coll/libnbc: add Rabenseifner's algorithm for MPI_Ireduce

An implementation of R. Rabenseifner's algorithm for MPI_Ireduce.
This algorithm is a combination of a reduce-scatter implemented with recursive vector halving
and recursive distance doubling, followed either by a gather.

Limitations:
-- count >= 2^{\floor{\log_2 p}}
-- commutative operations only
-- intra-communicators only

Signed-off-by: Mikhail Kurnosov <mkurnosov@gmail.com>

ompi/mca/coll/libnbc/coll_libnbc.h

@@ -71,6 +71,7 @@ BEGIN_C_DECLS
 
 extern bool libnbc_ibcast_skip_dt_decision;
 extern int libnbc_iexscan_algorithm;
+extern int libnbc_ireduce_algorithm;
 extern int libnbc_iscan_algorithm;
 
 struct ompi_coll_libnbc_component_t {

ompi/mca/coll/libnbc/coll_libnbc_component.c

@@ -54,6 +54,15 @@ static mca_base_var_enum_value_t iexscan_algorithms[] = {
     {0, NULL}
 };
 
+int libnbc_ireduce_algorithm = 0;            /* ireduce user forced algorithm */
+static mca_base_var_enum_value_t ireduce_algorithms[] = {
+    {0, "ignore"},
+    {1, "chain"},
+    {2, "binomial"},
+    {3, "rabenseifner"},
+    {0, NULL}
+};
+
 int libnbc_iscan_algorithm = 0;             /* iscan user forced algorithm */
 static mca_base_var_enum_value_t iscan_algorithms[] = {
     {0, "ignore"},
@@ -185,6 +194,16 @@ libnbc_register(void)
                                     &libnbc_iexscan_algorithm);
     OBJ_RELEASE(new_enum);
 
+    libnbc_ireduce_algorithm = 0;
+    (void) mca_base_var_enum_create("coll_libnbc_ireduce_algorithms", ireduce_algorithms, &new_enum);
+    mca_base_component_var_register(&mca_coll_libnbc_component.super.collm_version,
+                                    "ireduce_algorithm",
+                                    "Which ireduce algorithm is used: 0 ignore, 1 chain, 2 binomial, 3 rabenseifner",
+                                    MCA_BASE_VAR_TYPE_INT, new_enum, 0, MCA_BASE_VAR_FLAG_SETTABLE,
+                                    OPAL_INFO_LVL_5, MCA_BASE_VAR_SCOPE_ALL,
+                                    &libnbc_ireduce_algorithm);
+    OBJ_RELEASE(new_enum);
+
     libnbc_iscan_algorithm = 0;
     (void) mca_base_var_enum_create("coll_libnbc_iscan_algorithms", iscan_algorithms, &new_enum);
     mca_base_component_var_register(&mca_coll_libnbc_component.super.collm_version,

ompi/mca/coll/libnbc/nbc_ireduce.c

@@ -20,6 +20,7 @@
  */
 
 #include "opal/include/opal/align.h"
+#include "opal/util/bit_ops.h"
 #include "ompi/op/op.h"
 
 #include "nbc_internal.h"
@@ -31,6 +32,10 @@ static inline int red_sched_chain (int rank, int p, int root, const void *sendbu
 
 static inline int red_sched_linear (int rank, int rsize, int root, const void *sendbuf, void *recvbuf, void *tmpbuf, int count, MPI_Datatype datatype,
                                     MPI_Op op, NBC_Schedule *schedule);
+static inline int red_sched_redscat_gather(
+    int rank, int comm_size, int root, const void *sbuf, void *rbuf,
+    char tmpredbuf, int count, MPI_Datatype datatype, MPI_Op op, char inplace,
+    NBC_Schedule *schedule, void *tmp_buf, struct ompi_communicator_t *comm);
 
 #ifdef NBC_CACHE_SCHEDULE
 /* tree comparison function for schedule cache */
@@ -63,7 +68,7 @@ static int nbc_reduce_init(const void* sendbuf, void* recvbuf, int count, MPI_Da
   char *redbuf=NULL, inplace;
   void *tmpbuf;
   char tmpredbuf = 0;
-  enum { NBC_RED_BINOMIAL, NBC_RED_CHAIN } alg;
+  enum { NBC_RED_BINOMIAL, NBC_RED_CHAIN, NBC_RED_REDSCAT_GATHER} alg;
   ompi_coll_libnbc_module_t *libnbc_module = (ompi_coll_libnbc_module_t*) module;
   ptrdiff_t span, gap;
 
