static void Number_setat(storage_t *st, size_t off, at *x)
{
get_write_permit(st);
ifn (NUMBERP(x))
error(NIL, "not a number", x);
void (*set)(gptr,size_t,real) = storage_setd[st->type];
(*set)(st->data, off, Number(x));
}
void cg_grad_adaptor(double *g, double *x, int n)
{
static at *call = NIL;
static int nx = -1;
static storage_t *stx = NULL;
static storage_t *stg = NULL;
static at *(*listeval)(at *, at *) = NULL;
if (n == -1) {
/* initialize */
at *x0 = var_get(named("x0"));
at *vargs = var_get(named("vargs"));
at *g = var_get(named("g"));
ifn (x0)
error(NIL, "x0 not found", NIL);
ifn (INDEXP(x0) && IND_STTYPE((index_t *)Mptr(x0)))
error(NIL, "x0 not a double index", x0);
ifn (g)
error(NIL, "g not found", NIL);
listeval = Class(g)->listeval;
index_t *ind = Mptr(x0);
nx = storage_nelems(IND_ST(ind));
stx = new_storage(ST_DOUBLE);
stx->flags = STS_FOREIGN;
stx->size = nx;
stx->data = (char *)-1;
stg = new_storage(ST_DOUBLE);
stg->flags = STS_FOREIGN;
stg->size = nx;
stg->data = (char *)-1;
call = new_cons(g,
new_cons(NEW_INDEX(stg, IND_SHAPE(ind)),
new_cons(NEW_INDEX(stx, IND_SHAPE(ind)),
vargs)));
} else {
if (n != nx)
error(NIL, "vector of different size expected", NEW_NUMBER(n));
stx->data = x;
stg->data = g;
listeval(Car(call), call);
}
}
static void
clearconvert(void)
{
int i;
ifn (netconvert)
error(NIL,"you should perform (alloc-net xx xx)",NIL);
for (i=1; i<neurnombre; i++)
netconvert[i]= -1;
netconvert[0]=0;
}
object_t *object_from_cobject(struct CClass_object *cobj)
{
ifn (cobj->Vtbl && cobj->Vtbl->Cdoc && cobj->Vtbl->Cdoc->lispdata.atclass)
error(NIL, "attempt to access instance of unlinked class", NIL);
assert(cobj->Vtbl);
object_t *obj = cobj->__lptr;
ifn (obj) {
class_t *cl = Mptr(cobj->Vtbl->Cdoc->lispdata.atclass);
obj = _new_object(cl, cobj);
}
return obj;
}
static at *storage_listeval(at *p, at *q)
{
storage_t *st = Mptr(p);
if (!st->data)
error(NIL, "unsized storage", p);
q = eval_arglist(Cdr(q));
ifn (CONSP(q) && Car(q) && NUMBERP(Car(q)))
error(NIL, "illegal subscript", q);
ssize_t off = Number(Car(q));
if (off<0 || off>=st->size)
error(NIL, "subscript out of range", q);
if (Cdr(q)) {
ifn (CONSP(Cdr(q)) && !Cddr(q))
error(NIL, "one or two arguments expected",q);
storage_setat[st->type](st, off, Cadr(q));
return st->backptr;
} else
return storage_getat[st->type](st, off);
}
object_t *new_object(class_t *cl)
{
int n = 0;
while (unreachables && n++<2) {
object_t *obj = unreachables;
unreachables = obj->next_unreachable;
object_class->dispose(obj);
}
ifn (cl->live)
error(NIL, "class is obsolete", cl->classname);
return _new_object(cl, NULL);
}
double cg_value_adaptor(double *x, int n)
{
static at *call = NIL;
static int nx = -1;
static storage_t *st = NULL;
static at *(*listeval)(at *, at *) = NULL;
if (n == -1) {
/* initialize */
at *x0 = var_get(named("x0"));
at *vargs = var_get(named("vargs"));
at *f = var_get(named("f"));
ifn (x0)
error(NIL, "x0 not found", NIL);
ifn (INDEXP(x0) && IND_STTYPE((index_t *)Mptr(x0)))
error(NIL, "x0 not a double index", x0);
ifn (f)
error(NIL, "f not found", NIL);
listeval = Class(f)->listeval;
index_t *ind = Mptr(x0);
nx = storage_nelems(IND_ST(ind));
st = new_storage(ST_DOUBLE);
st->flags = STS_FOREIGN;
st->size = nx;
st->data = (char *)-1;
call = new_cons(f, new_cons(NEW_INDEX(st, IND_SHAPE(ind)), vargs));
return NAN;
} else {
if (n != nx)
