mirror of
https://github.com/tildearrow/furnace.git
synced 2024-11-24 05:25:12 +00:00
552 lines
16 KiB
C
552 lines
16 KiB
C
/*
|
|
* Copyright (c) 2003, 2007-14 Matteo Frigo
|
|
* Copyright (c) 1999-2003, 2007-8 Massachusetts Institute of Technology
|
|
*
|
|
* This program is free software; you can redistribute it and/or modify
|
|
* it under the terms of the GNU General Public License as published by
|
|
* the Free Software Foundation; either version 2 of the License, or
|
|
* (at your option) any later version.
|
|
*
|
|
* This program 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
|
|
* GNU General Public License for more details.
|
|
*
|
|
* You should have received a copy of the GNU General Public License
|
|
* along with this program; if not, write to the Free Software
|
|
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301 USA
|
|
*
|
|
*/
|
|
|
|
/**********************************************************************/
|
|
/* This is a modified and combined version of the sched.c and
|
|
test_sched.c files shipped with FFTW 2, written to implement and
|
|
test various all-to-all communications scheduling patterns.
|
|
|
|
It is not used in FFTW 3, but I keep it around in case we ever want
|
|
to play with this again or to change algorithms. In particular, I
|
|
used it to implement and test the fill1_comm_sched routine in
|
|
transpose-pairwise.c, which allows us to create a schedule for one
|
|
process at a time and is much more compact than the FFTW 2 code.
|
|
|
|
Note that the scheduling algorithm is somewhat modified from that
|
|
of FFTW 2. Originally, I thought that one "stall" in the schedule
|
|
was unavoidable for odd numbers of processes, since this is the
|
|
case for the soccer-timetabling problem. However, because of the
|
|
self-communication step, we can use the self-communication to fill
|
|
in the stalls. (Thanks to Ralf Wildenhues for pointing this out.)
|
|
This greatly simplifies the process re-sorting algorithm. */
|
|
|
|
/**********************************************************************/
|
|
|
|
#include <stdio.h>
|
|
#include <stdlib.h>
|
|
|
|
/* This file contains routines to compute communications schedules for
|
|
all-to-all communications (complete exchanges) that are performed
|
|
in-place. (That is, the block that processor x sends to processor
|
|
y gets replaced on processor x by a block received from processor y.)
|
|
|
|
A schedule, int **sched, is a two-dimensional array where
|
|
sched[pe][i] is the processor that pe expects to exchange a message
|
|
with on the i-th step of the exchange. sched[pe][i] == -1 for the
|
|
i after the last exchange scheduled on pe.
|
|
|
|
Here, processors (pe's, for processing elements), are numbered from
|
|
0 to npes-1.
|
|
|
|
There are a couple of constraints that a schedule should satisfy
|
|
(besides the obvious one that every processor has to communicate
|
|
with every other processor exactly once).
|
|
|
|
* First, and most importantly, there must be no deadlocks.
|
|
|
|
* Second, we would like to overlap communications as much as possible,
|
|
so that all exchanges occur in parallel. It turns out that perfect
|
|
overlap is possible for all number of processes (npes).
|
|
|
|
It turns out that this scheduling problem is actually well-studied,
|
|
and good solutions are known. The problem is known as a
|
|
"time-tabling" problem, and is specifically the problem of
|
|
scheduling a sports competition (where n teams must compete exactly
|
|
once with every other team). The problem is discussed and
|
|
algorithms are presented in:
|
|
|
|
[1] J. A. M. Schreuder, "Constructing Timetables for Sport
|
|
Competitions," Mathematical Programming Study 13, pp. 58-67 (1980).
|
|
|
|
[2] A. Schaerf, "Scheduling Sport Tournaments using Constraint
|
|
Logic Programming," Proc. of 12th Europ. Conf. on
|
|
Artif. Intell. (ECAI-96), pp. 634-639 (Budapest 1996).
|
|
http://hermes.dis.uniromal.it/~aschaerf/publications.html
|
|
|
|
(These people actually impose a lot of additional constraints that
|
|
we don't care about, so they are solving harder problems. [1] gives
|
|
a simple enough algorithm for our purposes, though.)
|
|
|
|
In the timetabling problem, N teams can all play one another in N-1
|
|
steps if N is even, and N steps if N is odd. Here, however,
|
|
there is a "self-communication" step (a team must also "play itself")
|
|
and so we can always make an optimal N-step schedule regardless of N.