@@ -98,22 +103,42 @@ static int nbc_reduce_init(const void* sendbuf, void* recvbuf, int count, MPI_Da
   span = opal_datatype_span(&datatype->super, count, &gap);
 
   /* algorithm selection */
-  if (p > 4 || size * count < 65536 || !ompi_op_is_commute(op)) {
-    alg = NBC_RED_BINOMIAL;
-    if(rank == root) {
-      /* root reduces in receivebuffer */
-      tmpbuf = malloc (span);
+  int nprocs_pof2 = opal_next_poweroftwo(p) >> 1;
+  if (libnbc_ireduce_algorithm == 0) {
+    if (ompi_op_is_commute(op) && p > 2 && count >= nprocs_pof2) {
+      alg = NBC_RED_REDSCAT_GATHER;
+    } else if (p > 4 || size * count < 65536 || !ompi_op_is_commute(op)) {
+      alg = NBC_RED_BINOMIAL;
+    } else {
+      alg = NBC_RED_CHAIN;
+    }
+  } else {
+    if (libnbc_ireduce_algorithm == 1) {
+      alg = NBC_RED_CHAIN;
+    } else if (libnbc_ireduce_algorithm == 2) {
+      alg = NBC_RED_BINOMIAL;
+    } else if (libnbc_ireduce_algorithm == 3 && ompi_op_is_commute(op) && p > 2 && count >= nprocs_pof2) {
+      alg = NBC_RED_REDSCAT_GATHER;
+    } else {
+      alg = NBC_RED_CHAIN;
+    }
+  }
+
+  /* allocate temporary buffers */
+  if (alg == NBC_RED_REDSCAT_GATHER || alg == NBC_RED_BINOMIAL) {
+    if (rank == root) {
+      /* root reduces in receive buffer */
+      tmpbuf = malloc(span);
       redbuf = recvbuf;
     } else {
       /* recvbuf may not be valid on non-root nodes */
       ptrdiff_t span_align = OPAL_ALIGN(span, datatype->super.align, ptrdiff_t);
-      tmpbuf = malloc (span_align + span);
-      redbuf = (char*)span_align - gap;
+      tmpbuf = malloc(span_align + span);
+      redbuf = (char *)span_align - gap;
       tmpredbuf = 1;
     }
   } else {
     tmpbuf = malloc (span);
-    alg = NBC_RED_CHAIN;
     segsize = 16384/2;
   }
 
@@ -151,6 +176,9 @@ static int nbc_reduce_init(const void* sendbuf, void* recvbuf, int count, MPI_Da
         case NBC_RED_CHAIN:
           res = red_sched_chain(rank, p, root, sendbuf, recvbuf, count, datatype, op, ext, size, schedule, tmpbuf, segsize);
           break;
+        case NBC_RED_REDSCAT_GATHER:
+          res = red_sched_redscat_gather(rank, p, root, sendbuf, redbuf, tmpredbuf, count, datatype, op, inplace, schedule, tmpbuf, comm);
+          break;
       }
     }
 
@@ -560,6 +588,350 @@ static inline int red_sched_linear (int rank, int rsize, int root, const void *s
   return OMPI_SUCCESS;
 }
 
