resubmitting ode

1 files changed, 2007 insertions, 0 deletions

diff --git a/libraries/ode-0.9/ode/src/lcp.cpp b/libraries/ode-0.9/ode/src/lcp.cpp
new file mode 100644
index 0000000..d03d3e8
--- /dev/null
+++ b/libraries/ode-0.9/ode/src/lcp.cpp
@@ -0,0 +1,2007 @@
+/*************************************************************************
+ *                                                                       *
+ * Open Dynamics Engine, Copyright (C) 2001,2002 Russell L. Smith.       *
+ * All rights reserved.  Email: russ@q12.org   Web: www.q12.org          *
+ *                                                                       *
+ * This library is free software; you can redistribute it and/or         *
+ * modify it under the terms of EITHER:                                  *
+ *   (1) The GNU Lesser General Public License as published by the Free  *
+ *       Software Foundation; either version 2.1 of the License, or (at  *
+ *       your option) any later version. The text of the GNU Lesser      *
+ *       General Public License is included with this library in the     *
+ *       file LICENSE.TXT.                                               *
+ *   (2) The BSD-style license that is included with this library in     *
+ *       the file LICENSE-BSD.TXT.                                       *
+ *                                                                       *
+ * This library is distributed in the hope that it will be useful,       *
+ * but WITHOUT ANY WARRANTY; without even the implied warranty of        *
+ * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the files    *
+ * LICENSE.TXT and LICENSE-BSD.TXT for more details.                     *
+ *                                                                       *
+ *************************************************************************/
+
+/*
+
+
+THE ALGORITHM
+-------------
+
+solve A*x = b+w, with x and w subject to certain LCP conditions.
+each x(i),w(i) must lie on one of the three line segments in the following
+diagram. each line segment corresponds to one index set :
+
+     w(i)
+     /|\      |           :
+      |       |           :
+      |       |i in N     :
+  w>0 |       |state[i]=0 :
+      |       |           :
+      |       |           :  i in C
+  w=0 +       +-----------------------+
+      |                   :           |
+      |                   :           |
+  w<0 |                   :           |i in N
+      |                   :           |state[i]=1
+      |                   :           |
+      |                   :           |
+      +-------|-----------|-----------|----------> x(i)
+             lo           0           hi
+
+the Dantzig algorithm proceeds as follows:
+  for i=1:n
+    * if (x(i),w(i)) is not on the line, push x(i) and w(i) positive or
+      negative towards the line. as this is done, the other (x(j),w(j))
+      for j<i are constrained to be on the line. if any (x,w) reaches the
+      end of a line segment then it is switched between index sets.
+    * i is added to the appropriate index set depending on what line segment
+      it hits.
+
+we restrict lo(i) <= 0 and hi(i) >= 0. this makes the algorithm a bit
+simpler, because the starting point for x(i),w(i) is always on the dotted
+line x=0 and x will only ever increase in one direction, so it can only hit
+two out of the three line segments.
+
+
+NOTES
+-----
+
+this is an implementation of "lcp_dantzig2_ldlt.m" and "lcp_dantzig_lohi.m".
+the implementation is split into an LCP problem object (dLCP) and an LCP
+driver function. most optimization occurs in the dLCP object.
+
+a naive implementation of the algorithm requires either a lot of data motion
+or a lot of permutation-array lookup, because we are constantly re-ordering
+rows and columns. to avoid this and make a more optimized algorithm, a
+non-trivial data structure is used to represent the matrix A (this is
+implemented in the fast version of the dLCP object).
+
+during execution of this algorithm, some indexes in A are clamped (set C),
+some are non-clamped (set N), and some are "don't care" (where x=0).
+A,x,b,w (and other problem vectors) are permuted such that the clamped
+indexes are first, the unclamped indexes are next, and the don't-care
+indexes are last. this permutation is recorded in the array `p'.
+initially p = 0..n-1, and as the rows and columns of A,x,b,w are swapped,
+the corresponding elements of p are swapped.
+
+because the C and N elements are grouped together in the rows of A, we can do
+lots of work with a fast dot product function. if A,x,etc were not permuted
+and we only had a permutation array, then those dot products would be much
+slower as we would have a permutation array lookup in some inner loops.
+
+A is accessed through an array of row pointers, so that element (i,j) of the
+permuted matrix is A[i][j]. this makes row swapping fast. for column swapping
+we still have to actually move the data.
+
+during execution of this algorithm we maintain an L*D*L' factorization of
+the clamped submatrix of A (call it `AC') which is the top left nC*nC
+submatrix of A. there are two ways we could arrange the rows/columns in AC.
+
+(1) AC is always permuted such that L*D*L' = AC. this causes a problem
+    when a row/column is removed from C, because then all the rows/columns of A
+    between the deleted index and the end of C need to be rotated downward.
+    this results in a lot of data motion and slows things down.
+(2) L*D*L' is actually a factorization of a *permutation* of AC (which is
+    itself a permutation of the underlying A). this is what we do - the
+    permutation is recorded in the vector C. call this permutation A[C,C].
+    when a row/column is removed from C, all we have to do is swap two
+    rows/columns and manipulate C.
+
+*/
+
+#include <ode/common.h>
+#include "lcp.h"
+#include <ode/matrix.h>
+#include <ode/misc.h>
+#include "mat.h"                // for testing
+#include <ode/timer.h>          // for testing
+
+//***************************************************************************
+// code generation parameters
+
+// LCP debugging (mosty for fast dLCP) - this slows things down a lot
+//#define DEBUG_LCP
+
+//#define dLCP_SLOW             // use slow dLCP object
+#define dLCP_FAST               // use fast dLCP object
+
+// option 1 : matrix row pointers (less data copying)
+#define ROWPTRS
+#define ATYPE dReal **
+#define AROW(i) (A[i])
+
+// option 2 : no matrix row pointers (slightly faster inner loops)
+//#define NOROWPTRS
+//#define ATYPE dReal *
+//#define AROW(i) (A+(i)*nskip)
+
+// use protected, non-stack memory allocation system
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+extern unsigned int dMemoryFlag;
+
+#define ALLOCA(t,v,s) t* v = (t*) malloc(s)
+#define UNALLOCA(t)  free(t)
+
+#else
+
+#define ALLOCA(t,v,s) t* v =(t*)dALLOCA16(s)
+#define UNALLOCA(t)  /* nothing */
+
+#endif
+
+#define NUB_OPTIMIZATIONS
+
+//***************************************************************************
+
+// swap row/column i1 with i2 in the n*n matrix A. the leading dimension of
+// A is nskip. this only references and swaps the lower triangle.
+// if `do_fast_row_swaps' is nonzero and row pointers are being used, then
+// rows will be swapped by exchanging row pointers. otherwise the data will
+// be copied.
