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[GH-PAGES] Updated website
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<EFBFBD><05>g<EFBFBD><00>sphinx.addnodes<65><73>document<6E><74><EFBFBD>)<29><>}<7D>(<28> rawsource<63><65><00><>children<65>]<5D>(<28>docutils.nodes<65><73>comment<6E><74><EFBFBD>)<29><>}<7D>(h<05> DO NOT EDIT.<2E>h]<5D>h <09>Text<78><74><EFBFBD><EFBFBD> DO NOT EDIT.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<06>parent<6E>h uba<62>
[GH-PAGES] Updated website
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attributes<EFBFBD>}<7D>(<28>ids<64>]<5D><>classes<65>]<5D><>names<65>]<5D><>dupnames<65>]<5D><>backrefs<66>]<5D><> xml:space<63><65>preserve<76>u<EFBFBD>tagname<6D>h
[GH-PAGES] Updated website
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hhhh<03>source<63><65>u/tmp/tmplh0mt6tq/2d6df9b518a8152f777eb79b6b0a84becb706353/docs/getting-started/tutorials/03-matrix-multiplication.rst<73><74>line<6E>Kubh )<29><>}<7D>(h<05>8THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.<2E>h]<5D>h<11>8THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhh)ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
hhhhh&h'h(Kubh )<29><>}<7D>(h<05>-TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:<3A>h]<5D>h<11>-TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhh7ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hhhhh&h'h(Kubh )<29><>}<7D>(h<05>7"getting-started/tutorials/03-matrix-multiplication.py"<22>h]<5D>h<11>7"getting-started/tutorials/03-matrix-multiplication.py"<22><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhhEubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hhhhh&h'h(Kubh )<29><>}<7D>(h<05>LINE NUMBERS ARE GIVEN BELOW.<2E>h]<5D>h<11>LINE NUMBERS ARE GIVEN BELOW.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhhSubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hhhhh&h'h(Kubh<00>only<6C><79><EFBFBD>)<29><>}<7D>(hhh]<5D>h <09>note<74><65><EFBFBD>)<29><>}<7D>(h<05>}Click :ref:`here <sphx_glr_download_getting-started_tutorials_03-matrix-multiplication.py>`
to download the full example code<64>h]<5D>h <09> paragraph<70><68><EFBFBD>)<29><>}<7D>(h<05>}Click :ref:`here <sphx_glr_download_getting-started_tutorials_03-matrix-multiplication.py>`
to download the full example code<64>h]<5D>(h<11>Click <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>Click <20>hhnubh<00> pending_xref<65><66><EFBFBD>)<29><>}<7D>(h<05>U:ref:`here <sphx_glr_download_getting-started_tutorials_03-matrix-multiplication.py>`<60>h]<5D>h <09>inline<6E><65><EFBFBD>)<29><>}<7D>(hh{h]<5D>h<11>here<72><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhhubah}<7D>(h]<5D>h]<5D>(<28>xref<65><66>std<74><64>std-ref<65>eh]<5D>h]<5D>h!]<5D>uh%h}hhyubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D><>refdoc<6F><63>2getting-started/tutorials/03-matrix-multiplication<6F><6E> refdomain<69>h<EFBFBD><68>reftype<70><65>ref<65><66> refexplicit<69><74><EFBFBD>refwarn<72><6E><EFBFBD> reftarget<65><74>Gsphx_glr_download_getting-started_tutorials_03-matrix-multiplication.py<70>uh%hwh&h'h(K hhnubh<11>"
to download the full example code<64><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>"
