[CPU] optimize Lp norm for 1-dimensional vector #122143
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🔗 Helpful Links🧪 See artifacts and rendered test results at hud.pytorch.org/pr/122143
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Fixes #120229 - Optimize vector norm by simplifying vector norm formula for 1-dimensional vector. - Vector norm formula for 1-dimensional vector simplifies to `abs(x)`. See below for proof. - Next step, we can similarly optimize matrix norm (`torch.linalg.matrix_norm`) for 1 x 1 matrix. - Additionally, avoids overflow in power, `abs(x) ** p` for large `p` or `x`, for 1-dimensional vector. ### Performance Avg Latency (ms) of `torch.norm` and `torch.linalg.vector_norm` for `torch.norm(torch.randn(2**18, 1), ord, -1)` `torch.linalg.vector_norm(torch.randn(2**18, 1), ord, -1)` Tested on 28 physical cores/socket, 1 socket on Skylake. | | | | | **Avg Latency (ms)** | | | |-------------------------- |----------------- |--------- |--------- |----------------------- |----------------------- |---------------------------------------- | | **op** | **input shape** | **dim** | **ord** | **baseline (master)** | **optimized (7102f1e)** | **speedup ratio (baseline/optimized)** | | torch.norm | (2**18, 1) | -1 | fro | 34.3755531 | 0.0125408 | 2741.094 | | | | | inf | 34.0952635 | 0.0122237 | 2789.271 | | | | | -inf | 34.3674493 | 0.0120759 | 2845.953 | | | | | 0 | 34.1004515 | 0.0175261 | 1945.69 | | | | | 1 | 34.1688442 | 0.0121593 | 2810.089 | | | | | -1 | 33.949492 | 0.0120282 | 2822.487 | | | | | 2 | 34.3669581 | 0.0120401 | 2854.366 | | | | | -2 | 33.9252067 | 0.0121069 | 2802.139 | | | | | | | | | | torch.linalg.vector_norm | (2**18, 1) | -1 | inf | 34.090879 | 0.0095105 | 3584.545 | | | | | -inf | 34.3708754 | 0.0099111 | 3467.931 | | | | | 0 | 34.0880775 | 0.0141716 | 2405.38 | | | | | 1 | 34.1392851 | 0.0093174 | 3664.036 | | | | | -1 | 33.925395 | 0.0092483 | 3668.302 | | | | | 2 | 34.3854165 | 0.0092459 | 3719.002 | | | | | -2 | 33.932972 | 0.0093007 | 3648.429 | ### Proof <details> <summary>For those interested :)</summary> <img width="382" alt="1_dim_vector_norm_proof1" src="https://github.com/pytorch/pytorch/assets/93151422/59b1e00b-8fcd-47cb-877d-d31403b5195b"> <img width="432" alt="1_dim_vector_norm_proof2" src="https://github.com/pytorch/pytorch/assets/93151422/236bea15-2dd5-480b-9871-58b2e3b24322"> </details> Pull Request resolved: #122143 Approved by: https://github.com/lezcano
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Fixes #120229
abs(x). See below for proof.torch.linalg.matrix_norm) for 1 x 1 matrix.abs(x) ** pfor largeporx, for 1-dimensional vector.Performance
Avg Latency (ms) of
torch.normandtorch.linalg.vector_normfortorch.norm(torch.randn(2**18, 1), ord, -1)torch.linalg.vector_norm(torch.randn(2**18, 1), ord, -1)Tested on 28 physical cores/socket, 1 socket on Skylake.
Proof
For those interested :)
cc @jgong5 @mingfeima @XiaobingSuper @sanchitintel @ashokei @jingxu10 @jianyuh @nikitaved @pearu @mruberry @walterddr @xwang233 @lezcano @voznesenskym @penguinwu @EikanWang @Guobing-Chen @zhuhaozhe @blzheng @wenzhe-nrv @jiayisunx @peterbell10 @ipiszy @yf225 @chenyang78 @kadeng @muchulee8 @aakhundov @ColinPeppler @amjames @desertfire @chauhang