371 lines
14 KiB
ReStructuredText
371 lines
14 KiB
ReStructuredText
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.. DO NOT EDIT.
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.. THIS FILE WAS AUTOMATICALLY GENERATED BY SPHINX-GALLERY.
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.. TO MAKE CHANGES, EDIT THE SOURCE PYTHON FILE:
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.. "getting-started/tutorials/05-layer-norm.py"
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.. LINE NUMBERS ARE GIVEN BELOW.
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.. only:: html
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.. note::
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:class: sphx-glr-download-link-note
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Click :ref:`here <sphx_glr_download_getting-started_tutorials_05-layer-norm.py>`
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to download the full example code
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.. rst-class:: sphx-glr-example-title
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.. _sphx_glr_getting-started_tutorials_05-layer-norm.py:
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Layer Normalization
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====================
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.. GENERATED FROM PYTHON SOURCE LINES 5-262
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.. image:: /getting-started/tutorials/images/sphx_glr_05-layer-norm_001.png
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:alt: 05 layer norm
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:class: sphx-glr-single-img
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.. rst-class:: sphx-glr-script-out
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Out:
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.. code-block:: none
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layer-norm-backward:
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N Triton Torch Apex
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0 1024.0 311.088617 98.303995 307.200008
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1 1536.0 347.773587 134.050910 344.523365
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2 2048.0 420.102553 161.684218 334.367350
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3 2560.0 455.111129 181.775141 328.556154
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4 3072.0 511.999982 192.501302 321.956335
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5 3584.0 547.872604 208.271186 311.652167
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6 4096.0 568.231237 220.412561 297.890900
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7 4608.0 504.986315 233.316456 287.251954
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8 5120.0 527.381977 242.845844 285.104413
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9 5632.0 545.032265 243.545956 289.438969
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10 6144.0 546.133354 248.661056 286.322318
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11 6656.0 534.260858 256.000009 286.279570
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12 7168.0 505.976473 260.654538 286.242939
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13 7680.0 482.513091 262.564106 279.272719
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14 8192.0 463.698115 267.493874 284.526763
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15 8704.0 418.629245 267.815384 284.987724
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16 9216.0 432.845409 272.394084 288.751954
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17 9728.0 438.857162 280.446849 290.027323
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18 10240.0 449.287041 286.767793 290.840246
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19 10752.0 426.525614 247.172406 290.922209
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20 11264.0 427.071098 245.760001 286.676558
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21 11776.0 423.724129 249.888595 288.981596
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22 12288.0 420.102570 254.673582 294.617366
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23 12800.0 413.458944 253.674644 288.450715
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24 13312.0 411.711355 252.759501 289.916513
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25 13824.0 405.594132 257.390218 292.056329
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26 14336.0 395.021816 254.297107 286.719986
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27 14848.0 386.498925 257.665934 289.246765
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28 15360.0 373.117425 257.970599 287.326580
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29 15872.0 371.274849 261.806182 289.899545
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.. code-block:: default
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import torch
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import triton
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import triton.language as tl
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try:
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# This is https://github.com/NVIDIA/apex, NOT the apex on PyPi, so it
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# should not be added to extras_require in setup.py.
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import apex
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HAS_APEX = True
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except ModuleNotFoundError:
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HAS_APEX = False
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# Forward Pass
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@triton.jit
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def _layer_norm_fwd_fused(X, Y, W, B, M, V, stride, N, eps,
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BLOCK_SIZE: tl.constexpr):
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# position of elements processed by this program
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row = tl.program_id(0)
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cols = tl.arange(0, BLOCK_SIZE)
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mask = cols < N
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# offset data pointers to start at the row of interest
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X += row * stride
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Y += row * stride
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# load data and cast to float32
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x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
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# compute mean
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mean = tl.sum(x, axis=0) / N
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# compute std
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xmean = tl.where(mask, x - mean, 0.)
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var = tl.sum(xmean * xmean, axis=0) / N
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rstd = 1 / tl.sqrt(var + eps)
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xhat = xmean * rstd
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# write-back mean/rstd
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tl.store(M + row, mean)
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tl.store(V + row, rstd)
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# multiply by weight and add bias
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w = tl.load(W + cols, mask=mask)
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b = tl.load(B + cols, mask=mask)
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y = xhat * w + b
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# write-back
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tl.store(Y + cols, y, mask=mask)
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# Backward pass (DX + partial DW + partial DB)
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@triton.jit
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def _layer_norm_bwd_dx_fused(DX, DY, DW, DB, X, W, B, M, V, Lock, stride, N, eps,
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GROUP_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr):
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# position of elements processed by this program
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row = tl.program_id(0)
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cols = tl.arange(0, BLOCK_SIZE_N)
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mask = cols < N
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# offset data pointers to start at the row of interest
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X += row * stride
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DY += row * stride
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DX += row * stride
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# offset locks and weight/bias gradient pointer
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# each kernel instance accumulates partial sums for
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# DW and DB into one of GROUP_SIZE_M independent buffers
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# these buffers stay in the L2, which allow this kernel
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# to be fast
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lock_id = row % GROUP_SIZE_M
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Lock += lock_id
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Count = Lock + GROUP_SIZE_M
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DW = DW + lock_id * N + cols
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DB = DB + lock_id * N + cols
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# load data to SRAM
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x = tl.load(X + cols, mask=mask, other=0).to(tl.float32)
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dy = tl.load(DY + cols, mask=mask, other=0).to(tl.float32)
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w = tl.load(W + cols, mask=mask).to(tl.float32)
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mean = tl.load(M + row)
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rstd = tl.load(V + row)
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# compute dx
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xhat = (x - mean) * rstd
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wdy = w * dy
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xhat = tl.where(mask, xhat, 0.)