to download the full example code<64>hhnubeh}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(K hhhubah}<7D>(h]<5D>h]<5D><>sphx-glr-download-link-note<74>ah]<5D>h]<5D>h!]<5D>uh%hfhhchhh&h'h(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D><>expr<70><72>html<6D>uh%hahhh&h'h(Khhubh <09>target<65><74><EFBFBD>)<29><>}<7D>(h<05>C.. _sphx_glr_getting-started_tutorials_03-matrix-multiplication.py:<3A>h]<5D>h}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D><>refid<69><64>>sphx-glr-getting-started-tutorials-03-matrix-multiplication-py<70>uh%h<>h(Khhhhh&h'ubh <09>section<6F><6E><EFBFBD>)<29><>}<7D>(hhh]<5D>(h <09>title<6C><65><EFBFBD>)<29><>}<7D>(h<05>Matrix Multiplication<6F>h]<5D>h<11>Matrix Multiplication<6F><6E><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hh<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(Kubhm)<29><>}<7D>(h<05><>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:<3A>h]<5D>h<11><>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:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hh<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Khh<>hhubh <09> bullet_list<73><74><EFBFBD>)<29><>}<7D>(hhh]<5D>(h <09> list_item<65><6D><EFBFBD>)<29><>}<7D>(h<05>"Block-level matrix multiplications<6E>h]<5D>hm)<29><>}<7D>(hh<>h]<5D>h<11>"Block-level matrix multiplications<6E><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hh<>hh<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Khh<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(Nubh<62>)<29><>}<7D>(h<05>$Multi-dimensional pointer arithmetic<69>h]<5D>hm)<29><>}<7D>(hj h]<5D>h<11>$Multi-dimensional pointer arithmetic<69><63><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj hj ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Khjubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(Nubh<62>)<29><>}<7D>(h<05>2Program re-ordering for improved L2 cache hit rate<74>h]<5D>hm)<29><>}<7D>(hj h]<5D>h<11>2Program re-ordering for improved L2 cache hit rate<74><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj hj"ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Khjubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(Nubh<62>)<29><>}<7D>(h<05>Automatic performance tuning
<EFBFBD>h]<5D>hm)<29><>}<7D>(h<05>Automatic performance tuning<6E>h]<5D>h<11>Automatic performance tuning<6E><67><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj;hj9ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Khj5ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(Nubeh}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D><>bullet<65><74>-<2D>uh%h<>h&h'h(Khh<>hhubh )<29><>}<7D>(h<05>(GENERATED FROM PYTHON SOURCE LINES 15-42<34>h]<5D>h<11>(GENERATED FROM PYTHON SOURCE LINES 15-42<34><32><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjUubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hh<>hhh&h'h(K!ubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05> Motivations<6E>h]<5D>h<11> Motivations<6E><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhhjfhhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hjchhh&h'h(K#ubhm)<29><>}<7D>(hX[Matrix multiplications are a key building block of most modern high-performance computing systems.
They are notoriously hard to optimize, hence their implementation is generally done by
hardware vendors themselves as part of so-called "kernel libraries" (e.g., cuBLAS).
Unfortunately, these libraries are often proprietary and cannot be easily customized
to accomodate the needs of modern deep learning workloads (e.g., fused activation functions).
In this tutorial, you will learn how to implement efficient matrix multiplications by
yourself with Triton, in a way that is easy to customize and extend.<2E>h]<5D>hX_Matrix multiplications are a key building block of most modern high-performance computing systems.
They are notoriously hard to optimize, hence their implementation is generally done by
hardware vendors themselves as part of so-called “kernel libraries” (e.g., cuBLAS).
Unfortunately, these libraries are often proprietary and cannot be easily customized
to accomodate the needs of modern deep learning workloads (e.g., fused activation functions).
