        int iput = hinrow[irow];
        int kput = mrstrt[irow];
        int nextRow = eta_next[irow];
        assert(kput > 0);
        kput += iput;
        if (kput < mrstrt[nextRow]) {
          /* there is room - append the pivot column;
	   * this corresponds making alpha_p the rightmost column of U (p. 268)*/
          hinrow[irow] = iput + 1;
          hcoli[kput] = kpivrw;
        } else {
          /* no room - switch off */
          doSparse = 0;
          /* possible kpivrw 1 */
          k1 = mrstrt[kpivrw];
          mrstrt[1] = -1;
          fact->rows_ok = false;
          goto L1226;
        }
      }
    } else {
      if (!doSparse) {
        /* we have both column indices and values by row */
        /* just like loop above, but with extra assign to de2val */
        for (iel = i1; iel <= i2; ++iel) {
          int irow = UNSHIFT_INDEX(hrowi[iel]);
          int iput = hinrow[irow];
          int kput = mrstrt[irow];
          int nextRow = eta_next[irow];
          assert(kput > 0);
          kput += iput;
          if (kput < mrstrt[nextRow]) {
            hinrow[irow] = iput + 1;
            hcoli[kput] = kpivrw;
            de2val[kput] = dluval[iel];
          } else {
            /* no room - switch off */
            doSparse = 0;
            /* possible kpivrw 1 */
            k1 = mrstrt[kpivrw];
            mrstrt[1] = -1;
            fact->rows_ok = false;
            goto L1226;
          }
        }
      } else {
        for (iel = i1; iel <= i2; ++iel) {
          int j, k;
          int irow = UNSHIFT_INDEX(hrowi[iel]);
          int iput = hinrow[irow];
          k = mrstrt[irow] + iput;
          j = eta_next[irow];
          if (k >= mrstrt[j]) {
            /* no room - can we make some? */
            int klast = eta_last[nrow + 1];
            int jput = mrstrt[klast] + hinrow[klast] + 2;
            int distance = mrstrt[nrow + 1] - jput;
            if (iput + 1 < distance) {
              /* this presumably copies the row to the end */
              int jn, jl;
              int kstart = mrstrt[irow];
              int nin = hinrow[irow];
              /* out */
              jn = eta_next[irow];
              jl = eta_last[irow];
              eta_next[jl] = jn;
              eta_last[jn] = jl;
              /* in */
              eta_next[klast] = irow;
              eta_last[nrow + 1] = irow;
              eta_last[irow] = klast;
              eta_next[irow] = nrow + 1;
              mrstrt[irow] = jput;
#if 0
	      memcpy(&hcoli[jput],&hcoli[kstart],nin*sizeof(int));
	      memcpy(&de2val[jput],&de2val[kstart],nin*sizeof(double));
#else
              c_ekkscpy(nin, hcoli + kstart, hcoli + jput);
              c_ekkdcpy(nin,
                (de2val + kstart), (de2val + jput));
#endif
              k = jput + iput;
            } else {
              /* shuffle down */
              int spare = (fact->nnetas - fact->nnentu - fact->nnentl - 3);
              if (spare > nrow << 1) {
                /* presumbly, this compacts the rows */
                int jrow, jput;
                if (1) {
                  if (fact->num_resets < 1000000) {
                    int etasize = CoinMax(4 * fact->nnentu + (fact->nnetas - fact->nnentl) + 1000, fact->eta_size);
                    if (ifrows) {
                      fact->num_resets++;
                      if (npivot > 40 && fact->num_resets << 4 > npivot) {
                        fact->eta_size = static_cast< int >(1.05 * fact->eta_size);
                        fact->num_resets = 1000000;
                      }
                    } else {
                      fact->eta_size = static_cast< int >(1.1 * fact->eta_size);
                      fact->num_resets = 1000000;
                    }
                    fact->eta_size = CoinMin(fact->eta_size, etasize);
                    if (fact->maxNNetas > 0 && fact->eta_size > fact->maxNNetas) {
                      fact->eta_size = fact->maxNNetas;
                    }
                  }
                }
                jrow = eta_next[0];
                jput = 1;
                for (j = 0; j < nrow; j++) {
                  int k, nin = hinrow[jrow];
                  k = mrstrt[jrow];
                  mrstrt[jrow] = jput;
                  for (; nin; nin--) {
                    hcoli[jput] = hcoli[k];
                    de2val[jput++] = de2val[k++];
                  }
                  jrow = eta_next[jrow];
                }
                if (spare > nrow << 3) {
                  spare = 3;
                } else if (spare > nrow << 2) {
                  spare = 1;
                } else {
                  spare = 0;
                }
                jput += nrow * spare;
                ;
                jrow = eta_last[nrow + 1];
                for (j = 0; j < nrow; j++) {
                  int k, nin = hinrow[jrow];
                  k = mrstrt[jrow] + nin;
                  jput -= spare;
                  for (; nin; nin--) {
                    hcoli[--jput] = hcoli[--k];
                    de2val[jput] = de2val[k];
                  }
                  mrstrt[jrow] = jput;
                  jrow = eta_last[jrow];
                }
                /* set up for copy below */
                k = mrstrt[irow] + iput;
              } else {
                /* no room - switch off */
                doSparse = 0;
                /* possible kpivrw 1 */
                k1 = mrstrt[kpivrw];
                mrstrt[1] = -1;
                fact->rows_ok = false;
                goto L1226;
              }
            }
          }
          /* now we have room - append the new value */
          hinrow[irow] = iput + 1;
          hcoli[k] = kpivrw;
          de2val[k] = dluval[iel];
        }
      }
    }

    /*       TAKE OUT ALL ELEMENTS IN PIVOT ROW */
    k1 = mrstrt[kpivrw];

  L1226 : {
    int k2 = k1 + hinrow[kpivrw] - 1;

    /* "delete" the row */
    hinrow[kpivrw] = 0;
    j = 0;
    if (doSparse) {
      /* remove pivot row entries from the corresponding columns */
      for (k = k1; k <= k2; ++k) {
        int icol = hcoli[k];
        int kx = mcstrt[icol];
        int nel = hrowi[kx];
        for (iel = kx + 1; iel <= kx + nel; iel++) {
          if (hrowi[iel] == jpivrw) {
            break;
          }
        }
        if (iel <= kx + nel) {
          /* this has to happen, right?? */

          /* copy the element into a temporary */
          dwork1[icol] = dluval[iel];
          mpt2[nincol++] = icol;
          /*nonzero[icol-1]=1;*/

          hrowi[kx] = nel - 1; /* column is shorter by one */
          j = 1;
          hrowi[iel] = hrowi[kx + nel];
          dluval[iel] = dluval[kx + nel];
#ifdef CLP_REUSE_ETAS
          hrowi[kx + nel] = jpivrw;
          dluval[kx + nel] = dwork1[icol];
#endif
        }
      }
      if (j != 0) {
        /* now compute r', the new R transform */
        orig_nincol = c_ekkbtju_sparse(fact, dwork1,
          mpt2, nincol,
          spare);
        dwork1[kpivrw] = 0.0;
      }
    } else {
      /* row version isn't ok (?) */
      for (k = k1; k <= k2; ++k) {
        int icol = hcoli[k];
        int kx = mcstrt[icol];
        int nel = hrowi[kx];
        j = kx + nel;
        int iel;
        for (iel = kx + 1; iel <= j; iel++) {
          if (hrowi[iel] == jpivrw)
            break;
        }
        dwork1[icol] = dluval[iel];
        if (kx < first_dense_mcstrt || kx > last_dense_mcstrt) {
          hrowi[kx] = nel - 1; /* shorten column */
          /* not packing - presumably column isn't sorted */
          hrowi[iel] = hrowi[j];
          dluval[iel] = dluval[j];
#ifdef CLP_REUSE_ETAS
          hrowi[j] = jpivrw;
          dluval[j] = dwork1[icol];
#endif
        } else {
          /* dense element - just zero it */
          dluval[iel] = 0.0;
        }
      }
      if (j != 0) {
        /* Find first nonzero */
        int ipiv = hpivco_new[kpivrw];
        while (ipiv <= nrow) {
          if (!dwork1[ipiv]) {
            ipiv = hpivco_new[ipiv];
          } else {
            break;
          }
        }
        if (ipiv <= nrow) {
          /*       DO U */
          /* now compute r', the new R transform */
          c_ekkbtju(fact, dwork1,
            ipiv);
        }
      }
    }
  }
  }

  if (kpivrw == fact->first_dense) {
    /* increase until valid pivot */
    fact->first_dense = hpivco_new[fact->first_dense];
  } else if (kpivrw == fact->last_dense) {
    fact->last_dense = back[fact->last_dense];
  }
  if (fact->first_dense == fact->last_dense) {
    fact->ndenuc = 0;
    fact->first_dense = 0;
    fact->last_dense = -1;
  }
  if (!(ifRowCopy && j == 0)) {

    /*     increase amount of work on Etas */

    /* **************************************************************** */
    /*       DO ROW ETAS IN L */
    {
      if (!doSparse) {
        dwork1[kpivrw] = 0.;
#if 0	
	orig_nincol=c_ekksczr(fact,nrow, dwork1, mpt2);
	del3=c_ekkputl(fact, mpt2, dwork1, del3, 
		     orig_nincol, nuspik);
#else
        orig_nincol = c_ekkputl2(fact,
          dwork1, &del3,
          nuspik);
#endif
      } else {
        del3 = c_ekkputl(fact, mpt2,
          dwork1, del3,
          orig_nincol, nuspik);
      }
    }
    if (orig_nincol != 0) {
      /* STORE AS A ROW VECTOR */
      int n = fact->nR_etas + 1;
      int i1 = fact->R_etas_start[n];
      fact->nR_etas = n;
      fact->R_etas_start[n + 1] = i1 - orig_nincol;
      hpivco[fact->nR_etas + nrow + 3] = kpivrw;
    }
  }

