From 1eee2d41379af1c43e05a9280f834eefa13a9c45 Mon Sep 17 00:00:00 2001 From: Philippe Tillet Date: Fri, 6 Aug 2021 20:03:44 +0000 Subject: [PATCH] [GH-PAGES] Updated website --- .../tutorials_jupyter.zip | Bin 35975 -> 35801 bytes .../tutorials_python.zip | Bin 28668 -> 28692 bytes .../03-matrix-multiplication.ipynb | 15 +-- .../03-matrix-multiplication.py | 10 +- _images/grouped_vs_row_major_ordering.png | Bin 0 -> 476275 bytes _images/sphx_glr_01-vector-add_001.png | Bin 25453 -> 25966 bytes _images/sphx_glr_01-vector-add_thumb.png | Bin 15922 -> 16037 bytes _images/sphx_glr_02-fused-softmax_001.png | Bin 38213 -> 38195 bytes _images/sphx_glr_02-fused-softmax_thumb.png | Bin 24422 -> 24240 bytes .../sphx_glr_03-matrix-multiplication_001.png | Bin 57116 -> 56484 bytes ...phx_glr_03-matrix-multiplication_thumb.png | Bin 32981 -> 32226 bytes .../tutorials/01-vector-add.rst.txt | 6 +- .../tutorials/02-fused-softmax.rst.txt | 12 +-- .../03-matrix-multiplication.rst.txt | 84 +++++++---------- .../tutorials/sg_execution_times.rst.txt | 8 +- getting-started/tutorials/01-vector-add.html | 6 +- .../tutorials/02-fused-softmax.html | 12 +-- .../tutorials/03-matrix-multiplication.html | 88 ++++++++---------- .../tutorials/sg_execution_times.html | 8 +- searchindex.js | 2 +- 20 files changed, 111 insertions(+), 140 deletions(-) create mode 100644 _images/grouped_vs_row_major_ordering.png diff --git a/_downloads/662999063954282841dc90b8945f85ce/tutorials_jupyter.zip b/_downloads/662999063954282841dc90b8945f85ce/tutorials_jupyter.zip index cfe2ddf502c84f548196c3c786d609eacd09e849..b2f6dc944c1eb7766c51019a19edb46d640fefbe 100644 GIT binary patch delta 228 zcmZpl$#io%lSF_wGm8iV2$U>f3%>BWzx9k01H&1ojS@|qn`d*nv2A|D|C@R843WUe zuSG&8JBkKRo+he2`LL(~Q%v6EAEIHC1H^(R7jWcl<`rM7;963YS(2X@pI=&1P+DSJ zjl!*sQPPabD=5m$E73@cQ7XwVO3py2MB;6JW`2vCsdoP6L(T?rOsWeue@Wb-$%pE` m$-BDkfJ!F+>Xu>Tm@M9-1XMTKx<`i5YH~!6Cflbjke2{&C08N< delta 241 zcmcaPovD2$lXQSLGm8iV2y9_w3y%HbSyJW9zyQK>lV!UVH`>H;GAeAI#p%Wdq#p49 zW}Y1CyOT*-Ve)O^KoF%P5(1(cM1n!oWf5%<^-sirRXHXP$TAQO0|~T=1~Dp6PBh8d z>?XEWL8rQ;D6=F#FFwDtq@c9Kwl+pdGbXQ~C^N4_BP~X$x+K3SIRhrS*~0u5HX-PZ6GWFb|QpW(zqGuL<2+JveaatO}dFG rDS8E!0p5&EBFqr4)B<(auAXOYAXQ7TY8vI{8Ju8k<}`$YlT@-ZlaN diff --git a/_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb b/_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb index 9fc82332e..a63d64e3a 100644 --- a/_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb +++ b/_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb @@ -29,18 +29,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "## Compute Kernel\n\nThe above algorithm is, actually, fairly straightforward to implement in Triton.\nThe main difficulty comes from the computation of the memory locations at which blocks\n of :code:`A` and :code:`B` must be read in the inner loop. For that, we need\nmulti-dimensional pointer arithmetics.\n\n### Pointer Arithmetics\n\nFor a row-major 2D tensor :code:`X`, the memory location of :code:`X[i, j]` is given b\ny :code:`&X[i, j] = X + i*stride_x_0 + j*stride_x_1`.