From 3c8c21573d8bd2f865138c3d90fed36098ec7662 Mon Sep 17 00:00:00 2001
From: LoserCheems <losercheems@gmail.com>
Date: Wed, 17 Dec 2025 19:59:58 +0800
Subject: [PATCH 1/2] Adds Triton GEMM implementation

Introduces a Triton-kernelized GEMM to update matrices with alpha/beta scaling, complete with autotuning, boundary masking, and torch integration to pave the way for efficient compute-bound workloads.
---
 kernel_course/triton_ops/gemm.py | 163 +++++++++++++++++++++++++++++++
 1 file changed, 163 insertions(+)
 create mode 100644 kernel_course/triton_ops/gemm.py

diff --git a/kernel_course/triton_ops/gemm.py b/kernel_course/triton_ops/gemm.py
new file mode 100644
index 0000000..724324e
--- /dev/null
+++ b/kernel_course/triton_ops/gemm.py
@@ -0,0 +1,163 @@
+import torch
+import triton
+import triton.language as tl
+
+
+@triton.autotune(
+    configs=[
+        triton.Config(
+            {"BLOCK_M": 64, "BLOCK_K": 64, "BLOCK_N": 64}, num_warps=4, num_stages=2
+        ),
+    ],
+    key=["n_elements_M", "n_elements_K", "n_elements_N"],
+)
+@triton.heuristics(
+    {
+        "EVEN_M": lambda args: args["n_elements_M"] % args["BLOCK_M"] == 0,
+        "EVEN_K": lambda args: args["n_elements_K"] % args["BLOCK_K"] == 0,
+        "EVEN_N": lambda args: args["n_elements_N"] % args["BLOCK_N"] == 0,
+    }
+)
+@triton.jit
+def gemm_kernel(
+    A,
+    B,
+    C,
+    stride_am,
+    stride_ak,
+    stride_bn,
+    stride_bk,
+    stride_cm,
+    stride_cn,
+    alpha,
+    beta,
+    n_elements_M,
+    n_elements_K,
+    n_elements_N,
+    BLOCK_M: tl.constexpr,
+    BLOCK_K: tl.constexpr,
+    BLOCK_N: tl.constexpr,
+    EVEN_M: tl.constexpr,
+    EVEN_K: tl.constexpr,
+    EVEN_N: tl.constexpr,
+):
+    # There are multiple program processing different blocks of data
+    # We identify which program we are in using program_id
+    start_m = tl.program_id(0)
+    start_n = tl.program_id(1)
+    # This program will process inputs that offset from the initial pointer
+    offs_m = start_m * BLOCK_M + tl.arange(0, BLOCK_M)
+    offs_kb = tl.arange(0, BLOCK_K)
+    offs_n = start_n * BLOCK_N + tl.arange(0, BLOCK_N)
+    # Initialize pointers to the start of the blocks
+    a_ptr = A + offs_m[:, None] * stride_am + tl.arange(0, BLOCK_K)[None, :] * stride_ak
+    b_ptr = B + tl.arange(0, BLOCK_K)[:, None] * stride_bk + offs_n[None, :] * stride_bn
+    c_ptr = C + offs_m[:, None] * stride_cm + offs_n[None, :] * stride_cn
+    # Create a mask to guard memory operations against out-of-bounds accesses
+    mask_m = offs_m < n_elements_M
+    mask_n = offs_n < n_elements_N
+    # Initialize the accumulator
+    acc = tl.zeros((BLOCK_M, BLOCK_N), dtype=tl.float32)
+    end_k = n_elements_K
+    # Loop over K dimension
+    for start_k in range(0, end_k, BLOCK_K):
+        # Align start_k to a multiple of BLOCK_K for efficient memory access
+        start_k = tl.multiple_of(start_k, BLOCK_K)
+        # This program will process inputs that offset from the initial pointer
+        offs_k = start_k + offs_kb
+        # Create a mask to guard memory operations against out-of-bounds accesses
+        mask_k = offs_k < n_elements_K
+        # Load a block of A and B from DRAM, masking out any extra elements in case the input is not a multiple of the block size
+        if EVEN_M & EVEN_K:
+            a = tl.load(a_ptr + start_k * stride_ak)
+        else:
+            a = tl.load(
+                a_ptr + start_k * stride_ak,
+                mask=mask_m[:, None] & mask_k[None, :],
+                other=0.0,
+            )
+        if EVEN_N & EVEN_K:
+            b = tl.load(b_ptr + start_k * stride_bk)
+        else:
+            b = tl.load(
+                b_ptr + start_k * stride_bk,
+                mask=mask_k[:, None] & mask_n[None, :],
+                other=0.0,
+            )
+        # Perform the matrix multiplication for the current block and accumulate the result
+        acc += tl.dot(a, b)
+    # Load C from DRAM, masking out any extra elements in case the input is not a multiple of the block size
+    if EVEN_M & EVEN_N:
+        c = tl.load(c_ptr)
+    else:
+        c = tl.load(
+            c_ptr,
+            mask=mask_m[:, None] & mask_n[None, :],
+            other=0.0,
+        )
+    # Compute C = alpha * A * B + beta * C
+    c = beta * c
+    c += alpha * acc
+    # Store the updated C back to DRAM
+    if EVEN_M & EVEN_N:
+        tl.store(c_ptr, c)
+    else:
+        tl.store(
+            c_ptr,
+            c,
+            mask=mask_m[:, None] & mask_n[None, :],
+        )
+
+
+def gemm(
+    A: torch.Tensor,
+    B: torch.Tensor,
+    C: torch.Tensor,
+    alpha: float,
+    beta: float,
+) -> torch.Tensor:
+    """
+    Updates tensor `C` by adding the product of matrices `A` and `B`
+    scaled by `alpha`, and `C` scaled by `beta` using Triton operations.
+
+    Args:
+        A (torch.Tensor): First matrix tensor.
+        B (torch.Tensor): Second matrix tensor to be multiplied with `A`.
+        C (torch.Tensor): Matrix tensor to be updated.
+        alpha (float): Scaling factor for the product of `A` and `B`.
+        beta (float): Scaling factor for `C`.
+
+    Returns:
+        torch.Tensor: The updated tensor `C`.
+    """
+
+    # Calculate the number of elements in the input tensors
+    n_elements_M, n_elements_K = A.shape
+    n_elements_K, n_elements_N = B.shape
+
+    # The SPMD grid is a 2D grid where each program computes a BLOCK_M x BLOCK_N block of the output matrix C
+    def grid(meta):
+        return (
+            triton.cdiv(n_elements_M, meta["BLOCK_M"]),
+            triton.cdiv(n_elements_N, meta["BLOCK_N"]),
+        )
+
+    # Launch the Triton kernel
+    gemm_kernel[grid](
+        A,
+        B,
+        C,
+        A.stride(0),
+        A.stride(1),
+        B.stride(1),
+        B.stride(0),
+        C.stride(0),
+        C.stride(1),
+        alpha,
+        beta,
+        n_elements_M,
+        n_elements_K,
+        n_elements_N,
+    )
+
+    return C