  /*       CHECK DEL3 AGAINST DALPHA/DOUT */
  {
    int kx = mcstrt[kpivrw];
    double dout = dluval[kx];
    double dcheck = fabs(dalpha / dout);
    double difference = 0.0;
    if (fabs(del3) > CoinMin(1.0e-8, fact->drtpiv * 0.99999)) {
      double checkTolerance;
      if (fact->npivots < 2) {
        checkTolerance = 1.0e-5;
      } else if (fact->npivots < 10) {
        checkTolerance = 1.0e-6;
      } else if (fact->npivots < 50) {
        checkTolerance = 1.0e-8;
      } else {
        checkTolerance = 1.0e-9;
      }
      difference = fabs(1.0 - fabs(del3) / dcheck);
      if (difference > 0.1 * checkTolerance) {
        if (difference < checkTolerance || (difference < 1.0e-7 && fact->npivots >= 50)) {
          irtcod = 1;
#ifdef PRINT_DEBUG
          printf("mildly bad %g after %d pivots, etsj %g ftncheck %g ftnalpha %g\n",
            difference, fact->npivots, del3, dcheck, dalpha);
#endif
        } else {
          irtcod = 2;
#ifdef PRINT_DEBUG
          printf("bad %g after %d pivots, etsj %g ftncheck %g ftnalpha %g\n",
            difference, fact->npivots, del3, dcheck, dalpha);
#endif
        }
      }
    } else {
      irtcod = 2;
#ifdef PRINT_DEBUG
      printf("bad small %g after %d pivots, etsj %g ftncheck %g ftnalpha %g\n",
        difference, fact->npivots, del3, dcheck, dalpha);
#endif
    }
    if (irtcod > 1)
      goto L8000;
    fact->npivots++;
  }

  mcstrt[kpivrw] = fact->nnentu;
#ifdef CLP_REUSE_ETAS
  {
    int *putSeq = fact->xrsadr + 2 * fact->nrowmx + 2;
    int *position = putSeq + fact->maxinv;
    int *putStart = position + fact->maxinv;
    putStart[fact->nrow + fact->npivots - 1] = fact->nnentu;
  }
#endif
  dluval[fact->nnentu] = 1. / del3; /* new pivot */
  hrowi[fact->nnentu] = nuspik; /* new nelems */
#ifndef NDEBUG
  {
    int lastSlack = fact->lastSlack;
    int firstDo = hpivco_new[lastSlack];
    int ipiv = hpivco_new[0];
    int now = fact->numberSlacks;
    if (now) {
      while (1) {
        if (ipiv > fact->nrow || ipiv == firstDo)
          break;
        assert(c_ekk_IsSet(fact->bitArray, ipiv));
        ipiv = hpivco_new[ipiv];
      }
      if (ipiv <= fact->nrow) {
        while (1) {
          if (ipiv > fact->nrow)
            break;
          assert(!c_ekk_IsSet(fact->bitArray, ipiv));
          ipiv = hpivco_new[ipiv];
        }
      }
    }
  }
#endif
  {
    /* do new hpivco */
    int inext = hpivco_new[kpivrw];
    int iback = back[kpivrw];
    if (inext != nrow + 1) {
      int ilast = back[nrow + 1];
      hpivco_new[iback] = inext;
      back[inext] = iback;
      assert(hpivco_new[ilast] == nrow + 1);
      hpivco_new[ilast] = kpivrw;
      back[kpivrw] = ilast;
      hpivco_new[kpivrw] = nrow + 1;
      back[nrow + 1] = kpivrw;
    }
  }
  {
    int lastSlack = fact->lastSlack;
    int now = fact->numberSlacks;
    if (now && mcstrt_piv <= mcstrt[lastSlack]) {
      if (c_ekk_IsSet(fact->bitArray, kpivrw)) {
        /*printf("piv %d lastSlack %d\n",mcstrt_piv,lastSlack);*/
        fact->numberSlacks--;
        now--;
        /* one less slack */
        c_ekk_Unset(fact->bitArray, kpivrw);
        if (now && kpivrw == lastSlack) {
          int i;
          int ipiv;
          ipiv = hpivco_new[0];
          for (i = 0; i < now - 1; i++)
            ipiv = hpivco_new[ipiv];
          lastSlack = ipiv;
          assert(c_ekk_IsSet(fact->bitArray, ipiv));
          assert(!c_ekk_IsSet(fact->bitArray, hpivco_new[ipiv]) || hpivco_new[ipiv] > fact->nrow);
          fact->lastSlack = lastSlack;
        } else if (!now) {
          fact->lastSlack = 0;
        }
      }
    }
    fact->firstNonSlack = hpivco_new[lastSlack];
#ifndef NDEBUG
    {
      int lastSlack = fact->lastSlack;
      int firstDo = hpivco_new[lastSlack];
      int ipiv = hpivco_new[0];
      int now = fact->numberSlacks;
      if (now) {
        while (1) {
          if (ipiv > fact->nrow || ipiv == firstDo)
            break;
          assert(c_ekk_IsSet(fact->bitArray, ipiv));
          ipiv = hpivco_new[ipiv];
        }
        if (ipiv <= fact->nrow) {
          while (1) {
            if (ipiv > fact->nrow)
              break;
            assert(!c_ekk_IsSet(fact->bitArray, ipiv));
            ipiv = hpivco_new[ipiv];
          }
        }
      }
    }
#endif
  }
  fact->nnentu += nuspik;
#ifdef CLP_REUSE_ETAS
  if (fact->first_dense >= fact->last_dense) {
    // save
    fact->nnentu++;
    dluval[fact->nnentu] = del3Orig;
    hrowi[fact->nnentu] = kpivrw;
    int *putSeq = fact->xrsadr + 2 * fact->nrowmx + 2;
    int *position = putSeq + fact->maxinv;
    int *putStart = position + fact->maxinv;
    int nnentu_at_factor = putStart[fact->nrow] & 0x7fffffff;
    //putStart[fact->nrow+fact->npivots]=fact->nnentu+1;
    int where;
    if (mcstrt_piv < nnentu_at_factor) {
      // original LU
      where = kpivrw - 1;
    } else {
      // could do binary search
      int *look = putStart + fact->nrow;
      for (where = fact->npivots - 1; where >= 0; where--) {
        if (mcstrt_piv == (look[where] & 0x7fffffff))
          break;
      }
      assert(where >= 0);
      where += fact->nrow;
    }
    position[fact->npivots - 1] = where;
    if (orig_nincol == 0) {
      // flag
      putStart[fact->nrow + fact->npivots - 1] |= 0x80000000;
    }
  }
#endif
  {
    int kdnspt = fact->nnetas - fact->nnentl;

    /* fact->R_etas_start[fact->nR_etas + 1] is -(the number of els in R) */
    nnentl = fact->nnetas - ((kdnspt - 1) + fact->R_etas_start[fact->nR_etas + 1]);
  }
  fact->demark = (fact->nnentu + nnentl) - fact->demark;

  /*     if need to redo row version */
  if (!fact->rows_ok && fact->first_dense >= fact->last_dense) {
    int extraSpace = 10000;
    int spareSpace;
    if (fact->if_sparse_update > 0) {
      spareSpace = (fact->nnetas - fact->nnentu - fact->nnentl);
    } else {
      /* missing out nnentl stuff */
      spareSpace = fact->nnetas - fact->nnentu;
    }
    /*       save clean row copy if enough room */
    nroom = spareSpace / nrow;

    if ((fact->nnentu << 3) > 150 * fact->maxinv) {
      extraSpace = 150 * fact->maxinv;
    } else {
      extraSpace = fact->nnentu << 3;
    }

    ifrows = false;
    if (fact->nnetas > fact->nnentu + fact->nnentl + extraSpace) {
      ifrows = true;
    }
    if (nroom < 5) {
      ifrows = false;
    }

    if (nroom > CoinMin(50, fact->maxinv - (fact->iterno - fact->iterin))) {
      ifrows = true;
    }

