Better tiling for GEMMs.

This change does the following:
 * Flip the order in which the GEMM tiles are computed (loop over `m`, then `n`),
 * Change GEMM task functions in `operator-run.c` to allow tiling over multiples of `mr`,
 * Tile GEMMs over multiples of `mr` and `nr` such that we keep the minimum number of tasks required,
 * Choose GEMM tile sizes that fit into the L1 or L2 data cache.

PiperOrigin-RevId: 708308468

BUILD.bazel

@@ -895,6 +895,8 @@ xnnpack_cc_library(
     hdrs = ["src/xnnpack/microkernel-utils.h"],
     deps = [
         ":common",
+        ":hardware_config",
+        ":logging",
         ":math",
     ],
 )

src/microkernel-utils.c

@@ -8,26 +8,126 @@
 #include <assert.h>
 #include <stddef.h>
 
+#include "xnnpack/common.h"
+#include "xnnpack/hardware-config.h"
+#include "xnnpack/log.h"
 #include "xnnpack/math.h"
 
-size_t xnn_gemm_best_nc(size_t num_groups, size_t m, size_t n, size_t mr,
-                        size_t nr, size_t num_threads) {
-  size_t nc = n;
-  if (num_threads > 1) {
-    const size_t min_num_tiles = num_threads * XNN_GEMM_TILES_PER_THREAD;
-    const size_t num_tile_rows = divide_round_up(m, mr) * num_groups;
-    const size_t num_tile_cols = divide_round_up(min_num_tiles, num_tile_rows);
-
-    // We are looking for an `nc` that is the smallest integer multiple of `nr`
-    // such that `divide_round_up(n, nc)` is `num_tile_cols`.
-    nc = max(1, round_up(n, nr) / (nr * num_tile_cols)) * nr;
-    while (nr < nc && divide_round_up(n, nc - nr) == divide_round_up(n, nc)) {
-      nc -= nr;
+static bool fits_in_cache(size_t mr, size_t nc, size_t m_stride,
+                          size_t n_stride, size_t cm_stride, size_t cn_stride,
+                          size_t cache_size, size_t cache_line_size) {
+  // Check if the bytes fit.
+  const size_t lines_mr = divide_round_up(mr * m_stride, cache_line_size);
+  const size_t lines_nc = divide_round_up(nc * n_stride, cache_line_size);
+  const size_t lines_output =
+      mr * divide_round_up(nc * cn_stride, cache_line_size);
+  const size_t lines_per_row = lines_mr + lines_nc + lines_output;
+  if (cache_size < lines_per_row * cache_line_size) {
+    return false;
+  }
+
+  // Otherwiese, we're good.
+  return true;
+}
+
+void xnn_gemm_best_tile_size(size_t num_groups, size_t m, size_t n,
+                             size_t m_stride, size_t n_stride, size_t cm_stride,
+                             size_t cn_stride, size_t mr, size_t nr,
+                             size_t num_threads, size_t *mc, size_t *nc) {
+  // Adjust `mr` and `nr` if they are larger than `m` and `n`, respectively.
+  mr = min(mr, m);
+  nr = min(nr, n);
+
+  // We only care about the number of tiles if we have more than one thread.
+  const size_t min_num_tiles =
+      num_threads > 1 ? XNN_GEMM_TILES_PER_THREAD * num_threads : 1;
+
+  // Start with a `mr`x`nr` tile.
+  *mc = mr;
+  *nc = nr;
+  size_t best_num_tiles =
+      divide_round_up(m, *mc) * divide_round_up(n, *nc) * num_groups;
+
+  // Select which cache we want the tiles to fit in. Start with L1, and if the
+  // smallest possible tile won't fit, try L2. If the smallest tile still won't
+  // fit, then don't try to fit to the cache size.
+  const struct xnn_hardware_config *hardware_config =
+      xnn_init_hardware_config();
+  size_t cache_size = hardware_config->l1_data_cache_bytes;
+  size_t cache_line_size = hardware_config->l1_data_cache_line_size;
+  if (XNN_ARCH_X86 || XNN_ARCH_X86_64 ||
+      (cache_size && !fits_in_cache(mr, nr, m_stride, n_stride, cm_stride,
+                                    cn_stride, cache_size, cache_line_size))) {
+    cache_size = hardware_config->l2_data_cache_bytes;
+    cache_line_size = hardware_config->l2_data_cache_line_size;
+    if (cache_size && !fits_in_cache(mr, nr, m_stride, n_stride, cm_stride,
+                                     cn_stride, cache_size, cache_line_size)) {
+      // Don't check for cache fit.
+      cache_size = 0;
+    }
+  }
+
+  // Loop over all multiples of `mr`.
+  for (int i = 1; (i - 1) * mr < m; i++) {
+    // Skip this `i` if it results in the same number of tiles as `i - 1`.
+    if (1 < i &&
+        divide_round_up(m, i * mr) == divide_round_up(m, (i - 1) * mr)) {
+      continue;
+    }
+
+    // Make sure this value of `i` generates enough tiles.
+    const size_t num_tiles_m = divide_round_up(m, i * mr);
+    const size_t num_tiles_n = divide_round_up(n, nr);
+    const size_t num_tiles = num_tiles_n * num_tiles_m * num_groups;
+    if (num_tiles < min_num_tiles) {
+      break;
+    }
+
+    // Loop over all multiples of `nr`.
+    for (int j = 1; (j - 1) * nr < n; j++) {
+      // Skip this `j` if it results in the same number of tiles as `j - 1`.
+      if (1 < j &&
+          divide_round_up(n, j * nr) == divide_round_up(n, (j - 1) * nr)) {
+        continue;
+      }
+
+      // If we have at most `mr` rows per group, then there will be no cache
+      // re-use across tile rows and we don't care about whether the data fits
+      // in cache or not.
+      // If, however, we have more than one tile row, then we want the data used
+      // to compute a tile of size `mr`x`j*nr` to fit in the cache.
+      if (mr < m && cache_size &&
+          !fits_in_cache(mr, j * nr, m_stride, n_stride, cm_stride, cn_stride,
+                         cache_size, cache_line_size)) {
+        break;
+      }
+
+      // Make sure this pair of `i` and `j` generates enough tiles.
+      const size_t num_tiles_n = divide_round_up(n, j * nr);
+      const size_t num_tiles = num_tiles_n * num_tiles_m * num_groups;
+      if (num_tiles < min_num_tiles) {
+        break;
+      }
+
+      // New best tile size? We define the "best" tiling as the smallest total
+      // number of tiles, and for tilings with the same number of tiles, we take
+      // the tiling with the largest `nc`.
+      if (num_tiles < best_num_tiles ||
+          (num_tiles == best_num_tiles && *nc < j * nr)) {
+        *mc = i * mr;
+        *nc = j * nr;
+        best_num_tiles = num_tiles;
+      }
     }
-    nc = min(nc, n);
   }
 
-  return nc;
+  // Restrict the resulting `mc` and `nc` to `m` and `n`, respectively.
+  *mc = min(*mc, m);
+  *nc = min(*nc, n);
+  xnn_log_debug(
+      "Tile size for GEMM with num_groups=%zi, m=%zi, n=%zi and mr=%zi, nr=%zi "
+      "set to [%zi, %zi]",
+      num_groups, m, n, mr, nr, *mc, *nc);
 }
 
 static size_t dwconv_num_middle_pass(