From e3b4440dffabef1b505b8ec7f0ef32eb99d39c39 Mon Sep 17 00:00:00 2001 From: Philippe Tillet Date: Wed, 9 Feb 2022 07:15:50 +0000 Subject: [PATCH] [GH-PAGES] Updated website --- master/.buildinfo | 2 +- master/.doctrees/environment.pickle | Bin 77129 -> 96603 bytes .../getting-started/installation.doctree | Bin 5899 -> 5899 bytes .../tutorials/01-vector-add.doctree | Bin 0 -> 27862 bytes .../tutorials/02-fused-softmax.doctree | Bin 0 -> 34027 bytes .../03-matrix-multiplication.doctree | Bin 0 -> 55897 bytes .../tutorials/04-low-memory-dropout.doctree | Bin 0 -> 35766 bytes .../tutorials/05-layer-norm.doctree | Bin 0 -> 32932 bytes .../getting-started/tutorials/index.doctree | Bin 0 -> 15854 bytes .../tutorials/sg_execution_times.doctree | Bin 0 -> 10002 bytes master/.doctrees/index.doctree | Bin 10041 -> 9700 bytes .../chapter-1/introduction.doctree | Bin 33772 -> 33772 bytes .../chapter-2/related-work.doctree | Bin 62848 -> 62848 bytes .../generated/triton.Config.doctree | Bin 13752 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a/master/_downloads/034d953b6214fedce6ea03803c712b89/02-fused-softmax.ipynb b/master/_downloads/034d953b6214fedce6ea03803c712b89/02-fused-softmax.ipynb new file mode 100644 index 000000000..f16e090cb --- /dev/null +++ b/master/_downloads/034d953b6214fedce6ea03803c712b89/02-fused-softmax.ipynb @@ -0,0 +1,161 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Fused Softmax\nIn this tutorial, you will write a fused softmax operation that is significantly faster\nthan PyTorch's native op for a particular class of matrices: those whose rows can fit in\nthe GPU's SRAM.\nYou will learn about:\n\n- The benefits of kernel fusion for bandwidth-bound operations.\n- Reduction operators in Triton.\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivations\nCustom GPU kernels for elementwise additions are educationally valuable but won't get you very far in practice.\nLet us consider instead the case of a simple (numerically stabilized) softmax operation:\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import torch\n\nimport triton\nimport triton.language as tl\n\n\n@torch.jit.script\ndef naive_softmax(x):\n \"\"\"Compute row-wise softmax of X using native pytorch\n\n We subtract the maximum element in order to avoid overflows. Softmax is invariant to\n this shift.\n \"\"\"\n # read MN elements ; write M elements\n x_max = x.max(dim=1)[0]\n # read MN + M elements ; write MN elements\n z = x - x_max[:, None]\n # read MN elements ; write MN elements\n numerator = torch.exp(z)\n # read MN elements ; write M elements\n denominator = numerator.sum(dim=1)\n # read MN + M elements ; write MN elements\n ret = numerator / denominator[:, None]\n # in total: read 5MN + 2M elements ; wrote 3MN + 2M elements\n return ret" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "When implemented naively in PyTorch, computing :code:`y = naive_softmax(x)` for $x \\in R^{M \\times N}$\nrequires reading $5MN + 2M$ elements from DRAM and writing back $3MN + 2M$ elements.\nThis is obviously wasteful; we'd prefer to have a custom \"fused\" kernel that only reads\nX once and does all the necessary computations on-chip.\nDoing so would require reading and writing back only $MN$ bytes, so we could\nexpect a theoretical speed-up of ~4x (i.e., $(8MN + 4M) / 2MN$).\nThe `torch.jit.script` flags aims to perform this kind of \"kernel fusion\" automatically\nbut, as we will see later, it is still far from ideal.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute Kernel\nOur softmax kernel works as follows: each program loads a row of the input matrix X,\nnormalizes it and writes back the result to the output Y.\nNote that one important limitation of Triton is that each block must have a\npower-of-two number of elements, so we need to internally \"pad\" each row and guard the\nmemory operations properly if we want to handle any possible input shapes:\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@triton.jit\ndef softmax_kernel(\n output_ptr, input_ptr, input_row_stride, output_row_stride, n_cols,\n BLOCK_SIZE: tl.constexpr\n):\n # The rows of the softmax are independent, so we parallelize across those\n row_idx = tl.program_id(0)\n # The stride represents how much we need to increase the pointer to advance 1 row\n row_start_ptr = input_ptr + row_idx * input_row_stride\n # The block size is the next power of two greater than n_cols, so we can fit each\n # row in a single block\n col_offsets = tl.arange(0, BLOCK_SIZE)\n input_ptrs = row_start_ptr + col_offsets\n # Load the row into SRAM, using a mask since BLOCK_SIZE may be > than n_cols\n row = tl.load(input_ptrs, mask=col_offsets < n_cols, other=-float('inf'))\n # Substract maximum for numerical stability\n row_minus_max = row - tl.max(row, axis=0)\n # Note that exponentials in Triton are fast but approximate (i.e., think __expf in CUDA)\n numerator = tl.exp(row_minus_max)\n denominator = tl.sum(numerator, axis=0)\n softmax_output = numerator / denominator\n # Write back output to DRAM\n output_row_start_ptr = output_ptr + row_idx * output_row_stride\n output_ptrs = output_row_start_ptr + col_offsets\n tl.store(output_ptrs, softmax_output, mask=col_offsets < n_cols)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can create a helper function that enqueues the kernel and its (meta-)arguments for any given input tensor.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def softmax(x):\n n_rows, n_cols = x.shape\n # The block size is the smallest power of two greater than the number of columns in `x`\n BLOCK_SIZE = triton.next_power_of_2(n_cols)\n # Another trick we can use is to ask the compiler to use more threads per row by\n # increasing the number of warps (`num_warps`) over which each row is distributed.\n # You will see in the next tutorial how to auto-tune this value in a more natural\n # way so you don't have to come up with manual heuristics yourself.\n num_warps = 4\n if BLOCK_SIZE >= 2048:\n num_warps = 8\n if BLOCK_SIZE >= 4096:\n num_warps = 16\n # Allocate output\n y = torch.empty_like(x)\n # Enqueue kernel. The 1D launch grid is simple: we have one kernel instance per row o\n # f the input matrix\n softmax_kernel[(n_rows,)](\n y,\n x,\n x.stride(0),\n y.stride(0),\n n_cols,\n num_warps=num_warps,\n BLOCK_SIZE=BLOCK_SIZE,\n )\n return y" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We make sure that we test our kernel on a matrix with an irregular number of rows and columns.\nThis will allow us to verify that our padding mechanism works.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "torch.manual_seed(0)\nx = torch.randn(1823, 781, device='cuda')\ny_triton = softmax(x)\ny_torch = torch.softmax(x, axis=1)\nassert torch.allclose(y_triton, y_torch), (y_triton, y_torch)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "As expected, the results are identical.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Benchmark\nHere we will benchmark our operation as a function of the number of columns in the input matrix -- assuming 4096 rows.\nWe will then compare its performance against (1) :code:`torch.softmax` and (2) the :code:`naive_softmax` defined above.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@triton.testing.perf_report(\n triton.testing.Benchmark(\n x_names=['N'], # argument names to use as an x-axis for the plot\n x_vals=[\n 128 * i for i in range(2, 100)\n ], # different possible values for `x_name`\n line_arg='provider', # argument name whose value corresponds to a different line in the plot\n line_vals=[\n 'triton',\n 'torch-native',\n 'torch-jit',\n ], # possible values for `line_arg``\n line_names=[\n \"Triton\",\n \"Torch (native)\",\n \"Torch (jit)\",\n ], # label name for the lines\n styles=[('blue', '-'), ('green', '-'), ('green', '--')], # line styles\n ylabel=\"GB/s\", # label name for the y-axis\n plot_name=\"softmax-performance\", # name for the plot. Used also as a file name for saving the plot.\n args={'M': 4096}, # values for function arguments not in `x_names` and `y_name`\n )\n)\ndef benchmark(M, N, provider):\n x = torch.randn(M, N, device='cuda', dtype=torch.float32)\n if provider == 'torch-native':\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.softmax(x, axis=-1))\n if provider == 'triton':\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: softmax(x))\n if provider == 'torch-jit':\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: naive_softmax(x))\n gbps = lambda ms: 2 * x.nelement() * x.element_size() * 1e-9 / (ms * 1e-3)\n return gbps(ms), gbps(max_ms), gbps(min_ms)\n\n\nbenchmark.run(show_plots=True, print_data=True)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "In the above plot, we can see that:\n\n - Triton is 4x faster than the Torch JIT. This confirms our suspicions that the Torch JIT does not do any fusion here.\n - Triton is noticeably faster than :code:`torch.softmax` -- in addition to being **easier to read, understand and maintain**.\n Note however that the PyTorch `softmax` operation is more general and will works on tensors of any shape.\n\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/master/_downloads/62d97d49a32414049819dd8bb8378080/01-vector-add.py b/master/_downloads/62d97d49a32414049819dd8bb8378080/01-vector-add.py new file mode 100644 index 000000000..d684106f1 --- /dev/null +++ b/master/_downloads/62d97d49a32414049819dd8bb8378080/01-vector-add.py @@ -0,0 +1,131 @@ +""" +Vector Addition +================= +In this tutorial, you will write a simple vector addition using Triton and learn about: + +- The basic programming model of Triton +- The `triton.jit` decorator, which is used to define Triton kernels. +- The best practices for validating and benchmarking your custom ops against native reference implementations +""" + +# %% +# Compute Kernel +# -------------------------- + +import torch + +import triton +import triton.language as tl + + +@triton.jit +def add_kernel( + x_ptr, # *Pointer* to first input vector + y_ptr, # *Pointer* to second input vector + output_ptr, # *Pointer* to output vector + n_elements, # Size of the vector + BLOCK_SIZE: tl.constexpr, # Number of elements each program should process + # NOTE: `constexpr` so it can be used as a shape value +): + # There are multiple 'program's processing different data. We identify which program + # we are here + pid = tl.program_id(axis=0) # We use a 1D launch grid so axis is 0 + # This program will process inputs that are offset from the initial data. + # for instance, if you had a vector of length 256 and block_size of 64, the programs + # would each access the elements [0:64, 64:128, 128:192, 192:256]. + # Note that offsets is a list of pointers + block_start = pid * BLOCK_SIZE + offsets = block_start + tl.arange(0, BLOCK_SIZE) + # Create a mask to guard memory operations against out-of-bounds accesses + mask = offsets < n_elements + # Load x and y from DRAM, masking out any extra elements in case the input is not a + # multiple of the block size + x = tl.load(x_ptr + offsets, mask=mask) + y = tl.load(y_ptr + offsets, mask=mask) + output = x + y + # Write x + y back to DRAM + tl.store(output_ptr + offsets, output, mask=mask) + + +# %% +# Let's also declare a helper function to (1) allocate the `z` tensor +# and (2) enqueue the above kernel with appropriate grid/block sizes. + + +def add(x: torch.Tensor, y: torch.Tensor): + # We need to preallocate the output + output = torch.empty_like(x) + assert x.is_cuda and y.is_cuda and output.is_cuda + n_elements = output.numel() + # The SPMD launch grid denotes the number of kernel instances that run in parallel. + # It is analogous to CUDA launch grids. It can be either Tuple[int], or Callable(metaparameters) -> Tuple[int] + # In this case, we use a 1D grid where the size is the number of blocks + grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),) + # NOTE: + # - each torch.tensor object is implicitly converted into a pointer to its first element. + # - `triton.jit`'ed functions can be index with a launch grid to obtain a callable GPU kernel + # - don't forget to pass meta-parameters as keywords arguments + add_kernel[grid](x, y, output, n_elements, BLOCK_SIZE=1024) + # We return a handle to z but, since `torch.cuda.synchronize()` hasn't been called, the kernel is still + # running asynchronously at this point. + return output + + +# %% +# We can now use the above function to compute the element-wise sum of two `torch.tensor` objects and test its correctness: + +torch.manual_seed(0) +size = 98432 +x = torch.rand(size, device='cuda') +y = torch.rand(size, device='cuda') +output_torch = x + y +output_triton = add(x, y) +print(output_torch) +print(output_triton) +print( + f'The maximum difference between torch and triton is ' + f'{torch.max(torch.abs(output_torch - output_triton))}' +) + +# %% +# Seems like we're good to go! + +# %% +# Benchmark +# ----------- +# We can now benchmark our custom op on vectors of increasing sizes to get a sense of how it does relative to PyTorch. +# To make things easier, Triton has a set of built-in utilities that allow us to concisely plot the performance of your custom ops +# for different problem sizes. + + +@triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['size'], # argument names to use as an x-axis for the plot + x_vals=[ + 2 ** i for i in range(12, 28, 1) + ], # different possible values for `x_name` + x_log=True, # x axis is logarithmic + line_arg='provider', # argument name whose value corresponds to a different line in the plot + line_vals=['triton', 'torch'], # possible values for `line_arg` + line_names=['Triton', 'Torch'], # label name for the lines + styles=[('blue', '-'), ('green', '-')], # line styles + ylabel='GB/s', # label name for the y-axis + plot_name='vector-add-performance', # name for the plot. Used also as a file name for saving the plot. + args={}, # values for function arguments not in `x_names` and `y_name` + ) +) +def benchmark(size, provider): + x = torch.rand(size, device='cuda', dtype=torch.float32) + y = torch.rand(size, device='cuda', dtype=torch.float32) + if provider == 'torch': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: x + y) + if provider == 'triton': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: add(x, y)) + gbps = lambda ms: 12 * size / ms * 1e-6 + return gbps(ms), gbps(max_ms), gbps(min_ms) + + +# %% +# We can now run the decorated function above. 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zcBCw<6J*8jlGGu^g)e>h^eC_=95x}4!k;4;`+GAj8-(GM5MqzW_4E{x+LsBu+ql$B z;ffyQU=uZi7We^oM*k{xmn-~(R(1cE#FLqTt(TD3eT2ytS~Muh3ml zpen-SkEA!uTDqmKugStXLU6z0R z5~v=e9ZepyYsA!Yn8K%t2 z1K)Yl04u($gSfxh7i|V_U~S&?cFUP>?HV_HIlKjP;Zqh=eH0vlKZsLt?(LXi@T|#t=M&H>QE9aG{N-13`!VuZyt$d9rV!H}_e~qt^ z$|BaNM$6yUUl?(;6kFcOZMc|0tgQ!i?r+DHnE26Evk2|ibkV-&?rH=W&gfFayz5eF zePpTx^U>mr4|`kW$CwDOcy*+wN9fg&{@d%)CghdA=Bp#4p!3*;Y7d+e;kMX5sRZuf z%qP6tg2rgidoB_nD`M+($DBkFA7IZ&%AY>olYB`N+(iV^Va}ACGMp zB6V>4uI@w!IUc1e_|y~#E BLOCK_SIZE: + raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.") + # heuristics for number of warps + num_warps = min(max(BLOCK_SIZE // 256, 1), 8) + # enqueue kernel + _layer_norm_fwd_fused[(M,)](x_arg, y, weight, bias, mean, rstd, + x_arg.stride(0), N, eps, + BLOCK_SIZE=BLOCK_SIZE, num_warps=num_warps) + ctx.save_for_backward(x, weight, bias, mean, rstd) + ctx.BLOCK_SIZE = BLOCK_SIZE + ctx.num_warps = num_warps + ctx.eps = eps + return y + + @staticmethod + def backward(ctx, dy): + x, w, b, m, v = ctx.saved_tensors + # heuristics for amount of parallel reduction stream for DG/DB + N = w.shape[0] + GROUP_SIZE_M = 64 + if N <= 8192: GROUP_SIZE_M = 96 + if N <= 4096: GROUP_SIZE_M = 128 + if N <= 1024: GROUP_SIZE_M = 256 + # allocate output + locks = torch.zeros(2 * GROUP_SIZE_M, dtype=torch.int32, device='cuda') + _dw = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device) + _db = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device) + dw = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device) + db = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device) + dx = torch.empty_like(dy) + # enqueue kernel using forward pass heuristics + # also compute partial sums for DW and DB + x_arg = x.reshape(-1, x.shape[-1]) + M, N = x_arg.shape + _layer_norm_bwd_dx_fused[(M,)](dx, dy, _dw, _db, x, w, b, m, v, locks, + x_arg.stride(0), N, ctx.eps, + BLOCK_SIZE_N=ctx.BLOCK_SIZE, + GROUP_SIZE_M=GROUP_SIZE_M, + num_warps=ctx.num_warps) + grid = lambda meta: [triton.cdiv(N, meta['BLOCK_SIZE_N'])] + # accumulate partial sums in separate kernel + _layer_norm_bwd_dwdb[grid](_dw, _db, dw, db, GROUP_SIZE_M, N, + BLOCK_SIZE_M=32, + BLOCK_SIZE_N=128) + return dx, None, dw, db, None + + +layer_norm = LayerNorm.apply + + +def test_layer_norm(M, N, dtype, eps=1e-5, device='cuda'): + # create data + x_shape = (M, N) + w_shape = (x_shape[-1], ) + weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda') + dy = .1 * torch.randn_like(x) + x.requires_grad_(True) + # forward pass + y_tri = layer_norm(x, w_shape, weight, bias, eps) + y_ref = torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps).to(dtype) + # backward pass (triton) + y_tri.backward(dy, retain_graph=True) + dx_tri, dw_tri, db_tri = [_.grad.clone() for _ in [x, weight, bias]] + x.grad, weight.grad, bias.grad = None, None, None + # backward pass (torch) + y_ref.backward(dy, retain_graph=True) + dx_ref, dw_ref, db_ref = [_.grad.clone() for _ in [x, weight, bias]] + # compare + triton.testing.assert_almost_equal(y_tri, y_ref) + triton.testing.assert_almost_equal(dx_tri, dx_ref) + triton.testing.assert_almost_equal(db_tri, db_ref, decimal=1) + triton.testing.assert_almost_equal(dw_tri, dw_ref, decimal=1) + + +@triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['N'], + x_vals=[512 * i for i in range(2, 32)], + line_arg='provider', + line_vals=['triton', 'torch'] + (['apex'] if HAS_APEX else []), + line_names=['Triton', 'Torch'] + (['Apex'] if HAS_APEX else []), + styles=[('blue', '-'), ('green', '-'), ('orange', '-')], + ylabel='GB/s', + plot_name='layer-norm-backward', + args={'M': 4096, 'dtype': torch.float16, 'mode': 'backward'} + ) +) +def bench_layer_norm(M, N, dtype, provider, mode='backward', eps=1e-5, device='cuda'): + # create data + x_shape = (M, N) + w_shape = (x_shape[-1], ) + weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda') + dy = .1 * torch.randn_like(x) + x.requires_grad_(True) + # utility functions + if provider == 'triton': + y_fwd = lambda: layer_norm(x, w_shape, weight, bias, eps) + if provider == 'torch': + y_fwd = lambda: torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps) + if provider == 'apex': + apex_layer_norm = apex.normalization.FusedLayerNorm(w_shape).to(x.device).to(x.dtype) + y_fwd = lambda: apex_layer_norm(x) + # forward pass + if mode == 'forward': + gbps = lambda ms: 2 * x.numel() * x.element_size() / ms * 1e-6 + ms, min_ms, max_ms = triton.testing.do_bench(y_fwd, rep=500) + # backward pass + if mode == 'backward': + gbps = lambda ms: 3 * x.numel() * x.element_size() / ms * 1e-6 + y = y_fwd() + ms, min_ms, max_ms = triton.testing.do_bench(lambda: y.backward(dy, retain_graph=True), + grad_to_none=[x], rep=500) + return gbps(ms), gbps(max_ms), gbps(min_ms) + + +bench_layer_norm.run(save_path='.', print_data=True) diff --git a/master/_downloads/ae7fff29e1b574187bc930ed94bcc353/05-layer-norm.ipynb b/master/_downloads/ae7fff29e1b574187bc930ed94bcc353/05-layer-norm.ipynb new file mode 100644 index 000000000..4d381dafc --- /dev/null +++ b/master/_downloads/ae7fff29e1b574187bc930ed94bcc353/05-layer-norm.ipynb @@ -0,0 +1,54 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Layer Normalization\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import torch\n\nimport triton\nimport triton.language as tl\n\ntry:\n # This is https://github.com/NVIDIA/apex, NOT the apex on PyPi, so it\n # should not be added to extras_require in setup.py.