#ifdef PRINT_DEBUGx
    printf(" redoing row copy %d %d %d\n", ifrows, nroom, spareSpace);
#endif
    if (1) {
      if (fact->num_resets < 1000000) {
        if (ifrows) {
          fact->num_resets++;
          if (npivot > 40 && fact->num_resets << 4 > npivot) {
            fact->eta_size = static_cast< int >(1.05 * fact->eta_size);
            fact->num_resets = 1000000;
          }
        } else {
          fact->eta_size = static_cast< int >(1.1 * fact->eta_size);
          fact->num_resets = 1000000;
        }
        if (fact->maxNNetas > 0 && fact->eta_size > fact->maxNNetas) {
          fact->eta_size = fact->maxNNetas;
        }
      }
    }
    fact->rows_ok = ifrows;
    if (ifrows) {
      int ibase = 1;
      c_ekkizero(nrow, &hinrow[1]);
      for (i = 1; i <= nrow; ++i) {
        int kx = mcstrt[i];
        int nel = hrowi[kx];
        int kcs = kx + 1;
        int kce = kx + nel;
        for (kc = kcs; kc <= kce; ++kc) {
          int irow = UNSHIFT_INDEX(hrowi[kc]);
          if (dluval[kc]) {
            hinrow[irow]++;
          }
        }
      }
      int *eta_last = mpermu + nrow * 2 + 3;
      int *eta_next = eta_last + nrow + 2;
      eta_next[0] = 1;
      for (i = 1; i <= nrow; ++i) {
        eta_next[i] = i + 1;
        eta_last[i] = i - 1;
        mrstrt[i] = ibase;
        ibase = ibase + hinrow[i] + nroom;
        hinrow[i] = 0;
      }
      eta_last[nrow + 1] = nrow;
      //eta_next[nrow+1]=nrow+2;
      mrstrt[nrow + 1] = ibase;
      if (fact->xe2adr == 0) {
        for (i = 1; i <= nrow; ++i) {
          int kx = mcstrt[i];
          int nel = hrowi[kx];
          int kcs = kx + 1;
          int kce = kx + nel;
          for (kc = kcs; kc <= kce; ++kc) {
            if (dluval[kc]) {
              int irow = UNSHIFT_INDEX(hrowi[kc]);
              int iput = hinrow[irow];
              assert(irow);
              hcoli[mrstrt[irow] + iput] = i;
              hinrow[irow] = iput + 1;
            }
          }
        }
      } else {
        for (i = 1; i <= nrow; ++i) {
          int kx = mcstrt[i];
          int nel = hrowi[kx];
          int kcs = kx + 1;
          int kce = kx + nel;
          for (kc = kcs; kc <= kce; ++kc) {
            int irow = UNSHIFT_INDEX(hrowi[kc]);
            int iput = hinrow[irow];
            hcoli[mrstrt[irow] + iput] = i;
            de2val[mrstrt[irow] + iput] = dluval[kc];
            hinrow[irow] = iput + 1;
          }
        }
      }
    } else {
      mrstrt[1] = 0;
      if (fact->if_sparse_update > 0 && fact->iterno - fact->iterin > 100) {
        goto L7000;
      }
    }
  }
  goto L8000;

  /*       OUT OF SPACE - COULD PACK DOWN */
L7000:
  irtcod = 1;
#ifdef PRINT_DEBUG
  printf(" out of space\n");
#endif
  if (1) {
    if ((npivot << 3) < fact->nbfinv) {
      /* low on space */
      if (npivot < 10) {
        fact->eta_size = fact->eta_size << 1;
      } else {
        double ratio = fact->nbfinv;
        double ratio2 = npivot << 3;
        ratio = ratio / ratio2;
        if (ratio > 2.0) {
          ratio = 2.0;
        } /* endif */
        fact->eta_size = static_cast< int >(ratio * fact->eta_size);
      } /* endif */
    } else {
      fact->eta_size = static_cast< int >(1.05 * fact->eta_size);
    } /* endif */
    if (fact->maxNNetas > 0 && fact->eta_size > fact->maxNNetas) {
      fact->eta_size = fact->maxNNetas;
    }
  }

  /* ================= IF ERROR SHOULD WE GET RID OF LAST ITERATION??? */
L8000:

  *nuspikp = nuspik;
#ifdef MORE_DEBUG
  for (int i = 1; i <= fact->nrow; i++) {
    int kx = mcstrt[i];
    int nel = hrowi[kx];
    for (int j = 0; j < nel; j++) {
      assert(i != hrowi[j + kx + 1]);
    }
  }
#endif
#ifdef CLP_REUSE_ETAS
  fact->save_nnentu = fact->nnentu;
#endif
  return (irtcod);
} /* c_ekketsj */
static void c_ekkftj4p(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, int firstNonZero)
{
  /* this is where the L factors start, because this is the place
   * where c_ekktria starts laying them down (see initialization of xnetal).
   */
  int lstart = fact->lstart;
  const int *COIN_RESTRICT hpivco = fact->kcpadr;
  int firstLRow = hpivco[lstart];
  if (firstNonZero > firstLRow) {
    lstart += firstNonZero - firstLRow;
  }
  assert(firstLRow == fact->firstLRow);
  int jpiv = hpivco[lstart];
  const double *COIN_RESTRICT dluval = fact->xeeadr;
  const int *COIN_RESTRICT hrowi = fact->xeradr;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr + lstart;
  int ndo = fact->xnetal - lstart;
  int i, iel;

  /* find first non-zero */
  for (i = 0; i < ndo; i++) {
    if (dwork1[i + jpiv] != 0.0)
      break;
  }
  for (; i < ndo; ++i) {
    double dv = dwork1[i + jpiv];

    if (dv != 0.) {
      int kce1 = mcstrt[i + 1];

      for (iel = mcstrt[i]; iel > kce1; --iel) {
        int irow0 = hrowi[iel];
        SHIFT_REF(dwork1, irow0) += dv * dluval[iel];
      }
    }
  }

} /* c_ekkftj4p */

/*
 * This version is more efficient for input columns that are sparse.
 * It is instructive to consider the case of an especially sparse column,
 * which is a slack.  The slack for row r has exactly one non-zero element,
 * in row r, which is +-1.0.  Let pr = mpermu[r].
 * In this case, nincol==1 and mpt[0] == pr on entry.
 * if mpt[0] == pr <= jpiv
 * then this slack is completely unaffected by L;
 *	this is reflected by the fact that save_where = last
 *	after the first loop, so none of the remaining loops
 *	ever execute,
 * else if mpt[0] == pr > jpiv, but pr-jpiv > ndo
 * then the slack is also unaffected by L, this time because
 *	its row is "after" L.  During factorization, it may
 *	be the case that the first part of the basis is upper
 *	triangular (c_ekktria), but it may also be the case that the
 *	last part of the basis is upper triangular (in which case the
 *	L triangle gets "chopped off" on the right).  In both cases,
 *	no L entries are required.  Since in this case the tests
 *	(i<=ndo) will fail (and dwork1[ipiv]==1.0), the code will
 *	do nothing.
 * else if mpt[0] == pr > jpiv and pr-jpiv <= ndo
 * then the slack *is* affected by L.
 *	the for-loop inside the second while-loop will discover
 *	that none of the factors for the corresponding column of L
 *	are non-zero in the slack column, so last will not be incremented.
 *	We multiply the eta-vector, and the last loop does nothing.
 */
static int c_ekkftj4_sparse(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, int *COIN_RESTRICT mpt,
  int nincol, int *COIN_RESTRICT spare)
{
  const int nrow = fact->nrow;
  /* this is where the L factors start, because this is the place
   * where c_ekktria starts laying them down (see initialization of xnetal).
   */
  int lstart = fact->lstart;
  const int *COIN_RESTRICT hpivco = fact->kcpadr;
  const double *COIN_RESTRICT dluval = fact->xeeadr;
  const int *COIN_RESTRICT hrowi = fact->xeradr;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr + lstart - 1;
  double tolerance = fact->zeroTolerance;
  int jpiv = hpivco[lstart] - 1;
  char *COIN_RESTRICT nonzero = fact->nonzero;
  int ndo = fact->xnetalval;
  int k, nStack;
  int nList = 0;
  int iPivot;
  int *COIN_RESTRICT list = spare;
  int *COIN_RESTRICT stack = spare + nrow;
  int *COIN_RESTRICT next = stack + nrow;
  double dv;
  int iel;
  int nput = 0, kput = nrow;
  int check = jpiv + ndo + 1;
  const int *COIN_RESTRICT mcstrt2 = mcstrt - jpiv;

  for (k = 0; k < nincol; k++) {
    nStack = 1;
    iPivot = mpt[k];
    if (nonzero[iPivot] != 1 && iPivot > jpiv && iPivot < check) {
      stack[0] = iPivot;
      next[0] = mcstrt2[iPivot + 1] + 1;
      while (nStack) {
        int kPivot, j;
        /* take off stack */
        kPivot = stack[--nStack];
        if (nonzero[kPivot] != 1 && kPivot > jpiv && kPivot < check) {
          j = next[nStack];
          if (j > mcstrt2[kPivot]) {
            /* finished so mark */
            list[nList++] = kPivot;
            nonzero[kPivot] = 1;
          } else {
            kPivot = UNSHIFT_INDEX(hrowi[j]);
            /* put back on stack */
            next[nStack++]++;
            if (!nonzero[kPivot]) {
              /* and new one */
              stack[nStack] = kPivot;
              nonzero[kPivot] = 2;
              next[nStack++] = mcstrt2[kPivot + 1] + 1;
            }
          }
        } else if (kPivot >= check) {
          list[--kput] = kPivot;
          nonzero[kPivot] = 1;
        }
      }
    } else if (nonzero[iPivot] != 1) {
      /* nothing to do (except check size at end) */
      list[--kput] = iPivot;
      nonzero[iPivot] = 1;
    }
  }
  for (k = nList - 1; k >= 0; k--) {
    double dv;
    iPivot = list[k];
    dv = dwork1[iPivot];
    nonzero[iPivot] = 0;
    if (fabs(dv) > tolerance) {
      /* the same code as in c_ekkftj4p */
      int kce1 = mcstrt2[iPivot + 1];
      for (iel = mcstrt2[iPivot]; iel > kce1; --iel) {
        int irow0 = hrowi[iel];
        SHIFT_REF(dwork1, irow0) += dv * dluval[iel];
      }
      mpt[nput++] = iPivot;
    } else {
      dwork1[iPivot] = 0.0; /* force to zero, not just near zero */
    }
  }
  /* check remainder */
  for (k = kput; k < nrow; k++) {
    iPivot = list[k];
    nonzero[iPivot] = 0;
    dv = dwork1[iPivot];
    if (fabs(dv) > tolerance) {
      mpt[nput++] = iPivot;
    } else {
      dwork1[iPivot] = 0.0; /* force to zero, not just near zero */
    }
  }

  return (nput);
} /* c_ekkftj4 */
/*
 * This applies the R transformations of the F-T LU update procedure,
 * equation 3.11 on p. 270 in the 1972 Math Programming paper.
 * Note that since the non-zero off-diagonal elements are in a row,
 * multiplying an R by a column is a reduction, not like applying
 * L or U.
 *
 * Note that this may introduce new non-zeros in dwork1,
 * since an hpivco entry may correspond to a zero element,
 * and that some non-zeros in dwork1 may be cancelled.
 */
static int c_ekkftjl_sparse3(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt,
  int *COIN_RESTRICT hput, double *COIN_RESTRICT dluput,
  int nincol)
{
  int i;
  int knext;
  int ipiv;
  double dv;
  const double *COIN_RESTRICT dluval = fact->R_etas_element + 1;
  const int *COIN_RESTRICT hrowi = fact->R_etas_index + 1;
  const int *COIN_RESTRICT mcstrt = fact->R_etas_start;
  int ndo = fact->nR_etas;
  double tolerance = fact->zeroTolerance;
  const int *COIN_RESTRICT hpivco = fact->hpivcoR;
  /* and make cleaner */
  hput++;
  dluput++;