In this tutorial, you will learn how to implement efficient matrix multiplications by
yourself with Triton, in a way that is easy to customize and extend.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjvhjthhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(K$hjchhubhm)<29><>}<7D>(h<05><>Roughly speaking, the kernel that we will write will implement the following blocked
algorithm to multiply a (M, K) by a (K, N) matrix:<3A>h]<5D>h<11><>Roughly speaking, the kernel that we will write will implement the following blocked
algorithm to multiply a (M, K) by a (K, N) matrix:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(K,hjchhubh <09> block_quote<74><65><EFBFBD>)<29><>}<7D>(hhh]<5D>h <09> literal_block<63><6B><EFBFBD>)<29><>}<7D>(hX<># 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;<3B>h]<5D>hX<># 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;<3B><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$<24>force<63><65><EFBFBD>language<67><65>python<6F><6E>highlight_args<67>}<7D>uh%j<>h&h'h(K/hj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%j<>hjchhh&Nh(Nubhm)<29><>}<7D>(h<05>gwhere each iteration of the doubly-nested for-loop is performed by a dedicated Triton program instance.<2E>h]<5D>h<11>gwhere each iteration of the doubly-nested for-loop is performed by a dedicated Triton program instance.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(K<hjchhubh )<29><>}<7D>(h<05>)GENERATED FROM PYTHON SOURCE LINES 44-137<33>h]<5D>h<11>)GENERATED FROM PYTHON SOURCE LINES 44-137<33><37><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hjchhh&h'h(K?ubeh}<7D>(h]<5D><> motivations<6E>ah]<5D>h]<5D><> motivations<6E>ah]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(K#ubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>Compute Kernel<65>h]<5D>h<11>Compute Kernel<65><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hj<>hhh&h'h(KAubhm)<29><>}<7D>(hXThe 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.<2E>h]<5D>(h<11><>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 <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05><>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 <20>hj<>hhh&Nh(Nubh <09>literal<61><6C><EFBFBD>)<29><>}<7D>(h<05> :code:`A`<60>h]<5D>h<11>A<><41><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>A<>hj<>ubah}<7D>(h]<5D>h]<5D><>code<64>ah]<5D>h]<5D>h!]<5D>uh%j<>hj<>ubh<11> and <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05> and <20>hj<>hhh&Nh(Nubj<62>)<29><>}<7D>(h<05> :code:`B`<60>h]<5D>h<11>B<><42><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>B<>hjubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj<>ubh<11>Y must be read in the inner loop. For that, we need
multi-dimensional pointer arithmetics.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>Y must be read in the inner loop. For that, we need
multi-dimensional pointer arithmetics.<2E>hj<>hhh&Nh(Nubeh}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(KChj<>hhubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>Pointer Arithmetics<63>h]<5D>h<11>Pointer Arithmetics<63><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj$hj"hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hjhhh&h'h(KIubhm)<29><>}<7D>(hX4For a row-major 2D tensor :code:`X`, the memory location of :code:`X[i, j]` is given b
y :code:`&X[i, j] = X + i*stride_xi + j*stride_xj`.
Therefore, blocks of pointers for :code:`A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]` and
:code:`B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]` can be defined in pseudo-code as:<3A>h]<5D>(h<11>For a row-major 2D tensor <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>For a row-major 2D tensor <20>hj0hhh&Nh(Nubj<62>)<29><>}<7D>(h<05> :code:`X`<60>h]<5D>h<11>X<><58><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>X<>hj9ubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj0ubh<11>, the memory location of <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>, the memory location of <20>hj0hhh&Nh(Nubj<62>)<29><>}<7D>(h<05>:code:`X[i, j]`<60>h]<5D>h<11>X[i, j]<5D><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>X[i, j]<5D>hjMubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj0ubh<11> is given b
y <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05> is given b
y <20>hj0hhh&Nh(Nubj<62>)<29><>}<7D>(h<05>0:code:`&X[i, j] = X + i*stride_xi + j*stride_xj`<60>h]<5D>h<11>(&X[i, j] = X + i*stride_xi + j*stride_xj<78><6A><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>(&X[i, j] = X + i*stride_xi + j*stride_xj<78>hjaubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj0ubh<11>$.
Therefore, blocks of pointers for <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>$.