+
+static void swapRowsAndCols (ATYPE A, int n, int i1, int i2, int nskip,
+                             int do_fast_row_swaps)
+{
+  int i;
+  dAASSERT (A && n > 0 && i1 >= 0 && i2 >= 0 && i1 < n && i2 < n &&
+            nskip >= n && i1 < i2);
+
+# ifdef ROWPTRS
+  for (i=i1+1; i<i2; i++) A[i1][i] = A[i][i1];
+  for (i=i1+1; i<i2; i++) A[i][i1] = A[i2][i];
+  A[i1][i2] = A[i1][i1];
+  A[i1][i1] = A[i2][i1];
+  A[i2][i1] = A[i2][i2];
+  // swap rows, by swapping row pointers
+  if (do_fast_row_swaps) {
+    dReal *tmpp;
+    tmpp = A[i1];
+    A[i1] = A[i2];
+    A[i2] = tmpp;
+  }
+  else {
+    ALLOCA (dReal,tmprow,n * sizeof(dReal));
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (tmprow == NULL) {
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;      
+      return;
+    }
+#endif
+
+    memcpy (tmprow,A[i1],n * sizeof(dReal));
+    memcpy (A[i1],A[i2],n * sizeof(dReal));
+    memcpy (A[i2],tmprow,n * sizeof(dReal));
+    UNALLOCA(tmprow);
+  }
+  // swap columns the hard way
+  for (i=i2+1; i<n; i++) {
+    dReal tmp = A[i][i1];
+    A[i][i1] = A[i][i2];
+    A[i][i2] = tmp;
+  }
+# else
+  dReal tmp;
+  ALLOCA (dReal,tmprow,n * sizeof(dReal));
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+  if (tmprow == NULL) {
+    return;
+  }
+#endif
+
+  if (i1 > 0) {
+    memcpy (tmprow,A+i1*nskip,i1*sizeof(dReal));
+    memcpy (A+i1*nskip,A+i2*nskip,i1*sizeof(dReal));
+    memcpy (A+i2*nskip,tmprow,i1*sizeof(dReal));
+  }
+  for (i=i1+1; i<i2; i++) {
+    tmp = A[i2*nskip+i];
+    A[i2*nskip+i] = A[i*nskip+i1];
+    A[i*nskip+i1] = tmp;
+  }
+  tmp = A[i1*nskip+i1];
+  A[i1*nskip+i1] = A[i2*nskip+i2];
+  A[i2*nskip+i2] = tmp;
+  for (i=i2+1; i<n; i++) {
+    tmp = A[i*nskip+i1];
+    A[i*nskip+i1] = A[i*nskip+i2];
+    A[i*nskip+i2] = tmp;
+  }
+  UNALLOCA(tmprow);
+# endif
+
+}
+
+
+// swap two indexes in the n*n LCP problem. i1 must be <= i2.
+
+static void swapProblem (ATYPE A, dReal *x, dReal *b, dReal *w, dReal *lo,
+                         dReal *hi, int *p, int *state, int *findex,
+                         int n, int i1, int i2, int nskip,
+                         int do_fast_row_swaps)
+{
+  dReal tmp;
+  int tmpi;
+  dIASSERT (n>0 && i1 >=0 && i2 >= 0 && i1 < n && i2 < n && nskip >= n &&
+            i1 <= i2);
+  if (i1==i2) return;
+  swapRowsAndCols (A,n,i1,i2,nskip,do_fast_row_swaps);
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+  if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY)
+    return;
+#endif
+  tmp = x[i1];
+  x[i1] = x[i2];
+  x[i2] = tmp;
+  tmp = b[i1];
+  b[i1] = b[i2];
+  b[i2] = tmp;
+  tmp = w[i1];
+  w[i1] = w[i2];
+  w[i2] = tmp;
+  tmp = lo[i1];
+  lo[i1] = lo[i2];
+  lo[i2] = tmp;
+  tmp = hi[i1];
+  hi[i1] = hi[i2];
+  hi[i2] = tmp;
+  tmpi = p[i1];
+  p[i1] = p[i2];
+  p[i2] = tmpi;
+  tmpi = state[i1];
+  state[i1] = state[i2];
+  state[i2] = tmpi;
+  if (findex) {
+    tmpi = findex[i1];
+    findex[i1] = findex[i2];
+    findex[i2] = tmpi;
+  }
+}
+
+
+// for debugging - check that L,d is the factorization of A[C,C].
+// A[C,C] has size nC*nC and leading dimension nskip.
+// L has size nC*nC and leading dimension nskip.
+// d has size nC.
+
+#ifdef DEBUG_LCP
+
+static void checkFactorization (ATYPE A, dReal *_L, dReal *_d,
+                                int nC, int *C, int nskip)
+{
+  int i,j;
+  if (nC==0) return;
+
+  // get A1=A, copy the lower triangle to the upper triangle, get A2=A[C,C]
+  dMatrix A1 (nC,nC);
+  for (i=0; i<nC; i++) {
+    for (j=0; j<=i; j++) A1(i,j) = A1(j,i) = AROW(i)[j];
+  }
+  dMatrix A2 = A1.select (nC,C,nC,C);
+
+  // printf ("A1=\n"); A1.print(); printf ("\n");
+  // printf ("A2=\n"); A2.print(); printf ("\n");
+
+  // compute A3 = L*D*L'
+  dMatrix L (nC,nC,_L,nskip,1);
+  dMatrix D (nC,nC);
+  for (i=0; i<nC; i++) D(i,i) = 1/_d[i];
+  L.clearUpperTriangle();
+  for (i=0; i<nC; i++) L(i,i) = 1;
+  dMatrix A3 = L * D * L.transpose();
+
+  // printf ("L=\n"); L.print(); printf ("\n");
+  // printf ("D=\n"); D.print(); printf ("\n");
+  // printf ("A3=\n"); A2.print(); printf ("\n");
+
+  // compare A2 and A3
+  dReal diff = A2.maxDifference (A3);
+  if (diff > 1e-8)
+    dDebug (0,"L*D*L' check, maximum difference = %.6e\n",diff);
+}
+
+#endif
+
+
+// for debugging
+
+#ifdef DEBUG_LCP
+
+static void checkPermutations (int i, int n, int nC, int nN, int *p, int *C)
+{
+  int j,k;
+  dIASSERT (nC>=0 && nN>=0 && (nC+nN)==i && i < n);
+  for (k=0; k<i; k++) dIASSERT (p[k] >= 0 && p[k] < i);
+  for (k=i; k<n; k++) dIASSERT (p[k] == k);
+  for (j=0; j<nC; j++) {
+    int C_is_bad = 1;
+    for (k=0; k<nC; k++) if (C[k]==j) C_is_bad = 0;
+    dIASSERT (C_is_bad==0);
+  }
+}
+
+#endif
+
+//***************************************************************************
+// dLCP manipulator object. this represents an n*n LCP problem.
+//
+// two index sets C and N are kept. each set holds a subset of
+// the variable indexes 0..n-1. an index can only be in one set.
+// initially both sets are empty.
+//
+// the index set C is special: solutions to A(C,C)\A(C,i) can be generated.
+
+#ifdef dLCP_SLOW
+
+// simple but slow implementation of dLCP, for testing the LCP drivers.
+
+#include "array.h"
+
+struct dLCP {
+  int n,nub,nskip;
+  dReal *Adata,*x,*b,*w,*lo,*hi;        // LCP problem data
+  ATYPE A;                              // A rows
+  dArray<int> C,N;                      // index sets
+  int last_i_for_solve1;                // last i value given to solve1
+
+  dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
+        dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
+        dReal *_Dell, dReal *_ell, dReal *_tmp,
+        int *_state, int *_findex, int *_p, int *_C, dReal **Arows);
+  // the constructor is given an initial problem description (A,x,b,w) and
+  // space for other working data (which the caller may allocate on the stack).
+  // some of this data is specific to the fast dLCP implementation.
+  // the matrices A and L have size n*n, vectors have size n*1.
+  // A represents a symmetric matrix but only the lower triangle is valid.
+  // `nub' is the number of unbounded indexes at the start. all the indexes
+  // 0..nub-1 will be put into C.
+
+  ~dLCP();
+
+  int getNub() { return nub; }
+  // return the value of `nub'. the constructor may want to change it,
+  // so the caller should find out its new value.
+
+  // transfer functions: transfer index i to the given set (C or N). indexes
+  // less than `nub' can never be given. A,x,b,w,etc may be permuted by these
+  // functions, the caller must be robust to this.
+
+  void transfer_i_to_C (int i);
+    // this assumes C and N span 1:i-1. this also assumes that solve1() has
+    // been recently called for the same i without any other transfer
+    // functions in between (thereby allowing some data reuse for the fast
+    // implementation).
+  void transfer_i_to_N (int i);
+    // this assumes C and N span 1:i-1.