error(NIL, "vector of different size expected", NEW_NUMBER(n));
st->data = x;
return Number(listeval(Car(call), call));
}
}
/* interface calling into the fortran routine */
static int lbfgs(index_t *x0, at *f, at *g, double gtol, htable_t *p, at *vargs)
{
/* argument checking and setup */
extern void lbfgs_(int *n, int *m, double *x, double *fval, double *gval, \
int *diagco, double *diag, int iprint[2], double *gtol, \
double *xtol, double *w, int *iflag);
ifn (IND_STTYPE(x0) == ST_DOUBLE)
error(NIL, "not an array of doubles", x0->backptr);
ifn (Class(f)->listeval)
error(NIL, "not a function", f);
ifn (Class(f)->listeval)
error(NIL, "not a function", g);
ifn (gtol > 0)
error(NIL, "threshold value not positive", NEW_NUMBER(gtol));
at *gx = copy_array(x0)->backptr;
at *(*listeval_f)(at *, at *) = Class(f)->listeval;
at *(*listeval_g)(at *, at *) = Class(g)->listeval;
at *callf = new_cons(f, new_cons(x0->backptr, vargs));
at *callg = new_cons(g, new_cons(gx, new_cons(x0->backptr, vargs)));
htable_t *params = lbfgs_params();
if (p) htable_update(params, p);
int iprint[2];
iprint[0] = (int)Number(htable_get(params, NEW_SYMBOL("iprint-1")));
iprint[1] = (int)Number(htable_get(params, NEW_SYMBOL("iprint-2")));
lb3_.gtol = Number(htable_get(params, NEW_SYMBOL("ls-gtol")));
lb3_.stpmin = Number(htable_get(params, NEW_SYMBOL("ls-stpmin")));
lb3_.stpmax = Number(htable_get(params, NEW_SYMBOL("ls-stpmax")));
int m = (int)Number(htable_get(params, NEW_SYMBOL("lbfgs-m")));
int n = index_nelems(x0);
double *x = IND_ST(x0)->data;
double fval;
double *gval = IND_ST(Mptr(gx))->data;
int diagco = false;
double *diag = mm_blob(n*sizeof(double));
double *w = mm_blob((n*(m+m+1)+m+m)*sizeof(double));
double xtol = eps(1); /* machine precision */
int iflag = 0;
ifn (n>0)
error(NIL, "empty array", x0->backptr);
ifn (m>0)
error(NIL, "m-parameter must be positive", NEW_NUMBER(m));
/* reverse communication loop */
do {
fval = Number(listeval_f(Car(callf), callf));
listeval_g(Car(callg), callg);
lbfgs_(&n, &m, x, &fval, gval, &diagco, diag, iprint, >ol, &xtol, w, &iflag);
assert(iflag<2);
} while (iflag > 0);
return iflag;
}
at *
new_string_bylen(int n)
{
at *q;
char *buffer;
struct string *st;
st = allocate(&alloc_string);
ifn (buffer = malloc(n+1))
error(NIL, "memory exhausted", NIL);
buffer[0] = 0;
buffer[n] = 0;
st->flag = STRING_ALLOCATED;
st->start = buffer;
st->cptr = 0;
q = new_extern(&string_class, st);
q->flags |= X_STRING;
return q;
}
inline void InsertHash(const STRPTR a, struct Hash *h)
{
struct HashEntry **he, *newhe;
if(!h->Index)
{
ifn((h->Index = calloc(HASH_SIZE, sizeof(struct HashEntry *))))
PrintPrgErr(pmWordListErr);
}
he = &h->Index[HashWord(a) % HASH_SIZE];
if((newhe = malloc(sizeof(struct HashEntry))))
{
newhe->Next = *he;
newhe->Str = a;
*he = newhe;
}
else
PrintPrgErr(pmWordListErr);
}
at *oostruct_getslot(at *p, at *prop)
{
at *slot = Car(prop);
ifn (SYMBOLP(slot))
error(NIL,"not a slot name", slot);
prop = Cdr(prop);
object_t *obj = Mptr(p);
class_t *cl = Class(obj->backptr);
for (int i=0; i<cl->num_slots; i++)
if (slot == cl->slots[i]) {
at *sloti = obj->slots[i];
if (i<cl->num_cslots)
sloti = eval(sloti);
if (prop)
return getslot(sloti, prop);
else
return sloti;
}
error(NIL, "not a slot", slot);
}
void oostruct_setslot(at *p, at *prop, at *val)
{
at *slot = Car(prop);
ifn (SYMBOLP(slot))
error(NIL, "not a slot name", slot);
prop = Cdr(prop);
