From 7d91e06e08dab3b7425b46ff384d6ea357a17b62 Mon Sep 17 00:00:00 2001 From: Philippe Tillet Date: Thu, 12 Aug 2021 00:39:35 +0000 Subject: [PATCH] [GH-PAGES] Updated website --- .../02-fused-softmax.ipynb | 6 +- .../tutorials_jupyter.zip | Bin 35801 -> 35534 bytes .../tutorials_python.zip | Bin 28692 -> 28424 bytes .../02-fused-softmax.py | 17 +++--- _images/sphx_glr_01-vector-add_001.png | Bin 25912 -> 25468 bytes _images/sphx_glr_01-vector-add_thumb.png | Bin 16070 -> 15890 bytes _images/sphx_glr_02-fused-softmax_001.png | Bin 38312 -> 38275 bytes _images/sphx_glr_02-fused-softmax_thumb.png | Bin 24161 -> 24229 bytes .../sphx_glr_03-matrix-multiplication_001.png | Bin 56540 -> 55926 bytes ...phx_glr_03-matrix-multiplication_thumb.png | Bin 32711 -> 32137 bytes .../tutorials/01-vector-add.rst.txt | 2 +- .../tutorials/02-fused-softmax.rst.txt | 29 +++++----- .../03-matrix-multiplication.rst.txt | 52 +++++++++--------- .../tutorials/sg_execution_times.rst.txt | 8 +-- getting-started/tutorials/01-vector-add.html | 2 +- .../tutorials/02-fused-softmax.html | 27 +++++---- .../tutorials/03-matrix-multiplication.html | 52 +++++++++--------- .../tutorials/sg_execution_times.html | 8 +-- searchindex.js | 2 +- 19 files changed, 101 insertions(+), 104 deletions(-) diff --git a/_downloads/034d953b6214fedce6ea03803c712b89/02-fused-softmax.ipynb b/_downloads/034d953b6214fedce6ea03803c712b89/02-fused-softmax.ipynb index d87c0748c..960e8fc30 100644 --- a/_downloads/034d953b6214fedce6ea03803c712b89/02-fused-softmax.ipynb +++ b/_downloads/034d953b6214fedce6ea03803c712b89/02-fused-softmax.ipynb @@ -33,14 +33,14 @@ }, "outputs": [], "source": [ - "import torch\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 2MN 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 2MN elements ; write MN elements\n ret = numerator / denominator[:, None]\n # in total: read 7MN elements ; wrote 3MN + 2M elements\n return ret" + "import torch\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 $7MN$ 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 ~5x (i.e., $(10MN + 2M) / 2MN$).\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" + "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" ] }, { @@ -133,7 +133,7 @@ "cell_type": "markdown", "metadata": {}, "source": [ - "In the above plot, we can see that:\n\n - Triton is 2-3x faster than the Torch JIT.\n - Triton is even faster than :code:`torch.softmax`. My guess from looking at the source-code of the `PyTorch kernel `_ is that PyTorch only partially fuses the computation of the softmax.\n This means that -- when temporary data is too large to fit entirely in the GPU's cache -- it transfers almost twice the amount of memory necessary.\n Note that our Triton kernel is not only faster than PyTorch's CUDA kernel, it is also **easier to read, understand and maintain**.\n\n" + "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" ] } ], diff --git a/_downloads/662999063954282841dc90b8945f85ce/tutorials_jupyter.zip b/_downloads/662999063954282841dc90b8945f85ce/tutorials_jupyter.zip index 6f953c9e2860838215973e14d53cc7e24aeffba2..ec455464300e563256046ce8d015836794ed5289 100644 GIT binary patch delta 431 zcmZ8e!AiqG5N*;}JQO`xL{MZ<4*^XPsi1-=6c1KYistB{G1)Y$>2BHG+U5gVEcIlN z;>92EBsuyIdiE}QZ1D@+#zVn93~y%Nn>RcAF;L$g)NJJ>t>seVGtyqNnWEa!;#_fa zdFENmo)3#@E!0z~P>;{-=AhIKHb-P+d#u0}`x{`7WowPnT~e_oknPxw%oE3`q! zd6eIPHGL=H72=<(!J<-#?z&4JSU%?9P~u@$=Rlhbc#}7%A4 zOA!Y`g#=)e5WFUrRPYf)`3nLDSPTnUkXK&PMS!YI%NoIh{#ePM{=Qsg8*8T yUCZ}K8$>u|5_-wJ+_xJjs+hTWwl`GNk#^rN$+btP{eyp7j~@GbneX2CcYXo-F^$#$ delta 690 zcmY*XL2DC16wW4E5P}B{rO+x5E7;a1yV*q2Emd102-bvv=|K>h+0EPRlHHjwGqKGn z7crQF2#XYN{sN2SPk8d~AMmcwyKiGEI55ncneTn`y>H(4kJ%q**?j9TccqX?$GPz} zzf{le8?!