\n import apex\n HAS_APEX = True\nexcept ModuleNotFoundError:\n HAS_APEX = False\n\n\n# Forward Pass\n@triton.jit\ndef _layer_norm_fwd_fused(X, Y, W, B, M, V, stride, N, eps,\n BLOCK_SIZE: tl.constexpr):\n # position of elements processed by this program\n row = tl.program_id(0)\n cols = tl.arange(0, BLOCK_SIZE)\n mask = cols < N\n # offset data pointers to start at the row of interest\n X += row * stride\n Y += row * stride\n # load data and cast to float32\n x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)\n # compute mean\n mean = tl.sum(x, axis=0) / N\n # compute std\n xmean = tl.where(mask, x - mean, 0.)\n var = tl.sum(xmean * xmean, axis=0) / N\n rstd = 1 / tl.sqrt(var + eps)\n xhat = xmean * rstd\n # write-back mean/rstd\n tl.store(M + row, mean)\n tl.store(V + row, rstd)\n # multiply by weight and add bias\n w = tl.load(W + cols, mask=mask)\n b = tl.load(B + cols, mask=mask)\n y = xhat * w + b\n # write-back\n tl.store(Y + cols, y, mask=mask)\n\n\n# Backward pass (DX + partial DW + partial DB)\n@triton.jit\ndef _layer_norm_bwd_dx_fused(DX, DY, DW, DB, X, W, B, M, V, Lock, stride, N, eps,\n GROUP_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr):\n # position of elements processed by this program\n row = tl.program_id(0)\n cols = tl.arange(0, BLOCK_SIZE_N)\n mask = cols < N\n # offset data pointers to start at the row of interest\n X += row * stride\n DY += row * stride\n DX += row * stride\n # offset locks and weight/bias gradient pointer\n # each kernel instance accumulates partial sums for\n # DW and DB into one of GROUP_SIZE_M independent buffers\n # these buffers stay in the L2, which allow this kernel\n # to be fast\n lock_id = row % GROUP_SIZE_M\n Lock += lock_id\n Count = Lock + GROUP_SIZE_M\n DW = DW + lock_id * N + cols\n DB = DB + lock_id * N + cols\n # load data to SRAM\n x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)\n dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)\n w = tl.load(W + cols, mask=mask).to(tl.float32)\n mean = tl.load(M + row)\n rstd = tl.load(V + row)\n # compute dx\n xhat = (x - mean) * rstd\n wdy = w * dy\n xhat = tl.where(mask, xhat, 0.)\n wdy = tl.where(mask, wdy, 0.)\n mean1 = tl.sum(xhat * wdy, axis=0) / N\n mean2 = tl.sum(wdy, axis=0) / N\n dx = (wdy - (xhat * mean1 + mean2)) * rstd\n # write-back dx\n tl.store(DX + cols, dx, mask=mask)\n # accumulate partial sums for dw/db\n partial_dw = (dy * xhat).to(w.dtype)\n partial_db = (dy).to(w.dtype)\n while tl.atomic_cas(Lock, 0, 1) == 1:\n pass\n count = tl.load(Count)\n # first store doesn't accumulate\n if count == 0:\n tl.atomic_xchg(Count, 1)\n else:\n partial_dw += tl.load(DW, mask=mask)\n partial_db += tl.load(DB, mask=mask)\n tl.store(DW, partial_dw, mask=mask)\n tl.store(DB, partial_db, mask=mask)\n # release lock\n tl.atomic_xchg(Lock, 0)\n\n# Backward pass (total DW + total DB)\n\n\n@triton.jit\ndef _layer_norm_bwd_dwdb(DW, DB, FINAL_DW, FINAL_DB, M, N,\n BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr):\n pid = tl.program_id(0)\n cols = pid * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)\n dw = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)\n db = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)\n for i in range(0, M, BLOCK_SIZE_M):\n rows = i + tl.arange(0, BLOCK_SIZE_M)\n mask = (rows[:, None] < M) & (cols[None, :] < N)\n offs = rows[:, None] * N + cols[None, :]\n dw += tl.load(DW + offs, mask=mask, other=0.)\n db += tl.load(DB + offs, mask=mask, other=0.)\n sum_dw = tl.sum(dw, axis=0)\n sum_db = tl.sum(db, axis=0)\n tl.store(FINAL_DW + cols, sum_dw, mask=cols < N)\n tl.store(FINAL_DB + cols, sum_db, mask=cols < N)\n\n\nclass LayerNorm(torch.autograd.Function):\n\n @staticmethod\n def forward(ctx, x, normalized_shape, weight, bias, eps):\n # allocate output\n y = torch.empty_like(x)\n # reshape input data into 2D tensor\n x_arg = x.reshape(-1, x.shape[-1])\n M, N = x_arg.shape\n mean = torch.empty((M, ), dtype=torch.float32, device='cuda')\n rstd = torch.empty((M, ), dtype=torch.float32, device='cuda')\n # Less than 64KB per feature: enqueue fused kernel\n MAX_FUSED_SIZE = 65536 // x.element_size()\n BLOCK_SIZE = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))\n if N > BLOCK_SIZE:\n raise RuntimeError(\"This layer norm doesn't support feature dim >= 64KB.\")\n # heuristics for number of warps\n num_warps = min(max(BLOCK_SIZE // 256, 1), 8)\n # enqueue kernel\n _layer_norm_fwd_fused[(M,)](x_arg, y, weight, bias, mean, rstd,\n x_arg.stride(0), N, eps,\n BLOCK_SIZE=BLOCK_SIZE, num_warps=num_warps)\n ctx.save_for_backward(x, weight, bias, mean, rstd)\n ctx.BLOCK_SIZE = BLOCK_SIZE\n ctx.num_warps = num_warps\n ctx.eps = eps\n return y\n\n @staticmethod\n def backward(ctx, dy):\n x, w, b, m, v = ctx.saved_tensors\n # heuristics for amount of parallel reduction stream for DG/DB\n N = w.shape[0]\n GROUP_SIZE_M = 64\n if N <= 8192: GROUP_SIZE_M = 96\n if N <= 4096: GROUP_SIZE_M = 128\n if N <= 1024: GROUP_SIZE_M = 256\n # allocate output\n locks = torch.zeros(2 * GROUP_SIZE_M, dtype=torch.int32, device='cuda')\n _dw = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device)\n _db = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device)\n dw = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device)\n db = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device)\n dx = torch.empty_like(dy)\n # enqueue kernel using forward pass heuristics\n # also compute partial sums for DW and DB\n x_arg = x.reshape(-1, x.shape[-1])\n M, N = x_arg.shape\n _layer_norm_bwd_dx_fused[(M,)](dx, dy, _dw, _db, x, w, b, m, v, locks,\n x_arg.stride(0), N, ctx.eps,\n BLOCK_SIZE_N=ctx.BLOCK_SIZE,\n GROUP_SIZE_M=GROUP_SIZE_M,\n num_warps=ctx.num_warps)\n grid = lambda meta: [triton.cdiv(N, meta['BLOCK_SIZE_N'])]\n # accumulate partial sums in separate kernel\n _layer_norm_bwd_dwdb[grid](_dw, _db, dw, db, GROUP_SIZE_M, N,\n BLOCK_SIZE_M=32,\n BLOCK_SIZE_N=128)\n return dx, None, dw, db, None\n\n\nlayer_norm = LayerNorm.apply\n\n\ndef test_layer_norm(M, N, dtype, eps=1e-5, device='cuda'):\n # create data\n x_shape = (M, N)\n w_shape = (x_shape[-1], )\n weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)\n bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)\n x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda')\n dy = .1 * torch.randn_like(x)\n x.requires_grad_(True)\n # forward pass\n y_tri = layer_norm(x, w_shape, weight, bias, eps)\n y_ref = torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps).to(dtype)\n # backward pass (triton)\n y_tri.backward(dy, retain_graph=True)\n dx_tri, dw_tri, db_tri = [_.grad.clone() for _ in [x, weight, bias]]\n x.grad, weight.grad, bias.grad = None, None, None\n # backward pass (torch)\n y_ref.backward(dy, retain_graph=True)\n dx_ref, dw_ref, db_ref = [_.grad.clone() for _ in [x, weight, bias]]\n # compare\n triton.testing.assert_almost_equal(y_tri, y_ref)\n triton.testing.assert_almost_equal(dx_tri, dx_ref)\n triton.testing.assert_almost_equal(db_tri, db_ref, decimal=1)\n triton.testing.assert_almost_equal(dw_tri, dw_ref, decimal=1)\n\n\n@triton.testing.perf_report(\n triton.testing.Benchmark(\n x_names=['N'],\n x_vals=[512 * i for i in range(2, 32)],\n line_arg='provider',\n line_vals=['triton', 'torch'] + (['apex'] if HAS_APEX else []),\n line_names=['Triton', 'Torch'] + (['Apex'] if HAS_APEX else []),\n styles=[('blue', '-'), ('green', '-'), ('orange', '-')],\n ylabel='GB/s',\n plot_name='layer-norm-backward',\n args={'M': 4096, 'dtype': torch.float16, 'mode': 'backward'}\n )\n)\ndef bench_layer_norm(M, N, dtype, provider, mode='backward', eps=1e-5, device='cuda'):\n # create data\n x_shape = (M, N)\n w_shape = (x_shape[-1], )\n weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)\n bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)\n x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda')\n dy = .1 * torch.randn_like(x)\n x.requires_grad_(True)\n # utility functions\n if provider == 'triton':\n y_fwd = lambda: layer_norm(x, w_shape, weight, bias, eps)\n if provider == 'torch':\n y_fwd = lambda: torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps)\n if provider == 'apex':\n apex_layer_norm = apex.normalization.FusedLayerNorm(w_shape).to(x.device).to(x.dtype)\n y_fwd = lambda: apex_layer_norm(x)\n # forward pass\n if mode == 'forward':\n gbps = lambda ms: 2 * x.numel() * x.element_size() / ms * 1e-6\n ms, min_ms, max_ms = triton.testing.do_bench(y_fwd, rep=500)\n # backward pass\n if mode == 'backward':\n gbps = lambda ms: 3 * x.numel() * x.element_size() / ms * 1e-6\n y = y_fwd()\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: y.backward(dy, retain_graph=True),\n grad_to_none=[x], rep=500)\n return gbps(ms), gbps(max_ms), gbps(min_ms)\n\n\nbench_layer_norm.run(save_path='.', print_data=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/master/_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb b/master/_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb new file mode 100644 index 000000000..f177fae9b --- /dev/null +++ b/master/_downloads/b51b68bc1c6b1a5e509f67800b6235af/03-matrix-multiplication.ipynb @@ -0,0 +1,129 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Matrix Multiplication\nIn this tutorial, you will write a 25-lines high-performance FP16 matrix multiplication\nkernel that achieves performance on par with cuBLAS.\nYou will specifically learn about:\n\n- Block-level matrix multiplications\n- Multi-dimensional pointer arithmetic\n- Program re-ordering for improved L2 cache hit rate\n- Automatic performance tuning\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Motivations\nMatrix multiplications are a key building block of most modern high-performance computing systems.\nThey are notoriously hard to optimize, hence their implementation is generally done by\nhardware vendors themselves as part of so-called \"kernel libraries\" (e.g., cuBLAS).\nUnfortunately, these libraries are often proprietary and cannot be easily customized\nto accomodate the needs of modern deep learning workloads (e.g., fused activation functions).\nIn this tutorial, you will learn how to implement efficient matrix multiplications by\nyourself with Triton, in a way that is easy to customize and extend.\n\nRoughly speaking, the kernel that we will write will implement the following blocked\nalgorithm to multiply a (M, K) by a (K, N) matrix:\n\n .. code-block:: python\n\n # do in parallel\n for m in range(0, M, BLOCK_SIZE_M):\n # do in parallel\n for n in range(0, N, BLOCK_SIZE_N):\n acc = zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=float32)\n for k in range(0, K, BLOCK_SIZE_K):\n a = A[m : m+BLOCK_SIZE_M, k : k+BLOCK_SIZE_K]\n b = B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]\n acc += dot(a, b)\n C[m : m+BLOCK_SIZE_M, n : n+BLOCK_SIZE_N] = acc;\n\nwhere each iteration of the doubly-nested for-loop is performed by a dedicated Triton program instance.\n\n" + ] + }, + { + "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\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_xi + j*stride_xj`.\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_ptr + (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_ptr + (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 offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)\n offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)\n offs_k = tl.arange(0, BLOCK_SIZE_K)\n a_ptrs = a_ptr + (offs_am[:, None]*stride_am + offs_k [None, :]*stride_ak)\n b_ptrs = b_ptr + (offs_k [:, None]*stride_bk + offs_bn[None, :]*stride_bn)\n\nAnd then updated in the inner loop as follows:\n\n .. code-block:: python\n\n pa += BLOCK_SIZE_K * stride_ak;\n pb += BLOCK_SIZE_K * stride_bk;\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 # program ID\n pid = tl.program_id(axis=0)\n # number of program ids along the M axis\n num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)\n # number of programs ids along the N axis\n num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)\n # number of programs in group\n num_pid_in_group = GROUP_SIZE_M * num_pid_n\n # id of the group this program is in\n group_id = pid // num_pid_in_group\n # row-id of the first program in the group\n first_pid_m = group_id * GROUP_SIZE_M\n # if `num_pid_m` isn't divisible by `GROUP_SIZE_M`, the last group is smaller\n group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M)\n # *within groups*, programs are ordered in a column-major order\n # row-id of the program in the *launch grid*\n pid_m = first_pid_m + (pid % group_size_m)\n # col-id of the program in the *launch grid*\n pid_n = (pid % num_pid_in_group) // group_size_m\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" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Final Result\n\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import torch\n\nimport triton\nimport triton.language as tl\n\n# %\n# :code:`triton.jit`'ed functions can be auto-tuned by using the `triton.autotune`\n# decorator, which consumes:\n# - A list of :code:`triton.Config` objects that define different configurations of\n# meta-parameters (e.g., BLOCK_SIZE_M) and compilation options (e.g., num_warps) to try\n# - An autotuning *key* whose change in values will trigger evaluation of all the\n# provided configs\n\n\n@triton.autotune(\n configs=[\n triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8),\n triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8),\n triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),\n triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),\n triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),\n triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),\n triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),\n triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4),\n triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2),\n triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2),\n ],\n key=['M', 'N', 'K'],\n)\n@triton.jit\ndef matmul_kernel(\n # Pointers to matrices\n a_ptr, b_ptr, c_ptr,\n # Matrix dimensions\n M, N, K,\n # The stride variables represent how much to increase the ptr by when moving by 1\n # element in a particular dimension. E.g. stride_am is how much to increase a_ptr\n # by to get the element one row down (A has M rows)\n stride_am, stride_ak,\n stride_bk, stride_bn,\n stride_cm, stride_cn,\n # Meta-parameters\n BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr,\n GROUP_SIZE_M: tl.constexpr,\n ACTIVATION: tl.constexpr,\n):\n \"\"\"Kernel for computing the matmul C = A x B.\n A has shape (M, K), B has shape (K, N) and C has shape (M, N)\n \"\"\"\n # -----------------------------------------------------------\n # Map program ids `pid` to the block of C it should compute.\n # This is done in a grouped ordering to promote L2 data reuse\n # See above `L2 Cache Optimizations` section for details\n pid = tl.program_id(axis=0)\n num_pid_m = tl.cdiv(M, BLOCK_SIZE_M)\n num_pid_n = tl.cdiv(N, BLOCK_SIZE_N)\n num_pid_in_group = GROUP_SIZE_M * num_pid_n\n group_id = pid // num_pid_in_group\n first_pid_m = group_id * GROUP_SIZE_M\n group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M)\n pid_m = first_pid_m + (pid % group_size_m)\n pid_n = (pid % num_pid_in_group) // group_size_m\n\n # ----------------------------------------------------------\n # Create pointers for the first blocks of A and B.\n # We will advance this pointer as we move in the K direction\n # and accumulate\n # a_ptrs is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers\n # b_ptrs is a block of [BLOCK_SIZE_K, BLOCK_SIZE_n] pointers\n # see above `Pointer Arithmetics` section for details\n offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)\n offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)\n offs_k = tl.arange(0, BLOCK_SIZE_K)\n a_ptrs = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak)\n b_ptrs = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn)\n\n # -----------------------------------------------------------\n # Iterate to compute a block of the C matrix\n # We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block\n # of fp32 values for higher accuracy.