object_t *obj = Mptr(p);
class_t *cl = Class(obj->backptr);
for(int i=0; i<cl->num_slots; i++)
if (slot == cl->slots[i]) {
if (prop)
setslot(&obj->slots[i], prop, val);
else if (i<cl->num_cslots) {
class_t *cl = classof(obj->slots[i]);
cl->setslot(obj->slots[i], NIL, val);
} else
obj->slots[i] = val;
return;
}
error(NIL, "not a slot", slot);
}
QStringList fieldList_indirect(QSettings *cfg, const QString& filename, const QString& type, QString *typeSuggestion, bool *complete) {
if ((!type.isEmpty() && !provides_indirect().contains(type)) || !understands_indirect(cfg, filename)) {
return QStringList();
}
QFile f(filename);
if (!f.open(QIODevice::ReadOnly)) {
return QStringList();
}
char* data;
if (0 >= f.readLine(data, 1000)) {
return QStringList();
}
QString ifn(data);
KUrl url(ifn);
if (url.isLocalFile() || url.protocol().isEmpty()) {
if (QFileInfo(ifn).isRelative()) {
ifn = QFileInfo(filename).absolutePath() + QDir::separator() + ifn;
}
}
return KstDataSource::fieldListForSource(ifn.trimmed(), type, typeSuggestion, complete);
}
int main(int argc, char *argv[]) {
int taskId, totaltasks, i, j;
int chunk;
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &taskId);
MPI_Comm_size(MPI_COMM_WORLD, &totaltasks);
chunk = NGRID / totaltasks;
FP_PREC xc[chunk + 2];
FP_PREC yc[chunk + 2];
FP_PREC dyc[chunk + 2];
FP_PREC derr[chunk + 2];
FP_PREC intg;
FP_PREC dx;
int prev_task = (taskId - 1) < 0 ? totaltasks - 1 : taskId - 1;
int next_task = (taskId + 1) % totaltasks;
MPI_Request reqs[4];
MPI_Status stats[4];
MPI_Irecv(&yc[0], 1, MPI_DOUBLE, prev_task, prev_task * 1000 + taskId,
MPI_COMM_WORLD, &reqs[0]);
MPI_Irecv(&yc[chunk + 1], 1, MPI_DOUBLE, next_task,
next_task * 1000 + taskId, MPI_COMM_WORLD, &reqs[1]);
for (i = 1; i <= chunk + 1; i++) {
xc[i] = (XI + (XF - XI) * (FP_PREC) (i - 1) / (FP_PREC) (NGRID - 1))
+ taskId * chunk;
}
//define the function
for (i = 1; i <= chunk; i++) {
yc[i] = fn(xc[i]);
}
MPI_Isend(&yc[chunk], 1, MPI_DOUBLE, next_task, taskId * 1000 + next_task,
MPI_COMM_WORLD, &reqs[3]);
MPI_Isend(&yc[1], 1, MPI_DOUBLE, prev_task, taskId * 1000 + prev_task,
MPI_COMM_WORLD, &reqs[2]);
MPI_Waitall(4, reqs, stats);
dx = xc[2] - xc[1];
if (taskId == ROOT) {
xc[0] = xc[1] - dx;
yc[0] = fn(xc[0]);
}
if (taskId == totaltasks - 1) {
xc[chunk + 1] = xc[chunk] + dx;
yc[chunk + 1] = fn(xc[chunk + 1]);
}
//compute the derivative using first-order finite differencing
for (i = 1; i <= chunk; i++) {
dyc[i] = (yc[i + 1] - yc[i - 1]) / (2.0 * dx);
}
//compute the integral using Trapazoidal rule
intg = 0.0;
for (i = 1; i <= chunk; i++) {
if (taskId == totaltasks - 1 && i == chunk)
continue;
intg += 0.5 * (xc[i + 1] - xc[i]) * (yc[i + 1] + yc[i]);
}
//compute the errors
for (i = 1; i <= chunk; i++) {
if (i - 1 != chunk - 1)
derr[i] = fabs((dyc[i] - dfn(xc[i])) / dfn(xc[i]));
}
if (taskId != ROOT) {
MPI_Request nreqs[2];
MPI_Status nstats[2];
MPI_Isend(derr + 1, chunk, MPI_DOUBLE, ROOT, taskId * 1000 + ROOT,
MPI_COMM_WORLD, &nreqs[0]);
MPI_Isend(&intg, 1, MPI_DOUBLE, ROOT, taskId * 1000 + ROOT,
MPI_COMM_WORLD, &nreqs[1]);
MPI_Waitall(2, nreqs, nstats);
}
else {
FP_PREC allxc[NGRID];
FP_PREC allderr[NGRID];
FP_PREC allintg[totaltasks];
FP_PREC davg_err = 0.0;
FP_PREC dstd_dev = 0.0;
FP_PREC intg_err = 0.0;
MPI_Request nreqs[2 * (totaltasks - 1)];
MPI_Status nstats[2 * (totaltasks - 1)];
for (i = 1; i < totaltasks; i++) {
