[
  {
    "path": ".gitignore",
    "content": "__pycache__/\nSlurmOutput/\ntemp/\n.vscode/\n*.ncu-rep\n"
  },
  {
    "path": ".gitmodules",
    "content": "[submodule \"cost_model/supply_chain\"]\n\tpath = cost_model/supply_chain\n\turl = https://github.com/PrincetonUniversity/ttm-cas.git\n"
  },
  {
    "path": "Dockerfile",
    "content": "# Start with a base image that includes Miniconda to manage our environment\nFROM continuumio/miniconda3\n\n# Set the working directory in the container to /app\nWORKDIR /app\n\n# Create the conda environment\nCOPY environment.yml /app/environment.yml\nRUN conda env create -f /app/environment.yml\n\n# Initialize conda in bash shell\nRUN echo \"source activate llmcompass_ae\" > ~/.bashrc\nENV PATH /opt/conda/envs/llmcompass_ae/bin:$PATH\n\n# Clone your GitHub repository\nRUN git clone https://github.com/HenryChang213/LLMCompass_ISCA_AE.git /app/LLMCompass_ISCA_AE\nRUN cd /app/LLMCompass_ISCA_AE && git submodule init && git submodule update --recursive\n\n# Expose the port your app runs on\nEXPOSE 8000\n\n\n"
  },
  {
    "path": "LICENSE",
    "content": "BSD 3-Clause License\n\nCopyright (c) 2024, Princeton University\n\nRedistribution and use in source and binary forms, with or without\nmodification, are permitted provided that the following conditions are met:\n\n1. Redistributions of source code must retain the above copyright notice, this\n   list of conditions and the following disclaimer.\n\n2. Redistributions in binary form must reproduce the above copyright notice,\n   this list of conditions and the following disclaimer in the documentation\n   and/or other materials provided with the distribution.\n\n3. Neither the name of the copyright holder nor the names of its\n   contributors may be used to endorse or promote products derived from\n   this software without specific prior written permission.\n\nTHIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS \"AS IS\"\nAND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE\nIMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE\nDISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE\nFOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL\nDAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR\nSERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER\nCAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY,\nOR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE\nOF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.\n"
  },
  {
    "path": "README.md",
    "content": "[![DOI](https://zenodo.org/badge/779008229.svg)](https://zenodo.org/doi/10.5281/zenodo.10892431)\n\n# LLMCompass\n\nThis repository provides the implementation of **LLMCompass** from the following papers:\n\n[**LLMCompass: Enabling Efficient Hardware Design for Large Language Model Inference**](https://parallel.princeton.edu/papers/isca24_llmcompass.pdf)\n\n*Hengrui Zhang, August Ning, Rohan Baskar Prabhakar, David Wentzlaff*\n\n\nIn the Proceedings of the 51st Annual International Symposium on Computer Architecture:\n\n```\n@inproceedings{LLMCompass,\nauthor = {Zhang, Hengrui and Ning, August and Prabhakar, Rohan Baskar and Wentzlaff, David},\ntitle = {LLMCompass: Enabling Efficient Hardware Design for Large Language Model Inference},\nyear = {2024},\nbooktitle = {Proceedings of the 51st Annual International Symposium on Computer Architecture},\n}\n```\n\n\n## Set up the environment\n\n```\n$ conda create -n llmcompass_ae python=3.9\n$ conda activate llmcompass_ae\n$ pip3 install scalesim\n$ conda install pytorch==2.0.0 -c pytorch\n$ pip3 install matplotlib\n$ pip3 install seaborn\n$ pip3 install scipy\n```\n\n## Installation\n\n### If using Github\n```\n$ git clone -b ISCA_AE https://github.com/PrincetonUniversity/LLMCompass\n$ cd LLMCompass\n$ git submodule init\n$ git submodule update --recursive\n```\n\n### If using Zenodo\nUnzip the file and download from https://github.com/PrincetonUniversity/ttm-cas.git as `cost_model\\supply_chain`\n\n\n### If using Docker\nA Dockerfile has been provided (`./Dockerfile`), including all the software dependencies and the LLMCompass source code.\n\nA docker image has been provided [here](https://github.com/HenryChang213/LLMCompass_ISCA_AE_docker).\n\n## AE Experiment workflow\n```\n# Figure 5 (around 100 min) \n$ cd ae/figure5\n$ bash run_figure5.sh \n\n# Figure 6 (around 1 min)\n$ cd ae/figure6\n$ bash run_figure6.sh\n\n# Figure 7 (around 20 min)\n$ cd ae/figure7\n$ bash run_figure7.sh\n\n# Figure 8 (around 40 min)\n$ cd ae/figure8\n$ bash run_figure8.sh\n\n# Figure 9 (around 30 min)\n$ cd ae/figure9\n$ bash run_figure9.sh\n\n# Figure 10 (around 45 min)\n$ cd ae/figure10\n$ bash run_figure10.sh\n\n# Figure 11 (around 5 min) \n$ cd ae/figure11\n$ bash run_figure11.sh\n\n# Figure 12 (around 4 hours) \n$ cd ae/figure12\n$ bash run_figure12.sh\n```\n\n## AE Expected result\n\nAfter running each script above, the corresponding figures\nwill be generated under the corresponding directory as suggested by its name.\n\nFor comparison, a copy of the expected results can be found in `ae\\expected_results`\n\n\n## User Guide\n\nA guide on \"How to Run a LLMCompass Simulation\" is shown [here](./docs/run.md)."
  },
  {
    "path": "__init__.py",
    "content": ""
  },
  {
    "path": "ae/.gitignore",
    "content": "*.pdf\n*.csv\n!**/real_hardware/**/*.csv\n!expected_results/*"
  },
  {
    "path": "ae/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure10/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure10/plot_latency.py",
    "content": "import pandas as pd\nimport numpy as np\nimport seaborn as sns\nimport matplotlib.pyplot as plt\n\n\nour_decoding = pd.read_csv(\n    \"our_decoding.csv\", header=None, names=[\"bs\", \"s\", \"latency\"]\n).sort_values(by=\"s\")\nour_prefill = pd.read_csv(\"our_prefill.csv\", header=None, names=[\"bs\", \"s\", \"latency\"])\nA100_decoding = pd.read_csv(\n    \"A100_decoding.csv\", header=None, names=[\"bs\", \"s\", \"latency\"]\n).sort_values(by=\"s\")\nA100_prefill = pd.read_csv(\n    \"A100_prefill.csv\", header=None, names=[\"bs\", \"s\", \"latency\"]\n)\n\n\ndef get_total_decoding_latency(df: pd.DataFrame, start, end):\n    df_filtered = df[(df[\"s\"] >= start) & (df[\"s\"] <= end)]\n    total_latency = 0\n\n    # Calculate the mean of the values for each length interval and add to the sum\n    for i in range(len(df_filtered) - 1):\n        # Calculate the mean of current and next value\n        mean = (df_filtered.iloc[i][\"latency\"] + df_filtered.iloc[i + 1][\"latency\"]) / 2\n        # Calculate the difference in length\n        length_interval = df_filtered.iloc[i + 1][\"s\"] - df_filtered.iloc[i][\"s\"]\n        # Multiply the mean value by the length interval and add to the sum\n        total_latency += mean * length_interval\n\n    # print(total_latency)\n    return total_latency\n\n\nnorm_perf = []\nfor input_length in [256, 512, 1024, 2048]:\n    temp_list = []\n    our_prefill_latency = our_prefill[our_prefill[\"s\"] == input_length][\n        \"latency\"\n    ].values[0]\n    A100_prefill_latency = A100_prefill[A100_prefill[\"s\"] == input_length][\n        \"latency\"\n    ].values[0]\n    for output_length in [256, 512, 768, 1024, 1280, 1536, 1792, 2048]:\n        our_total_latency = our_prefill_latency + get_total_decoding_latency(\n            our_decoding, input_length, input_length + output_length\n        )\n        A100_total_latency = A100_prefill_latency + get_total_decoding_latency(\n            A100_decoding, input_length, input_length + output_length\n        )\n        temp_list.append(A100_total_latency / our_total_latency)\n    norm_perf.append(temp_list)\n\ncmap = sns.color_palette(\"viridis\", as_cmap=True)\ndata = np.array(norm_perf)\nimport statistics\n\nprint(statistics.geometric_mean(data.flatten()))\nfig, ax = plt.subplots()\ncax = ax.imshow(data, interpolation=\"nearest\", cmap=cmap, vmin=0.8, vmax=1)\n# cax = sns.heatmap(data, cmap=\"viridis\")\n\n# Add a colorbar\nfig.colorbar(cax, shrink=0.5)\n\n\n# Function to convert RGB to grayscale intensity\ndef get_intensity(color):\n    return color[0] * 0.299 + color[1] * 0.587 + color[2] * 0.114\n\n\n# Set a threshold for deciding text color\nintensity_threshold = 0.5\nfor i in range(data.shape[0]):\n    for j in range(data.shape[1]):\n        # Get the color from the colormap\n        cell_color = cax.cmap(cax.norm(data[i, j]))\n        # Calculate intensity of the cell color\n        intensity = get_intensity(cell_color)\n        # Choose text color based on intensity\n        text_color = \"white\" if intensity < intensity_threshold else \"black\"\n        text = ax.text(\n            j, i, round(data[i, j], 2), ha=\"center\", va=\"center\", color=text_color\n        )\n\n# Set the x-axis and y-axis values\nx_axis_labels = [256, 512, 768, 1024, 1280, 1536, 1792, 2048]\ny_axis_labels = [256, 512, 1024, 2048]\n\n# Set ticks positions\nax.set_xticks(np.arange(len(x_axis_labels)))\nax.set_yticks(np.arange(len(y_axis_labels)))\n\n# Set ticks labels\nax.set_xticklabels(x_axis_labels)\nax.set_yticklabels(y_axis_labels)\n\n# Set labels for axes\nax.set_xlabel(\"Output Length\")\nax.set_ylabel(\"Input Length\")\nax.invert_yaxis()\n# # Rotate the tick labels for the x-axis if needed\n# plt.setp(ax.get_xticklabels(), rotation=45, ha=\"right\", rotation_mode=\"anchor\")\n\n# Show the plot\nplt.tight_layout()\nplt.savefig(\"figure10.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\n\n\n# norm_perf = []\n# norm_perf_ttft = []\n# for input_length in [256, 512, 1024, 2048]:\n#     temp_list = []\n#     our_prefill_latency = our_prefill[our_prefill[\"s\"] == input_length][\n#         \"latency\"\n#     ].values[0]\n#     A100_prefill_latency = A100_prefill[A100_prefill[\"s\"] == input_length][\n#         \"latency\"\n#     ].values[0]\n#     for output_length in [256, 512, 768, 1024, 1280, 1536, 1792, 2048]:\n#         our_tbt_latency = get_total_decoding_latency(\n#             our_decoding, input_length, input_length + output_length\n#         )\n#         A100_tbt_latency = get_total_decoding_latency(\n#             A100_decoding, input_length, input_length + output_length\n#         )\n#         temp_list.append(our_tbt_latency / A100_tbt_latency)\n#     norm_perf.append(temp_list)\n#     norm_perf_ttft.append(our_prefill_latency / A100_prefill_latency)\n\n# cmap = sns.color_palette(\"viridis\", as_cmap=True)\n# data = np.array(norm_perf)\n# data_ttft = np.array(norm_perf_ttft)\n# print(data)\n# print(data_ttft)\n# import statistics\n# from matplotlib import gridspec\n\n# print(statistics.geometric_mean(data.flatten()))\n# print(statistics.geometric_mean(data_ttft))\n# # fig, axs = plt.subplots(1, 2, figsize=(8, 4),\n# # \t\t\tgridspec_kw={'width_ratios': [3, 1]}, sharey=True)\n# fig = plt.figure(figsize=(8, 3))  # Define the figure size\n# gs = gridspec.GridSpec(\n#     1, 2, width_ratios=[4, 1]\n# )  # 2 rows, 1 column, with the first row 3 times the height of the second\n# ax = fig.add_subplot(gs[0])\n# # ax=axs[0]\n# cax = ax.imshow(data, interpolation=\"nearest\", cmap=cmap, vmin=1.015, vmax=1.045)\n# # cax = sns.heatmap(data, cmap=\"viridis\")\n\n# # Add a colorbar\n# fig.colorbar(cax, shrink=1)\n\n\n# # Function to convert RGB to grayscale intensity\n# def get_intensity(color):\n#     return color[0] * 0.299 + color[1] * 0.587 + color[2] * 0.114\n\n\n# # Set a threshold for deciding text color\n# intensity_threshold = 0.5\n# for i in range(data.shape[0]):\n#     for j in range(data.shape[1]):\n#         # Get the color from the colormap\n#         cell_color = cax.cmap(cax.norm(data[i, j]))\n#         # Calculate intensity of the cell color\n#         intensity = get_intensity(cell_color)\n#         # Choose text color based on intensity\n#         text_color = \"white\" if intensity < intensity_threshold else \"black\"\n#         text = ax.text(\n#             j, i, round(data[i, j], 3), ha=\"center\", va=\"center\", color=text_color\n#         )\n\n# # Set the x-axis and y-axis values\n# x_axis_labels = [256, 512, 768, 1024, 1280, 1536, 1792, 2048]\n# y_axis_labels = [256, 512, 1024, 2048]\n\n# # Set ticks positions\n# ax.set_xticks(np.arange(len(x_axis_labels)))\n# ax.set_yticks(np.arange(len(y_axis_labels)))\n\n\n# # Set ticks labels\n# ax.set_xticklabels(x_axis_labels)\n# ax.set_yticklabels(y_axis_labels)\n\n\n# # Set labels for axes\n# ax.set_xlabel(\"Output Length\\n\" + r\"$\\mathbf{Normalized\\ TBT}$\")\n# ax.set_ylabel(\"Input Length\")\n# ax.invert_yaxis()\n# # # Rotate the tick labels for the x-axis if needed\n# # plt.setp(ax.get_xticklabels(), rotation=45, ha=\"right\", rotation_mode=\"anchor\")\n\n\n# # fig = plt.figure(figsize=(10, 5))  # Define the figure size\n# axs1 = fig.add_subplot(gs[0, 1])\n# axs1.barh(np.arange(len(data_ttft)) / 2 + 0.2, data_ttft, color=\"steelblue\", height=0.3)\n# axs1.set_yticks(np.arange(len(y_axis_labels)) / 2 + 0.2)\n# axs1.set_yticklabels(y_axis_labels)\n# axs1.set_xlabel(r\"$\\mathbf{Normalized\\ TTFT}$\")\n# axs1.set_xlim(1, 2)\n\n# # Show the plot\n# plt.tight_layout()\n# plt.savefig(\"figure11.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\n"
  },
  {
    "path": "ae/figure10/run_figure10.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../..\n\npython -m ae.figure10.test_latency\n\ncd ae/figure10\npython plot_latency.py"
  },
  {
    "path": "ae/figure10/test_latency.py",
    "content": "from software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\nfrom design_space_exploration.dse import template_to_system, read_architecture_template\nfrom multiprocessing import Process, Lock\nfrom cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nimport time\n\nA100_specs = read_architecture_template(\"configs/GA100.json\")\nA100_system = template_to_system(A100_specs)\nour_specs = read_architecture_template(\"configs/latency_design.json\")\nour_system = template_to_system(our_specs)\nA100_compute_area_mm2 = calc_compute_chiplet_area_mm2(A100_specs)\nA100_io_area_mm2 = calc_io_die_area_mm2(A100_specs)\nour_compute_area_mm2 = calc_compute_chiplet_area_mm2(our_specs)\nour_io_area_mm2 = calc_io_die_area_mm2(our_specs)\nprint(f\"A100 compute area: {A100_compute_area_mm2} mm2\")\nprint(f\"A100 IO area: {A100_io_area_mm2} mm2\")\nprint(f\"A100 total area: {A100_compute_area_mm2+A100_io_area_mm2} mm2\")\nprint(f\"Our compute area: {our_compute_area_mm2} mm2\")\nprint(f\"Our IO area: {our_io_area_mm2} mm2\")\nprint(f\"Our total area: {our_compute_area_mm2+our_io_area_mm2} mm2\")\n\nwith open(\"ae/figure10/area.csv\", \"w\") as f:\n    f.write(f\"A100 compute area: {A100_compute_area_mm2} mm2\\n\")\n    f.write(f\"A100 IO area: {A100_io_area_mm2} mm2\\n\")\n    f.write(f\"A100 total area: {A100_compute_area_mm2+A100_io_area_mm2} mm2\\n\")\n    f.write(f\"Our compute area: {our_compute_area_mm2} mm2\\n\")\n    f.write(f\"Our IO area: {our_io_area_mm2} mm2\\n\")\n    f.write(f\"Our total area: {our_compute_area_mm2+our_io_area_mm2} mm2\\n\")\n\n\ndef simulate_decoding_latency(system, bs, seq_len, name, lock):\n    model_auto_regression = TransformerBlockAutoRegressionTP(\n        d_model=12288,\n        n_heads=96,\n        device_count=4,\n        data_type=data_type_dict[\"fp16\"],\n    )\n    _ = model_auto_regression(\n        Tensor([bs, 1, 12288], data_type_dict[\"fp16\"]),\n        seq_len,\n    )\n    auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(\n        system, \"heuristic-GPU\"\n    )\n    with lock:\n        with open(f\"ae/figure10/{name}_decoding.csv\", \"a\") as f:\n            f.write(f\"{bs}, {seq_len}, {auto_regression_latency_simulated}\\n\")\n\n\ndef simulate_prefill_latency(system, bs, seq_len, name, lock):\n    model = TransformerBlockInitComputationTP(\n        d_model=12288,\n        n_heads=96,\n        device_count=4,\n        data_type=data_type_dict[\"fp16\"],\n    )\n    _ = model(\n        Tensor([bs, seq_len, 12288], data_type_dict[\"fp16\"]),\n    )\n    latency_simulated = model.compile_and_simulate(system, \"heuristic-GPU\")\n    with lock:\n        with open(f\"ae/figure10/{name}_prefill.csv\", \"a\") as f:\n            f.write(f\"{bs}, {seq_len}, {latency_simulated}\\n\")\n\n\nlock_our_prefill = Lock()\nlock_our_decoding = Lock()\nlock_A100_prefill = Lock()\nlock_A100_decoding = Lock()\n\nprocesses = []\nfor bs in [16]:  # [1, 4, 8, 16, 32, 64]:\n    for seq_len in [256, 512, 1024, 2048]:\n        for system in [our_system, A100_system]:\n            if system == A100_system:\n                name = \"A100\"\n                lock = lock_A100_prefill\n            else:\n                name = \"our\"\n                lock = lock_our_prefill\n            p = Process(\n                target=simulate_prefill_latency, args=(system, bs, seq_len, name, lock)\n            )\n            processes.append(p)\n    for seq_len in range(256, 4096 + 64, 64):\n        for system in [our_system, A100_system]:\n            if system == A100_system:\n                name = \"A100\"\n                lock = lock_A100_decoding\n            else:\n                name = \"our\"\n                lock = lock_our_decoding\n            p = Process(\n                target=simulate_decoding_latency, args=(system, bs, seq_len, name, lock)\n            )\n            processes.append(p)\n\n\ntry:\n    for p in processes:\n        p.start()\n    print(\"Processes started.\")\n    print(\"number of process:\", len(processes))\n    while any(p.is_alive() for p in processes):\n        time.sleep(1)\nexcept KeyboardInterrupt:\n    print(\"Terminating processes...\")\n    for p in processes:\n        p.terminate()\n        p.join()\n\n\nprint(\"All processes have finished.\")\n"
  },
  {
    "path": "ae/figure11/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure11/plot_decoding.py",
