Optimize prefill performance on cpu backend (#8750)

sgl-kernel/csrc/cpu/common.h

@@ -105,7 +105,19 @@ namespace {
 
 #define CHECK_EQ(a, b) TORCH_CHECK((a) == (b), "CHECK_EQ(" #a ", " #b ") failed. ", a, " vs ", b)
 
-// parallel routines
+// [NB] Parallel Routines
+//
+//  * at::parallel_for - applies for most of generic use cases, this will be compiled
+//                       against openmp in default torch release.
+//
+//  * parallel_for     - same function as above, can choose payload partition scheme in
+//                       balance211.
+//
+//  * parallel_2d      - parallel for 2 dimensions, used in GEMM, etc.
+//                       this one will do payload balance across 2 dimensions.
+//
+
+// grain size for each thread
 constexpr int GRAIN_SIZE = 1024;
 
 template <typename T, typename std::enable_if<std::is_integral<T>::value, int>::type = 0>
@@ -113,6 +125,17 @@ inline T div_up(T x, T y) {
   return (x + y - 1) / y;
 }
 
+// you can only use at::get_thread_num() with at::parallel_for()
+// as it is lazy initialized, otherwise it will always return 0.
+inline int get_thread_num() {
+#if defined(_OPENMP)
+  return omp_get_thread_num();
+#else
+  return 0;
+#endif
+}
+
+// balance payload across each thread
 template <typename T>
 inline void balance211(T n, T nth, T ith, T& n_start, T& n_end) {
 #if 0
@@ -153,6 +176,100 @@ inline void parallel_for(int n, const func_t& f) {
 #endif
 }
 
+// for 1d parallel, use `actual_nth`
+// for 2d parallel, use even nths, e.g. 43->42
+int inline adjust_num_threads(int m) {
+  int actual_nth = at::get_num_threads();
+  if (m == 1) {
+    return actual_nth;
+  }
+  return std::max(1, (actual_nth >> 1) * 2);
+}
+
+template <typename func_t>
+inline void parallel_2d(int m, int n, const func_t& f) {
+  // make sure we have even num_threads
+  int nth = adjust_num_threads(m);
+
+  // [NOTE] thread blocking:
+  //
+  //   1) prefer square block per thread
+  //   2) use even number of CPU cores
+  //   3) use all `num_threads` cores
+  //
+  //   we have:
+  //     TM * TN = T
+  //     BM / TM = BN / TN
+  //   then:
+  //     TM = ((BM / BN) * T) ^ 0.5
+  //
+  float r = float(m) / n;
+  int nth_m = std::ceil(std::sqrt(r * nth));
+  int nth_n = 1;
+  for (; nth_m > 0; --nth_m) {
+    nth_n = nth / nth_m;
+    if (nth_m * nth_n == nth) {
+      break;
+    }
+  }
+
+#if defined(_OPENMP)
+#pragma omp parallel num_threads(nth)
+  {
+    int ith = omp_get_thread_num();
+    int ith_m = ith / nth_n;
+    int ith_n = ith % nth_n;
+
+    int thread_block_m = div_up(m, nth_m);
+    int thread_block_n = div_up(n, nth_n);
+
+    int begin_m = ith_m * thread_block_m;
+    int end_m = std::min(m, begin_m + thread_block_m);
+    int begin_n = ith_n * thread_block_n;
+    int end_n = std::min(n, begin_n + thread_block_n);
+
+    f(begin_m, end_m, begin_n, end_n);
+  }
+#else
+  f(0, m, 0, n);
+#endif
+}
+
+// limit max cache blocks
+// when we need to do pre-unpack for weights, e.g. fp8
+#define MAX_CACHE_BLOCK_SIZE 4
+
+template <typename T>
+inline int get_cache_blocks(int chunk_size) {
+  // L2 2MB and ratio of 50%
+  const int L2_size = 2048 * 1024 >> 1;
+  return std::max(1, int(L2_size / (chunk_size * sizeof(T))));
+}
+
+template <>
+inline int get_cache_blocks<at::Float8_e4m3fn>(int chunk_size) {
+  // fp8 uses bf16 as accumulate type
+  int cache_block_size = get_cache_blocks<at::BFloat16>(chunk_size);
+  return std::min(MAX_CACHE_BLOCK_SIZE, cache_block_size);
+}
+
+// 2d sequential loop in range : [mb0, mb1), [nb0, nb1)
+template <typename T, typename func_t>
+inline void loop_2d(int64_t mb0, int64_t mb1, int64_t nb0, int64_t nb1, int64_t chunk_size, const func_t& f) {
+  // get number of blocks for L2 in most inner loop
+  int64_t cache_blocks_nb = get_cache_blocks<T>(chunk_size);
+
+  // loop order: [NB / cache_blocks_nb, MB, cache_blocks_nb]
+  // TODO: implement reverse order of [MB / cache_blocks_mb, NB, cache_blocks_mb]
+  for (int64_t nbb = nb0; nbb < nb1; nbb += cache_blocks_nb) {
+    for (int64_t mb = mb0; mb < mb1; ++mb) {
+      for (int64_t nb = nbb; nb < std::min(nbb + cache_blocks_nb, nb1); ++nb) {
+        f(mb, nb, nb - nbb);
+      }
+    }
+  }
+}
+
 // data indexing for dimension collapse
 template <typename T>
 inline T data_index_init(T offset) {