  /* DO ANY ROW TRANSFORMATIONS */

  /* Function Body */
  /* mpt has correct list of nonzeros */
  if (ndo != 0) {
    knext = mcstrt[1];
    for (i = 1; i <= ndo; ++i) {
      int k1 = knext; /* == mcstrt[i] */
      int iel;
      ipiv = hpivco[i];
      dv = dwork1[ipiv];
      bool onList = (dv != 0.0);
      knext = mcstrt[i + 1];

      for (iel = knext; iel < k1; ++iel) {
        int irow = hrowi[iel];
        dv += SHIFT_REF(dwork1, irow) * dluval[iel];
      }
      /* (1) if dwork[ipiv] == 0.0, then this may add a non-zero.
       * (2) if dwork[ipiv] != 0.0, then this may cancel out a non-zero.
       */
      if (onList) {
        if (fabs(dv) > tolerance) {
          dwork1[ipiv] = dv;
        } else {
          dwork1[ipiv] = 1.0e-128;
        }
      } else {
        if (fabs(dv) > tolerance) {
          /* put on list if not there */
          mpt[nincol++] = ipiv;
          dwork1[ipiv] = dv;
        }
      }
    }
  }
  knext = 0;
  for (i = 0; i < nincol; i++) {
    ipiv = mpt[i];
    dv = dwork1[ipiv];
    if (fabs(dv) > tolerance) {
      hput[knext] = SHIFT_INDEX(ipiv);
      dluput[knext] = dv;
      mpt[knext++] = ipiv;
    } else {
      dwork1[ipiv] = 0.0;
    }
  }
  return knext;
} /* c_ekkftjl */

static int c_ekkftjl_sparse2(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  int *COIN_RESTRICT mpt,
  int nincol)
{
  double tolerance = fact->zeroTolerance;
  const double *COIN_RESTRICT dluval = fact->R_etas_element + 1;
  const int *COIN_RESTRICT hrowi = fact->R_etas_index + 1;
  const int *COIN_RESTRICT mcstrt = fact->R_etas_start;
  int ndo = fact->nR_etas;
  const int *COIN_RESTRICT hpivco = fact->hpivcoR;
  int i;
  int knext;
  int ipiv;
  double dv;

  /* DO ANY ROW TRANSFORMATIONS */

  /* Function Body */
  /* mpt has correct list of nonzeros */
  if (ndo != 0) {
    knext = mcstrt[1];
    for (i = 1; i <= ndo; ++i) {
      int k1 = knext; /* == mcstrt[i] */
      int iel;
      ipiv = hpivco[i];
      dv = dwork1[ipiv];
      bool onList = (dv != 0.0);
      knext = mcstrt[i + 1];

      for (iel = knext; iel < k1; ++iel) {
        int irow = hrowi[iel];
        dv += SHIFT_REF(dwork1, irow) * dluval[iel];
      }
      /* (1) if dwork[ipiv] == 0.0, then this may add a non-zero.
       * (2) if dwork[ipiv] != 0.0, then this may cancel out a non-zero.
       */
      if (onList) {
        if (fabs(dv) > tolerance) {
          dwork1[ipiv] = dv;
        } else {
          dwork1[ipiv] = 1.0e-128;
        }
      } else {
        if (fabs(dv) > tolerance) {
          /* put on list if not there */
          mpt[nincol++] = ipiv;
          dwork1[ipiv] = dv;
        }
      }
    }
  }
  knext = 0;
  for (i = 0; i < nincol; i++) {
    ipiv = mpt[i];
    dv = dwork1[ipiv];
    if (fabs(dv) > tolerance) {
      mpt[knext++] = ipiv;
    } else {
      dwork1[ipiv] = 0.0;
    }
  }
  return knext;
} /* c_ekkftjl */

static void c_ekkftjl(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1)
{
  double tolerance = fact->zeroTolerance;
  const double *COIN_RESTRICT dluval = fact->R_etas_element + 1;
  const int *COIN_RESTRICT hrowi = fact->R_etas_index + 1;
  const int *COIN_RESTRICT mcstrt = fact->R_etas_start;
  int ndo = fact->nR_etas;
  const int *COIN_RESTRICT hpivco = fact->hpivcoR;
  int i;
  int knext;

  /* DO ANY ROW TRANSFORMATIONS */

  /* Function Body */
  if (ndo != 0) {
    /*
     * The following three lines are here just to ensure that this
     * new formulation of the loop has exactly the same effect
     * as the original.
     */
    {
      int ipiv = hpivco[1];
      double dv = dwork1[ipiv];
      dwork1[ipiv] = (fabs(dv) > tolerance) ? dv : 0.0;
    }

    knext = mcstrt[1];
    for (i = 1; i <= ndo; ++i) {
      int k1 = knext; /* == mcstrt[i] */
      int ipiv = hpivco[i];
      double dv = dwork1[ipiv];
      int iel;
      //#define UNROLL3 2
#ifndef UNROLL3
#if CLP_OSL == 2 || CLP_OSL == 3
#define UNROLL3 2
#else
#define UNROLL3 1
#endif
#endif
      knext = mcstrt[i + 1];

#if UNROLL3 < 2
      for (iel = knext; iel < k1; ++iel) {
        int irow = hrowi[iel];
        dv += SHIFT_REF(dwork1, irow) * dluval[iel];
      }
#else
      iel = knext;
      if (((k1 - knext) & 1) != 0) {
        int irow = hrowi[iel];
        dv += SHIFT_REF(dwork1, irow) * dluval[iel];
        iel++;
      }
      for (; iel < k1; iel += 2) {
        int irow0 = hrowi[iel];
        double dval0 = dluval[iel];
        int irow1 = hrowi[iel + 1];
        double dval1 = dluval[iel + 1];
        dv += SHIFT_REF(dwork1, irow0) * dval0;
        dv += SHIFT_REF(dwork1, irow1) * dval1;
      }
#endif
      /* (1) if dwork[ipiv] == 0.0, then this may add a non-zero.
       * (2) if dwork[ipiv] != 0.0, then this may cancel out a non-zero.
       */
      dwork1[ipiv] = (fabs(dv) > tolerance) ? dv : 0.0;
    }
  }
} /* c_ekkftjl */
/* this assumes it is ok to reference back[loop_limit] */
/* another 3 seconds from a ~570 second run can be trimmed
 * by using two routines, one with scan==true and the other false,
 * since that eliminates the branch instructions involving them
 * entirely.  This was how the code was originally written.
 * However, I'm still hoping that eventually we can use
 * C++ templates to do that for us automatically.
 */
static void
c_ekkftjup_scan_aux(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, double *COIN_RESTRICT dworko,
  int loop_limit, int *ip, int **mptp)
{
  const double *COIN_RESTRICT dluval = fact->xeeadr + 1;
  const int *COIN_RESTRICT hrowi = fact->xeradr + 1;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr;
  const int *COIN_RESTRICT hpivro = fact->krpadr;
  const int *COIN_RESTRICT back = fact->back;
  double tolerance = fact->zeroTolerance;
  int ipiv = *ip;
  double dv = dwork1[ipiv];

  int *mptX = *mptp;
  assert(mptX);
  while (ipiv != loop_limit) {
    int next_ipiv = back[ipiv];

    dwork1[ipiv] = 0.0;
#ifndef UNROLL4
#define UNROLL4 2
#endif
    /* invariant:  dv == dwork1[ipiv] */

    /* in the case of world.mps with dual, this condition is true
     * only 20-60% of the time. */
    if (fabs(dv) > tolerance) {
      const int kx = mcstrt[ipiv];
      const int nel = hrowi[kx - 1];
      const double dpiv = dluval[kx - 1];
#if UNROLL4 > 1
      const int *hrowi2 = hrowi + kx;
      const int *hrowi2end = hrowi2 + nel;
      const double *dluval2 = dluval + kx;
#else
      int iel;
#endif

      dv *= dpiv;