    "content": "import pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport numpy as np\nfrom scipy.stats import gmean\n\ncategories = [\"bs\", \"seq_len\", \"latency\"] + [\n    \"Q_K_V\",\n    \"Q_mul_K\",\n    \"A_mul_V\",\n    \"Wo_proj\",\n    \"W1_proj\",\n    \"W2_proj\",\n    \"Softmax\",\n    \"LayerNorm_MHA\",\n    \"LayerNorm_FFN\",\n    \"GeLU\",\n    \"AllReduce_MHA\",\n    \"AllReduce_FFN\",\n]\n\nA100 = pd.read_csv(\"A100.csv\", header=None, names=categories)\nA100[\"latency\"] = A100[\"latency\"] * 1000\nour = pd.read_csv(\"our.csv\", header=None, names=categories)\nour[\"latency\"] = our[\"latency\"] * 1000\n\nbs_list = [1, 2, 4, 8, 16, 32]\ncolors_our = sns.color_palette(\"Blues\", 3)[1:]\ncolors_a100 = sns.color_palette(\"summer_r\", 2)\nour_512 = our[our.seq_len == 512][our[\"bs\"].isin(bs_list)][\"latency\"].tolist()\nour_2048 = our[our.seq_len == 2048][our[\"bs\"].isin(bs_list)][\"latency\"].tolist()\na100_512 = A100[A100.seq_len == 512][A100[\"bs\"].isin(bs_list)][\"latency\"].tolist()\na100_2048 = A100[A100.seq_len == 2048][A100[\"bs\"].isin(bs_list)][\"latency\"].tolist()\navg_speedup = gmean(\n    np.concatenate(\n        (\n            np.array(a100_512) / np.array(our_512),\n            np.array(a100_2048) / np.array(our_2048),\n        )\n    )\n)\nprint(avg_speedup)\n\nplt.figure(figsize=(8, 3.5))\n\nx_pos = 0.25\nfor bs in bs_list:\n    if bs == 1:\n        seq_len = 512\n        plt.bar(\n            x_pos,\n            A100[(A100.bs == bs) & (A100.seq_len == seq_len)].latency,\n            width=0.5,\n            label=f\"GA100 (seq_len={seq_len})\",\n            color=colors_a100[0],\n        )\n        bars = plt.bar(\n            x_pos + 0.5,\n            our[(our.bs == bs) & (our.seq_len == seq_len)].latency,\n            width=0.5,\n            label=f\"Latency design (seq_len={seq_len})\",\n            color=colors_our[0],\n        )\n        for bar in bars:\n            bar.set_hatch(\"//\")  # Add diagonal stripes\n        seq_len = 2048\n        plt.bar(\n            x_pos + 1,\n            A100[(A100.bs == bs) & (A100.seq_len == seq_len)].latency,\n            width=0.5,\n            label=f\"GA100 (seq_len={seq_len})\",\n            color=colors_a100[1],\n        )\n        bars = plt.bar(\n            x_pos + 1.5,\n            our[(our.bs == bs) & (our.seq_len == seq_len)].latency,\n            width=0.5,\n            label=f\"Latency design (seq_len={seq_len})\",\n            color=colors_our[1],\n        )\n        for bar in bars:\n            bar.set_hatch(\"//\")  # Add diagonal stripes\n    else:\n        seq_len = 512\n        plt.bar(\n            x_pos,\n            A100[(A100.bs == bs) & (A100.seq_len == seq_len)].latency,\n            width=0.5,\n            color=colors_a100[0],\n        )\n        bars = plt.bar(\n            x_pos + 0.5,\n            our[(our.bs == bs) & (our.seq_len == seq_len)].latency,\n            width=0.5,\n            color=colors_our[0],\n        )\n        for bar in bars:\n            bar.set_hatch(\"//\")  # Add diagonal stripes\n        seq_len = 2048\n        if bs < 164:\n            plt.bar(\n                x_pos + 1,\n                A100[(A100.bs == bs) & (A100.seq_len == seq_len)].latency,\n                width=0.5,\n                color=colors_a100[1],\n            )\n            bars = plt.bar(\n                x_pos + 1.5,\n                our[(our.bs == bs) & (our.seq_len == seq_len)].latency,\n                width=0.5,\n                color=colors_our[1],\n            )\n            for bar in bars:\n                bar.set_hatch(\"//\")  # Add diagonal stripes\n    x_pos += 3\n\nplt.xticks([1, 4, 7, 10, 13, 16], bs_list)\nplt.xlabel(\"Batch Size\")\nplt.ylabel(\"Latency (ms)\")\nplt.legend(loc=\"upper left\")\nplt.tight_layout()\nplt.grid(True, axis=\"y\", ls=\"--\", c=\"0.8\")\nplt.savefig(\"figure11.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\nplt.show()"
  },
  {
    "path": "ae/figure11/run_figure11.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../..\n\npython -m ae.figure11.test_decoding\n\ncd ae/figure11\npython plot_decoding.py"
  },
  {
    "path": "ae/figure11/test_decoding.py",
    "content": "from software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\nfrom design_space_exploration.dse import template_to_system, read_architecture_template\nfrom multiprocessing import Process, Lock\nfrom cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nimport time\n\nA100_specs = read_architecture_template(\"configs/GA100.json\")\nA100_system = template_to_system(A100_specs)\nour_specs = read_architecture_template(\"configs/latency_design.json\")\nour_system = template_to_system(our_specs)\nA100_compute_area_mm2 = calc_compute_chiplet_area_mm2(A100_specs)\nA100_io_area_mm2 = calc_io_die_area_mm2(A100_specs)\nour_compute_area_mm2 = calc_compute_chiplet_area_mm2(our_specs)\nour_io_area_mm2 = calc_io_die_area_mm2(our_specs)\nprint(f\"A100 compute area: {A100_compute_area_mm2} mm2\")\nprint(f\"A100 IO area: {A100_io_area_mm2} mm2\")\nprint(f\"A100 total area: {A100_compute_area_mm2+A100_io_area_mm2} mm2\")\nprint(f\"Our compute area: {our_compute_area_mm2} mm2\")\nprint(f\"Our IO area: {our_io_area_mm2} mm2\")\nprint(f\"Our total area: {our_compute_area_mm2+our_io_area_mm2} mm2\")\n\n\ndef simulate_latency(system, bs, seq_len, name, lock):\n    model_auto_regression = TransformerBlockAutoRegressionTP(\n        d_model=12288,\n        n_heads=96,\n        device_count=4,\n        data_type=data_type_dict[\"fp16\"],\n    )\n    _ = model_auto_regression(\n        Tensor([bs, 1, 12288], data_type_dict[\"fp16\"]),\n        seq_len,\n    )\n    auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(\n        system, \"heuristic-GPU\"\n    )\n    with lock:\n        with open(f\"ae/figure11/{name}.csv\", \"a\") as f:\n            f.write(\n                f\"{bs}, {seq_len}, {auto_regression_latency_simulated}, {model_auto_regression.simluate_log}\\n\"\n            )\n\n\nlock = Lock()\n\nprocesses = []\nfor bs in [1, 2, 4, 8, 16, 32, 64]:\n    for seq_len in [512, 2048]:\n        for system in [our_system, A100_system]:\n            if system == A100_system:\n                name = \"A100\"\n            else:\n                name = \"our\"\n            p = Process(target=simulate_latency, args=(system, bs, seq_len, name, lock))\n            processes.append(p)\n\ntry:\n    for p in processes:\n        p.start()\n\n    while any(p.is_alive() for p in processes):\n        time.sleep(1)\nexcept KeyboardInterrupt:\n    print(\"Terminating processes...\")\n    for p in processes:\n        p.terminate()\n        p.join()\n\n\nprint(\"All processes have finished.\")\n"
  },
  {
    "path": "ae/figure12/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure12/plot_throughput.py",
    "content": "import pandas as pd\nimport numpy as np\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport statistics\n\nour_directory = \"our/our\"\nA100_directory = \"A100/A100\"\n\ncategories = [\"bs\", \"s\", \"latency\"] + [\n    \"Q_K_V\",\n    \"Q_mul_K\",\n    \"A_mul_V\",\n    \"Wo_proj\",\n    \"W1_proj\",\n    \"W2_proj\",\n    \"Softmax\",\n    \"LayerNorm_MHA\",\n    \"LayerNorm_FFN\",\n    \"GeLU\",\n    \"AllReduce_MHA\",\n    \"AllReduce_FFN\",\n]\n\nthroughput_our = []\nbs_our = []\nlatency_our = []\nthroughput_A100 = []\nbs_A100 = []\nlatency_A100 = []\n\n\ndef get_total_decoding_latency(df: pd.DataFrame, start, end):\n    df_filtered = df[(df[\"s\"] >= start) & (df[\"s\"] <= end)]\n    total_latency = 0\n\n    # Calculate the mean of the values for each length interval and add to the sum\n    for i in range(len(df_filtered) - 1):\n        # Calculate the mean of current and next value\n        mean = (df_filtered.iloc[i][\"latency\"] + df_filtered.iloc[i + 1][\"latency\"]) / 2\n        # Calculate the difference in length\n        length_interval = df_filtered.iloc[i + 1][\"s\"] - df_filtered.iloc[i][\"s\"]\n        # Multiply the mean value by the length interval and add to the sum\n        total_latency += mean * length_interval\n\n    # print(total_latency)\n    return total_latency\n\n\nfor input_length in [256, 512, 1024, 2048]:\n    temp_our = []\n    temp_A100 = []\n    temp_our_bs = []\n    temp_A100_bs = []\n    temp_our_latency = []\n    temp_A100_latency = []\n    for output_length in [256, 512, 768, 1024, 1280, 1536, 1792, 2048]:\n        our_prefill_df = pd.read_csv(\n            f\"{our_directory}_{input_length}_{output_length}_prefill.csv\",\n            header=None,\n            names=categories,\n        )\n        # print(our_prefill_df)\n        our_prefill_latency = our_prefill_df.iloc[0][\"latency\"]\n        our_bs = our_prefill_df.iloc[0][\"bs\"]\n        temp_our_bs.append(our_bs)\n        our_decoding_df = pd.read_csv(\n            f\"{our_directory}_{input_length}_{output_length}_decoding.csv\",\n            header=None,\n            names=categories,\n        ).sort_values(by=\"s\")\n        our_decoding_latency = get_total_decoding_latency(\n            our_decoding_df, input_length, input_length + output_length\n        )\n        # print(our_decoding_latency)\n        our_throughput = (\n            our_bs * output_length / (our_prefill_latency + our_decoding_latency) / 12\n        )\n        temp_our.append(our_throughput)\n        temp_our_latency.append(our_prefill_latency + our_decoding_latency)\n\n        A100_prefill_df = pd.read_csv(\n            f\"{A100_directory}_{input_length}_{output_length}_prefill.csv\",\n            header=None,\n            names=categories,\n        )\n        A100_prefill_latency = A100_prefill_df.iloc[0][\"latency\"]\n        A100_bs = A100_prefill_df.iloc[0][\"bs\"]\n        temp_A100_bs.append(A100_bs)\n        A100_decoding_df = pd.read_csv(\n            f\"{A100_directory}_{input_length}_{output_length}_decoding.csv\",\n            header=None,\n            names=categories,\n        ).sort_values(by=\"s\")\n        A100_decoding_latency = get_total_decoding_latency(\n            A100_decoding_df, input_length, input_length + output_length\n        )\n        A100_throughput = (\n            A100_bs\n            * output_length\n            / (A100_prefill_latency + A100_decoding_latency)\n            / 12\n        )\n        temp_A100.append(A100_throughput)\n        temp_A100_latency.append(A100_prefill_latency + A100_decoding_latency)\n\n    throughput_our.append(temp_our)\n    throughput_A100.append(temp_A100)\n    bs_our.append(temp_our_bs)\n    bs_A100.append(temp_A100_bs)\n    latency_our.append(temp_our_latency)\n    latency_A100.append(temp_A100_latency)\n# print(throughput_our)\n# print(throughput_A100)\nprint(latency_our)\nprint(latency_A100)\nprint(\n    statistics.geometric_mean(\n        (np.array(latency_our) / np.array(latency_A100)).flatten()\n    )\n)\n\n\n# Function to convert RGB to grayscale intensity\ndef get_intensity(color):\n    return color[0] * 0.299 + color[1] * 0.587 + color[2] * 0.114\n\n\ncmap = sns.color_palette(\"viridis\", as_cmap=True)\ndata = np.array(throughput_our)  # / np.array(throughput_A100)\nprint(data.mean())\nfig, ax = plt.subplots()\ncax = ax.imshow(data, interpolation=\"nearest\", cmap=cmap)\n# cax = sns.heatmap(data, cmap=\"Blues\")\n\n# Add a colorbar\nfig.colorbar(cax, shrink=0.5)\n\n# Set a threshold for deciding text color\nintensity_threshold = 0.5\nfor i in range(data.shape[0]):\n    for j in range(data.shape[1]):\n        # Get the color from the colormap\n        cell_color = cax.cmap(cax.norm(data[i, j]))\n        # Calculate intensity of the cell color\n        intensity = get_intensity(cell_color)\n        # Choose text color based on intensity\n        text_color = \"white\" if intensity < intensity_threshold else \"black\"\n        text = ax.text(\n            j, i, int(data[i, j]), ha=\"center\", va=\"center\", color=text_color\n        )\n\n# Set the x-axis and y-axis values\nx_axis_labels = [256, 512, 768, 1024, 1280, 1536, 1792, 2048]\ny_axis_labels = [256, 512, 1024, 2048]\n\n# Set ticks positions\nax.set_xticks(np.arange(len(x_axis_labels)))\nax.set_yticks(np.arange(len(y_axis_labels)))\n\n# Set ticks labels\nax.set_xticklabels(x_axis_labels)\nax.set_yticklabels(y_axis_labels)\n\n# Set labels for axes\nax.set_xlabel(\"Output Length\")\nax.set_ylabel(\"Input Length\")\nax.invert_yaxis()\n# # Rotate the tick labels for the x-axis if needed\n# plt.setp(ax.get_xticklabels(), rotation=45, ha=\"right\", rotation_mode=\"anchor\")\n\n# Show the plot\nplt.tight_layout()\nplt.savefig(\"figure12a.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\n\n\nimport statistics\n\ncmap = sns.color_palette(\"viridis\", as_cmap=True)\ndata = np.array(throughput_our) / np.array(throughput_A100)\nprint(statistics.geometric_mean(data.flatten()))\nfig, ax = plt.subplots()\ncax = ax.imshow(\n    data,\n    interpolation=\"nearest\",\n    cmap=cmap,\n)\n# cax = sns.heatmap(data, cmap=\"viridis\")\n\n# Add a colorbar\nfig.colorbar(cax, shrink=0.5)\n\n# Set a threshold for deciding text color\nintensity_threshold = 0.5\nfor i in range(data.shape[0]):\n    for j in range(data.shape[1]):\n        # Get the color from the colormap\n        cell_color = cax.cmap(cax.norm(data[i, j]))\n        # Calculate intensity of the cell color\n        intensity = get_intensity(cell_color)\n        # Choose text color based on intensity\n        text_color = \"white\" if intensity < intensity_threshold else \"black\"\n        text = ax.text(\n            j, i, round(data[i, j], 2), ha=\"center\", va=\"center\", color=text_color\n        )\n\n# Set the x-axis and y-axis values\nx_axis_labels = [256, 512, 768, 1024, 1280, 1536, 1792, 2048]\ny_axis_labels = [256, 512, 1024, 2048]\n\n# Set ticks positions\nax.set_xticks(np.arange(len(x_axis_labels)))\nax.set_yticks(np.arange(len(y_axis_labels)))\n\n# Set ticks labels\nax.set_xticklabels(x_axis_labels)\nax.set_yticklabels(y_axis_labels)\n\n# Set labels for axes\nax.set_xlabel(\"Output Length\")\nax.set_ylabel(\"Input Length\")\nax.invert_yaxis()\n# # Rotate the tick labels for the x-axis if needed\n# plt.setp(ax.get_xticklabels(), rotation=45, ha=\"right\", rotation_mode=\"anchor\")\n\n# Show the plot\nplt.tight_layout()\nplt.savefig(\"figure12b.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\n"
  },
  {
    "path": "ae/figure12/run_figure12.sh",
    "content": "rm A100/*.csv\nrm our/*.csv\nrm *.pdf\n\nmkdir A100\nmkdir our\n\ncd ../..\n\npython -m ae.figure12.test_throughput\n\ncd ae/figure12\npython plot_throughput.py"
  },
  {
    "path": "ae/figure12/test_throughput.py",
    "content": "from software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\nfrom design_space_exploration.dse import template_to_system, read_architecture_template\nfrom multiprocessing import Process, Lock\nfrom cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nimport time\n\nA100_specs = read_architecture_template(\"configs/GA100.json\")\nA100_system = template_to_system(A100_specs)\nour_specs = read_architecture_template(\"configs/prefilling_system.json\")\nour_system = template_to_system(our_specs)\nA100_compute_area_mm2 = calc_compute_chiplet_area_mm2(A100_specs)\nA100_io_area_mm2 = calc_io_die_area_mm2(A100_specs)\nour_compute_area_mm2 = calc_compute_chiplet_area_mm2(our_specs)\nour_io_area_mm2 = calc_io_die_area_mm2(our_specs)\nprint(f\"A100 compute area: {A100_compute_area_mm2} mm2\")\nprint(f\"A100 IO area: {A100_io_area_mm2} mm2\")\nprint(f\"A100 total area: {A100_compute_area_mm2+A100_io_area_mm2} mm2\")\nprint(f\"Our compute area: {our_compute_area_mm2} mm2\")\nprint(f\"Our IO area: {our_io_area_mm2} mm2\")\nprint(f\"Our total area: {our_compute_area_mm2+our_io_area_mm2} mm2\")\nwith open(\"ae/figure12/area.csv\", \"w\") as f:\n    f.write(f\"A100 compute area: {A100_compute_area_mm2} mm2\\n\")\n    f.write(f\"A100 IO area: {A100_io_area_mm2} mm2\\n\")\n    f.write(f\"A100 total area: {A100_compute_area_mm2+A100_io_area_mm2} mm2\\n\")\n    f.write(f\"Our compute area: {our_compute_area_mm2} mm2\\n\")\n    f.write(f\"Our IO area: {our_io_area_mm2} mm2\\n\")\n    f.write(f\"Our total area: {our_compute_area_mm2+our_io_area_mm2} mm2\\n\")\n\n\ndef simulate_decoding_latency(system, bs, seq_len, name, lock, heuristics):\n    model_auto_regression = TransformerBlockAutoRegressionTP(\n        d_model=12288,\n        n_heads=96,\n        device_count=1,\n        data_type=data_type_dict[\"fp16\"],\n    )\n    _ = model_auto_regression(\n        Tensor([bs, 1, 12288], data_type_dict[\"fp16\"]),\n        seq_len,\n    )\n    auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(\n        system, heuristics\n    )\n    with lock:\n        with open(f\"ae/figure12/{name}_decoding.csv\", \"a\") as f:\n            f.write(\n                f\"{bs}, {seq_len}, {auto_regression_latency_simulated}, {model_auto_regression.simluate_log}\\n\"\n            )\n\n\ndef simulate_prefill_latency(system, bs, seq_len, name, lock, heuristics):\n    model = TransformerBlockInitComputationTP(\n        d_model=12288,\n        n_heads=96,\n        device_count=1,\n        data_type=data_type_dict[\"fp16\"],\n    )\n    _ = model(\n        Tensor([bs, seq_len, 12288], data_type_dict[\"fp16\"]),\n    )\n    latency_simulated = model.compile_and_simulate(system, heuristics)\n    with lock:\n        with open(f\"ae/figure12/{name}_prefill.csv\", \"a\") as f:\n            f.write(f\"{bs}, {seq_len}, {latency_simulated}, {model.simluate_log}\\n\")\n\n\nlock_our_prefill = Lock()\nlock_our_decoding = Lock()\nlock_A100_prefill = Lock()\nlock_A100_decoding = Lock()\n\nprocesses = []\n\nfor input_seq_len in [\n    256,\n    512,\n    1024,\n    2048,\n]:\n    for output_seq_len in [\n        256,\n        512,\n        768,\n        1024,\n        1280,\n        1536,\n        1792,\n        2048,\n    ]:\n        seq_len = input_seq_len + output_seq_len\n        for system in [our_system, A100_system]:\n            if system == A100_system:\n                name = f\"A100/A100_{input_seq_len}_{output_seq_len}\"\n                lock = lock_A100_prefill\n                bs = (80e9 - 2 * 12 * 12288**2 * 12) // ((12 * 4 + 8) * seq_len * 12288)\n                heuristics = \"heuristic-GPU\"\n            else:\n                name = f\"our/our_{input_seq_len}_{output_seq_len}\"\n                lock = lock_our_prefill\n                bs = (512e9 - 2 * 12 * 12288**2 * 12) // (\n                    (12 * 4 + 8) * seq_len * 12288\n                )\n                heuristics = \"heuristic-our-throughput\"\n            bs = int(bs)\n            # print(bs)\n            p = Process(\n                target=simulate_prefill_latency,\n                args=(system, bs, input_seq_len, name, lock, heuristics),\n            )\n            processes.append(p)\n\n            for decoding_seq_len in range(input_seq_len, seq_len + 64, 64):\n                if system == A100_system:\n                    name = f\"A100/A100_{input_seq_len}_{output_seq_len}\"\n                    lock = lock_A100_decoding\n                    heuristics = \"heuristic-GPU\"\n                else:\n                    name = f\"our/our_{input_seq_len}_{output_seq_len}\"\n                    lock = lock_our_decoding\n                    heuristics = \"heuristic-our-throughput\"\n                p = Process(\n                    target=simulate_decoding_latency,\n                    args=(system, bs, decoding_seq_len, name, lock, heuristics),\n                )\n                processes.append(p)\n\nprint(len(processes))\n# exit()\ntry:\n    for p in processes:\n        p.start()\n    print(\"Processes started.\")\n    print(\"number of process:\", len(processes))\n    while any(p.is_alive() for p in processes):\n        time.sleep(1)\nexcept KeyboardInterrupt:\n    print(\"Terminating processes...\")\n    for p in processes:\n        p.terminate()\n        p.join()\n\n\nprint(\"All processes have finished.\")\n"