>)x_!ep@-K{Ay^A-SnM^vDGs)-a%8avbS95lwne6p`F4pzrFnE}&HJY;z z!Ll(AzJ&Wm;lU|vge5F(!`+Rt)o8+fuxCd9Y&B;WE6Jy~Yd2qUC_-C?T5t#z;A`Z` z>g3M21dS2&hNu+yQp6Am(GPhKm%2mg8?d}fk*p7pi=Txg@%W=`Kd3Me8 znD3))iUCSSM9Ngc*D*Ui76VoChU?Gms`aRIoED-3QhKRK@Mr`BCUwXniu|EMm2|GH zj2HPOasi+nP+p9TFS3h8I0=x0#&{qklOyOd&F17nK*VGZK@0Fh4ajvUk*Gt0lRZyc zNB0zX%%hlS2%#nM`Y08!C>DwiPC{=?1cYF*7;>HZ7-KBx9gZFuPcQxz))YDgQbFYU z8 X)OpFl^zrro8!vf3-Cg=UO&jzNbdTh< diff --git a/_downloads/763344228ae6bc253ed1a6cf586aa30d/tutorials_python.zip b/_downloads/763344228ae6bc253ed1a6cf586aa30d/tutorials_python.zip index 0e0047796e6ef84045494826aa0bbed7f3c7dec3..a5b6a97d1349c5f6f61dd8fb5923ee2ba280547e 100644 GIT binary patch delta 475 zcmZ8eF-w9$7}hkAkQ!33MP6!=Qim{#kCq^a5>4rt1$h zJBfP@wKlg!OMjrXrTdfuyWx1>=bq<%pX0gz2oB$av2r04jtBfR3XfxBYvDRPd9sp; z<=b$qa&eOwW>SGbCN=pyeF#O0CD?+ZKB%nffxV(fmB)Fg5Z#$lwu}1Je*SAF`m7XO z%l9D7ax|9#t3{M+RnvP@a(?oC{*oA&XNO2d1t^zrb5XES)Ll3^wsT;+OhO&G!$eC0 zb_B?dY_mE;E`5QT7eE841dhrSKzJXVjxTTv4+O#irhJh?s8Pn7I*Qo=_-cR>Dhe)k>DA2eY=5~wvs{(vs21r}0ozoN=@hf5 zg@QtpaszqBRRg-r^Pr33(tOG6pLBzD5v<>8C>Z|=4?3x)RP^3RjEMZ-#e3~!_#hM)56bkr@jdj0h0=t~xt z@5X)O>g^NQ4r;u%3!R8*zcbn1tM~e_1J<(i?CW~bsy5Q^;k8O>3!n-k8E6y`DB#bz zNS{X67d7b3VU}>Ez>^q3h%yX;!^Msy1v%2 z>X_y%(0=07T#U?kt~1EL=!EE)cC&7?25Z<(Yp-cLjx}x5jML z#v-q;Wi|ked@77M6M1>H3dcSdpm`LdWO5Eurr9|=B7{uNIA{bf(7=TbBq#2G;N;K# zV0=@7%UsHdh7ej3ug9eV7DlM(;5b;gL_i1@VIp*9WW*z+cLaCId3rHd)<>NosU`A# z^F9*!S9$bV%wlR_0NR0y}y*U`?E(%`^Ys}xuBm$t<| V&0qRbbpIQ_^qXj1yo1@8{ss2?`_ is that PyTorch only partially fuses the computation of the softmax. -# This means that -- when temporary data is too large to fit entirely in the GPU's cache -- it transfers almost twice the amount of memory necessary. -# Note that our Triton kernel is not only faster than PyTorch's CUDA kernel, it is also **easier to read, understand and maintain**. +# - Triton is 4x faster than the Torch JIT. 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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:** ( 1 minutes 12.602 seconds) + **Total running time of the script:** ( 1 minutes 12.617 seconds) .. _sphx_glr_download_getting-started_tutorials_02-fused-softmax.py: diff --git a/_sources/getting-started/tutorials/03-matrix-multiplication.rst.txt b/_sources/getting-started/tutorials/03-matrix-multiplication.rst.txt index 3ec26a71b..08614bc72 100644 --- a/_sources/getting-started/tutorials/03-matrix-multiplication.rst.txt +++ b/_sources/getting-started/tutorials/03-matrix-multiplication.rst.txt @@ -471,37 +471,37 @@ We can now compare the performance of our kernel against that of cuBLAS. Here we matmul-performance: M cuBLAS ... Triton Triton (+ LeakyReLU) 0 128.0 0.455111 ... 0.512000 0.512000 - 1 256.0 2.978909 ... 3.276800 2.978909 + 1 256.0 2.730667 ... 2.978909 2.978909 2 384.0 7.372800 ... 8.507077 8.507077 - 3 512.0 14.563555 ... 16.384000 15.420235 - 4 640.0 22.260869 ... 24.380953 24.380953 + 3 512.0 14.563555 ... 15.420235 16.384000 + 4 640.0 22.260869 ... 24.380953 23.272727 5 768.0 32.768000 ... 34.028308 34.028308 6 896.0 39.025776 ... 40.140799 39.025776 7 1024.0 49.932191 ... 53.773130 52.428801 8 1152.0 45.242181 ... 46.656000 46.656000 - 9 1280.0 51.200001 ... 56.888887 56.109587 + 9 1280.0 51.200001 ... 56.888887 56.888887 10 1408.0 64.138541 ... 64.902096 64.902096 - 11 1536.0 80.430545 ... 76.106321 76.106321 - 12 1664.0 63.372618 ... 62.061463 62.061463 - 13 1792.0 72.983276 ... 69.810085 69.810085 - 14 1920.0 69.120002 ... 70.172588 69.120002 - 15 2048.0 73.584279 ... 74.898285 73.584279 - 16 2176.0 82.813365 ... 78.916269 79.540109 - 17 2304.0 68.056616 ... 73.275679 73.275679 - 18 2432.0 71.125224 ... 81.197876 81.908060 - 19 2560.0 77.649287 ... 76.560748 75.676673 - 20 2688.0 84.108772 ... 