Therefore, blocks of pointers for <20>hj0hhh&Nh(Nubj<62>)<29><>}<7D>(h<05>/:code:`A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]`<60>h]<5D>h<11>'A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]<5D><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>'A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K]<5D>hjuubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj0ubh<11> and
<EFBFBD><EFBFBD><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05> and
<EFBFBD>hj0hhh&Nh(Nubj<62>)<29><>}<7D>(h<05>1:code:`B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]`<60>h]<5D>h<11>)B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]<5D><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>)B[k : k+BLOCK_SIZE_K, n : n+BLOCK_SIZE_N]<5D>hj<>ubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj0ubh<11>" can be defined in pseudo-code as:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>" can be defined in pseudo-code as:<3A>hj0hhh&Nh(Nubeh}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(KKhjhhubj<62>)<29><>}<7D>(hhh]<5D>j<EFBFBD>)<29><>}<7D>(hX&A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K] = a_ptr + (m : m+BLOCK_SIZE_M)[:, None]*A.stride(0) + (k : k+BLOCK_SIZE_K)[None, :]*A.stride(1);
&B[k : k+BLOCK_SIZE_K, n:n+BLOCK_SIZE_N] = b_ptr + (k : k+BLOCK_SIZE_K)[:, None]*B.stride(0) + (n : n+BLOCK_SIZE_N)[None, :]*B.stride(1);<3B>h]<5D>hX&A[m : m+BLOCK_SIZE_M, k:k+BLOCK_SIZE_K] = a_ptr + (m : m+BLOCK_SIZE_M)[:, None]*A.stride(0) + (k : k+BLOCK_SIZE_K)[None, :]*A.stride(1);
&B[k : k+BLOCK_SIZE_K, n:n+BLOCK_SIZE_N] = b_ptr + (k : k+BLOCK_SIZE_K)[:, None]*B.stride(0) + (n : n+BLOCK_SIZE_N)[None, :]*B.stride(1);<3B><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>python<6F>j<EFBFBD>}<7D>uh%j<>h&h'h(KPhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%j<>hjhhh&Nh(Nubhm)<29><>}<7D>(h<05>dWhich means that pointers for blocks of A and B can be initialized (i.e., :code:`k=0`) in Triton as:<3A>h]<5D>(h<11>JWhich means that pointers for blocks of A and B can be initialized (i.e., <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>JWhich means that pointers for blocks of A and B can be initialized (i.e., <20>hj<>hhh&Nh(Nubj<62>)<29><>}<7D>(h<05> :code:`k=0`<60>h]<5D>h<11>k=0<><30><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>k=0<>hj<>ubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj<>ubh<11>) in Triton as:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>) in Triton as:<3A>hj<>hhh&Nh(Nubeh}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(KUhjhhubj<62>)<29><>}<7D>(hhh]<5D>j<EFBFBD>)<29><>}<7D>(hX1offs_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)<29>h]<5D>hX1offs_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)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>python<6F>j<EFBFBD>}<7D>uh%j<>h&h'h(KWhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%j<>hjhhh&Nh(Nubhm)<29><>}<7D>(h<05>.And then updated in the inner loop as follows:<3A>h]<5D>h<11>.And then updated in the inner loop as follows:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(K_hjhhubj<62>)<29><>}<7D>(hhh]<5D>j<EFBFBD>)<29><>}<7D>(h<05>?pa += BLOCK_SIZE_K * stride_ak;
pb += BLOCK_SIZE_K * stride_bk;<3B>h]<5D>h<11>?pa += BLOCK_SIZE_K * stride_ak;
pb += BLOCK_SIZE_K * stride_bk;<3B><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>python<6F>j<EFBFBD>}<7D>uh%j<>h&h'h(Kahjubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%j<>hjhhh&Nh(Nubeh}<7D>(h]<5D><>pointer-arithmetics<63>ah]<5D>h]<5D><>pointer arithmetics<63>ah]<5D>h!]<5D>uh%h<>hj<>hhh&h'h(KIubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>L2 Cache Optimizations<6E>h]<5D>h<11>L2 Cache Optimizations<6E><73><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj,hj*hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hj'hhh&h'h(Khubhm)<29><>}<7D>(hX0As 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<6E>h]<5D>(h<11>5As mentioned above, each program instance computes a <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>5As mentioned above, each program instance computes a <20>hj8hhh&Nh(Nubj<62>)<29><>}<7D>(h<05>$:code:`[BLOCK_SIZE_M, BLOCK_SIZE_N]`<60>h]<5D>h<11>[BLOCK_SIZE_M, BLOCK_SIZE_N]<5D><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>[BLOCK_SIZE_M, BLOCK_SIZE_N]<5D>hjAubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj8ubh<11>
block of <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>
block of <20>hj8hhh&Nh(Nubj<62>)<29><>}<7D>(h<05> :code:`C`<60>h]<5D>h<11>C<><43><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>C<>hjUubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj8ubh<11><>.