|
|
|
|
However, we have to do more: for a particular processor, the
|
|
communications schedule must be sorted in ascending or descending
|
|
order of processor index. (This is necessary so that the data
|
|
coming in for the transpose does not overwrite data that will be
|
|
sent later; for that processor the incoming and outgoing blocks are
|
|
of different non-zero sizes.) Fortunately, because the schedule
|
|
is stall free, each parallel step of the schedule is independent
|
|
of every other step, and we can reorder the steps arbitrarily
|
|
to achieve any desired order on a particular process.
|
|
*/
|
|
|
|
void free_comm_schedule(int **sched, int npes)
|
|
{
|
|
if (sched) {
|
|
int i;
|
|
|
|
for (i = 0; i < npes; ++i)
|
|
free(sched[i]);
|
|
free(sched);
|
|
}
|
|
}
|
|
|
|
void empty_comm_schedule(int **sched, int npes)
|
|
{
|
|
int i;
|
|
for (i = 0; i < npes; ++i)
|
|
sched[i][0] = -1;
|
|
}
|
|
|
|
extern void fill_comm_schedule(int **sched, int npes);
|
|
|
|
/* Create a new communications schedule for a given number of processors.
|
|
The schedule is initialized to a deadlock-free, maximum overlap
|
|
schedule. Returns NULL on an error (may print a message to
|
|
stderr if there is a program bug detected). */
|
|
int **make_comm_schedule(int npes)
|
|
{
|
|
int **sched;
|
|
int i;
|
|
|
|
sched = (int **) malloc(sizeof(int *) * npes);
|
|
if (!sched)
|
|
return NULL;
|
|
|
|
for (i = 0; i < npes; ++i)
|
|
sched[i] = NULL;
|
|
|
|
for (i = 0; i < npes; ++i) {
|
|
sched[i] = (int *) malloc(sizeof(int) * 10 * (npes + 1));
|
|
if (!sched[i]) {
|
|
free_comm_schedule(sched,npes);
|
|
return NULL;
|
|
}
|
|
}
|
|
|
|
empty_comm_schedule(sched,npes);
|
|
fill_comm_schedule(sched,npes);
|
|
|
|
if (!check_comm_schedule(sched,npes)) {
|
|
free_comm_schedule(sched,npes);
|
|
return NULL;
|
|
}
|
|
|
|
return sched;
|
|
}
|
|
|
|
static void add_dest_to_comm_schedule(int **sched, int pe, int dest)
|
|
{
|
|
int i;
|
|
|
|
for (i = 0; sched[pe][i] != -1; ++i)
|
|
;
|
|
|
|
sched[pe][i] = dest;
|
|
sched[pe][i+1] = -1;
|
|
}
|
|
|
|
static void add_pair_to_comm_schedule(int **sched, int pe1, int pe2)
|
|
{
|
|
add_dest_to_comm_schedule(sched, pe1, pe2);
|
|
if (pe1 != pe2)
|
|
add_dest_to_comm_schedule(sched, pe2, pe1);
|
|
}
|
|
|
|
/* Simplification of algorithm presented in [1] (we have fewer
|
|
constraints). Produces a perfect schedule (npes steps). */
|
|
|
|
void fill_comm_schedule(int **sched, int npes)
|
|
{
|
|
int pe, i, n;
|
|
|
|
if (npes % 2 == 0) {
|
|
n = npes;
|
|
for (pe = 0; pe < npes; ++pe)
|
|
add_pair_to_comm_schedule(sched,pe,pe);
|
|
}
|
|
else
|
|
n = npes + 1;
|
|
|
|
for (pe = 0; pe < n - 1; ++pe) {
|
|
add_pair_to_comm_schedule(sched, pe, npes % 2 == 0 ? npes - 1 : pe);
|
|
|
|
for (i = 1; i < n/2; ++i) {
|
|
int pe_a, pe_b;
|
|
|
|
pe_a = pe - i;
|
|
if (pe_a < 0)
|
|
pe_a += n - 1;
|
|
|
|
pe_b = (pe + i) % (n - 1);
|
|
|
|
add_pair_to_comm_schedule(sched,pe_a,pe_b);
|
|
}
|
|
}
|
|
}
|
|
|
|
/* given an array sched[npes], fills it with the communications
|
|
schedule for process pe. */
|
|
void fill1_comm_sched(int *sched, int which_pe, int npes)
|
|
{
|
|
int pe, i, n, s = 0;
|
|
if (npes % 2 == 0) {
|
|
n = npes;
|
|
sched[s++] = which_pe;
|
|
}
|
|
else
|
|
n = npes + 1;
|
|
for (pe = 0; pe < n - 1; ++pe) {
|
|
