"""
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.
In doing so, 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'))
# Subtract maximum for numerical stability
row_minus_max = row - tl.max(row, axis=0)
# Note that exponentiation in Triton is 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)
quantiles = [0.5, 0.2, 0.8]
if provider == 'torch-native':
ms, min_ms, max_ms = triton.testing.do_bench(lambda: torch.softmax(x, axis=-1), quantiles=quantiles)
if provider == 'triton':
ms, min_ms, max_ms = triton.testing.do_bench(lambda: softmax(x), quantiles=quantiles)
if provider == 'torch-jit':
ms, min_ms, max_ms = triton.testing.do_bench(lambda: naive_softmax(x), quantiles=quantiles)
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 work on tensors of any shape.