  },
  {
    "path": "ae/figure5/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure5/ab/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure5/ab/plot_matmul.py",
    "content": "import pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport numpy as np\n\n\nmatmul_TPUv3_sim = pd.read_csv(\n    \"matmul_TPUv3_sim.csv\", header=None, names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"]\n)\nmatmul_TPUv3_sim[\"throughput\"] = (\n    matmul_TPUv3_sim[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_TPUv3_sim.set_index([\"M\", \"N\", \"K\"], inplace=True)\nmatmul_TPUv3_roofline = pd.read_csv(\n    \"matmul_TPUv3_roofline.csv\",\n    header=None,\n    names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"],\n)\nmatmul_TPUv3_roofline[\"throughput\"] = (\n    matmul_TPUv3_roofline[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_TPUv3_roofline.set_index([\"M\", \"N\", \"K\"], inplace=True)\nmatmul_A100 = pd.read_csv(\n    \"real_hardware/matmul_A100.csv\", header=None, names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"]\n)\nmatmul_A100[\"throughput\"] = (\n    matmul_A100[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_A100.set_index([\"M\", \"N\", \"K\"], inplace=True)\nmatmul_A100_sim = pd.read_csv(\n    \"matmul_A100_sim.csv\", header=None, names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"]\n)\nmatmul_A100_sim[\"throughput\"] = (\n    matmul_A100_sim[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_A100_sim.set_index([\"M\", \"N\", \"K\"], inplace=True)\nmatmul_A100_roofline = pd.read_csv(\n    \"matmul_A100_roofline.csv\",\n    header=None,\n    names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"],\n)\nmatmul_A100_roofline[\"throughput\"] = (\n    matmul_A100_roofline[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_A100_roofline.set_index([\"M\", \"N\", \"K\"], inplace=True)\nmatmul_MI210 = pd.read_csv(\n    \"real_hardware/matmul_MI210.csv\", header=None, names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"]\n)\nmatmul_MI210[\"throughput\"] = (\n    matmul_MI210[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_MI210.set_index([\"M\", \"N\", \"K\"], inplace=True)\nmatmul_MI210_sim = pd.read_csv(\n    \"matmul_MI210_sim.csv\", header=None, names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"]\n)\nmatmul_MI210_sim[\"throughput\"] = (\n    matmul_MI210_sim[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_MI210_sim.set_index([\"M\", \"N\", \"K\"], inplace=True)\nmatmul_MI210_roofline = pd.read_csv(\n    \"matmul_MI210_roofline.csv\",\n    header=None,\n    names=[\"M\", \"N\", \"K\", \"latency\", \"throughput\"],\n)\nmatmul_MI210_roofline[\"throughput\"] = (\n    matmul_MI210_roofline[\"throughput\"].str.extract(r\"(\\d+\\.?\\d*)\").astype(float)\n)\nmatmul_MI210_roofline.set_index([\"M\", \"N\", \"K\"], inplace=True)\n\ncolor_NV = sns.color_palette(\"Greens_d\", 4)[1:]\ncolor_Google = sns.color_palette(\"Blues_d\", 4)[1:]\ncolor_AMD = sns.color_palette(\"flare\", 3)\n\nK = 12288\nN = K\ntitle = f\"Performance of Matmul with K={K}, N={N}\"\nM_list = []\nthroughput_TPU_list = []\nthroughput_TPU_sim_list = []\nthroughput_TPU_roofline_list = []\nthroughput_GPU_list = []\nthroughput_GPU_sim_list = []\nthroughput_GPU_roofline_list = []\nthroughput_AMD_list = []\nthroughput_AMD_sim_list = []\nthroughput_AMD_roofline_list = []\nfor M in range(6, 16):\n    M = 2**M\n    M_list.append(M)\n    throughput_TPU_sim_list.append(matmul_TPUv3_sim.loc[(M, N, K), \"throughput\"])\n    throughput_TPU_roofline_list.append(\n        matmul_TPUv3_roofline.loc[(M, N, K), \"throughput\"]\n    )\n    throughput_GPU_list.append(matmul_A100.loc[(M, N, K), \"throughput\"])\n    throughput_GPU_sim_list.append(matmul_A100_sim.loc[(M, N, K), \"throughput\"])\n    throughput_GPU_roofline_list.append(\n        matmul_A100_roofline.loc[(M, N, K), \"throughput\"]\n    )\n    throughput_AMD_list.append(matmul_MI210.loc[(M, N, K), \"throughput\"])\n    throughput_AMD_sim_list.append(matmul_MI210_sim.loc[(M, N, K), \"throughput\"])\n    throughput_AMD_roofline_list.append(\n        matmul_MI210_roofline.loc[(M, N, K), \"throughput\"]\n    )\n\n\n# plt.figure(figsize=(6, 2.8))\nplt.figure(figsize=(3.64, 2.8))\nplt.xscale(\"log\", base=2)\nplt.plot(\n    M_list,\n    throughput_GPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of NVIDIA A100\",\n    color=color_NV[0],\n)\nplt.plot(\n    M_list, throughput_GPU_list, marker=\"o\", label=\"Real NVIDIA A100\", color=color_NV[1]\n)\nplt.plot(\n    M_list,\n    throughput_GPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated NVIDIA A100\",\n    color=color_NV[2],\n)\nplt.plot(\n    M_list,\n    throughput_AMD_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of AMD MI210\",\n    color=color_AMD[0],\n)\nplt.plot(\n    M_list, throughput_AMD_list, marker=\"o\", label=\"Real AMD MI210\", color=color_AMD[1]\n)\nplt.plot(\n    M_list,\n    throughput_AMD_sim_list,\n    marker=\"x\",\n    label=\"Simulated AMD MI210\",\n    color=color_AMD[2],\n)\nplt.plot(\n    M_list,\n    throughput_TPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of Google TPUv3\",\n    color=color_Google[0],\n)\nplt.plot(\n    M_list,\n    throughput_TPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated Google TPUv3\",\n    color=color_Google[2],\n)\n\n\n# handles, labels = plt.gca().get_legend_handles_labels()\n# plt.legend(handles, labels, loc=\"upper left\", bbox_to_anchor=(1, 1))\n# plt.title(title)\nplt.xlabel(\"M\")\nplt.ylabel(\"TFLOPS\")\nplt.grid(True, which=\"both\", ls=\"--\", c=\"0.7\")  # Adding a grid for better readability\nplt.tight_layout()\nplt.savefig(\"figure5b.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n\n\nM = 8192\ntitle = f\"Performance of Matmul with M={M}\"\nK_list = []\nthroughput_TPU_list = []\nthroughput_TPU_sim_list = []\nthroughput_TPU_roofline_list = []\nthroughput_GPU_list = []\nthroughput_GPU_sim_list = []\nthroughput_GPU_roofline_list = []\nthroughput_AMD_list = []\nthroughput_AMD_sim_list = []\nthroughput_AMD_roofline_list = []\nfor K in range(6, 16):\n    K = 2**K\n    N = K\n    K_list.append(K)\n    throughput_TPU_sim_list.append(matmul_TPUv3_sim.loc[(M, N, K), \"throughput\"])\n    throughput_TPU_roofline_list.append(\n        matmul_TPUv3_roofline.loc[(M, N, K), \"throughput\"]\n    )\n    throughput_GPU_list.append(matmul_A100.loc[(M, N, K), \"throughput\"])\n    throughput_GPU_sim_list.append(matmul_A100_sim.loc[(M, N, K), \"throughput\"])\n    throughput_GPU_roofline_list.append(\n        matmul_A100_roofline.loc[(M, N, K), \"throughput\"]\n    )\n    throughput_AMD_list.append(matmul_MI210.loc[(M, N, K), \"throughput\"])\n    throughput_AMD_sim_list.append(matmul_MI210_sim.loc[(M, N, K), \"throughput\"])\n    throughput_AMD_roofline_list.append(\n        matmul_MI210_roofline.loc[(M, N, K), \"throughput\"]\n    )\n\n\nplt.figure(figsize=(3.64, 2.8))\nplt.xscale(\"log\", base=2)\nplt.plot(\n    K_list,\n    throughput_GPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of NVIDIA A100\",\n    color=color_NV[0],\n)\nplt.plot(\n    K_list, throughput_GPU_list, marker=\"o\", label=\"Real NVIDIA A100\", color=color_NV[1]\n)\nplt.plot(\n    K_list,\n    throughput_GPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated NVIDIA A100\",\n    color=color_NV[2],\n)\nplt.plot(\n    K_list,\n    throughput_AMD_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of AMD MI210\",\n    color=color_AMD[0],\n)\nplt.plot(\n    K_list, throughput_AMD_list, marker=\"o\", label=\"Real AMD MI210\", color=color_AMD[1]\n)\nplt.plot(\n    K_list,\n    throughput_AMD_sim_list,\n    marker=\"x\",\n    label=\"Simulated AMD MI210\",\n    color=color_AMD[2],\n)\nplt.plot(\n    K_list,\n    throughput_TPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of Google TPUv3\",\n    color=color_Google[0],\n)\nplt.plot(\n    K_list,\n    throughput_TPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated Google TPUv3\",\n    color=color_Google[2],\n)\n# plt.legend()\n# plt.title(title)\nplt.xlabel(\"N=K\")\nplt.ylabel(\"TFLOPS\")\nplt.grid(True, which=\"both\", ls=\"--\", c=\"0.7\")  # Adding a grid for better readability\nplt.tight_layout()\nplt.savefig(\"figure5a.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)"
  },
  {
    "path": "ae/figure5/ab/real_hardware/matmul_A100.csv",
    "content": "64, 12288, 12288, 0.1900ms, 101.7124Tflops\n128, 12288, 12288, 0.2003ms, 193.0114Tflops\n256, 12288, 12288, 0.3185ms, 242.7090Tflops\n512, 12288, 12288, 0.6118ms, 252.7351Tflops\n1024, 12288, 12288, 1.1990ms, 257.9115Tflops\n2048, 12288, 12288, 2.3586ms, 262.2263Tflops\n4096, 12288, 12288, 4.4576ms, 277.4929Tflops\n8192, 12288, 12288, 8.6216ms, 286.9431Tflops\n16384, 12288, 12288, 17.0307ms, 290.5223Tflops\n32768, 12288, 12288, 35.4407ms, 279.2160Tflops\n8192, 64, 64, 0.0296ms, 2.2700Tflops\n8192, 128, 128, 0.0310ms, 8.6608Tflops\n8192, 256, 256, 0.0356ms, 30.1244Tflops\n8192, 512, 512, 0.0471ms, 91.2121Tflops\n8192, 1024, 1024, 0.0927ms, 185.2380Tflops\n8192, 2048, 2048, 0.2818ms, 243.8497Tflops\n8192, 4096, 4096, 1.0210ms, 269.2169Tflops\n8192, 8192, 8192, 3.9614ms, 277.5532Tflops\n8192, 16384, 16384, 15.0087ms, 293.0334Tflops\n8192, 32768, 32768, 61.1346ms, 287.7616Tflops"
  },
  {
    "path": "ae/figure5/ab/real_hardware/matmul_MI210.csv",
    "content": "32, 12288, 12288, 0.5493ms, 17.5922Tflops\n64, 12288, 12288, 0.5584ms, 34.6135Tflops\n128, 12288, 12288, 0.5932ms, 65.1646Tflops\n256, 12288, 12288, 0.7699ms, 100.4209Tflops\n512, 12288, 12288, 1.4054ms, 110.0209Tflops\n1024, 12288, 12288, 2.7173ms, 113.8051Tflops\n2048, 12288, 12288, 5.3905ms, 114.7338Tflops\n4096, 12288, 12288, 10.4494ms, 118.3752Tflops\n8192, 12288, 12288, 20.7849ms, 119.0242Tflops\n16384, 12288, 12288, 41.1353ms, 120.2811Tflops\n32768, 12288, 12288, 81.4046ms, 121.5608Tflops\n8192, 32, 32, 0.0333ms, 0.5044Tflops\n8192, 64, 64, 0.0345ms, 1.9479Tflops\n8192, 128, 128, 0.0396ms, 6.7825Tflops\n8192, 256, 256, 0.0485ms, 22.1307Tflops\n8192, 512, 512, 0.0863ms, 49.7635Tflops\n8192, 1024, 1024, 0.1950ms, 88.0900Tflops\n8192, 2048, 2048, 0.5822ms, 118.0305Tflops\n8192, 4096, 4096, 2.2901ms, 120.0272Tflops\n8192, 8192, 8192, 9.4150ms, 116.7826Tflops\n8192, 16384, 16384, 36.7552ms, 119.6578Tflops\n8192, 32768, 32768, 146.2553ms, 120.2841Tflops"
  },
  {
    "path": "ae/figure5/ab/run.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../../..\n\npython -m ae.figure5.ab.test_matmul --simgpu --roofline\npython -m ae.figure5.ab.test_matmul --simtpu --roofline\npython -m ae.figure5.ab.test_matmul --simamd --roofline\n\npython -m ae.figure5.ab.test_matmul --simgpu\npython -m ae.figure5.ab.test_matmul --simtpu\npython -m ae.figure5.ab.test_matmul --simamd\n\ncd ae/figure5/ab\npython plot_matmul.py"
  },
  {
    "path": "ae/figure5/ab/test_matmul.py",
    "content": "from software_model.matmul import Matmul\nfrom software_model.utils import data_type_dict, Tensor\nfrom hardware_model.device import device_dict\nimport argparse\n\nif __name__ == \"__main__\":\n    parser = argparse.ArgumentParser()\n    parser.add_argument(\"--gpu\", action=\"store_true\", help=\"Enable GPU\")\n    parser.add_argument(\"--simtpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simtpu-new\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simgpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simamd\", action=\"store_true\", help=\"amd simulation\")\n    parser.add_argument(\"--roofline\", action=\"store_true\", help=\"Roofline simulation\")\n    args = parser.parse_args()\n\n    if args.simtpu:\n        pcb = device_dict[\"TPUv3\"]\n    if args.simtpu_new:\n        pcb = device_dict[\"TPUv3_new\"]\n    if args.simgpu:\n        pcb = device_dict[\"A100_80GB_fp16\"]\n\n    MI210 = device_dict[\"MI210\"]\n    amd_overhead = MI210.compute_module.overhead.softmax\n\n    K = 12288\n    N = K\n    titile = f\"Performance of Matmul with K={K}, N={N}\"\n    print(f\"{titile}\")\n\n    test_overhead = True\n\n    for M in range(5, 16):\n        M = 2**M\n        model = Matmul(data_type=data_type_dict[\"fp16\"])\n        _ = model(\n            Tensor([M, K]),\n            Tensor([K, N]),\n        )\n        if args.gpu:\n            if test_overhead:\n                model.gpu_kernel_launch_overhead()\n                test_overhead = False\n            latency = model.run_on_gpu()\n        if args.simtpu:\n            if args.roofline:\n                latency = model.roofline_model(pcb) + 110e-6\n                file_name='matmul_TPUv3_roofline.csv'\n            else:\n                latency = (\n                    model.compile_and_simulate(pcb, compile_mode=\"heuristic-TPU\")\n                    + 110e-6\n                )\n                file_name='matmul_TPUv3_sim.csv'\n\n        if args.simtpu_new:\n            if args.roofline:\n                latency = model.roofline_model(pcb) + 110e-6\n            else:\n                latency = (\n                    model.compile_and_simulate(pcb, compile_mode=\"heuristic-TPU-new\")\n                    + 110e-6\n                )\n        if args.simgpu:\n            if args.roofline:\n                latency = model.roofline_model(pcb) + 2.1e-5\n                file_name='matmul_A100_roofline.csv'\n            else:\n                latency = (\n                    model.compile_and_simulate(pcb, compile_mode=\"heuristic-GPU\")\n                    + 2.1e-5\n                )\n                file_name='matmul_A100_sim.csv'\n        if args.simamd:\n            if args.roofline:\n                latency = model.roofline_model(pcb_module=MI210) + amd_overhead\n                file_name='matmul_MI210_roofline.csv'\n            else:\n                latency = (\n                    model.compile_and_simulate(\n                        pcb_module=MI210, compile_mode=\"heuristic-GPU\"\n                    )\n                    + amd_overhead\n                )\n                file_name='matmul_MI210_sim.csv'\n        tflops = 2 * M * N * K / latency / 1e12\n        print(f\"{M}, {N}, {K}, {latency*1e3:.4f}ms, {tflops:.4f}Tflops\", flush=True)\n        with open(f'ae/figure5/ab/{file_name}', 'a') as f:\n            f.write(f\"{M}, {N}, {K}, {latency*1e3:.4f}ms, {tflops:.4f}Tflops\\n\")\n\n    M = 8192\n    print(f\"Performance of Matmul with M={M}, N=K\")\n    for K in range(5, 16):\n        K = 2**K\n        N = K\n        model = Matmul(data_type=data_type_dict[\"fp16\"])\n        _ = model(\n            Tensor([M, K]),\n            Tensor([K, N]),\n        )\n        if args.gpu:\n            latency = model.run_on_gpu()\n        if args.simtpu:\n            if args.roofline:\n                latency = model.roofline_model(pcb) + 110e-6\n            else:\n                latency = (\n                    model.compile_and_simulate(pcb, compile_mode=\"heuristic-TPU\")\n                    + 110e-6\n                )\n        if args.simtpu_new:\n            if args.roofline:\n                latency = model.roofline_model(pcb) + 110e-6\n            else:\n                latency = (\n                    model.compile_and_simulate(pcb, compile_mode=\"heuristic-TPU-new\")\n                    + 110e-6\n                )\n        if args.simgpu:\n            if args.roofline:\n                latency = model.roofline_model(pcb) + 2.1e-5\n            else:\n                latency = (\n                    model.compile_and_simulate(pcb, compile_mode=\"heuristic-GPU\")\n                    + 2.1e-5\n                )\n        if args.simamd:\n            if args.roofline:\n                latency = model.roofline_model(pcb_module=MI210) + amd_overhead\n            else:\n                latency = (\n                    model.compile_and_simulate(\n                        pcb_module=MI210, compile_mode=\"heuristic-GPU\"\n                    )\n                    + amd_overhead\n                )\n        tflops = 2 * M * N * K / latency / 1e12\n        print(f\"{M}, {N}, {K}, {latency*1e3:.4f}ms, {tflops:.4f}Tflops\", flush=True)\n        with open(f'ae/figure5/ab/{file_name}', 'a') as f:\n            f.write(f\"{M}, {N}, {K}, {latency*1e3:.4f}ms, {tflops:.4f}Tflops\\n\")\n"