      /*
       * The following loop is the unrolled version of this:
       *
       * for (iel = kx+1; iel <= kx + nel; iel++) {
       *   SHIFT_REF(dwork1, hrowi[iel]) -= dv * dluval[iel];
       * }
       */
#if UNROLL4 < 2
      iel = kx;
      if (nel & 1) {
        int irow = hrowi[iel];
        double dval = dluval[iel];
        SHIFT_REF(dwork1, irow) -= dv * dval;
        iel++;
      }
      for (; iel < kx + nel; iel += 2) {
        int irow0 = hrowi[iel];
        int irow1 = hrowi[iel + 1];
        double dval0 = dluval[iel];
        double dval1 = dluval[iel + 1];
        double d0 = SHIFT_REF(dwork1, irow0);
        double d1 = SHIFT_REF(dwork1, irow1);

        d0 -= dv * dval0;
        d1 -= dv * dval1;
        SHIFT_REF(dwork1, irow0) = d0;
        SHIFT_REF(dwork1, irow1) = d1;
      } /* end loop */
#else
      if ((nel & 1) != 0) {
        int irow = *hrowi2;
        double dval = *dluval2;
        SHIFT_REF(dwork1, irow) -= dv * dval;
        hrowi2++;
        dluval2++;
      }
      for (; hrowi2 < hrowi2end; hrowi2 += 2, dluval2 += 2) {
        int irow0 = hrowi2[0];
        int irow1 = hrowi2[1];
        double dval0 = dluval2[0];
        double dval1 = dluval2[1];
        double d0 = SHIFT_REF(dwork1, irow0);
        double d1 = SHIFT_REF(dwork1, irow1);

        d0 -= dv * dval0;
        d1 -= dv * dval1;
        SHIFT_REF(dwork1, irow0) = d0;
        SHIFT_REF(dwork1, irow1) = d1;
      }
#endif
      /* put this down here so that dv is less likely to cause a stall */
      if (fabs(dv) >= tolerance) {
        int iput = hpivro[ipiv];
        dworko[iput] = dv;
        *mptX++ = iput - 1;
      }
    }

    dv = dwork1[next_ipiv];
    ipiv = next_ipiv;
  } /* endwhile */

  *mptp = mptX;
  *ip = ipiv;
}
static void c_ekkftjup_aux3(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, double *COIN_RESTRICT dworko,
  const int *COIN_RESTRICT back,
  const int *COIN_RESTRICT hpivro,
  int *ipivp, int loop_limit,
  int **mptXp)

{
  double tolerance = fact->zeroTolerance;
  int ipiv = *ipivp;
  if (ipiv != loop_limit) {
    int *mptX = *mptXp;

    double dv = dwork1[ipiv];

    do {
      int next_ipiv = back[ipiv];
      double next_dv = dwork1[next_ipiv];

      dwork1[ipiv] = 0.0;

      if (fabs(dv) >= tolerance) {
        int iput = hpivro[ipiv];
        dworko[iput] = dv;
        *mptX++ = iput - 1;
      }

      ipiv = next_ipiv;
      dv = next_dv;
    } while (ipiv != loop_limit);

    *mptXp = mptX;
    *ipivp = ipiv;
  }
}
static void c_ekkftju_dense(const double *dluval,
  const int *COIN_RESTRICT hrowi,
  const int *COIN_RESTRICT mcstrt,
  const int *COIN_RESTRICT back,
  double *COIN_RESTRICT dwork1,
  int *start, int last,
  int offset, double *densew)
{
  int ipiv = *start;

  while (ipiv > last) {
    const int ipiv1 = ipiv;
    double dv1 = dwork1[ipiv1];
    ipiv = back[ipiv];
    if (fabs(dv1) > 1.0e-14) {
      const int kx1 = mcstrt[ipiv1];
      const int nel1 = hrowi[kx1 - 1];
      const double dpiv1 = dluval[kx1 - 1];

      int iel, k;
      const int n1 = offset + ipiv1; /* number in dense part */

      const int nsparse1 = nel1 - n1;
      const int k1 = kx1 + nsparse1;
      const double *dlu1 = &dluval[k1];

      int ipiv2 = back[ipiv1];
      const int nskip = ipiv1 - ipiv2;

      dv1 *= dpiv1;

      dwork1[ipiv1] = dv1;

      for (k = n1 - (nskip - 1) - 1; k >= 0; k--) {
        const double dval = dv1 * dlu1[k];
        double dv2 = densew[k] - dval;
        ipiv = back[ipiv];
        if (fabs(dv2) > 1.0e-14) {
          const int kx2 = mcstrt[ipiv2];
          const int nel2 = hrowi[kx2 - 1];
          const double dpiv2 = dluval[kx2 - 1];

          /* number in dense part is k */
          const int nsparse2 = nel2 - k;

          const int k2 = kx2 + nsparse2;
          const double *dlu2 = &dluval[k2];

          dv2 *= dpiv2;
          densew[k] = dv2; /* was dwork1[ipiv2]=dv2; */

          k--;

          /*
	   * The following loop is the unrolled version of:
	   *
	   * for (; k >= 0; k--) {
	   *   densew[k]-=dv1*dlu1[k]+dv2*dlu2[k];
	   * }
	   */
          if ((k & 1) == 0) {
            densew[k] -= dv1 * dlu1[k] + dv2 * dlu2[k];
            k--;
          }
          for (; k >= 0; k -= 2) {
            double da, db;
            da = densew[k];
            db = densew[k - 1];
            da -= dv1 * dlu1[k];
            db -= dv1 * dlu1[k - 1];
            da -= dv2 * dlu2[k];
            db -= dv2 * dlu2[k - 1];
            densew[k] = da;
            densew[k - 1] = db;
          }
          /* end loop */

          /*
	   * The following loop is the unrolled version of:
	   *
	   * for (iel=kx2+nsparse2-1; iel >= kx2; iel--) {
	   *   SHIFT_REF(dwork1, hrowi[iel]) -= dv2*dluval[iel];
	   * }
	   */
          iel = kx2 + nsparse2 - 1;
          if ((nsparse2 & 1) != 0) {
            int irow0 = hrowi[iel];
            double dval = dluval[iel];
            SHIFT_REF(dwork1, irow0) -= dv2 * dval;
            iel--;
          }
          for (; iel >= kx2; iel -= 2) {
            double dval0 = dluval[iel];
            double dval1 = dluval[iel - 1];
            int irow0 = hrowi[iel];
            int irow1 = hrowi[iel - 1];
            double d0 = SHIFT_REF(dwork1, irow0);
            double d1 = SHIFT_REF(dwork1, irow1);

            d0 -= dv2 * dval0;
            d1 -= dv2 * dval1;
            SHIFT_REF(dwork1, irow0) = d0;
            SHIFT_REF(dwork1, irow1) = d1;
          }
          /* end loop */

        } else {
          densew[k] = 0.0;
          /* skip if next deleted */
          k -= ipiv2 - ipiv - 1;
          ipiv2 = ipiv;
          if (ipiv < last) {
            k--;
            for (; k >= 0; k--) {
              double dval;
              dval = dv1 * dlu1[k];
              densew[k] = densew[k] - dval;
            }
          }
        }
      }

      /*
       * The following loop is the unrolled version of:
       *
       * for (iel=kx1+nsparse1-1; iel >= kx1; iel--) {
       *   SHIFT_REF(dwork1, hrowi[iel]) -= dv1*dluval[iel];
       * }
       */
      iel = kx1 + nsparse1 - 1;
      if ((nsparse1 & 1) != 0) {
        int irow0 = hrowi[iel];
        double dval = dluval[iel];
        SHIFT_REF(dwork1, irow0) -= dv1 * dval;
        iel--;
      }
      for (; iel >= kx1; iel -= 2) {
        double dval0 = dluval[iel];
        double dval1 = dluval[iel - 1];
        int irow0 = hrowi[iel];
        int irow1 = hrowi[iel - 1];
        double d0 = SHIFT_REF(dwork1, irow0);
        double d1 = SHIFT_REF(dwork1, irow1);

        d0 -= dv1 * dval0;
        d1 -= dv1 * dval1;
        SHIFT_REF(dwork1, irow0) = d0;
        SHIFT_REF(dwork1, irow1) = d1;
      }
      /* end loop */
    } else {
      dwork1[ipiv1] = 0.0;
    } /* endif */
  } /* endwhile */
  *start = ipiv;
}

/* do not use return value if mpt==0 */
/* using dual, this is usually called via c_ekkftrn_ft, from c_ekksdul
 * (so mpt is non-null).
 * it is generally called every iteration, but sometimes several iterations
 * are skipped (null moves?).
 *
 * generally, back[i] == i-1 (initialized in c_ekkshfv towards the end).
 */
static int c_ekkftjup(COIN_REGISTER3 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, int last,
  double *COIN_RESTRICT dworko, int *COIN_RESTRICT mpt)
{
  const double *COIN_RESTRICT dluval = fact->xeeadr;
  const int *COIN_RESTRICT hrowi = fact->xeradr;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr;
  const int *COIN_RESTRICT hpivro = fact->krpadr;
  double tolerance = fact->zeroTolerance;
  int ndenuc = fact->ndenuc;
  const int first_dense = fact->first_dense;
  const int last_dense = fact->last_dense;
  int i;
  int *mptX = mpt;

  const int nrow = fact->nrow;
  const int *COIN_RESTRICT back = fact->back;
  int ipiv = back[nrow + 1];

  if (last_dense > first_dense && mcstrt[ipiv] >= mcstrt[last_dense]) {
    c_ekkftjup_scan_aux(fact,
      dwork1, dworko, last_dense, &ipiv,
      &mptX);

    {
      int j;
      int n = 0;
      const int firstDense = nrow - ndenuc + 1;
      double *densew = &dwork1[firstDense];
      int offset;

