dont ask

1 files changed, 0 insertions, 1170 deletions

diff --git a/libraries/ode-0.9/contrib/BreakableJoints/step.cpp b/libraries/ode-0.9/contrib/BreakableJoints/step.cpp
deleted file mode 100644
index 38aed6c..0000000
--- a/libraries/ode-0.9/contrib/BreakableJoints/step.cpp
+++ /dev/null
@@ -1,1170 +0,0 @@
-/*************************************************************************
- *                                                                       *
- * 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.                     *
- *                                                                       *
- *************************************************************************/
-
-#include "objects.h"
-#include "joint.h"
-#include <ode/config.h>
-#include <ode/odemath.h>
-#include <ode/rotation.h>
-#include <ode/timer.h>
-#include <ode/error.h>
-#include <ode/matrix.h>
-#include "lcp.h"
-
-//****************************************************************************
-// misc defines
-
-#define FAST_FACTOR
-//#define TIMING
-
-#define ALLOCA dALLOCA16
-
-//****************************************************************************
-// debugging - comparison of various vectors and matrices produced by the
-// slow and fast versions of the stepper.
-
-//#define COMPARE_METHODS
-
-#ifdef COMPARE_METHODS
-#include "testing.h"
-dMatrixComparison comparator;
-#endif
-
-//****************************************************************************
-// special matrix multipliers
-
-// this assumes the 4th and 8th rows of B and C are zero.
-
-static void Multiply2_p8r (dReal *A, dReal *B, dReal *C,
-                           int p, int r, int Askip)
-{
-  int i,j;
-  dReal sum,*bb,*cc;
-  dIASSERT (p>0 && r>0 && A && B && C);
-  bb = B;
-  for (i=p; i; i--) {
-    cc = C;
-    for (j=r; j; j--) {
-      sum = bb[0]*cc[0];
-      sum += bb[1]*cc[1];
-      sum += bb[2]*cc[2];
-      sum += bb[4]*cc[4];
-      sum += bb[5]*cc[5];
-      sum += bb[6]*cc[6];
-      *(A++) = sum; 
-      cc += 8;
-    }
-    A += Askip - r;
-    bb += 8;
-  }
-}
-
-
-// this assumes the 4th and 8th rows of B and C are zero.
-
-static void MultiplyAdd2_p8r (dReal *A, dReal *B, dReal *C,
-                              int p, int r, int Askip)
-{
-  int i,j;
-  dReal sum,*bb,*cc;
-  dIASSERT (p>0 && r>0 && A && B && C);
-  bb = B;
-  for (i=p; i; i--) {
-    cc = C;
-    for (j=r; j; j--) {
-      sum = bb[0]*cc[0];
-      sum += bb[1]*cc[1];
-      sum += bb[2]*cc[2];
-      sum += bb[4]*cc[4];
-      sum += bb[5]*cc[5];
-      sum += bb[6]*cc[6];
-      *(A++) += sum; 
-      cc += 8;
-    }
-    A += Askip - r;
-    bb += 8;
-  }
-}
-
-
-// this assumes the 4th and 8th rows of B are zero.
-
-static void Multiply0_p81 (dReal *A, dReal *B, dReal *C, int p)
-{
-  int i;
-  dIASSERT (p>0 && A && B && C);
-  dReal sum;
-  for (i=p; i; i--) {
-    sum =  B[0]*C[0];
-    sum += B[1]*C[1];
-    sum += B[2]*C[2];
-    sum += B[4]*C[4];
-    sum += B[5]*C[5];
-    sum += B[6]*C[6];
-    *(A++) = sum;
-    B += 8;
-  }
-}
-
-
-// this assumes the 4th and 8th rows of B are zero.
-
-static void MultiplyAdd0_p81 (dReal *A, dReal *B, dReal *C, int p)
-{
-  int i;
-  dIASSERT (p>0 && A && B && C);
-  dReal sum;
-  for (i=p; i; i--) {
-    sum =  B[0]*C[0];
-    sum += B[1]*C[1];
-    sum += B[2]*C[2];
-    sum += B[4]*C[4];
-    sum += B[5]*C[5];
-    sum += B[6]*C[6];
-    *(A++) += sum;
-    B += 8;
-  }
-}
-
-
-// this assumes the 4th and 8th rows of B are zero.
-
-static void MultiplyAdd1_8q1 (dReal *A, dReal *B, dReal *C, int q)
-{
-  int k;
-  dReal sum;
-  dIASSERT (q>0 && A && B && C);
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[k*8] * C[k];
-  A[0] += sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[1+k*8] * C[k];
-  A[1] += sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[2+k*8] * C[k];
-  A[2] += sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[4+k*8] * C[k];
-  A[4] += sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[5+k*8] * C[k];
-  A[5] += sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[6+k*8] * C[k];
-  A[6] += sum;
-}
-
-
-// this assumes the 4th and 8th rows of B are zero.
-
-static void Multiply1_8q1 (dReal *A, dReal *B, dReal *C, int q)
-{
-  int k;
-  dReal sum;
-  dIASSERT (q>0 && A && B && C);
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[k*8] * C[k];
-  A[0] = sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[1+k*8] * C[k];
-  A[1] = sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[2+k*8] * C[k];
-  A[2] = sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[4+k*8] * C[k];
-  A[4] = sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[5+k*8] * C[k];
-  A[5] = sum;
-  sum = 0;
-  for (k=0; k<q; k++) sum += B[6+k*8] * C[k];
-  A[6] = sum;
-}
-
-//****************************************************************************
-// body rotation
-
-// return sin(x)/x. this has a singularity at 0 so special handling is needed
-// for small arguments.
-
-static inline dReal sinc (dReal x)
-{
-  // if |x| < 1e-4 then use a taylor series expansion. this two term expansion
-  // is actually accurate to one LS bit within this range if double precision
-  // is being used - so don't worry!
-  if (dFabs(x) < 1.0e-4) return REAL(1.0) - x*x*REAL(0.166666666666666666667);
-  else return dSin(x)/x;
-}
-
-
-// given a body b, apply its linear and angular rotation over the time
-// interval h, thereby adjusting its position and orientation.