MPI_Irecv(allderr + (i * chunk), chunk,
MPI_DOUBLE, i, i * 1000 + ROOT, MPI_COMM_WORLD,
&nreqs[2 * (i - 1)]);
MPI_Irecv(allintg + i, 1, MPI_DOUBLE, i, i * 1000 + ROOT,
MPI_COMM_WORLD, &nreqs[2 * (i - 1) + 1]);
}
for (i = 0; i < chunk; i++) {
allderr[i] = derr[i + 1];
}
MPI_Waitall(2 * (totaltasks - 1), nreqs, nstats);
//find the average error
for (i = 0; i < NGRID; i++)
davg_err += allderr[i];
for (i = 1; i < totaltasks; i++) {
intg += allintg[i];
}
davg_err /= (FP_PREC) NGRID;
dstd_dev = 0.0;
for (i = 0; i < NGRID; i++) {
dstd_dev += pow(allderr[i] - davg_err, 2);
}
dstd_dev = sqrt(dstd_dev / (FP_PREC) NGRID);
intg_err = fabs((ifn(XI, XF) - intg) / ifn(XI, XF));
for (i = 0; i < NGRID; i++) {
allxc[i] = XI + (XF - XI) * (FP_PREC) i / (FP_PREC) (NGRID - 1);
}
//print_error_data(NGRID, davg_err, dstd_dev, &xc[1], derr, intg_err);
print_error_data(NGRID, davg_err, dstd_dev, allxc, allderr, intg_err);
}
MPI_Finalize();
}
class_t *new_ooclass(at *classname, at *atsuper, at *new_slots, at *defaults)
{
ifn (SYMBOLP(classname))
error(NIL, "not a valid class name", classname);
ifn (length(new_slots) == length(defaults))
error(NIL, "number of slots must match number of defaults", NIL);
ifn (CLASSP(atsuper))
error(NIL, "not a class", atsuper);
class_t *super = Mptr(atsuper);
if (builtin_class_p(super))
error(NIL, "superclass not descendend of class <object>", atsuper);
at *p = new_slots;
at *q = defaults;
int n = 0;
while (CONSP(p) && CONSP(q)) {
ifn (SYMBOLP(Car(p)))
error(NIL, "not a symbol", Car(p));
for (int i=0; i<super->num_slots; i++)
if (Car(p) == super->slots[i])
error(NIL, "a superclass has slot of this name", Car(p));
p = Cdr(p);
q = Cdr(q);
n++;
}
assert(!p && !q);
/* builds the new class */
class_t *cl = mm_alloc(mt_class);
*cl = *object_class;
if (new_slots) {
int num_slots = n + super->num_slots;
cl->slots = mm_allocv(mt_refs, num_slots*sizeof(at *));
cl->defaults = mm_allocv(mt_refs, num_slots*sizeof(at *));
int i = 0;
for (; i<super->num_slots; i++) {
cl->slots[i] = super->slots[i];
cl->defaults[i] = super->defaults[i];
}
for (at *s = new_slots, *d = defaults; CONSP(s); i++, s = Cdr(s), d = Cdr(d)) {
cl->slots[i] = Car(s);
cl->defaults[i] = Car(d);
}
assert(i == num_slots);
cl->num_slots = num_slots;
} else {
cl->slots = super->slots;
cl->defaults = super->defaults;
cl->num_slots = super->num_slots;
}
/* Sets up classname */
cl->classname = classname;
cl->priminame = classname;
/* Sets up lists */
cl->super = super;
cl->atsuper = atsuper;
cl->nextclass = super->subclasses;
cl->subclasses = 0L;
super->subclasses = cl;
/* Initialize the slots */
cl->myslots = new_slots;
cl->mydefaults = defaults;
/* Initialize the methods and hash table */
cl->methods = NIL;
cl->hashtable = 0L;
cl->hashsize = 0;
cl->hashok = 0;
/* Initialize DHCLASS stuff */
cl->has_compiled_part = super->has_compiled_part;
cl->num_cslots = super->num_cslots;
cl->classdoc = 0;
cl->kname = 0;
/* Create AT and returns it */
assert(class_class);
cl->backptr = new_at(class_class, cl);
return cl;
}
void* _ksmem_mbat_alloc (client* c, memunit* unit, uvar32_64 size) {
struct timeb tb;
svar32_64 no, pf, pu, nf, nu, tmp; /* prevoius and next free and used block numbers corresopndevly */
isclientn (c);
ismemunitn (unit, c);
isvalidn (size, c, KSERR_MEMZEROSIZE);
isownern (c, unit);
/* no = index of free and suitable unit->mbat[] entry */
ifn ((no = _ksmem_mbat_find_free (c, unit, size)) == -1);