      /* check first dense to see where in triangle it is */
      int last = first_dense;
      const int k1 = mcstrt[last];
      const int k2 = k1 + hrowi[k1];

      for (j = k2; j > k1; j--) {
        int irow = UNSHIFT_INDEX(hrowi[j]);
        if (irow < firstDense) {
          break;
        } else {
#ifdef DEBUG
          if (irow != last - 1) {
            abort();
          }
#endif
          last = irow;
          n++;
        }
      }
      offset = n - first_dense;
      i = ipiv;
      /* loop counter i may be modified by this call */
      c_ekkftju_dense(&dluval[1], &hrowi[1], mcstrt, back,
        dwork1, &i, first_dense, offset, densew);

      c_ekkftjup_aux3(fact, dwork1, dworko, back, hpivro, &ipiv, i, &mptX);
    }
  }

  c_ekkftjup_scan_aux(fact,
    dwork1, dworko, last, &ipiv,
    &mptX);

  if (ipiv != 0) {
    double dv = dwork1[ipiv];

    do {
      int next_ipiv = back[ipiv];
      double next_dv = dwork1[next_ipiv];

      dwork1[ipiv] = 0.0;

      if (fabs(dv) >= tolerance) {
        int iput = hpivro[ipiv];
        dworko[iput] = -dv;
        *mptX++ = iput - 1;
      }

      ipiv = next_ipiv;
      dv = next_dv;
    } while (ipiv != 0);
  }
  return static_cast< int >(mptX - mpt);
}
/* this assumes it is ok to reference back[loop_limit] */
/* another 3 seconds from a ~570 second run can be trimmed
 * by using two routines, one with scan==true and the other false,
 * since that eliminates the branch instructions involving them
 * entirely.  This was how the code was originally written.
 * However, I'm still hoping that eventually we can use
 * C++ templates to do that for us automatically.
 */
static void
c_ekkftjup_scan_aux_pack(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, double *COIN_RESTRICT dworko,
  int loop_limit, int *ip, int **mptp)
{
  double tolerance = fact->zeroTolerance;
  const double *dluval = fact->xeeadr + 1;
  const int *hrowi = fact->xeradr + 1;
  const int *mcstrt = fact->xcsadr;
  const int *hpivro = fact->krpadr;
  const int *back = fact->back;
  int ipiv = *ip;
  double dv = dwork1[ipiv];

  int *mptX = *mptp;
#if 0
  int inSlacks=0;
  int lastSlack;
  if (fact->numberSlacks!=0)
    lastSlack=fact->lastSlack;
  else
    lastSlack=0;
  if (c_ekk_IsSet(fact->bitArray,ipiv)) {
    printf("already in slacks - ipiv %d\n",ipiv);
    inSlacks=1;
    return;
  }
#endif
  assert(mptX);
  while (ipiv != loop_limit) {
    int next_ipiv = back[ipiv];
#if 0
    if (ipiv==lastSlack) {
      printf("now in slacks - ipiv %d\n",ipiv);
      inSlacks=1;
      break;
    }
    if (inSlacks) {
      assert (c_ekk_IsSet(fact->bitArray,ipiv));
      assert (dluval[mcstrt[ipiv]-1]==-1.0);
      assert (hrowi[mcstrt[ipiv]-1]==0);
    }
#endif
    dwork1[ipiv] = 0.0;
    /* invariant:  dv == dwork1[ipiv] */

    /* in the case of world.mps with dual, this condition is true
     * only 20-60% of the time. */
    if (fabs(dv) > tolerance) {
      const int kx = mcstrt[ipiv];
      const int nel = hrowi[kx - 1];
      const double dpiv = dluval[kx - 1];
#ifndef UNROLL5
#define UNROLL5 2
#endif
#if UNROLL5 > 1
      const int *hrowi2 = hrowi + kx;
      const int *hrowi2end = hrowi2 + nel;
      const double *dluval2 = dluval + kx;
#else
      int iel;
#endif

      dv *= dpiv;

      /*
       * The following loop is the unrolled version of this:
       *
       * for (iel = kx+1; iel <= kx + nel; iel++) {
       *   SHIFT_REF(dwork1, hrowi[iel]) -= dv * dluval[iel];
       * }
       */
#if UNROLL5 < 2
      iel = kx;
      if (nel & 1) {
        int irow = hrowi[iel];
        double dval = dluval[iel];
        SHIFT_REF(dwork1, irow) -= dv * dval;
        iel++;
      }
      for (; iel < kx + nel; iel += 2) {
        int irow0 = hrowi[iel];
        int irow1 = hrowi[iel + 1];
        double dval0 = dluval[iel];
        double dval1 = dluval[iel + 1];
        double d0 = SHIFT_REF(dwork1, irow0);
        double d1 = SHIFT_REF(dwork1, irow1);

        d0 -= dv * dval0;
        d1 -= dv * dval1;
        SHIFT_REF(dwork1, irow0) = d0;
        SHIFT_REF(dwork1, irow1) = d1;
      } /* end loop */
#else
      if ((nel & 1) != 0) {
        int irow = *hrowi2;
        double dval = *dluval2;
        SHIFT_REF(dwork1, irow) -= dv * dval;
        hrowi2++;
        dluval2++;
      }
      for (; hrowi2 < hrowi2end; hrowi2 += 2, dluval2 += 2) {
        int irow0 = hrowi2[0];
        int irow1 = hrowi2[1];
        double dval0 = dluval2[0];
        double dval1 = dluval2[1];
        double d0 = SHIFT_REF(dwork1, irow0);
        double d1 = SHIFT_REF(dwork1, irow1);

        d0 -= dv * dval0;
        d1 -= dv * dval1;
        SHIFT_REF(dwork1, irow0) = d0;
        SHIFT_REF(dwork1, irow1) = d1;
      }
#endif
      /* put this down here so that dv is less likely to cause a stall */
      if (fabs(dv) >= tolerance) {
        int iput = hpivro[ipiv];
        *dworko++ = dv;
        *mptX++ = iput - 1;
      }
    }

    dv = dwork1[next_ipiv];
    ipiv = next_ipiv;
  } /* endwhile */

  *mptp = mptX;
  *ip = ipiv;
}
static void c_ekkftjup_aux3_pack(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, double *COIN_RESTRICT dworko,
  const int *COIN_RESTRICT back,
  const int *COIN_RESTRICT hpivro,
  int *ipivp, int loop_limit,
  int **mptXp)

{
  double tolerance = fact->zeroTolerance;
  int ipiv = *ipivp;
  if (ipiv != loop_limit) {
    int *mptX = *mptXp;

    double dv = dwork1[ipiv];
    do {
      int next_ipiv = back[ipiv];
      double next_dv = dwork1[next_ipiv];

      dwork1[ipiv] = 0.0;

      if (fabs(dv) >= tolerance) {
        int iput = hpivro[ipiv];
        *dworko++ = dv;
        *mptX++ = iput - 1;
      }

      ipiv = next_ipiv;
      dv = next_dv;
    } while (ipiv != loop_limit);

    *mptXp = mptX;

    *ipivp = ipiv;
  }
}

/* do not use return value if mpt==0 */
/* using dual, this is usually called via c_ekkftrn_ft, from c_ekksdul
 * (so mpt is non-null).
 * it is generally called every iteration, but sometimes several iterations
 * are skipped (null moves?).
 *
 * generally, back[i] == i-1 (initialized in c_ekkshfv towards the end).
 */
static int c_ekkftjup_pack(COIN_REGISTER3 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1, int last,
  double *COIN_RESTRICT dworko, int *COIN_RESTRICT mpt)
{
  const double *COIN_RESTRICT dluval = fact->xeeadr;
  const int *COIN_RESTRICT hrowi = fact->xeradr;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr;
  const int *COIN_RESTRICT hpivro = fact->krpadr;
  double tolerance = fact->zeroTolerance;
  int ndenuc = fact->ndenuc;
  const int first_dense = fact->first_dense;
  const int last_dense = fact->last_dense;
  int *mptX = mpt;
  int *mptY = mpt;

  const int nrow = fact->nrow;
  const int *COIN_RESTRICT back = fact->back;
  int ipiv = back[nrow + 1];
  assert(mpt);

  if (last_dense > first_dense && mcstrt[ipiv] >= mcstrt[last_dense]) {
    c_ekkftjup_scan_aux_pack(fact,
      dwork1, dworko, last_dense, &ipiv,
      &mptX);
    /* adjust */
    dworko += (mptX - mpt);
    mpt = mptX;
    {
      int j;
      int n = 0;
      const int firstDense = nrow - ndenuc + 1;
      double *densew = &dwork1[firstDense];
      int offset;