-
-static inline void moveAndRotateBody (dxBody *b, dReal h)
-{
-  int j;
-
-  // handle linear velocity
-  for (j=0; j<3; j++) b->pos[j] += h * b->lvel[j];
-
-  if (b->flags & dxBodyFlagFiniteRotation) {
-    dVector3 irv;       // infitesimal rotation vector
-    dQuaternion q;      // quaternion for finite rotation
-
-    if (b->flags & dxBodyFlagFiniteRotationAxis) {
-      // split the angular velocity vector into a component along the finite
-      // rotation axis, and a component orthogonal to it.
-      dVector3 frv,irv;         // finite rotation vector
-      dReal k = dDOT (b->finite_rot_axis,b->avel);
-      frv[0] = b->finite_rot_axis[0] * k;
-      frv[1] = b->finite_rot_axis[1] * k;
-      frv[2] = b->finite_rot_axis[2] * k;
-      irv[0] = b->avel[0] - frv[0];
-      irv[1] = b->avel[1] - frv[1];
-      irv[2] = b->avel[2] - frv[2];
-
-      // make a rotation quaternion q that corresponds to frv * h.
-      // compare this with the full-finite-rotation case below.
-      h *= REAL(0.5);
-      dReal theta = k * h;
-      q[0] = dCos(theta);
-      dReal s = sinc(theta) * h;
-      q[1] = frv[0] * s;
-      q[2] = frv[1] * s;
-      q[3] = frv[2] * s;
-    }
-    else {
-      // make a rotation quaternion q that corresponds to w * h
-      dReal wlen = dSqrt (b->avel[0]*b->avel[0] + b->avel[1]*b->avel[1] +
-                          b->avel[2]*b->avel[2]);
-      h *= REAL(0.5);
-      dReal theta = wlen * h;
-      q[0] = dCos(theta);
-      dReal s = sinc(theta) * h;
-      q[1] = b->avel[0] * s;
-      q[2] = b->avel[1] * s;
-      q[3] = b->avel[2] * s;
-    }
-
-    // do the finite rotation
-    dQuaternion q2;
-    dQMultiply0 (q2,q,b->q);
-    for (j=0; j<4; j++) b->q[j] = q2[j];
-
-    // do the infitesimal rotation if required
-    if (b->flags & dxBodyFlagFiniteRotationAxis) {
-      dReal dq[4];
-      dWtoDQ (irv,b->q,dq);
-      for (j=0; j<4; j++) b->q[j] += h * dq[j];
-    }
-  }
-  else {
-    // the normal way - do an infitesimal rotation
-    dReal dq[4];
-    dWtoDQ (b->avel,b->q,dq);
-    for (j=0; j<4; j++) b->q[j] += h * dq[j];
-  }
-
-  // normalize the quaternion and convert it to a rotation matrix
-  dNormalize4 (b->q);
-  dQtoR (b->q,b->R);
-
-  // notify all attached geoms that this body has moved
-  for (dxGeom *geom = b->geom; geom; geom = dGeomGetBodyNext (geom))
-    dGeomMoved (geom);
-}
-
-//****************************************************************************
-// the slow, but sure way
-// note that this does not do any joint feedback!
-
-// given lists of bodies and joints that form an island, perform a first
-// order timestep.
-//
-// `body' is the body array, `nb' is the size of the array.
-// `_joint' is the body array, `nj' is the size of the array.
-
-void dInternalStepIsland_x1 (dxWorld *world, dxBody * const *body, int nb,
-                             dxJoint * const *_joint, int nj, dReal stepsize)
-{
-  int i,j,k;
-  int n6 = 6*nb;
-
-# ifdef TIMING
-  dTimerStart("preprocessing");
-# endif
-
-  // number all bodies in the body list - set their tag values
-  for (i=0; i<nb; i++) body[i]->tag = i;
-
-  // make a local copy of the joint array, because we might want to modify it.
-  // (the "dxJoint *const*" declaration says we're allowed to modify the joints
-  // but not the joint array, because the caller might need it unchanged).
-  dxJoint **joint = (dxJoint**) ALLOCA (nj * sizeof(dxJoint*));
-  memcpy (joint,_joint,nj * sizeof(dxJoint*));
-
-  // for all bodies, compute the inertia tensor and its inverse in the global
-  // frame, and compute the rotational force and add it to the torque
-  // accumulator.
-  // @@@ check computation of rotational force.
-  dReal *I = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
-  dReal *invI = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
-
-  //dSetZero (I,3*nb*4);
-  //dSetZero (invI,3*nb*4);
-  for (i=0; i<nb; i++) {
-    dReal tmp[12];
-    // compute inertia tensor in global frame
-    dMULTIPLY2_333 (tmp,body[i]->mass.I,body[i]->R);
-    dMULTIPLY0_333 (I+i*12,body[i]->R,tmp);
-    // compute inverse inertia tensor in global frame
-    dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->R);
-    dMULTIPLY0_333 (invI+i*12,body[i]->R,tmp);
-    // compute rotational force
-    dMULTIPLY0_331 (tmp,I+i*12,body[i]->avel);
-    dCROSS (body[i]->tacc,-=,body[i]->avel,tmp);
-  }
-
-  // add the gravity force to all bodies
-  for (i=0; i<nb; i++) {
-    if ((body[i]->flags & dxBodyNoGravity)==0) {
-      body[i]->facc[0] += body[i]->mass.mass * world->gravity[0];
-      body[i]->facc[1] += body[i]->mass.mass * world->gravity[1];
-      body[i]->facc[2] += body[i]->mass.mass * world->gravity[2];
-    }
-  }
-
-  // get m = total constraint dimension, nub = number of unbounded variables.
-  // create constraint offset array and number-of-rows array for all joints.
-  // the constraints are re-ordered as follows: the purely unbounded
-  // constraints, the mixed unbounded + LCP constraints, and last the purely
-  // LCP constraints.
-  //
-  // joints with m=0 are inactive and are removed from the joints array
-  // entirely, so that the code that follows does not consider them.