+  void transfer_i_from_N_to_C (int i);
+  void transfer_i_from_C_to_N (int i);
+
+  int numC();
+  int numN();
+  // return the number of indexes in set C/N
+
+  int indexC (int i);
+  int indexN (int i);
+  // return index i in set C/N.
+
+  // accessor and arithmetic functions. Aij translates as A(i,j), etc.
+  // make sure that only the lower triangle of A is ever referenced.
+
+  dReal Aii (int i);
+  dReal AiC_times_qC (int i, dReal *q);
+  dReal AiN_times_qN (int i, dReal *q);                 // for all Nj
+  void pN_equals_ANC_times_qC (dReal *p, dReal *q);     // for all Nj
+  void pN_plusequals_ANi (dReal *p, int i, int sign=1);
+    // for all Nj. sign = +1,-1. assumes i > maximum index in N.
+  void pC_plusequals_s_times_qC (dReal *p, dReal s, dReal *q);
+  void pN_plusequals_s_times_qN (dReal *p, dReal s, dReal *q); // for all Nj
+  void solve1 (dReal *a, int i, int dir=1, int only_transfer=0);
+    // get a(C) = - dir * A(C,C) \ A(C,i). dir must be +/- 1.
+    // the fast version of this function computes some data that is needed by
+    // transfer_i_to_C(). if only_transfer is nonzero then this function
+    // *only* computes that data, it does not set a(C).
+
+  void unpermute();
+  // call this at the end of the LCP function. if the x/w values have been
+  // permuted then this will unscramble them.
+};
+
+
+dLCP::dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
+            dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
+            dReal *_Dell, dReal *_ell, dReal *_tmp,
+            int *_state, int *_findex, int *_p, int *_C, dReal **Arows)
+{
+  dUASSERT (_findex==0,"slow dLCP object does not support findex array");
+
+  n = _n;
+  nub = _nub;
+  Adata = _Adata;
+  A = 0;
+  x = _x;
+  b = _b;
+  w = _w;
+  lo = _lo;
+  hi = _hi;
+  nskip = dPAD(n);
+  dSetZero (x,n);
+  last_i_for_solve1 = -1;
+
+  int i,j;
+  C.setSize (n);
+  N.setSize (n);
+  for (i=0; i<n; i++) {
+    C[i] = 0;
+    N[i] = 0;
+  }
+
+# ifdef ROWPTRS
+  // make matrix row pointers
+  A = Arows;
+  for (i=0; i<n; i++) A[i] = Adata + i*nskip;
+# else
+  A = Adata;
+# endif
+
+  // lets make A symmetric
+  for (i=0; i<n; i++) {
+    for (j=i+1; j<n; j++) AROW(i)[j] = AROW(j)[i];
+  }
+
+  // if nub>0, put all indexes 0..nub-1 into C and solve for x
+  if (nub > 0) {
+    for (i=0; i<nub; i++) memcpy (_L+i*nskip,AROW(i),(i+1)*sizeof(dReal));
+    dFactorLDLT (_L,_d,nub,nskip);
+    memcpy (x,b,nub*sizeof(dReal));
+    dSolveLDLT (_L,_d,x,nub,nskip);
+    dSetZero (_w,nub);
+    for (i=0; i<nub; i++) C[i] = 1;
+  }
+}
+
+
+dLCP::~dLCP()
+{
+}
+
+
+void dLCP::transfer_i_to_C (int i)
+{
+  if (i < nub) dDebug (0,"bad i");
+  if (C[i]) dDebug (0,"i already in C");
+  if (N[i]) dDebug (0,"i already in N");
+  for (int k=0; k<i; k++) {
+    if (!(C[k] ^ N[k])) dDebug (0,"assumptions for C and N violated");
+  }
+  for (int k=i; k<n; k++)
+    if (C[k] || N[k]) dDebug (0,"assumptions for C and N violated");
+  if (i != last_i_for_solve1) dDebug (0,"assumptions for i violated");
+  last_i_for_solve1 = -1;
+  C[i] = 1;
+}
+
+
+void dLCP::transfer_i_to_N (int i)
+{
+  if (i < nub) dDebug (0,"bad i");
+  if (C[i]) dDebug (0,"i already in C");
+  if (N[i]) dDebug (0,"i already in N");
+  for (int k=0; k<i; k++)
+    if (!C[k] && !N[k]) dDebug (0,"assumptions for C and N violated");
+  for (int k=i; k<n; k++)
+    if (C[k] || N[k]) dDebug (0,"assumptions for C and N violated");
+  last_i_for_solve1 = -1;
+  N[i] = 1;
+}
+
+
+void dLCP::transfer_i_from_N_to_C (int i)
+{
+  if (i < nub) dDebug (0,"bad i");
+  if (C[i]) dDebug (0,"i already in C");
+  if (!N[i]) dDebug (0,"i not in N");
+  last_i_for_solve1 = -1;
+  N[i] = 0;
+  C[i] = 1;
+}
+
+
+void dLCP::transfer_i_from_C_to_N (int i)
+{
+  if (i < nub) dDebug (0,"bad i");
+  if (N[i]) dDebug (0,"i already in N");
+  if (!C[i]) dDebug (0,"i not in C");
+  last_i_for_solve1 = -1;
+  C[i] = 0;
+  N[i] = 1;
+}
+
+
+int dLCP::numC()
+{
+  int i,count=0;
+  for (i=0; i<n; i++) if (C[i]) count++;
+  return count;
+}
+
+
+int dLCP::numN()
+{
+  int i,count=0;
+  for (i=0; i<n; i++) if (N[i]) count++;
+  return count;
+}
+
+
+int dLCP::indexC (int i)
+{
+  int k,count=0;
+  for (k=0; k<n; k++) {
+    if (C[k]) {
+      if (count==i) return k;
+      count++;
+    }
+  }
+  dDebug (0,"bad index C (%d)",i);
+  return 0;
+}
+
+
+int dLCP::indexN (int i)
+{
+  int k,count=0;
+  for (k=0; k<n; k++) {
+    if (N[k]) {
+      if (count==i) return k;
+      count++;
+    }
+  }
+  dDebug (0,"bad index into N");
+  return 0;
+}
+
+
+dReal dLCP::Aii (int i)
+{
+  return AROW(i)[i];
+}
+
+
+dReal dLCP::AiC_times_qC (int i, dReal *q)
+{
+  dReal sum = 0;
+  for (int k=0; k<n; k++) if (C[k]) sum += AROW(i)[k] * q[k];
+  return sum;
+}
+
+
+dReal dLCP::AiN_times_qN (int i, dReal *q)
+{
+  dReal sum = 0;
+  for (int k=0; k<n; k++) if (N[k]) sum += AROW(i)[k] * q[k];
+  return sum;
+}
+
+
+void dLCP::pN_equals_ANC_times_qC (dReal *p, dReal *q)
+{
+  dReal sum;
+  for (int ii=0; ii<n; ii++) if (N[ii]) {
+    sum = 0;
+    for (int jj=0; jj<n; jj++) if (C[jj]) sum += AROW(ii)[jj] * q[jj];
+    p[ii] = sum;
+  }
+}
+
+
+void dLCP::pN_plusequals_ANi (dReal *p, int i, int sign)
+{
+  int k;
+  for (k=0; k<n; k++) if (N[k] && k >= i) dDebug (0,"N assumption violated");
+  if (sign > 0) {
+    for (k=0; k<n; k++) if (N[k]) p[k] += AROW(i)[k];
+  }
+  else {
+    for (k=0; k<n; k++) if (N[k]) p[k] -= AROW(i)[k];
+  }
+}
+
+
+void dLCP::pC_plusequals_s_times_qC (dReal *p, dReal s, dReal *q)
+{
+  for (int k=0; k<n; k++) if (C[k]) p[k] += s*q[k];
+}
+
+
+void dLCP::pN_plusequals_s_times_qN (dReal *p, dReal s, dReal *q)
+{
+  for (int k=0; k<n; k++) if (N[k]) p[k] += s*q[k];
+}
+
+
+void dLCP::solve1 (dReal *a, int i, int dir, int only_transfer)
+{
+
+  ALLOCA (dReal,AA,n*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (AA == NULL) {
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,dd,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (dd == NULL) {
+      UNALLOCA(AA);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,bb,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (bb == NULL) {
+      UNALLOCA(AA);
+      UNALLOCA(dd);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+
+  int ii,jj,AAi,AAj;
+
+  last_i_for_solve1 = i;
+  AAi = 0;
+  for (ii=0; ii<n; ii++) if (C[ii]) {
+    AAj = 0;
+    for (jj=0; jj<n; jj++) if (C[jj]) {
+      AA[AAi*nskip+AAj] = AROW(ii)[jj];
+      AAj++;
+    }
+    bb[AAi] = AROW(i)[ii];
+    AAi++;
+  }
+  if (AAi==0) {
+      UNALLOCA (AA);
+      UNALLOCA (dd);
+      UNALLOCA (bb);
+      return;
+  }
+
+  dFactorLDLT (AA,dd,AAi,nskip);
+  dSolveLDLT (AA,dd,bb,AAi,nskip);
+
+  AAi=0;
+  if (dir > 0) {
+    for (ii=0; ii<n; ii++) if (C[ii]) a[ii] = -bb[AAi++];
+  }
+  else {
+    for (ii=0; ii<n; ii++) if (C[ii]) a[ii] = bb[AAi++];
+  }
+
+  UNALLOCA (AA);
+  UNALLOCA (dd);
+  UNALLOCA (bb);
+}
+
+
+void dLCP::unpermute()
+{
+}
+
+#endif // dLCP_SLOW
+
+//***************************************************************************
+// fast implementation of dLCP. see the above definition of dLCP for
+// interface comments.