      /* check first dense to see where in triangle it is */
      int last = first_dense;
      const int k1 = mcstrt[last];
      const int k2 = k1 + hrowi[k1];

      for (j = k2; j > k1; j--) {
        int irow = UNSHIFT_INDEX(hrowi[j]);
        if (irow < firstDense) {
          break;
        } else {
#ifdef DEBUG
          if (irow != last - 1) {
            abort();
          }
#endif
          last = irow;
          n++;
        }
      }
      offset = n - first_dense;
      int ipiv2 = ipiv;
      /* loop counter i may be modified by this call */
      c_ekkftju_dense(&dluval[1], &hrowi[1], mcstrt, back,
        dwork1, &ipiv2, first_dense, offset, densew);

      c_ekkftjup_aux3_pack(fact, dwork1, dworko, back, hpivro, &ipiv, ipiv2, &mptX);
      /* adjust dworko */
      dworko += (mptX - mpt);
      mpt = mptX;
    }
  }

  c_ekkftjup_scan_aux_pack(fact,
    dwork1, dworko, last, &ipiv,
    &mptX);
  /* adjust dworko */
  dworko += (mptX - mpt);
  while (ipiv != 0) {
    double dv = dwork1[ipiv];
    int next_ipiv = back[ipiv];

    dwork1[ipiv] = 0.0;

    if (fabs(dv) >= tolerance) {
      int iput = hpivro[ipiv];
      *dworko++ = -dv;
      *mptX++ = iput - 1;
    }

    ipiv = next_ipiv;
  }

  return static_cast< int >(mptX - mptY);
}
static int c_ekkftju_sparse_a(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  int *COIN_RESTRICT mpt,
  int nincol, int *COIN_RESTRICT spare)
{
  const int *COIN_RESTRICT hrowi = fact->xeradr + 1;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr;
  const int nrow = fact->nrow;
  char *COIN_RESTRICT nonzero = fact->nonzero;

  int k, nStack, kx, nel;
  int nList = 0;
  int iPivot;
  /*int kkk=nincol;*/
  int *COIN_RESTRICT list = spare;
  int *COIN_RESTRICT stack = spare + nrow;
  int *COIN_RESTRICT next = stack + nrow;
  for (k = 0; k < nincol; k++) {
    nStack = 1;
    iPivot = mpt[k];
    stack[0] = iPivot;
    next[0] = 0;
    while (nStack) {
      int kPivot, j;
      /* take off stack */
      kPivot = stack[--nStack];
      if (nonzero[kPivot] != 1) {
        kx = mcstrt[kPivot];
        nel = hrowi[kx - 1];
        j = next[nStack];
        if (j == nel) {
          /* finished so mark */
          list[nList++] = kPivot;
          nonzero[kPivot] = 1;
        } else {
          kPivot = hrowi[kx + j];
          /* put back on stack */
          next[nStack++]++;
          if (!nonzero[kPivot]) {
            /* and new one */
            stack[nStack] = kPivot;
            nonzero[kPivot] = 2;
            next[nStack++] = 0;
            /*kkk++;*/
          }
        }
      }
    }
  }
  return (nList);
}
static int c_ekkftju_sparse_b(COIN_REGISTER2 const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  double *COIN_RESTRICT dworko, int *COIN_RESTRICT mpt,
  int nList, int *COIN_RESTRICT spare)
{

  const double *COIN_RESTRICT dluval = fact->xeeadr + 1;
  const int *COIN_RESTRICT hrowi = fact->xeradr + 1;
  const int *COIN_RESTRICT mcstrt = fact->xcsadr;
  const int *COIN_RESTRICT hpivro = fact->krpadr;
  double tolerance = fact->zeroTolerance;
  char *COIN_RESTRICT nonzero = fact->nonzero;
  int i, k, kx, nel;
  int iPivot;
  /*int kkk=nincol;*/
  int *COIN_RESTRICT list = spare;
  i = nList - 1;
  nList = 0;
  for (; i >= 0; i--) {
    double dpiv;
    double dv;
    iPivot = list[i];
    /*printf("pivot %d %d\n",i,iPivot);*/
    dv = dwork1[iPivot];
    kx = mcstrt[iPivot];
    nel = hrowi[kx - 1];
    dwork1[iPivot] = 0.0;
    dpiv = dluval[kx - 1];
    dv *= dpiv;
    nonzero[iPivot] = 0;
    iPivot = hpivro[iPivot];
    if (fabs(dv) >= tolerance) {
      *dworko++ = dv;
      mpt[nList++] = iPivot - 1;
      for (k = kx; k < kx + nel; k++) {
        double dval;
        double dd;
        int irow = hrowi[k];
        dval = dluval[k];
        dd = dwork1[irow];
        dd -= dv * dval;
        dwork1[irow] = dd;
      }
    }
  }
  return (nList);
}
/* dwork1 = (B^-1)dwork1;
 * I think dpermu[1..nrow+1] is zeroed on exit (?)
 * I don't think it is expected to have any particular value on entry (?)
 */
int c_ekkftrn(COIN_REGISTER const EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1,
  double *COIN_RESTRICT dpermu, int *COIN_RESTRICT mpt, int numberNonZero)
{
  const int *COIN_RESTRICT mpermu = fact->mpermu;
  int lastNonZero;
  int firstNonZero = c_ekkshfpi_list2(mpermu + 1, dwork1 + 1, dpermu, mpt,
    numberNonZero, &lastNonZero);
  if (fact->nnentl && lastNonZero >= fact->firstLRow) {
    /* dpermu = (L^-1)dpermu */
    c_ekkftj4p(fact, dpermu, firstNonZero);
  }

  int lastSlack;

  /* dpermu = (R^-1) dpermu */
  c_ekkftjl(fact, dpermu);

  assert(fact->numberSlacks != 0 || !fact->lastSlack);
  lastSlack = fact->lastSlack;

  /* dwork1 = (U^-1)dpermu; dpermu zeroed (?) */
  return c_ekkftjup(fact,
    dpermu, lastSlack, dwork1, mpt);

} /* c_ekkftrn */

int c_ekkftrn_ft(COIN_REGISTER EKKfactinfo *COIN_RESTRICT2 fact,
  double *COIN_RESTRICT dwork1_ft, int *COIN_RESTRICT mpt_ft, int *nincolp_ft)
{
  double *COIN_RESTRICT dpermu_ft = fact->kadrpm;
  int *COIN_RESTRICT spare = reinterpret_cast< int * >(fact->kp1adr);
  int nincol = *nincolp_ft;

  int nuspik;
  double *COIN_RESTRICT dluvalPut = fact->xeeadr + fact->nnentu + 1;
  int *COIN_RESTRICT hrowiPut = fact->xeradr + fact->nnentu + 1;

  const int nrow = fact->nrow;
  /* mpermu contains the permutation */
  const int *COIN_RESTRICT mpermu = fact->mpermu;

  int lastSlack;

  int kdnspt = fact->nnetas - fact->nnentl;
  bool isRoom = (fact->nnentu + (nrow << 1) < (kdnspt - 2)
      + fact->R_etas_start[fact->nR_etas + 1]);

  /* say F-T will be sorted */
  fact->sortedEta = 1;

  assert(fact->numberSlacks != 0 || !fact->lastSlack);
  lastSlack = fact->lastSlack;
#ifdef CLP_REUSE_ETAS
  bool skipStuff = (fact->reintro >= 0);

  int save_nR_etas = fact->nR_etas;
  int *save_hpivcoR = fact->hpivcoR;
  int *save_R_etas_start = fact->R_etas_start;
  if (skipStuff) {
    // just move
    int *putSeq = fact->xrsadr + 2 * fact->nrowmx + 2;
    int *position = putSeq + fact->maxinv;
    int *putStart = position + fact->maxinv;
    memset(dwork1_ft, 0, nincol * sizeof(double));
    int iPiv = fact->reintro;
    int start = putStart[iPiv] & 0x7fffffff;
    int end = putStart[iPiv + 1] & 0x7fffffff;
    double *COIN_RESTRICT dluval = fact->xeeadr;
    int *COIN_RESTRICT hrowi = fact->xeradr;
    double dValue;
    if (fact->reintro < fact->nrow) {
      iPiv++;
      dValue = 1.0 / dluval[start++];
    } else {
      iPiv = hrowi[--end];
      dValue = dluval[end];
      start++;
      int ndoSkip = 0;
      for (int i = fact->nrow; i < fact->reintro; i++) {
        if ((putStart[i] & 0x80000000) == 0)
          ndoSkip++;
      }
      fact->nR_etas -= ndoSkip;
      fact->hpivcoR += ndoSkip;
      fact->R_etas_start += ndoSkip;
    }
    dpermu_ft[iPiv] = dValue;
    if (fact->if_sparse_update > 0 && DENSE_THRESHOLD < nrow) {
      nincol = 0;
      if (dValue)
        mpt_ft[nincol++] = iPiv;
      for (int i = start; i < end; i++) {
        int iRow = hrowi[i];
        dpermu_ft[iRow] = dluval[i];
        mpt_ft[nincol++] = iRow;
      }
    } else {
      for (int i = start; i < end; i++) {
        int iRow = hrowi[i];
        dpermu_ft[iRow] = dluval[i];
      }
    }
  }
#else
  bool skipStuff = false;
#endif
  if (fact->if_sparse_update > 0 && DENSE_THRESHOLD < nrow) {
    if (!skipStuff) {
      /* iterating so c_ekkgtcl will have list */
      /* in order for this to make sense, nonzero[1..nrow] must already be zeroed */
      c_ekkshfpi_list3(mpermu + 1, dwork1_ft, dpermu_ft, mpt_ft, nincol);