-  int m = 0;
-  dxJoint::Info1 *info = (dxJoint::Info1*) ALLOCA (nj*sizeof(dxJoint::Info1));
-  int *ofs = (int*) ALLOCA (nj*sizeof(int));
-  for (i=0, j=0; j<nj; j++) {   // i=dest, j=src
-    joint[j]->vtable->getInfo1 (joint[j],info+i);
-    dIASSERT (info[i].m >= 0 && info[i].m <= 6 &&
-              info[i].nub >= 0 && info[i].nub <= info[i].m);
-    if (info[i].m > 0) {
-      joint[i] = joint[j];
-      i++;
-    }
-  }
-  nj = i;
-
-  // the purely unbounded constraints
-  for (i=0; i<nj; i++) if (info[i].nub == info[i].m) {
-    ofs[i] = m;
-    m += info[i].m;
-  }
-  int nub = m;
-  // the mixed unbounded + LCP constraints
-  for (i=0; i<nj; i++) if (info[i].nub > 0 && info[i].nub < info[i].m) {
-    ofs[i] = m;
-    m += info[i].m;
-  }
-  // the purely LCP constraints
-  for (i=0; i<nj; i++) if (info[i].nub == 0) {
-    ofs[i] = m;
-    m += info[i].m;
-  }
-
-  // create (6*nb,6*nb) inverse mass matrix `invM', and fill it with mass
-  // parameters
-# ifdef TIMING
-  dTimerNow ("create mass matrix");
-# endif
-  int nskip = dPAD (n6);
-  dReal *invM = (dReal*) ALLOCA (n6*nskip*sizeof(dReal));
-  dSetZero (invM,n6*nskip);
-  for (i=0; i<nb; i++) {
-    dReal *MM = invM+(i*6)*nskip+(i*6);
-    MM[0] = body[i]->invMass;
-    MM[nskip+1] = body[i]->invMass;
-    MM[2*nskip+2] = body[i]->invMass;
-    MM += 3*nskip+3;
-    for (j=0; j<3; j++) for (k=0; k<3; k++) {
-      MM[j*nskip+k] = invI[i*12+j*4+k];
-    }
-  }
-
-  // assemble some body vectors: fe = external forces, v = velocities
-  dReal *fe = (dReal*) ALLOCA (n6 * sizeof(dReal));
-  dReal *v = (dReal*) ALLOCA (n6 * sizeof(dReal));
-  //dSetZero (fe,n6);
-  //dSetZero (v,n6);
-  for (i=0; i<nb; i++) {
-    for (j=0; j<3; j++) fe[i*6+j] = body[i]->facc[j];
-    for (j=0; j<3; j++) fe[i*6+3+j] = body[i]->tacc[j];
-    for (j=0; j<3; j++) v[i*6+j] = body[i]->lvel[j];
-    for (j=0; j<3; j++) v[i*6+3+j] = body[i]->avel[j];
-  }
-
-  // this will be set to the velocity update
-  dReal *vnew = (dReal*) ALLOCA (n6 * sizeof(dReal));
-  dSetZero (vnew,n6);
-
-  // if there are constraints, compute cforce
-  if (m > 0) {
-    // create a constraint equation right hand side vector `c', a constraint
-    // force mixing vector `cfm', and LCP low and high bound vectors, and an
-    // 'findex' vector.
-    dReal *c = (dReal*) ALLOCA (m*sizeof(dReal));
-    dReal *cfm = (dReal*) ALLOCA (m*sizeof(dReal));
-    dReal *lo = (dReal*) ALLOCA (m*sizeof(dReal));
-    dReal *hi = (dReal*) ALLOCA (m*sizeof(dReal));
-    int *findex = (int*) alloca (m*sizeof(int));
-    dSetZero (c,m);
-    dSetValue (cfm,m,world->global_cfm);
-    dSetValue (lo,m,-dInfinity);
-    dSetValue (hi,m, dInfinity);
-    for (i=0; i<m; i++) findex[i] = -1;
-
-    // create (m,6*nb) jacobian mass matrix `J', and fill it with constraint
-    // data. also fill the c vector.
-#   ifdef TIMING
-    dTimerNow ("create J");
-#   endif
-    dReal *J = (dReal*) ALLOCA (m*nskip*sizeof(dReal));
-    dSetZero (J,m*nskip);
-    dxJoint::Info2 Jinfo;
-    Jinfo.rowskip = nskip;
-    Jinfo.fps = dRecip(stepsize);
-    Jinfo.erp = world->global_erp;
-    for (i=0; i<nj; i++) {
-      Jinfo.J1l = J + nskip*ofs[i] + 6*joint[i]->node[0].body->tag;
-      Jinfo.J1a = Jinfo.J1l + 3;
-      if (joint[i]->node[1].body) {
-        Jinfo.J2l = J + nskip*ofs[i] + 6*joint[i]->node[1].body->tag;
-        Jinfo.J2a = Jinfo.J2l + 3;
-      }
-      else {
-        Jinfo.J2l = 0;
-        Jinfo.J2a = 0;
-      }
-      Jinfo.c = c + ofs[i];
-      Jinfo.cfm = cfm + ofs[i];
-      Jinfo.lo = lo + ofs[i];
-      Jinfo.hi = hi + ofs[i];
-      Jinfo.findex = findex + ofs[i];
-      joint[i]->vtable->getInfo2 (joint[i],&Jinfo);
-      // adjust returned findex values for global index numbering
-      for (j=0; j<info[i].m; j++) {
-        if (findex[ofs[i] + j] >= 0) findex[ofs[i] + j] += ofs[i];
-      }
-    }
-
-    // compute A = J*invM*J'
-#   ifdef TIMING
-    dTimerNow ("compute A");
-#   endif
-    dReal *JinvM = (dReal*) ALLOCA (m*nskip*sizeof(dReal));
-    //dSetZero (JinvM,m*nskip);
-    dMultiply0 (JinvM,J,invM,m,n6,n6);
-    int mskip = dPAD(m);
-    dReal *A = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
-    //dSetZero (A,m*mskip);
-    dMultiply2 (A,JinvM,J,m,n6,m);
-
-    // add cfm to the diagonal of A
-    for (i=0; i<m; i++) A[i*mskip+i] += cfm[i] * Jinfo.fps;
-
-#   ifdef COMPARE_METHODS
-    comparator.nextMatrix (A,m,m,1,"A");
-#   endif
-
-    // compute `rhs', the right hand side of the equation J*a=c
-#   ifdef TIMING
-    dTimerNow ("compute rhs");
-#   endif
-    dReal *tmp1 = (dReal*) ALLOCA (n6 * sizeof(dReal));
-    //dSetZero (tmp1,n6);
-    dMultiply0 (tmp1,invM,fe,n6,n6,1);
-    for (i=0; i<n6; i++) tmp1[i] += v[i]/stepsize;
-    dReal *rhs = (dReal*) ALLOCA (m * sizeof(dReal));
-    //dSetZero (rhs,m);
-    dMultiply0 (rhs,J,tmp1,m,n6,1);
-    for (i=0; i<m; i++) rhs[i] = c[i]/stepsize - rhs[i];
-
-#   ifdef COMPARE_METHODS
-    comparator.nextMatrix (c,m,1,0,"c");
-    comparator.nextMatrix (rhs,m,1,0,"rhs");
-#   endif
-
-    // solve the LCP problem and get lambda.
