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