It is important to remember that the order in which these blocks are computed does
matter, since it affects the L2 cache hit rate of our program. and unfortunately, a
a simple row-major ordering<6E><67><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05><>.
It is important to remember that the order in which these blocks are computed does
matter, since it affects the L2 cache hit rate of our program. and unfortunately, a
a simple row-major ordering<6E>hj8hhh&Nh(Nubeh}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Kjhj'hhubj<62>)<29><>}<7D>(hhh]<5D>j<EFBFBD>)<29><>}<7D>(h<05><>pid = triton.program_id(0);
grid_m = (M + BLOCK_SIZE_M - 1) // BLOCK_SIZE_M;
grid_n = (N + BLOCK_SIZE_N - 1) // BLOCK_SIZE_N;
pid_m = pid / grid_n;
pid_n = pid % grid_n;<3B>h]<5D>h<11><>pid = triton.program_id(0);
grid_m = (M + BLOCK_SIZE_M - 1) // BLOCK_SIZE_M;
grid_n = (N + BLOCK_SIZE_N - 1) // BLOCK_SIZE_N;
pid_m = pid / grid_n;
pid_n = pid % grid_n;<3B><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjrubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>Python<6F>j<EFBFBD>}<7D>uh%j<>h&h'h(Kphjoubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%j<>hj'hhh&Nh(Nubhm)<29><>}<7D>(h<05>is just not going to cut it.<2E>h]<5D>h<11>is just not going to cut it.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Kxhj'hhubhm)<29><>}<7D>(h<05><>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:<3A>h]<5D>(h<11><>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 <20><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05><>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 <20>hj<>hhh&Nh(Nubj<62>)<29><>}<7D>(h<05>:code:`GROUP_M`<60>h]<5D>h<11>GROUP_M<5F><4D><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>GROUP_M<5F>hj<>ubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>uh%j<>hj<>ubh<11>* rows before
switching to the next column:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05>* rows before
switching to the next column:<3A>hj<>hhh&Nh(Nubeh}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Kzhj'hhubj<62>)<29><>}<7D>(hhh]<5D>j<EFBFBD>)<29><>}<7D>(hX&# 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<5F>h]<5D>hX&# 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<5F><6D><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>python<6F>j<EFBFBD>}<7D>uh%j<>h&h'h(K~hj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%j<>hj'hhh&Nh(Nubhm)<29><>}<7D>(hXFor 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.<2E>h]<5D>hXFor 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.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(K<>hj'hhubj<62>)<29><>}<7D>(hhh]<5D>h <09>image<67><65><EFBFBD>)<29><>}<7D>(h<05>-.. image:: grouped_vs_row_major_ordering.png
<EFBFBD>h]<5D>h}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D><>uri<72><69>;getting-started/tutorials/grouped_vs_row_major_ordering.png<6E><67>
candidates<EFBFBD>}<7D><>*<2A>j<EFBFBD>suh%j<>hj<>h&h'h(Kubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%j<>hj'hhh&Nh(Nubhm)<29><>}<7D>(h<05><>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).<2E>h]<5D>h<11><>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).<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(h<05><>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).<2E>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(K<>hj'hhubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 139-142<34>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 139-142<34><32><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj'hhh&h'h(K<>ubeh}<7D>(h]<5D><>l2-cache-optimizations<6E>ah]<5D>h]<5D><>l2 cache optimizations<6E>ah]<5D>h!]<5D>uh%h<>hj<>hhh&h'h(Khubeh}<7D>(h]<5D><>compute-kernel<65>ah]<5D>h]<5D><>compute kernel<65>ah]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(KAubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05> Final Result<6C>h]<5D>h<11> Final Result<6C><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj,hj*hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hj'hhh&h'h(K<>ubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 142-262<36>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 142-262<36><32><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj8ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj'hhh&h'h(K<>ubj<62>)<29><>}<7D>(hX<>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'],