-    // this will destroy A but that's okay
-#   ifdef TIMING
-    dTimerNow ("solving LCP problem");
-#   endif
-    dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
-    dReal *residual = (dReal*) ALLOCA (m * sizeof(dReal));
-    dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex);
-
-//  OLD WAY - direct factor and solve
-//
-//    // factorize A (L*L'=A)
-//#   ifdef TIMING
-//    dTimerNow ("factorize A");
-//#   endif
-//    dReal *L = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
-//    memcpy (L,A,m*mskip*sizeof(dReal));
-//    if (dFactorCholesky (L,m)==0) dDebug (0,"A is not positive definite");
-//
-//    // compute lambda
-//#   ifdef TIMING
-//    dTimerNow ("compute lambda");
-//#   endif
-//    dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
-//    memcpy (lambda,rhs,m * sizeof(dReal));
-//    dSolveCholesky (L,lambda,m);
-
-#   ifdef COMPARE_METHODS
-    comparator.nextMatrix (lambda,m,1,0,"lambda");
-#   endif
-
-    // compute the velocity update `vnew'
-#   ifdef TIMING
-    dTimerNow ("compute velocity update");
-#   endif
-    dMultiply1 (tmp1,J,lambda,n6,m,1);
-    for (i=0; i<n6; i++) tmp1[i] += fe[i];
-    dMultiply0 (vnew,invM,tmp1,n6,n6,1);
-    for (i=0; i<n6; i++) vnew[i] = v[i] + stepsize*vnew[i];
-
-    // see if the constraint has worked: compute J*vnew and make sure it equals
-    // `c' (to within a certain tolerance).
-#   ifdef TIMING
-    dTimerNow ("verify constraint equation");
-#   endif
-    dMultiply0 (tmp1,J,vnew,m,n6,1);
-    dReal err = 0;
-    for (i=0; i<m; i++) err += dFabs(tmp1[i]-c[i]);
-    printf ("%.6e\n",err);
-  }
-  else {
-    // no constraints
-    dMultiply0 (vnew,invM,fe,n6,n6,1);
-    for (i=0; i<n6; i++) vnew[i] = v[i] + stepsize*vnew[i];
-  }
-
-# ifdef COMPARE_METHODS
-  comparator.nextMatrix (vnew,n6,1,0,"vnew");
-# endif
-
-  // apply the velocity update to the bodies
-# ifdef TIMING
-  dTimerNow ("update velocity");
-# endif
-  for (i=0; i<nb; i++) {
-    for (j=0; j<3; j++) body[i]->lvel[j] = vnew[i*6+j];
-    for (j=0; j<3; j++) body[i]->avel[j] = vnew[i*6+3+j];
-  }
-
-  // update the position and orientation from the new linear/angular velocity
-  // (over the given timestep)
-# ifdef TIMING
-  dTimerNow ("update position");
-# endif
-  for (i=0; i<nb; i++) moveAndRotateBody (body[i],stepsize);
-
-# ifdef TIMING
-  dTimerNow ("tidy up");
-# endif
-
-  // zero all force accumulators
-  for (i=0; i<nb; i++) {
-    body[i]->facc[0] = 0;
-    body[i]->facc[1] = 0;
-    body[i]->facc[2] = 0;
-    body[i]->facc[3] = 0;
-    body[i]->tacc[0] = 0;
-    body[i]->tacc[1] = 0;
-    body[i]->tacc[2] = 0;
-    body[i]->tacc[3] = 0;
-  }
-
-# ifdef TIMING
-  dTimerEnd();
-  if (m > 0) dTimerReport (stdout,1);
-# endif
-}
-
-//****************************************************************************
-// an optimized version of dInternalStepIsland1()
-
-void dInternalStepIsland_x2 (dxWorld *world, dxBody * const *body, int nb,
-                             dxJoint * const *_joint, int nj, dReal stepsize)
-{
-  int i,j,k;
-# ifdef TIMING
-  dTimerStart("preprocessing");
-# endif
-
-  dReal stepsize1 = dRecip(stepsize);
-
-  // number all bodies in the body list - set their tag values
-  for (i=0; i<nb; i++) body[i]->tag = i;
-
-  // make a local copy of the joint array, because we might want to modify it.
-  // (the "dxJoint *const*" declaration says we're allowed to modify the joints
-  // but not the joint array, because the caller might need it unchanged).
-  dxJoint **joint = (dxJoint**) ALLOCA (nj * sizeof(dxJoint*));
-  memcpy (joint,_joint,nj * sizeof(dxJoint*));
-
-  // for all bodies, compute the inertia tensor and its inverse in the global
-  // frame, and compute the rotational force and add it to the torque
-  // accumulator. I and invI are vertically stacked 3x4 matrices, one per body.