+//
+// `p' records the permutation of A,x,b,w,etc. p is initially 1:n and is
+// permuted as the other vectors/matrices are permuted.
+//
+// A,x,b,w,lo,hi,state,findex,p,c are permuted such that sets C,N have
+// contiguous indexes. the don't-care indexes follow N.
+//
+// an L*D*L' factorization is maintained of A(C,C), and whenever indexes are
+// added or removed from the set C the factorization is updated.
+// thus L*D*L'=A[C,C], i.e. a permuted top left nC*nC submatrix of A.
+// the leading dimension of the matrix L is always `nskip'.
+//
+// at the start there may be other indexes that are unbounded but are not
+// included in `nub'. dLCP will permute the matrix so that absolutely all
+// unbounded vectors are at the start. thus there may be some initial
+// permutation.
+//
+// the algorithms here assume certain patterns, particularly with respect to
+// index transfer.
+
+#ifdef dLCP_FAST
+
+struct dLCP {
+  int n,nskip,nub;
+  ATYPE A;                              // A rows
+  dReal *Adata,*x,*b,*w,*lo,*hi;        // permuted LCP problem data
+  dReal *L,*d;                          // L*D*L' factorization of set C
+  dReal *Dell,*ell,*tmp;
+  int *state,*findex,*p,*C;
+  int nC,nN;                            // size of each index set
+
+  dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
+        dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
+        dReal *_Dell, dReal *_ell, dReal *_tmp,
+        int *_state, int *_findex, int *_p, int *_C, dReal **Arows);
+  int getNub() { return nub; }
+  void transfer_i_to_C (int i);
+  void transfer_i_to_N (int i)
+    { nN++; }                   // because we can assume C and N span 1:i-1
+  void transfer_i_from_N_to_C (int i);
+  void transfer_i_from_C_to_N (int i);
+  int numC() { return nC; }
+  int numN() { return nN; }
+  int indexC (int i) { return i; }
+  int indexN (int i) { return i+nC; }
+  dReal Aii (int i) { return AROW(i)[i]; }
+  dReal AiC_times_qC (int i, dReal *q) { return dDot (AROW(i),q,nC); }
+  dReal AiN_times_qN (int i, dReal *q) { return dDot (AROW(i)+nC,q+nC,nN); }
+  void pN_equals_ANC_times_qC (dReal *p, dReal *q);
+  void pN_plusequals_ANi (dReal *p, int i, int sign=1);
+  void pC_plusequals_s_times_qC (dReal *p, dReal s, dReal *q)
+    { for (int i=0; i<nC; i++) p[i] += s*q[i]; }
+  void pN_plusequals_s_times_qN (dReal *p, dReal s, dReal *q)
+    { for (int i=0; i<nN; i++) p[i+nC] += s*q[i+nC]; }
+  void solve1 (dReal *a, int i, int dir=1, int only_transfer=0);
+  void unpermute();
+};
+
+
+dLCP::dLCP (int _n, int _nub, dReal *_Adata, dReal *_x, dReal *_b, dReal *_w,
+            dReal *_lo, dReal *_hi, dReal *_L, dReal *_d,
+            dReal *_Dell, dReal *_ell, dReal *_tmp,
+            int *_state, int *_findex, int *_p, int *_C, dReal **Arows)
+{
+  n = _n;
+  nub = _nub;
+  Adata = _Adata;
+  A = 0;
+  x = _x;
+  b = _b;
+  w = _w;
+  lo = _lo;
+  hi = _hi;
+  L = _L;
+  d = _d;
+  Dell = _Dell;
+  ell = _ell;
+  tmp = _tmp;
+  state = _state;
+  findex = _findex;
+  p = _p;
+  C = _C;
+  nskip = dPAD(n);
+  dSetZero (x,n);
+
+  int k;
+
+# ifdef ROWPTRS
+  // make matrix row pointers
+  A = Arows;
+  for (k=0; k<n; k++) A[k] = Adata + k*nskip;
+# else
+  A = Adata;
+# endif
+
+  nC = 0;
+  nN = 0;
+  for (k=0; k<n; k++) p[k]=k;           // initially unpermuted
+
+  /*
+  // for testing, we can do some random swaps in the area i > nub
+  if (nub < n) {
+    for (k=0; k<100; k++) {
+      int i1,i2;
+      do {
+        i1 = dRandInt(n-nub)+nub;
+        i2 = dRandInt(n-nub)+nub;
+      }
+      while (i1 > i2); 
+      //printf ("--> %d %d\n",i1,i2);
+      swapProblem (A,x,b,w,lo,hi,p,state,findex,n,i1,i2,nskip,0);
+    }
+  }
+  */
+
+  // permute the problem so that *all* the unbounded variables are at the
+  // start, i.e. look for unbounded variables not included in `nub'. we can
+  // potentially push up `nub' this way and get a bigger initial factorization.
+  // note that when we swap rows/cols here we must not just swap row pointers,
+  // as the initial factorization relies on the data being all in one chunk.
+  // variables that have findex >= 0 are *not* considered to be unbounded even
+  // if lo=-inf and hi=inf - this is because these limits may change during the
+  // solution process.
+
+  for (k=nub; k<n; k++) {
+    if (findex && findex[k] >= 0) continue;
+    if (lo[k]==-dInfinity && hi[k]==dInfinity) {
+      swapProblem (A,x,b,w,lo,hi,p,state,findex,n,nub,k,nskip,0);
+      nub++;
+    }
+  }
+
+  // if there are unbounded variables at the start, factorize A up to that
+  // point and solve for x. this puts all indexes 0..nub-1 into C.