\nTherefore, blocks of pointers for :code:`A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]` and\n:code:`B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]` can be defined in pseudo-code as:\n\n .. code-block:: python\n\n &A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K] = A + (m : m+BLOCK_SIZE_M)[:, None]*A.stride(0) + (k : k+BLOCK_SIZE_K)[None, :]*A.stride(1);\n &B[k : k+BLOCK_SIZE_K, n:n+BLOCK_SIZE_N] = B + (k : k+BLOCK_SIZE_K)[:, None]*B.stride(0) + (n : n+BLOCK_SIZE_N)[None, :]*B.stride(1);\n\nWhich means that pointers for blocks of A and B can be initialized (i.e., :code:`k=0`) in Triton as:\n\n .. code-block:: python\n\n pid_m = triton.program_id(0)\n pid_n = triton.program_id(1)\n rm = pid_m * BLOCK_SIZE_M + triton.arange(0, BLOCK_SIZE_M)\n rn = pid_n * BLOCK_SIZE_N + triton.arange(0, BLOCK_SIZE_N)\n rk = triton.arange(0, BLOCK_SIZE_K)\n // pointer for A operand\n pa = A + (rm[:, None] * stride_a_0 + rk[None, :] * stride_a_1);\n // pointer for B operand\n pb = B + (rk[:, None] * stride_b_0 + rn[None, :] * stride_b_1);\n\nAnd then updated in the inner loop as follows:\n\n .. code-block:: python\n\n pa += BLOCK_SIZE_K * stride_a_1;\n pb += BLOCK_SIZE_K * stride_b_0;\n\n\n### L2 Cache Optimizations\n\nAs mentioned above, each program instance computes a :code:`[BLOCK_SIZE_M, BLOCK_SIZE_N]`\n block of :code:`C`.\nIt is important to remember that the order in which these blocks are computed does\nmatter, since it affects the L2 cache hit rate of our program. and unfortunately, a\na simple row-major ordering\n\n .. code-block:: Python\n\n pid = triton.program_id(0);\n grid_m = (M + BLOCK_SIZE_M - 1) // BLOCK_SIZE_M;\n grid_n = (N + BLOCK_SIZE_N - 1) // BLOCK_SIZE_N;\n pid_m = pid / grid_n;\n pid_n = pid % grid_n;\n\nis just not going to cut it.\n\nOne possible solution is to launch blocks in an order that promotes data reuse.\nThis can be done by 'super-grouping' blocks in groups of :code:`GROUP_M` rows before\nswitching to the next column:\n\n .. code-block:: python\n\n pid = triton.program_id(0);\n width = GROUP_M * grid_n;\n group_id = pid // width;\n # we need to handle the case where M % (GROUP_M*BLOCK_SIZE_M) != 0\n group_size = min(grid_m - group_id * GROUP_M, GROUP_M);\n pid_m = group_id * GROUP_M + (pid % group_size);\n pid_n = (pid % width) // (group_size);\n\n" - ] - }, - { - "cell_type": "code", - "execution_count": null, - "metadata": { - "collapsed": false - }, - "outputs": [], - "source": [ - "# For example, in the following matmul where each matrix is 9 blocks by 9 blocks,\n# we can see that if we compute the output in row-major ordering, we need to load 90\n# blocks into SRAM to compute the first 9 output blocks, but if we do it in grouped\n# ordering, we only need to load 54 blocks.\n# .. image:: grouped_vs_row_major_ordering.png\n#\n# In practice, this can improve the performance of our matrix multiplication kernel by\n# more than 10\\% on some hardware architecture (e.g., 220 to 245 TFLOPS on A100).\n#" + "## Compute Kernel\n\nThe above algorithm is, actually, fairly straightforward to implement in Triton.\nThe main difficulty comes from the computation of the memory locations at which blocks\nof :code:`A` and :code:`B` must be read in the inner loop. For that, we need\nmulti-dimensional pointer arithmetics.\n\n### Pointer Arithmetics\n\nFor a row-major 2D tensor :code:`X`, the memory location of :code:`X[i, j]` is given b\ny :code:`&X[i, j] = X + i*stride_x_0 + j*stride_x_1`.