if (npes % 2 == 0) {
|
|
if (pe == which_pe) sched[s++] = npes - 1;
|
|
else if (npes - 1 == which_pe) sched[s++] = pe;
|
|
}
|
|
else if (pe == which_pe) sched[s++] = pe;
|
|
|
|
if (pe != which_pe && which_pe < n - 1) {
|
|
i = (pe - which_pe + (n - 1)) % (n - 1);
|
|
if (i < n/2)
|
|
sched[s++] = (pe + i) % (n - 1);
|
|
|
|
i = (which_pe - pe + (n - 1)) % (n - 1);
|
|
if (i < n/2)
|
|
sched[s++] = (pe - i + (n - 1)) % (n - 1);
|
|
}
|
|
}
|
|
if (s != npes) {
|
|
fprintf(stderr, "bug in fill1_com_schedule (%d, %d/%d)\n",
|
|
s, which_pe, npes);
|
|
exit(EXIT_FAILURE);
|
|
}
|
|
}
|
|
|
|
/* sort the communication schedule sched for npes so that the schedule
|
|
on process sortpe is ascending or descending (!ascending). */
|
|
static void sort1_comm_sched(int *sched, int npes, int sortpe, int ascending)
|
|
{
|
|
int *sortsched, i;
|
|
sortsched = (int *) malloc(npes * sizeof(int) * 2);
|
|
fill1_comm_sched(sortsched, sortpe, npes);
|
|
if (ascending)
|
|
for (i = 0; i < npes; ++i)
|
|
sortsched[npes + sortsched[i]] = sched[i];
|
|
else
|
|
for (i = 0; i < npes; ++i)
|
|
sortsched[2*npes - 1 - sortsched[i]] = sched[i];
|
|
for (i = 0; i < npes; ++i)
|
|
sched[i] = sortsched[npes + i];
|
|
free(sortsched);
|
|
}
|
|
|
|
/* Below, we have various checks in case of bugs: */
|
|
|
|
/* check for deadlocks by simulating the schedule and looking for
|
|
cycles in the dependency list; returns 0 if there are deadlocks
|
|
(or other errors) */
|
|
static int check_schedule_deadlock(int **sched, int npes)
|
|
{
|
|
int *step, *depend, *visited, pe, pe2, period, done = 0;
|
|
int counter = 0;
|
|
|
|
/* step[pe] is the step in the schedule that a given pe is on */
|
|
step = (int *) malloc(sizeof(int) * npes);
|
|
|
|
/* depend[pe] is the pe' that pe is currently waiting for a message
|
|
from (-1 if none) */
|
|
depend = (int *) malloc(sizeof(int) * npes);
|
|
|
|
/* visited[pe] tells whether we have visited the current pe already
|
|
when we are looking for cycles. */
|
|
visited = (int *) malloc(sizeof(int) * npes);
|
|
|
|
if (!step || !depend || !visited) {
|
|
free(step); free(depend); free(visited);
|
|
return 0;
|
|
}
|
|
|
|
for (pe = 0; pe < npes; ++pe)
|
|
step[pe] = 0;
|
|
|
|
while (!done) {
|
|
++counter;
|
|
|
|
for (pe = 0; pe < npes; ++pe)
|
|
depend[pe] = sched[pe][step[pe]];
|
|
|
|
/* now look for cycles in the dependencies with period > 2: */
|
|
for (pe = 0; pe < npes; ++pe)
|
|
if (depend[pe] != -1) {
|
|
for (pe2 = 0; pe2 < npes; ++pe2)
|
|
visited[pe2] = 0;
|
|
|
|
period = 0;
|
|
pe2 = pe;
|
|
do {
|
|
visited[pe2] = period + 1;
|
|
pe2 = depend[pe2];
|
|
period++;
|
|
} while (pe2 != -1 && !visited[pe2]);
|
|
|
|
if (pe2 == -1) {
|
|
fprintf(stderr,
|
|
"BUG: unterminated cycle in schedule!\n");
|
|
free(step); free(depend);
|
|
free(visited);
|
|
return 0;
|
|
}
|
|
if (period - (visited[pe2] - 1) > 2) {
|
|
fprintf(stderr,"BUG: deadlock in schedule!\n");
|
|
free(step); free(depend);
|
|
free(visited);
|
|
return 0;
|
|
}
|
|
|
|
if (pe2 == pe)
|
|
step[pe]++;
|
|
}
|
|
|
|
done = 1;
|
|
for (pe = 0; pe < npes; ++pe)
|
|
if (sched[pe][step[pe]] != -1) {
|
|
done = 0;
|
|
break;
|
|
}
|
|
}
|
|
|
|
free(step); free(depend); free(visited);
|
|
return (counter > 0 ? counter : 1);
|
|
}
|
|
|
|
/* sanity checks; prints message and returns 0 on failure.