_ksmem_mbat_neighboors (unit, no, unit->ffb, unit->lfb, &pf, &nf);
_ksmem_mbat_neighboors (unit, no, unit->fub, unit->lub, &pu, &nu);
/* Allocated new block */
atomic(unit)
if (unit->maxfb == unit->mbat[no].size) {
unit->maxfb = 0;
for (tmp = unit->ffb; tmp != -1; tmp = unit->mbat[tmp].next)
if (unit->maxfb < unit->mbat[tmp].size)
unit->maxfb = unit->mbat[tmp].size;
if (unit->maxfb < unit->psize - unit->pbottom)
unit->maxfb = unit->psize - unit->pbottom;
}
if (unit->minfb == unit->mbat[no].size) {
unit->minfb = (uvar32_64)-1;
for (tmp = unit->ffb; tmp != -1; tmp = unit->mbat[tmp].next)
if (unit->minfb > unit->mbat[tmp].size)
unit->minfb = unit->mbat[tmp].size;
if (unit->minfb > unit->psize - unit->pbottom)
unit->minfb = unit->psize - unit->pbottom;
}
if (no == unit->ffb)
unit->ffb = unit->mbat[no].next;
if (no == (svar32_64)unit->tbottom) {
unit->mbat[no].offset = unit->pbottom;
unit->mbat[no].size = size;
unit->pbottom += size;
unit->tbottom++;
unit->tfree--;
} else if (unit->mbat[no].size != size && unit->tbottom < unit->tsize) {
unit->mbat[unit->tbottom].size = unit->mbat[no].size - size;
unit->mbat[unit->tbottom].offset = unit->mbat[no].offset + size;
unit->mbat[unit->tbottom].next = -1;
unit->mbat[no].size = size;
if (unit->mbat[unit->tbottom].size < unit->minfb)
unit->minfb = unit->mbat[unit->tbottom].size;
if (unit->mbat[unit->tbottom].size > unit->maxfb)
unit->maxfb = unit->mbat[unit->tbottom].size;
if (unit->lfb != -1) {
unit->mbat[unit->lfb].next = unit->tbottom;
unit->lfb = unit->tbottom;
} else
unit->lfb = unit->tbottom;
if (unit->ffb == -1)
unit->ffb = unit->tbottom;
if (nf == -1)
nf = unit->tbottom;
unit->tbottom++;
}
if (unit->lfb == no)
unit->lfb = pf;
if (unit->fub > no || unit->fub == -1)
unit->fub = no;
if (unit->lub < no || unit->lub == -1)
unit->lub = no;
if (pu != -1)
unit->mbat[pu].next = no;
if (pf != -1)
unit->mbat[pf].next = nf;
unit->mbat[no].next = nu;
ftime (&tb);
unit->modified = tb.time;
unit->pfree -= size;
unit->maxfb -= size;
unit->minfb = (unit->minfb < unit->maxfb) ? unit->minfb : unit->maxfb;
endatomic
return ((void *)((uvar32_64)(unit->mpage) + unit->mbat[no].offset));
}
int main (int argc, char *argv[])
{
int numproc, rank, len,i;
char hostname[MPI_MAX_PROCESSOR_NAME];
MPI_Init(&argc, &argv);
MPI_Comm_size(MPI_COMM_WORLD, &numproc);
MPI_Comm_rank(MPI_COMM_WORLD, &rank);
MPI_Get_processor_name(hostname, &len);
FP_PREC *yc, *dyc, *derr, *fullerr;
FP_PREC *xc, dx, intg, davg_err, dstd_dev, intg_err;
FP_PREC globalSum = 0.0;
// MPI vailables
MPI_Request *requestList,request;
MPI_Status *status;
//"real" grid indices
int imin, imax;
imin = 1 + (rank * (NGRID/numproc));
if(rank == numproc - 1)
imax = NGRID;
else
imax = (rank+1) * (NGRID/numproc);
int range = imax - imin + 1;
xc = (FP_PREC*) malloc((range + 2) * sizeof(FP_PREC));
yc = (FP_PREC*) malloc((range + 2) * sizeof(FP_PREC));
dyc = (FP_PREC*) malloc((range + 2) * sizeof(FP_PREC));
dx = (XF - XI)/(double)NGRID;
for (i = 1; i <= range ; i++)
{
//xc[i] = imin + (XF - XI) * (FP_PREC)(i - 1)/(FP_PREC)(NGRID - 1);
xc[i] = XI + dx * (imin + i - 2);
}
xc[0] = xc[1] - dx;
xc[range + 1] = xc[range] + dx;
for( i = 1; i <= range; i++ )
{
yc[i] = fn(xc[i]);
}
yc[0] = fn(xc[0]);
yc[range + 1] = fn(xc[range + 1]);
for (i = 1; i <= range; i++)
{
dyc[i] = (yc[i + 1] - yc[i - 1])/(2.0 * dx);
}
intg = 0.0;
for (i = 1; i <= range; i++)