+/*
+ * red_sched_redscat_gather:
+ *
+ * Description: an implementation of Rabenseifner's Reduce algorithm [1, 2].
+ *   [1] Rajeev Thakur, Rolf Rabenseifner and William Gropp.
+ *       Optimization of Collective Communication Operations in MPICH //
+ *       The Int. Journal of High Performance Computing Applications. Vol 19,
+ *       Issue 1, pp. 49--66.
+ *   [2] http://www.hlrs.de/mpi/myreduce.html.
+ *
+ * This algorithm is a combination of a reduce-scatter implemented with
+ * recursive vector halving and recursive distance doubling, followed either
+ * by a binomial tree gather.
+ *
+ * Step 1. If the number of processes is not a power of two, reduce it to
+ * the nearest lower power of two (p' = 2^{\floor{\log_2 p}})
+ * by removing r = p - p' extra processes as follows. In the first 2r processes
+ * (ranks 0 to 2r - 1), all the even ranks send the second half of the input
+ * vector to their right neighbor (rank + 1), and all the odd ranks send
+ * the first half of the input vector to their left neighbor (rank - 1).
+ * The even ranks compute the reduction on the first half of the vector and
+ * the odd ranks compute the reduction on the second half. The odd ranks then
+ * send the result to their left neighbors (the even ranks). As a result,
+ * the even ranks among the first 2r processes now contain the reduction with
+ * the input vector on their right neighbors (the odd ranks). These odd ranks
+ * do not participate in the rest of the algorithm, which leaves behind
+ * a power-of-two number of processes. The first r even-ranked processes and
+ * the last p - 2r processes are now renumbered from 0 to p' - 1.
+ *
+ * Step 2. The remaining processes now perform a reduce-scatter by using
+ * recursive vector halving and recursive distance doubling. The even-ranked
+ * processes send the second half of their buffer to rank + 1 and the odd-ranked
+ * processes send the first half of their buffer to rank - 1. All processes
+ * then compute the reduction between the local buffer and the received buffer.
+ * In the next log_2(p') - 1 steps, the buffers are recursively halved, and the
+ * distance is doubled. At the end, each of the p' processes has 1 / p' of the
+ * total reduction result.
+ *
+ * Step 3. A binomial tree gather is performed by using recursive vector
+ * doubling and distance halving. In the non-power-of-two case, if the root
+ * happens to be one of those odd-ranked processes that would normally
+ * be removed in the first step, then the role of this process and process 0
+ * are interchanged.
+ *
+ * Limitations:
+ *   count >= 2^{\floor{\log_2 p}}
+ *   commutative operations only
+ *   intra-communicators only
+ *
+ * Memory requirements (per process):
+ *   rank != root: 2 * count * typesize + 4 * \log_2(p) * sizeof(int) = O(count)
+ *   rank == root: count * typesize + 4 * \log_2(p) * sizeof(int) = O(count)
+ *
+ * Schedule length (rounds): O(\log(p))
+ * Recommendations: root = 0, otherwise it is required additional steps
+ *                  in the root process.
+ */
+static inline int red_sched_redscat_gather(
+    int rank, int comm_size, int root, const void *sbuf, void *rbuf,
+    char tmpredbuf, int count, MPI_Datatype datatype, MPI_Op op, char inplace,
+    NBC_Schedule *schedule, void *tmp_buf, struct ompi_communicator_t *comm)
+{
+    int res = OMPI_SUCCESS;
+    int *rindex = NULL, *rcount = NULL, *sindex = NULL, *scount = NULL;
+
+    /* Find nearest power-of-two less than or equal to comm_size */
+    int nsteps = opal_hibit(comm_size, comm->c_cube_dim + 1);   /* ilog2(comm_size) */
+    int nprocs_pof2 = 1 << nsteps;                              /* flp2(comm_size) */
+
+    ptrdiff_t lb, extent;
+    ompi_datatype_get_extent(datatype, &lb, &extent);
+
+    if ((rank != root) || !inplace) {
+        res = NBC_Sched_copy((char *)sbuf, false, count, datatype,
+                             rbuf, tmpredbuf, count, datatype, schedule, true);
+        if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+    }
+
+    /*
+     * Step 1. Reduce the number of processes to the nearest lower power of two
+     * p' = 2^{\floor{\log_2 p}} by removing r = p - p' processes.
+     * 1. In the first 2r processes (ranks 0 to 2r - 1), all the even ranks send
+     *    the second half of the input vector to their right neighbor (rank + 1)
+     *    and all the odd ranks send the first half of the input vector to their
+     *    left neighbor (rank - 1).
+     * 2. All 2r processes compute the reduction on their half.
+     * 3. The odd ranks then send the result to their left neighbors
+     *    (the even ranks).
+     *
+     * The even ranks (0 to 2r - 1) now contain the reduction with the input
+     * vector on their right neighbors (the odd ranks). The first r even
+     * processes and the p - 2r last processes are renumbered from
+     * 0 to 2^{\floor{\log_2 p}} - 1. These odd ranks do not participate in the
+     * rest of the algorithm.
+     */
+
+    int vrank, step, wsize;
+    int nprocs_rem = comm_size - nprocs_pof2;
+
+    if (rank < 2 * nprocs_rem) {
+        int count_lhalf = count / 2;
+        int count_rhalf = count - count_lhalf;
+
+        if (rank % 2 != 0) {
+            /*
+             * Odd process -- exchange with rank - 1