  },
  {
    "path": "ae/figure5/cf/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure5/cf/plot_softmax.py",
    "content": "import pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport numpy as np\n\n\nsoftmax_TPUv3_sim = pd.read_csv(\n    \"softmax_TPUv3_sim.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_TPUv3_sim.set_index([\"M\", \"N\"], inplace=True)\nsoftmax_TPUv3_roofline = pd.read_csv(\n    \"softmax_TPUv3_roofline.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_TPUv3_roofline.set_index([\"M\", \"N\"], inplace=True)\nsoftmax_A100 = pd.read_csv(\n    \"real_hardware/softmax_A100.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_A100.set_index([\"M\", \"N\"], inplace=True)\nsoftmax_A100_sim = pd.read_csv(\n    \"softmax_A100_sim.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_A100_sim.set_index([\"M\", \"N\"], inplace=True)\nsoftmax_A100_roofline = pd.read_csv(\n    \"softmax_A100_roofline.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_A100_roofline.set_index([\"M\", \"N\"], inplace=True)\nsoftmax_MI210 = pd.read_csv(\n    \"real_hardware/softmax_MI210.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_MI210.set_index([\"M\", \"N\"], inplace=True)\nsoftmax_MI210_sim = pd.read_csv(\n    \"softmax_MI210_sim.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_MI210_sim.set_index([\"M\", \"N\"], inplace=True)\nsoftmax_MI210_roofline = pd.read_csv(\n    \"softmax_MI210_roofline.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nsoftmax_MI210_roofline.set_index([\"M\", \"N\"], inplace=True)\n\ncolor_NV = sns.color_palette(\"Greens_d\", 4)[1:]\ncolor_Google = sns.color_palette(\"Blues_d\", 4)[1:]\ncolor_AMD = sns.color_palette(\"flare\", 3)\n\nM = 4096\ntitle = f\"Performance of softmax with M={M}\"\nN_list = []\nthroughput_TPU_list = []\nthroughput_TPU_sim_list = []\nthroughput_TPU_roofline_list = []\nthroughput_GPU_list = []\nthroughput_GPU_sim_list = []\nthroughput_GPU_roofline_list = []\nthroughput_AMD_list = []\nthroughput_AMD_sim_list = []\nthroughput_AMD_roofline_list = []\nfor N in range(6, 16):\n    N = 2**N\n    N_list.append(N)\n    # print(M,N)\n    # print(softmax_TPUv3.loc[(M, N), 'throughput'])\n\n    throughput_TPU_sim_list.append(\n        softmax_TPUv3_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_TPU_roofline_list.append(\n        softmax_TPUv3_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_GPU_list.append(softmax_A100.loc[(M, N), \"throughput\"].values[0])\n    throughput_GPU_sim_list.append(softmax_A100_sim.loc[(M, N), \"throughput\"].values[0])\n    throughput_GPU_roofline_list.append(\n        softmax_A100_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_AMD_list.append(softmax_MI210.loc[(M, N), \"throughput\"].values[0])\n    throughput_AMD_sim_list.append(\n        softmax_MI210_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_AMD_roofline_list.append(\n        softmax_MI210_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n\nplt.figure(figsize=(3.7, 2))\nplt.xscale(\"log\", base=2)\nplt.plot(\n    N_list,\n    throughput_GPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of NVIDIA A100\",\n    color=color_NV[0],\n)\nplt.plot(\n    N_list, throughput_GPU_list, marker=\"o\", label=\"Real NVIDIA A100\", color=color_NV[1]\n)\nplt.plot(\n    N_list,\n    throughput_GPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated NVIDIA A100\",\n    color=color_NV[2],\n)\nplt.plot(\n    N_list,\n    throughput_AMD_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of AMD MI210\",\n    color=color_AMD[0],\n)\nplt.plot(\n    N_list, throughput_AMD_list, marker=\"o\", label=\"Real AMD MI210\", color=color_AMD[1]\n)\nplt.plot(\n    N_list,\n    throughput_AMD_sim_list,\n    marker=\"x\",\n    label=\"Simulated AMD MI210\",\n    color=color_AMD[2],\n)\nplt.plot(\n    N_list,\n    throughput_TPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of Google TPUv3\",\n    color=color_Google[0],\n)\n\nplt.plot(\n    N_list,\n    throughput_TPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated Google TPUv3\",\n    color=color_Google[2],\n)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles, labels, loc=\"upper left\", bbox_to_anchor=(1, 1.1))\n# plt.legend()\n# plt.title(title)\nplt.xlabel(\"N\")\nplt.ylabel(\"G Elements/s\")\nplt.grid(True, which=\"both\", ls=\"--\", c=\"0.7\")  # Adding a grid for better readability\nplt.savefig(\"figure5f.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n\n\nN = 4096\ntitle = f\"Performance of softmax with N={N}\"\nM_list = []\nthroughput_TPU_list = []\nthroughput_TPU_sim_list = []\nthroughput_TPU_roofline_list = []\nthroughput_GPU_list = []\nthroughput_GPU_sim_list = []\nthroughput_GPU_roofline_list = []\nthroughput_AMD_list = []\nthroughput_AMD_sim_list = []\nthroughput_AMD_roofline_list = []\nfor M in range(6, 16):\n    M = 2**M\n    M_list.append(M)\n    throughput_TPU_sim_list.append(\n        softmax_TPUv3_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_TPU_roofline_list.append(\n        softmax_TPUv3_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_GPU_list.append(softmax_A100.loc[(M, N), \"throughput\"].values[0])\n    throughput_GPU_sim_list.append(softmax_A100_sim.loc[(M, N), \"throughput\"].values[0])\n    throughput_GPU_roofline_list.append(\n        softmax_A100_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_AMD_list.append(softmax_MI210.loc[(M, N), \"throughput\"].values[0])\n    throughput_AMD_sim_list.append(\n        softmax_MI210_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_AMD_roofline_list.append(\n        softmax_MI210_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n\n\nplt.figure(figsize=(3.7, 2.8))\nplt.xscale(\"log\", base=2)\nplt.plot(\n    M_list,\n    throughput_GPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of NVIDIA A100\",\n    color=color_NV[0],\n)\nplt.plot(\n    M_list, throughput_GPU_list, marker=\"o\", label=\"Real NVIDIA A100\", color=color_NV[1]\n)\nplt.plot(\n    M_list,\n    throughput_GPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated NVIDIA A100\",\n    color=color_NV[2],\n)\nplt.plot(\n    M_list,\n    throughput_AMD_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of AMD MI210\",\n    color=color_AMD[0],\n)\nplt.plot(\n    M_list, throughput_AMD_list, marker=\"o\", label=\"Real AMD MI210\", color=color_AMD[1]\n)\nplt.plot(\n    M_list,\n    throughput_AMD_sim_list,\n    marker=\"x\",\n    label=\"Simulated AMD MI210\",\n    color=color_AMD[2],\n)\nplt.plot(\n    M_list,\n    throughput_TPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of Google TPUv3\",\n    color=color_Google[0],\n)\nplt.plot(\n    M_list,\n    throughput_TPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated Google TPUv3\",\n    color=color_Google[2],\n)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles, labels, loc=\"upper left\", bbox_to_anchor=(1, 1))\n# plt.legend()\n# plt.title(title)\nplt.xlabel(\"M\")\nplt.ylabel(\"G Elements/s\")\nplt.grid(True, which=\"both\", ls=\"--\", c=\"0.7\")  # Adding a grid for better readability\nplt.savefig(\"figure5c.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n"
  },
  {
    "path": "ae/figure5/cf/real_hardware/softmax_A100.csv",
    "content": "4096, 32, 9.99556025250909\n4096, 64, 19.634136210285714\n4096, 128, 37.27158060257627\n4096, 256, 68.719476736\n4096, 512, 111.34294964820253\n4096, 1024, 152.9755308210087\n4096, 2048, 167.5446289944381\n4096, 4096, 204.5603028420465\n4096, 8192, 216.51921285435077\n4096, 16384, 242.0249154863766\n4096, 32768, 240.88573103179803\n32, 4096, 8.457781752123077\n64, 4096, 16.65926708751515\n128, 4096, 30.97215852890141\n256, 4096, 57.11748715719481\n512, 4096, 96.6603628814066\n1024, 4096, 137.438953472\n2048, 4096, 166.75057862005687\n4096, 4096, 203.9673744280116\n8192, 4096, 229.96321626687583\n16384, 4096, 247.12465031664266\n32768, 4096, 278.826128490001"
  },
  {
    "path": "ae/figure5/cf/real_hardware/softmax_MI210.csv",
    "content": "4096, 32, 5.389762881254902\n4096, 64, 10.372751205433962\n4096, 128, 13.49094021811043\n4096, 256, 36.049561566426235\n4096, 512, 60.662710497986204\n4096, 1024, 87.52331365381094\n4096, 2048, 75.18028224109402\n4096, 4096, 80.05545412703526\n4096, 8192, 70.97200623062432\n4096, 16384, 66.22940628486023\n4096, 32768, 61.59189862377593\n32, 4096, 4.822419420070175\n64, 4096, 9.012390391606559\n128, 4096, 15.820311191021583\n256, 4096, 28.28325730613505\n512, 4096, 43.76165682690547\n1024, 4096, 60.662710497986204\n2048, 4096, 72.54509709037526\n4096, 4096, 80.28379255865829\n8192, 4096, 84.78161949116145\n16384, 4096, 86.98237846435599\n32768, 4096, 88.01594018469544"
  },
  {
    "path": "ae/figure5/cf/run.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../../..\n\npython -m ae.figure5.cf.test_softmax --simgpu --roofline\npython -m ae.figure5.cf.test_softmax --simtpu --roofline\npython -m ae.figure5.cf.test_softmax --simamd --roofline\n\npython -m ae.figure5.cf.test_softmax --simgpu\npython -m ae.figure5.cf.test_softmax --simtpu\npython -m ae.figure5.cf.test_softmax --simamd\n\ncd ae/figure5/cf\npython plot_softmax.py"
  },
  {
    "path": "ae/figure5/cf/test_softmax.py",
    "content": "from software_model.softmax import Softmax\nfrom software_model.utils import data_type_dict, Tensor\nfrom hardware_model.device import device_dict\nimport argparse\n\nif __name__ == \"__main__\":\n    parser = argparse.ArgumentParser()\n    parser.add_argument(\"--gpu\", action=\"store_true\", help=\"Enable GPU\")\n    parser.add_argument(\"--simgpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simtpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simamd\", action=\"store_true\", help=\"amd simulation\")\n    parser.add_argument(\"--roofline\", action=\"store_true\", help=\"Roofline simulation\")\n    args = parser.parse_args()\n\n    A100 = device_dict[\"A100_80GB_fp16\"]\n    TPU = device_dict[\"TPUv3\"]\n    MI210 = device_dict[\"MI210\"]\n    tpu_overhead = 300e-6\n    gpu_overhead = 12e-6\n    amd_overhead = MI210.compute_module.overhead.softmax\n\n    if args.gpu:\n        gpu_kernel_launch_overhead = Softmax.gpu_kernel_launch_overhead()\n\n    print(f\"Performance of Softmax\")\n    M = 2**12\n    for N in range(5, 16):\n        N = 2**N\n        if args.simtpu:\n            model = Softmax(data_type=data_type_dict[\"fp32\"])\n            _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n            if args.roofline:\n                latency = model.roofline_model(pcb_module=TPU) + tpu_overhead\n                file_name = \"softmax_TPUv3_roofline.csv\"\n            else:\n                latency = model.compile_and_simulate(pcb_module=TPU) + tpu_overhead\n                file_name = \"softmax_TPUv3_sim.csv\"\n        else:\n            model = Softmax(data_type=data_type_dict[\"fp16\"])\n            _ = model(\n                Tensor([M, N]),\n            )\n            if args.gpu:\n                latency = model.run_on_gpu()\n            if args.simgpu:\n                if args.roofline:\n                    latency = model.roofline_model(pcb_module=A100) + gpu_overhead\n                    file_name = \"softmax_A100_roofline.csv\"\n                else:\n                    latency = model.compile_and_simulate(pcb_module=A100) + gpu_overhead\n                    file_name = \"softmax_A100_sim.csv\"\n            if args.simamd:\n                model = Softmax(data_type=data_type_dict[\"fp32\"])\n                _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n                if args.roofline:\n                    latency = model.roofline_model(pcb_module=MI210) + amd_overhead\n                    file_name = \"softmax_MI210_roofline.csv\"\n                else:\n                    latency = (\n                        model.compile_and_simulate(pcb_module=MI210) + amd_overhead\n                    )\n                    file_name = \"softmax_MI210_sim.csv\"\n\n        print(f\"{M}, {N}, {M*N/latency/1e9}\")\n        with open(f\"ae/figure5/cf/{file_name}\", \"a\") as f:\n            f.write(f\"{M}, {N}, {M*N/latency/1e9}\\n\")\n\n    N = 2**12\n    for M in range(5, 16):\n        M = 2**M\n        if args.simtpu:\n            model = Softmax(data_type=data_type_dict[\"fp32\"])\n            _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n            if args.roofline:\n                latency = model.roofline_model(pcb_module=TPU) + tpu_overhead\n            else:\n                latency = model.compile_and_simulate(pcb_module=TPU) + tpu_overhead\n        else:\n            model = Softmax(data_type=data_type_dict[\"fp16\"])\n            _ = model(\n                Tensor([M, N]),\n            )\n            if args.gpu:\n                latency = model.run_on_gpu()\n            if args.simgpu:\n                if args.roofline:\n                    latency = model.roofline_model(pcb_module=A100) + gpu_overhead\n                else:\n                    latency = model.compile_and_simulate(pcb_module=A100) + gpu_overhead\n            if args.simamd:\n                model = Softmax(data_type=data_type_dict[\"fp32\"])\n                _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n                if args.roofline:\n                    latency = model.roofline_model(pcb_module=MI210) + amd_overhead\n                else:\n                    latency = (\n                        model.compile_and_simulate(pcb_module=MI210) + amd_overhead\n                    )\n        print(f\"{M}, {N}, {M*N/latency/1e9}\")\n        with open(f\"ae/figure5/cf/{file_name}\", \"a\") as f:\n            f.write(f\"{M}, {N}, {M*N/latency/1e9}\\n\")\n"
  },
  {
    "path": "ae/figure5/de/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure5/de/plot_layernorm.py",
    "content": "import pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport numpy as np\n\n\nlayernorm_TPUv3_sim = pd.read_csv(\n    \"layernorm_TPUv3_sim.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nlayernorm_TPUv3_sim.set_index([\"M\", \"N\"], inplace=True)\nlayernorm_TPUv3_roofline = pd.read_csv(\n    \"layernorm_TPUv3_roofline.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nlayernorm_TPUv3_roofline.set_index([\"M\", \"N\"], inplace=True)\nlayernorm_A100 = pd.read_csv(\n    \"real_hardware/layernorm_A100.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nlayernorm_A100.set_index([\"M\", \"N\"], inplace=True)\nlayernorm_A100_sim = pd.read_csv(\n    \"layernorm_A100_sim.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nlayernorm_A100_sim.set_index([\"M\", \"N\"], inplace=True)\nlayernorm_A100_roofline = pd.read_csv(\n    \"layernorm_A100_roofline.csv\", header=None, names=[\"M\", \"N\", \"throughput\"]\n)\nlayernorm_A100_roofline.set_index([\"M\", \"N\"], inplace=True)\n\n\ncolor_NV = sns.color_palette(\"Greens_d\", 4)[1:]\ncolor_Google = sns.color_palette(\"Blues_d\", 4)[1:]\ncolor_AMD = sns.color_palette(\"flare\", 3)\n\nM = 4096\ntitle = f\"Performance of layernorm with M={M}\"\nN_list = []\nthroughput_TPU_list = []\nthroughput_TPU_sim_list = []\nthroughput_TPU_roofline_list = []\nthroughput_GPU_list = []\nthroughput_GPU_sim_list = []\nthroughput_GPU_roofline_list = []\n\nfor N in range(6, 16):\n    N = 2**N\n    N_list.append(N)\n    throughput_TPU_sim_list.append(\n        layernorm_TPUv3_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_TPU_roofline_list.append(\n        layernorm_TPUv3_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_GPU_list.append(layernorm_A100.loc[(M, N), \"throughput\"].values[0])\n    throughput_GPU_sim_list.append(\n        layernorm_A100_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_GPU_roofline_list.append(\n        layernorm_A100_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n\nplt.figure(figsize=(3.64, 2))\nplt.xscale(\"log\", base=2)\nplt.plot(\n    N_list,\n    throughput_GPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of NVIDIA A100\",\n    color=color_NV[0],\n)\nplt.plot(\n    N_list, throughput_GPU_list, marker=\"o\", label=\"Real NVIDIA A100\", color=color_NV[1]\n)\nplt.plot(\n    N_list,\n    throughput_GPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated NVIDIA A100\",\n    color=color_NV[2],\n)\nplt.plot(\n    N_list,\n    throughput_TPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of Google TPUv3\",\n    color=color_Google[0],\n)\n\nplt.plot(\n    N_list,\n    throughput_TPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated Google TPUv3\",\n    color=color_Google[2],\n)\n\n\n# plt.legend()\n# plt.title(title)\nplt.xlabel(\"N\")\nplt.ylabel(\"G Elements/s\")\nplt.grid(True, which=\"both\", ls=\"--\", c=\"0.7\")  # Adding a grid for better readability\nplt.savefig(\"figure5e.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n\nN = 4096\ntitle = f\"Performance of layernorm with N={N}\"\nM_list = []\nthroughput_TPU_list = []\nthroughput_TPU_sim_list = []\nthroughput_TPU_roofline_list = []\nthroughput_GPU_list = []\nthroughput_GPU_sim_list = []\nthroughput_GPU_roofline_list = []\n\nfor M in range(6, 16):\n    M = 2**M\n    M_list.append(M)\n    throughput_TPU_sim_list.append(\n        layernorm_TPUv3_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_TPU_roofline_list.append(\n        layernorm_TPUv3_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_GPU_list.append(layernorm_A100.loc[(M, N), \"throughput\"].values[0])\n    throughput_GPU_sim_list.append(\n        layernorm_A100_sim.loc[(M, N), \"throughput\"].values[0]\n    )\n    throughput_GPU_roofline_list.append(\n        layernorm_A100_roofline.loc[(M, N), \"throughput\"].values[0]\n    )\n\n\nplt.figure(figsize=(3.64, 2))\nplt.xscale(\"log\", base=2)\nplt.plot(\n    M_list,\n    throughput_GPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of NVIDIA A100\",\n    color=color_NV[0],\n)\nplt.plot(\n    M_list, throughput_GPU_list, marker=\"o\", label=\"Real NVIDIA A100\", color=color_NV[1]\n)\nplt.plot(\n    M_list,\n    throughput_GPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated NVIDIA A100\",\n    color=color_NV[2],\n)\nplt.plot(\n    M_list,\n    throughput_TPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of Google TPUv3\",\n    color=color_Google[0],\n)\n\nplt.plot(\n    M_list,\n    throughput_TPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated Google TPUv3\",\n    color=color_Google[2],\n)\n\n# plt.legend()\n# plt.title(title)\nplt.xlabel(\"M\")\nplt.ylabel(\"G Elements/s\")\nplt.grid(True, which=\"both\", ls=\"--\", c=\"0.7\")  # Adding a grid for better readability\nplt.savefig(\"figure5d.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n"