\n # `accumulator` will be converted back to fp16 after the loop\n accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)\n for k in range(0, K, BLOCK_SIZE_K):\n # Note that for simplicity, we don't apply a mask here.\n # This means that if K is not a multiple of BLOCK_SIZE_K,\n # this will access out-of-bounds memory and produce an\n # error or (worse!) incorrect results.\n a = tl.load(a_ptrs)\n b = tl.load(b_ptrs)\n # We accumulate along the K dimension\n accumulator += tl.dot(a, b)\n # Advance the ptrs to the next K block\n a_ptrs += BLOCK_SIZE_K * stride_ak\n b_ptrs += BLOCK_SIZE_K * stride_bk\n # you can fuse arbitrary activation functions here\n # while the accumulator is still in FP32!\n if ACTIVATION:\n accumulator = ACTIVATION(accumulator)\n c = accumulator.to(tl.float16)\n\n # -----------------------------------------------------------\n # Write back the block of the output matrix C\n offs_cm = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M)\n offs_cn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)\n c_ptrs = c_ptr + stride_cm * offs_cm[:, None] + stride_cn * offs_cn[None, :]\n c_mask = (offs_cm[:, None] < M) & (offs_cn[None, :] < N)\n tl.store(c_ptrs, c, mask=c_mask)\n\n\n# we can fuse `leaky_relu` by providing it as an `ACTIVATION` meta-parameter in `_matmul`\n@triton.jit\ndef leaky_relu(x):\n return tl.where(x >= 0, x, 0.01 * x)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now create a convenience wrapper function that only takes two input tensors\nand (1) checks any shape constraint; (2) allocates the output; (3) launches the above kernel\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def matmul(a, b, activation=None):\n # checks constraints\n assert a.shape[1] == b.shape[0], \"incompatible dimensions\"\n assert a.is_contiguous(), \"matrix A must be contiguous\"\n assert b.is_contiguous(), \"matrix B must be contiguous\"\n M, K = a.shape\n K, N = b.shape\n assert (\n K % 32 == 0\n ), \"We don't check memory-out-of-bounds with K so K must be divisible by BLOCK_SIZE_K\"\n # allocates output\n c = torch.empty((M, N), device=a.device, dtype=a.dtype)\n # 1D launch kernel where each block gets its own program.\n grid = lambda META: (\n triton.cdiv(M, META['BLOCK_SIZE_M']) * triton.cdiv(N, META['BLOCK_SIZE_N']),\n )\n matmul_kernel[grid](\n a, b, c,\n M, N, K,\n a.stride(0), a.stride(1),\n b.stride(0), b.stride(1),\n c.stride(0), c.stride(1),\n ACTIVATION=activation,\n )\n return c" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Unit Test\n\nWe can test our custom matrix multiplication operation against a native torch implementation (i.e., cuBLAS)\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "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={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\")" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Benchmark\n\n### Square Matrix Performance\nWe can now compare the performance of our kernel against that of cuBLAS. Here we focus on square matrices, but feel free to arrange this script as you wish to benchmark any other matrix shape.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@triton.testing.perf_report(\n triton.testing.Benchmark(\n x_names=['M', 'N', 'K'], # argument names to use as an x-axis for the plot\n x_vals=[\n 128 * i for i in range(2, 33)\n ], # different possible values for `x_name`\n line_arg='provider', # argument name whose value corresponds to a different line in the plot\n # possible values for `line_arg``\n line_vals=['cublas', 'cublas + relu', 'triton', 'triton + relu'],\n # label name for the lines\n line_names=[\"cuBLAS\", \"cuBLAS (+ torch.nn.LeakyReLU)\", \"Triton\", \"Triton (+ LeakyReLU)\"],\n # line styles\n styles=[('green', '-'), ('green', '--'), ('blue', '-'), ('blue', '--')],\n ylabel=\"TFLOPS\", # label name for the y-axis\n plot_name=\"matmul-performance\", # name for the plot. Used also as a file name for saving the plot.\n args={},\n )\n)\ndef benchmark(M, N, K, provider):\n a = torch.randn((M, K), device='cuda', dtype=torch.float16)\n b = torch.randn((K, N), device='cuda', dtype=torch.float16)\n if provider == 'cublas':\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.matmul(a, b))\n if provider == 'triton':\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: matmul(a, b))\n if provider == 'cublas + relu':\n torch_relu = torch.nn.ReLU(inplace=True)\n ms, min_ms, max_ms = triton.testing.do_bench(\n lambda: torch_relu(torch.matmul(a, b))\n )\n if provider == 'triton + relu':\n ms, min_ms, max_ms = triton.testing.do_bench(\n lambda: matmul(a, b, activation=leaky_relu)\n )\n perf = lambda ms: 2 * M * N * K * 1e-12 / (ms * 1e-3)\n return perf(ms), perf(max_ms), perf(min_ms)\n\n\nbenchmark.run(show_plots=True, print_data=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/master/_downloads/bc847dec325798bdc436c4ef5ac8b78a/04-low-memory-dropout.ipynb b/master/_downloads/bc847dec325798bdc436c4ef5ac8b78a/04-low-memory-dropout.ipynb new file mode 100644 index 000000000..5a6b1d8fa --- /dev/null +++ b/master/_downloads/bc847dec325798bdc436c4ef5ac8b78a/04-low-memory-dropout.ipynb @@ -0,0 +1,100 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Low-Memory Dropout\n\nIn this tutorial, you will write a memory-efficient implementation of dropout whose state\nwill be composed of a single int32 seed. This differs from more traditional implementations of dropout,\nwhose state is generally composed of a bit mask tensor of the same shape as the input. You will learn about:\n\n- The limitations of naive implementations of Dropout with PyTorch\n- Parallel pseudo-random number generation in Triton\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Baseline\nThe *dropout* operator was first introduced in [SRIVASTAVA2014]_ as a way to improve the performance\nof deep neural networks in low-data regime (i.e. regularization).\n\nIt takes a vector as input and produces a vector of the same shape as output. Each scalar in the\noutput has a probability $p$ of being changed to zero and otherwise it is copied from the input.\nThis forces the network to perform well even when only $1 - p$ scalars from the input are available.\n\nAt evaluation time we want to use the full power of the network so we set $p=0$. Naively this would\nincrease the norm of the output (which can be a bad thing, e.g. it can lead to artificial decrease\nin the output softmax temperature). To prevent this we multiply the output by $\\frac{1}{1 - p}$, which\nkeeps the norm consistent regardless of the dropout probability.\n\nLet's first take a look at the baseline implementation.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import tabulate\nimport torch\n\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef _dropout(\n x_ptr, # pointer to the input\n x_keep_ptr, # pointer to a mask of 0s and 1s\n output_ptr, # pointer to the output\n n_elements, # number of elements in the `x` tensor\n p, # probability that an element of `x` is changed to zero\n BLOCK_SIZE: tl.constexpr,\n):\n pid = tl.program_id(axis=0)\n block_start = pid * BLOCK_SIZE\n offsets = block_start + tl.arange(0, BLOCK_SIZE)\n mask = offsets < n_elements\n # Load data\n x = tl.load(x_ptr + offsets, mask=mask)\n x_keep = tl.load(x_keep_ptr + offsets, mask=mask)\n # The line below is the crucial part, described in the paragraph above!\n output = tl.where(x_keep, x / (1 - p), 0.0)\n # Write-back output\n tl.store(output_ptr + offsets, output, mask=mask)\n\n\ndef dropout(x, x_keep, p):\n output = torch.empty_like(x)\n assert x.is_contiguous()\n n_elements = x.numel()\n grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),)\n _dropout[grid](x, x_keep, output, n_elements, p, BLOCK_SIZE=1024)\n return output\n\n\n# Input tensor\nx = torch.randn(size=(10,)).cuda()\n# Dropout mask\np = 0.5\nx_keep = (torch.rand(size=(10,)) > p).to(torch.int32).cuda()\n#\noutput = dropout(x, x_keep=x_keep, p=p)\nprint(tabulate.tabulate([\n [\"input\"] + x.tolist(),\n [\"keep mask\"] + x_keep.tolist(),\n [\"output\"] + output.tolist()\n]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Seeded dropout\nAbove implementation of dropout works fine, but it can be a bit awkward to deal with. Firstly\nwe need to store the dropout mask for backpropagation. Secondly, dropout state management can get\nvery tricky when using recompute/checkpointing (e.g. see all the notes about `preserve_rng_state` in\nhttps://pytorch.org/docs/1.9.0/checkpoint.html). In this tutorial we'll describe an alternative implementation\nthat (1) has a smaller memory footprint; (2) requires less data movement; and (3) simplifies the management\nof persisting randomness across multiple invocations of the kernel.\n\nPseudorandom number generation in Triton is simple! In this tutorial we will use the\n:code:`triton.language.rand` function which generates a block of uniformly distributed :code:`float32`\nvalues in [0, 1), given a seed and a block of :code:`int32` offsets. But if you need it, Triton also provides\nother `random number generation strategies `.\n\n

    Note

    Triton's implementation of PRNG is based on the Philox algorithm (described on [SALMON2011]_).

    \n\nLet's put it all together.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@triton.jit\ndef _seeded_dropout(\n x_ptr,\n output_ptr,\n n_elements,\n p,\n seed,\n BLOCK_SIZE: tl.constexpr,\n):\n # compute memory offsets of elements handled by this instance\n pid = tl.program_id(axis=0)\n block_start = pid * BLOCK_SIZE\n offsets = block_start + tl.arange(0, BLOCK_SIZE)\n # load data from x\n mask = offsets < n_elements\n x = tl.load(x_ptr + offsets, mask=mask)\n # randomly prune it\n random = tl.rand(seed, offsets)\n x_keep = random > p\n # write-back\n output = tl.where(x_keep, x / (1 - p), 0.0)\n tl.store(output_ptr + offsets, output, mask=mask)\n\n\ndef seeded_dropout(x, p, seed):\n output = torch.empty_like(x)\n assert x.is_contiguous()\n n_elements = x.numel()\n grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),)\n _seeded_dropout[grid](x, output, n_elements, p, seed, BLOCK_SIZE=1024)\n return output\n\n\nx = torch.randn(size=(10,)).cuda()\n# Compare this to the baseline - dropout mask is never instantiated!\noutput = seeded_dropout(x, p=0.5, seed=123)\noutput2 = seeded_dropout(x, p=0.5, seed=123)\noutput3 = seeded_dropout(x, p=0.5, seed=512)\n\nprint(tabulate.tabulate([\n [\"input\"] + x.tolist(),\n [\"output (seed = 123)\"] + output.tolist(),\n [\"output (seed = 123)\"] + output2.tolist(),\n [\"output (seed = 512)\"] + output3.tolist()\n]))" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Et Voil\u00e0! We have a triton kernel that applies the same dropout mask provided the seed is the same!\nIf you'd like explore further applications of pseudorandomness in GPU programming, we encourage you\nto explore the `triton/language/random` folder!\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Exercises\n1. Extend the kernel to operate over a matrix and use a vector of seeds - one per row.\n2. Add support for striding.\n3. (challenge) Implement a kernel for sparse Johnson-Lindenstrauss transform which generates the projection matrix one the fly each time using a seed.\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## References\n\n.. [SALMON2011] John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw, \"Parallel Random Numbers: As Easy as 1, 2, 3\", 2011\n.. [SRIVASTAVA2014] Nitish Srivastava and Geoffrey Hinton and Alex Krizhevsky and Ilya Sutskever and Ruslan Salakhutdinov, \"Dropout: A Simple Way to Prevent Neural Networks from Overfitting\", JMLR 2014\n\n" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/master/_downloads/c9aed78977a4c05741d675a38dde3d7d/04-low-memory-dropout.py b/master/_downloads/c9aed78977a4c05741d675a38dde3d7d/04-low-memory-dropout.py new file mode 100644 index 000000000..cf172537a --- /dev/null +++ b/master/_downloads/c9aed78977a4c05741d675a38dde3d7d/04-low-memory-dropout.py @@ -0,0 +1,166 @@ +""" +Low-Memory Dropout +================= + +In this tutorial, you will write a memory-efficient implementation of dropout whose state +will be composed of a single int32 seed. This differs from more traditional implementations of dropout, +whose state is generally composed of a bit mask tensor of the same shape as the input. You will learn about: + +- The limitations of naive implementations of Dropout with PyTorch +- Parallel pseudo-random number generation in Triton +""" + +# %% +# Baseline +# ------------- +# The *dropout* operator was first introduced in [SRIVASTAVA2014]_ as a way to improve the performance +# of deep neural networks in low-data regime (i.e. regularization). +# +# It takes a vector as input and produces a vector of the same shape as output. Each scalar in the +# output has a probability :math:`p` of being changed to zero and otherwise it is copied from the input. +# This forces the network to perform well even when only :math:`1 - p` scalars from the input are available. +# +# At evaluation time we want to use the full power of the network so we set :math:`p=0`. Naively this would +# increase the norm of the output (which can be a bad thing, e.g. it can lead to artificial decrease +# in the output softmax temperature). To prevent this we multiply the output by :math:`\frac{1}{1 - p}`, which +# keeps the norm consistent regardless of the dropout probability. +# +# Let's first take a look at the baseline implementation. + + +import tabulate +import torch + +import triton +import triton.language as tl + + +@triton.jit +def _dropout( + x_ptr, # pointer to the input + x_keep_ptr, # pointer to a mask of 0s and 1s + output_ptr, # pointer to the output + n_elements, # number of elements in the `x` tensor + p, # probability that an element of `x` is changed to zero + BLOCK_SIZE: tl.constexpr, +): + pid = tl.program_id(axis=0) + block_start = pid * BLOCK_SIZE + offsets = block_start + tl.arange(0, BLOCK_SIZE) + mask = offsets < n_elements + # Load data + x = tl.load(x_ptr + offsets, mask=mask) + x_keep = tl.load(x_keep_ptr + offsets, mask=mask) + # The line below is the crucial part, described in the paragraph above! + output = tl.where(x_keep, x / (1 - p), 0.0) + # Write-back output + tl.store(output_ptr + offsets, output, mask=mask) + + +def dropout(x, x_keep, p): + output = torch.empty_like(x) + assert x.is_contiguous() + n_elements = x.numel() + grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),) + _dropout[grid](x, x_keep, output, n_elements, p, BLOCK_SIZE=1024) + return output + + +# Input tensor +x = torch.randn(size=(10,)).cuda() +# Dropout mask +p = 0.5 +x_keep = (torch.rand(size=(10,)) > p).to(torch.int32).cuda() +# +output = dropout(x, x_keep=x_keep, p=p) +print(tabulate.tabulate([ + ["input"] + x.tolist(), + ["keep mask"] + x_keep.tolist(), + ["output"] + output.tolist() +])) + +# %% +# Seeded dropout +# ------------- +# Above implementation of dropout works fine, but it can be a bit awkward to deal with. Firstly +# we need to store the dropout mask for backpropagation. Secondly, dropout state management can get +# very tricky when using recompute/checkpointing (e.g. see all the notes about `preserve_rng_state` in +# https://pytorch.org/docs/1.9.0/checkpoint.html). In this tutorial we'll describe an alternative implementation +# that (1) has a smaller memory footprint; (2) requires less data movement; and (3) simplifies the management +# of persisting randomness across multiple invocations of the kernel. +# +# Pseudorandom number generation in Triton is simple! In this tutorial we will use the +# :code:`triton.language.rand` function which generates a block of uniformly distributed :code:`float32` +# values in [0, 1), given a seed and a block of :code:`int32` offsets. But if you need it, Triton also provides +# other :ref:`random number generation strategies `. +# +# .. note:: +# Triton's implementation of PRNG is based on the Philox algorithm (described on [SALMON2011]_). +# +# Let's put it all together. + + +@triton.jit +def _seeded_dropout( + x_ptr, + output_ptr, + n_elements, + p, + seed, + BLOCK_SIZE: tl.constexpr, +): + # compute memory offsets of elements handled by this instance + pid = tl.program_id(axis=0) + block_start = pid * BLOCK_SIZE + offsets = block_start + tl.arange(0, BLOCK_SIZE) + # load data from x + mask = offsets < n_elements + x = tl.load(x_ptr + offsets, mask=mask) + # randomly prune it + random = tl.rand(seed, offsets) + x_keep = random > p + # write-back + output = tl.where(x_keep, x / (1 - p), 0.0) + tl.store(output_ptr + offsets, output, mask=mask) + + +def seeded_dropout(x, p, seed): + output = torch.empty_like(x) + assert x.is_contiguous() + n_elements = x.numel() + grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),) + _seeded_dropout[grid](x, output, n_elements, p, seed, BLOCK_SIZE=1024) + return output + + +x = torch.randn(size=(10,)).cuda() +# Compare this to the baseline - dropout mask is never instantiated! +output = seeded_dropout(x, p=0.5, seed=123) +output2 = seeded_dropout(x, p=0.5, seed=123) +output3 = seeded_dropout(x, p=0.5, seed=512) + +print(tabulate.tabulate([ + ["input"] + x.tolist(), + ["output (seed = 123)"] + output.tolist(), + ["output (seed = 123)"] + output2.tolist(), + ["output (seed = 512)"] + output3.tolist() +])) + +# %% +# Et Voilà! We have a triton kernel that applies the same dropout mask provided the seed is the same! +# If you'd like explore further applications of pseudorandomness