+  if (nub > 0) {
+    for (k=0; k<nub; k++) memcpy (L+k*nskip,AROW(k),(k+1)*sizeof(dReal));
+    dFactorLDLT (L,d,nub,nskip);
+    memcpy (x,b,nub*sizeof(dReal));
+    dSolveLDLT (L,d,x,nub,nskip);
+    dSetZero (w,nub);
+    for (k=0; k<nub; k++) C[k] = k;
+    nC = nub;
+  }
+
+  // permute the indexes > nub such that all findex variables are at the end
+  if (findex) {
+    int num_at_end = 0;
+    for (k=n-1; k >= nub; k--) {
+      if (findex[k] >= 0) {
+        swapProblem (A,x,b,w,lo,hi,p,state,findex,n,k,n-1-num_at_end,nskip,1);
+        num_at_end++;
+      }
+    }
+  }
+
+  // print info about indexes
+  /*
+  for (k=0; k<n; k++) {
+    if (k<nub) printf ("C");
+    else if (lo[k]==-dInfinity && hi[k]==dInfinity) printf ("c");
+    else printf (".");
+  }
+  printf ("\n");
+  */
+}
+
+
+void dLCP::transfer_i_to_C (int i)
+{
+  int j;
+  if (nC > 0) {
+    // ell,Dell were computed by solve1(). note, ell = D \ L1solve (L,A(i,C))
+    for (j=0; j<nC; j++) L[nC*nskip+j] = ell[j];
+    d[nC] = dRecip (AROW(i)[i] - dDot(ell,Dell,nC));
+  }
+  else {
+    d[0] = dRecip (AROW(i)[i]);
+  }
+  swapProblem (A,x,b,w,lo,hi,p,state,findex,n,nC,i,nskip,1);
+  C[nC] = nC;
+  nC++;
+
+# ifdef DEBUG_LCP
+  checkFactorization (A,L,d,nC,C,nskip);
+  if (i < (n-1)) checkPermutations (i+1,n,nC,nN,p,C);
+# endif
+}
+
+
+void dLCP::transfer_i_from_N_to_C (int i)
+{
+  int j;
+  if (nC > 0) {
+    dReal *aptr = AROW(i);
+#   ifdef NUB_OPTIMIZATIONS
+    // if nub>0, initial part of aptr unpermuted
+    for (j=0; j<nub; j++) Dell[j] = aptr[j];
+    for (j=nub; j<nC; j++) Dell[j] = aptr[C[j]];
+#   else
+    for (j=0; j<nC; j++) Dell[j] = aptr[C[j]];
+#   endif
+    dSolveL1 (L,Dell,nC,nskip);
+    for (j=0; j<nC; j++) ell[j] = Dell[j] * d[j];
+    for (j=0; j<nC; j++) L[nC*nskip+j] = ell[j];
+    d[nC] = dRecip (AROW(i)[i] - dDot(ell,Dell,nC));
+  }
+  else {
+    d[0] = dRecip (AROW(i)[i]);
+  }
+  swapProblem (A,x,b,w,lo,hi,p,state,findex,n,nC,i,nskip,1);
+  C[nC] = nC;
+  nN--;
+  nC++;
+
+  // @@@ TO DO LATER
+  // if we just finish here then we'll go back and re-solve for
+  // delta_x. but actually we can be more efficient and incrementally
+  // update delta_x here. but if we do this, we wont have ell and Dell
+  // to use in updating the factorization later.
+
+# ifdef DEBUG_LCP
+  checkFactorization (A,L,d,nC,C,nskip);
+# endif
+}
+
+
+void dLCP::transfer_i_from_C_to_N (int i)
+{
+  // remove a row/column from the factorization, and adjust the
+  // indexes (black magic!)
+  int j,k;
+  for (j=0; j<nC; j++) if (C[j]==i) {
+    dLDLTRemove (A,C,L,d,n,nC,j,nskip);
+    for (k=0; k<nC; k++) if (C[k]==nC-1) {
+      C[k] = C[j];
+      if (j < (nC-1)) memmove (C+j,C+j+1,(nC-j-1)*sizeof(int));
+      break;
+    }
+    dIASSERT (k < nC);
+    break;
+  }
+  dIASSERT (j < nC);
+  swapProblem (A,x,b,w,lo,hi,p,state,findex,n,i,nC-1,nskip,1);
+  nC--;
+  nN++;
+
+# ifdef DEBUG_LCP
+  checkFactorization (A,L,d,nC,C,nskip);
+# endif
+}
+
+
+void dLCP::pN_equals_ANC_times_qC (dReal *p, dReal *q)
+{
+  // we could try to make this matrix-vector multiplication faster using
+  // outer product matrix tricks, e.g. with the dMultidotX() functions.
+  // but i tried it and it actually made things slower on random 100x100
+  // problems because of the overhead involved. so we'll stick with the
+  // simple method for now.
+  for (int i=0; i<nN; i++) p[i+nC] = dDot (AROW(i+nC),q,nC);
+}
+
+
+void dLCP::pN_plusequals_ANi (dReal *p, int i, int sign)
+{
+  dReal *aptr = AROW(i)+nC;
+  if (sign > 0) {
+    for (int i=0; i<nN; i++) p[i+nC] += aptr[i];
+  }
+  else {
+    for (int i=0; i<nN; i++) p[i+nC] -= aptr[i];
+  }
+}
+
+
+void dLCP::solve1 (dReal *a, int i, int dir, int only_transfer)
+{
+  // the `Dell' and `ell' that are computed here are saved. if index i is
+  // later added to the factorization then they can be reused.
+  //
+  // @@@ question: do we need to solve for entire delta_x??? yes, but
+  //     only if an x goes below 0 during the step.
+
+  int j;
+  if (nC > 0) {
+    dReal *aptr = AROW(i);
+#   ifdef NUB_OPTIMIZATIONS
+    // if nub>0, initial part of aptr[] is guaranteed unpermuted
+    for (j=0; j<nub; j++) Dell[j] = aptr[j];
+    for (j=nub; j<nC; j++) Dell[j] = aptr[C[j]];
+#   else
+    for (j=0; j<nC; j++) Dell[j] = aptr[C[j]];
+#   endif
+    dSolveL1 (L,Dell,nC,nskip);
+    for (j=0; j<nC; j++) ell[j] = Dell[j] * d[j];
+
+    if (!only_transfer) {
+      for (j=0; j<nC; j++) tmp[j] = ell[j];
+      dSolveL1T (L,tmp,nC,nskip);
+      if (dir > 0) {
+        for (j=0; j<nC; j++) a[C[j]] = -tmp[j];
+      }
+      else {
+        for (j=0; j<nC; j++) a[C[j]] = tmp[j];
+      }
+    }
+  }
+}
+
+
+void dLCP::unpermute()
+{
+  // now we have to un-permute x and w
+  int j;
+  ALLOCA (dReal,tmp,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (tmp == NULL) {
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  memcpy (tmp,x,n*sizeof(dReal));
+  for (j=0; j<n; j++) x[p[j]] = tmp[j];
+  memcpy (tmp,w,n*sizeof(dReal));
+  for (j=0; j<n; j++) w[p[j]] = tmp[j];
+
+  UNALLOCA (tmp);
+}
+
+#endif // dLCP_FAST
+
+//***************************************************************************
+// an unoptimized Dantzig LCP driver routine for the basic LCP problem.
+// must have lo=0, hi=dInfinity, and nub=0.