  },
  {
    "path": "ae/figure5/de/real_hardware/layernorm_A100.csv",
    "content": "4096, 32, 2.476377540036036\n4096, 64, 4.8436635584845815\n4096, 128, 10.064179659276888\n4096, 256, 19.590407621844097\n4096, 512, 39.26827242057143\n4096, 1024, 78.888726656574\n4096, 2048, 139.06866438273516\n4096, 4096, 211.31755008307508\n4096, 8192, 265.2921552409576\n4096, 16384, 210.44858071824746\n4096, 32768, 199.2743197951547\n32, 4096, 2.4988900631272726\n64, 4096, 5.020601040073059\n128, 4096, 9.99556025250909\n256, 4096, 20.082404160292235\n512, 4096, 40.16480832058447\n1024, 4096, 79.6026517846878\n2048, 4096, 141.87246810012903\n4096, 4096, 211.6353208350797\n8192, 4096, 284.89370112414576\n16384, 4096, 345.7923546813956\n32768, 4096, 385.84643825998086"
  },
  {
    "path": "ae/figure5/de/real_hardware/layernorm_MI210.csv",
    "content": "4096, 32, 2.3695247806698823\n4096, 64, 4.729122950631834\n4096, 128, 9.17590195596949\n4096, 256, 18.43588592802619\n4096, 512, 31.59641013907877\n4096, 1024, 52.44807583429779\n4096, 2048, 83.74459902278055\n4096, 4096, 89.41186119969811\n4096, 8192, 86.39576298097589\n4096, 16384, 86.3601901230308\n4096, 32768, 78.76990948928942\n32, 4096, 3.885694391427885\n64, 4096, 6.742243759280835\n128, 4096, 11.78431162745035\n256, 4096, 22.64512970663591\n512, 4096, 39.53264699736632\n1024, 4096, 58.88026281772146\n2048, 4096, 75.69152349271899\n4096, 4096, 89.32684940809148\n8192, 4096, 97.43158473170392\n16384, 4096, 101.13477801032278\n32768, 4096, 104.08326540288465"
  },
  {
    "path": "ae/figure5/de/run.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../../..\n\npython -m ae.figure5.de.test_layernorm --simgpu --roofline\npython -m ae.figure5.de.test_layernorm --simtpu --roofline\n\npython -m ae.figure5.de.test_layernorm --simgpu\npython -m ae.figure5.de.test_layernorm --simtpu\n\ncd ae/figure5/de\npython plot_layernorm.py"
  },
  {
    "path": "ae/figure5/de/test_layernorm.py",
    "content": "from software_model.layernorm import LayerNorm\nfrom software_model.utils import data_type_dict, Tensor\nfrom hardware_model.device import device_dict\nimport argparse\n\nif __name__ == \"__main__\":\n    parser = argparse.ArgumentParser()\n    parser.add_argument(\"--gpu\", action=\"store_true\", help=\"Enable GPU\")\n    parser.add_argument(\"--amd\", action=\"store_true\", help=\"Enable AMD\")\n    parser.add_argument(\"--simgpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simtpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simamd\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--roofline\", action=\"store_true\", help=\"Roofline simulation\")\n    args = parser.parse_args()\n\n    A100 = device_dict[\"A100_80GB_fp16\"]\n    TPU = device_dict[\"TPUv3\"]\n    MI210 = device_dict[\"MI210\"]\n\n    if args.gpu:\n        gpu_kernel_launch_overhead = LayerNorm.gpu_kernel_launch_overhead()\n\n    print(f\"Performance of LayerNorm\")\n    M = 2**12\n    for N in range(5, 16):\n        N = 2**N\n        # N = 2**15\n        if args.simtpu:\n            model = LayerNorm(data_type=data_type_dict[\"fp32\"])\n            _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n            if args.roofline:\n                latency = model.roofline_model(TPU) + 140e-6\n                file_name = \"layernorm_TPUv3_roofline.csv\"\n            else:\n                latency = (\n                    model.compile_and_simulate(\n                        pcb_module=TPU, compile_mode=\"heuristic-TPU\"\n                    )\n                    + 140e-6\n                )\n                file_name = \"layernorm_TPUv3_sim.csv\"\n        else:\n            model = LayerNorm(data_type=data_type_dict[\"fp16\"])\n            _ = model(\n                Tensor([M, N]),\n            )\n            if args.gpu:\n                latency = model.run_on_gpu()\n            if args.amd:\n                # model.amd_kernel_launch_overhead()\n                latency = model.run_on_amd()\n            if args.simgpu:\n                if args.roofline:\n                    latency = model.roofline_model(A100) + 4.5e-5\n                    file_name = \"layernorm_A100_roofline.csv\"\n                else:\n                    latency = (\n                        model.compile_and_simulate(\n                            pcb_module=A100, compile_mode=\"heuristic-GPU\"\n                        )\n                        + 4.5e-5\n                    )\n                    file_name = \"layernorm_A100_sim.csv\"\n            if args.simamd:\n                model = LayerNorm(data_type=data_type_dict[\"fp32\"])\n                _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n                if args.roofline:\n                    latency = (\n                        model.roofline_model(MI210)\n                        + MI210.compute_module.overhead.layernorm\n                    )\n                    file_name = \"layernorm_MI210_roofline.csv\"\n                else:\n                    latency = (\n                        model.compile_and_simulate(\n                            pcb_module=MI210, compile_mode=\"heuristic-GPU\"\n                        )\n                        + MI210.compute_module.overhead.layernorm\n                    )\n                    file_name = \"layernorm_MI210_sim.csv\"\n        print(f\"{M}, {N}, {M*N/latency/1e9}\")\n        with open(f\"ae/figure5/de/{file_name}\", \"a\") as f:\n            f.write(f\"{M}, {N}, {M*N/latency/1e9}\\n\")\n\n    N = 2**12\n    for M in range(5, 16):\n        M = 2**M\n        if args.simtpu:\n            model = LayerNorm(data_type=data_type_dict[\"fp32\"])\n            _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n            if args.roofline:\n                latency = model.roofline_model(TPU) + 140e-6\n            else:\n                latency = (\n                    model.compile_and_simulate(\n                        pcb_module=TPU, compile_mode=\"heuristic-TPU\"\n                    )\n                    + 140e-6\n                )\n        else:\n            model = LayerNorm(data_type=data_type_dict[\"fp16\"])\n            _ = model(\n                Tensor([M, N]),\n            )\n            if args.gpu:\n                latency = model.run_on_gpu()\n            if args.amd:\n                latency = model.run_on_amd()\n            if args.simgpu:\n                if args.roofline:\n                    latency = model.roofline_model(A100) + 4.5e-5\n                else:\n                    latency = (\n                        model.compile_and_simulate(\n                            pcb_module=A100, compile_mode=\"heuristic-GPU\"\n                        )\n                        + 4.5e-5\n                    )\n            if args.simamd:\n                model = LayerNorm(data_type=data_type_dict[\"fp32\"])\n                _ = model(Tensor([M, N], data_type=data_type_dict[\"fp32\"]))\n                if args.roofline:\n                    latency = (\n                        model.roofline_model(MI210)\n                        + MI210.compute_module.overhead.layernorm\n                    )\n                else:\n                    latency = (\n                        model.compile_and_simulate(\n                            pcb_module=MI210, compile_mode=\"heuristic-GPU\"\n                        )\n                        + MI210.compute_module.overhead.layernorm\n                    )\n        print(f\"{M}, {N}, {M*N/latency/1e9}\")\n        with open(f\"ae/figure5/de/{file_name}\", \"a\") as f:\n            f.write(f\"{M}, {N}, {M*N/latency/1e9}\\n\")\n"
  },
  {
    "path": "ae/figure5/g/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure5/g/plot_gelu.py",
    "content": "import pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport numpy as np\n\n\ngelu_TPUv3_sim = pd.read_csv(\n    \"gelu_TPUv3_sim.csv\", header=None, names=[\"M\", \"throughput\"]\n)\ngelu_TPUv3_roofline = pd.read_csv(\n    \"gelu_TPUv3_roofline.csv\", header=None, names=[\"M\", \"throughput\"]\n)\ngelu_A100 = pd.read_csv(\"real_hardware/gelu_A100.csv\", header=None, names=[\"M\", \"throughput\"])\ngelu_A100_sim = pd.read_csv(\"gelu_A100_sim.csv\", header=None, names=[\"M\", \"throughput\"])\ngelu_A100_roofline = pd.read_csv(\n    \"gelu_A100_roofline.csv\", header=None, names=[\"M\", \"throughput\"]\n)\ngelu_MI210 = pd.read_csv(\"real_hardware/gelu_MI210.csv\", header=None, names=[\"M\", \"throughput\"])\ngelu_MI210_sim = pd.read_csv(\n    \"gelu_MI210_sim.csv\", header=None, names=[\"M\", \"throughput\"]\n)\ngelu_MI210_roofline = pd.read_csv(\n    \"gelu_MI210_roofline.csv\", header=None, names=[\"M\", \"throughput\"]\n)\n\ncolor_NV = sns.color_palette(\"Greens_d\", 4)[1:]\ncolor_Google = sns.color_palette(\"Blues_d\", 4)[1:]\ncolor_AMD = sns.color_palette(\"flare\", 3)\n\nM = 4096\ntitle = f\"Performance of gelu with M={M}\"\nM_list = []\nthroughput_TPU_list = []\nthroughput_TPU_sim_list = []\nthroughput_TPU_roofline_list = []\nthroughput_GPU_list = []\nthroughput_GPU_sim_list = []\nthroughput_GPU_roofline_list = []\nthroughput_AMD_list = []\nthroughput_AMD_sim_list = []\nthroughput_AMD_roofline_list = []\nfor M in range(10, 30):\n    M = 2**M\n    M_list.append(M)\n    \n    throughput_TPU_sim_list.append(\n        gelu_TPUv3_sim[gelu_TPUv3_sim[\"M\"] == M][\"throughput\"].iloc[0]\n    )\n    throughput_TPU_roofline_list.append(\n        gelu_TPUv3_roofline[gelu_TPUv3_roofline[\"M\"] == M][\"throughput\"].iloc[0]\n    )\n    throughput_GPU_list.append(gelu_A100[gelu_A100[\"M\"] == M][\"throughput\"].iloc[0])\n    throughput_GPU_sim_list.append(\n        gelu_A100_sim[gelu_A100_sim[\"M\"] == M][\"throughput\"].iloc[0]\n    )\n    throughput_GPU_roofline_list.append(\n        gelu_A100_roofline[gelu_A100_roofline[\"M\"] == M][\"throughput\"].iloc[0]\n    )\n    throughput_AMD_list.append(gelu_MI210[gelu_MI210[\"M\"] == M][\"throughput\"].iloc[0])\n    throughput_AMD_sim_list.append(\n        gelu_MI210_sim[gelu_MI210_sim[\"M\"] == M][\"throughput\"].iloc[0]\n    )\n    throughput_AMD_roofline_list.append(\n        gelu_MI210_roofline[gelu_MI210_roofline[\"M\"] == M][\"throughput\"].iloc[0]\n    )\n\nplt.figure(figsize=(6, 2.3))\nplt.xscale(\"log\", base=2)\nplt.plot(\n    M_list,\n    throughput_GPU_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of NVIDIA A100\",\n    color=color_NV[0],\n)\nplt.plot(\n    M_list, throughput_GPU_list, marker=\"o\", label=\"Real NVIDIA A100\", color=color_NV[1]\n)\nplt.plot(\n    M_list,\n    throughput_GPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated NVIDIA A100\",\n    color=color_NV[2],\n)\nplt.plot(\n    M_list,\n    throughput_AMD_roofline_list,\n    marker=\" \",\n    linewidth=1.5,\n    linestyle=\"--\",\n    label=\"Roofline of AMD MI210\",\n    color=color_AMD[0],\n)\nplt.plot(\n    M_list, throughput_AMD_list, marker=\"o\", label=\"Real AMD MI210\", color=color_AMD[1]\n)\nplt.plot(\n    M_list,\n    throughput_AMD_sim_list,\n    marker=\"x\",\n    label=\"Simulated AMD MI210\",\n    color=color_AMD[2],\n)\nplt.plot(\n    M_list,\n    throughput_TPU_roofline_list,\n    marker=\" \",\n    linewidth=3.5,\n    linestyle=\"--\",\n    label=\"Roofline of Google TPUv3\",\n    color=color_Google[0],\n)\nplt.plot(\n    M_list,\n    throughput_TPU_sim_list,\n    marker=\"x\",\n    label=\"Simulated Google TPUv3\",\n    color=color_Google[2],\n)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles, labels, loc=\"upper left\", bbox_to_anchor=(1, 1.05))\n# plt.title(title)\nplt.xlabel(\"# Elements\")\nplt.ylabel(\"G Elements/s\")\nplt.grid(True, which=\"both\", ls=\"--\", c=\"0.7\")  # Adding a grid for better readability\nplt.savefig(f\"figure5g.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\n"
  },
  {
    "path": "ae/figure5/g/real_hardware/gelu_A100.csv",
    "content": "1024, 0.021262214336633663\n2048, 0.04338350804040404\n4096, 0.08547198599004975\n8192, 0.1700977146930693\n16384, 0.3368601800784314\n32768, 0.6889170600100251\n65536, 1.38129601479397\n131072, 2.735103551681592\n262144, 5.52518405917588\n524288, 11.19095804352163\n1048576, 21.935394070344138\n2097152, 43.980465111040004\n4194304, 86.66101499712316\n8388608, 141.87246810012903\n16777216, 210.36993775086398\n33554432, 277.042299912063\n67108864, 328.2507017033889\n134217728, 360.17271492086496\n268435456, 379.53814489891255\n536870912, 390.32758080867535"
  },
  {
    "path": "ae/figure5/g/real_hardware/gelu_MI210.csv",
    "content": "1024, 0.047197442813186816\n2048, 0.09761289309090909\n4096, 0.19522578618181818\n8192, 0.39045157236363637\n16384, 0.7898790429425288\n32768, 1.5618062894545455\n65536, 3.0885158083595505\n131072, 6.108397932088889\n262144, 11.822705675010754\n524288, 21.55905152501961\n1048576, 37.27158060257627\n2097152, 59.43306096086487\n4194304, 87.96093022208001\n8388608, 114.60707520792182\n16777216, 133.52702880012146\n33554432, 146.984322042118\n67108864, 151.08694402074934\n134217728, 152.91320207016489\n268435456, 154.04294798777178\n536870912, 154.44972829556897"
  },
  {
    "path": "ae/figure5/g/run.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../../..\n\npython -m ae.figure5.g.test_gelu --simgpu --roofline\npython -m ae.figure5.g.test_gelu --simtpu --roofline\npython -m ae.figure5.g.test_gelu --simamd --roofline\n\npython -m ae.figure5.g.test_gelu --simgpu\npython -m ae.figure5.g.test_gelu --simtpu\npython -m ae.figure5.g.test_gelu --simamd\n\ncd ae/figure5/g\npython plot_gelu.py"
  },
  {
    "path": "ae/figure5/g/test_gelu.py",
    "content": "from software_model.gelu import GeLU\nfrom software_model.utils import data_type_dict, Tensor\nfrom hardware_model.device import device_dict\nimport argparse\n\nif __name__ == \"__main__\":\n    parser = argparse.ArgumentParser()\n    parser.add_argument(\"--gpu\", action=\"store_true\", help=\"Enable GPU\")\n    parser.add_argument(\"--simgpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simtpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--roofline\", action=\"store_true\", help=\"Roofline simulation\")\n    parser.add_argument(\"--amd\", action=\"store_true\", help=\"Enable AMD\")\n    parser.add_argument(\"--simamd\", action=\"store_true\", help=\"Enable simulation\")\n    args = parser.parse_args()\n\n    A100 = device_dict[\"A100_80GB_fp16\"]\n    TPU = device_dict[\"TPUv3\"]\n    MI210 = device_dict[\"MI210\"]\n\n    if args.gpu:\n        gpu_kernel_launch_overhead = GeLU.gpu_kernel_launch_overhead()\n\n    print(f\"Performance of GELU\")\n    for M in range(10, 30):\n        M = 2**M\n        # N = 2**15\n        if args.simtpu:\n            model = GeLU(data_type=data_type_dict[\"fp32\"])\n            _ = model(Tensor([M], data_type=data_type_dict[\"fp32\"]))\n            if args.roofline:\n                latency = model.roofline_model(TPU) + 100e-6\n                file_name = \"gelu_TPUv3_roofline.csv\"\n            else:\n                latency = (\n                    model.compile_and_simulate(\n                        pcb_module=TPU, compile_mode=\"heuristic-TPU\"\n                    )\n                    + 100e-6\n                )\n                file_name = \"gelu_TPUv3_sim.csv\"\n        else:\n            model = GeLU(data_type=data_type_dict[\"fp16\"])\n            _ = model(\n                Tensor([M]),\n            )\n            if args.gpu:\n                latency = model.run_on_gpu()\n            if args.amd:\n                model.amd_kernel_launch_overhead()\n                latency = model.run_on_amd()\n            if args.simgpu:\n                if args.roofline:\n                    latency = model.roofline_model(A100) + 4.5e-5\n                    file_name = \"gelu_A100_roofline.csv\"\n                else:\n                    latency = (\n                        model.compile_and_simulate(\n                            pcb_module=A100, compile_mode=\"heuristic-GPU\"\n                        )\n                        + 4.5e-5\n                    )\n                    file_name = \"gelu_A100_sim.csv\"\n            if args.simamd:\n                if args.roofline:\n                    latency = (\n                        model.roofline_model(MI210) + MI210.compute_module.overhead.gelu\n                    )\n                    file_name = \"gelu_MI210_roofline.csv\"\n                else:\n                    latency = (\n                        model.compile_and_simulate(\n                            pcb_module=MI210, compile_mode=\"heuristic-GPU\"\n                        )\n                        + MI210.compute_module.overhead.gelu\n                    )\n                    file_name = \"gelu_MI210_sim.csv\"\n        print(f\"{M}, {M/latency/1e9}\")\n        with open(f\"ae/figure5/g/{file_name}\", \"a\") as f:\n            f.write(f\"{M}, {M/latency/1e9}\\n\")\n"
  },
  {