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wdy = tl.where(mask, wdy, 0.)
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mean1 = tl.sum(xhat * wdy, axis=0) / N
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mean2 = tl.sum(wdy, axis=0) / N
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dx = (wdy - (xhat * mean1 + mean2)) * rstd
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# write-back dx
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tl.store(DX + cols, dx, mask=mask)
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# accumulate partial sums for dw/db
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partial_dw = (dy * xhat).to(w.dtype)
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partial_db = (dy).to(w.dtype)
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while tl.atomic_cas(Lock, 0, 1) == 1:
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pass
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count = tl.load(Count)
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# first store doesn't accumulate
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if count == 0:
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tl.atomic_xchg(Count, 1)
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else:
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partial_dw += tl.load(DW, mask=mask)
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partial_db += tl.load(DB, mask=mask)
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tl.store(DW, partial_dw, mask=mask)
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tl.store(DB, partial_db, mask=mask)
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# release lock
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tl.atomic_xchg(Lock, 0)
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# Backward pass (total DW + total DB)
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@triton.jit
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def _layer_norm_bwd_dwdb(DW, DB, FINAL_DW, FINAL_DB, M, N,
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BLOCK_SIZE_M: tl.constexpr, BLOCK_SIZE_N: tl.constexpr):
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pid = tl.program_id(0)
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cols = pid * BLOCK_SIZE_N + tl.arange(0, BLOCK_SIZE_N)
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dw = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
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db = tl.zeros((BLOCK_SIZE_M, BLOCK_SIZE_N), dtype=tl.float32)
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for i in range(0, M, BLOCK_SIZE_M):
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rows = i + tl.arange(0, BLOCK_SIZE_M)
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mask = (rows[:, None] < M) & (cols[None, :] < N)
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offs = rows[:, None] * N + cols[None, :]
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dw += tl.load(DW + offs, mask=mask, other=0.)
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db += tl.load(DB + offs, mask=mask, other=0.)
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sum_dw = tl.sum(dw, axis=0)
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sum_db = tl.sum(db, axis=0)
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tl.store(FINAL_DW + cols, sum_dw, mask=cols < N)
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tl.store(FINAL_DB + cols, sum_db, mask=cols < N)
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class LayerNorm(torch.autograd.Function):
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@staticmethod
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def forward(ctx, x, normalized_shape, weight, bias, eps):
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# allocate output
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y = torch.empty_like(x)
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# reshape input data into 2D tensor
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x_arg = x.reshape(-1, x.shape[-1])
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M, N = x_arg.shape
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mean = torch.empty((M, ), dtype=torch.float32, device='cuda')
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rstd = torch.empty((M, ), dtype=torch.float32, device='cuda')
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# Less than 64KB per feature: enqueue fused kernel
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MAX_FUSED_SIZE = 65536 // x.element_size()
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BLOCK_SIZE = min(MAX_FUSED_SIZE, triton.next_power_of_2(N))
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if N > BLOCK_SIZE:
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raise RuntimeError("This layer norm doesn't support feature dim >= 64KB.")