\nTherefore, blocks of pointers for :code:`A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]` and\n:code:`B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]` can be defined in pseudo-code as:\n\n .. code-block:: python\n\n &A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K] = A + (m : m+BLOCK_SIZE_M)[:, None]*A.stride(0) + (k : k+BLOCK_SIZE_K)[None, :]*A.stride(1);\n &B[k : k+BLOCK_SIZE_K, n:n+BLOCK_SIZE_N] = B + (k : k+BLOCK_SIZE_K)[:, None]*B.stride(0) + (n : n+BLOCK_SIZE_N)[None, :]*B.stride(1);\n\nWhich means that pointers for blocks of A and B can be initialized (i.e., :code:`k=0`) in Triton as:\n\n .. code-block:: python\n\n pid_m = triton.program_id(0)\n pid_n = triton.program_id(1)\n rm = pid_m * BLOCK_SIZE_M + triton.arange(0, BLOCK_SIZE_M)\n rn = pid_n * BLOCK_SIZE_N + triton.arange(0, BLOCK_SIZE_N)\n rk = triton.arange(0, BLOCK_SIZE_K)\n // pointer for A operand\n pa = A + (rm[:, None] * stride_a_0 + rk[None, :] * stride_a_1);\n // pointer for B operand\n pb = B + (rk[:, None] * stride_b_0 + rn[None, :] * stride_b_1);\n\nAnd then updated in the inner loop as follows:\n\n .. code-block:: python\n\n pa += BLOCK_SIZE_K * stride_a_1;\n pb += BLOCK_SIZE_K * stride_b_0;\n\n\n### L2 Cache Optimizations\n\nAs mentioned above, each program instance computes a :code:`[BLOCK_SIZE_M, BLOCK_SIZE_N]`\nblock of :code:`C`.\nIt is important to remember that the order in which these blocks are computed does\nmatter, since it affects the L2 cache hit rate of our program. and unfortunately, a\na simple row-major ordering\n\n .. code-block:: Python\n\n pid = triton.program_id(0);\n grid_m = (M + BLOCK_SIZE_M - 1) // BLOCK_SIZE_M;\n grid_n = (N + BLOCK_SIZE_N - 1) // BLOCK_SIZE_N;\n pid_m = pid / grid_n;\n pid_n = pid % grid_n;\n\nis just not going to cut it.\n\nOne possible solution is to launch blocks in an order that promotes data reuse.\nThis can be done by 'super-grouping' blocks in groups of :code:`GROUP_M` rows before\nswitching to the next column:\n\n .. code-block:: python\n\n pid = triton.program_id(0);\n width = GROUP_M * grid_n;\n group_id = pid // width;\n # we need to handle the case where M % (GROUP_M*BLOCK_SIZE_M) != 0\n group_size = min(grid_m - group_id * GROUP_M, GROUP_M);\n pid_m = group_id * GROUP_M + (pid % group_size);\n pid_n = (pid % width) // (group_size);\n\nFor example, in the following matmul where each matrix is 9 blocks by 9 blocks,\nwe can see that if we compute the output in row-major ordering, we need to load 90\nblocks into SRAM to compute the first 9 output blocks, but if we do it in grouped\nordering, we only need to load 54 blocks.\n .. image:: grouped_vs_row_major_ordering.png\n\nIn practice, this can improve the performance of our matrix multiplication kernel by\nmore than 10\\% on some hardware architecture (e.g., 220 to 245 TFLOPS on A100).\n\n\n" ] }, { @@ -94,7 +83,7 @@ }, "outputs": [], "source": [ - "torch.manual_seed(0)\na = torch.randn((512, 512), device='cuda', dtype=torch.float16)\nb = torch.randn((512, 512), device='cuda', dtype=torch.float16)\ntriton_output = matmul(a, b, activation=None)\ntorch_output = torch.matmul(a, b)\nprint(f\"{triton_output=}\")\nprint(f\"{torch_output=}\")\nif triton.testing.allclose(triton_output, torch_output):\n print(\"\u2705 Triton and Torch match\")\nelse:\n print(\"\u274c Triton and Torch differ\")" + "torch.manual_seed(0)\na = torch.randn((512, 512), device='cuda', dtype=torch.float16)\nb = torch.randn((512, 512), device='cuda', dtype=torch.float16)\ntriton_output = matmul(a, b, activation=None)\ntorch_output = torch.matmul(a, b)\nprint(f\"triton_output={triton_output}\")\nprint(f\"torch_output={torch_output}\")\nif triton.testing.allclose(triton_output, torch_output):\n print(\"\u2705 Triton and Torch match\")\nelse:\n print(\"\u274c Triton and Torch differ\")" ] }, { diff --git a/_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py