+
+void dSolveLCPBasic (int n, dReal *A, dReal *x, dReal *b,
+                     dReal *w, int nub, dReal *lo, dReal *hi)
+{
+  dAASSERT (n>0 && A && x && b && w && nub == 0);
+
+  int i,k;
+  int nskip = dPAD(n);
+  ALLOCA (dReal,L,n*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (L == NULL) {
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,d,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (d == NULL) {
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,delta_x,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (delta_x == NULL) {
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,delta_w,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (delta_w == NULL) {
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,Dell,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (Dell == NULL) {
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,ell,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (ell == NULL) {
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,tmp,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (tmp == NULL) {
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal*,Arows,n*sizeof(dReal*));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (Arows == NULL) {
+      UNALLOCA(tmp);
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (int,p,n*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (p == NULL) {
+      UNALLOCA(Arows);
+      UNALLOCA(tmp);
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (int,C,n*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (C == NULL) {
+      UNALLOCA(p);
+      UNALLOCA(Arows);
+      UNALLOCA(tmp);
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (int,dummy,n*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (dummy == NULL) {
+      UNALLOCA(C);
+      UNALLOCA(p);
+      UNALLOCA(Arows);
+      UNALLOCA(tmp);
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+
+
+  dLCP lcp (n,0,A,x,b,w,tmp,tmp,L,d,Dell,ell,tmp,dummy,dummy,p,C,Arows);
+  nub = lcp.getNub();
+
+  for (i=0; i<n; i++) {
+    w[i] = lcp.AiC_times_qC (i,x) - b[i];
+    if (w[i] >= 0) {
+      lcp.transfer_i_to_N (i);
+    }
+    else {
+      for (;;) {
+        // compute: delta_x(C) = -A(C,C)\A(C,i)
+        dSetZero (delta_x,n);
+        lcp.solve1 (delta_x,i);
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+        if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
+          UNALLOCA(dummy);
+          UNALLOCA(C);
+          UNALLOCA(p);
+          UNALLOCA(Arows);
+          UNALLOCA(tmp);
+          UNALLOCA(ell);
+          UNALLOCA(Dell);
+          UNALLOCA(delta_w);
+          UNALLOCA(delta_x);
+          UNALLOCA(d);
+          UNALLOCA(L);
+          return;
+        }
+#endif
+        delta_x[i] = 1;
+
+        // compute: delta_w = A*delta_x
+        dSetZero (delta_w,n);
+        lcp.pN_equals_ANC_times_qC (delta_w,delta_x);
+        lcp.pN_plusequals_ANi (delta_w,i);
+        delta_w[i] = lcp.AiC_times_qC (i,delta_x) + lcp.Aii(i);
+
+        // find index to switch
+        int si = i;             // si = switch index
+        int si_in_N = 0;        // set to 1 if si in N
+        dReal s = -w[i]/delta_w[i];
+
+        if (s <= 0) {
+          dMessage (d_ERR_LCP, "LCP internal error, s <= 0 (s=%.4e)",s);
+          if (i < (n-1)) {
+            dSetZero (x+i,n-i);
+            dSetZero (w+i,n-i);
+          }
+          goto done;
+        }
+
+        for (k=0; k < lcp.numN(); k++) {
+          if (delta_w[lcp.indexN(k)] < 0) {
+            dReal s2 = -w[lcp.indexN(k)] / delta_w[lcp.indexN(k)];
+            if (s2 < s) {
+              s = s2;
+              si = lcp.indexN(k);
+              si_in_N = 1;
+            }
+          }
+        }
+        for (k=0; k < lcp.numC(); k++) {
+          if (delta_x[lcp.indexC(k)] < 0) {
+            dReal s2 = -x[lcp.indexC(k)] / delta_x[lcp.indexC(k)];
+            if (s2 < s) {
+              s = s2;
+              si = lcp.indexC(k);
+              si_in_N = 0;
+            }
+          }
+        }
+
+        // apply x = x + s * delta_x
+        lcp.pC_plusequals_s_times_qC (x,s,delta_x);
+        x[i] += s;
+        lcp.pN_plusequals_s_times_qN (w,s,delta_w);
+        w[i] += s * delta_w[i];
+
+        // switch indexes between sets if necessary
+        if (si==i) {
+          w[i] = 0;
+          lcp.transfer_i_to_C (i);
+          break;
+        }
+        if (si_in_N) {
+          w[si] = 0;
+          lcp.transfer_i_from_N_to_C (si);
+        }
+        else {
+          x[si] = 0;
+          lcp.transfer_i_from_C_to_N (si);
+        }
+      }
+    }
+  }
+
+ done:
+  lcp.unpermute();
+
+  UNALLOCA (L);
+  UNALLOCA (d);
+  UNALLOCA (delta_x);
+  UNALLOCA (delta_w);
+  UNALLOCA (Dell);
+  UNALLOCA (ell);
+  UNALLOCA (tmp);
+  UNALLOCA (Arows);
+  UNALLOCA (p);
+  UNALLOCA (C);
+  UNALLOCA (dummy);
+}
+
+//***************************************************************************
+// an optimized Dantzig LCP driver routine for the lo-hi LCP problem.
+
+void dSolveLCP (int n, dReal *A, dReal *x, dReal *b,
+                dReal *w, int nub, dReal *lo, dReal *hi, int *findex)
+{
+  dAASSERT (n>0 && A && x && b && w && lo && hi && nub >= 0 && nub <= n);
+
+  int i,k,hit_first_friction_index = 0;
+  int nskip = dPAD(n);
+
+  // if all the variables are unbounded then we can just factor, solve,
+  // and return
+  if (nub >= n) {
+    dFactorLDLT (A,w,n,nskip);          // use w for d
+    dSolveLDLT (A,w,b,n,nskip);
+    memcpy (x,b,n*sizeof(dReal));
+    dSetZero (w,n);
+
+    return;
+  }
+# ifndef dNODEBUG
+  // check restrictions on lo and hi
+  for (k=0; k<n; k++) dIASSERT (lo[k] <= 0 && hi[k] >= 0);
+# endif
+  ALLOCA (dReal,L,n*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (L == NULL) {
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,d,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (d == NULL) {
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,delta_x,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (delta_x == NULL) {
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,delta_w,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (delta_w == NULL) {
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,Dell,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (Dell == NULL) {
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,ell,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (ell == NULL) {
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal*,Arows,n*sizeof(dReal*));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (Arows == NULL) {
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (int,p,n*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (p == NULL) {
+      UNALLOCA(Arows);
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (int,C,n*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (C == NULL) {
+      UNALLOCA(p);
+      UNALLOCA(Arows);
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+
+  int dir;
+  dReal dirf;
+
+  // for i in N, state[i] is 0 if x(i)==lo(i) or 1 if x(i)==hi(i)
+  ALLOCA (int,state,n*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (state == NULL) {
+      UNALLOCA(C);
+      UNALLOCA(p);
+      UNALLOCA(Arows);
+      UNALLOCA(ell);
+      UNALLOCA(Dell);
+      UNALLOCA(delta_w);
+      UNALLOCA(delta_x);
+      UNALLOCA(d);
+      UNALLOCA(L);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+
+  // create LCP object. note that tmp is set to delta_w to save space, this
+  // optimization relies on knowledge of how tmp is used, so be careful!
+  dLCP *lcp=new dLCP(n,nub,A,x,b,w,lo,hi,L,d,Dell,ell,delta_w,state,findex,p,C,Arows);
+  nub = lcp->getNub();
+
+  // loop over all indexes nub..n-1. for index i, if x(i),w(i) satisfy the
+  // LCP conditions then i is added to the appropriate index set. otherwise
+  // x(i),w(i) is driven either +ve or -ve to force it to the valid region.
+  // as we drive x(i), x(C) is also adjusted to keep w(C) at zero.
+  // while driving x(i) we maintain the LCP conditions on the other variables
+  // 0..i-1. we do this by watching out for other x(i),w(i) values going
+  // outside the valid region, and then switching them between index sets
+  // when that happens.
+
+  for (i=nub; i<n; i++) {
+    // the index i is the driving index and indexes i+1..n-1 are "dont care",
+    // i.e. when we make changes to the system those x's will be zero and we
+    // don't care what happens to those w's. in other words, we only consider
+    // an (i+1)*(i+1) sub-problem of A*x=b+w.
+
+    // if we've hit the first friction index, we have to compute the lo and
+    // hi values based on the values of x already computed. we have been
+    // permuting the indexes, so the values stored in the findex vector are
+    // no longer valid. thus we have to temporarily unpermute the x vector. 
