--- /dev/null Thu Jan 01 00:00:00 1970 +0000
+++ b/ode/src/step.cpp Tue Feb 02 01:00:49 2010 +0200
@@ -0,0 +1,1578 @@
+/*************************************************************************
+ * *
+ * 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 "object.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"
+#include "util.h"
+
+//****************************************************************************
+// misc defines
+
+// memory allocation system
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+unsigned int dMemoryFlag;
+#define REPORT_OUT_OF_MEMORY fprintf(stderr, "Insufficient memory to complete rigid body simulation. Results will not be accurate.\n")
+
+#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
+
+
+// undef to use the fast decomposition
+#define DIRECT_CHOLESKY
+
+//****************************************************************************
+// 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;
+
+ bb = B;
+ for (i=p; i; i--) {
+ cc = C;
+ for (j=r; j; j--) {
+ sum = dMUL(bb[0],cc[0]);
+ sum += dMUL(bb[1],cc[1]);
+ sum += dMUL(bb[2],cc[2]);
+ sum += dMUL(bb[4],cc[4]);
+ sum += dMUL(bb[5],cc[5]);
+ sum += dMUL(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;
+
+ bb = B;
+ for (i=p; i; i--) {
+ cc = C;
+ for (j=r; j; j--) {
+ sum = dMUL(bb[0],cc[0]);
+ sum += dMUL(bb[1],cc[1]);
+ sum += dMUL(bb[2],cc[2]);
+ sum += dMUL(bb[4],cc[4]);
+ sum += dMUL(bb[5],cc[5]);
+ sum += dMUL(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;
+
+ dReal sum;
+ for (i=p; i; i--) {
+ sum = dMUL(B[0],C[0]);
+ sum += dMUL(B[1],C[1]);
+ sum += dMUL(B[2],C[2]);
+ sum += dMUL(B[4],C[4]);
+ sum += dMUL(B[5],C[5]);
+ sum += dMUL(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;
+
+ dReal sum;
+ for (i=p; i; i--) {
+ sum = dMUL(B[0],C[0]);
+ sum += dMUL(B[1],C[1]);
+ sum += dMUL(B[2],C[2]);
+ sum += dMUL(B[4],C[4]);
+ sum += dMUL(B[5],C[5]);
+ sum += dMUL(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;
+
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[k*8],C[k]);
+ A[0] += sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[1+k*8],C[k]);
+ A[1] += sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[2+k*8],C[k]);
+ A[2] += sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[4+k*8],C[k]);
+ A[4] += sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[5+k*8],C[k]);
+ A[5] += sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(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;
+
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[k*8],C[k]);
+ A[0] = sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[1+k*8],C[k]);
+ A[1] = sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[2+k*8],C[k]);
+ A[2] = sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[4+k*8],C[k]);
+ A[4] = sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[5+k*8],C[k]);
+ A[5] = sum;
+ sum = 0;
+ for (k=0; k<q; k++) sum += dMUL(B[6+k*8],C[k]);
+ A[6] = sum;
+}
+
+//****************************************************************************
+// 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;
+
+
+ // 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).
+ ALLOCA(dxJoint*,joint,nj*sizeof(dxJoint*));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (joint == NULL) {
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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.
+ ALLOCA(dReal,I,3*nb*4*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (I == NULL) {
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,invI,3*nb*4*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (invI == NULL) {
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+ //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]->posr.R);
+ dMULTIPLY0_333 (I+i*12,body[i]->posr.R,tmp);
+ // compute inverse inertia tensor in global frame
+ dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->posr.R);
+ dMULTIPLY0_333 (invI+i*12,body[i]->posr.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] += dMUL(body[i]->mass.mass,world->gravity[0]);
+ body[i]->facc[1] += dMUL(body[i]->mass.mass,world->gravity[1]);
+ body[i]->facc[2] += dMUL(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;
+ ALLOCA(dxJoint::Info1,info,nj*sizeof(dxJoint::Info1));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (info == NULL) {
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+ ALLOCA(int,ofs,nj*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (ofs == NULL) {
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+ for (i=0, j=0; j<nj; j++) { // i=dest, j=src
+ joint[j]->vtable->getInfo1 (joint[j],info+i);
+
+ 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;
+ }
+ // 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
+ int nskip = dPAD (n6);
+ ALLOCA(dReal, invM, n6*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (invM == NULL) {
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+ 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
+ ALLOCA(dReal,fe,n6*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (fe == NULL) {
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+ ALLOCA(dReal,v,n6*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (v == NULL) {
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+ //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
+ ALLOCA(dReal,vnew,n6*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (vnew == NULL) {
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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.
+ ALLOCA(dReal,c,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (c == NULL) {
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,cfm,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (cfm == NULL) {
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,lo,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (lo == NULL) {
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,hi,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (hi == NULL) {
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(int,findex,m*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (findex == NULL) {
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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.