      /* it may be the case that the basis was entirely upper-triangular */
      if (fact->nnentl) {
        nincol = c_ekkftj4_sparse(fact,
          dpermu_ft, mpt_ft,
          nincol, spare);
      }
    }
    /*       DO ROW ETAS IN L */
    if (isRoom) {
      ++fact->nnentu;
      nincol = c_ekkftjl_sparse3(fact,
        dpermu_ft,
        mpt_ft, hrowiPut,
        dluvalPut, nincol);
      nuspik = nincol;
      /* temporary */
      /* say not sorted */
      fact->sortedEta = 0;
    } else {
      /* no room */
      nuspik = -3;
      nincol = c_ekkftjl_sparse2(fact,
        dpermu_ft,
        mpt_ft, nincol);
    }
    /*         DO U */
    if (DENSE_THRESHOLD > nrow - fact->numberSlacks) {
      nincol = c_ekkftjup_pack(fact,
        dpermu_ft, lastSlack, dwork1_ft,
        mpt_ft);
    } else {
      nincol = c_ekkftju_sparse_a(fact,
        mpt_ft,
        nincol, spare);
      nincol = c_ekkftju_sparse_b(fact,
        dpermu_ft,
        dwork1_ft, mpt_ft,
        nincol, spare);
    }
  } else {
    if (!skipStuff) {
      int lastNonZero;
      int firstNonZero = c_ekkshfpi_list(mpermu + 1, dwork1_ft, dpermu_ft,
        mpt_ft, nincol, &lastNonZero);
      if (fact->nnentl && lastNonZero >= fact->firstLRow) {
        /* dpermu_ft = (L^-1)dpermu_ft */
        c_ekkftj4p(fact, dpermu_ft, firstNonZero);
      }
    }

    /* dpermu_ft = (R^-1) dpermu_ft */
    c_ekkftjl(fact, dpermu_ft);

    if (isRoom) {

      /*        fake start to allow room for pivot */
      /* dluval[fact->nnentu...] = non-zeros of dpermu_ft;
       * hrowi[fact->nnentu..] = indices of these non-zeros;
       * near-zeros in dluval flattened
       */
      ++fact->nnentu;
      nincol = c_ekkscmv(fact, fact->nrow, dpermu_ft, hrowiPut,
        dluvalPut);

      /*
       * note that this is not the value of nincol determined by c_ekkftjup. 
       * For Forrest-Tomlin update we want vector before U
       * this vector will replace one in U
       */
      nuspik = nincol;
    } else {
      /* no room */
      nuspik = -3;
    }

    /* dwork1_ft = (U^-1)dpermu_ft; dpermu_ft zeroed (?) */
    nincol = c_ekkftjup_pack(fact,
      dpermu_ft, lastSlack, dwork1_ft, mpt_ft);
  }
#ifdef CLP_REUSE_ETAS
  fact->nR_etas = save_nR_etas;
  fact->hpivcoR = save_hpivcoR;
  fact->R_etas_start = save_R_etas_start;
#endif

  *nincolp_ft = nincol;
  return (nuspik);
} /* c_ekkftrn */
void c_ekkftrn2(COIN_REGISTER EKKfactinfo *COIN_RESTRICT2 fact, double *COIN_RESTRICT dwork1,
  double *COIN_RESTRICT dpermu1, int *COIN_RESTRICT mpt1, int *nincolp,
  double *COIN_RESTRICT dwork1_ft, int *COIN_RESTRICT mpt_ft, int *nincolp_ft)
{
  double *COIN_RESTRICT dluvalPut = fact->xeeadr + fact->nnentu + 1;
  int *COIN_RESTRICT hrowiPut = fact->xeradr + fact->nnentu + 1;

  const int nrow = fact->nrow;
  /* mpermu contains the permutation */
  const int *COIN_RESTRICT mpermu = fact->mpermu;

  int lastSlack;
  assert(fact->numberSlacks != 0 || !fact->lastSlack);
  lastSlack = fact->lastSlack;

  int nincol = *nincolp_ft;

  /* using dwork1 instead double *dpermu_ft = fact->kadrpm; */
  int *spare = reinterpret_cast< int * >(fact->kp1adr);

  int kdnspt = fact->nnetas - fact->nnentl;
  bool isRoom = (fact->nnentu + (nrow << 1) < (kdnspt - 2)
      + fact->R_etas_start[fact->nR_etas + 1]);
  /* say F-T will be sorted */
  fact->sortedEta = 1;
  int lastNonZero;
  int firstNonZero = c_ekkshfpi_list2(mpermu + 1, dwork1 + 1, dpermu1,
    mpt1, *nincolp, &lastNonZero);
  if (fact->nnentl && lastNonZero >= fact->firstLRow) {
    /* dpermu1 = (L^-1)dpermu1 */
    c_ekkftj4p(fact, dpermu1, firstNonZero);
  }

#ifdef CLP_REUSE_ETAS
  bool skipStuff = (fact->reintro >= 0);
  int save_nR_etas = fact->nR_etas;
  int *save_hpivcoR = fact->hpivcoR;
  int *save_R_etas_start = fact->R_etas_start;
  if (skipStuff) {
    // just move
    int *putSeq = fact->xrsadr + 2 * fact->nrowmx + 2;
    int *position = putSeq + fact->maxinv;
    int *putStart = position + fact->maxinv;
    memset(dwork1_ft, 0, nincol * sizeof(double));
    int iPiv = fact->reintro;
    int start = putStart[iPiv] & 0x7fffffff;
    int end = putStart[iPiv + 1] & 0x7fffffff;
    double *COIN_RESTRICT dluval = fact->xeeadr;
    int *COIN_RESTRICT hrowi = fact->xeradr;
    double dValue;
    if (fact->reintro < fact->nrow) {
      iPiv++;
      dValue = 1.0 / dluval[start++];
    } else {
      iPiv = hrowi[--end];
      dValue = dluval[end];
      start++;
      int ndoSkip = 0;
      for (int i = fact->nrow; i < fact->reintro; i++) {
        if ((putStart[i] & 0x80000000) == 0)
          ndoSkip++;
      }
      fact->nR_etas -= ndoSkip;
      fact->hpivcoR += ndoSkip;
      fact->R_etas_start += ndoSkip;
    }
    dwork1[iPiv] = dValue;
    if (fact->if_sparse_update > 0 && DENSE_THRESHOLD < nrow) {
      nincol = 0;
      if (dValue)
        mpt_ft[nincol++] = iPiv;
      for (int i = start; i < end; i++) {
        int iRow = hrowi[i];
        dwork1[iRow] = dluval[i];
        mpt_ft[nincol++] = iRow;
      }
    } else {
      for (int i = start; i < end; i++) {
        int iRow = hrowi[i];
        dwork1[iRow] = dluval[i];
      }
    }
  }
#else
  bool skipStuff = false;
#endif
  if (fact->if_sparse_update > 0 && DENSE_THRESHOLD < nrow) {
    if (!skipStuff) {
      /* iterating so c_ekkgtcl will have list */
      /* in order for this to make sense, nonzero[1..nrow] must already be zeroed */
      c_ekkshfpi_list3(mpermu + 1, dwork1_ft, dwork1, mpt_ft, nincol);

      /* it may be the case that the basis was entirely upper-triangular */
      if (fact->nnentl) {
        nincol = c_ekkftj4_sparse(fact,
          dwork1, mpt_ft,
          nincol, spare);
      }
    }
    /*       DO ROW ETAS IN L */
    if (isRoom) {
      ++fact->nnentu;
      nincol = c_ekkftjl_sparse3(fact,
        dwork1,
        mpt_ft, hrowiPut,
        dluvalPut,
        nincol);
      fact->nuspike = nincol;
      /* say not sorted */
      fact->sortedEta = 0;
    } else {
      /* no room */
      fact->nuspike = -3;
      nincol = c_ekkftjl_sparse2(fact,
        dwork1,
        mpt_ft, nincol);
    }
  } else {
    if (!skipStuff) {
      int lastNonZero;
      int firstNonZero = c_ekkshfpi_list(mpermu + 1, dwork1_ft, dwork1,
        mpt_ft, nincol, &lastNonZero);
      if (fact->nnentl && lastNonZero >= fact->firstLRow) {
        /* dpermu_ft = (L^-1)dpermu_ft */
        c_ekkftj4p(fact, dwork1, firstNonZero);
      }
    }
    c_ekkftjl(fact, dwork1);

    if (isRoom) {

      /*        fake start to allow room for pivot */
      /* dluval[fact->nnentu...] = non-zeros of dpermu_ft;
       * hrowi[fact->nnentu..] = indices of these non-zeros;
       * near-zeros in dluval flattened
       */
      ++fact->nnentu;
      nincol = c_ekkscmv(fact, fact->nrow, dwork1,
        hrowiPut,
        dluvalPut);

      /*
       * note that this is not the value of nincol determined by c_ekkftjup. 
       * For Forrest-Tomlin update we want vector before U
       * this vector will replace one in U
       */
      fact->nuspike = nincol;
    } else {
      /* no room */
      fact->nuspike = -3;
    }
  }
#ifdef CLP_REUSE_ETAS
  fact->nR_etas = save_nR_etas;
  fact->hpivcoR = save_hpivcoR;
  fact->R_etas_start = save_R_etas_start;
#endif

  /* dpermu1 = (R^-1) dpermu1 */
  c_ekkftjl(fact, dpermu1);

  /*         DO U */
  if (fact->if_sparse_update <= 0 || DENSE_THRESHOLD > nrow - fact->numberSlacks) {
    nincol = c_ekkftjup_pack(fact,
      dwork1, lastSlack, dwork1_ft, mpt_ft);
  } else {
    nincol = c_ekkftju_sparse_a(fact,
      mpt_ft,
      nincol, spare);
    nincol = c_ekkftju_sparse_b(fact,
      dwork1,
      dwork1_ft, mpt_ft,
      nincol, spare);
  }
  *nincolp_ft = nincol;
  /* dwork1 = (U^-1)dpermu1; dpermu1 zeroed (?) */
  *nincolp = c_ekkftjup(fact,
    dpermu1, lastSlack, dwork1, mpt1);
}
#endif

/* vi: softtabstop=2 shiftwidth=2 expandtab tabstop=2
*/