in GPU programming, we encourage you +# to explore the `triton/language/random` folder! + +# %% +# Exercises +# ------------- +# 1. Extend the kernel to operate over a matrix and use a vector of seeds - one per row. +# 2. Add support for striding. +# 3. (challenge) Implement a kernel for sparse Johnson-Lindenstrauss transform which generates the projection matrix one the fly each time using a seed. + +# %% +# References +# -------------- +# +# .. [SALMON2011] John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw, "Parallel Random Numbers: As Easy as 1, 2, 3", 2011 +# .. [SRIVASTAVA2014] Nitish Srivastava and Geoffrey Hinton and Alex Krizhevsky and Ilya Sutskever and Ruslan Salakhutdinov, "Dropout: A Simple Way to Prevent Neural Networks from Overfitting", JMLR 2014 diff --git a/master/_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py b/master/_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py new file mode 100644 index 000000000..f773a3787 --- /dev/null +++ b/master/_downloads/d5fee5b55a64e47f1b5724ec39adf171/03-matrix-multiplication.py @@ -0,0 +1,355 @@ +""" +Matrix Multiplication +====================== +In this tutorial, you will write a 25-lines high-performance FP16 matrix multiplication +kernel that achieves performance on par with cuBLAS. +You will specifically learn about: + +- Block-level matrix multiplications +- Multi-dimensional pointer arithmetic +- Program re-ordering for improved L2 cache hit rate +- Automatic performance tuning +""" + +# %% +# Motivations +# ------------- +# Matrix multiplications are a key building block of most modern high-performance computing systems. +# They are notoriously hard to optimize, hence their implementation is generally done by +# hardware vendors themselves as part of so-called "kernel libraries" (e.g., cuBLAS). +# Unfortunately, these libraries are often proprietary and cannot be easily customized +# to accomodate the needs of modern deep learning workloads (e.g., fused activation functions). +# In this tutorial, you will learn how to implement efficient matrix multiplications by +# yourself with Triton, in a way that is easy to customize and extend. +# +# Roughly speaking, the kernel that we will write will implement the following blocked +# algorithm to multiply a (M, K) by a (K, N) matrix: +# +# .. code-block:: python +# +# # do in parallel +# for m in range(0, M, BLOCK_SIZE_M): +# # do in parallel +# for n in range(0, N, BLOCK_SIZE_N): +# acc = zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=float32) +# for k in range(0, K, BLOCK_SIZE_K): +# a = A[m : m+BLOCK_SIZE_M, k : k+BLOCK_SIZE_K] +# b = B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N] +# acc += dot(a, b) +# C[m : m+BLOCK_SIZE_M, n : n+BLOCK_SIZE_N] = acc; +# +# where each iteration of the doubly-nested for-loop is performed by a dedicated Triton program instance. + +# %% +# Compute Kernel +# ---------------- +# +# 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 +# multi-dimensional pointer arithmetics. +# +# Pointer Arithmetics +# ~~~~~~~~~~~~~~~~~~~~ +# +# For a row-major 2D tensor :code:`X`, the memory location of :code:`X[i, j]` is given b +# y :code:`&X[i, j] = X + i*stride_xi + j*stride_xj`. +# Therefore, blocks of pointers for :code:`A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]` and +# :code:`B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]` can be defined in pseudo-code as: +# +# .. code-block:: python +# +# &A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K] = a_ptr + (m : m+BLOCK_SIZE_M)[:, None]*A.stride(0) + (k : k+BLOCK_SIZE_K)[None, :]*A.stride(1); +# &B[k : k+BLOCK_SIZE_K, n:n+BLOCK_SIZE_N] = b_ptr + (k : k+BLOCK_SIZE_K)[:, None]*B.stride(0) + (n : n+BLOCK_SIZE_N)[None, :]*B.stride(1); +# +# Which means that pointers for blocks of A and B can be initialized (i.e., :code:`k=0`) in Triton as: +# +# .. code-block:: python +# +# offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M) +# offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N) +# offs_k = tl.arange(0, BLOCK_SIZE_K) +# a_ptrs = a_ptr + (offs_am[:, None]*stride_am + offs_k [None, :]*stride_ak) +# b_ptrs = b_ptr + (offs_k [:, None]*stride_bk + offs_bn[None, :]*stride_bn) +# +# And then updated in the inner loop as follows: +# +# .. code-block:: python +# +# pa += BLOCK_SIZE_K * stride_ak; +# pb += BLOCK_SIZE_K * stride_bk; +# +# +# L2 Cache Optimizations +# ~~~~~~~~~~~~~~~~~~~~~~~~ +# +# As mentioned above, each program instance computes a :code:`[BLOCK_SIZE_M, BLOCK_SIZE_N]` +# 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 +# +# .. code-block:: Python +# +# pid = triton.program_id(0); +# grid_m = (M + BLOCK_SIZE_M - 1) // BLOCK_SIZE_M; +# grid_n = (N + BLOCK_SIZE_N - 1) // BLOCK_SIZE_N; +# pid_m = pid / grid_n; +# pid_n = pid % grid_n; +# +# is just not going to cut it. +# +# One possible solution is to launch blocks in an order that promotes data reuse. +# This can be done by 'super-grouping' blocks in groups of :code:`GROUP_M` rows before +# switching to the next column: +# +# .. code-block:: python +# +# # program ID +# pid = tl.program_id(axis=0) +# # number of program ids along the M axis +# num_pid_m = tl.cdiv(M, BLOCK_SIZE_M) +# # number of programs ids along the N axis +# num_pid_n = tl.cdiv(N, BLOCK_SIZE_N) +# # number of programs in group +# num_pid_in_group = GROUP_SIZE_M * num_pid_n +# # id of the group this program is in +# group_id = pid // num_pid_in_group +# # row-id of the first program in the group +# first_pid_m = group_id * GROUP_SIZE_M +# # if `num_pid_m` isn't divisible by `GROUP_SIZE_M`, the last group is smaller +# group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M) +# # *within groups*, programs are ordered in a column-major order +# # row-id of the program in the *launch grid* +# pid_m = first_pid_m + (pid % group_size_m) +# # col-id of the program in the *launch grid* +# pid_n = (pid % num_pid_in_group) // group_size_m +# +# 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 +# ordering, we only need to load 54 blocks. +# .. image:: grouped_vs_row_major_ordering.png +# +# In practice, this can improve the performance of our matrix multiplication kernel by +# more than 10\% on some hardware architecture (e.g., 220 to 245 TFLOPS on A100). +# + +# %% +# Final Result +# ------------- +# + +import torch + +import triton +import triton.language as tl + +# % +# :code:`triton.jit`'ed functions can be auto-tuned by using the `triton.autotune` +# decorator, which consumes: +# - A list of :code:`triton.Config` objects that define different configurations of +# meta-parameters (e.g., BLOCK_SIZE_M) and compilation options (e.g., num_warps) to try +# - An autotuning *key* whose change in values will trigger evaluation of all the +# provided configs + + +@triton.autotune( + configs=[ + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8), + triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8), + triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2), + triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2), + ], + key=['M', 'N', 'K'], +) +@triton.jit +def matmul_kernel( + # Pointers to matrices + a_ptr, b_ptr, c_ptr, + # Matrix dimensions + M, N, K, + # The stride variables represent how much to increase the ptr by when moving by 1 + # element in a particular dimension. E.g. stride_am is how much to increase a_ptr + # by to get the element one row down (A has M rows) + stride_am, stride_ak, + stride_bk, stride_bn, + stride_cm, stride_cn, + # Meta-parameters + BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr, + GROUP_SIZE_M: tl.constexpr, + ACTIVATION: tl.constexpr, +): + """Kernel for computing the matmul C = A x B. + A has shape (M, K), B has shape (K, N) and C has shape (M, N) + """ + # ----------------------------------------------------------- + # Map program ids `pid` to the block of C it should compute. + # This is done in a grouped ordering to promote L2 data reuse + # See above `L2 Cache Optimizations` section for details + pid = tl.program_id(axis=0) + num_pid_m = tl.cdiv(M, BLOCK_SIZE_M) + num_pid_n = tl.cdiv(N, BLOCK_SIZE_N) + num_pid_in_group = GROUP_SIZE_M * num_pid_n + group_id = pid // num_pid_in_group + first_pid_m = group_id * GROUP_SIZE_M + group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M) + pid_m = first_pid_m + (pid % group_size_m) + pid_n = (pid % num_pid_in_group) // group_size_m + + # ---------------------------------------------------------- + # Create pointers for the first blocks of A and B. + # We will advance this pointer as we move in the K direction + # and accumulate + # a_ptrs is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers + # b_ptrs is a block of [BLOCK_SIZE_K, BLOCK_SIZE_n] pointers + # see above `Pointer Arithmetics` section for details + offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M) + offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N) + offs_k = tl.arange(0, BLOCK_SIZE_K) + a_ptrs = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak) + b_ptrs = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn) + + # ----------------------------------------------------------- + # Iterate to compute a block of the C matrix + # We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block + # of fp32 values for higher accuracy. + # `accumulator` will be converted back to fp16 after the loop + accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32) + for k in range(0, K, BLOCK_SIZE_K): + # Note that for simplicity, we don't apply a mask here. + # This means that if K is not a multiple of BLOCK_SIZE_K, + # this will access out-of-bounds memory and produce an + # error or (worse!) incorrect results. + a = tl.load(a_ptrs) + b = tl.load(b_ptrs) + # We accumulate along the K dimension + accumulator += tl.dot(a, b) + # Advance the ptrs to the next K block + a_ptrs += BLOCK_SIZE_K * stride_ak + b_ptrs += BLOCK_SIZE_K * stride_bk + # you can fuse arbitrary activation functions here + # while the accumulator is still in FP32! + if ACTIVATION: + accumulator = ACTIVATION(accumulator) + c = accumulator.to(tl.float16) + + # ----------------------------------------------------------- + # Write back the block of the output matrix C + 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) + + +# we can fuse `leaky_relu` by providing it as an `ACTIVATION` meta-parameter in `_matmul` +@triton.jit +def leaky_relu(x): + return tl.where(x >= 0, x, 0.01 * x) + + +# %% +# We can now create a convenience wrapper function that only takes two input tensors +# and (1) checks any shape constraint; (2) allocates the output; (3) launches the above kernel + + +def matmul(a, b, activation=None): + # checks constraints + assert a.shape[1] == b.shape[0], "incompatible dimensions" + assert a.is_contiguous(), "matrix A must be contiguous" + assert b.is_contiguous(), "matrix B must be contiguous" + M, K = a.shape + K, N = b.shape + assert ( + K % 32 == 0 + ), "We don't check memory-out-of-bounds with K so K must be divisible by BLOCK_SIZE_K" + # allocates output + c = torch.empty((M, N), device=a.device, dtype=a.dtype) + # 1D launch kernel where each block gets its own program. + grid = lambda META: ( + triton.cdiv(M, META['BLOCK_SIZE_M']) * triton.cdiv(N, META['BLOCK_SIZE_N']), + ) + matmul_kernel[grid]( + a, b, c, + M, N, K, + a.stride(0), a.stride(1), + b.stride(0), b.stride(1), + c.stride(0), c.stride(1), + ACTIVATION=activation, + ) + return c + + +# %% +# Unit Test +# ----------- +# +# We can test our custom matrix multiplication operation against a native torch implementation (i.e., cuBLAS) + +torch.manual_seed(0) +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={triton_output}") +print(f"torch_output={torch_output}") +if triton.testing.allclose(triton_output, torch_output): + print("✅ Triton and Torch match") +else: + print("❌ Triton and Torch differ") + +# %% +# Benchmark +# -------------- +# +# Square Matrix Performance +# ~~~~~~~~~~~~~~~~~~~~~~~~~~ +# We can now compare the performance of our kernel against that of cuBLAS. Here we focus on square matrices, but feel free to arrange this script as you wish to benchmark any other matrix shape. + + +@triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['M', 'N', 'K'], # argument names to use as an x-axis for the plot + x_vals=[ + 128 * i for i in range(2, 33) + ], # different possible values for `x_name` + line_arg='provider', # argument name whose value corresponds to a different line in the plot + # possible values for `line_arg`` + line_vals=['cublas', 'cublas + relu', 'triton', 'triton + relu'], + # label name for the lines + line_names=["cuBLAS", "cuBLAS (+ torch.nn.LeakyReLU)", "Triton", "Triton (+ LeakyReLU)"], + # line styles + styles=[('green', '-'), ('green', '--'), ('blue', '-'), ('blue', '--')], + ylabel="TFLOPS", # label name for the y-axis + plot_name="matmul-performance", # name for the plot. Used also as a file name for saving the plot. + args={}, + ) +) +def benchmark(M, N, K, provider): + a = torch.randn((M, K), device='cuda', dtype=torch.float16) + b = torch.randn((K, N), device='cuda', dtype=torch.float16) + if provider == 'cublas': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.matmul(a, b)) + if provider == 'triton': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: matmul(a, b)) + if provider == 'cublas + relu': + torch_relu = torch.nn.ReLU(inplace=True) + ms, min_ms, max_ms = triton.testing.do_bench( + lambda: torch_relu(torch.matmul(a, b)) + ) + if provider == 'triton + relu': + ms, min_ms, max_ms = triton.testing.do_bench( + lambda: matmul(a, b, activation=leaky_relu) + ) + perf = lambda ms: 2 * M * N * K * 1e-12 / (ms * 1e-3) + return perf(ms), perf(max_ms), perf(min_ms) + + +benchmark.run(show_plots=True, print_data=True) diff --git a/master/_downloads/d91442ac2982c4e0cc3ab0f43534afbc/02-fused-softmax.py b/master/_downloads/d91442ac2982c4e0cc3ab0f43534afbc/02-fused-softmax.py new file mode 100644 index 000000000..7af24e18d --- /dev/null +++ b/master/_downloads/d91442ac2982c4e0cc3ab0f43534afbc/02-fused-softmax.py @@ -0,0 +1,191 @@ +""" +Fused Softmax +================= +In this tutorial, you will write a fused softmax operation that is significantly faster +than PyTorch's native op for a particular class of matrices: those whose rows can fit in +the GPU's SRAM. +You will learn about: + +- The benefits of kernel fusion for bandwidth-bound operations. +- Reduction operators in Triton. +""" + +# %% +# Motivations +# ------------ +# Custom GPU kernels for elementwise additions are educationally valuable but won't get you very far in practice. +# Let us consider instead the case of a simple (numerically stabilized) softmax operation: + +import torch + +import triton +import triton.language as tl + + +@torch.jit.script +def naive_softmax(x): + """Compute row-wise softmax of X using native pytorch + + We subtract the maximum element in order to avoid overflows. Softmax is invariant to + this shift. + """ + # read MN elements ; write M elements + x_max = x.max(dim=1)[0] + # read MN + M elements ; write MN elements + z = x - x_max[:, None] + # read MN elements ; write MN elements + numerator = torch.exp(z) + # read MN elements ; write M elements + denominator = numerator.sum(dim=1) + # read MN + M elements ; write MN elements + ret = numerator / denominator[:, None] + # in total: read 5MN + 2M elements ; wrote 3MN + 2M elements + return ret + + +# %% +# When implemented naively in PyTorch, computing :code:`y = naive_softmax(x)` for :math:`x \in R^{M \times N}` +# requires reading :math:`5MN + 2M` elements from DRAM and writing back :math:`3MN + 2M` elements. +# This is obviously wasteful; we'd prefer to have a custom "fused" kernel that only reads +# X once and does all the necessary computations on-chip. +# Doing so would require reading and writing back only :math:`MN` bytes, so we could +# expect a theoretical speed-up of ~4x (i.e., :math:`(8MN + 4M) / 2MN`). +# The `torch.jit.script` flags aims to perform this kind of "kernel fusion" automatically +# but, as we will see later, it is still far from ideal. + +# %% +# Compute Kernel +# ---------------- +# Our softmax kernel works as follows: each program loads a row of the input matrix X, +# normalizes it and writes back the result to the output Y. +# Note that one important limitation of Triton is that each block must have a +# power-of-two number of elements, so we need to internally "pad" each row and guard the +# memory operations properly if we want to handle any possible input shapes: + + +@triton.jit +def softmax_kernel( + output_ptr, input_ptr, input_row_stride, output_row_stride, n_cols, + BLOCK_SIZE: tl.constexpr +): + # The rows of the softmax are independent, so we parallelize across those + row_idx = tl.program_id(0) + # The stride represents how much we need to increase the pointer to advance 1 row + row_start_ptr = input_ptr + row_idx * input_row_stride + # The block size is the next power of two greater than n_cols, so we can fit each + # row in a single block + col_offsets = tl.arange(0, BLOCK_SIZE) + input_ptrs = row_start_ptr + col_offsets + # Load the row into SRAM, using a mask since BLOCK_SIZE may be > than n_cols + row = tl.load(input_ptrs, mask=col_offsets < n_cols, other=-float('inf')) + # Substract maximum for numerical stability + row_minus_max = row - tl.max(row, axis=0) + # Note that exponentials in Triton are fast but approximate (i.e., think __expf in CUDA) + numerator = tl.exp(row_minus_max) + denominator = tl.sum(numerator, axis=0) + softmax_output = numerator / denominator + # Write back output to DRAM + output_row_start_ptr = output_ptr + row_idx * output_row_stride + output_ptrs = output_row_start_ptr + col_offsets + tl.store(output_ptrs, softmax_output, mask=col_offsets < n_cols) + + +# %% +# We can create a helper function that enqueues the kernel and its (meta-)arguments for any given input tensor. + +def softmax(x): + n_rows, n_cols = x.shape + # The block size is the smallest power of two greater than the number of columns in `x` + BLOCK_SIZE = triton.next_power_of_2(n_cols) + # Another trick we can use is to ask the compiler to use more threads per row by + # increasing the number of warps (`num_warps`) over which each row is distributed. + # You will see in the next tutorial how to auto-tune this value in a more natural + # way so you don't have to come up with manual heuristics yourself. + num_warps = 4 + if BLOCK_SIZE >= 2048: + num_warps = 8 + if BLOCK_SIZE >= 4096: + num_warps = 16 + # Allocate output + y = torch.empty_like(x) + # Enqueue kernel. The 1D launch grid is simple: we have one kernel instance per row o + # f the input matrix + softmax_kernel[(n_rows,)]( + y, + x, + x.stride(0), + y.stride(0), + n_cols, + num_warps=num_warps, + BLOCK_SIZE=BLOCK_SIZE, + ) + return y + + +# %% +# Unit Test +# ---------- + +# %% +# We make sure that we test our kernel on a matrix with an irregular number of rows and columns. +# This will allow us to verify that our padding mechanism works. + +torch.manual_seed(0) +x = torch.randn(1823, 781, device='cuda') +y_triton = softmax(x) +y_torch = torch.softmax(x, axis=1) +assert torch.allclose(y_triton, y_torch), (y_triton, y_torch) + +# %% +# As expected, the results are identical. + +# %% +# Benchmark +# ------------- +# Here we will benchmark our operation as a function of the number of columns in the input matrix -- assuming 4096 rows. +# We will then compare its performance against (1) :code:`torch.softmax` and (2) the :code:`naive_softmax` defined above. + + +@triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['N'], # argument names to use as an x-axis for the plot + x_vals=[ + 128 * i for i in range(2, 100) + ], # different possible values for `x_name` + line_arg='provider', # argument name whose value corresponds to a different line in the plot + line_vals=[ + 'triton', + 'torch-native', + 'torch-jit', + ], # possible values for `line_arg`` + line_names=[ + "Triton", + "Torch (native)", + "Torch (jit)", + ], # label name for the lines + styles=[('blue', '-'), ('green', '-'), ('green', '--')], # line styles + ylabel="GB/s", # label name for the y-axis + plot_name="softmax-performance", # name for the plot. Used also as a file name for saving the plot. + args={'M': 4096}, # values for function arguments not in `x_names` and `y_name` + ) +) +def benchmark(M, N, provider): + x = torch.randn(M, N, device='cuda', dtype=torch.float32) + if provider == 'torch-native': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.softmax(x, axis=-1)) + if provider == 'triton': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: softmax(x)) + if provider == 'torch-jit': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: naive_softmax(x)) + gbps = lambda ms: 2 * x.nelement() * x.element_size() * 1e-9 / (ms * 1e-3) + return gbps(ms), gbps(max_ms), gbps(min_ms) + + +benchmark.run(show_plots=True, print_data=True) + +# %% +# In the above plot, we can see that: +# +# - Triton is 4x faster than the Torch JIT. This confirms our suspicions that the Torch JIT does not do any fusion here. +# - Triton is noticeably faster than :code:`torch.softmax` -- in addition to being **easier to read, understand and maintain**. +# Note however that the PyTorch `softmax` operation is more general and will works on tensors of any shape. diff --git a/master/_downloads/f191ee1e78dc52eb5f7cba88f71cef2f/01-vector-add.ipynb b/master/_downloads/f191ee1e78dc52eb5f7cba88f71cef2f/01-vector-add.ipynb new file mode 100644 index 000000000..a88ec6569 --- /dev/null +++ b/master/_downloads/f191ee1e78dc52eb5f7cba88f71cef2f/01-vector-add.ipynb @@ -0,0 +1,140 @@ +{ + "cells": [ + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "%matplotlib inline" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "\n# Vector Addition\nIn this tutorial, you will write a simple vector addition using Triton and learn about:\n\n- The basic programming model of Triton\n- The `triton.jit` decorator, which is used to define Triton kernels.\n- The best practices for validating and benchmarking your custom ops against native reference implementations\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Compute Kernel\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "import torch\n\nimport triton\nimport triton.language as tl\n\n\n@triton.jit\ndef add_kernel(\n x_ptr, # *Pointer* to first input vector\n y_ptr, # *Pointer* to second input vector\n output_ptr, # *Pointer* to output vector\n n_elements, # Size of the vector\n BLOCK_SIZE: tl.constexpr, # Number of elements each program should process\n # NOTE: `constexpr` so it can be used as a shape value\n):\n # There are multiple 'program's processing different data. We identify which program\n # we are here\n pid = tl.program_id(axis=0) # We use a 1D launch grid so axis is 0\n # This program will process inputs that are offset from the initial data.\n # for instance, if you had a vector of length 256 and block_size of 64, the programs\n # would each access the elements [0:64, 64:128, 128:192, 192:256].\n # Note that offsets is a list of pointers\n block_start = pid * BLOCK_SIZE\n offsets = block_start + tl.arange(0, BLOCK_SIZE)\n # Create a mask to guard memory operations against out-of-bounds accesses\n mask = offsets < n_elements\n # Load x and y from DRAM, masking out any extra elements in case the input is not a\n # multiple of the block size\n x = tl.load(x_ptr + offsets, mask=mask)\n y = tl.load(y_ptr + offsets, mask=mask)\n output = x + y\n # Write x + y back to DRAM\n tl.store(output_ptr + offsets, output, mask=mask)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Let's also declare a helper function to (1) allocate the `z` tensor\nand (2) enqueue the above kernel with appropriate grid/block sizes.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "def add(x: torch.Tensor, y: torch.Tensor):\n # We need to preallocate the output\n output = torch.empty_like(x)\n assert x.is_cuda and y.is_cuda and output.is_cuda\n n_elements = output.numel()\n # The SPMD launch grid denotes the number of kernel instances that run in parallel.\n # It is analogous to CUDA launch grids. It can be either Tuple[int], or Callable(metaparameters) -> Tuple[int]\n # In this case, we use a 1D grid where the size is the number of blocks\n grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),)\n # NOTE:\n # - each torch.tensor object is implicitly converted into a pointer to its first element.\n # - `triton.jit`'ed functions can be index with a launch grid to obtain a callable GPU kernel\n # - don't forget to pass meta-parameters as keywords arguments\n add_kernel[grid](x, y, output, n_elements, BLOCK_SIZE=1024)\n # We return a handle to z but, since `torch.cuda.synchronize()` hasn't been called, the kernel is still\n # running asynchronously at this point.\n return output" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now use the above function to compute the element-wise sum of two `torch.tensor` objects and test its correctness:\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "torch.manual_seed(0)\nsize = 98432\nx = torch.rand(size, device='cuda')\ny = torch.rand(size, device='cuda')\noutput_torch = x + y\noutput_triton = add(x, y)\nprint(output_torch)\nprint(output_triton)\nprint(\n f'The maximum difference between torch and triton is '\n f'{torch.max(torch.abs(output_torch - output_triton))}'\n)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "Seems like we're good to go!\n\n" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "## Benchmark\nWe can now benchmark our custom op on vectors of increasing sizes to get a sense of how it does relative to PyTorch.\nTo make things easier, Triton has a set of built-in utilities that allow us to concisely plot the performance of your custom ops\nfor different problem sizes.\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "@triton.testing.perf_report(\n triton.testing.Benchmark(\n x_names=['size'], # argument names to use as an x-axis for the plot\n x_vals=[\n 2 ** i for i in range(12, 28, 1)\n ], # different possible values for `x_name`\n x_log=True, # x axis is logarithmic\n line_arg='provider', # argument name whose value corresponds to a different line in the plot\n line_vals=['triton', 'torch'], # possible values for `line_arg`\n line_names=['Triton', 'Torch'], # label name for the lines\n styles=[('blue', '-'), ('green', '-')], # line styles\n ylabel='GB/s', # label name for the y-axis\n plot_name='vector-add-performance', # name for the plot. Used also as a file name for saving the plot.\n args={}, # values for function arguments not in `x_names` and `y_name`\n )\n)\ndef benchmark(size, provider):\n x = torch.rand(size, device='cuda', dtype=torch.float32)\n y = torch.rand(size, device='cuda', dtype=torch.float32)\n if provider == 'torch':\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: x + y)\n if provider == 'triton':\n ms, min_ms, max_ms = triton.testing.do_bench(lambda: add(x, y))\n gbps = lambda ms: 12 * size / ms * 1e-6\n return gbps(ms), gbps(max_ms), gbps(min_ms)" + ] + }, + { + "cell_type": "markdown", + "metadata": {}, + "source": [ + "We can now run the decorated function above. Pass `print_data=True` to see the performance number, `show_plots=True` to plot them, and/or\n`save_path='/path/to/results/' to save them to disk along with raw CSV data\n\n" + ] + }, + { + "cell_type": "code", + "execution_count": null, + "metadata": { + "collapsed": false + }, + "outputs": [], + "source": [ + "benchmark.run(print_data=True, show_plots=True)" + ] + } + ], + "metadata": { + "kernelspec": { + "display_name": "Python 3", + "language": "python", + "name": "python3" + }, + "language_info": { + "codemirror_mode": { + "name": "ipython", + "version": 3 + }, + "file_extension": ".py", + "mimetype": "text/x-python", + "name": "python", + "nbconvert_exporter": "python", + "pygments_lexer": "ipython3", + "version": "3.8.10" + } + }, + "nbformat": 4, + "nbformat_minor": 0 +} \ No newline at end of file diff --git a/master/_images/grouped_vs_row_major_ordering.png b/master/_images/grouped_vs_row_major_ordering.png new file mode 100644 index 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b/master/_sources/getting-started/tutorials/01-vector-add.rst.txt new file mode 100644 index 000000000..9bf7322f7 --- /dev/null +++ b/master/_sources/getting-started/tutorials/01-vector-add.rst.txt @@ -0,0 +1,286 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "getting-started/tutorials/01-vector-add.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + Click :ref:`here ` + to download the full example code + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_getting-started_tutorials_01-vector-add.py: + + +Vector Addition +================= +In this tutorial, you will write a simple vector addition using Triton and learn about: + +- The basic programming model of Triton +- The `triton.jit` decorator, which is used to define Triton kernels. +- The best practices for validating and benchmarking your custom ops against native reference implementations + +.. GENERATED FROM PYTHON SOURCE LINES 12-14 + +Compute Kernel +-------------------------- + +.. GENERATED FROM PYTHON SOURCE LINES 14-50 + +.. code-block:: default + + + import torch + + import triton + import triton.language as tl + + + @triton.jit + def add_kernel( + x_ptr, # *Pointer* to first input vector + y_ptr, # *Pointer* to second input vector + output_ptr, # *Pointer* to output vector + n_elements, # Size of the vector + BLOCK_SIZE: tl.constexpr, # Number of elements each program should process + # NOTE: `constexpr` so it can be used as a shape value + ): + # There are multiple 'program's processing different data. We identify which program + # we are here + pid = tl.program_id(axis=0) # We use a 1D launch grid so axis is 0 + # This program will process inputs that are offset from the initial data. + # for instance, if you had a vector of length 256 and block_size of 64, the programs + # would each access the elements [0:64, 64:128, 128:192, 192:256]. + # Note that offsets is a list of pointers + block_start = pid * BLOCK_SIZE + offsets = block_start + tl.arange(0, BLOCK_SIZE) + # Create a mask to guard memory operations against out-of-bounds accesses + mask = offsets < n_elements + # Load x and y from DRAM, masking out any extra elements in case the input is not a + # multiple of the block size + x = tl.load(x_ptr + offsets, mask=mask) + y = tl.load(y_ptr + offsets, mask=mask) + output = x + y + # Write x + y back to DRAM + tl.store(output_ptr + offsets, output, mask=mask) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 51-53 + +Let's also declare a helper function to (1) allocate the `z` tensor +and (2) enqueue the above kernel with appropriate grid/block sizes. + +.. GENERATED FROM PYTHON SOURCE LINES 53-74 + +.. code-block:: default + + + + def add(x: torch.Tensor, y: torch.Tensor): + # We need to preallocate the output + output = torch.empty_like(x) + assert x.is_cuda and y.is_cuda and output.is_cuda + n_elements = output.numel() + # The SPMD launch grid denotes the number of kernel instances that run in parallel. + # It is analogous to CUDA launch grids. It can be either Tuple[int], or Callable(metaparameters) -> Tuple[int] + # In this case, we use a 1D grid where the size is the number of blocks + grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),) + # NOTE: + # - each torch.tensor object is implicitly converted into a pointer to its first element. + # - `triton.jit`'ed functions can be index with a launch grid to obtain a callable GPU kernel + # - don't forget to pass meta-parameters as keywords arguments + add_kernel[grid](x, y, output, n_elements, BLOCK_SIZE=1024) + # We return a handle to z but, since `torch.cuda.synchronize()` hasn't been called, the kernel is still + # running asynchronously at this point. + return output + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 75-76 + +We can now use the above function to compute the element-wise sum of two `torch.tensor` objects and test its correctness: + +.. GENERATED FROM PYTHON SOURCE LINES 76-90 + +.. code-block:: default + + + torch.manual_seed(0) + size = 98432 + x = torch.rand(size, device='cuda') + y = torch.rand(size, device='cuda') + output_torch = x + y + output_triton = add(x, y) + print(output_torch) + print(output_triton) + print( + f'The maximum difference between torch and triton is ' + f'{torch.max(torch.abs(output_torch - output_triton))}' + ) + + + + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + tensor([1.3713, 1.3076, 0.4940, ..., 0.6724, 1.2141, 0.9733], device='cuda:0') + tensor([1.3713, 1.3076, 0.4940, ..., 0.6724, 1.2141, 0.9733], device='cuda:0') + The maximum difference between torch and triton is 0.0 + + + + +.. GENERATED FROM PYTHON SOURCE LINES 91-92 + +Seems like we're good to go! + +.. GENERATED FROM PYTHON SOURCE LINES 94-99 + +Benchmark +----------- +We can now benchmark our custom op on vectors of increasing sizes to get a sense of how it does relative to PyTorch. +To make things easier, Triton has a set of built-in utilities that allow us to concisely plot the performance of your custom ops +for different problem sizes. + +.. GENERATED FROM PYTHON SOURCE LINES 99-128 + +.. code-block:: default + + + + @triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['size'], # argument names to use as an x-axis for the plot + x_vals=[ + 2 ** i for i in range(12, 28, 1) + ], # different possible values for `x_name` + x_log=True, # x axis is logarithmic + line_arg='provider', # argument name whose value corresponds to a different line in the plot + line_vals=['triton', 'torch'], # possible values for `line_arg` + line_names=['Triton', 'Torch'], # label name for the lines + styles=[('blue', '-'), ('green', '-')], # line styles + ylabel='GB/s', # label name for the y-axis + plot_name='vector-add-performance', # name for the plot. Used also as a file name for saving the plot. + args={}, # values for function arguments not in `x_names` and `y_name` + ) + ) + def benchmark(size, provider): + x = torch.rand(size, device='cuda', dtype=torch.float32) + y = torch.rand(size, device='cuda', dtype=torch.float32) + if provider == 'torch': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: x + y) + if provider == 'triton': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: add(x, y)) + gbps = lambda ms: 12 * size / ms * 1e-6 + return gbps(ms), gbps(max_ms), gbps(min_ms) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 129-131 + +We can now run the decorated function above. Pass `print_data=True` to see the performance number, `show_plots=True` to plot them, and/or +`save_path='/path/to/results/' to save them to disk along with raw CSV data + +.. GENERATED FROM PYTHON SOURCE LINES 131-132 + +.. code-block:: default + + benchmark.run(print_data=True, show_plots=True) + + + +.. image:: /getting-started/tutorials/images/sphx_glr_01-vector-add_001.png + :alt: 01 vector add + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + vector-add-performance: + size Triton Torch + 0 4096.0 9.600000 9.600000 + 1 8192.0 19.200000 19.200000 + 2 16384.0 38.400001 38.400001 + 3 32768.0 63.999998 63.999998 + 4 65536.0 127.999995 127.999995 + 5 131072.0 219.428568 219.428568 + 6 262144.0 384.000001 384.000001 + 7 524288.0 472.615390 472.615390 + 8 1048576.0 614.400016 614.400016 + 9 2097152.0 722.823517 722.823517 + 10 4194304.0 780.190482 780.190482 + 11 8388608.0 812.429770 812.429770 + 12 16777216.0 833.084721 833.084721 + 13 33554432.0 842.004273 842.004273 + 14 67108864.0 847.448255 848.362445 + 15 134217728.0 849.737435 850.656574 + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** ( 1 minutes 42.537 seconds) + + +.. _sphx_glr_download_getting-started_tutorials_01-vector-add.py: + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-example + + + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: 01-vector-add.py <01-vector-add.py>` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: 01-vector-add.ipynb <01-vector-add.