+             * Send the left half of the input vector to the left neighbor,
+             * Recv the right half of the input vector from the left neighbor
+             */
+            res = NBC_Sched_send(rbuf, tmpredbuf, count_lhalf, datatype, rank - 1,
+                                 schedule, false);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            res = NBC_Sched_recv((char *)tmp_buf + (ptrdiff_t)count_lhalf * extent,
+                                 false, count_rhalf, datatype, rank - 1, schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            res = NBC_Sched_op((char *)tmp_buf + (ptrdiff_t)count_lhalf * extent,
+                               false, (char *)rbuf + (ptrdiff_t)count_lhalf * extent,
+                               tmpredbuf, count_rhalf, datatype, op, schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            /* Send the right half to the left neighbor */
+            res = NBC_Sched_send((char *)rbuf + (ptrdiff_t)count_lhalf * extent,
+                                 tmpredbuf, count_rhalf, datatype, rank - 1, schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            /* This process does not participate in recursive doubling phase */
+            vrank = -1;
+
+        } else {
+            /*
+             * Even process -- exchange with rank + 1
+             * Send the right half of the input vector to the right neighbor,
+             * Recv the left half of the input vector from the right neighbor
+             */
+            res = NBC_Sched_send((char *)rbuf + (ptrdiff_t)count_lhalf * extent,
+                                 tmpredbuf, count_rhalf, datatype, rank + 1, schedule, false);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            res = NBC_Sched_recv((char *)tmp_buf, false, count_lhalf, datatype, rank + 1,
+                                 schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            res = NBC_Sched_op(tmp_buf, false, rbuf, tmpredbuf, count_lhalf,
+                               datatype, op, schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            /* Recv the right half from the right neighbor */
+            res = NBC_Sched_recv((char *)rbuf + (ptrdiff_t)count_lhalf * extent,
+                                 tmpredbuf, count_rhalf, datatype, rank + 1, schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            vrank = rank / 2;
+        }
+    } else { /* rank >= 2 * nprocs_rem */
+        vrank = rank - nprocs_rem;
+    }
+
+    /*
+     * Step 2. Reduce-scatter implemented with recursive vector halving and
+     * recursive distance doubling. We have p' = 2^{\floor{\log_2 p}}
+     * power-of-two number of processes with new ranks (vrank) and result in rbuf.
+     *
+     * The even-ranked processes send the right half of their buffer to rank + 1
+     * and the odd-ranked processes send the left half of their buffer to
+     * rank - 1. All processes then compute the reduction between the local
+     * buffer and the received buffer. In the next \log_2(p') - 1 steps, the
+     * buffers are recursively halved, and the distance is doubled. At the end,
+     * each of the p' processes has 1 / p' of the total reduction result.
+     */
+
+    rindex = malloc(sizeof(*rindex) * nsteps);    /* O(\log_2(p)) */
+    sindex = malloc(sizeof(*sindex) * nsteps);
+    rcount = malloc(sizeof(*rcount) * nsteps);
+    scount = malloc(sizeof(*scount) * nsteps);
+    if (NULL == rindex || NULL == sindex || NULL == rcount || NULL == scount) {
+        res = OMPI_ERR_OUT_OF_RESOURCE;
+        goto cleanup_and_return;
+    }
+
+    if (vrank != -1) {
+        step = 0;
+        wsize = count;
+        sindex[0] = rindex[0] = 0;
+
+        for (int mask = 1; mask < nprocs_pof2; mask <<= 1) {
+            /*
+             * On each iteration: rindex[step] = sindex[step] -- begining of the
+             * current window. Length of the current window is storded in wsize.
+             */
+            int vdest = vrank ^ mask;
+            /* Translate vdest virtual rank to real rank */
+            int dest = (vdest < nprocs_rem) ? vdest * 2 : vdest + nprocs_rem;
+
+            if (rank < dest) {
+                /*
+                 * Recv into the left half of the current window, send the right
+                 * half of the window to the peer (perform reduce on the left
+                 * half of the current window)
+                 */
+                rcount[step] = wsize / 2;
+                scount[step] = wsize - rcount[step];
+                sindex[step] = rindex[step] + rcount[step];
+            } else {
+                /*
+                 * Recv into the right half of the current window, send the left
+                 * half of the window to the peer (perform reduce on the right
+                 * half of the current window)
+                 */
+                scount[step] = wsize / 2;
+                rcount[step] = wsize - scount[step];
+                rindex[step] = sindex[step] + scount[step];
+            }
+
+            /* Send part of data from the rbuf, recv into the tmp_buf */
+            res = NBC_Sched_send((char *)rbuf + (ptrdiff_t)sindex[step] * extent,
+                                 tmpredbuf, scount[step], datatype, dest, schedule, false);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+            res = NBC_Sched_recv((char *)tmp_buf + (ptrdiff_t)rindex[step] * extent,