-  // @@@ check computation of rotational force.
-  dReal *I = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
-  dReal *invI = (dReal*) ALLOCA (3*nb*4 * sizeof(dReal));
-
-  //dSetZero (I,3*nb*4);
-  //dSetZero (invI,3*nb*4);
-  for (i=0; i<nb; i++) {
-    dReal tmp[12];
-    // compute inertia tensor in global frame
-    dMULTIPLY2_333 (tmp,body[i]->mass.I,body[i]->R);
-    dMULTIPLY0_333 (I+i*12,body[i]->R,tmp);
-    // compute inverse inertia tensor in global frame
-    dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->R);
-    dMULTIPLY0_333 (invI+i*12,body[i]->R,tmp);
-    // compute rotational force
-    dMULTIPLY0_331 (tmp,I+i*12,body[i]->avel);
-    dCROSS (body[i]->tacc,-=,body[i]->avel,tmp);
-  }
-
-  // add the gravity force to all bodies
-  for (i=0; i<nb; i++) {
-    if ((body[i]->flags & dxBodyNoGravity)==0) {
-      body[i]->facc[0] += body[i]->mass.mass * world->gravity[0];
-      body[i]->facc[1] += body[i]->mass.mass * world->gravity[1];
-      body[i]->facc[2] += body[i]->mass.mass * world->gravity[2];
-    }
-  }
-
-  // get m = total constraint dimension, nub = number of unbounded variables.
-  // create constraint offset array and number-of-rows array for all joints.
-  // the constraints are re-ordered as follows: the purely unbounded
-  // constraints, the mixed unbounded + LCP constraints, and last the purely
-  // LCP constraints. this assists the LCP solver to put all unbounded
-  // variables at the start for a quick factorization.
-  //
-  // joints with m=0 are inactive and are removed from the joints array
-  // entirely, so that the code that follows does not consider them.
-  // also number all active joints in the joint list (set their tag values).
-  // inactive joints receive a tag value of -1.
-
-  int m = 0;
-  dxJoint::Info1 *info = (dxJoint::Info1*) ALLOCA (nj*sizeof(dxJoint::Info1));
-  int *ofs = (int*) ALLOCA (nj*sizeof(int));
-  for (i=0, j=0; j<nj; j++) {   // i=dest, j=src
-    joint[j]->vtable->getInfo1 (joint[j],info+i);
-    dIASSERT (info[i].m >= 0 && info[i].m <= 6 &&
-              info[i].nub >= 0 && info[i].nub <= info[i].m);
-    if (info[i].m > 0) {
-      joint[i] = joint[j];
-      joint[i]->tag = i;
-      i++;
-    }
-    else {
-      joint[j]->tag = -1;
-    }
-  }
-  nj = i;
-
-  // the purely unbounded constraints
-  for (i=0; i<nj; i++) if (info[i].nub == info[i].m) {
-    ofs[i] = m;
-    m += info[i].m;
-  }
-  int nub = m;
-  // the mixed unbounded + LCP constraints
-  for (i=0; i<nj; i++) if (info[i].nub > 0 && info[i].nub < info[i].m) {
-    ofs[i] = m;
-    m += info[i].m;
-  }
-  // the purely LCP constraints
-  for (i=0; i<nj; i++) if (info[i].nub == 0) {
-    ofs[i] = m;
-    m += info[i].m;
-  }
-
-  // this will be set to the force due to the constraints
-  dReal *cforce = (dReal*) ALLOCA (nb*8 * sizeof(dReal));
-  dSetZero (cforce,nb*8);
-
-  // if there are constraints, compute cforce
-  if (m > 0) {
-    // create a constraint equation right hand side vector `c', a constraint
-    // force mixing vector `cfm', and LCP low and high bound vectors, and an
-    // 'findex' vector.
-    dReal *c = (dReal*) ALLOCA (m*sizeof(dReal));
-    dReal *cfm = (dReal*) ALLOCA (m*sizeof(dReal));
-    dReal *lo = (dReal*) ALLOCA (m*sizeof(dReal));
-    dReal *hi = (dReal*) ALLOCA (m*sizeof(dReal));
-    int *findex = (int*) alloca (m*sizeof(int));
-    dSetZero (c,m);
-    dSetValue (cfm,m,world->global_cfm);
-    dSetValue (lo,m,-dInfinity);
-    dSetValue (hi,m, dInfinity);
-    for (i=0; i<m; i++) findex[i] = -1;
-
-    // get jacobian data from constraints. a (2*m)x8 matrix will be created
-    // to store the two jacobian blocks from each constraint. it has this
-    // format:
-    //
-    //   l l l 0 a a a 0  \    .
-    //   l l l 0 a a a 0   }-- jacobian body 1 block for joint 0 (3 rows)
-    //   l l l 0 a a a 0  /
-    //   l l l 0 a a a 0  \    .
-    //   l l l 0 a a a 0   }-- jacobian body 2 block for joint 0 (3 rows)
-    //   l l l 0 a a a 0  /
-    //   l l l 0 a a a 0  }--- jacobian body 1 block for joint 1 (1 row)
-    //   l l l 0 a a a 0  }--- jacobian body 2 block for joint 1 (1 row)
-    //   etc...
-    //
-    //   (lll) = linear jacobian data
-    //   (aaa) = angular jacobian data
-    //
-#   ifdef TIMING
-    dTimerNow ("create J");
-#   endif
-    dReal *J = (dReal*) ALLOCA (2*m*8*sizeof(dReal));
-    dSetZero (J,2*m*8);
-    dxJoint::Info2 Jinfo;
-    Jinfo.rowskip = 8;
-    Jinfo.fps = stepsize1;
-    Jinfo.erp = world->global_erp;
-    for (i=0; i<nj; i++) {
-      Jinfo.J1l = J + 2*8*ofs[i];
-      Jinfo.J1a = Jinfo.J1l + 4;
-      Jinfo.J2l = Jinfo.J1l + 8*info[i].m;
-      Jinfo.J2a = Jinfo.J2l + 4;
-      Jinfo.c = c + ofs[i];
-      Jinfo.cfm = cfm + ofs[i];
-      Jinfo.lo = lo + ofs[i];
-      Jinfo.hi = hi + ofs[i];
-      Jinfo.findex = findex + ofs[i];
-      joint[i]->vtable->getInfo2 (joint[i],&Jinfo);
-      // adjust returned findex values for global index numbering
-      for (j=0; j<info[i].m; j++) {
-        if (findex[ofs[i] + j] >= 0) findex[ofs[i] + j] += ofs[i];
-      }
-    }
-
-    // compute A = J*invM*J'. first compute JinvM = J*invM. this has the same
-    // format as J so we just go through the constraints in J multiplying by
-    // the appropriate scalars and matrices.