+    // for the purposes of this computation, 0*infinity = 0 ... so if the
+    // contact constraint's normal force is 0, there should be no tangential
+    // force applied.
+
+    if (hit_first_friction_index == 0 && findex && findex[i] >= 0) {
+      // un-permute x into delta_w, which is not being used at the moment
+      for (k=0; k<n; k++) delta_w[p[k]] = x[k];
+
+      // set lo and hi values
+      for (k=i; k<n; k++) {
+        dReal wfk = delta_w[findex[k]];
+        if (wfk == 0) {
+          hi[k] = 0;
+          lo[k] = 0;
+        }
+        else {
+          hi[k] = dFabs (hi[k] * wfk);
+          lo[k] = -hi[k];
+        }
+      }
+      hit_first_friction_index = 1;
+    }
+
+    // thus far we have not even been computing the w values for indexes
+    // greater than i, so compute w[i] now.
+    w[i] = lcp->AiC_times_qC (i,x) + lcp->AiN_times_qN (i,x) - b[i];
+
+    // if lo=hi=0 (which can happen for tangential friction when normals are
+    // 0) then the index will be assigned to set N with some state. however,
+    // set C's line has zero size, so the index will always remain in set N.
+    // with the "normal" switching logic, if w changed sign then the index
+    // would have to switch to set C and then back to set N with an inverted
+    // state. this is pointless, and also computationally expensive. to
+    // prevent this from happening, we use the rule that indexes with lo=hi=0
+    // will never be checked for set changes. this means that the state for
+    // these indexes may be incorrect, but that doesn't matter.
+
+    // see if x(i),w(i) is in a valid region
+    if (lo[i]==0 && w[i] >= 0) {
+      lcp->transfer_i_to_N (i);
+      state[i] = 0;
+    }
+    else if (hi[i]==0 && w[i] <= 0) {
+      lcp->transfer_i_to_N (i);
+      state[i] = 1;
+    }
+    else if (w[i]==0) {
+      // this is a degenerate case. by the time we get to this test we know
+      // that lo != 0, which means that lo < 0 as lo is not allowed to be +ve,
+      // and similarly that hi > 0. this means that the line segment
+      // corresponding to set C is at least finite in extent, and we are on it.
+      // NOTE: we must call lcp->solve1() before lcp->transfer_i_to_C()
+      lcp->solve1 (delta_x,i,0,1);
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+      if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
+        UNALLOCA(state);
+        UNALLOCA(C);
+        UNALLOCA(p);
+        UNALLOCA(Arows);
+        UNALLOCA(ell);
+        UNALLOCA(Dell);
+        UNALLOCA(delta_w);
+        UNALLOCA(delta_x);
+        UNALLOCA(d);
+        UNALLOCA(L);
+        return;
+      }
+#endif
+
+      lcp->transfer_i_to_C (i);
+    }
+    else {
+      // we must push x(i) and w(i)
+      for (;;) {
+        // find direction to push on x(i)
+        if (w[i] <= 0) {
+          dir = 1;
+          dirf = REAL(1.0);
+        }
+        else {
+          dir = -1;
+          dirf = REAL(-1.0);
+        }
+
+        // compute: delta_x(C) = -dir*A(C,C)\A(C,i)
+        lcp->solve1 (delta_x,i,dir);
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+        if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
+          UNALLOCA(state);
+          UNALLOCA(C);
+          UNALLOCA(p);
+          UNALLOCA(Arows);
+          UNALLOCA(ell);
+          UNALLOCA(Dell);
+          UNALLOCA(delta_w);
+          UNALLOCA(delta_x);
+          UNALLOCA(d);
+          UNALLOCA(L);
+          return;
+        }
+#endif
+
+        // note that delta_x[i] = dirf, but we wont bother to set it
+
+        // compute: delta_w = A*delta_x ... note we only care about
+        // delta_w(N) and delta_w(i), the rest is ignored
+        lcp->pN_equals_ANC_times_qC (delta_w,delta_x);
+        lcp->pN_plusequals_ANi (delta_w,i,dir);
+        delta_w[i] = lcp->AiC_times_qC (i,delta_x) + lcp->Aii(i)*dirf;
+
+        // find largest step we can take (size=s), either to drive x(i),w(i)
+        // to the valid LCP region or to drive an already-valid variable
+        // outside the valid region.
+
+        int cmd = 1;            // index switching command
+        int si = 0;             // si = index to switch if cmd>3
+        dReal s = -w[i]/delta_w[i];
+        if (dir > 0) {
+          if (hi[i] < dInfinity) {
+            dReal s2 = (hi[i]-x[i])/dirf;               // step to x(i)=hi(i)
+            if (s2 < s) {
+              s = s2;
+              cmd = 3;
+            }
+          }
+        }
+        else {
+          if (lo[i] > -dInfinity) {
+            dReal s2 = (lo[i]-x[i])/dirf;               // step to x(i)=lo(i)
+            if (s2 < s) {
+              s = s2;
+              cmd = 2;
+            }
+          }
+        }
+
+        for (k=0; k < lcp->numN(); k++) {
+          if ((state[lcp->indexN(k)]==0 && delta_w[lcp->indexN(k)] < 0) ||
+              (state[lcp->indexN(k)]!=0 && delta_w[lcp->indexN(k)] > 0)) {
+            // don't bother checking if lo=hi=0
+            if (lo[lcp->indexN(k)] == 0 && hi[lcp->indexN(k)] == 0) continue;
+            dReal s2 = -w[lcp->indexN(k)] / delta_w[lcp->indexN(k)];
+            if (s2 < s) {
+              s = s2;
+              cmd = 4;
+              si = lcp->indexN(k);
+            }
+          }
+        }
+
+        for (k=nub; k < lcp->numC(); k++) {
+          if (delta_x[lcp->indexC(k)] < 0 && lo[lcp->indexC(k)] > -dInfinity) {
+            dReal s2 = (lo[lcp->indexC(k)]-x[lcp->indexC(k)]) /
+              delta_x[lcp->indexC(k)];
+            if (s2 < s) {
+              s = s2;
+              cmd = 5;
+              si = lcp->indexC(k);
+            }
+          }
+          if (delta_x[lcp->indexC(k)] > 0 && hi[lcp->indexC(k)] < dInfinity) {
+            dReal s2 = (hi[lcp->indexC(k)]-x[lcp->indexC(k)]) /
+              delta_x[lcp->indexC(k)];
+            if (s2 < s) {
+              s = s2;
+              cmd = 6;
+              si = lcp->indexC(k);
+            }
+          }
+        }
+
+        //static char* cmdstring[8] = {0,"->C","->NL","->NH","N->C",
+        //                           "C->NL","C->NH"};
+        //printf ("cmd=%d (%s), si=%d\n",cmd,cmdstring[cmd],(cmd>3) ? si : i);
+
+        // if s <= 0 then we've got a problem. if we just keep going then
+        // we're going to get stuck in an infinite loop. instead, just cross
+        // our fingers and exit with the current solution.