b/_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py index 838ddc0b0..e71fae2d6 100644 --- a/_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py +++ b/_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py @@ -46,7 +46,7 @@ You will specifically learn about: # # The above algorithm is, actually, fairly straightforward to implement in Triton. # The main difficulty comes from the computation of the memory locations at which blocks -# of :code:`A` and :code:`B` must be read in the inner loop. For that, we need +# of :code:`A` and :code:`B` must be read in the inner loop. For that, we need # multi-dimensional pointer arithmetics. # # Pointer Arithmetics @@ -88,7 +88,7 @@ You will specifically learn about: # ~~~~~~~~~~~~~~~~~~~~~~~~ # # As mentioned above, each program instance computes a :code:`[BLOCK_SIZE_M, BLOCK_SIZE_N]` -# block of :code:`C`. +# block of :code:`C`. # It is important to remember that the order in which these blocks are computed does # matter, since it affects the L2 cache hit rate of our program. and unfortunately, a # a simple row-major ordering @@ -116,7 +116,7 @@ You will specifically learn about: # group_size = min(grid_m - group_id * GROUP_M, GROUP_M); # pid_m = group_id * GROUP_M + (pid % group_size); # pid_n = (pid % width) // (group_size); - +# # For example, in the following matmul where each matrix is 9 blocks by 9 blocks, # we can see that if we compute the output in row-major ordering, we need to load 90 # blocks into SRAM to compute the first 9 output blocks, but if we do it in grouped @@ -310,8 +310,8 @@ a = torch.randn((512, 512), device='cuda', dtype=torch.float16) b = torch.randn((512, 512), device='cuda', dtype=torch.float16) triton_output = matmul(a, b, activation=None) torch_output = torch.matmul(a, b) -print(f"{triton_output=}") -print(f"{torch_output=}") +print(f"triton_output={triton_output}") +print(f"torch_output={torch_output}") if triton.testing.allclose(triton_output, torch_output): print("✅ Triton and Torch match") else: diff --git a/_images/grouped_vs_row_major_ordering.png b/_images/grouped_vs_row_major_ordering.png new file mode 100644 index 0000000000000000000000000000000000000000..46a356de7fe4683c7f9cd97edcd5c829285049cc GIT binary patch literal 476275 zcmZU)1ymc|_CAahcPQ=-MS@c_#odZSaVSs<6nBCb3dNn`F2$ud6ew=R-KDr|NWSp) zzV~<6|I1pFIhi>!bM`*Z+43YpT~!VXoeUig4h~B}UivK@9Fim)9AXD5GVDrstD`m? z9Hzakl$5%HloXA+v*UZ)k5+JS@)1e8D0-TML|KOMv9S{fsPbs-Xur{D7(pzRyB%!@jeWaU zYvygfh0D1QWQ*I*H-LK?j!}rV(H+HY`v>zaGYx{#8)TNV-3v>6opSkYhM0FTQOqyW?E93M?u`<0IHu3 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    Out:

    vector-add-performance:
                size      Triton       Torch
    -0        4096.0    9.600000    9.600000
    +0        4096.0    9.540372    9.600000
     1        8192.0   19.200000   19.200000
     2       16384.0   38.400001   38.400001
    -3       32768.0   63.999998   63.999998
    +3       32768.0   76.800002   76.800002
     4       65536.0  127.999995  127.999995
     5      131072.0  219.428568  219.428568
     6      262144.0  341.333321  384.000001
    @@ -337,7 +337,7 @@ for different problem sizes.

    15 134217728.0 851.577704 850.656574
    -

    Total running time of the script: ( 0 minutes 10.981 seconds)

    +

    Total running time of the script: ( 0 minutes 10.987 seconds)

    -

    Total running time of the script: ( 2 minutes 30.126 seconds)

    +

    Total running time of the script: ( 2 minutes 29.710 seconds)