-#   ifdef TIMING
-    dTimerNow ("compute A");
-#   endif
-    dReal *JinvM = (dReal*) ALLOCA (2*m*8*sizeof(dReal));
-    dSetZero (JinvM,2*m*8);
-    for (i=0; i<nj; i++) {
-      int b = joint[i]->node[0].body->tag;
-      dReal body_invMass = body[b]->invMass;
-      dReal *body_invI = invI + b*12;
-      dReal *Jsrc = J + 2*8*ofs[i];
-      dReal *Jdst = JinvM + 2*8*ofs[i];
-      for (j=info[i].m-1; j>=0; j--) {
-        for (k=0; k<3; k++) Jdst[k] = Jsrc[k] * body_invMass;
-        dMULTIPLY0_133 (Jdst+4,Jsrc+4,body_invI);
-        Jsrc += 8;
-        Jdst += 8;
-      }
-      if (joint[i]->node[1].body) {
-        b = joint[i]->node[1].body->tag;
-        body_invMass = body[b]->invMass;
-        body_invI = invI + b*12;
-        for (j=info[i].m-1; j>=0; j--) {
-          for (k=0; k<3; k++) Jdst[k] = Jsrc[k] * body_invMass;
-          dMULTIPLY0_133 (Jdst+4,Jsrc+4,body_invI);
-          Jsrc += 8;
-          Jdst += 8;
-        }
-      }
-    }
-
-    // now compute A = JinvM * J'. A's rows and columns are grouped by joint,
-    // i.e. in the same way as the rows of J. block (i,j) of A is only nonzero
-    // if joints i and j have at least one body in common. this fact suggests
-    // the algorithm used to fill A:
-    //
-    //    for b = all bodies
-    //      n = number of joints attached to body b
-    //      for i = 1..n
-    //        for j = i+1..n
-    //          ii = actual joint number for i
-    //          jj = actual joint number for j
-    //          // (ii,jj) will be set to all pairs of joints around body b
-    //          compute blockwise: A(ii,jj) += JinvM(ii) * J(jj)'
-    //
-    // this algorithm catches all pairs of joints that have at least one body
-    // in common. it does not compute the diagonal blocks of A however -
-    // another similar algorithm does that.
-
-    int mskip = dPAD(m);
-    dReal *A = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
-    dSetZero (A,m*mskip);
-    for (i=0; i<nb; i++) {
-      for (dxJointNode *n1=body[i]->firstjoint; n1; n1=n1->next) {
-        for (dxJointNode *n2=n1->next; n2; n2=n2->next) {
-          // get joint numbers and ensure ofs[j1] >= ofs[j2]
-          int j1 = n1->joint->tag;
-          int j2 = n2->joint->tag;
-          if (ofs[j1] < ofs[j2]) {
-            int tmp = j1;
-            j1 = j2;
-            j2 = tmp;
-          }
-
-          // if either joint was tagged as -1 then it is an inactive (m=0)
-          // joint that should not be considered
-          if (j1==-1 || j2==-1) continue;
-
-          // determine if body i is the 1st or 2nd body of joints j1 and j2
-          int jb1 = (joint[j1]->node[1].body == body[i]);
-          int jb2 = (joint[j2]->node[1].body == body[i]);
-          // jb1/jb2 must be 0 for joints with only one body
-          dIASSERT(joint[j1]->node[1].body || jb1==0);
-          dIASSERT(joint[j2]->node[1].body || jb2==0);
-
-          // set block of A
-          MultiplyAdd2_p8r (A + ofs[j1]*mskip + ofs[j2],
-                            JinvM + 2*8*ofs[j1] + jb1*8*info[j1].m,
-                            J     + 2*8*ofs[j2] + jb2*8*info[j2].m,
-                            info[j1].m,info[j2].m, mskip);
-        }
-      }
-    }
-    // compute diagonal blocks of A
-    for (i=0; i<nj; i++) {
-      Multiply2_p8r (A + ofs[i]*(mskip+1),
-                     JinvM + 2*8*ofs[i],
-                     J + 2*8*ofs[i],
-                     info[i].m,info[i].m, mskip);
-      if (joint[i]->node[1].body) {
-        MultiplyAdd2_p8r (A + ofs[i]*(mskip+1),
-                          JinvM + 2*8*ofs[i] + 8*info[i].m,
-                          J + 2*8*ofs[i] + 8*info[i].m,
-                          info[i].m,info[i].m, mskip);
-      }
-    }
-
-    // add cfm to the diagonal of A
-    for (i=0; i<m; i++) A[i*mskip+i] += cfm[i] * stepsize1;
-
-#   ifdef COMPARE_METHODS
-    comparator.nextMatrix (A,m,m,1,"A");
-#   endif
-
-    // compute the right hand side `rhs'
-#   ifdef TIMING
-    dTimerNow ("compute rhs");
-#   endif
-    dReal *tmp1 = (dReal*) ALLOCA (nb*8 * sizeof(dReal));
-    //dSetZero (tmp1,nb*8);
-    // put v/h + invM*fe into tmp1
-    for (i=0; i<nb; i++) {
-      dReal body_invMass = body[i]->invMass;
-      dReal *body_invI = invI + i*12;
-      for (j=0; j<3; j++) tmp1[i*8+j] = body[i]->facc[j] * body_invMass +
-                            body[i]->lvel[j] * stepsize1;
-      dMULTIPLY0_331 (tmp1 + i*8 + 4,body_invI,body[i]->tacc);
-      for (j=0; j<3; j++) tmp1[i*8+4+j] += body[i]->avel[j] * stepsize1;
-    }
-    // put J*tmp1 into rhs
-    dReal *rhs = (dReal*) ALLOCA (m * sizeof(dReal));
-    //dSetZero (rhs,m);
-    for (i=0; i<nj; i++) {
-      dReal *JJ = J + 2*8*ofs[i];
-      Multiply0_p81 (rhs+ofs[i],JJ,
-                     tmp1 + 8*joint[i]->node[0].body->tag, info[i].m);
-      if (joint[i]->node[1].body) {
-        MultiplyAdd0_p81 (rhs+ofs[i],JJ + 8*info[i].m,
-                          tmp1 + 8*joint[i]->node[1].body->tag, info[i].m);
-      }
-    }
-    // complete rhs
-    for (i=0; i<m; i++) rhs[i] = c[i]*stepsize1 - rhs[i];
-
-#   ifdef COMPARE_METHODS
-    comparator.nextMatrix (c,m,1,0,"c");
-    comparator.nextMatrix (rhs,m,1,0,"rhs");
-#   endif
-
-    // solve the LCP problem and get lambda.