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# heuristics for number of warps
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num_warps = min(max(BLOCK_SIZE // 256, 1), 8)
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# enqueue kernel
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_layer_norm_fwd_fused[(M,)](x_arg, y, weight, bias, mean, rstd,
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x_arg.stride(0), N, eps,
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BLOCK_SIZE=BLOCK_SIZE, num_warps=num_warps)
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ctx.save_for_backward(x, weight, bias, mean, rstd)
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ctx.BLOCK_SIZE = BLOCK_SIZE
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ctx.num_warps = num_warps
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ctx.eps = eps
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return y
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@staticmethod
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def backward(ctx, dy):
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x, w, b, m, v = ctx.saved_tensors
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# heuristics for amount of parallel reduction stream for DG/DB
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N = w.shape[0]
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GROUP_SIZE_M = 64
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if N <= 8192: GROUP_SIZE_M = 96
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if N <= 4096: GROUP_SIZE_M = 128
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if N <= 1024: GROUP_SIZE_M = 256
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# allocate output
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locks = torch.zeros(2 * GROUP_SIZE_M, dtype=torch.int32, device='cuda')
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_dw = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device)
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_db = torch.empty((GROUP_SIZE_M, w.shape[0]), dtype=x.dtype, device=w.device)
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dw = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device)
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db = torch.empty((w.shape[0],), dtype=w.dtype, device=w.device)
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dx = torch.empty_like(dy)
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# enqueue kernel using forward pass heuristics
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# also compute partial sums for DW and DB
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x_arg = x.reshape(-1, x.shape[-1])
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M, N = x_arg.shape
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_layer_norm_bwd_dx_fused[(M,)](dx, dy, _dw, _db, x, w, b, m, v, locks,
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x_arg.stride(0), N, ctx.eps,
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BLOCK_SIZE_N=ctx.BLOCK_SIZE,
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GROUP_SIZE_M=GROUP_SIZE_M,
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num_warps=ctx.num_warps)
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grid = lambda meta: [triton.cdiv(N, meta['BLOCK_SIZE_N'])]
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# accumulate partial sums in separate kernel
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_layer_norm_bwd_dwdb[grid](_dw, _db, dw, db, GROUP_SIZE_M, N,
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BLOCK_SIZE_M=32,
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BLOCK_SIZE_N=128)
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return dx, None, dw, db, None
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layer_norm = LayerNorm.apply
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def test_layer_norm(M, N, dtype, eps=1e-5, device='cuda'):
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# create data
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x_shape = (M, N)
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w_shape = (x_shape[-1], )
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weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)
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bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)
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x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda')
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dy = .1 * torch.randn_like(x)
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x.requires_grad_(True)
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# forward pass
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y_tri = layer_norm(x, w_shape, weight, bias, eps)
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y_ref = torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps).to(dtype)
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# backward pass (triton)
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y_tri.backward(dy, retain_graph=True)
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dx_tri, dw_tri, db_tri = [_.grad.clone() for _ in [x, weight, bias]]
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x.grad, weight.grad, bias.grad = None, None, None
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# backward pass (torch)
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y_ref.backward(dy, retain_graph=True)
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dx_ref, dw_ref, db_ref = [_.grad.clone() for _ in [x, weight, bias]]
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# compare
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triton.testing.assert_almost_equal(y_tri, y_ref)
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triton.testing.assert_almost_equal(dx_tri, dx_ref)
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triton.testing.assert_almost_equal(db_tri, db_ref, decimal=1)
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triton.testing.assert_almost_equal(dw_tri, dw_ref, decimal=1)
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@triton.testing.perf_report(
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triton.testing.Benchmark(
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x_names=['N'],
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x_vals=[512 * i for i in range(2, 32)],
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line_arg='provider',
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line_vals=['triton', 'torch'] + (['apex'] if HAS_APEX else []),
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line_names=['Triton', 'Torch'] + (['Apex'] if HAS_APEX else []),
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styles=[('blue', '-'), ('green', '-'), ('orange', '-')],
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ylabel='GB/s',
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plot_name='layer-norm-backward',
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args={'M': 4096, 'dtype': torch.float16, 'mode': 'backward'}
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)
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)
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def bench_layer_norm(M, N, dtype, provider, mode='backward', eps=1e-5, device='cuda'):
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# create data
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x_shape = (M, N)
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w_shape = (x_shape[-1], )
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weight = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)
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bias = torch.rand(w_shape, dtype=dtype, device='cuda', requires_grad=True)
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x = -2.3 + 0.5 * torch.randn(x_shape, dtype=dtype, device='cuda')
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dy = .1 * torch.randn_like(x)
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x.requires_grad_(True)
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# utility functions
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if provider == 'triton':
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y_fwd = lambda: layer_norm(x, w_shape, weight, bias, eps)
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if provider == 'torch':
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y_fwd = lambda: torch.nn.functional.layer_norm(x, w_shape, weight, bias, eps)
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if provider == 'apex':
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apex_layer_norm = apex.normalization.FusedLayerNorm(w_shape).to(x.device).to(x.dtype)
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y_fwd = lambda: apex_layer_norm(x)
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# forward pass
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if mode == 'forward':
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gbps = lambda ms: 2 * x.numel() * x.element_size() / ms * 1e-6
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ms, min_ms, max_ms = triton.testing.do_bench(y_fwd, rep=500)
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# backward pass
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if mode == 'backward':
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gbps = lambda ms: 3 * x.numel() * x.element_size() / ms * 1e-6
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y = y_fwd()
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ms, min_ms, max_ms = triton.testing.do_bench(lambda: y.backward(dy, retain_graph=True),
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grad_to_none=[x], rep=500)
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return gbps(ms), gbps(max_ms), gbps(min_ms)
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bench_layer_norm.run(save_path='.', print_data=True)
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.. rst-class:: sphx-glr-timing
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**Total running time of the script:** ( 2 minutes 12.386 seconds)
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.. _sphx_glr_download_getting-started_tutorials_05-layer-norm.py:
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.. only :: html
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.. container:: sphx-glr-footer
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:class: sphx-glr-footer-example
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.. container:: sphx-glr-download sphx-glr-download-python
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:download:`Download Python source code: 05-layer-norm.py <05-layer-norm.py>`
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.. container:: sphx-glr-download sphx-glr-download-jupyter
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:download:`Download Jupyter notebook: 05-layer-norm.ipynb <05-layer-norm.ipynb>`
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.. only:: html
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.. rst-class:: sphx-glr-signature
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`Gallery generated by Sphinx-Gallery <https://sphinx-gallery.github.io>`_
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