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/master/_sources/getting-started/tutorials/02-fused-softmax.rst.txt b/master/_sources/getting-started/tutorials/02-fused-softmax.rst.txt new file mode 100644 index 000000000..5d9c1a595 --- /dev/null +++ b/master/_sources/getting-started/tutorials/02-fused-softmax.rst.txt @@ -0,0 +1,337 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "getting-started/tutorials/02-fused-softmax.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + Click :ref:`here ` + to download the full example code + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_getting-started_tutorials_02-fused-softmax.py: + + +Fused Softmax +================= +In this tutorial, you will write a fused softmax operation that is significantly faster +than PyTorch's native op for a particular class of matrices: those whose rows can fit in +the GPU's SRAM. +You will learn about: + +- The benefits of kernel fusion for bandwidth-bound operations. +- Reduction operators in Triton. + +.. GENERATED FROM PYTHON SOURCE LINES 14-18 + +Motivations +------------ +Custom GPU kernels for elementwise additions are educationally valuable but won't get you very far in practice. +Let us consider instead the case of a simple (numerically stabilized) softmax operation: + +.. GENERATED FROM PYTHON SOURCE LINES 18-46 + +.. code-block:: default + + + import torch + + import triton + import triton.language as tl + + + @torch.jit.script + def naive_softmax(x): + """Compute row-wise softmax of X using native pytorch + + We subtract the maximum element in order to avoid overflows. Softmax is invariant to + this shift. + """ + # read MN elements ; write M elements + x_max = x.max(dim=1)[0] + # read MN + M elements ; write MN elements + z = x - x_max[:, None] + # read MN elements ; write MN elements + numerator = torch.exp(z) + # read MN elements ; write M elements + denominator = numerator.sum(dim=1) + # read MN + M elements ; write MN elements + ret = numerator / denominator[:, None] + # in total: read 5MN + 2M elements ; wrote 3MN + 2M elements + return ret + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 47-55 + +When implemented naively in PyTorch, computing :code:`y = naive_softmax(x)` for :math:`x \in R^{M \times N}` +requires reading :math:`5MN + 2M` elements from DRAM and writing back :math:`3MN + 2M` elements. +This is obviously wasteful; we'd prefer to have a custom "fused" kernel that only reads +X once and does all the necessary computations on-chip. +Doing so would require reading and writing back only :math:`MN` bytes, so we could +expect a theoretical speed-up of ~4x (i.e., :math:`(8MN + 4M) / 2MN`). +The `torch.jit.script` flags aims to perform this kind of "kernel fusion" automatically +but, as we will see later, it is still far from ideal. + +.. GENERATED FROM PYTHON SOURCE LINES 57-64 + +Compute Kernel +---------------- +Our softmax kernel works as follows: each program loads a row of the input matrix X, +normalizes it and writes back the result to the output Y. +Note that one important limitation of Triton is that each block must have a +power-of-two number of elements, so we need to internally "pad" each row and guard the +memory operations properly if we want to handle any possible input shapes: + +.. GENERATED FROM PYTHON SOURCE LINES 64-93 + +.. code-block:: default + + + + @triton.jit + def softmax_kernel( + output_ptr, input_ptr, input_row_stride, output_row_stride, n_cols, + BLOCK_SIZE: tl.constexpr + ): + # The rows of the softmax are independent, so we parallelize across those + row_idx = tl.program_id(0) + # The stride represents how much we need to increase the pointer to advance 1 row + row_start_ptr = input_ptr + row_idx * input_row_stride + # The block size is the next power of two greater than n_cols, so we can fit each + # row in a single block + col_offsets = tl.arange(0, BLOCK_SIZE) + input_ptrs = row_start_ptr + col_offsets + # Load the row into SRAM, using a mask since BLOCK_SIZE may be > than n_cols + row = tl.load(input_ptrs, mask=col_offsets < n_cols, other=-float('inf')) + # Substract maximum for numerical stability + row_minus_max = row - tl.max(row, axis=0) + # Note that exponentials in Triton are fast but approximate (i.e., think __expf in CUDA) + numerator = tl.exp(row_minus_max) + denominator = tl.sum(numerator, axis=0) + softmax_output = numerator / denominator + # Write back output to DRAM + output_row_start_ptr = output_ptr + row_idx * output_row_stride + output_ptrs = output_row_start_ptr + col_offsets + tl.store(output_ptrs, softmax_output, mask=col_offsets < n_cols) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 94-95 + +We can create a helper function that enqueues the kernel and its (meta-)arguments for any given input tensor. + +.. GENERATED FROM PYTHON SOURCE LINES 95-125 + +.. code-block:: default + + + def softmax(x): + n_rows, n_cols = x.shape + # The block size is the smallest power of two greater than the number of columns in `x` + BLOCK_SIZE = triton.next_power_of_2(n_cols) + # Another trick we can use is to ask the compiler to use more threads per row by + # increasing the number of warps (`num_warps`) over which each row is distributed. + # You will see in the next tutorial how to auto-tune this value in a more natural + # way so you don't have to come up with manual heuristics yourself. + num_warps = 4 + if BLOCK_SIZE >= 2048: + num_warps = 8 + if BLOCK_SIZE >= 4096: + num_warps = 16 + # Allocate output + y = torch.empty_like(x) + # Enqueue kernel. The 1D launch grid is simple: we have one kernel instance per row o + # f the input matrix + softmax_kernel[(n_rows,)]( + y, + x, + x.stride(0), + y.stride(0), + n_cols, + num_warps=num_warps, + BLOCK_SIZE=BLOCK_SIZE, + ) + return y + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 126-128 + +Unit Test +---------- + +.. GENERATED FROM PYTHON SOURCE LINES 130-132 + +We make sure that we test our kernel on a matrix with an irregular number of rows and columns. +This will allow us to verify that our padding mechanism works. + +.. GENERATED FROM PYTHON SOURCE LINES 132-139 + +.. code-block:: default + + + torch.manual_seed(0) + x = torch.randn(1823, 781, device='cuda') + y_triton = softmax(x) + y_torch = torch.softmax(x, axis=1) + assert torch.allclose(y_triton, y_torch), (y_triton, y_torch) + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 140-141 + +As expected, the results are identical. + +.. GENERATED FROM PYTHON SOURCE LINES 143-147 + +Benchmark +------------- +Here we will benchmark our operation as a function of the number of columns in the input matrix -- assuming 4096 rows. +We will then compare its performance against (1) :code:`torch.softmax` and (2) the :code:`naive_softmax` defined above. + +.. GENERATED FROM PYTHON SOURCE LINES 147-186 + +.. code-block:: default + + + + @triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['N'], # argument names to use as an x-axis for the plot + x_vals=[ + 128 * i for i in range(2, 100) + ], # different possible values for `x_name` + line_arg='provider', # argument name whose value corresponds to a different line in the plot + line_vals=[ + 'triton', + 'torch-native', + 'torch-jit', + ], # possible values for `line_arg`` + line_names=[ + "Triton", + "Torch (native)", + "Torch (jit)", + ], # label name for the lines + styles=[('blue', '-'), ('green', '-'), ('green', '--')], # line styles + ylabel="GB/s", # label name for the y-axis + plot_name="softmax-performance", # name for the plot. Used also as a file name for saving the plot. + args={'M': 4096}, # values for function arguments not in `x_names` and `y_name` + ) + ) + def benchmark(M, N, provider): + x = torch.randn(M, N, device='cuda', dtype=torch.float32) + if provider == 'torch-native': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.softmax(x, axis=-1)) + if provider == 'triton': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: softmax(x)) + if provider == 'torch-jit': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: naive_softmax(x)) + gbps = lambda ms: 2 * x.nelement() * x.element_size() * 1e-9 / (ms * 1e-3) + return gbps(ms), gbps(max_ms), gbps(min_ms) + + + benchmark.run(show_plots=True, print_data=True) + + + + +.. image:: /getting-started/tutorials/images/sphx_glr_02-fused-softmax_001.png + :alt: 02 fused softmax + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + softmax-performance: + N Triton Torch (native) Torch (jit) + 0 256.0 512.000001 546.133347 190.511628 + 1 384.0 614.400016 585.142862 153.600004 + 2 512.0 655.360017 606.814814 154.566038 + 3 640.0 706.206879 640.000002 160.000000 + 4 768.0 722.823517 664.216187 162.754967 + .. ... ... ... ... + 93 12160.0 814.058574 406.179533 198.733401 + 94 12288.0 814.111783 415.661740 198.995960 + 95 12416.0 814.163950 412.149375 198.556711 + 96 12544.0 814.214963 412.971190 198.815254 + 97 12672.0 814.265046 412.097543 198.873965 + + [98 rows x 4 columns] + + + + +.. GENERATED FROM PYTHON SOURCE LINES 187-192 + +In the above plot, we can see that: + + - Triton is 4x faster than the Torch JIT. This confirms our suspicions that the Torch JIT does not do any fusion here. + - Triton is noticeably faster than :code:`torch.softmax` -- in addition to being **easier to read, understand and maintain**. + Note however that the PyTorch `softmax` operation is more general and will works on tensors of any shape. + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** ( 3 minutes 22.066 seconds) + + +.. _sphx_glr_download_getting-started_tutorials_02-fused-softmax.py: + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-example + + + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: 02-fused-softmax.py <02-fused-softmax.py>` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: 02-fused-softmax.ipynb <02-fused-softmax.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/master/_sources/getting-started/tutorials/03-matrix-multiplication.rst.txt b/master/_sources/getting-started/tutorials/03-matrix-multiplication.rst.txt new file mode 100644 index 000000000..0673f8bf1 --- /dev/null +++ b/master/_sources/getting-started/tutorials/03-matrix-multiplication.rst.txt @@ -0,0 +1,529 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "getting-started/tutorials/03-matrix-multiplication.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + Click :ref:`here ` + to download the full example code + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_getting-started_tutorials_03-matrix-multiplication.py: + + +Matrix Multiplication +====================== +In this tutorial, you will write a 25-lines high-performance FP16 matrix multiplication +kernel that achieves performance on par with cuBLAS. +You will specifically learn about: + +- Block-level matrix multiplications +- Multi-dimensional pointer arithmetic +- Program re-ordering for improved L2 cache hit rate +- Automatic performance tuning + +.. GENERATED FROM PYTHON SOURCE LINES 15-42 + +Motivations +------------- +Matrix multiplications are a key building block of most modern high-performance computing systems. +They are notoriously hard to optimize, hence their implementation is generally done by +hardware vendors themselves as part of so-called "kernel libraries" (e.g., cuBLAS). +Unfortunately, these libraries are often proprietary and cannot be easily customized +to accomodate the needs of modern deep learning workloads (e.g., fused activation functions). +In this tutorial, you will learn how to implement efficient matrix multiplications by +yourself with Triton, in a way that is easy to customize and extend. + +Roughly speaking, the kernel that we will write will implement the following blocked +algorithm to multiply a (M, K) by a (K, N) matrix: + + .. code-block:: python + + # do in parallel + for m in range(0, M, BLOCK_SIZE_M): + # do in parallel + for n in range(0, N, BLOCK_SIZE_N): + acc = zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=float32) + for k in range(0, K, BLOCK_SIZE_K): + a = A[m : m+BLOCK_SIZE_M, k : k+BLOCK_SIZE_K] + b = B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N] + acc += dot(a, b) + C[m : m+BLOCK_SIZE_M, n : n+BLOCK_SIZE_N] = acc; + +where each iteration of the doubly-nested for-loop is performed by a dedicated Triton program instance. + +.. GENERATED FROM PYTHON SOURCE LINES 44-137 + +Compute Kernel +---------------- + +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 +multi-dimensional pointer arithmetics. + +Pointer Arithmetics +~~~~~~~~~~~~~~~~~~~~ + +For a row-major 2D tensor :code:`X`, the memory location of :code:`X[i, j]` is given b +y :code:`&X[i, j] = X + i*stride_xi + j*stride_xj`. +Therefore, blocks of pointers for :code:`A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]` and +:code:`B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]` can be defined in pseudo-code as: + + .. code-block:: python + + &A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K] = a_ptr + (m : m+BLOCK_SIZE_M)[:, None]*A.stride(0) + (k : k+BLOCK_SIZE_K)[None, :]*A.stride(1); + &B[k : k+BLOCK_SIZE_K, n:n+BLOCK_SIZE_N] = b_ptr + (k : k+BLOCK_SIZE_K)[:, None]*B.stride(0) + (n : n+BLOCK_SIZE_N)[None, :]*B.stride(1); + +Which means that pointers for blocks of A and B can be initialized (i.e., :code:`k=0`) in Triton as: + + .. code-block:: python + + offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M) + offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N) + offs_k = tl.arange(0, BLOCK_SIZE_K) + a_ptrs = a_ptr + (offs_am[:, None]*stride_am + offs_k [None, :]*stride_ak) + b_ptrs = b_ptr + (offs_k [:, None]*stride_bk + offs_bn[None, :]*stride_bn) + +And then updated in the inner loop as follows: + + .. code-block:: python + + pa += BLOCK_SIZE_K * stride_ak; + pb += BLOCK_SIZE_K * stride_bk; + + +L2 Cache Optimizations +~~~~~~~~~~~~~~~~~~~~~~~~ + +As mentioned above, each program instance computes a :code:`[BLOCK_SIZE_M, BLOCK_SIZE_N]` +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 + + .. code-block:: Python + + pid = triton.program_id(0); + grid_m = (M + BLOCK_SIZE_M - 1) // BLOCK_SIZE_M; + grid_n = (N + BLOCK_SIZE_N - 1) // BLOCK_SIZE_N; + pid_m = pid / grid_n; + pid_n = pid % grid_n; + +is just not going to cut it. + +One possible solution is to launch blocks in an order that promotes data reuse. +This can be done by 'super-grouping' blocks in groups of :code:`GROUP_M` rows before +switching to the next column: + + .. code-block:: python + + # program ID + pid = tl.program_id(axis=0) + # number of program ids along the M axis + num_pid_m = tl.cdiv(M, BLOCK_SIZE_M) + # number of programs ids along the N axis + num_pid_n = tl.cdiv(N, BLOCK_SIZE_N) + # number of programs in group + num_pid_in_group = GROUP_SIZE_M * num_pid_n + # id of the group this program is in + group_id = pid // num_pid_in_group + # row-id of the first program in the group + first_pid_m = group_id * GROUP_SIZE_M + # if `num_pid_m` isn't divisible by `GROUP_SIZE_M`, the last group is smaller + group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M) + # *within groups*, programs are ordered in a column-major order + # row-id of the program in the *launch grid* + pid_m = first_pid_m + (pid % group_size_m) + # col-id of the program in the *launch grid* + pid_n = (pid % num_pid_in_group) // group_size_m + +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 +ordering, we only need to load 54 blocks. + .. image:: grouped_vs_row_major_ordering.png + +In practice, this can improve the performance of our matrix multiplication kernel by +more than 10\% on some hardware architecture (e.g., 220 to 245 TFLOPS on A100). + + +.. GENERATED FROM PYTHON SOURCE LINES 139-142 + +Final Result +------------- + + +.. GENERATED FROM PYTHON SOURCE LINES 142-258 + +.. code-block:: default + + + import torch + + import triton + import triton.language as tl + + # % + # :code:`triton.jit`'ed functions can be auto-tuned by using the `triton.autotune` + # decorator, which consumes: + # - A list of :code:`triton.Config` objects that define different configurations of + # meta-parameters (e.g., BLOCK_SIZE_M) and compilation options (e.g., num_warps) to try + # - An autotuning *key* whose change in values will trigger evaluation of all the + # provided configs + + + @triton.autotune( + configs=[ + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8), + triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=3, num_warps=8), + triton.Config({'BLOCK_SIZE_M': 256, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 256, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 128, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 128, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=4, num_warps=4), + triton.Config({'BLOCK_SIZE_M': 64, 'BLOCK_SIZE_N': 32, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2), + triton.Config({'BLOCK_SIZE_M': 32, 'BLOCK_SIZE_N': 64, 'BLOCK_SIZE_K': 32, 'GROUP_SIZE_M': 8}, num_stages=5, num_warps=2), + ], + key=['M', 'N', 'K'], + ) + @triton.jit + def matmul_kernel( + # Pointers to matrices + a_ptr, b_ptr, c_ptr, + # Matrix dimensions + M, N, K, + # The stride variables represent how much to increase the ptr by when moving by 1 + # element in a particular dimension. E.g. stride_am is how much to increase a_ptr + # by to get the element one row down (A has M rows) + stride_am, stride_ak, + stride_bk, stride_bn, + stride_cm, stride_cn, + # Meta-parameters + BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr, BLOCK_SIZE_K: tl.constexpr, + GROUP_SIZE_M: tl.constexpr, + ACTIVATION: tl.constexpr, + ): + """Kernel for computing the matmul C = A x B. + A has shape (M, K), B has shape (K, N) and C has shape (M, N) + """ + # ----------------------------------------------------------- + # Map program ids `pid` to the block of C it should compute. + # This is done in a grouped ordering to promote L2 data reuse + # See above `L2 Cache Optimizations` section for details + pid = tl.program_id(axis=0) + num_pid_m = tl.cdiv(M, BLOCK_SIZE_M) + num_pid_n = tl.cdiv(N, BLOCK_SIZE_N) + num_pid_in_group = GROUP_SIZE_M * num_pid_n + group_id = pid // num_pid_in_group + first_pid_m = group_id * GROUP_SIZE_M + group_size_m = min(num_pid_m - first_pid_m, GROUP_SIZE_M) + pid_m = first_pid_m + (pid % group_size_m) + pid_n = (pid % num_pid_in_group) // group_size_m + + # ---------------------------------------------------------- + # Create pointers for the first blocks of A and B. + # We will advance this pointer as we move in the K direction + # and accumulate + # a_ptrs is a block of [BLOCK_SIZE_M, BLOCK_SIZE_K] pointers + # b_ptrs is a block of [BLOCK_SIZE_K, BLOCK_SIZE_n] pointers + # see above `Pointer Arithmetics` section for details + offs_am = pid_m * BLOCK_SIZE_M + tl.arange(0, BLOCK_SIZE_M) + offs_bn = pid_n * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N) + offs_k = tl.arange(0, BLOCK_SIZE_K) + a_ptrs = a_ptr + (offs_am[:, None] * stride_am + offs_k[None, :] * stride_ak) + b_ptrs = b_ptr + (offs_k[:, None] * stride_bk + offs_bn[None, :] * stride_bn) + + # ----------------------------------------------------------- + # Iterate to compute a block of the C matrix + # We accumulate into a `[BLOCK_SIZE_M, BLOCK_SIZE_N]` block + # of fp32 values for higher accuracy. + # `accumulator` will be converted back to fp16 after the loop + accumulator = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32) + for k in range(0, K, BLOCK_SIZE_K): + # Note that for simplicity, we don't apply a mask here. + # This means that if K is not a multiple of BLOCK_SIZE_K, + # this will access out-of-bounds memory and produce an + # error or (worse!) incorrect results. + a = tl.load(a_ptrs) + b = tl.load(b_ptrs) + # We accumulate along the K dimension + accumulator += tl.dot(a, b) + # Advance the ptrs to the next K block + a_ptrs += BLOCK_SIZE_K * stride_ak + b_ptrs += BLOCK_SIZE_K * stride_bk + # you can fuse arbitrary activation functions here + # while the accumulator is still in FP32! + if ACTIVATION: + accumulator = ACTIVATION(accumulator) + c = accumulator.to(tl.float16) + + # ----------------------------------------------------------- + # Write back the block of the output matrix C + 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) + + + # we can fuse `leaky_relu` by providing it as an `ACTIVATION` meta-parameter in `_matmul` + @triton.jit + def leaky_relu(x): + return tl.where(x >= 0, x, 0.01 * x) + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 259-261 + +We can now create a convenience wrapper function that only takes two input tensors +and (1) checks any shape constraint; (2) allocates the output; (3) launches the above kernel + +.. GENERATED FROM PYTHON SOURCE LINES 261-290 + +.. code-block:: default + + + + def matmul(a, b, activation=None): + # checks constraints + assert a.shape[1] == b.shape[0], "incompatible dimensions" + assert a.is_contiguous(), "matrix A must be contiguous" + assert b.is_contiguous(), "matrix B must be contiguous" + M, K = a.shape + K, N = b.shape + assert ( + K % 32 == 0 + ), "We don't check memory-out-of-bounds with K so K must be divisible by BLOCK_SIZE_K" + # allocates output + c = torch.empty((M, N), device=a.device, dtype=a.dtype) + # 1D launch kernel where each block gets its own program. + grid = lambda META: ( + triton.cdiv(M, META['BLOCK_SIZE_M']) * triton.cdiv(N, META['BLOCK_SIZE_N']), + ) + matmul_kernel[grid]( + a, b, c, + M, N, K, + a.stride(0), a.stride(1), + b.stride(0), b.stride(1), + c.stride(0), c.stride(1), + ACTIVATION=activation, + ) + return c + + + + + + + + + +.. GENERATED FROM PYTHON SOURCE LINES 291-295 + +Unit Test +----------- + +We can test our custom matrix multiplication operation against a native torch implementation (i.e., cuBLAS) + +.. GENERATED FROM PYTHON SOURCE LINES 295-308 + +.. code-block:: default + + + torch.manual_seed(0) + 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={triton_output}") + print(f"torch_output={torch_output}") + if triton.testing.allclose(triton_output, torch_output): + print("✅ Triton and Torch match") + else: + print("❌ Triton and Torch differ") + + + + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + triton_output=tensor([[ 1.1045, -36.9688, 31.4688, ..., -11.3984, 24.4531, -32.3438], + [ 6.3555, -19.6094, 34.0938, ..., -5.8945, 5.2891, 6.8867], + [-32.0625, 5.9492, 15.3984, ..., -21.3906, -23.9844, -10.1328], + ..., + [ -5.7031, 7.4492, 8.2656, ..., -10.6953, -40.0000, 17.7500], + [ 25.5000, 24.3281, -8.4688, ..., -18.9375, 32.5312, -29.9219], + [ -5.3477, 4.9844, 11.8906, ..., 5.5898, 6.4023, -17.3125]], + device='cuda:0', dtype=torch.float16) + torch_output=tensor([[ 1.1045, -36.9688, 31.4688, ..., -11.3906, 24.4531, -32.3438], + [ 6.3516, -19.6094, 34.0938, ..., -5.8906, 5.2812, 6.8828], + [-32.0625, 5.9531, 15.3984, ..., -21.4062, -23.9844, -10.1328], + ..., + [ -5.7070, 7.4492, 8.2656, ..., -10.6953, -40.0000, 17.7500], + [ 25.5000, 24.3438, -8.4609, ..., -18.9375, 32.5312, -29.9219], + [ -5.3477, 4.9805, 11.8828, ..., 5.5859, 6.4023, -17.3125]], + device='cuda:0', dtype=torch.float16) + ✅ Triton and Torch match + + + + +.. GENERATED FROM PYTHON SOURCE LINES 309-315 + +Benchmark +-------------- + +Square Matrix Performance +~~~~~~~~~~~~~~~~~~~~~~~~~~ +We can now compare the performance of our kernel against that of cuBLAS. Here we focus on square matrices, but feel free to arrange this script as you wish to benchmark any other matrix shape. + +.. GENERATED FROM PYTHON SOURCE LINES 315-356 + +.. code-block:: default + + + + @triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['M', 'N', 'K'], # argument names to use as an x-axis for the plot + x_vals=[ + 128 * i for i in range(2, 33) + ], # different possible values for `x_name` + line_arg='provider', # argument name whose value corresponds to a different line in the plot + # possible values for `line_arg`` + line_vals=['cublas', 'cublas + relu', 'triton', 'triton + relu'], + # label name for the lines + line_names=["cuBLAS", "cuBLAS (+ torch.nn.LeakyReLU)", "Triton", "Triton (+ LeakyReLU)"], + # line styles + styles=[('green', '-'), ('green', '--'), ('blue', '-'), ('blue', '--')], + ylabel="TFLOPS", # label name for the y-axis + plot_name="matmul-performance", # name for the plot. Used also as a file name for saving the plot. + args={}, + ) + ) + def benchmark(M, N, K, provider): + a = torch.randn((M, K), device='cuda', dtype=torch.float16) + b = torch.randn((K, N), device='cuda', dtype=torch.float16) + if provider == 'cublas': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.matmul(a, b)) + if provider == 'triton': + ms, min_ms, max_ms = triton.testing.do_bench(lambda: matmul(a, b)) + if provider == 'cublas + relu': + torch_relu = torch.nn.ReLU(inplace=True) + ms, min_ms, max_ms = triton.testing.do_bench( + lambda: torch_relu(torch.matmul(a, b)) + ) + if provider == 'triton + relu': + ms, min_ms, max_ms = triton.testing.do_bench( + lambda: matmul(a, b, activation=leaky_relu) + ) + perf = lambda ms: 2 * M * N * K * 1e-12 / (ms * 1e-3) + return perf(ms), perf(max_ms), perf(min_ms) + + + benchmark.run(show_plots=True, print_data=True) + + + +.. image:: /getting-started/tutorials/images/sphx_glr_03-matrix-multiplication_001.png + :alt: 03 matrix multiplication + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + matmul-performance: + M cuBLAS ... Triton Triton (+ LeakyReLU) + 0 256.0 2.730667 ... 2.978909 2.978909 + 1 384.0 7.372800 ... 8.507077 7.899428 + 2 512.0 14.563555 ... 16.384000 16.384000 + 3 640.0 22.260869 ... 24.380953 24.380953 + 4 768.0 32.768000 ... 34.028308 34.028308 + 5 896.0 39.025776 ... 39.025776 39.025776 + 6 1024.0 49.932191 ... 52.428801 52.428801 + 7 1152.0 45.242181 ... 46.656000 46.656000 + 8 1280.0 51.200001 ... 56.888887 56.888887 + 9 1408.0 64.138541 ... 67.305878 66.485074 + 10 1536.0 80.430545 ... 79.526831 78.643199 + 11 1664.0 62.929456 ... 62.492442 62.061463 + 12 1792.0 72.512412 ... 71.588687 72.047592 + 13 1920.0 69.467336 ... 70.172588 70.172588 + 14 2048.0 73.262953 ... 76.608294 76.608294 + 15 2176.0 83.500614 ... 85.998493 85.998493 + 16 2304.0 68.446623 ... 76.563695 76.319081 + 17 2432.0 71.305746 ... 74.521127 85.134737 + 18 2560.0 78.019048 ... 80.908642 81.108913 + 19 2688.0 82.823267 ... 89.888756 89.464755 + 20 2816.0 83.233226 ... 82.916747 82.759409 + 21 2944.0 81.967162 ... 82.509987 82.237674 + 22 3072.0 82.181572 ... 88.197981 87.651868 + 23 3200.0 84.099871 ... 93.567248 94.674553 + 24 3328.0 79.901550 ... 84.945483 84.496824 + 25 3456.0 81.600781 ... 91.511426 84.775569 + 26 3584.0 83.798127 ... 86.542919 95.148565 + 27 3712.0 81.615477 ... 88.640059 82.017526 + 28 3840.0 84.744825 ... 91.777595 85.399230 + 29 3968.0 92.024087 ... 84.183469 89.558851 + 30 4096.0 86.424811 ... 87.438257 91.992956 + + [31 rows x 5 columns] + + + + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** ( 6 minutes 4.559 seconds) + + +.. _sphx_glr_download_getting-started_tutorials_03-matrix-multiplication.py: + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-example + + + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: 03-matrix-multiplication.py <03-matrix-multiplication.py>` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: 03-matrix-multiplication.ipynb <03-matrix-multiplication.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/master/_sources/getting-started/tutorials/04-low-memory-dropout.rst.txt b/master/_sources/getting-started/tutorials/04-low-memory-dropout.rst.txt new file mode 100644 index 000000000..edf37f86f --- /dev/null +++ b/master/_sources/getting-started/tutorials/04-low-memory-dropout.rst.txt @@ -0,0 +1,271 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "getting-started/tutorials/04-low-memory-dropout.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + Click :ref:`here ` + to download the full example code + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_getting-started_tutorials_04-low-memory-dropout.py: + + +Low-Memory Dropout +================= + +In this tutorial, you will write a memory-efficient implementation of dropout whose state +will be composed of a single int32 seed. This differs from more traditional implementations of dropout, +whose state is generally composed of a bit mask tensor of the same shape as the input. You will learn about: + +- The limitations of naive implementations of Dropout with PyTorch +- Parallel pseudo-random number generation in Triton + +.. GENERATED FROM PYTHON SOURCE LINES 14-29 + +Baseline +------------- +The *dropout* operator was first introduced in [SRIVASTAVA2014]_ as a way to improve the performance +of deep neural networks in low-data regime (i.e. regularization). + +It takes a vector as input and produces a vector of the same shape as output. Each scalar in the +output has a probability :math:`p` of being changed to zero and otherwise it is copied from the input. +This forces the network to perform well even when only :math:`1 - p` scalars from the input are available. + +At evaluation time we want to use the full power of the network so we set :math:`p=0`. Naively this would +increase the norm of the output (which can be a bad thing, e.g. it can lead to artificial decrease +in the output softmax temperature). To prevent this we multiply the output by :math:`\frac{1}{1 - p}`, which +keeps the norm consistent regardless of the dropout probability. + +Let's first take a look at the baseline implementation. + +.. GENERATED FROM PYTHON SOURCE LINES 29-82 + +.. code-block:: default + + + + import tabulate + import torch + + import triton + import triton.language as tl + + + @triton.jit + def _dropout( + x_ptr, # pointer to the input + x_keep_ptr, # pointer to a mask of 0s and 1s + output_ptr, # pointer to the output + n_elements, # number of elements in the `x` tensor + p, # probability that an element of `x` is changed to zero + BLOCK_SIZE: tl.constexpr, + ): + pid = tl.program_id(axis=0) + block_start = pid * BLOCK_SIZE + offsets = block_start + tl.arange(0, BLOCK_SIZE) + mask = offsets < n_elements + # Load data + x = tl.load(x_ptr + offsets, mask=mask) + x_keep = tl.load(x_keep_ptr + offsets, mask=mask) + # The line below is the crucial part, described in the paragraph above! + output = tl.where(x_keep, x / (1 - p), 0.0) + # Write-back output + tl.store(output_ptr + offsets, output, mask=mask) + + + def dropout(x, x_keep, p): + output = torch.empty_like(x) + assert x.is_contiguous() + n_elements = x.numel() + grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),) + _dropout[grid](x, x_keep, output, n_elements, p, BLOCK_SIZE=1024) + return output + + + # Input tensor + x = torch.randn(size=(10,)).cuda() + # Dropout mask + p = 0.5 + x_keep = (torch.rand(size=(10,)) > p).to(torch.int32).cuda() + # + output = dropout(x, x_keep=x_keep, p=p) + print(tabulate.tabulate([ + ["input"] + x.tolist(), + ["keep mask"] + x_keep.tolist(), + ["output"] + output.tolist() + ])) + + + + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + --------- ------- --------- -------- -------- -------- -------- -------- -------- --------- --------- + input 1.541 -0.293429 -2.17879 0.568431 -1.08452 -1.3986 0.403347 0.838026 -0.719258 -0.403344 + keep mask 1 1 0 1 0 1 1 0 0 0 + output 3.08199 -0.586858 0 1.13686 0 -2.79719 0.806694 0 0 0 + --------- ------- --------- -------- -------- -------- -------- -------- -------- --------- --------- + + + + +.. GENERATED FROM PYTHON SOURCE LINES 83-101 + +Seeded dropout +------------- +Above implementation of dropout works fine, but it can be a bit awkward to deal with. Firstly +we need to store the dropout mask for backpropagation. Secondly, dropout state management can get +very tricky when using recompute/checkpointing (e.g. see all the notes about `preserve_rng_state` in +https://pytorch.org/docs/1.9.0/checkpoint.html). In this tutorial we'll describe an alternative implementation +that (1) has a smaller memory footprint; (2) requires less data movement; and (3) simplifies the management +of persisting randomness across multiple invocations of the kernel. + +Pseudorandom number generation in Triton is simple! In this tutorial we will use the +:code:`triton.language.rand` function which generates a block of uniformly distributed :code:`float32` +values in [0, 1), given a seed and a block of :code:`int32` offsets. But if you need it, Triton also provides +other :ref:`random number generation strategies `. + +.. note:: + Triton's implementation of PRNG is based on the Philox algorithm (described on [SALMON2011]_). + +Let's put it all together. + +.. GENERATED FROM PYTHON SOURCE LINES 101-149 + +.. code-block:: default + + + + @triton.jit + def _seeded_dropout( + x_ptr, + output_ptr, + n_elements, + p, + seed, + BLOCK_SIZE: tl.constexpr, + ): + # compute memory offsets of elements handled by this instance + pid = tl.program_id(axis=0) + block_start = pid * BLOCK_SIZE + offsets = block_start + tl.arange(0, BLOCK_SIZE) + # load data from x + mask = offsets < n_elements + x = tl.load(x_ptr + offsets, mask=mask) + # randomly prune it + random = tl.rand(seed, offsets) + x_keep = random > p + # write-back + output = tl.where(x_keep, x / (1 - p), 0.0) + tl.store(output_ptr + offsets, output, mask=mask) + + + def seeded_dropout(x, p, seed): + output = torch.empty_like(x) + assert x.is_contiguous() + n_elements = x.numel() + grid = lambda meta: (triton.cdiv(n_elements, meta['BLOCK_SIZE']),) + _seeded_dropout[grid](x, output, n_elements, p, seed, BLOCK_SIZE=1024) + return output + + + x = torch.randn(size=(10,)).cuda() + # Compare this to the baseline - dropout mask is never instantiated! + output = seeded_dropout(x, p=0.5, seed=123) + output2 = seeded_dropout(x, p=0.5, seed=123) + output3 = seeded_dropout(x, p=0.5, seed=512) + + print(tabulate.tabulate([ + ["input"] + x.tolist(), + ["output (seed = 123)"] + output.tolist(), + ["output (seed = 123)"] + output2.tolist(), + ["output (seed = 512)"] + output3.tolist() + ])) + + + + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + ------------------- --------- -------- -------- ------- -------- -------- --------- --------- --------- --------- + input -0.952835 0.371721 0.408716 1.42142 0.149397 -0.67086 -0.214186 -0.431969 -0.707878 -0.106434 + output (seed = 123) 0 0.743443 0 0 0 -1.34172 0 0 -1.41576 -0.212868 + output (seed = 123) 0 0.743443 0 0 0 -1.34172 0 0 -1.41576 -0.212868 + output (seed = 512) 0 0 0.817432 2.84284 0 -1.34172 -0.428372 0 0 0 + ------------------- --------- -------- -------- ------- -------- -------- --------- --------- --------- --------- + + + + +.. GENERATED FROM PYTHON SOURCE LINES 150-153 + +Et Voilà! We have a triton kernel that applies the same dropout mask provided the seed is the same! +If you'd like explore further applications of pseudorandomness in GPU programming, we encourage you +to explore the `triton/language/random` folder! + +.. GENERATED FROM PYTHON SOURCE LINES 155-160 + +Exercises +------------- +1. Extend the kernel to operate over a matrix and use a vector of seeds - one per row. +2. Add support for striding. +3. (challenge) Implement a kernel for sparse Johnson-Lindenstrauss transform which generates the projection matrix one the fly each time using a seed. + +.. GENERATED FROM PYTHON SOURCE LINES 162-167 + +References +-------------- + +.. [SALMON2011] John K. Salmon, Mark A. Moraes, Ron O. Dror, and David E. Shaw, "Parallel Random Numbers: As Easy as 1, 2, 3", 2011 +.. [SRIVASTAVA2014] Nitish Srivastava and Geoffrey Hinton and Alex Krizhevsky and Ilya Sutskever and Ruslan Salakhutdinov, "Dropout: A Simple Way to Prevent Neural Networks from Overfitting", JMLR 2014 + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** ( 0 minutes 0.480 seconds) + + +.. _sphx_glr_download_getting-started_tutorials_04-low-memory-dropout.py: + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-example + + + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: 04-low-memory-dropout.py <04-low-memory-dropout.py>` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: 04-low-memory-dropout.ipynb <04-low-memory-dropout.