{
intg += 0.5 * (xc[i + 1] - xc[i]) * (yc[i + 1] + yc[i]);
}
MPI_Reduce(&intg, &globalSum, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
//compute the error, average error of the derivatives
derr = (FP_PREC*)malloc((range + 2) * sizeof(FP_PREC));
//compute the errors
for(i = 1; i <= range; i++)
{
derr[i] = fabs((dyc[i] - dfn(xc[i]))/dfn(xc[i]));
}
derr[0] = derr[range + 1] = 0.0;
if(rank == 0)
{
fullerr = (FP_PREC *)malloc(sizeof(FP_PREC)*NGRID);
requestList =(MPI_Request*)malloc((numproc-1)*sizeof(MPI_Request));
for(i = 0;i<range;i++)
{
fullerr[i] = derr[i+1];
}
for(i = 1; i<numproc; i++)
{
int rmin, rmax, *indx;
rmin = 1 + (i * (NGRID/numproc));
if(i == numproc - 1)
rmax = NGRID;
else
rmax = (i+1) * (NGRID/numproc);
MPI_Irecv(fullerr+rmin-1, rmax-rmin+1, MPI_DOUBLE, i, 1, MPI_COMM_WORLD, &(requestList[i-1]));
}
double sum = 0.0;
for(i=0; i<NGRID; i++)
{
sum+=fullerr[i];
}
davg_err = sum/(FP_PREC)NGRID;
dstd_dev = 0.0;
for(i = 0; i< NGRID; i++)
{
dstd_dev += pow(derr[i] - davg_err, 2);
}
dstd_dev = sqrt(dstd_dev/(FP_PREC)NGRID);
intg_err = fabs((ifn(XI, XF) - globalSum)/ifn(XI, XF));
printf("%0.4e: %0.4e: %0.4e\n", davg_err, dstd_dev, intg_err);
}
else
{
MPI_Isend(derr+1, imax-imin+1, MPI_DOUBLE, 0, rank, MPI_COMM_WORLD, &request);
fflush(stdout);
}
MPI_Finalize();
}
int main (int argc, char *argv[])
{
int procid, num_procs;
MPI_Status status;
// derivative_time, integral_time, err_time is the local sum of runtime for each computation
// tick is used to mark time
double derivative_time = 0, integral_time = 0, err_time = 0, tick;
MPI_Init(&argc, &argv);
MPI_Comm_rank(MPI_COMM_WORLD, &procid);
MPI_Comm_size(MPI_COMM_WORLD, &num_procs);
// Calculate grid-points per process
if(NGRID % num_procs > 0)
{
if(procid == 0) printf("NGRID should be divisible by the number of processes!");
MPI_Finalize();
return 1;
}
int points_per_node = NGRID / num_procs;
//loop index
int i;
//domain array and step size
FP_PREC xc[points_per_node], dx;
//function array and derivative
//the size will be dependent on the
//number of processors used
//to the program
FP_PREC yc[points_per_node], dyc[points_per_node];
//integration values
FP_PREC local_intg, intg;
//error analysis array
FP_PREC derr[points_per_node];
//error analysis values
FP_PREC dlocal_sum_err, davg_err, dlocal_std_dev, dstd_dev, intg_err;
//calculate dx
dx = (FP_PREC)(XF - XI)/(FP_PREC)(NGRID - 1);
// get start X for each process (my_XI)
int bins_before_me = procid * points_per_node;
FP_PREC my_XI = XI + bins_before_me * dx;
//construct grid
for (i = 0; i < points_per_node; ++i)
{
xc[i] = my_XI + i * dx;
}
//define the function
for(i = 0; i < points_per_node; ++i)
{
yc[i] = fn(xc[i]);
}
//define holders for left and right bound value
FP_PREC left_bound_yc, right_bound_yc;
if(procid == 0) left_bound_yc = fn(XI-dx);
if(procid == num_procs - 1) right_bound_yc = fn(XF+dx);
tick = MPI_Wtime();
#if BLOCKING
if(procid == 0) printf("Using blocking message! \n");
//Step 1: even nodes send to the right then receive back
//Step 2: even nodes receive from the left then send back
if(procid % 2 == 0)
{
if(procid < num_procs - 1)
{
MPI_Send(&yc[points_per_node-1], 1, MPI_DOUBLE, procid+1, 0, MPI_COMM_WORLD);
MPI_Recv(&right_bound_yc, 1, MPI_DOUBLE, procid+1, 0, MPI_COMM_WORLD, &status);
}
if(procid > 0)
{
MPI_Recv(&left_bound_yc, 1, MPI_DOUBLE, procid-1, 0, MPI_COMM_WORLD, &status);
