TMM_128_1024_1000.DisjunctiveFilter: explain disjunctive filter

Closes #503

Author: Sven Verdoolaege

test/cuda/test_tc_mapper_bugs.cc

@@ -695,8 +695,26 @@ def layernorm(float(T, B, C) I) -> (O, mean, centered, var) {
 // (#200).  It calls code generation on a schedule tree containing a
 // disjunctive filter, which results in an expression with more than
 // one disjunct that was not handled properly.
-// TODO: the disjunctive filter in the schedule is unexpected and its origin
-// should be identified and explained.
+//
+// A disjunctive filter is introduced by the full/partial tile separation
+// of the reduction detection.  The domain is of the form
+// { S_1[O_s1_b, O_s1_y, O_s1_r_x] :
+//   0 <= O_s1_b <= 127 and 0 <= O_s1_y <= 999 and 0 <= O_s1_r_x <= 1023 }.
+// An outer tiling with size (1, 32, 63) is performed, which means
+// in particular that O_s1_r_x is tiled in blocks of size 63.
+// Within these blocks a full thread mapping tile is of size 2,
+// which means that the final element of the even blocks and
+// the initial element of the odd blocks do not belong to a full tile.
+// In particular, O_s1_r_x = 62 (final element of block 0) and
+// O_s1_r_x = 63 (initial element of block 1) do not belong to a full tile.
+// The constraints
+// -61 + O_s1_r_x <= 126*floor((63 + O_s1_r_x)/126) <= 62 + O_s1_r_x
+// perform this filtering.
+// In the O_s1_y direction, tiles are of size 32, resulting
+// in the constraint O_s1_y <= 991 on full tiles.
+// The partial tiles are described by the complement
+// O_s1_y >= 992 or (63 + O_s1_r_x) mod 126 = 0 or (-62 + O_s1_r_x) mod 126 = 0
+// which is disjunctive.
 TEST(TMM_128_1024_1000, DisjunctiveFilter) {
   at::Tensor I = at::CUDA(at::kFloat).rand({128, 1024});
   at::Tensor W = at::CUDA(at::kFloat).rand({1000, 1024});