├── LICENSE ├── README.md ├── main.cpp ├── matmult.cu └── train.py /LICENSE: -------------------------------------------------------------------------------- 1 | Apache License 2 | Version 2.0, January 2004 3 | http://www.apache.org/licenses/ 4 | 5 | TERMS AND CONDITIONS FOR USE, REPRODUCTION, AND DISTRIBUTION 6 | 7 | 1. Definitions. 8 | 9 | "License" shall mean the terms and conditions for use, reproduction, 10 | and distribution as defined by Sections 1 through 9 of this document. 11 | 12 | "Licensor" shall mean the copyright owner or entity authorized by 13 | the copyright owner that is granting the License. 14 | 15 | "Legal Entity" shall mean the union of the acting entity and all 16 | other entities that control, are controlled by, or are under common 17 | control with that entity. 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We also recommend that a 185 | file or class name and description of purpose be included on the 186 | same "printed page" as the copyright notice for easier 187 | identification within third-party archives. 188 | 189 | Copyright [yyyy] [name of copyright owner] 190 | 191 | Licensed under the Apache License, Version 2.0 (the "License"); 192 | you may not use this file except in compliance with the License. 193 | You may obtain a copy of the License at 194 | 195 | http://www.apache.org/licenses/LICENSE-2.0 196 | 197 | Unless required by applicable law or agreed to in writing, software 198 | distributed under the License is distributed on an "AS IS" BASIS, 199 | WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. 200 | See the License for the specific language governing permissions and 201 | limitations under the License. 202 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # mixed-precision-from-scratch 2 | 3 | This is an educational repo that exposes all the details of mixed 4 | precision training. I apply it to accelerate training on a 2-layer 5 | MLP, using a rewritten matmult call with CUDA (`matmult.cu`) to demonstrate clearly 6 | where the acceleration is coming from. 7 | 8 | To compare single precision vs. mixed precision training, run: 9 | 10 | ```bash 11 | python train.py false 12 | python train.py true 13 | ``` 14 | 15 | to get something like this: 16 | ```bash 17 | $ python train.py false 18 | device: cuda, mixed precision training: False (torch.float32) 19 | model memory: 26.05 MB 20 | act/grad memory: 1100.45 MB 21 | total memory: 1126.50 MB 22 | 1: loss 2.327, time: 139.196ms 23 | 2: loss 2.237, time: 16.598ms 24 | 3: loss 2.175, time: 16.179ms 25 | 4: loss 2.117, time: 16.206ms 26 | 5: loss 2.058, time: 16.187ms 27 | 6: loss 2.006, time: 16.207ms 28 | 7: loss 1.948, time: 16.304ms 29 | avg: 16.280ms 30 | $ python train.py true 31 | device: cuda, mixed precision training: True (torch.float16) 32 | model memory: 39.08 MB 33 | act/grad memory: 563.25 MB 34 | total memory: 602.33 MB 35 | 1: loss 2.328, time: 170.039ms 36 | 2: loss 2.236, time: 8.513ms 37 | 3: loss 2.176, time: 8.440ms 38 | 4: loss 2.117, time: 8.356ms 39 | 5: loss 2.059, time: 8.133ms 40 | 6: loss 2.006, time: 8.370ms 41 | 7: loss 1.948, time: 8.402ms 42 | avg: 8.369ms 43 | ``` 44 | 45 | Read my [blog](https://tspeterkim.github.io/posts/mixed-precision-from-scratch) for more details. 46 | -------------------------------------------------------------------------------- /main.cpp: -------------------------------------------------------------------------------- 1 | #include 2 | 3 | void matmult(torch::Tensor A, torch::Tensor B, torch::Tensor C, bool transpose_A, bool transpose_B, float alpha, float beta); 4 | 5 | PYBIND11_MODULE(TORCH_EXTENSION_NAME, m) { 6 | m.def("matmult", torch::wrap_pybind_function(matmult), "matmult"); 7 | } -------------------------------------------------------------------------------- /matmult.cu: -------------------------------------------------------------------------------- 1 | #include 2 | #include 3 | #include 4 | #include 5 | #include 6 | #include 7 | 8 | // TODO: is there a better way to get the handle? 