MPI_Send(&yc[0], 1, MPI_DOUBLE, procid-1, 0, MPI_COMM_WORLD);
}
} else
{
MPI_Recv(&left_bound_yc, 1, MPI_DOUBLE, procid-1, 0, MPI_COMM_WORLD, &status);
MPI_Send(&yc[0], 1, MPI_DOUBLE, procid-1, 0, MPI_COMM_WORLD);
if(procid < num_procs - 1)
{
MPI_Send(&yc[points_per_node-1], 1, MPI_DOUBLE, procid+1, 0, MPI_COMM_WORLD);
MPI_Recv(&right_bound_yc, 1, MPI_DOUBLE, procid+1, 0, MPI_COMM_WORLD, &status);
}
}
#else
if(procid == 0) printf("Using non-blocking message! \n");
MPI_Request request[4];
int current_request = 0;
if(procid < num_procs - 1)
{ // receive right bound yc
MPI_Irecv(&right_bound_yc, 1, MPI_DOUBLE, procid+1, 0, MPI_COMM_WORLD, &request[current_request]);
++current_request;
}
if(procid > 0)
{ // receive left bound yc
MPI_Irecv(&left_bound_yc, 1, MPI_DOUBLE, procid-1, 0, MPI_COMM_WORLD, &request[current_request]);
++current_request;
}
if(procid < num_procs - 1)
{ // send right bound yc to right node
MPI_Isend(&yc[points_per_node-1], 1, MPI_DOUBLE, procid+1, 0, MPI_COMM_WORLD, &request[current_request]);
++current_request;
}
if(procid > 0)
{ // send left bound yc to left node
MPI_Isend(&yc[0], 1, MPI_DOUBLE, procid-1, 0, MPI_COMM_WORLD, &request[current_request]);
++current_request;
}
#endif
derivative_time += MPI_Wtime() - tick;
integral_time += MPI_Wtime() - tick;
// Overlap computation and communication BEGIN
//compute the derivative using first-order finite differencing
tick = MPI_Wtime();
for (i = 1; i < points_per_node-1; ++i)
{
dyc[i] = (yc[i + 1] - yc[i - 1])/(2.0 * dx);
}
derivative_time += MPI_Wtime() - tick;
//compute the integral using Trapazoidal rule
tick = MPI_Wtime();
local_intg = 0.0;
for (i = 0; i < points_per_node-1; ++i)
{
local_intg += 0.5 * (yc[i] + yc[i + 1]) * dx;
}
integral_time += MPI_Wtime() - tick;
// Overlap computation and communication END
// WAIT for non-blocking message complete before continue
#if !BLOCKING
tick = MPI_Wtime();
MPI_Waitall(current_request, request, MPI_STATUSES_IGNORE);
derivative_time += MPI_Wtime() - tick;
integral_time += MPI_Wtime() - tick;
#endif
// compute derivative of boundary points, runtime is not counted because it's quite small
dyc[0] = (yc[1] - left_bound_yc)/(2.0 * dx);
dyc[points_per_node-1] = (right_bound_yc - yc[points_per_node-2])/(2.0 * dx);
// compute integral at right boundary point, runtime is not counted because it's quite small
if(procid < num_procs-1) local_intg += 0.5 * (yc[points_per_node-1] + right_bound_yc) * dx;
tick = MPI_Wtime();
//compute the error, average error of the derivatives
for(i = 0; i < points_per_node; ++i)
{
if(dfn(xc[i]) == 0)
{
printf("WARNING: derivative at point %d on process %d is zero.\n", i, procid);
derr[i] = 0;
}
else derr[i] = fabs((dyc[i] - dfn(xc[i]))/dfn(xc[i]));
}
//find the local average error
dlocal_sum_err = 0.0;
for(i = 0; i < points_per_node; ++i)
{
dlocal_sum_err += derr[i];
}
//calculate and output errors
#if SINGLE_CALL_REDUCTION
if(procid == 0) printf("Using single call reduction! \n");
//all nodes collect sum err and convert it to the mean value
MPI_Allreduce(&dlocal_sum_err, &davg_err, 1, MPI_DOUBLE, MPI_SUM, MPI_COMM_WORLD);
davg_err /= (FP_PREC)NGRID; // each process calculates global average
#else
if(procid == 0) printf("Using manual call reduction! \n");
//all nodes collect sum err and convert it to the mean value
if(procid != 0) MPI_Send(&dlocal_sum_err, 1, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD);
