[BACKEND] Pipeline pass rewrite part 1: functionality fixes (#1716)

Support the following three cases:
1. Operands of `load` depend on induction variables before `load`s.
2. Mixed use of induction variables and offset to update the `ptr`.
3. Cross iteration (>1) dependency values.

python/test/regression/test_functional_regressions.py

@@ -1,4 +1,5 @@
 import numpy as np
+import pytest
 import torch
 from numpy.random import RandomState
 
@@ -134,3 +135,96 @@ def test_vecmat():
     C_ref = np.sum(AB, axis=2)
 
     np.testing.assert_allclose(C_ref, C_tri.cpu().numpy(), rtol=0.01, atol=1e-3)
+
+
+@pytest.mark.parametrize("type", ["pre_load", "post_load", "post_pre_mixed", "post_load_two_iters", "post_load_three_iters"])
+def test_iv_dependent_matmul(type):
+    @triton.jit
+    def kernel(
+        a_ptr, b_ptr, c_ptr,
+        M, N, K,
+        stride_am, stride_ak,
+        stride_bk, stride_bn,
+        stride_cm, stride_cn,
+        BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr,
+        type: tl.constexpr
+    ):
+        pid = tl.program_id(axis=0)
+        num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)
+        pid_m = pid // num_pid_n
+        pid_n = pid % num_pid_n
+
+        offs_am = (pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)) % M
+        offs_bn = (pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)) % N
+        offs_k = tl.arange(0, BLOCK_SIZE_K)
+        a_ptr = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak)
+        b_ptr = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn)
+        a_ptrs = a_ptr
+        b_ptrs = b_ptr
+        if type == "post_load_two_iters":
+            a_ptrs_next = a_ptr + BLOCK_SIZE_K * stride_ak
+            b_ptrs_next = b_ptr + BLOCK_SIZE_K * stride_bk
+        elif type == "post_load_three_iters":
+            a_ptrs_next = a_ptr + BLOCK_SIZE_K * stride_ak
+            b_ptrs_next = b_ptr + BLOCK_SIZE_K * stride_bk
+            a_ptrs_next_next = a_ptr + 2 * BLOCK_SIZE_K * stride_ak
+            b_ptrs_next_next = b_ptr + 2 * BLOCK_SIZE_K * stride_bk
+
+        accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
+        for k in range(0, tl.cdiv(K, BLOCK_SIZE_K)):
+            if type == "pre_load":
+                a_ptrs = a_ptr + k * BLOCK_SIZE_K * stride_ak
+                b_ptrs = b_ptr + k * BLOCK_SIZE_K * stride_bk
+            elif type == "post_pre_mixed":
+                a_ptrs = a_ptr + k * BLOCK_SIZE_K * stride_ak
+            a = tl.load(a_ptrs, mask=offs_k[None, :] < K - k * BLOCK_SIZE_K, other=0.0)
+            b = tl.load(b_ptrs, mask=offs_k[:, None] < K - k * BLOCK_SIZE_K, other=0.0)
+            accumulator += tl.dot(a, b)
+            if type == "post_load":
+                a_ptrs = a_ptr + (k + 1) * BLOCK_SIZE_K * stride_ak
+                b_ptrs = b_ptr + (k + 1) * BLOCK_SIZE_K * stride_bk
+            elif type == "post_pre_mixed":
+                b_ptrs = b_ptr + (k + 1) * BLOCK_SIZE_K * stride_bk
+            elif type == "post_load_two_iters":
+                a_ptrs = a_ptrs_next
+                b_ptrs = b_ptrs_next
+                a_ptrs_next = a_ptr + (k + 2) * BLOCK_SIZE_K * stride_ak
+                b_ptrs_next = b_ptr + (k + 2) * BLOCK_SIZE_K * stride_bk
+            elif type == "post_load_three_iters":
+                a_ptrs = a_ptrs_next
+                b_ptrs = b_ptrs_next
+                a_ptrs_next = a_ptrs_next_next
+                b_ptrs_next = b_ptrs_next_next
+                a_ptrs_next_next = a_ptr + (k + 3) * BLOCK_SIZE_K * stride_ak
+                b_ptrs_next_next = b_ptr + (k + 3) * BLOCK_SIZE_K * stride_bk
+        c = accumulator.to(tl.float16)
+
+        offs_cm = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)
+        offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
+        c_ptrs = c_ptr + stride_cm * offs_cm[:, None] + stride_cn * offs_cn[None, :]
+        c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)
+        tl.store(c_ptrs, c, mask=c_mask)
+
+    M = 256
+    K = 256
+    N = 256
+    BLOCK_SIZE_K = 32
+    BLOCK_SIZE_N = 32
+    BLOCK_SIZE_M = 32
+
+    a = torch.rand((M, K), device='cuda')
+    b = torch.rand((K, N), device='cuda')
+
+    torch_output = torch.mm(a, b)
+    triton_output = torch.empty_like(
+        torch_output, device=torch_output.device)
+
+    def grid(META):
+        return (triton.cdiv(M, META['BLOCK_SIZE_M']) * triton.cdiv(N, META['BLOCK_SIZE_N']),)
+
+    num_stages = 4 if type == "post_load_three_iters" else 3
+    kernel[grid](a, b, triton_output, M, N, K, a.stride(0), a.stride(1),
+                 b.stride(0), b.stride(1), triton_output.stride(0), triton_output.stride(1),
+                 BLOCK_SIZE_M=BLOCK_SIZE_M, BLOCK_SIZE_N=BLOCK_SIZE_N, BLOCK_SIZE_K=BLOCK_SIZE_K,
+                 type=type, num_stages=num_stages)
+    torch.testing.assert_allclose(torch_output, triton_output, rtol=1e-2, atol=1e-2)