+
+ ALLOCA(dReal,J,m*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (J == NULL) {
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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'
+
+ ALLOCA(dReal,JinvM,m*nskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (JinvM == NULL) {
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ //dSetZero (JinvM,m*nskip);
+ dMultiply0 (JinvM,J,invM,m,n6,n6);
+ int mskip = dPAD(m);
+ ALLOCA(dReal,A,m*mskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (A == NULL) {
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ //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] += dMUL(cfm[i],Jinfo.fps);
+
+ // compute `rhs', the right hand side of the equation J*a=c
+ ALLOCA(dReal,tmp1,n6*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (tmp1 == NULL) {
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ //dSetZero (tmp1,n6);
+ dMultiply0 (tmp1,invM,fe,n6,n6,1);
+ for (i=0; i<n6; i++) tmp1[i] += dDIV(v[i],stepsize);
+ ALLOCA(dReal,rhs,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (rhs == NULL) {
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ //dSetZero (rhs,m);
+ dMultiply0 (rhs,J,tmp1,m,n6,1);
+ for (i=0; i<m; i++) rhs[i] = dDIV(c[i],stepsize) - rhs[i];
+
+
+
+
+#ifndef DIRECT_CHOLESKY
+ // solve the LCP problem and get lambda.
+ // this will destroy A but that's okay
+ ALLOCA(dReal,lambda,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (lambda == NULL) {
+ UNALLOCA(rhs);
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,residual,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (residual == NULL) {
+ UNALLOCA(lambda);
+ UNALLOCA(rhs);
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex);
+ UNALLOCA(residual);
+ UNALLOCA(lambda);
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY)
+ return;
+#endif
+
+
+#else
+
+ // OLD WAY - direct factor and solve
+
+ // factorize A (L*L'=A)
+
+ ALLOCA(dReal,L,m*mskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (L == NULL) {
+ UNALLOCA(rhs);
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ memcpy (L,A,m*mskip*sizeof(dReal));
+
+ // compute lambda
+
+ ALLOCA(dReal,lambda,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (lambda == NULL) {
+ UNALLOCA(L);
+ UNALLOCA(rhs);
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(vnew);
+ UNALLOCA(v);
+ UNALLOCA(fe);
+ UNALLOCA(invM);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ memcpy (lambda,rhs,m * sizeof(dReal));
+ dSolveCholesky (L,lambda,m);
+#endif
+
+
+ // compute the velocity update `vnew'
+ 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] + dMUL(stepsize,vnew[i]);
+
+
+ UNALLOCA(c);
+ UNALLOCA(cfm);
+ UNALLOCA(lo);
+ UNALLOCA(hi);
+ UNALLOCA(findex);
+ UNALLOCA(J);
+ UNALLOCA(JinvM);
+ UNALLOCA(A);
+ UNALLOCA(tmp1);
+ UNALLOCA(rhs);
+ UNALLOCA(lambda);
+ UNALLOCA(L);
+ }
+ else {
+ // no constraints
+ dMultiply0 (vnew,invM,fe,n6,n6,1);
+ for (i=0; i<n6; i++) vnew[i] = v[i] + dMUL(stepsize,vnew[i]);
+ }
+
+ // apply the velocity update to the bodies
+ 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)
+
+ for (i=0; i<nb; i++) dxStepBody (body[i],stepsize);
+
+ // 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;
+ }
+
+
+ UNALLOCA(joint);
+ UNALLOCA(I);
+ UNALLOCA(invI);
+ UNALLOCA(info);
+ UNALLOCA(ofs);
+ UNALLOCA(invM);
+ UNALLOCA(fe);
+ UNALLOCA(v);
+ UNALLOCA(vnew);
+}
+
+//****************************************************************************
+// 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;
+ 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).
+ ALLOCA(dxJoint*,joint,nj*sizeof(dxJoint*));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (joint == NULL) {
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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 = NULL;
+
+ ALLOCA(dReal,invI,3*nb*4*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (invI == NULL) {
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+ //dSetZero (I,3*nb*4);
+ //dSetZero (invI,3*nb*4);
+ for (i=0; i<nb; i++) {
+ dReal tmp[12];
+
+ // compute inverse inertia tensor in global frame
+ dMULTIPLY2_333 (tmp,body[i]->invI,body[i]->posr.R);
+ dMULTIPLY0_333 (invI+i*12,body[i]->posr.R,tmp);
+ }
+
+ // add the gravity force to all bodies
+ for (i=0; i<nb; i++) {
+ if ((body[i]->flags & dxBodyNoGravity)==0) {
+ body[i]->facc[0] += dMUL(body[i]->mass.mass,world->gravity[0]);
+ body[i]->facc[1] += dMUL(body[i]->mass.mass,world->gravity[1]);
+ body[i]->facc[2] += dMUL(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;
+ ALLOCA(dxJoint::Info1,info,nj*sizeof(dxJoint::Info1));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (info == NULL) {
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(int,ofs,nj*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (ofs == NULL) {
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ for (i=0, j=0; j<nj; j++) { // i=dest, j=src
+ joint[j]->vtable->getInfo1 (joint[j],info+i);
+
+ 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
+ ALLOCA(dReal,cforce,nb*8*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (cforce == NULL) {
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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.