else if(procid == 0)
{
davg_err = dlocal_sum_err;
for(i = 1; i < num_procs; ++i)
{
MPI_Recv(&dlocal_sum_err, 1, MPI_DOUBLE, MPI_ANY_SOURCE, 0, MPI_COMM_WORLD, &status);
davg_err += dlocal_sum_err;
}
davg_err /= (FP_PREC)NGRID;
}
MPI_Bcast(&davg_err, 1, MPI_DOUBLE, 0, MPI_COMM_WORLD);
#endif
//now all nodes have davg_err, find sum squared differences of local derr
dlocal_std_dev = 0.0;
for(i = 0; i < points_per_node; ++i)
{
dlocal_std_dev += pow(derr[i] - davg_err, 2);
}
err_time += MPI_Wtime() - tick;
#if SINGLE_CALL_REDUCTION
//reduce local integral & local (sum squared differences of derr) to root
tick = MPI_Wtime();
MPI_Reduce(&dlocal_std_dev, &dstd_dev, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
err_time += MPI_Wtime() - tick;
tick = MPI_Wtime();
MPI_Reduce(&local_intg, &intg, 1, MPI_DOUBLE, MPI_SUM, 0, MPI_COMM_WORLD);
integral_time += MPI_Wtime() - tick;
#else
//reduce local integral & local (sum squared differences of derr) to root
if(procid != 0)
{
tick = MPI_Wtime();
MPI_Send(&dlocal_std_dev, 1, MPI_DOUBLE, 0, 0, MPI_COMM_WORLD);
err_time += MPI_Wtime() - tick;
tick = MPI_Wtime();
MPI_Send(&local_intg, 1, MPI_DOUBLE, 0, 1, MPI_COMM_WORLD);
integral_time += MPI_Wtime() - tick;
} else if(procid == 0)
{
dstd_dev = dlocal_std_dev;
intg = local_intg;
tick = MPI_Wtime();
for(i = 1; i < num_procs; ++i)
{
MPI_Recv(&dlocal_std_dev, 1, MPI_DOUBLE, MPI_ANY_SOURCE, 0, MPI_COMM_WORLD, &status);
dstd_dev += dlocal_std_dev;
}
err_time += MPI_Wtime() - tick;
tick = MPI_Wtime();
for(i = 1; i < num_procs; ++i)
{
MPI_Recv(&local_intg, 1, MPI_DOUBLE, MPI_ANY_SOURCE, 1, MPI_COMM_WORLD, &status);
intg+= local_intg;
}
integral_time += MPI_Wtime() - tick;
}
#endif
// print out the max runtime for each calculation
double max_derivative_time, max_integral_time, max_err_time;
MPI_Reduce(&derivative_time, &max_derivative_time, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
MPI_Reduce(&integral_time, &max_integral_time, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
MPI_Reduce(&err_time, &max_err_time, 1, MPI_DOUBLE, MPI_MAX, 0, MPI_COMM_WORLD);
if(procid == 0)
{
printf("Max runtime to calculate derivatives is %e\n", max_derivative_time);
printf("Max runtime to calculate integral is %e\n", max_integral_time);
printf("Max runtime to calculate derivative errors is %e\n", max_err_time);
}
//gather derivative results & errors for output
//this part shouldn't be included in running time measurements
FP_PREC *final_dyc = NULL;
FP_PREC *final_derr = NULL;
if(procid == 0)
{
final_dyc = (FP_PREC*)malloc(NGRID * sizeof(FP_PREC));
final_derr = (FP_PREC*)malloc(NGRID * sizeof(FP_PREC));
}
MPI_Gather(dyc, points_per_node, MPI_DOUBLE, final_dyc, points_per_node, MPI_DOUBLE, 0, MPI_COMM_WORLD);
MPI_Gather(derr, points_per_node, MPI_DOUBLE, final_derr, points_per_node, MPI_DOUBLE, 0, MPI_COMM_WORLD);
//final output at root node (rank 0)
if(procid == 0)
{
dstd_dev = sqrt(dstd_dev/(FP_PREC)NGRID);
if(ifn(XI, XF) == 0) {
printf("WARNING: true integral value from XI to XF is equal zero.\n");
intg_err = 0;
} else {
intg_err = fabs((ifn(XI, XF) - intg)/ifn(XI, XF));
}
print_function_data(NGRID, dx, final_dyc);
print_error_data(NGRID, davg_err, dstd_dev, intg_err, dx, final_derr);
free(final_dyc);
free(final_derr);
}
MPI_Finalize();
return 0;
}
at *cdr(at *q)
{
ifn (LISTP(q))
RAISEF("not a list", q);
return q ? Cdr(q) : q;
}