)
# %
# We can now define our kernel as normal, using all the techniques presented above
@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
**meta,
):
"""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)
"""
# extract meta-parameters
BLOCK_SIZE_M = meta['BLOCK_SIZE_M']
BLOCK_SIZE_N = meta['BLOCK_SIZE_N']
BLOCK_SIZE_K = meta['BLOCK_SIZE_K']
GROUP_SIZE_M = 8
# -----------------------------------------------------------
# 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 meta['ACTIVATION']:
accumulator = meta['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)<29>h]<5D>hX<>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'],
)
# %
# We can now define our kernel as normal, using all the techniques presented above
@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
**meta,
):
"""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)
"""
# extract meta-parameters
BLOCK_SIZE_M = meta['BLOCK_SIZE_M']
BLOCK_SIZE_N = meta['BLOCK_SIZE_N']
BLOCK_SIZE_K = meta['BLOCK_SIZE_K']
GROUP_SIZE_M = 8
# -----------------------------------------------------------
# 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 meta['ACTIVATION']:
accumulator = meta['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)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjFubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>default<6C>j<EFBFBD>}<7D>uh%j<>h&h'h(K<>hj'hhubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 263-265<36>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 263-265<36><35><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjVubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj'hhh&h'h(M(ubhm)<29><>}<7D>(h<05><>We can now create a convenience wrapper function that only takes two input tensors
and (1) checks any shape constraint; (2) allocates the output; (3) launches the above kernel<65>h]<5D>h<11><>We can now create a convenience wrapper function that only takes two input tensors
and (1) checks any shape constraint; (2) allocates the output; (3) launches the above kernel<65><6C><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjfhjdhhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(M)hj'hhubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 265-294<39>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 265-294<39><34><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjrubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj'hhh&h'h(M-ubj<62>)<29><>}<7D>(hXmdef 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<>h]<5D>hXmdef 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<><63><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>default<6C>j<EFBFBD>}<7D>uh%j<>h&h'h(M.hj'hhubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 295-299<39>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 295-299<39><39><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj'hhh&h'h(MUubeh}<7D>(h]<5D><> final-result<6C>ah]<5D>h]<5D><> final result<6C>ah]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(K<>ubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05> Unit Test<73>h]<5D>h<11> Unit Test<73><74><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hj<>hhh&h'h(MWubhm)<29><>}<7D>(h<05>kWe can test our custom matrix multiplication operation against a native torch implementation (i.e., cuBLAS)<29>h]<5D>h<11>kWe can test our custom matrix multiplication operation against a native torch implementation (i.e., cuBLAS)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(MYhj<>hhubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 299-312<31>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 299-312<31><32><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj<>hhh&h'h(M\ubj<62>)<29><>}<7D>(hX<>torch.manual_seed(0)