+ ALLOCA(dReal,c,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (c == NULL) {
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,cfm,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (cfm == NULL) {
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,lo,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (lo == NULL) {
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,hi,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (hi == NULL) {
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(int,findex,m*sizeof(int));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (findex == NULL) {
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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
+ //
+ ALLOCA(dReal,J,2*m*8*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (J == NULL) {
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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.
+
+ ALLOCA(dReal,JinvM,2*m*8*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (JinvM == NULL) {
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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] = dMUL(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] = dMUL(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);
+ ALLOCA(dReal,A,m*mskip*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (A == NULL) {
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ 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
+
+
+ // 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] += dMUL(cfm[i],stepsize1);
+
+ // compute the right hand side `rhs'
+ ALLOCA(dReal,tmp1,nb*8*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (tmp1 == NULL) {
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ //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] = dMUL(body[i]->facc[j],body_invMass) +
+ dMUL(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] += dMUL(body[i]->avel[j],stepsize1);
+ }
+ // put J*tmp1 into rhs
+ ALLOCA(dReal,rhs,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (rhs == NULL) {
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ //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] = dMUL(c[i],stepsize1) - rhs[i];
+
+ // solve the LCP problem and get lambda.
+ // this will destroy A but that's okay
+ ALLOCA(dReal,lambda,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (lambda == NULL) {
+ UNALLOCA(rhs);
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ ALLOCA(dReal,residual,m*sizeof(dReal));
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (residual == NULL) {
+ UNALLOCA(lambda);
+ UNALLOCA(rhs);
+ UNALLOCA(tmp1);
+ UNALLOCA(A);
+ UNALLOCA(JinvM);
+ UNALLOCA(J);
+ UNALLOCA(findex);
+ UNALLOCA(hi);
+ UNALLOCA(lo);
+ UNALLOCA(cfm);
+ UNALLOCA(c);
+ UNALLOCA(cforce);
+ UNALLOCA(ofs);
+ UNALLOCA(info);
+ UNALLOCA(invI);
+ UNALLOCA(I);
+ UNALLOCA(joint);
+ dMemoryFlag = d_MEMORY_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+ dSolveLCP (m,A,lambda,rhs,residual,nub,lo,hi,findex);
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY)
+ return;
+#endif
+
+
+// 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);
+
+
+ // compute the constraint force `cforce'
+ // 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;
+
+ if (fb) {
+ // the user has requested 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.
+ dReal data1[8],data2[8];
+ Multiply1_8q1 (data1, JJ, lambda+ofs[i], info[i].m);
+ dReal *cf1 = cforce + 8*b1->tag;
+ cf1[0] += (fb->f1[0] = data1[0]);
+ cf1[1] += (fb->f1[1] = data1[1]);
+ cf1[2] += (fb->f1[2] = data1[2]);
+ cf1[4] += (fb->t1[0] = data1[4]);
+ cf1[5] += (fb->t1[1] = data1[5]);
+ cf1[6] += (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] += (fb->f2[0] = data2[0]);
+ cf2[1] += (fb->f2[1] = data2[1]);
+ cf2[2] += (fb->f2[2] = data2[2]);
+ cf2[4] += (fb->t2[0] = data2[4]);
+ cf2[5] += (fb->t2[1] = data2[5]);
+ cf2[6] += (fb->t2[2] = data2[6]);
+ }
+ }
+ 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);
+ }
+ }
+ }
+ UNALLOCA(c);
+ UNALLOCA(cfm);
+ UNALLOCA(lo);
+ UNALLOCA(hi);
+ UNALLOCA(findex);
+ UNALLOCA(J);
+ UNALLOCA(JinvM);
+ UNALLOCA(A);
+ UNALLOCA(tmp1);
+ UNALLOCA(rhs);
+ UNALLOCA(lambda);
+ UNALLOCA(residual);
+ }
+
+ // compute the velocity update
+ // 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] = dMUL(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] += dMUL(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)
+ for (i=0; i<nb; i++) dxStepBody (body[i],stepsize);
+
+ // 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;
+ }
+
+ UNALLOCA(joint);
+ UNALLOCA(I);
+ UNALLOCA(invI);
+ UNALLOCA(info);
+ UNALLOCA(ofs);
+ UNALLOCA(cforce);
+}
+
+//****************************************************************************
+
+void dInternalStepIsland (dxWorld *world, dxBody * const *body, int nb,
+ dxJoint * const *joint, int nj, dReal stepsize)
+{
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ dMemoryFlag = d_MEMORY_OK;
+#endif
+
+#ifndef COMPARE_METHODS
+ dInternalStepIsland_x2 (world,body,nb,joint,nj,stepsize);
+
+#ifdef dUSE_MALLOC_FOR_ALLOCA
+ if (dMemoryFlag == d_MEMORY_OUT_OF_MEMORY) {
+ REPORT_OUT_OF_MEMORY;
+ return;
+ }
+#endif
+
+#endif
+
+}
+
+