    "path": "ae/figure5/h/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure5/h/run.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../../..\n\npython -m ae.figure5.h.test_allreduce\n"
  },
  {
    "path": "ae/figure5/h/test_allreduce.py",
    "content": "from software_model.communication_primitives import AllReduceMultiPCB\nfrom software_model.utils import data_type_dict, Tensor\nfrom hardware_model.interconnect import interconnect_module_dict\nimport pandas as pd\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport numpy as np\n\nif __name__ == \"__main__\":\n    interconnect_module = interconnect_module_dict[\"NVLinkV3_FC_4\"]\n    gpu_latency_list = [\n        12.52,\n        13.92,\n        12.39,\n        13.22,\n        12.35,\n        12.45,\n        13.12,\n        13.02,\n        15.12,\n        15.23,\n        15.99,\n        17.39,\n        20.00,\n        22.93,\n        28.66,\n        35.93,\n        47.27,\n        60.75,\n        66.40,\n        84.75,\n        128.8,\n        195.7,\n        279.7,\n        532.3,\n        961.7,\n        1883.7,\n        3659.0,\n        7219.2,\n        14136,\n        27944,\n        55384,\n        110277,\n    ]\n    size_list = [\n        8,\n        16,\n        32,\n        64,\n        128,\n        256,\n        512,\n        1024,\n        2048,\n        4096,\n        8192,\n        16384,\n        32768,\n        65536,\n        131072,\n        262144,\n        524288,\n        1048576,\n        2097152,\n        4194304,\n        8388608,\n        16777216,\n        33554432,\n        67108864,\n        134217728,\n        268435456,\n        536870912,\n        1073741824,\n        2147483648,\n        4294967296,\n        8589934592,\n        17179869184,\n    ]\n    simulated_latency_list = []\n    data_type = data_type_dict[\"fp16\"]\n    for data_size in size_list:\n        model = AllReduceMultiPCB(data_type=data_type)\n        _ = model(\n            Tensor([data_size / 2]),\n        )\n        our_latency = model.simulate(interconnect_module=interconnect_module)\n        simulated_latency_list.append(our_latency * 1e6)\n\n    gpu_bandwidth_list = np.array(size_list) / np.array(gpu_latency_list) / 1e3\n    simulated_gpu_bandwidth_list = (\n        np.array(size_list) / np.array(simulated_latency_list) / 1e3\n    )\n\n    size_list = size_list[9:]\n    gpu_bandwidth_list = gpu_bandwidth_list[9:]\n    simulated_gpu_bandwidth_list = simulated_gpu_bandwidth_list[9:]\n\n    color_NV = sns.color_palette(\"Greens_d\", 4)[1:]\n    color_Google = sns.color_palette(\"Blues_d\", 4)[1:]\n\n    plt.figure(figsize=(6, 2.3))\n    plt.xscale(\"log\", base=2)\n    plt.plot(\n        size_list,\n        gpu_bandwidth_list,\n        marker=\"o\",\n        label=\"Real NVIDIA A100 Node\",\n        color=color_NV[0],\n    )\n    plt.plot(\n        size_list,\n        simulated_gpu_bandwidth_list,\n        marker=\"x\",\n        label=\"Simulated NVIDIA A100 Node\",\n        color=color_NV[2],\n    )\n\n    interconnect_module = interconnect_module_dict[\"TPUv3Link_8\"]\n    simulated_tpu_bandwidth_list = []\n    data_type = data_type_dict[\"fp16\"]\n    for data_size in size_list:\n        model = AllReduceMultiPCB(data_type=data_type)\n        _ = model(\n            Tensor([data_size // 2]),\n        )\n        our_latency = model.simulate(interconnect_module=interconnect_module)\n        simulated_tpu_bandwidth_list.append(data_size / our_latency / 1e9)\n\n    \n    plt.plot(\n        size_list,\n        simulated_tpu_bandwidth_list,\n        marker=\"x\",\n        label=\"Simulated Google TPU v3 Node\",\n        color=color_Google[2],\n    )\n    plt.xlabel(\"Data Size (Bytes)\")\n    plt.ylabel(\"Bandwidth (GB/s)\")\n    plt.grid(\n        True, which=\"both\", ls=\"--\", c=\"0.7\"\n    )  # Adding a grid for better readability\n    plt.legend()\n    plt.savefig(\n        \"ae/figure5/h/figure5h.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300\n    )\n"
  },
  {
    "path": "ae/figure5/ijkl/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure5/ijkl/plot_transformer.py",
    "content": "import matplotlib.pyplot as plt\nimport seaborn as sns\nimport csv\nimport pandas as pd\n\ndef read_csv(filename: str):\n    numbers = []\n    # Open the CSV file and read the numbers\n    with open(filename, \"r\") as csvfile:\n        reader = csv.reader(csvfile)\n        for row in reader:\n            # Since each row contains only one number, we use row[0]\n            numbers.append(float(row[0]))\n    return numbers\n\n\ncategories = [\n    \"Q_K_V\",\n    \"Q_mul_K\",\n    \"A_mul_V\",\n    \"Wo_proj\",\n    \"W1_proj\",\n    \"W2_proj\",\n    \"Softmax\",\n    \"LayerNorm_MHA\",\n    \"LayerNorm_FFN\",\n    \"GeLU\",\n    \"AllReduce_MHA\",\n    \"AllReduce_FFN\",\n]\ncolors_matmul = sns.color_palette(\"flare_r\", 6)\ncolors_normalization = sns.color_palette(\"summer\", 3)\ncolors_gelu = sns.color_palette(\"pink\", 1)\ncolors_allreduce = sns.color_palette(\"Blues_r\", 2)\ncolors = colors_matmul + colors_normalization + colors_gelu + colors_allreduce\n# values_simgpu = read_csv(\"transformer_A100_sim.csv\")\nvalues_simgpu = pd.read_csv(\"transformer_A100_sim.csv\", header=None, names=categories, index_col=None).iloc[0].tolist()\nprint(values_simgpu)\nvalues_gpu = read_csv(\"real_hardware/transformer_A100.csv\")\n# values_gpu_roofline = read_csv(\"transformer_A100_roofline.csv\")\nvalues_gpu_roofline = pd.read_csv(\"transformer_A100_roofline.csv\", header=None, names=categories, index_col=None).iloc[0].tolist()\n# values_simtpu = read_csv(\"transformer_TPUv3_sim.csv\")\nvalues_simtpu = pd.read_csv(\"transformer_TPUv3_sim.csv\", header=None, names=categories, index_col=None).iloc[0].tolist()\n\n# values_tpu_roofline = read_csv(\"transformer_TPUv3_roofline.csv\")\nvalues_tpu_roofline = pd.read_csv(\"transformer_TPUv3_roofline.csv\", header=None, names=categories, index_col=None).iloc[0].tolist()\n\nplt.figure(figsize=(3, 2.8))\n\n# Create the stacked bar graph\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_gpu)):\n    plt.bar(1, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n    bottom += value\nvalue_gt = bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_simgpu)):\n    plt.bar(2, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nvalue_sim = bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_gpu_roofline)):\n    plt.bar(3, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nvalue_roofline = bottom\n\nprint(f\"gpu prefilling: {value_sim/value_gt}, {value_roofline/value_gt}\")\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"GPU Runtime Breakdown of One Transformer Layer in GPT-3 \\n(Initial computation, batch size = 8, sequence length = 2048)\"\n# )\nplt.ylabel(\"Latency (s)\")\n# plt.xlabel('Bar Sets')\nplt.xticks([1, 2, 3], [\"Real\\nA100\", \"Simulated\\nA100\", \"Roofline\\nModel\"])\n# handles, labels = plt.gca().get_legend_handles_labels()\n# plt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1))\nplt.tight_layout()\nplt.savefig(\"figure5i.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n\n\nplt.figure(figsize=(3, 2.8))\n\n# Create the stacked bar graph\n# bottom = 0\n# for i, (category, value) in enumerate(zip(categories, values_tpu)):\n#     plt.bar(1, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n#     bottom += value\n# value_gt = bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_simtpu)):\n    plt.bar(2, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nvalue_sim = bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_tpu_roofline)):\n    plt.bar(3, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nvalue_roofline = bottom\n# print(f\"tpu prefilling: {value_sim/value_gt}, {value_roofline/value_gt}\")\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"TPU Runtime Breakdown of One Transformer Layer in GPT-3 \\n(Initial computation, batch size = 8, sequence length = 2048)\"\n# )\nplt.ylabel(\"Latency (s)\")\n# plt.xlabel('Bar Sets')\nplt.xticks([1, 2, 3], [\"Real\\nTPUv3\", \"Simulated\\nTPUv3\", \"Roofline\\nModel\"])\n# handles, labels = plt.gca().get_legend_handles_labels()\n# plt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1))\nplt.tight_layout()\nplt.savefig(\"figure5j.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n\n\n# values_simgpu = read_csv(\"transformerAR_A100_sim.csv\")\nvalues_simgpu=pd.read_csv(\"transformerAR_A100_sim.csv\",header=None,names=categories,index_col=None).iloc[0].tolist()\nvalues_gpu = read_csv(\"real_hardware/transformerAR_A100.csv\")\n# values_gpu_roofline = read_csv(\"transformerAR_A100_roofline.csv\")\nvalues_gpu_roofline=pd.read_csv(\"transformerAR_A100_roofline.csv\",header=None,names=categories,index_col=None).iloc[0].tolist()\n\nplt.figure(figsize=(3, 2.8))\n\n# Create the stacked bar graph\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_gpu)):\n    value = value * 1e3\n    plt.bar(1, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n    bottom += value\nvalue_gt = bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_simgpu)):\n    value = value * 1e3\n    plt.bar(2, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nvalue_sim = bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_gpu_roofline)):\n    value = value * 1e3\n    plt.bar(3, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nvalue_roofline = bottom\n\nprint(value_sim / value_gt, value_roofline / value_gt)\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"GPU Runtime Breakdown of One Transformer Layer in GPT-3 \\n(Auto regression, batch size = 8, sequence length = 2048)\"\n# )\nplt.ylabel(\"Latency (ms)\")\n# plt.xlabel('Bar Sets')\nplt.xticks([1, 2, 3], [\"Real\\nA100\", \"Simulated\\nA100\", \"Roofline\\nModel\"])\n# handles, labels = plt.gca().get_legend_handles_labels()\n# plt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1))\nplt.tight_layout()\nplt.savefig(\"figure5k.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n\n\n\n\n# values_simtpu = read_csv(\"transformerAR_TPUv3_sim.csv\")\nvalues_simtpu = pd.read_csv(\"transformerAR_TPUv3_sim.csv\", header=None, names=categories, index_col=None).iloc[0].tolist()\n# values_tpu = read_csv(\"real_hardware/transformerAR_TPUv3.csv\")\n# values_tpu_roofline=read_csv(\"transformerAR_TPUv3_roofline.csv\")\nvalues_tpu_roofline=pd.read_csv(\"transformerAR_TPUv3_roofline.csv\",header=None,names=categories,index_col=None).iloc[0].tolist()\n\nplt.figure(figsize=(4.5, 2.8))\n\n# Create the stacked bar graph\n# bottom = 0\n# for i, (category, value) in enumerate(zip(categories, values_tpu)):\n#     value=value*1e3\n#     plt.bar(1, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n#     bottom += value\n# value_gt=bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_simtpu)):\n    value=value*1e3\n    plt.bar(2, value, bottom=bottom, color=colors[i], label=category,width=0.5)\n    bottom += value\nvalue_sim=bottom\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_tpu_roofline)):\n    value=value*1e3\n    plt.bar(3, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nvalue_roofline=bottom\nprint(value_sim/value_gt,value_roofline/value_gt)\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"GPU Runtime Breakdown of One Transformer Layer in GPT-3 \\n(Auto regression, batch size = 8, input(output) sequence length = 2048(1024))\"\n# )\nplt.ylabel(\"Latency (ms)\")\n# plt.xlabel('Bar Sets')\nplt.xticks([1, 2, 3], [\"Real\\nTPUv3\", \"Simulated\\nTPUv3\", \"Roofline\\nModel\"])\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1.05))\nplt.tight_layout()\nplt.savefig(\"figure5l.pdf\",bbox_inches=\"tight\", pad_inches=0.01, dpi=300)"
  },
  {
    "path": "ae/figure5/ijkl/real_hardware/transformerAR_A100.csv",
    "content": "0.0002124309539794922\n0.00010609626770019531\n0.0001386404037475586\n6.890296936035156e-05\n0.00018596649169921875\n0.00018608570098876953\n1.6689300537109375e-05\n4.8041343688964844e-05\n4.8041343688964844e-05\n4.792213439941406e-05\n26.04e-06\n26.04e-06"
  },
  {
    "path": "ae/figure5/ijkl/real_hardware/transformer_A100.csv",
    "content": "0.013721823692321777\n0.0018811225891113281\n0.001183152198791504\n0.0045403242111206055\n0.017464280128479004\n0.017485618591308594\n0.00280153751373291\n0.0006816387176513672\n0.0006816387176513672\n0.0005242824554443359\n0.0028909\n0.0028909"
  },
  {
    "path": "ae/figure5/ijkl/run.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../../..\n\npython -m ae.figure5.ijkl.test_transformer --simgpu --roofline\npython -m ae.figure5.ijkl.test_transformer --simtpu --roofline\npython -m ae.figure5.ijkl.test_transformer --simgpu --init --roofline\npython -m ae.figure5.ijkl.test_transformer --simtpu --init --roofline\n\npython -m ae.figure5.ijkl.test_transformer --simgpu\npython -m ae.figure5.ijkl.test_transformer --simtpu\npython -m ae.figure5.ijkl.test_transformer --simgpu --init\npython -m ae.figure5.ijkl.test_transformer --simtpu --init\n\ncd ae/figure5/ijkl\npython plot_transformer.py"
  },
  {
    "path": "ae/figure5/ijkl/test_transformer.py",
    "content": "from software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\nfrom hardware_model.system import system_dict\nimport argparse\n\nif __name__ == \"__main__\":\n    parser = argparse.ArgumentParser()\n    parser.add_argument(\"--init\", action=\"store_true\", help=\"initial computation\")\n    parser.add_argument(\"--gpu\", action=\"store_true\", help=\"Enable GPU\")\n    parser.add_argument(\"--simgpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--simtpu\", action=\"store_true\", help=\"Enable simulation\")\n    parser.add_argument(\"--roofline\", action=\"store_true\", help=\"use roofline\")\n    args = parser.parse_args()\n\n    bs = 8\n    s = 2048\n    if args.init:\n        print(\"Initial computation\")\n        if args.simgpu:\n            model = TransformerBlockInitComputationTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=4,\n                data_type=data_type_dict[\"fp16\"],\n            )\n            A100_system = system_dict[\"A100_4_fp16\"]\n            # from design_space_exploration.dse import read_architecture_template, template_to_system\n            # arch_specs = read_architecture_template(\"configs/template.json\")\n            # A100_system = template_to_system(arch_specs)\n            _ = model(Tensor([bs, s, 12288], data_type_dict[\"fp16\"]))\n            if args.roofline:\n                model.roofline_model(A100_system)\n                file_name = \"transformer_A100_roofline.csv\"\n            else:\n                model.compile_and_simulate(A100_system, compile_mode=\"heuristic-GPU\")\n                file_name = \"transformer_A100_sim.csv\"\n        if args.simtpu:\n            model = TransformerBlockInitComputationTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=8,\n                data_type=data_type_dict[\"fp16\"],\n            )\n            TPU_system = system_dict[\"TPUv3_8\"]\n            _ = model(Tensor([bs, s, 12288], data_type_dict[\"fp16\"]))\n            if args.roofline:\n                model.roofline_model(TPU_system)\n                file_name = \"transformer_TPUv3_roofline.csv\"\n            else:\n                model.compile_and_simulate(TPU_system, compile_mode=\"heuristic-TPU\")\n                file_name = \"transformer_TPUv3_sim.csv\"\n        if args.gpu:\n            model = TransformerBlockInitComputationTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=4,\n                data_type=data_type_dict[\"fp16\"],\n            )\n            _ = model(Tensor([bs, s, 12288], data_type_dict[\"fp16\"]))\n            model.run_on_gpu()\n    else:\n        print(\"Auto-regression\")\n        output_token_length = 1024\n        if args.simgpu:\n            model = TransformerBlockAutoRegressionTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=4,\n                data_type=data_type_dict[\"fp16\"],\n            )\n            A100_system = system_dict[\"A100_4_fp16\"]\n            _ = model(\n                Tensor([bs, 1, 12288], data_type_dict[\"fp16\"]), s + output_token_length\n            )\n            if args.roofline:\n                model.roofline_model(A100_system)\n                file_name = \"transformerAR_A100_roofline.csv\"\n            else:\n                model.compile_and_simulate(A100_system, compile_mode=\"heuristic-GPU\")\n                file_name = \"transformerAR_A100_sim.csv\"\n        if args.simtpu:\n            model = TransformerBlockAutoRegressionTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=8,\n                data_type=data_type_dict[\"fp16\"],\n            )\n            TPU_system = system_dict[\"TPUv3_8\"]\n            _ = model(\n                Tensor([bs, 1, 12288], data_type_dict[\"fp16\"]), s + output_token_length\n            )\n            if args.roofline:\n                model.roofline_model(TPU_system)\n                file_name = \"transformerAR_TPUv3_roofline.csv\"\n            else:\n                model.compile_and_simulate(TPU_system, compile_mode=\"heuristic-TPU\")\n                file_name = \"transformerAR_TPUv3_sim.csv\"\n        if args.gpu:\n            model = TransformerBlockAutoRegressionTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=4,\n                data_type=data_type_dict[\"fp16\"],\n            )\n            _ = model(\n                Tensor([bs, 1, 12288], data_type_dict[\"fp16\"]), s + output_token_length\n            )\n            model.run_on_gpu()\n    with open(f\"ae/figure5/ijkl/{file_name}\", \"w\") as f:\n        if args.roofline:\n            f.write(model.roofline_log)\n        else:\n            f.write(model.simluate_log)\n"
  },
  {
    "path": "ae/figure5/run_figure5.sh",
    "content": "cd ab\nbash run.sh\ncd ..\n\ncd cf\nbash run.sh\ncd ..\n\ncd de\nbash run.sh\ncd ..\n\ncd g\nbash run.sh\ncd ..\n\ncd h\nbash run.sh\ncd ..\n\ncd ijkl\nbash run.sh\ncd .."