+                                 false, rcount[step], datatype, dest, schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            /* Local reduce: rbuf[] = tmp_buf[] <op> rbuf[] */
+            res = NBC_Sched_op((char *)tmp_buf + (ptrdiff_t)rindex[step] * extent,
+                               false, (char *)rbuf + (ptrdiff_t)rindex[step] * extent,
+                               tmpredbuf, rcount[step], datatype, op, schedule, true);
+            if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+
+            /* Move the current window to the received message */
+            if (step + 1 < nsteps) {
+                rindex[step + 1] = rindex[step];
+                sindex[step + 1] = rindex[step];
+                wsize = rcount[step];
+                step++;
+            }
+        }
+    }
+    /*
+     * Assertion: each process has 1 / p' of the total reduction result:
+     * rcount[nsteps - 1] elements in the rbuf[rindex[nsteps - 1], ...].
+     */
+
+    /*
+     * Setup the root process for gather operation.
+     * Case 1: root < 2r and root is odd -- root process was excluded on step 1
+     *         Recv data from process 0, vroot = 0, vrank = 0
+     * Case 2: root < 2r and root is even: vroot = root / 2
+     * Case 3: root >= 2r: vroot = root - r
+     */
+    int vroot = 0;
+    if (root < 2 * nprocs_rem) {
+        if (root % 2 != 0) {
+            vroot = 0;
+            if (rank == root) {
+                /*
+                 * Case 1: root < 2r and root is odd -- root process was
+                 * excluded on step 1 (newrank == -1).
+                 * Recv a data from the process 0.
+                 */
+                rindex[0] = 0;
+                step = 0, wsize = count;
+                for (int mask = 1; mask < nprocs_pof2; mask *= 2) {
+                    rcount[step] = wsize / 2;
+                    scount[step] = wsize - rcount[step];
+                    rindex[step] = 0;
+                    sindex[step] = rcount[step];
+                    step++;
+                    wsize /= 2;
+                }
+
+                res = NBC_Sched_recv(rbuf, tmpredbuf, rcount[nsteps - 1], datatype,
+                                     0, schedule, true);
+                if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+                vrank = 0;
+
+            } else if (vrank == 0) {
+                /* Send a data to the root */
+                res = NBC_Sched_send(rbuf, tmpredbuf, rcount[nsteps - 1], datatype,
+                                     root, schedule, true);
+                if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+                vrank = -1;
+            }
+        } else {
+            /* Case 2: root < 2r and a root is even: vroot = root / 2 */
+            vroot = root / 2;
+        }
+    } else {
+        /* Case 3: root >= 2r: newroot = root - r */
+        vroot = root - nprocs_rem;
+    }
+
+    /*
+     * Step 3. Gather result at the vroot by the binomial tree algorithm.
+     * Each process has 1 / p' of the total reduction result:
+     * rcount[nsteps - 1] elements in the rbuf[rindex[nsteps - 1], ...].
+     * All exchanges are executed in reverse order relative
+     * to recursive doubling (previous step).
+     */
+
+    if (vrank != -1) {
+        int vdest_tree, vroot_tree;
+        step = nsteps - 1; /* step = ilog2(p') - 1 */
+
+        for (int mask = nprocs_pof2 >> 1; mask > 0; mask >>= 1) {
+            int vdest = vrank ^ mask;
+            /* Translate vdest virtual rank to real rank */
+            int dest = (vdest < nprocs_rem) ? vdest * 2 : vdest + nprocs_rem;
+            if ((vdest == 0) && (root < 2 * nprocs_rem) && (root % 2 != 0))
+                dest = root;
+
+            vdest_tree = vdest >> step;
+            vdest_tree <<= step;
+            vroot_tree = vroot >> step;
+            vroot_tree <<= step;
+            if (vdest_tree == vroot_tree) {
+                /* Send data from rbuf and exit */
+
+                res = NBC_Sched_send((char *)rbuf + (ptrdiff_t)rindex[step] * extent,
+                                     tmpredbuf, rcount[step], datatype, dest, schedule, false);
+                if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+                break;
+            } else {
+                /* Recv and continue */
+                res = NBC_Sched_recv((char *)rbuf + (ptrdiff_t)sindex[step] * extent,
+                                     tmpredbuf, scount[step], datatype, dest, schedule, true);
+                if (OPAL_UNLIKELY(OMPI_SUCCESS != res)) { goto cleanup_and_return; }
+            }
+            step--;
+        }
+    }
+
+  cleanup_and_return:
+    if (NULL != rindex)
+        free(rindex);
+    if (NULL != sindex)
+        free(sindex);
+    if (NULL != rcount)
+        free(rcount);
+    if (NULL != scount)
+        free(scount);
+    return res;
+}
+
 int ompi_coll_libnbc_reduce_init(const void* sendbuf, void* recvbuf, int count, MPI_Datatype datatype,
                                  MPI_Op op, int root, struct ompi_communicator_t *comm, MPI_Info info, ompi_request_t ** request,
                                  struct mca_coll_base_module_2_3_0_t *module) {