+        if (s <= 0) {
+          dMessage (d_ERR_LCP, "LCP internal error, s <= 0 (s=%.4e)",s);
+          if (i < (n-1)) {
+            dSetZero (x+i,n-i);
+            dSetZero (w+i,n-i);
+          }
+          goto done;
+        }
+
+        // apply x = x + s * delta_x
+        lcp->pC_plusequals_s_times_qC (x,s,delta_x);
+        x[i] += s * dirf;
+
+        // apply w = w + s * delta_w
+        lcp->pN_plusequals_s_times_qN (w,s,delta_w);
+        w[i] += s * delta_w[i];
+
+        // switch indexes between sets if necessary
+        switch (cmd) {
+        case 1:         // done
+          w[i] = 0;
+          lcp->transfer_i_to_C (i);
+          break;
+        case 2:         // done
+          x[i] = lo[i];
+          state[i] = 0;
+          lcp->transfer_i_to_N (i);
+          break;
+        case 3:         // done
+          x[i] = hi[i];
+          state[i] = 1;
+          lcp->transfer_i_to_N (i);
+          break;
+        case 4:         // keep going
+          w[si] = 0;
+          lcp->transfer_i_from_N_to_C (si);
+          break;
+        case 5:         // keep going
+          x[si] = lo[si];
+          state[si] = 0;
+          lcp->transfer_i_from_C_to_N (si);
+          break;
+        case 6:         // keep going
+          x[si] = hi[si];
+          state[si] = 1;
+          lcp->transfer_i_from_C_to_N (si);
+          break;
+        }
+
+        if (cmd <= 3) break;
+      }
+    }
+  }
+
+ done:
+  lcp->unpermute();
+  delete lcp;
+
+  UNALLOCA (L);
+  UNALLOCA (d);
+  UNALLOCA (delta_x);
+  UNALLOCA (delta_w);
+  UNALLOCA (Dell);
+  UNALLOCA (ell);
+  UNALLOCA (Arows);
+  UNALLOCA (p);
+  UNALLOCA (C);
+  UNALLOCA (state);
+}
+
+//***************************************************************************
+// accuracy and timing test
+
+extern "C" ODE_API void dTestSolveLCP()
+{
+  int n = 100;
+  int i,nskip = dPAD(n);
+#ifdef dDOUBLE
+  const dReal tol = REAL(1e-9);
+#endif
+#ifdef dSINGLE
+  const dReal tol = REAL(1e-4);
+#endif
+  printf ("dTestSolveLCP()\n");
+
+  ALLOCA (dReal,A,n*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (A == NULL) {
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,x,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (x == NULL) {
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,b,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (b == NULL) {
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,w,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (w == NULL) {
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,lo,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (lo == NULL) {
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,hi,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (hi == NULL) {
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+
+  ALLOCA (dReal,A2,n*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (A2 == NULL) {
+      UNALLOCA (hi);
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,b2,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (b2 == NULL) {
+      UNALLOCA (A2);
+      UNALLOCA (hi);
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,lo2,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (lo2 == NULL) {
+      UNALLOCA (b2);
+      UNALLOCA (A2);
+      UNALLOCA (hi);
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,hi2,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (hi2 == NULL) {
+      UNALLOCA (lo2);
+      UNALLOCA (b2);
+      UNALLOCA (A2);
+      UNALLOCA (hi);
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,tmp1,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (tmp1 == NULL) {
+      UNALLOCA (hi2);
+      UNALLOCA (lo2);
+      UNALLOCA (b2);
+      UNALLOCA (A2);
+      UNALLOCA (hi);
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+  ALLOCA (dReal,tmp2,n*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (tmp2 == NULL) {
+      UNALLOCA (tmp1);
+      UNALLOCA (hi2);
+      UNALLOCA (lo2);
+      UNALLOCA (b2);
+      UNALLOCA (A2);
+      UNALLOCA (hi);
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+      return;
+    }
+#endif
+
+  double total_time = 0;
+  for (int count=0; count < 1000; count++) {
+
+    // form (A,b) = a random positive definite LCP problem
+    dMakeRandomMatrix (A2,n,n,1.0);
+    dMultiply2 (A,A2,A2,n,n,n);
+    dMakeRandomMatrix (x,n,1,1.0);
+    dMultiply0 (b,A,x,n,n,1);
+    for (i=0; i<n; i++) b[i] += (dRandReal()*REAL(0.2))-REAL(0.1);
+
+    // choose `nub' in the range 0..n-1
+    int nub = 50; //dRandInt (n);
+
+    // make limits
+    for (i=0; i<nub; i++) lo[i] = -dInfinity;
+    for (i=0; i<nub; i++) hi[i] = dInfinity;
+    //for (i=nub; i<n; i++) lo[i] = 0;
+    //for (i=nub; i<n; i++) hi[i] = dInfinity;
+    //for (i=nub; i<n; i++) lo[i] = -dInfinity;
+    //for (i=nub; i<n; i++) hi[i] = 0;
+    for (i=nub; i<n; i++) lo[i] = -(dRandReal()*REAL(1.0))-REAL(0.01);
+    for (i=nub; i<n; i++) hi[i] =  (dRandReal()*REAL(1.0))+REAL(0.01);
+
+    // set a few limits to lo=hi=0
+    /*
+    for (i=0; i<10; i++) {
+      int j = dRandInt (n-nub) + nub;
+      lo[j] = 0;
+      hi[j] = 0;
+    }
+    */
+
+    // solve the LCP. we must make copy of A,b,lo,hi (A2,b2,lo2,hi2) for
+    // SolveLCP() to permute. also, we'll clear the upper triangle of A2 to
+    // ensure that it doesn't get referenced (if it does, the answer will be
+    // wrong).
+
+    memcpy (A2,A,n*nskip*sizeof(dReal));
+    dClearUpperTriangle (A2,n);
+    memcpy (b2,b,n*sizeof(dReal));
+    memcpy (lo2,lo,n*sizeof(dReal));
+    memcpy (hi2,hi,n*sizeof(dReal));
+    dSetZero (x,n);
+    dSetZero (w,n);
+
+    dStopwatch sw;
+    dStopwatchReset (&sw);
+    dStopwatchStart (&sw);
+
+    dSolveLCP (n,A2,x,b2,w,nub,lo2,hi2,0);
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+    if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
+      UNALLOCA (tmp2);
+      UNALLOCA (tmp1);
+      UNALLOCA (hi2);
+      UNALLOCA (lo2);
+      UNALLOCA (b2);
+      UNALLOCA (A2);
+      UNALLOCA (hi);
+      UNALLOCA (lo);
+      UNALLOCA (w);
+      UNALLOCA (b);
+      UNALLOCA (x);
+      UNALLOCA (A);
+      return;
+    }
+#endif
+
+    dStopwatchStop (&sw);
+    double time = dStopwatchTime(&sw);
+    total_time += time;
+    double average = total_time / double(count+1) * 1000.0;
+
+    // check the solution
+
+    dMultiply0 (tmp1,A,x,n,n,1);
+    for (i=0; i<n; i++) tmp2[i] = b[i] + w[i];
+    dReal diff = dMaxDifference (tmp1,tmp2,n,1);
+    // printf ("\tA*x = b+w, maximum difference = %.6e - %s (1)\n",diff,
+    //      diff > tol ? "FAILED" : "passed");
+    if (diff > tol) dDebug (0,"A*x = b+w, maximum difference = %.6e",diff);
+    int n1=0,n2=0,n3=0;
+    for (i=0; i<n; i++) {
+      if (x[i]==lo[i] && w[i] >= 0) {
+        n1++;   // ok
+      }
+      else if (x[i]==hi[i] && w[i] <= 0) {
+        n2++;   // ok
+      }
+      else if (x[i] >= lo[i] && x[i] <= hi[i] && w[i] == 0) {
+        n3++;   // ok
+      }
+      else {
+        dDebug (0,"FAILED: i=%d x=%.4e w=%.4e lo=%.4e hi=%.4e",i,
+                x[i],w[i],lo[i],hi[i]);
+      }
+    }
+
+    // pacifier
+    printf ("passed: NL=%3d NH=%3d C=%3d   ",n1,n2,n3);
+    printf ("time=%10.3f ms  avg=%10.4f\n",time * 1000.0,average);
+  }
+
+  UNALLOCA (A);
+  UNALLOCA (x);
+  UNALLOCA (b);
+  UNALLOCA (w);
+  UNALLOCA (lo);
+  UNALLOCA (hi);
+  UNALLOCA (A2);
+  UNALLOCA (b2);
+  UNALLOCA (lo2);
+  UNALLOCA (hi2);
+  UNALLOCA (tmp1);
+  UNALLOCA (tmp2);
+}