81.053536 84.108772 - 21 2816.0 80.469019 ... 79.298560 78.726003 - 22 2944.0 81.832567 ... 79.737653 79.104810 - 23 3072.0 82.540970 ... 80.890151 83.146995 - 24 3200.0 84.210524 ... 89.260810 87.791493 - 25 3328.0 83.130825 ... 86.736504 82.275764 - 26 3456.0 78.578525 ... 83.459178 85.767626 - 27 3584.0 87.808000 ... 92.410473 95.148565 - 28 3712.0 85.601834 ... 85.601834 88.876645 - 29 3840.0 84.615146 ... 86.875096 87.148936 - 30 3968.0 92.512459 ... 83.807647 83.520835 - 31 4096.0 93.596744 ... 90.748973 90.321484 + 11 1536.0 78.643199 ... 76.106321 75.296679 + 12 1664.0 62.929456 ... 62.061463 62.061463 + 13 1792.0 72.983276 ... 69.810085 69.379162 + 14 1920.0 67.434145 ... 70.892307 70.530615 + 15 2048.0 73.908442 ... 74.898285 74.565406 + 16 2176.0 83.500614 ... 78.916269 79.855747 + 17 2304.0 68.251065 ... 73.275679 72.828879 + 18 2432.0 71.125224 ... 80.731218 80.731218 + 19 2560.0 77.649287 ... 76.560748 76.382283 + 20 2688.0 81.928846 ... 80.366642 82.823267 + 21 2816.0 77.743683 ... 78.868366 78.301990 + 22 2944.0 81.832567 ... 79.610276 78.605729 + 23 3072.0 81.005868 ... 81.005868 82.420822 + 24 3200.0 84.321474 ... 89.635851 85.106381 + 25 3328.0 83.226931 ... 87.156532 86.113988 + 26 3456.0 81.932484 ... 83.632331 85.313831 + 27 3584.0 87.211821 ... 87.211821 91.563533 + 28 3712.0 85.896254 ... 82.491612 84.874549 + 29 3840.0 85.070769 ... 87.493673 87.701820 + 30 3968.0 92.935215 ... 83.865247 83.578035 + 31 4096.0 93.662059 ... 85.926841 84.840533 [32 rows x 5 columns] @@ -511,7 +511,7 @@ We can now compare the performance of our kernel against that of cuBLAS. Here we .. rst-class:: sphx-glr-timing - **Total running time of the script:** ( 2 minutes 16.405 seconds) + **Total running time of the script:** ( 2 minutes 9.226 seconds) .. _sphx_glr_download_getting-started_tutorials_03-matrix-multiplication.py: diff --git a/_sources/getting-started/tutorials/sg_execution_times.rst.txt b/_sources/getting-started/tutorials/sg_execution_times.rst.txt index e978d0a23..41acb9ef9 100644 --- a/_sources/getting-started/tutorials/sg_execution_times.rst.txt +++ b/_sources/getting-started/tutorials/sg_execution_times.rst.txt @@ -5,12 +5,12 @@ Computation times ================= -**03:39.988** total execution time for **getting-started_tutorials** files: +**03:32.837** total execution time for **getting-started_tutorials** files: +---------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_getting-started_tutorials_03-matrix-multiplication.py` (``03-matrix-multiplication.py``) | 02:16.405 | 0.0 MB | +| :ref:`sphx_glr_getting-started_tutorials_03-matrix-multiplication.py` (``03-matrix-multiplication.py``) | 02:09.226 | 0.0 MB | +---------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_getting-started_tutorials_02-fused-softmax.py` (``02-fused-softmax.py``) | 01:12.602 | 0.0 MB | +| :ref:`sphx_glr_getting-started_tutorials_02-fused-softmax.py` (``02-fused-softmax.py``) | 01:12.617 | 0.0 MB | +---------------------------------------------------------------------------------------------------------+-----------+--------+ -| :ref:`sphx_glr_getting-started_tutorials_01-vector-add.py` (``01-vector-add.py``) | 00:10.981 | 0.0 MB | +| :ref:`sphx_glr_getting-started_tutorials_01-vector-add.py` (``01-vector-add.py``) | 00:10.994 | 0.0 MB | +---------------------------------------------------------------------------------------------------------+-----------+--------+ diff --git a/getting-started/tutorials/01-vector-add.html b/getting-started/tutorials/01-vector-add.html index 3d55a5244..14cfc89a5 100644 --- a/getting-started/tutorials/01-vector-add.html +++ b/getting-started/tutorials/01-vector-add.html @@ -337,7 +337,7 @@ for different problem sizes.