a = torch.randn((512, 512), device='cuda', dtype=torch.float16)
b = torch.randn((512, 512), device='cuda', dtype=torch.float16)
triton_output = matmul(a, b, activation=None)
torch_output = torch.matmul(a, b)
print(f"triton_output={triton_output}")
print(f"torch_output={torch_output}")
if triton.testing.allclose(triton_output, torch_output):
print("✅ Triton and Torch match")
else:
print("❌ Triton and Torch differ")<29>h]<5D>hX<>torch.manual_seed(0)
a = torch.randn((512, 512), device='cuda', dtype=torch.float16)
b = torch.randn((512, 512), device='cuda', dtype=torch.float16)
triton_output = matmul(a, b, activation=None)
torch_output = torch.matmul(a, b)
print(f"triton_output={triton_output}")
print(f"torch_output={torch_output}")
if triton.testing.allclose(triton_output, torch_output):
print("✅ Triton and Torch match")
else:
print("❌ Triton and Torch differ")<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>default<6C>j<EFBFBD>}<7D>uh%j<>h&h'h(M]hj<>hhubhm)<29><>}<7D>(h<05>Out:<3A>h]<5D>h<11>Out:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<>hj<>hhh&Nh(Nubah}<7D>(h]<5D>h]<5D><>sphx-glr-script-out<75>ah]<5D>h]<5D>h!]<5D>uh%hlh&h'h(Mrhj<>hhubj<62>)<29><>}<7D>(hX;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<63>h]<5D>hX;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<63><68><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhj<>ubah}<7D>(h]<5D>h]<5D>j<EFBFBD>ah]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>none<6E>j<EFBFBD>}<7D>uh%j<>h&h'h(Mthj<>hhubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 313-319<31>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 313-319<31><39><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj<>hhh&h'h(M<>ubeh}<7D>(h]<5D><> unit-test<73>ah]<5D>h]<5D><> unit test<73>ah]<5D>h!]<5D>uh%h<>hh<>hhh&h'h(MWubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05> Benchmark<72>h]<5D>h<11> Benchmark<72><6B><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjhjhhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hjhhh&h'h(M<>ubh<62>)<29><>}<7D>(hhh]<5D>(h<>)<29><>}<7D>(h<05>Square Matrix Performance<63>h]<5D>h<11>Square Matrix Performance<63><65><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj.hj,hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%h<>hj)hhh&h'h(M<>ubhm)<29><>}<7D>(h<05><>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.<2E>h]<5D>h<11><>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.<2E><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hj<hj:hhh&Nh(Nubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>uh%hlh&h'h(M<>hj)hhubh )<29><>}<7D>(h<05>*GENERATED FROM PYTHON SOURCE LINES 319-360<36>h]<5D>h<11>*GENERATED FROM PYTHON SOURCE LINES 319-360<36><30><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjHubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$uh%h
hj)hhh&h'h(M<>ubj<62>)<29><>}<7D>(hX<>@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)<29>h]<5D>hX<>@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)<29><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hhhjVubah}<7D>(h]<5D>h]<5D>h]<5D>h]<5D>h!]<5D>h#h$j<><00>j<EFBFBD><00>default<6C>j<EFBFBD>}<7D>uh%j<>h&h'h(M<>hj)hhubj<62>)<29><>}<7D>(h<05><>.. image:: /getting-started/tutorials/images/sphx_glr_03-matrix-multiplication_001.png
:alt: 03 matrix multiplication
:class: sphx-glr-single-img