From 603d8662a0f4094baa12741b24e265fe9c44f669 Mon Sep 17 00:00:00 2001
From: LoserCheems <losercheems@gmail.com>
Date: Wed, 17 Dec 2025 20:00:25 +0800
Subject: [PATCH 2/2] Update GEMM entry in README to reflect Triton
 implementation status

---
 README.md | 2 +-
 1 file changed, 1 insertion(+), 1 deletion(-)

diff --git a/README.md b/README.md
index f2097bc..b54c4ab 100644
--- a/README.md
+++ b/README.md
@@ -24,7 +24,7 @@ The following common BLAS kernels have been implemented in multiple frameworks.
 | [dot](./docs/dot.md) | dot product | $z = x^\top y$ | $2n$ | $2n$ | [✅](./kernel_course/python_ops/dot.py) | [✅](./kernel_course/pytorch_ops/dot.py) | [✅](./kernel_course/triton_ops/dot.py) | ❌ | [✅](./tests/test_dot.py) |
 | [gemv](./docs/gemv.md) | general matrix-vector multiply | $y = \alpha A x + \beta y$ | $2mn$ | $mn + n + 2m$ | [✅](./kernel_course/python_ops/gemv.py) | [✅](./kernel_course/pytorch_ops/gemv.py) | [✅](./kernel_course/triton_ops/gemv.py) | ❌ | [✅](./tests/test_gemv.py) |
 | [geru](./docs/geru.md) | general rank-1 update | $A = A + \alpha x y^\top$ | $2mn$ | $2mn + m + n$ | [✅](./kernel_course/python_ops/geru.py) | [✅](./kernel_course/pytorch_ops/geru.py) | [✅](./kernel_course/triton_ops/geru.py) | ❌ | [✅](./tests/test_geru.py) |
-| [gemm](./docs/gemm.md) | general matrix-matrix multiply | $C = \alpha A B + \beta C$ | $2mnk$ | $mk + nk + 2mn$ | [✅](./kernel_course/python_ops/gemm.py) | [✅](./kernel_course/pytorch_ops/gemm.py) | ❌ | ❌ | ❌ |
+| [gemm](./docs/gemm.md) | general matrix-matrix multiply | $C = \alpha A B + \beta C$ | $2mnk$ | $mk + nk + 2mn$ | [✅](./kernel_course/python_ops/gemm.py) | [✅](./kernel_course/pytorch_ops/gemm.py) | [✅](./kernel_course/triton_ops/gemm.py) | ❌ | ❌ |
 
 
 ## Transformer Modules