  },
  {
    "path": "ae/figure6/real_hardware/die_area.csv",
    "content": "476.25,\t446.22\n76.44,\t33\n119.31,\t25.2\n58,\t83.26\n31.77,\t40.83\n20.95,\t45.52\n0,\t42\n40,\t4"
  },
  {
    "path": "ae/figure6/run_figure6.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../..\n\npython -m ae.figure6.test_cost_model"
  },
  {
    "path": "ae/figure6/test_cost_model.py",
    "content": "from cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nfrom design_space_exploration.dse import read_architecture_template\nimport matplotlib.pyplot as plt\nimport seaborn as sns\nimport pandas as pd\n\narch_specs = read_architecture_template(\"configs/GA100.json\")\n\ncompute_chiplet_area_mm2, A100_core_breakdown_map, compute_total_die_map = (\n    calc_compute_chiplet_area_mm2(arch_specs, verbose=True)\n)\nio_die_area_mm2, io_total_die_map = calc_io_die_area_mm2(arch_specs, verbose=True)\n\n\ncategories = [\n    \"Cores\",\n    \"On-chip interconnect\",\n    \"Global buffer\",\n    \"Memory(PHY)\",\n    \"Memory(Control)\",\n    \"Off-chip interconnect\\n(PHY)\",\n    \"Off-chip interconnect\\n(Control)\",\n    \"Other\",\n]\n\ndie_area = pd.read_csv(\n    \"ae/figure6/real_hardware/die_area.csv\", header=None, names=[\"A100\", \"MI210\"]\n)\n\nvalues_a100 = die_area[\"A100\"].tolist()\nvalues_mi210 = die_area[\"MI210\"].tolist()\n\nvalues_a100_sim = [\n    compute_total_die_map[\"cores_area\"],\n    compute_total_die_map[\"crossbar_area\"],\n    io_total_die_map[\"global_buffer_area\"],\n    io_total_die_map[\"mem_phy_area\"],\n    io_total_die_map[\"mem_controller_area\"],\n    io_total_die_map[\"device_phy_area\"],\n    io_total_die_map[\"device_controller_area\"],\n    0,\n]\n\n\narch_specs = read_architecture_template(\"configs/mi210_template.json\")\n\ncompute_chiplet_area_mm2, MI210_core_breakdown_map, compute_total_die_map = (\n    calc_compute_chiplet_area_mm2(arch_specs, verbose=True)\n)\nio_die_area_mm2, io_total_die_map = calc_io_die_area_mm2(arch_specs, verbose=True)\n\n\nvalues_mi210_sim = [\n    compute_total_die_map[\"cores_area\"],\n    compute_total_die_map[\"crossbar_area\"],\n    io_total_die_map[\"global_buffer_area\"],\n    io_total_die_map[\"mem_phy_area\"],\n    io_total_die_map[\"mem_controller_area\"],\n    io_total_die_map[\"device_phy_area\"],\n    io_total_die_map[\"device_controller_area\"],\n    0,\n]\n\nplt.figure(figsize=(4, 2))\n\ncolors_matmul = sns.color_palette(\"flare_r\", 7)[5:6]\ncolors_normalization = sns.color_palette(\"summer\", 2)\ncolors_gelu = sns.color_palette(\"pink\", 5)[2:4]\ncolors_allreduce = sns.color_palette(\"Blues_r\", 2)\ncolors = (\n    colors_matmul\n    + colors_normalization\n    + colors_gelu\n    + colors_allreduce\n    + sns.color_palette(\"Greys_r\", 1)\n)\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_a100)):\n    plt.bar(1, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n    bottom += value\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_a100_sim)):\n    plt.bar(2, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_mi210)):\n    plt.bar(3, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_mi210_sim)):\n    plt.bar(4, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\nplt.ylabel(\"Area ($mm^2$)\")\nplt.xticks(\n    [1, 2, 3, 4],\n    [\"Real\\nGA100\", \"Simulated\\nGA100\", \"Real\\nAldebaran\", \"Simulated\\nAldebaran\"],\n)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1.1))\nplt.savefig(\"ae/figure6/figure6a.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n\n\nvalues_a100 = [3.75]\nvalues_mi210 = [4.02]\n\nvalues_a100_sim = [\n    A100_core_breakdown_map[\"control_area\"],\n    A100_core_breakdown_map[\"alu_area\"],\n    A100_core_breakdown_map[\"sa_area\"],\n    A100_core_breakdown_map[\"regfile_area\"],\n    A100_core_breakdown_map[\"local_buffer_area\"],\n]\n\nvalues_mi210_sim = [\n    MI210_core_breakdown_map[\"control_area\"],\n    MI210_core_breakdown_map[\"alu_area\"],\n    MI210_core_breakdown_map[\"sa_area\"],\n    MI210_core_breakdown_map[\"regfile_area\"],\n    MI210_core_breakdown_map[\"local_buffer_area\"],\n]\n\ncategories = [\n    \"Control logic\",\n    \"ALUs\",\n    \"Systolic array\",\n    \"Register file\",\n    \"Local buffer\",\n]\n\ncolors = colors_matmul + colors_normalization + colors_allreduce\ncolor_gt = sns.color_palette(\"Greys_r\", 1)[0]\n\nplt.figure(figsize=(4, 1.5))\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_a100)):\n    plt.bar(1, value, bottom=bottom, color=color_gt, width=0.5)\n    bottom += value\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_a100_sim)):\n    plt.bar(2, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n    bottom += value\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_mi210)):\n    plt.bar(3, value, bottom=bottom, color=color_gt, width=0.5)\n    bottom += value\n\nbottom = 0\nfor i, (category, value) in enumerate(zip(categories, values_mi210_sim)):\n    plt.bar(4, value, bottom=bottom, color=colors[i], width=0.5)\n    bottom += value\n\nplt.ylabel(\"Area ($mm^2$)\")\nplt.xticks(\n    [1, 2, 3, 4],\n    [\"Real\\nGA100\", \"Simulated\\nGA100\", \"Real\\nAldebaran\", \"Simulated\\nAldebaran\"],\n)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1))\nplt.savefig(\"ae/figure6/figure6b.pdf\", bbox_inches=\"tight\", pad_inches=0.01, dpi=300)\n"
  },
  {
    "path": "ae/figure7/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure7/change_core_size.py",
    "content": "from software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\nfrom design_space_exploration.dse import template_to_system, read_architecture_template\nfrom multiprocessing import Process, Lock\nfrom cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nimport time\n\ninput_seq_length = 2048\nbatch_size = 8\noutput_seq_length = 1024\narch_specs = read_architecture_template(\"configs/GA100.json\")\ndevice_count = arch_specs[\"device_count\"]\n\nmodel_init = TransformerBlockInitComputationTP(\n    d_model=12288,\n    n_heads=96,\n    device_count=device_count,\n    data_type=data_type_dict[\"fp16\"],\n)\nmodel_auto_regression = TransformerBlockAutoRegressionTP(\n    d_model=12288,\n    n_heads=96,\n    device_count=device_count,\n    data_type=data_type_dict[\"fp16\"],\n)\n_ = model_init(\n    Tensor([batch_size, input_seq_length, model_init.d_model], data_type_dict[\"fp16\"])\n)\n_ = model_auto_regression(\n    Tensor([batch_size, 1, model_init.d_model], data_type_dict[\"fp16\"]),\n    input_seq_length + output_seq_length,\n)\n\n\ndef test_core_size(core_configs, lock):\n    name, core_count, sublane_count, array_width, vector_width, sram_KB = core_configs\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core_count\"] = core_count\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"sublane_count\"] = sublane_count\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"systolic_array\"][\n        \"array_width\"\n    ] = array_width\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"systolic_array\"][\n        \"array_height\"\n    ] = array_width\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"vector_unit\"][\n        \"vector_width\"\n    ] = vector_width\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"SRAM_KB\"] = sram_KB\n    # for area\n    arch_specs[\"device\"][\"compute_chiplet\"][\"physical_core_count\"] = core_count\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"vector_unit\"][\"int32_count\"] = (\n        vector_width // 2\n    )\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"vector_unit\"][\"fp32_count\"] = (\n        vector_width // 2\n    )\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"vector_unit\"][\"fp64_count\"] = (\n        vector_width // 4\n    )\n    if vector_width <= 32:\n        arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"register_file\"][\n            \"num_registers\"\n        ] = (vector_width * 512)\n    else:\n        arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"register_file\"][\n            \"num_reg_files\"\n        ] = (vector_width // 32)\n    compute_area_mm2 = calc_compute_chiplet_area_mm2(arch_specs)\n    io_area_mm2 = calc_io_die_area_mm2(arch_specs)\n    print(f\"{name}, {compute_area_mm2}, {io_area_mm2}, {compute_area_mm2+io_area_mm2}\")\n    # exit()\n    system = template_to_system(arch_specs)\n    auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(\n        system, \"heuristic-GPU\"\n    )\n    init_latency_simulated = model_init.compile_and_simulate(system, \"heuristic-GPU\")\n    print(f\"{name}, {init_latency_simulated}, {auto_regression_latency_simulated}\")\n    with lock:\n        with open(f\"ae/figure7/core_size_results_init.csv\", \"a\") as f:\n            f.write(\n                f\"{name}, {compute_area_mm2+io_area_mm2}, {init_latency_simulated}, {model_init.simluate_log}\\n\"\n            )\n        with open(f\"ae/figure7/core_size_results_ar.csv\", \"a\") as f:\n            f.write(\n                f\"{name}, {compute_area_mm2+io_area_mm2}, {auto_regression_latency_simulated}, {model_auto_regression.simluate_log}\\n\"\n            )\n\n\nlock = Lock()\nconfigs = [\n    (\"A\", 128, 4, 8, 8, 192),\n    (\"B\", 128, 4, 16, 32, 192),\n    (\"C\", 128, 1, 32, 128, 192),\n    (\"D\", 32, 1, 64, 512, 768),\n    (\"E\", 8, 1, 128, 2048, 3072),\n]\n\nprocesses = [Process(target=test_core_size, args=(i, lock)) for i in configs]\n\ntry:\n    for p in processes:\n        p.start()\n\n    while any(p.is_alive() for p in processes):\n        time.sleep(1)\nexcept KeyboardInterrupt:\n    print(\"Terminating processes...\")\n    for p in processes:\n        p.terminate()\n        p.join()\n\n\nprint(\"All processes have finished.\")\n"
  },
  {
    "path": "ae/figure7/plot_core_size.py",
    "content": "import matplotlib.pyplot as plt\nimport seaborn as sns\nimport csv\nimport pandas as pd\n\ncategories = [\n    \"Q_K_V\",\n    \"Q_mul_K\",\n    \"A_mul_V\",\n    \"Wo_proj\",\n    \"W1_proj\",\n    \"W2_proj\",\n    \"Softmax\",\n    \"LayerNorm_MHA\",\n    \"LayerNorm_FFN\",\n    \"GeLU\",\n    \"AllReduce_MHA\",\n    \"AllReduce_FFN\",\n]\ncol_names = [\"area\", \"latency\"] + categories\n\ncolors_matmul = sns.color_palette(\"flare_r\", 6)\ncolors_normalization = sns.color_palette(\"summer\", 3)\ncolors_gelu = sns.color_palette(\"pink\", 1)\ncolors_allreduce = sns.color_palette(\"Blues_r\", 2)\ncolors = colors_matmul + colors_normalization + colors_gelu + colors_allreduce\n\ncore_size_init = pd.read_csv(\n    \"core_size_results_init.csv\", header=None, names=col_names, index_col=0\n)\ncore_size_init.index.astype(str)\ncore_size_ar = pd.read_csv(\n    \"core_size_results_ar.csv\", header=None, names=col_names, index_col=0\n)\ncore_size_ar.index.astype(str)\n\n\ndf_sorted = core_size_init.sort_index()\nareas = df_sorted[\"area\"].tolist()\n# print(areas)\n# exit()\n# areas = [\n#     475.52039916931585,\n#     826.76355498007,\n#     826.76355498007,\n#     793.3380639020086,\n#     763.3465573533286,\n# ]\n\nplt.figure(figsize=(7, 3))\n\n# Create the stacked bar graph\nx = 0\nfor row_index in [\"A\", \"B\", \"C\", \"D\", \"E\"]:\n    x = x + 1\n    values = core_size_init.loc[row_index].tolist()\n    bottom = 0\n    for i, (category, value) in enumerate(zip(categories, values[2:])):\n        if row_index == \"A\":\n            plt.bar(x, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n        else:\n            plt.bar(x, value, bottom=bottom, color=colors[i], width=0.5)\n        bottom += value\n\nplt.ylabel(\"Latency (s)\")\nplt.xlabel(\"Configurations\")\nplt.xticks([1, 2, 3, 4, 5], [\"A\", \"B\", \"C\", \"D\", \"E\"])\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1.2, 1.05))\nplt.tight_layout()\nxticks = plt.gca().get_xticks()\nxticklabels = plt.gca().get_xticklabels()\nindex_to_color_red = list(xticks).index(2)\nxticklabels[index_to_color_red].set_color(\"#76B900\")\n\nax1 = plt.gca()\nax2 = ax1.twinx()\nax2.plot(\n    [1, 2, 3, 4, 5],\n    areas,\n    color=\"dimgray\",\n    linestyle=\"dashed\",\n    marker=\"x\",\n    label=\"Area\",\n)\nax2.set_ylabel(\"Area ($mm^2$)\")\nax2.set_ylim([0, 1000])\nplt.legend(loc=\"upper right\")\nplt.savefig(\n    \"figure7a.pdf\",\n    dpi=300,\n    bbox_inches=\"tight\",\n    pad_inches=0.01,\n)\nplt.show()\n\n\nplt.figure(figsize=(7, 3))\nx = 0\nfor row_index in [\"A\", \"B\", \"C\", \"D\", \"E\"]:\n    x = x + 1\n    values = core_size_ar.loc[row_index].tolist()\n    bottom = 0\n    for i, (category, value) in enumerate(zip(categories, values[2:])):\n        value = value * 1e3\n        if row_index == \"A\":\n            plt.bar(x, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n        else:\n            plt.bar(x, value, bottom=bottom, color=colors[i], width=0.5)\n        bottom += value\n\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"Generation latency under different organization\"\n# )\nplt.ylabel(\"Latency (ms)\")\nplt.xlabel(\"Configurations\")\nplt.xticks([1, 2, 3, 4, 5], [\"A\", \"B\", \"C\", \"D\", \"E\"])\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1.2, 1.05))\nplt.tight_layout()\nxticks = plt.gca().get_xticks()\nxticklabels = plt.gca().get_xticklabels()\nindex_to_color_red = list(xticks).index(2)\nxticklabels[index_to_color_red].set_color(\"#76B900\")\nax1 = plt.gca()\nax2 = ax1.twinx()\nax2.plot(\n    [1, 2, 3, 4, 5],\n    areas,\n    color=\"dimgrey\",\n    linestyle=\"dashed\",\n    marker=\"x\",\n    label=\"Area\",\n)\nax2.set_ylabel(\"Area ($mm^2$)\")\nax2.set_ylim([0, 1000])\nplt.legend(loc=\"upper left\")\nplt.savefig(\n    \"figure7b.pdf\",\n    dpi=300,\n    bbox_inches=\"tight\",\n    pad_inches=0.01,\n)\n"
  },
  {
    "path": "ae/figure7/run_figure7.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../..\n\npython -m ae.figure7.change_core_size\n\ncd ae/figure7\npython plot_core_size.py"
  },
  {
    "path": "ae/figure8/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure8/change_memory_bw.py",
    "content": "import json, re\nfrom hardware_model.compute_module import (\n    VectorUnit,\n    SystolicArray,\n    Core,\n    ComputeModule,\n    overhead_dict,\n)\nfrom hardware_model.io_module import IOModule\nfrom hardware_model.memory_module import MemoryModule\nfrom hardware_model.device import Device\nfrom hardware_model.interconnect import LinkModule, InterConnectModule, TopologyType\nfrom hardware_model.system import System\nfrom software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\nfrom cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nfrom math import ceil\n\nfrom design_space_exploration.dse import template_to_system, read_architecture_template\nfrom multiprocessing import Process, Lock\nimport time\nfrom cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\n\n\ninput_seq_length = 2048\nbatch_size = 8\noutput_seq_length = 1024\narch_specs = read_architecture_template(\"configs/template.json\")\ndevice_count = arch_specs[\"device_count\"]\nmodel_init = TransformerBlockInitComputationTP(\n    d_model=12288,\n    n_heads=96,\n    device_count=device_count,\n    data_type=data_type_dict[\"fp16\"],\n)\nmodel_auto_regression = TransformerBlockAutoRegressionTP(\n    d_model=12288,\n    n_heads=96,\n    device_count=device_count,\n    data_type=data_type_dict[\"fp16\"],\n)\n_ = model_init(\n    Tensor([batch_size, input_seq_length, model_init.d_model], data_type_dict[\"fp16\"])\n)\n_ = model_auto_regression(\n    Tensor([batch_size, 1, model_init.d_model], data_type_dict[\"fp16\"]),\n    input_seq_length + output_seq_length,\n)\n\n\ndef test_memory_bandwidth(memory_bandwidth, lock):\n    arch_specs[\"device\"][\"io\"][\"memory_channel_physical_count\"] = memory_bandwidth\n    arch_specs[\"device\"][\"io\"][\"memory_channel_active_count\"] = memory_bandwidth\n    compute_area_mm2 = calc_compute_chiplet_area_mm2(arch_specs)\n    io_area_mm2 = calc_io_die_area_mm2(arch_specs)\n    print(\n        f\"{memory_bandwidth}, {compute_area_mm2}, {io_area_mm2}, {compute_area_mm2+io_area_mm2}\"\n    )\n    system = template_to_system(arch_specs)\n    auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(\n        system, \"heuristic-GPU\"\n    )\n    init_latency_simulated = model_init.compile_and_simulate(system, \"heuristic-GPU\")\n    print(\n        f\"{memory_bandwidth}, {init_latency_simulated}, {auto_regression_latency_simulated}\"\n    )\n    with lock:\n        with open(f\"ae/figure8/memory_bw_results_bs{batch_size}_init.csv\", \"a\") as f:\n            f.write(\n                f\"{memory_bandwidth*400}, {compute_area_mm2+io_area_mm2}, {init_latency_simulated}, {model_init.simluate_log}\\n\"\n            )\n        with open(f\"ae/figure8/memory_bw_results_bs{batch_size}_ar.csv\", \"a\") as f:\n            f.write(\n                f\"{memory_bandwidth*400}, {compute_area_mm2+io_area_mm2}, {auto_regression_latency_simulated}, {model_auto_regression.simluate_log}\\n\"\n            )\n\n\nlock = Lock()\nprocesses = [\n    Process(target=test_memory_bandwidth, args=(i, lock))\n    for i in [1, 2, 3, 4, 5, 6, 7, 8]\n]\n\ntry:\n    for p in processes:\n        p.start()\n\n    while any(p.is_alive() for p in processes):\n        time.sleep(1)\nexcept KeyboardInterrupt:\n    print(\"Terminating processes...\")\n    for p in processes:\n        p.terminate()\n        p.join()\n\n\nprint(\"All processes have finished.\")\n"
  },
  {
    "path": "ae/figure8/plot_memory_bw.py",
    "content": "import matplotlib.pyplot as plt\nimport seaborn as sns\nimport csv\nimport pandas as pd\n\ncategories = [\n    \"Q_K_V\",\n    \"Q_mul_K\",\n    \"A_mul_V\",\n    \"Wo_proj\",\n    \"W1_proj\",\n    \"W2_proj\",\n    \"Softmax\",\n    \"LayerNorm_MHA\",\n    \"LayerNorm_FFN\",\n    \"GeLU\",\n    \"AllReduce_MHA\",\n    \"AllReduce_FFN\",\n]\ncol_names = [\"area\", \"latency\"] + categories\n\ncolors_matmul = sns.color_palette(\"flare_r\", 6)\ncolors_normalization = sns.color_palette(\"summer\", 3)\ncolors_gelu = sns.color_palette(\"pink\", 1)\ncolors_allreduce = sns.color_palette(\"Blues_r\", 2)\ncolors = colors_matmul + colors_normalization + colors_gelu + colors_allreduce\n\nbatch_size = 8\n\nresults_init = pd.read_csv(\n    f\"memory_bw_results_bs{batch_size}_init.csv\",\n    header=None,\n    names=col_names,\n    index_col=0,\n)\nresults_init.index.astype(int)\nresults_ar = pd.read_csv(\n    f\"memory_bw_results_bs{batch_size}_ar.csv\",\n    header=None,\n    names=col_names,\n    index_col=0,\n)\nresults_ar.index.astype(int)\n\n\nplt.figure(figsize=(7, 3))\n\n# Create the stacked bar graph\nx = 0\nx_labels = [i * 400 for i in [1, 2, 3, 4, 5, 6, 7, 8]]\nfor row_index in x_labels:\n    x = x + 1\n    values = results_init.loc[row_index].tolist()\n    bottom = 0\n    for i, (category, value) in enumerate(zip(categories, values[2:])):\n        if row_index == x_labels[0]:\n            plt.bar(x, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n        else:\n            plt.bar(x, value, bottom=bottom, color=colors[i], width=0.5)\n        bottom += value\n\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"Prefilling Latency per Layer\"\n# )\nplt.ylabel(\"Latency (s)\")\nplt.xlabel(\"Memory bandwidth (GB/s)\")\nplt.xticks([1, 2, 3, 4, 5, 6, 7, 8], x_labels)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1.05))\nplt.tight_layout()\nxticks = plt.gca().get_xticks()\nxticklabels = plt.gca().get_xticklabels()\nindex_to_color_red = list(xticks).index(5)\nxticklabels[index_to_color_red].set_color(\"red\")\nplt.savefig(f\"figure8a.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\nplt.show()\n\n\nplt.figure(figsize=(7, 3))\nx = 0\nfor row_index in x_labels:\n    x = x + 1\n    values = results_ar.loc[row_index].tolist()\n    bottom = 0\n    for i, (category, value) in enumerate(zip(categories, values[2:])):\n        value = value * 1e3\n        if row_index == x_labels[0]:\n            plt.bar(x, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n        else:\n            plt.bar(x, value, bottom=bottom, color=colors[i], width=0.5)\n        bottom += value\n\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"Generation Latency per Layer per Token\"\n# )\nplt.ylabel(\"Latency (ms)\")\nplt.xlabel(\"Memory bandwidth (GB/s)\")\nplt.xticks([1, 2, 3, 4, 5, 6, 7, 8], x_labels)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1, 1.05))\nplt.tight_layout()\nxticks = plt.gca().get_xticks()\nxticklabels = plt.gca().get_xticklabels()\nindex_to_color_red = list(xticks).index(5)\nxticklabels[index_to_color_red].set_color(\"red\")\nplt.savefig(f\"figure8b.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\n"
  },
  {