|
|
undocumented feature: the return value on success is actually the
|
|
number of steps required for the schedule to complete, counting
|
|
stalls. */
|
|
int check_comm_schedule(int **sched, int npes)
|
|
{
|
|
int pe, i, comm_pe;
|
|
|
|
for (pe = 0; pe < npes; ++pe) {
|
|
for (comm_pe = 0; comm_pe < npes; ++comm_pe) {
|
|
for (i = 0; sched[pe][i] != -1 && sched[pe][i] != comm_pe; ++i)
|
|
;
|
|
if (sched[pe][i] == -1) {
|
|
fprintf(stderr,"BUG: schedule never sends message from "
|
|
"%d to %d.\n",pe,comm_pe);
|
|
return 0; /* never send message to comm_pe */
|
|
}
|
|
}
|
|
for (i = 0; sched[pe][i] != -1; ++i)
|
|
;
|
|
if (i != npes) {
|
|
fprintf(stderr,"BUG: schedule sends too many messages from "
|
|
"%d\n",pe);
|
|
return 0;
|
|
}
|
|
}
|
|
return check_schedule_deadlock(sched,npes);
|
|
}
|
|
|
|
/* invert the order of all the schedules; this has no effect on
|
|
its required properties. */
|
|
void invert_comm_schedule(int **sched, int npes)
|
|
{
|
|
int pe, i;
|
|
|
|
for (pe = 0; pe < npes; ++pe)
|
|
for (i = 0; i < npes/2; ++i) {
|
|
int dummy = sched[pe][i];
|
|
sched[pe][i] = sched[pe][npes-1-i];
|
|
sched[pe][npes-1-i] = dummy;
|
|
}
|
|
}
|
|
|
|
/* Sort the schedule for sort_pe in ascending order of processor
|
|
index. Unfortunately, for odd npes (when schedule has a stall
|
|
to begin with) this will introduce an extra stall due to
|
|
the motion of the self-communication past a stall. We could
|
|
fix this if it were really important. Actually, we don't
|
|
get an extra stall when sort_pe == 0 or npes-1, which is sufficient
|
|
for our purposes. */
|
|
void sort_comm_schedule(int **sched, int npes, int sort_pe)
|
|
{
|
|
int i,j,pe;
|
|
|
|
/* Note that we can do this sort in O(npes) swaps because we know
|
|
that the numbers we are sorting are just 0...npes-1. But we'll
|
|
just do a bubble sort for simplicity here. */
|
|
|
|
for (i = 0; i < npes - 1; ++i)
|
|
for (j = i + 1; j < npes; ++j)
|
|
if (sched[sort_pe][i] > sched[sort_pe][j]) {
|
|
for (pe = 0; pe < npes; ++pe) {
|
|
int s = sched[pe][i];
|
|
sched[pe][i] = sched[pe][j];
|
|
sched[pe][j] = s;
|
|
}
|
|
}
|
|
}
|
|
|
|
/* print the schedule (for debugging purposes) */
|
|
void print_comm_schedule(int **sched, int npes)
|
|
{
|
|
int pe, i, width;
|
|
|
|
if (npes < 10)
|
|
width = 1;
|
|
else if (npes < 100)
|
|
width = 2;
|
|
else
|
|
width = 3;
|
|
|
|
for (pe = 0; pe < npes; ++pe) {
|
|
printf("pe %*d schedule:", width, pe);
|
|
for (i = 0; sched[pe][i] != -1; ++i)
|
|
printf(" %*d",width,sched[pe][i]);
|
|
printf("\n");
|
|
}
|
|
}
|
|
|
|
int main(int argc, char **argv)
|
|
{
|
|
int **sched;
|
|
int npes = -1, sortpe = -1, steps, i;
|
|
|
|
if (argc >= 2) {
|
|
npes = atoi(argv[1]);
|
|
if (npes <= 0) {
|
|
fprintf(stderr,"npes must be positive!");
|
|
return 1;
|
|
}
|
|
}
|
|
if (argc >= 3) {
|
|
sortpe = atoi(argv[2]);
|
|
if (sortpe < 0 || sortpe >= npes) {