-    // this will destroy A but that's okay
-#   ifdef TIMING
-    dTimerNow ("solving LCP problem");
-#   endif
-    dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
-    dReal *residual = (dReal*) ALLOCA (m * sizeof(dReal));
-    dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex);
-
-//  OLD WAY - direct factor and solve
-//
-//    // factorize A (L*L'=A)
-//#   ifdef TIMING
-//    dTimerNow ("factorize A");
-//#   endif
-//    dReal *L = (dReal*) ALLOCA (m*mskip*sizeof(dReal));
-//    memcpy (L,A,m*mskip*sizeof(dReal));
-//#   ifdef FAST_FACTOR
-//    dFastFactorCholesky (L,m);  // does not report non positive definiteness
-//#   else
-//    if (dFactorCholesky (L,m)==0) dDebug (0,"A is not positive definite");
-//#   endif
-//
-//    // compute lambda
-//#   ifdef TIMING
-//    dTimerNow ("compute lambda");
-//#   endif
-//    dReal *lambda = (dReal*) ALLOCA (m * sizeof(dReal));
-//    memcpy (lambda,rhs,m * sizeof(dReal));
-//    dSolveCholesky (L,lambda,m);
-
-#   ifdef COMPARE_METHODS
-    comparator.nextMatrix (lambda,m,1,0,"lambda");
-#   endif
-
-    // compute the constraint force `cforce'
-#   ifdef TIMING
-    dTimerNow ("compute constraint force");
-#   endif
-    // compute cforce = J'*lambda
-    for (i=0; i<nj; i++) {
-      dReal *JJ = J + 2*8*ofs[i];
-      dxBody* b1 = joint[i]->node[0].body;
-      dxBody* b2 = joint[i]->node[1].body;
-      dJointFeedback *fb = joint[i]->feedback;
-
-/******************** breakable joint contribution ***********************/
-    // this saves us a few dereferences
-    dxJointBreakInfo *jBI = joint[i]->breakInfo;
-    // we need joint feedback if the joint is breakable or if the user
-    // requested feedback.
-        if (jBI||fb) {
-      // we need feedback on the amount of force that this joint is
-      // applying to the bodies. we use a slightly slower computation
-      // that splits out the force components and puts them in the
-      // feedback structure.
-      dJointFeedback temp_fb; // temporary storage for joint feedback
-          dReal data1[8],data2[8];
-          Multiply1_8q1 (data1, JJ, lambda+ofs[i], info[i].m);
-          dReal *cf1 = cforce + 8*b1->tag;
-          cf1[0] += (temp_fb.f1[0] = data1[0]);
-          cf1[1] += (temp_fb.f1[1] = data1[1]);
-          cf1[2] += (temp_fb.f1[2] = data1[2]);
-          cf1[4] += (temp_fb.t1[0] = data1[4]);
-          cf1[5] += (temp_fb.t1[1] = data1[5]);
-          cf1[6] += (temp_fb.t1[2] = data1[6]);
-          if (b2) {
-            Multiply1_8q1 (data2, JJ + 8*info[i].m, lambda+ofs[i], info[i].m);
-            dReal *cf2 = cforce + 8*b2->tag;
-            cf2[0] += (temp_fb.f2[0] = data2[0]);
-            cf2[1] += (temp_fb.f2[1] = data2[1]);
-            cf2[2] += (temp_fb.f2[2] = data2[2]);
-            cf2[4] += (temp_fb.t2[0] = data2[4]);
-            cf2[5] += (temp_fb.t2[1] = data2[5]);
-            cf2[6] += (temp_fb.t2[2] = data2[6]);
-          }
-          // if the user requested so we must copy the feedback information to
-          // the feedback struct that the user suplied.