9 | cublasHandle_t get_handle() { 10 | return at::cuda::getCurrentCUDABlasHandle(); 11 | } 12 | 13 | // C = alpha AB + beta C 14 | void matmult(torch::Tensor A, torch::Tensor B, torch::Tensor C, 15 | bool transpose_A, bool transpose_B, float alpha, float beta) { 16 | 17 | cublasOperation_t op_A = CUBLAS_OP_N; 18 | cublasOperation_t op_B = CUBLAS_OP_N; 19 | int m = A.size(0); int k = B.size(0); int n = B.size(1); 20 | if (transpose_A) { 21 | op_A = CUBLAS_OP_T; 22 | m = A.size(1); 23 | } 24 | if (transpose_B) { 25 | op_B = CUBLAS_OP_T; 26 | k = B.size(1); 27 | n = B.size(0); 28 | } 29 | 30 | // Depending on the tensor precision, call cuBLAS with appropriate parameters. 31 | // Small but important detail: notice how we use CUBLAS_COMPUTE_32F for fp16. 32 | // This is for the numerical stability of vector dot-products (another reason why 33 | // it's called *mixed* precision. 34 | if (A.dtype() == torch::kFloat32) { 35 | cublasGemmEx(get_handle(), op_B, op_A, n, m, k, &alpha, 36 | B.data_ptr(), CUDA_R_32F, B.size(1), 37 | A.data_ptr(), CUDA_R_32F, A.size(1), 38 | &beta, C.data_ptr(), CUDA_R_32F, C.size(1), 39 | CUBLAS_COMPUTE_32F, CUBLAS_GEMM_DEFAULT_TENSOR_OP); 40 | } else if (A.dtype() == torch::kFloat16) { 41 | cublasGemmEx(get_handle(), op_B, op_A, n, m, k, &alpha, 42 | B.data_ptr(), CUDA_R_16F, B.size(1), 43 | A.data_ptr(), CUDA_R_16F, A.size(1), 44 | &beta, C.data_ptr(), CUDA_R_16F, C.size(1), 45 | CUBLAS_COMPUTE_32F, CUBLAS_GEMM_DEFAULT_TENSOR_OP); 46 | } 47 | } -------------------------------------------------------------------------------- /train.py: -------------------------------------------------------------------------------- 1 | import sys 2 | import time 3 | 4 | import numpy as np 5 | import torch 6 | from torch.nn import functional as F 7 | from torch.utils.cpp_extension import load 8 | import torchvision 9 | import torchvision.transforms as transforms 10 | from torch.utils.data import DataLoader 11 | 12 | def cmp(s, a, b): # utility function to compare tensors 13 | ex = torch.all(a == b).item() 14 | app = torch.allclose(a, b) 15 | maxdiff = (a - b).abs().max().item() 16 | print(f'{s:15s} | exact: {str(ex):5s} | approximate: {str(app):5s} | maxdiff: {maxdiff}') 17 | 18 | device = 'cuda' if torch.cuda.is_available() else 'cpu' 19 | MP = sys.argv[1] == 'true' 20 | dtype = torch.float16 if MP else torch.float32 21 | print(f'device: {device}, mixed precision training: {MP} ({dtype})') 22 | scale = 128 if MP else 1 # loss scaling 23 | 24 | # load mixed precision training CUDA kernels 25 | mpt = load(name='mixed_precision_training', 26 | sources=['main.cpp', 'matmult.cu'], 27 | extra_cuda_cflags=['-O2', '-lcublas']) 28 | 29 | # define model 30 | batch_size = n = 8192 # n for convenience 31 | g = torch.Generator(device=device).manual_seed(42) # for reproducibility 32 | n_embd = 784 33 | n_hidden = 8192 34 | num_classes = 10 35 | 36 | # master weights 37 | # linear layer 1 38 | a, b = - ((1/n_embd) ** 0.5), ((1/n_embd) ** 0.5) # kaiming uniform init 39 | m_W1 = (b-a) * torch.rand((n_embd, n_hidden), generator=g, dtype=torch.float32, device=device) + a 40 | m_b1 = (b-a) * torch.rand(n_hidden, generator=g, dtype=torch.float32, device=device) + a 41 | 42 | # linear layer 2 43 | a, b = - ((1/n_hidden) ** 0.5), ((1/n_hidden) ** 0.5) 44 | m_W2 = (b-a) * torch.rand((n_hidden, num_classes), generator=g, dtype=torch.float32, device=device) + a 45 | m_b2 = (b-a) * torch.rand(num_classes, generator=g, dtype=torch.float32, device=device) + a 46 | 47 | parameters = [m_W1, m_b1, m_W2, m_b2] # updating fp32 master weights 48 | 49 | # allocate activations, gradients memory on global DRAM 50 | # doing this to avoid allocating memory inside the CUDA kernels (unnecessary overhead) 51 | a1 = torch.empty((n, n_hidden), dtype=dtype, device=device) 52 | z1 = torch.empty_like(a1) 53 | logits = torch.empty((n, num_classes), dtype=dtype, device=device) 54 | dlogits = torch.empty_like(logits) 55 | dz1 = torch.empty_like(a1) 56 | dW2 = torch.empty_like(m_W2, dtype=dtype) 57 | db2 = torch.empty_like(m_b2, dtype=dtype) 58 | da1 = torch.empty_like(a1) 59 | dW1 = torch.empty_like(m_W1, dtype=dtype) 60 | db1 = torch.empty_like(m_b1, dtype=dtype) 61 | 62 | intermediates = [a1, z1, logits, dlogits, dz1, da1] 63 | 64 | # calculate memory consumption 65 | mem_model = 0 66 | for p in parameters: 67 | mem_model += p.element_size() * p.nelement() 68 | if MP: # for 16-bit copies for forward/backward 69 | mem_model += p.element_size()/2 * p.nelement() 70 | print(f'model memory: {mem_model / 1e6:.2f} MB') 71 | 72 | mem_rest = 0 73 | for p in parameters + intermediates: 74 | mem_rest += p.element_size() * p.nelement() 75 | print(f'act/grad memory: {mem_rest / 1e6:.2f} MB') 76 | print(f'total memory: {(mem_model+mem_rest) / 1e6:.2f} MB') 77 | 78 | # load mnist 79 | transform = transforms.Compose([transforms.ToTensor(), transforms.Normalize((0.5,), (0.5,))]) 80 | dset = torchvision.datasets.MNIST(root='./data', train=True, download=True, transform=transform) 81 | dloader = DataLoader(dset, batch_size=n, shuffle=False, pin_memory=True) 82 | 83 | timings = [] 84 | for i, (x,y) in enumerate(dloader): 85 | 86 | t0 = time.time() 87 | x, y = x.to(dtype).to(device), y.to(device) 88 | 89 | if len(y) != n: # ignore the last batch 90 | break 91 | 92 | # 1. forward pass 93 | x = x.view(-1, n_embd) # flatten 2d img to 1d 94 | W1, b1 = m_W1.half() if MP else m_W1, m_b1.half() if MP else m_b1 # use fp16 weight copies 95 | a1 = b1.repeat((n,1)) # set a1 as biases for cublas GEMM 96 | mpt.matmult(x, W1, a1, False, False, 1.0, 1.0) # a1 = x @ W1 + b1 97 | # cmp('a1', a1, x @ W1 + b1) 98 | 99 | z1 = F.relu(a1) # (n, n_hidden) 100 | 101 | W2, b2 = m_W2.half() if MP else m_W2, m_b2.half() if MP else m_b2 # use fp16 weight copies 102 | logits = b2.repeat((n,1)) # set logits as biases for GEMM 103 | 104 | mpt.matmult(z1, W2, logits, False, False, 1.0, 1.0) # logits = z1 @ W2 + b2 105 | # cmp('logits', logits, z1 @ W2 + b2) 106 | 107 | loss = F.cross_entropy(logits, y) 108 | 109 | # 2. manual backward pass. Kudos to Andrej, for making me a backprop ninja 110 | dlogits = F.softmax(logits, 1, dtype=torch.float32) # cast logits to fp32 before softmax 111 | dlogits[range(n), y] -= 1 112 | dlogits /= n 113 | 114 | # loss scaling 115 | # note: we multiply dlogits, instead of loss, by scale. This is because 116 | # we are doing backprop manually. The first gradient is dlogits, and the 117 | # scale will propogate through all gradients. 118 | dlogits *= scale 119 | if MP: # no underflow occurs because we scaled 120 | dlogits = dlogits.to(torch.float16) 121 | 122 | mpt.matmult(dlogits, W2, dz1, False, True, 1.0, 0.0) # dz1 = dlogits @ W2.T 123 | # cmp('dz1', dz1, dlogits @ W2.T) 124 | 125 | mpt.matmult(z1, dlogits, dW2, True, False, 1.0, 0.0) # dW2 = z1.T @ dlogits 126 | # cmp('dW2', dW2, z1.T @ dlogits) 127 | 128 | db2 = dlogits.sum(0) 129 | da1 = dz1 * (a1 > 0).to(dtype) 130 | mpt.matmult(x, da1, dW1, True, False, 1.0, 0.0) # dW1 = x.T @ da1 131 | # cmp('dW1', dW1, x.T @ da1) 132 | 133 | db1 = da1.sum(0) 134 | 135 | # 3. SGD update 136 | grads = [dW1, db1, dW2, db2] 137 | lr = 0.01 138 | for p, grad in zip(parameters, grads): 139 | p.data += -lr * (grad.to(torch.float32) / scale) # cast grad to fp32 before unscale 140 | 141 | t1 = time.time() 142 | print(f'{i+1:2d}: loss {loss.item():.3f}, time: {(t1-t0)*1000:.3f}ms') 143 | timings.append(t1-t0) 144 | 145 | print(f'avg: {np.mean(timings[1:])*1000:.3f}ms') # ignore first as outlier 146 | --------------------------------------------------------------------------------