<EFBFBD>h]<5D>h}<7D>(h]<5D>h]<5D><>sphx-glr-single-img<6D>ah]<5D>h]<5D>h!]<5D><>alt<6C><74>03 matrix multiplication<6F><6E>uri<72><69>Jgetting-started/tutorials/images/sphx_glr_03-matrix-multiplication_001.png<6E>j<EFBFBD>}<7D>j<EFBFBD>jtsuh%j<>hj)hhh&h'h(Nubhm)<29><>}<7D>(h<05>Out:<3A>h]<5D>h<11>Out:<3A><><EFBFBD><EFBFBD><EFBFBD>}<7D>(hjxhjvhhh&Nh(Nubah}<7D>(h]<5D>h]<5D><>sphx-glr-script-out<75>ah]<5D>h]<5D>h!]<5D>uh%hlh&h'h(M<>hj)hhubj<62>)<29><>}<7D>(hX<>matmul-performance:
M cuBLAS ... Triton Triton (+ LeakyReLU)
[GH-PAGES] Updated website
2022-02-16 00:38:53 +00:00
0 256.0 2.730667 ... 2.978909 2.978909
1 384.0 7.372800 ... 7.899428 7.899428
[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
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
[GH-PAGES] Updated website
2022-02-13 00:39:42 +00:00
5 896.0 39.025776 ... 40.140799 39.025776
6 1024.0 51.150050 ... 53.773130 52.428801
[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
7 1152.0 45.242181 ... 46.656000 46.656000
[GH-PAGES] Updated website
2022-02-14 00:38:35 +00:00
8 1280.0 51.200001 ... 56.888887 56.888887
9 1408.0 64.138541 ... 67.305878 67.305878
[GH-PAGES] Updated website
2022-02-16 00:38:53 +00:00
10 1536.0 80.430545 ... 79.526831 79.526831
[GH-PAGES] Updated website
2022-02-15 00:41:00 +00:00
11 1664.0 62.929456 ... 62.492442 62.061463
[GH-PAGES] Updated website
2022-02-16 00:38:53 +00:00
12 1792.0 72.512412 ... 72.512412 71.588687
13 1920.0 69.467336 ... 70.172588 70.172588
14 2048.0 73.908442 ... 76.959706 76.608294
15 2176.0 83.500614 ... 86.367588 85.632545
16 2304.0 68.446623 ... 77.057651 76.563695
17 2432.0 71.487187 ... 85.393507 84.877538
18 2560.0 78.019048 ... 80.709358 80.511054
19 2688.0 83.186525 ... 89.888756 89.464755
20 2816.0 83.392363 ... 83.074685 82.602666
21 2944.0 82.509987 ... 82.509987 81.967162
22 3072.0 81.825298 ... 88.612060 87.651868
23 3200.0 82.262212 ... 94.674553 94.256261
24 3328.0 82.275764 ... 83.905938 83.613586
25 3456.0 81.518262 ... 84.954233 88.497878
26 3584.0 86.540320 ... 97.840469 98.160909
27 3712.0 85.970176 ... 87.860458 84.017953
28 3840.0 84.356981 ... 89.548180 86.467555
29 3968.0 85.934238 ... 90.960819 86.726322
30 4096.0 93.077479 ... 92.309303 85.270056
[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
[31 rows x 5 columns]<5D>h]<5D>hX<>matmul-performance:
M cuBLAS ... Triton Triton (+ LeakyReLU)
[GH-PAGES] Updated website
2022-02-16 00:38:53 +00:00
0 256.0 2.730667 ... 2.978909 2.978909
1 384.0 7.372800 ... 7.899428 7.899428
[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
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
[GH-PAGES] Updated website
2022-02-13 00:39:42 +00:00
5 896.0 39.025776 ... 40.140799 39.025776
6 1024.0 51.150050 ... 53.773130 52.428801
[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
7 1152.0 45.242181 ... 46.656000 46.656000
[GH-PAGES] Updated website
2022-02-14 00:38:35 +00:00
8 1280.0 51.200001 ... 56.888887 56.888887
9 1408.0 64.138541 ... 67.305878 67.305878
[GH-PAGES] Updated website
2022-02-16 00:38:53 +00:00
10 1536.0 80.430545 ... 79.526831 79.526831
[GH-PAGES] Updated website
2022-02-15 00:41:00 +00:00
11 1664.0 62.929456 ... 62.492442 62.061463
[GH-PAGES] Updated website
2022-02-16 00:38:53 +00:00
12 1792.0 72.512412 ... 72.512412 71.588687
13 1920.0 69.467336 ... 70.172588 70.172588
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[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
[GH-PAGES] Updated website
2022-02-16 00:38:53 +00:00
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[GH-PAGES] Updated website
2022-02-09 07:15:50 +00:00
:download:`Download Python source code: 03-matrix-multiplication.py <03-matrix-multiplication.py>`
.. container:: sphx-glr-download sphx-glr-download-jupyter
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