-          if (fb) {
-            // copy temp_fb to fb
-            fb->f1[0] = temp_fb.f1[0];
-            fb->f1[1] = temp_fb.f1[1];
-            fb->f1[2] = temp_fb.f1[2];
-            fb->t1[0] = temp_fb.t1[0];
-            fb->t1[1] = temp_fb.t1[1];
-            fb->t1[2] = temp_fb.t1[2];
-            if (b2) {
-              fb->f2[0] = temp_fb.f2[0];
-              fb->f2[1] = temp_fb.f2[1];
-              fb->f2[2] = temp_fb.f2[2];
-              fb->t2[0] = temp_fb.t2[0];
-              fb->t2[1] = temp_fb.t2[1];
-              fb->t2[2] = temp_fb.t2[2];
-            }
-          }
-          // if the joint is breakable we need to check the breaking conditions
-      if (jBI) {
-        dReal relCF1[3];
-                dReal relCT1[3];
-                // multiply the force and torque vectors by the rotation matrix of body 1
-                dMULTIPLY1_331 (&relCF1[0],b1->R,&temp_fb.f1[0]);
-                dMULTIPLY1_331 (&relCT1[0],b1->R,&temp_fb.t1[0]);
-                if (jBI->flags & dJOINT_BREAK_AT_B1_FORCE) {
-                  // check if the force is to high
-          for (int i = 0; i < 3; i++) {
-            if (relCF1[i] > jBI->b1MaxF[i]) {
-                      jBI->flags |= dJOINT_BROKEN;
-                      goto doneCheckingBreaks;
-                    }
-          }
-                }
-                if (jBI->flags & dJOINT_BREAK_AT_B1_TORQUE) {
-                  // check if the torque is to high
-          for (int i = 0; i < 3; i++) {
-            if (relCT1[i] > jBI->b1MaxT[i]) {
-                      jBI->flags |= dJOINT_BROKEN;
-                      goto doneCheckingBreaks;
-            }
-          }
-                }
-        if (b2) {
-          dReal relCF2[3];
-          dReal relCT2[3];
-          // multiply the force and torque vectors by the rotation matrix of body 2
-          dMULTIPLY1_331 (&relCF2[0],b2->R,&temp_fb.f2[0]);
-          dMULTIPLY1_331 (&relCT2[0],b2->R,&temp_fb.t2[0]);
-                  if (jBI->flags & dJOINT_BREAK_AT_B2_FORCE) {
-            // check if the force is to high
-            for (int i = 0; i < 3; i++) {
-              if (relCF2[i] > jBI->b2MaxF[i]) {
-                jBI->flags |= dJOINT_BROKEN;
-                goto doneCheckingBreaks;
-              }
-            }
-                  }
-                  if (jBI->flags & dJOINT_BREAK_AT_B2_TORQUE) {
-                  // check if the torque is to high
-            for (int i = 0; i < 3; i++) {
-              if (relCT2[i] > jBI->b2MaxT[i]) {
-                jBI->flags |= dJOINT_BROKEN;
-                goto doneCheckingBreaks;
-              }
-            }
-                  }
-        }
-                doneCheckingBreaks:
-                ;
-      }
-    }
-/*************************************************************************/
-      else {
-        // no feedback is required, let's compute cforce the faster way
-        MultiplyAdd1_8q1 (cforce + 8*b1->tag,JJ, lambda+ofs[i], info[i].m);
-        if (b2) {
-          MultiplyAdd1_8q1 (cforce + 8*b2->tag,
-                            JJ + 8*info[i].m, lambda+ofs[i], info[i].m);
-        }
-      }
-    }
-  }
-
-  // compute the velocity update
-# ifdef TIMING
-  dTimerNow ("compute velocity update");
-# endif
-
-  // add fe to cforce
-  for (i=0; i<nb; i++) {
-    for (j=0; j<3; j++) cforce[i*8+j] += body[i]->facc[j];
-    for (j=0; j<3; j++) cforce[i*8+4+j] += body[i]->tacc[j];
-  }
-  // multiply cforce by stepsize
-  for (i=0; i < nb*8; i++) cforce[i] *= stepsize;
-  // add invM * cforce to the body velocity
-  for (i=0; i<nb; i++) {
-    dReal body_invMass = body[i]->invMass;
-    dReal *body_invI = invI + i*12;
-    for (j=0; j<3; j++) body[i]->lvel[j] += body_invMass * cforce[i*8+j];
-    dMULTIPLYADD0_331 (body[i]->avel,body_invI,cforce+i*8+4);
-  }
-
-  // update the position and orientation from the new linear/angular velocity
-  // (over the given timestep)
-# ifdef TIMING
-  dTimerNow ("update position");
-# endif
-  for (i=0; i<nb; i++) moveAndRotateBody (body[i],stepsize);
-
-# ifdef COMPARE_METHODS
-  dReal *tmp_vnew = (dReal*) ALLOCA (nb*6*sizeof(dReal));
-  for (i=0; i<nb; i++) {
-    for (j=0; j<3; j++) tmp_vnew[i*6+j] = body[i]->lvel[j];
-    for (j=0; j<3; j++) tmp_vnew[i*6+3+j] = body[i]->avel[j];
-  }
-  comparator.nextMatrix (tmp_vnew,nb*6,1,0,"vnew");
-# endif
-
-# ifdef TIMING
-  dTimerNow ("tidy up");
-# endif
-
-  // zero all force accumulators
-  for (i=0; i<nb; i++) {
-    body[i]->facc[0] = 0;
-    body[i]->facc[1] = 0;
-    body[i]->facc[2] = 0;
-    body[i]->facc[3] = 0;
-    body[i]->tacc[0] = 0;
-    body[i]->tacc[1] = 0;
-    body[i]->tacc[2] = 0;
-    body[i]->tacc[3] = 0;
-  }
-
-# ifdef TIMING
-  dTimerEnd();
-  if (m > 0) dTimerReport (stdout,1);
-# endif
-}
-
-//****************************************************************************
-
-void dInternalStepIsland (dxWorld *world, dxBody * const *body, int nb,
-                          dxJoint * const *joint, int nj, dReal stepsize)
-{
-# ifndef COMPARE_METHODS
-  dInternalStepIsland_x2 (world,body,nb,joint,nj,stepsize);
-# endif
-
-# ifdef COMPARE_METHODS
-  int i;
-
-  // save body state
-  dxBody *state = (dxBody*) ALLOCA (nb*sizeof(dxBody));
-  for (i=0; i<nb; i++) memcpy (state+i,body[i],sizeof(dxBody));
-
-  // take slow step
-  comparator.reset();
-  dInternalStepIsland_x1 (world,body,nb,joint,nj,stepsize);
-  comparator.end();
-
-  // restore state
-  for (i=0; i<nb; i++) memcpy (body[i],state+i,sizeof(dxBody));
-
-  // take fast step
-  dInternalStepIsland_x2 (world,body,nb,joint,nj,stepsize);
-  comparator.end();
-
-  //comparator.dump();
-  //_exit (1);
-# endif
-}