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+"""
+Vector Addition
+=================
+In this tutorial, we will see how to construct a simple, high-performance vector addition using Triton. You will learn:
+* The basic syntax of the Triton programming language
+* The best practices for creating PyTorch custom operators using the `triton.kernel` Python API
+* The best practices for validating and benchmarking custom ops against native reference implementations
+"""
+
+# %%
+# Writing the Compute Kernel
+# --------------------------
+#
+# Each compute kernel is declared using the `__global__` attribute, and executed many times in parallel
+# on different chunks of data (See the [Single Program, Multiple Data](https://en.wikipedia.org/wiki/SPMD)
+# programming model for more details).
+# .. code-block:: c
+#   :linenos:
+#   __global__ void add(float* z, float* x, float* y, int N){
+#       // The `get_program_id(i)` returns the i-th coordinate
+#       // of the program in the overaching SPMD context
+#       // (a.k.a launch grid). This is what allows us to process
+#       // different chunks of data in parallel.
+#       // For those similar with CUDA, `get_program_id({0,1,2})`
+#       // is similar to blockIdx.{x,y,z}
+#       int pid = get_program_id(0);
+#       // In Triton, arrays are first-class citizen. In other words,
+#       // they are primitives data-types and are -- contrary to C and
+#       // CUDA -- not implemented as pointers to contiguous chunks of
+#       // memory.
+#       // In the few lines below, we create an array of `BLOCK` pointers
+#       // whose memory values are, e.g.:
+#       // [z + pid*BLOCK + 0, z + pid*BLOCK + 1, ..., z + pid*BLOCK + BLOCK - 1]
+#       // Note: here BLOCK is expected to be a pre-processor macro defined at compile-time
+#       int offset[BLOCK] = pid * BLOCK + 0 ... BLOCK;
+#       float* pz [BLOCK] = z + offset;
+#       float* px [BLOCK] = x + offset;
+#       float* py [BLOCK] = y + offset;
+#       // Simple element-wise control-flow for load/store operations can
+#       // be achieved using the the ternary operator `cond ? val_true : val_false`
+#       // or the conditional dereferencing operator `*?(cond)ptr
+#       // Here, we make sure that we do not access memory out-of-bounds when we
+#       // write-back `z`
+#       bool check[BLOCK] = offset < N;
+#       *?(check)pz = *?(check)px + *?(check)py;
+#   }
+# ```
+# The existence of arrays as a primitive data-type for Triton comes with a number of advantages that are highlighted in the [MAPL'2019 Triton paper](http://www.eecs.harvard.edu/~htk/publication/2019-mapl-tillet-kung-cox.pdf).
+
+# %%
+# Writing the Torch bindings
+# --------------------------
+# The only thing that matters when it comes to Triton and Torch is the `triton.kernel` class. This allows you to transform the above C-like function into a callable python object that can be used to modify `torch.tensor` objects.
+#
+# To create a `triton.kernel`, you only need three things:
+# - `source: string`: the source-code of the kernel you want to create
+# - `device: torch.device`: the device you want to compile this code for
+# - `defines: dict`: the set of macros that you want the pre-processor to `#define` for you
+
+import torch
+import triton
+
+# %%
+# source-code for Triton compute kernel
+# here we just copy-paste the above code without the extensive comments.
+# you may prefer to store it in a .c file and load it from there instead.
+
+_src = """
+__global__ void add(float* z, float* x, float* y, int N){
+    // program id
+    int pid = get_program_id(0);
+    // create arrays of pointers
+    int offset[BLOCK] = pid * BLOCK + 0 ... BLOCK;
+    float* pz[BLOCK] = z + offset;
+    float* px[BLOCK] = x + offset;
+    float* py[BLOCK] = y + offset;
+    // bounds checking
+    bool check[BLOCK] = offset < N;
+    // write-back
+    *?(check)pz = *?(check)px + *?(check)py;
+}
+    """
+
+# %%
+# This function returns a callable `triton.kernel` object
+# created from the above source code.
+# For portability, we maintain a cache of kernels for different `torch.device`
+# We compile the kernel with -DBLOCK=1024
+
+
+def make_add_kernel(device):
+    cache = make_add_kernel.cache
+    if device not in cache:
+        defines = {'BLOCK': 1024}
+        cache[device] = triton.kernel(_src, device=device, defines=defines)
+    return cache[device]
+
+
+make_add_kernel.cache = dict()
+
+# %%
+# This is a standard torch custom autograd Function
+# The only difference is that we can now use the above kernel
+# in the `forward` and `backward` functions.`
+
+
+class _add(torch.autograd.Function):
+    @staticmethod
+    def forward(ctx, x, y):
+        # constraints of the op
+        assert x.dtype == torch.float32
+        # *allocate output*
+        z = torch.empty_like(x)
+        # *create launch grid*:
+        # this is a function which takes compilation parameters `opt`
+        # as input and returns a tuple of int (i.e., launch grid) for the kernel.
+        # triton.cdiv is a shortcut for ceil division:
+        # triton.cdiv(a, b) = (a + b - 1) // b
+        N = z.shape[0]
+        grid = lambda opt: (triton.cdiv(N, opt.BLOCK), )
+        # *launch kernel*:
+        # pointer to the data of torch tensors can be retrieved with
+        # the `.data_ptr()` method
+        kernel = make_add_kernel(z.device)
+        kernel(z.data_ptr(), x.data_ptr(), y.data_ptr(), N, grid=grid)
+        return z
+
+
+# %%
+# Just like we standard PyTorch ops
+# We use the `.apply` method to create a
+# callable object for our function
+add = _add.apply
+
+# %%
+# Writing a Unit Test
+# --------------------------
+torch.manual_seed(0)
+x = torch.rand(98432, device='cuda')
+y = torch.rand(98432, device='cuda')
+za = x + y
+zb = add(x, y)
+print(za)
+print(zb)
+print(f'The maximum difference between torch and triton is ' f'{torch.max(torch.abs(za - zb))}')
+
+# %%
+# Writing a Benchmark
+# --------------------------
+# We can now benchmark our custom op for vectors of increasing sizes to get a sense of how it does
+
+warmup = 10
+rep = 200
+for N in [2**i for i in range(17, 26, 1)]:
+    x = torch.rand(N, device='cuda')
+    y = torch.rand(N, device='cuda')
+    triton_ms = triton.testing.do_bench(lambda: add(x, y), warmup=warmup, rep=rep)
+    torch_ms = triton.testing.do_bench(lambda: x + y, warmup=warmup, rep=rep)
+    # print the performance of triton and torch as well as the achieved bandwidth
+    print(f'{N} {triton_ms:.3f} {torch_ms:.3f}')
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