|
|
fprintf(stderr,"sortpe must be between 0 and npes-1.\n");
|
|
return 1;
|
|
}
|
|
}
|
|
|
|
if (npes != -1) {
|
|
printf("Computing schedule for npes = %d:\n",npes);
|
|
sched = make_comm_schedule(npes);
|
|
if (!sched) {
|
|
fprintf(stderr,"Out of memory!");
|
|
return 6;
|
|
}
|
|
|
|
if (steps = check_comm_schedule(sched,npes))
|
|
printf("schedule OK (takes %d steps to complete).\n", steps);
|
|
else
|
|
printf("schedule not OK.\n");
|
|
|
|
print_comm_schedule(sched, npes);
|
|
|
|
if (sortpe != -1) {
|
|
printf("\nRe-creating schedule for pe = %d...\n", sortpe);
|
|
int *sched1 = (int*) malloc(sizeof(int) * npes);
|
|
for (i = 0; i < npes; ++i) sched1[i] = -1;
|
|
fill1_comm_sched(sched1, sortpe, npes);
|
|
printf(" =");
|
|
for (i = 0; i < npes; ++i)
|
|
printf(" %*d", npes < 10 ? 1 : (npes < 100 ? 2 : 3),
|
|
sched1[i]);
|
|
printf("\n");
|
|
|
|
printf("\nSorting schedule for sortpe = %d...\n", sortpe);
|
|
sort_comm_schedule(sched,npes,sortpe);
|
|
|
|
if (steps = check_comm_schedule(sched,npes))
|
|
printf("schedule OK (takes %d steps to complete).\n",
|
|
steps);
|
|
else
|
|
printf("schedule not OK.\n");
|
|
|
|
print_comm_schedule(sched, npes);
|
|
|
|
printf("\nInverting schedule...\n");
|
|
invert_comm_schedule(sched,npes);
|
|
|
|
if (steps = check_comm_schedule(sched,npes))
|
|
printf("schedule OK (takes %d steps to complete).\n",
|
|
steps);
|
|
else
|
|
printf("schedule not OK.\n");
|
|
|
|
print_comm_schedule(sched, npes);
|
|
|
|
free_comm_schedule(sched,npes);
|
|
|
|
free(sched1);
|
|
}
|
|
}
|
|
else {
|
|
printf("Doing infinite tests...\n");
|
|
for (npes = 1; ; ++npes) {
|
|
int *sched1 = (int*) malloc(sizeof(int) * npes);
|
|
printf("npes = %d...",npes);
|
|
sched = make_comm_schedule(npes);
|
|
if (!sched) {
|
|
fprintf(stderr,"Out of memory!\n");
|
|
return 5;
|
|
}
|
|
for (sortpe = 0; sortpe < npes; ++sortpe) {
|
|
empty_comm_schedule(sched,npes);
|
|
fill_comm_schedule(sched,npes);
|
|
if (!check_comm_schedule(sched,npes)) {
|
|
fprintf(stderr,
|
|
"\n -- fill error for sortpe = %d!\n",sortpe);
|
|
return 2;
|
|
}
|
|
|
|
for (i = 0; i < npes; ++i) sched1[i] = -1;
|
|
fill1_comm_sched(sched1, sortpe, npes);
|
|
for (i = 0; i < npes; ++i)
|
|
if (sched1[i] != sched[sortpe][i])
|
|
fprintf(stderr,
|
|
"\n -- fill1 error for pe = %d!\n",
|
|
sortpe);
|
|
|
|
sort_comm_schedule(sched,npes,sortpe);
|
|
if (!check_comm_schedule(sched,npes)) {
|
|
fprintf(stderr,
|
|
"\n -- sort error for sortpe = %d!\n",sortpe);
|
|
return 3;
|
|
}
|
|
invert_comm_schedule(sched,npes);
|
|
if (!check_comm_schedule(sched,npes)) {
|
|
fprintf(stderr,
|
|
"\n -- invert error for sortpe = %d!\n",
|
|
sortpe);
|
|
return 4;
|
|
}
|
|
}
|
|
free_comm_schedule(sched,npes);
|
|
printf("OK\n");
|
|
if (npes % 50 == 0)
|
|
printf("(...Hit Ctrl-C to stop...)\n");
|
|
free(sched1);
|
|
}
|
|
}
|
|
|
|
return 0;
|
|
}
|