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/master/_sources/getting-started/tutorials/05-layer-norm.rst.txt b/master/_sources/getting-started/tutorials/05-layer-norm.rst.txt new file mode 100644 index 000000000..28e5d273d --- /dev/null +++ b/master/_sources/getting-started/tutorials/05-layer-norm.rst.txt @@ -0,0 +1,370 @@ + +.. DO NOT EDIT. +.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY. +.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE: +.. "getting-started/tutorials/05-layer-norm.py" +.. LINE NUMBERS ARE GIVEN BELOW. + +.. only:: html + + .. note:: + :class: sphx-glr-download-link-note + + Click :ref:`here ` + to download the full example code + +.. rst-class:: sphx-glr-example-title + +.. _sphx_glr_getting-started_tutorials_05-layer-norm.py: + + +Layer Normalization +==================== + +.. GENERATED FROM PYTHON SOURCE LINES 5-262 + + + +.. image:: /getting-started/tutorials/images/sphx_glr_05-layer-norm_001.png + :alt: 05 layer norm + :class: sphx-glr-single-img + + +.. rst-class:: sphx-glr-script-out + + Out: + + .. code-block:: none + + layer-norm-backward: + N Triton Torch Apex + 0 1024.0 307.200008 98.303995 307.200008 + 1 1536.0 347.773587 134.050910 341.333333 + 2 2048.0 420.102553 161.684218 325.509933 + 3 2560.0 458.507457 181.238943 326.808501 + 4 3072.0 511.999982 191.999993 317.793096 + 5 3584.0 547.872604 208.271186 310.527060 + 6 4096.0 564.965515 220.412561 294.323343 + 7 4608.0 504.986315 232.825259 290.267724 + 8 5120.0 527.381977 242.845844 287.775181 + 9 5632.0 542.843364 243.545956 288.820505 + 10 6144.0 546.133354 248.661056 285.767458 + 11 6656.0 532.479975 256.000009 285.767438 + 12 7168.0 507.469040 260.260201 286.242939 + 13 7680.0 479.999983 262.564106 279.272719 + 14 8192.0 462.607053 267.130429 284.526763 + 15 8704.0 417.791980 267.815384 284.599455 + 16 9216.0 431.157889 272.394084 288.751954 + 17 9728.0 438.857162 280.278512 290.027323 + 18 10240.0 449.287041 286.433562 290.153487 + 19 10752.0 427.231788 246.935876 290.594591 + 20 11264.0 426.397479 245.760001 286.676558 + 21 11776.0 423.089806 249.888595 288.981596 + 22 12288.0 419.504980 254.673582 294.323369 + 23 12800.0 414.016170 253.674644 288.180121 + 24 13312.0 411.181478 252.959629 289.916513 + 25 13824.0 404.112047 257.190689 292.056329 + 26 14336.0 393.215988 254.485198 286.719986 + 27 14848.0 385.245405 257.665934 289.012175 + 28 15360.0 373.495460 257.970599 286.211174 + 29 15872.0 371.637071 261.626369 289.899545 + + + + + + +| + +.. code-block:: default + + + import torch + + import triton + import triton.language as tl + + try: + # This is https://github.com/NVIDIA/apex, NOT the apex on PyPi, so it + # should not be added to extras_require in setup.py. + import apex + HAS_APEX = True + except ModuleNotFoundError: + HAS_APEX = False + + + # Forward Pass + @triton.jit + def _layer_norm_fwd_fused(X, Y, W, B, M, V, stride, N, eps, + BLOCK_SIZE: tl.constexpr): + # position of elements processed by this program + row = tl.program_id(0) + cols = tl.arange(0, BLOCK_SIZE) + mask = cols < N + # offset data pointers to start at the row of interest + X += row * stride + Y += row * stride + # load data and cast to float32 + x = tl.load(X + cols, mask=mask, other=0).to(tl.float32) + # compute mean + mean = tl.sum(x, axis=0) / N + # compute std + xmean = tl.where(mask, x - mean, 0.) + var = tl.sum(xmean * xmean, axis=0) / N + rstd = 1 / tl.sqrt(var + eps) + xhat = xmean * rstd + # write-back mean/rstd + tl.store(M + row, mean) + tl.store(V + row, rstd) + # multiply by weight and add bias + w = tl.load(W + cols, mask=mask) + b = tl.load(B + cols, mask=mask) + y = xhat * w + b + # write-back + tl.store(Y + cols, y, mask=mask) + + + # Backward pass (DX + partial DW + partial DB) + @triton.jit + def _layer_norm_bwd_dx_fused(DX, DY, DW, DB, X, W, B, M, V, Lock, stride, N, eps, + GROUP_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr): + # position of elements processed by this program + row = tl.program_id(0) + cols = tl.arange(0, BLOCK_SIZE_N) + mask = cols < N + # offset data pointers to start at the row of interest + X += row * stride + DY += row * stride + DX += row * stride + # offset locks and weight/bias gradient pointer + # each kernel instance accumulates partial sums for + # DW and DB into one of GROUP_SIZE_M independent buffers + # these buffers stay in the L2, which allow this kernel + # to be fast + lock_id = row % GROUP_SIZE_M + Lock += lock_id + Count = Lock + GROUP_SIZE_M + DW = DW + lock_id * N + cols + DB = DB + lock_id * N + cols + # load data to SRAM + x = tl.load(X + cols, mask=mask, other=0).to(tl.float32) + dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32) + w = tl.load(W + cols, mask=mask).to(tl.float32) + mean = tl.load(M + row) + rstd = tl.load(V + row) + # compute dx + xhat = (x - mean) * rstd + wdy = w * dy + xhat = tl.where(mask, xhat, 0.) + wdy = tl.where(mask, wdy, 0.) + mean1 = tl.sum(xhat * wdy, axis=0) / N + mean2 = tl.sum(wdy, axis=0) / N + dx = (wdy - (xhat * mean1 + mean2)) * rstd + # write-back dx + tl.store(DX + cols, dx, mask=mask) + # accumulate partial sums for dw/db + partial_dw = (dy * xhat).to(w.dtype) + partial_db = (dy).to(w.dtype) + while tl.atomic_cas(Lock, 0, 1) == 1: + pass + count = tl.load(Count) + # first store doesn't accumulate + if count == 0: + tl.atomic_xchg(Count, 1) + else: + partial_dw += tl.load(DW, mask=mask) + partial_db += tl.load(DB, mask=mask) + tl.store(DW, partial_dw, mask=mask) + tl.store(DB, partial_db, mask=mask) + # release lock + tl.atomic_xchg(Lock, 0) + + # Backward pass (total DW + total DB) + + + @triton.jit + def _layer_norm_bwd_dwdb(DW, DB, FINAL_DW, FINAL_DB, M, N, + BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr): + pid = tl.program_id(0) + cols = pid * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N) + dw = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32) + db = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32) + for i in range(0, M, BLOCK_SIZE_M): + rows = i + tl.arange(0, BLOCK_SIZE_M) + mask = (rows[:, None] < M) & (cols[None, :] < N) + offs = rows[:, None] * N + cols[None, :] + dw += tl.load(DW + offs, mask=mask, other=0.) + db += tl.load(DB + offs, mask=mask, other=0.) + sum_dw = tl.sum(dw, axis=0) + sum_db = tl.sum(db, axis=0) + tl.store(FINAL_DW + cols, sum_dw, mask=cols < N) + tl.store(FINAL_DB + cols, sum_db, mask=cols < N) + + + class LayerNorm(torch.autograd.Function): + + @staticmethod + def forward(ctx, x, normalized_shape, weight, bias, eps): + # allocate output + y = torch.empty_like(x) + # reshape input data into 2D tensor + x_arg = x.reshape(-1, x.shape[-1]) + M, N = x_arg.shape + mean = torch.empty((M, ), dtype=torch.float32, device='cuda') + rstd = torch.empty((M, ), dtype=torch.float32, device='cuda') + # Less than 64KB per feature: enqueue fused kernel + MAX_FUSED_SIZE = 65536 // x.element_size() + BLOCK_SIZE = min(MAX_FUSED_SIZE, triton.next_power_of_2(N)) + if N > BLOCK_SIZE: + raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.") + # heuristics for number of warps + num_warps = min(max(BLOCK_SIZE // 256, 1), 8) + # enqueue kernel + _layer_norm_fwd_fused[(M,)](x_arg, y, weight, bias, mean, rstd, + x_arg.stride(0), N, eps, + BLOCK_SIZE=BLOCK_SIZE, num_warps=num_warps) + ctx.save_for_backward(x, weight, bias, mean, rstd) + ctx.BLOCK_SIZE = BLOCK_SIZE + ctx.num_warps = num_warps + ctx.eps = eps + return y + + @staticmethod + def backward(ctx, dy): + x, w, b, m, v = ctx.saved_tensors + # heuristics for amount of parallel reduction stream for DG/DB + N = w.shape[0] + GROUP_SIZE_M = 64 + if N <= 8192: GROUP_SIZE_M = 96 + if N <= 4096: GROUP_SIZE_M = 128 + if N <= 1024: GROUP_SIZE_M = 256 + # allocate output + locks = torch.zeros(2 * GROUP_SIZE_M, dtype=torch.int32, device='cuda') + _dw = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device) + _db = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device) + dw = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device) + db = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device) + dx = torch.empty_like(dy) + # enqueue kernel using forward pass heuristics + # also compute partial sums for DW and DB + x_arg = x.reshape(-1, x.shape[-1]) + M, N = x_arg.shape + _layer_norm_bwd_dx_fused[(M,)](dx, dy, _dw, _db, x, w, b, m, v, locks, + x_arg.stride(0), N, ctx.eps, + BLOCK_SIZE_N=ctx.BLOCK_SIZE, + GROUP_SIZE_M=GROUP_SIZE_M, + num_warps=ctx.num_warps) + grid = lambda meta: [triton.cdiv(N, meta['BLOCK_SIZE_N'])] + # accumulate partial sums in separate kernel + _layer_norm_bwd_dwdb[grid](_dw, _db, dw, db, GROUP_SIZE_M, N, + BLOCK_SIZE_M=32, + BLOCK_SIZE_N=128) + return dx, None, dw, db, None + + + layer_norm = LayerNorm.apply + + + def test_layer_norm(M, N, dtype, eps=1e-5, device='cuda'): + # create data + x_shape = (M, N) + w_shape = (x_shape[-1], ) + weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda') + dy = .1 * torch.randn_like(x) + x.requires_grad_(True) + # forward pass + y_tri = layer_norm(x, w_shape, weight, bias, eps) + y_ref = torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps).to(dtype) + # backward pass (triton) + y_tri.backward(dy, retain_graph=True) + dx_tri, dw_tri, db_tri = [_.grad.clone() for _ in [x, weight, bias]] + x.grad, weight.grad, bias.grad = None, None, None + # backward pass (torch) + y_ref.backward(dy, retain_graph=True) + dx_ref, dw_ref, db_ref = [_.grad.clone() for _ in [x, weight, bias]] + # compare + triton.testing.assert_almost_equal(y_tri, y_ref) + triton.testing.assert_almost_equal(dx_tri, dx_ref) + triton.testing.assert_almost_equal(db_tri, db_ref, decimal=1) + triton.testing.assert_almost_equal(dw_tri, dw_ref, decimal=1) + + + @triton.testing.perf_report( + triton.testing.Benchmark( + x_names=['N'], + x_vals=[512 * i for i in range(2, 32)], + line_arg='provider', + line_vals=['triton', 'torch'] + (['apex'] if HAS_APEX else []), + line_names=['Triton', 'Torch'] + (['Apex'] if HAS_APEX else []), + styles=[('blue', '-'), ('green', '-'), ('orange', '-')], + ylabel='GB/s', + plot_name='layer-norm-backward', + args={'M': 4096, 'dtype': torch.float16, 'mode': 'backward'} + ) + ) + def bench_layer_norm(M, N, dtype, provider, mode='backward', eps=1e-5, device='cuda'): + # create data + x_shape = (M, N) + w_shape = (x_shape[-1], ) + weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True) + x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda') + dy = .1 * torch.randn_like(x) + x.requires_grad_(True) + # utility functions + if provider == 'triton': + y_fwd = lambda: layer_norm(x, w_shape, weight, bias, eps) + if provider == 'torch': + y_fwd = lambda: torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps) + if provider == 'apex': + apex_layer_norm = apex.normalization.FusedLayerNorm(w_shape).to(x.device).to(x.dtype) + y_fwd = lambda: apex_layer_norm(x) + # forward pass + if mode == 'forward': + gbps = lambda ms: 2 * x.numel() * x.element_size() / ms * 1e-6 + ms, min_ms, max_ms = triton.testing.do_bench(y_fwd, rep=500) + # backward pass + if mode == 'backward': + gbps = lambda ms: 3 * x.numel() * x.element_size() / ms * 1e-6 + y = y_fwd() + ms, min_ms, max_ms = triton.testing.do_bench(lambda: y.backward(dy, retain_graph=True), + grad_to_none=[x], rep=500) + return gbps(ms), gbps(max_ms), gbps(min_ms) + + + bench_layer_norm.run(save_path='.', print_data=True) + + +.. rst-class:: sphx-glr-timing + + **Total running time of the script:** ( 2 minutes 12.003 seconds) + + +.. _sphx_glr_download_getting-started_tutorials_05-layer-norm.py: + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-example + + + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download Python source code: 05-layer-norm.py <05-layer-norm.py>` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download Jupyter notebook: 05-layer-norm.ipynb <05-layer-norm.ipynb>` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/master/_sources/getting-started/tutorials/index.rst.txt b/master/_sources/getting-started/tutorials/index.rst.txt new file mode 100644 index 000000000..c8a39cdaf --- /dev/null +++ b/master/_sources/getting-started/tutorials/index.rst.txt @@ -0,0 +1,152 @@ +:orphan: + + + +.. _sphx_glr_getting-started_tutorials: + +Tutorials +================== + +Below is a gallery of tutorials for writing various basic operations with Triton. It is recommended that you read through the tutorials in order, starting with the simplest one. + +To install the dependencies for the tutorials: + +.. code-block:: bash + + cd triton + pip install -e './python[tutorials]' + + + +.. raw:: html + +

    + +.. only:: html + + .. figure:: /getting-started/tutorials/images/thumb/sphx_glr_01-vector-add_thumb.png + :alt: Vector Addition + + :ref:`sphx_glr_getting-started_tutorials_01-vector-add.py` + +.. raw:: html + +
    + + +.. toctree:: + :hidden: + + /getting-started/tutorials/01-vector-add + +.. raw:: html + +
    + +.. only:: html + + .. figure:: /getting-started/tutorials/images/thumb/sphx_glr_02-fused-softmax_thumb.png + :alt: Fused Softmax + + :ref:`sphx_glr_getting-started_tutorials_02-fused-softmax.py` + +.. raw:: html + +
    + + +.. toctree:: + :hidden: + + /getting-started/tutorials/02-fused-softmax + +.. raw:: html + +
    + +.. only:: html + + .. figure:: /getting-started/tutorials/images/thumb/sphx_glr_03-matrix-multiplication_thumb.png + :alt: Matrix Multiplication + + :ref:`sphx_glr_getting-started_tutorials_03-matrix-multiplication.py` + +.. raw:: html + +
    + + +.. toctree:: + :hidden: + + /getting-started/tutorials/03-matrix-multiplication + +.. raw:: html + +
    + +.. only:: html + + .. figure:: /getting-started/tutorials/images/thumb/sphx_glr_04-low-memory-dropout_thumb.png + :alt: Low-Memory Dropout + + :ref:`sphx_glr_getting-started_tutorials_04-low-memory-dropout.py` + +.. raw:: html + +
    + + +.. toctree:: + :hidden: + + /getting-started/tutorials/04-low-memory-dropout + +.. raw:: html + +
    + +.. only:: html + + .. figure:: /getting-started/tutorials/images/thumb/sphx_glr_05-layer-norm_thumb.png + :alt: Layer Normalization + + :ref:`sphx_glr_getting-started_tutorials_05-layer-norm.py` + +.. raw:: html + +
    + + +.. toctree:: + :hidden: + + /getting-started/tutorials/05-layer-norm +.. raw:: html + +
    + + + +.. only :: html + + .. container:: sphx-glr-footer + :class: sphx-glr-footer-gallery + + + .. container:: sphx-glr-download sphx-glr-download-python + + :download:`Download all examples in Python source code: tutorials_python.zip ` + + + + .. container:: sphx-glr-download sphx-glr-download-jupyter + + :download:`Download all examples in Jupyter notebooks: tutorials_jupyter.zip ` + + +.. only:: html + + .. rst-class:: sphx-glr-signature + + `Gallery generated by Sphinx-Gallery `_ diff --git a/master/_sources/getting-started/tutorials/sg_execution_times.rst.txt b/master/_sources/getting-started/tutorials/sg_execution_times.rst.txt new file mode 100644 index 000000000..7319b7b50 --- /dev/null +++ b/master/_sources/getting-started/tutorials/sg_execution_times.rst.txt @@ -0,0 +1,20 @@ + +:orphan: + +.. _sphx_glr_getting-started_tutorials_sg_execution_times: + +Computation times +================= +**13:21.645** total execution time for **getting-started_tutorials** files: + ++---------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_getting-started_tutorials_03-matrix-multiplication.py` (``03-matrix-multiplication.py``) | 06:04.559 | 0.0 MB | ++---------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_getting-started_tutorials_02-fused-softmax.py` (``02-fused-softmax.py``) | 03:22.066 | 0.0 MB | ++---------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_getting-started_tutorials_05-layer-norm.py` (``05-layer-norm.py``) | 02:12.003 | 0.0 MB | ++---------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_getting-started_tutorials_01-vector-add.py` (``01-vector-add.py``) | 01:42.537 | 0.0 MB | ++---------------------------------------------------------------------------------------------------------+-----------+--------+ +| :ref:`sphx_glr_getting-started_tutorials_04-low-memory-dropout.py` (``04-low-memory-dropout.py``) | 00:00.480 | 0.0 MB | ++---------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/master/_static/binder_badge_logo.svg b/master/_static/binder_badge_logo.svg new file mode 100644 index 000000000..327f6b639 --- /dev/null +++ b/master/_static/binder_badge_logo.svg @@ -0,0 +1 @@ + launchlaunchbinderbinder \ No newline at end of file diff --git a/master/_static/broken_example.png b/master/_static/broken_example.png new file mode 100644 index 0000000000000000000000000000000000000000..4fea24e7df4781c2c32c8d7995511ac89e953145 GIT binary patch literal 21404 zcmaHTWmKEb({>2%?jE#QaVRdqp+KR9;KkkDwKxQKD^i>mcWI%x7Y&k9+}-8j_dn93t*7AV|HwhohmqKD$2joW8ywxydML 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    Getting Started

    Python API

      diff --git a/master/getting-started/installation.html b/master/getting-started/installation.html index 81d637580..7b7428ca0 100644 --- a/master/getting-started/installation.html +++ b/master/getting-started/installation.html @@ -15,6 +15,10 @@ + + + + @@ -42,7 +46,7 @@ - + @@ -98,6 +102,7 @@
    • +
  • Tutorials

    • Python API