15 134217728.0 851.577704 850.656574 -

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

+

Total running time of the script: ( 0 minutes 10.994 seconds)

When implemented naively in PyTorch, computing y = naive_softmax(x) for \(x \in R^{M \times N}\) -requires reading \(7MN\) elements from DRAM and writing back \(3MN + 2M\) elements. +requires reading \(5MN + 2M\) elements from DRAM and writing back \(3MN + 2M\) 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 \(MN\) bytes, so we could -expect a theoretical speed-up of ~5x (i.e., \((10MN + 2M) / 2MN\)). +expect a theoretical speed-up of ~4x (i.e., \((8MN + 4M) / 2MN\)). 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.

@@ -391,11 +391,11 @@ We will then compare its performance against (1) In the above plot, we can see that:

    -
  • Triton is 2-3x faster than the Torch JIT.

  • -
  • Triton is even faster than torch.softmax. My guess from looking at the source-code of the PyTorch kernel is that PyTorch only partially fuses the computation of the softmax. -This means that – when temporary data is too large to fit entirely in the GPU’s cache – it transfers almost twice the amount of memory necessary. -Note that our Triton kernel is not only faster than PyTorch’s CUDA kernel, it is also easier to read, understand and maintain.

  • +
  • 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 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.

-

Total running time of the script: ( 1 minutes 12.602 seconds)

+

Total running time of the script: ( 1 minutes 12.617 seconds)