    "path": "ae/figure8/run_figure8.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../..\n\npython -m ae.figure8.change_memory_bw\n\ncd ae/figure8\npython plot_memory_bw.py"
  },
  {
    "path": "ae/figure9/__init__.py",
    "content": ""
  },
  {
    "path": "ae/figure9/change_l1_cache.py",
    "content": "from software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\nfrom design_space_exploration.dse import template_to_system, read_architecture_template\nfrom multiprocessing import Process, Lock\nfrom cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nimport time\n\ninput_seq_length = 2048\nbatch_size = 8\noutput_seq_length = 1024\narch_specs = read_architecture_template(\"configs/template.json\")\ndevice_count = arch_specs[\"device_count\"]\n\nmodel_init = TransformerBlockInitComputationTP(\n    d_model=12288,\n    n_heads=96,\n    device_count=device_count,\n    data_type=data_type_dict[\"fp16\"],\n)\nmodel_auto_regression = TransformerBlockAutoRegressionTP(\n    d_model=12288,\n    n_heads=96,\n    device_count=device_count,\n    data_type=data_type_dict[\"fp16\"],\n)\n_ = model_init(\n    Tensor([batch_size, input_seq_length, model_init.d_model], data_type_dict[\"fp16\"])\n)\n_ = model_auto_regression(\n    Tensor([batch_size, 1, model_init.d_model], data_type_dict[\"fp16\"]),\n    input_seq_length + output_seq_length,\n)\n\n\ndef test_SRAM_KB(SRAM_KB, lock):\n    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\"SRAM_KB\"] = SRAM_KB\n    compute_area_mm2 = calc_compute_chiplet_area_mm2(arch_specs)\n    io_area_mm2 = calc_io_die_area_mm2(arch_specs)\n    print(\n        f\"{SRAM_KB}, {compute_area_mm2}, {io_area_mm2}, {compute_area_mm2+io_area_mm2}\"\n    )\n    system = template_to_system(arch_specs)\n    auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(\n        system, \"heuristic-GPU\"\n    )\n    init_latency_simulated = model_init.compile_and_simulate(system, \"heuristic-GPU\")\n    print(f\"{SRAM_KB}, {init_latency_simulated}, {auto_regression_latency_simulated}\")\n    with lock:\n        with open(f\"ae/figure9/l1_cache_results_init.csv\", \"a\") as f:\n            f.write(\n                f\"{SRAM_KB}, {compute_area_mm2+io_area_mm2}, {init_latency_simulated}, {model_init.simluate_log}\\n\"\n            )\n        with open(f\"ae/figure9/l1_cache_results_ar.csv\", \"a\") as f:\n            f.write(\n                f\"{SRAM_KB}, {compute_area_mm2+io_area_mm2}, {auto_regression_latency_simulated}, {model_auto_regression.simluate_log}\\n\"\n            )\n\n\n# for SRAM_KB in [64, 128, 192, 256, 512, 1024]:\n#     test_SRAM_KB(SRAM_KB, None)\n\nlock = Lock()\nprocesses = [\n    Process(target=test_SRAM_KB, args=(i, lock)) for i in [64, 128, 192, 256, 512, 1024]\n]\n\ntry:\n    for p in processes:\n        p.start()\n\n    while any(p.is_alive() for p in processes):\n        time.sleep(1)\nexcept KeyboardInterrupt:\n    print(\"Terminating processes...\")\n    for p in processes:\n        p.terminate()\n        p.join()\n\n\nprint(\"All processes have finished.\")\n\n# for SRAM_KB in [64, 128, 192, 256, 512, 1024]:\n#     arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\n#                                     \"SRAM_KB\"\n#                                 ] = SRAM_KB\n#     system=template_to_system(arch_specs)\n#     auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(system, 'heuristic-GPU')\n#     init_latency_simulated = model_init.compile_and_simulate(system, 'heuristic-GPU')\n#     print(f'{SRAM_KB}, {init_latency_simulated}, {auto_regression_latency_simulated}')\n#     with open(f'test/case_study/l1_cache/l1_cache_results.csv', 'a') as f:\n#         f.write(f'{SRAM_KB}, {init_latency_simulated}, {auto_regression_latency_simulated}\\n')\n"
  },
  {
    "path": "ae/figure9/plot_l1_cache.py",
    "content": "import matplotlib.pyplot as plt\nimport seaborn as sns\nimport csv\nimport pandas as pd\n\ncategories = [\n    \"Q_K_V\",\n    \"Q_mul_K\",\n    \"A_mul_V\",\n    \"Wo_proj\",\n    \"W1_proj\",\n    \"W2_proj\",\n    \"Softmax\",\n    \"LayerNorm_MHA\",\n    \"LayerNorm_FFN\",\n    \"GeLU\",\n    \"AllReduce_MHA\",\n    \"AllReduce_FFN\",\n]\ncol_names = [\"area\", \"latency\"] + categories\n\ncolors_matmul = sns.color_palette(\"flare_r\", 6)\ncolors_normalization = sns.color_palette(\"summer\", 3)\ncolors_gelu = sns.color_palette(\"pink\", 1)\ncolors_allreduce = sns.color_palette(\"Blues_r\", 2)\ncolors = colors_matmul + colors_normalization + colors_gelu + colors_allreduce\n\nresults_init = pd.read_csv(\n    \"l1_cache_results_init.csv\", header=None, names=col_names, index_col=0\n)\nresults_init.index.astype(int)\nresults_ar = pd.read_csv(\n    \"l1_cache_results_ar.csv\", header=None, names=col_names, index_col=0\n)\nresults_ar.index.astype(int)\n\nareas = [\n    782.1048032068737,\n    794.1065561553206,\n    826.76355498007,\n    848.4527315580167,\n    913.304090096728,\n    1064.9121549472263,\n]\n\nplt.figure(figsize=(7, 3))\n\n# Create the stacked bar graph\nx = 0\nx_labels = [64, 128, 192, 256, 512, 1024]\nfor row_index in x_labels:\n    x = x + 1\n    values = results_init.loc[row_index].tolist()\n    bottom = 0\n    for i, (category, value) in enumerate(zip(categories, values[2:])):\n        if row_index == x_labels[0]:\n            plt.bar(x, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n        else:\n            plt.bar(x, value, bottom=bottom, color=colors[i], width=0.5)\n        bottom += value\n\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"Prefilling Latency per Layer\"\n# )\nplt.ylabel(\"Latency (s)\")\nplt.xlabel(\"Local buffer size (KB)\")\nplt.xticks([1, 2, 3, 4, 5, 6], x_labels)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1.2, 1.03))\nplt.tight_layout()\nxticks = plt.gca().get_xticks()\nxticklabels = plt.gca().get_xticklabels()\nindex_to_color_red = list(xticks).index(3)\nxticklabels[index_to_color_red].set_color(\"#76B900\")\n\nax1 = plt.gca()\nax2 = ax1.twinx()\nax2.plot(\n    [1, 2, 3, 4, 5, 6],\n    areas,\n    color=\"dimgray\",\n    linestyle=\"dashed\",\n    marker=\"x\",\n    label=\"Area\",\n)\nax2.set_ylabel(\"Area ($mm^2$)\")\nax2.set_ylim([0, 1200])\nplt.legend(loc=\"upper center\")\n\nplt.savefig(\"figure9a.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\nplt.show()\n\n\nplt.figure(figsize=(7, 3))\nx = 0\nfor row_index in x_labels:\n    x = x + 1\n    values = results_ar.loc[row_index].tolist()\n    bottom = 0\n    for i, (category, value) in enumerate(zip(categories, values[2:])):\n        value = value * 1e3\n        if row_index == x_labels[0]:\n            plt.bar(x, value, bottom=bottom, color=colors[i], label=category, width=0.5)\n        else:\n            plt.bar(x, value, bottom=bottom, color=colors[i], width=0.5)\n        bottom += value\n\n\n# Set the title, legend, and display the graph\n# plt.title(\n#     \"Generation Latency per Layer per Token\"\n# )\nplt.ylabel(\"Latency (ms)\")\nplt.xlabel(\"Local buffer size (KB)\")\nplt.xticks([1, 2, 3, 4, 5, 6], x_labels)\nhandles, labels = plt.gca().get_legend_handles_labels()\nplt.legend(handles[::-1], labels[::-1], loc=\"upper left\", bbox_to_anchor=(1.2, 1.03))\nplt.tight_layout()\nxticks = plt.gca().get_xticks()\nxticklabels = plt.gca().get_xticklabels()\nindex_to_color_red = list(xticks).index(3)\nxticklabels[index_to_color_red].set_color(\"#76B900\")\nax1 = plt.gca()\nax1.set_ylim([0, 1.2])\nax2 = ax1.twinx()\nax2.plot(\n    [1, 2, 3, 4, 5, 6],\n    areas,\n    color=\"dimgray\",\n    linestyle=\"dashed\",\n    marker=\"x\",\n    label=\"Area\",\n)\nax2.set_ylabel(\"Area ($mm^2$)\")\nax2.set_ylim([0, 1200])\nplt.legend(loc=\"upper center\")\nplt.savefig(\"figure9b.pdf\", dpi=300, bbox_inches=\"tight\", pad_inches=0.01)\n"
  },
  {
    "path": "ae/figure9/run_figure9.sh",
    "content": "rm *.csv\nrm *.pdf\n\ncd ../..\n\npython -m ae.figure9.change_l1_cache\n\ncd ae/figure9\npython plot_l1_cache.py"
  },
  {
    "path": "configs/GA100.json",
    "content": "{\n    \"name\": \"NVIDIA A100(80GB)x4\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 128,\n            \"core_count\": 128,\n            \"process_node\": \"7nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 16,\n                    \"array_height\": 16,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 32,\n                    \"flop_per_cycle\": 4,\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 16,\n                    \"fp16_count\": 0,\n                    \"fp32_count\": 16,\n                    \"fp64_count\": 8\n                },\n                \"register_file\": {\n                    \"num_reg_files\": 1,\n                    \"num_registers\": 16384,\n                    \"register_bitwidth\":32,\n                    \"num_rdwr_ports\":4\n                },\n                \"SRAM_KB\": 192\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 48,\n            \"physical_global_buffer_MB\": 48,\n            \"global_buffer_bandwidth_per_cycle_byte\": 5120,\n            \"memory_channel_physical_count\": 6,\n            \"memory_channel_active_count\": 5,\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 80\n        }\n    }\n}"
  },
  {
    "path": "configs/ga102_template.json",
    "content": "{\n    \"name\": \"NVIDIA A100(80GB)x4\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 128,\n            \"core_count\": 108,\n            \"process_node\": \"7nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 16,\n                    \"array_height\": 16,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 32,\n                    \"flop_per_cycle\": 4,\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 16,\n                    \"fp16_count\": 0,\n                    \"fp32_count\": 32,\n                    \"fp64_count\": 0.5\n                },\n                \"SRAM_KB\": 128\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 40,\n            \"physical_global_buffer_MB\": 48,\n            \"global_buffer_bandwidth_per_cycle_byte\": 5120,\n            \"memory_channel_physical_count\": 6,\n            \"memory_channel_active_count\": 5,\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 80\n        }\n    }\n}"
  },
  {
    "path": "configs/generation_system.json",
    "content": "{\n    \"name\": \"NVIDIA A100(80GB)x4\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 128,\n            \"core_count\": 128,\n            \"process_node\": \"7nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 8,\n                    \"array_height\": 8,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 8,\n                    \"flop_per_cycle\": 4,\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 4,\n                    \"fp16_count\": 32,\n                    \"fp32_count\": 0,\n                    \"fp64_count\": 0\n                },\n                \"register_file\": {\n                    \"num_reg_files\": 1,\n                    \"num_registers\": 4096,\n                    \"register_bitwidth\": 32,\n                    \"num_rdwr_ports\": 4\n                },\n                \"SRAM_KB\": 48\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 24,\n            \"physical_global_buffer_MB\": 24,\n            \"global_buffer_bandwidth_per_cycle_byte\": 2560,\n            \"memory_channel_physical_count\": 6,\n            \"memory_channel_active_count\": 5,\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 80\n        }\n    }\n}"
  },
  {
    "path": "configs/latency_design.json",
    "content": "{\n    \"name\": \"NVIDIA A100(80GB)x4\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 64,\n            \"core_count\": 64,\n            \"process_node\": \"7nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 16,\n                    \"array_height\": 16,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 32,\n                    \"flop_per_cycle\": 4,\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 16,\n                    \"fp16_count\": 0,\n                    \"fp32_count\": 16,\n                    \"fp64_count\": 8\n                },\n                \"register_file\": {\n                    \"num_reg_files\": 1,\n                    \"num_registers\": 16384,\n                    \"register_bitwidth\": 32,\n                    \"num_rdwr_ports\": 4\n                },\n                \"SRAM_KB\": 192\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 24,\n            \"physical_global_buffer_MB\": 24,\n            \"global_buffer_bandwidth_per_cycle_byte\": 2560,\n            \"memory_channel_physical_count\": 6,\n            \"memory_channel_active_count\": 5,\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 80\n        }\n    }\n}"
  },
  {
    "path": "configs/mi210.json",
    "content": "{\n    \"name\": \"AMD MI210\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1400e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"core_count\": 104,\n            \"process_node\": \"7nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 16,\n                    \"array_height\": 16,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 16,\n                    \"flop_per_cycle\": 2,\n                    \"data_type\": \"fp32\",\n                    \"int32_count\": 16,\n                    \"fp32_count\": 16,\n                    \"fp64_count\": 8\n                },\n                \"SRAM_KB\": 128\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 8,\n            \"global_buffer_bandwidth_per_cycle_byte\": 4096,\n            \"memory_channel_physical_count\": 6,\n            \"memory_channel_active_count\": 4,\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 64\n        }\n    }\n}"
  },
  {
    "path": "configs/mi210_template.json",
    "content": "{\n    \"name\": \"AMD MI210\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"InfinityFabric\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 8,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 112,\n            \"core_count\": 108,\n            \"process_node\": \"6nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 16,\n                    \"array_height\": 16,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 16,\n                    \"flop_per_cycle\": 4,\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 16,\n                    \"fp16_count\": 0,\n                    \"fp32_count\": 0,\n                    \"fp64_count\": 16\n                },\n                \"register_file\": {\n                    \"num_reg_files\": 64,\n                    \"num_registers\": 512,\n                    \"register_bitwidth\":32,\n                    \"num_rdwr_ports\":4\n                },\n                \"SRAM_KB\": 80\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"6nm\",\n            \"global_buffer_MB\": 8,\n            \"physical_global_buffer_MB\": 8,\n            \"global_buffer_bandwidth_per_cycle_byte\": 5120,\n            \"memory_channel_physical_count\": 8,\n            \"memory_channel_active_count\": 8,\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 80\n        }\n    }\n}"
  },
  {
    "path": "configs/prefilling_system.json",
    "content": "{\n    \"name\": \"NVIDIA A100(80GB)x4\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 64,\n            \"core_count\": 64,\n            \"process_node\": \"7nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 32,\n                    \"array_height\": 32,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 32,\n                    \"flop_per_cycle\": 4,\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 16,\n                    \"fp16_count\": 0,\n                    \"fp32_count\": 16,\n                    \"fp64_count\": 8\n                },\n                \"register_file\": {\n                    \"num_reg_files\": 1,\n                    \"num_registers\": 16384,\n                    \"register_bitwidth\": 32,\n                    \"num_rdwr_ports\": 4\n                },\n                \"SRAM_KB\": 768\n            }\n        },\n        \"memory_protocol\": \"PCIe5\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 48,\n            \"physical_global_buffer_MB\": 48,\n            \"global_buffer_bandwidth_per_cycle_byte\": 5120,\n            \"memory_channel_physical_count\": 256,\n            \"memory_channel_active_count\": 256,\n            \"pin_count_per_channel\": 1,\n            \"bandwidth_per_pin_bit\": 32e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 160\n        }\n    }\n}"
  },
  {
    "path": "configs/template.json",
    "content": "{\n    \"name\": \"NVIDIA A100(80GB)x4\",\n    \"device_count\": 4,\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\"\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 128,\n            \"core_count\": 108,\n            \"process_node\": \"7nm\",\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 16,\n                    \"array_height\": 16,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 32,\n                    \"flop_per_cycle\": 4,\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 16,\n                    \"fp16_count\": 0,\n                    \"fp32_count\": 16,\n                    \"fp64_count\": 8\n                },\n                \"register_file\": {\n                    \"num_reg_files\": 1,\n                    \"num_registers\": 16384,\n                    \"register_bitwidth\":32,\n                    \"num_rdwr_ports\":4\n                },\n                \"SRAM_KB\": 192\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 40,\n            \"physical_global_buffer_MB\": 48,\n            \"global_buffer_bandwidth_per_cycle_byte\": 5120,\n            \"memory_channel_physical_count\": 6,\n            \"memory_channel_active_count\": 5,\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 80\n        }\n    }\n}"
  },
  {
    "path": "cost_model/__init__.py",
    "content": "## made this for first commit\n"
  },
  {
    "path": "cost_model/cost_examples.py",
    "content": "import cost_model.cost_model as cost_model\nimport json\n\n# example chip with a 32 wide vector, 16x16 SA, 256kb cache core, 8 cores per die\n# io die with 64 mb cache, 8 nvlinks, 32 pcie phys\n# all at 5nm and 7nm\n\nwith open(\"./configs/prefilling_system.json\", \"r\") as f:\n    # with open('../configs/mi210_template.json', 'r') as f:\n    configs_dict = json.load(f)\n\n# print(configs_dict['device'])\n# print(data['device']['compute_chiplet_count'])\n\ncompute_area = cost_model.calc_compute_chiplet_area_mm2(configs_dict)\nio_area = cost_model.calc_io_die_area_mm2(configs_dict)\nprint(\n    f\"compute area: {compute_area}, io area: {io_area}, total area: {compute_area+io_area}\"\n)\n\nexit(0)\ncore_compute_area_mm2 = cost_model.calc_compute_core_area_mm2(\n    32,\n    16,\n    2**18,\n    cost_model.transistor_density_7nm,\n    cost_model.sram_bit_cell_density_7nm,\n)\nio_die_area_mm2 = cost_model.calc_io_die_area_mm2(\n    2**25,\n    cost_model.PCIE5,\n    32,\n    8,\n    cost_model.transistor_density_7nm,\n    cost_model.sram_bit_cell_density_7nm,\n)\nprint(core_compute_area_mm2)\nprint(io_die_area_mm2)\n"
  },
  {
    "path": "cost_model/cost_model.py",
    "content": "# Author: August Ning aning@princeton.edu\n# Date started: 12 October 2023\n# This file is the cost model for Naivesim\n\nimport numpy as np\nimport math\n# import supply_chain.supply_chain_model as scm\nimport cost_model.supply_chain.supply_chain_model as scm\n\n# lots of parameters required for calculating silicon die area cost\n\n# these are in terms of million transistors per mm2\ntransistor_density_7nm = scm.transistor_density_arr[scm.PN_7_INDEX]\ntransistor_density_6nm = 114.2\ntransistor_density_5nm = scm.transistor_density_arr[scm.PN_5_INDEX]\n\nsram_bit_cell_density_7nm = 1.70e-07\nsram_bit_cell_density_6nm = 1.40e-07\nsram_bit_cell_density_5nm = 1.25e-07\n\n# cache size overheads derived from cacti for cache sizes\n# 4096, 8192, 16384, ..., 1 MB\ncache_area_efficiency_arr = [0.076, 0.142, 0.247, 0.393, 0.559, \\\n                             0.704, 0.526, 0.602, 0.561]\n\n# fpu transistor counts are for 64 bit FPU, based off Ariane and OpenPiton's SPARC T1\n# assume that fp32 are half the transistors\n# int32 transistor count is based off of Ariane's Mult and OpenPiton's SPARC T1\n# systolic array is for 1x1 area\n\n# scale FPU area by mantissa bits quadratically\nfpu64_transistor_count = 685300\nfpu32_transistor_count = fpu64_transistor_count * ((23 / 52) ** 2)\nfpu16_transistor_count = fpu64_transistor_count * ((10 / 52) ** 2)\n\nint32_transistor_count = 177690\n\n# based off of A100 SM and MI 210 CU\n# these overheads are per sublane, per vector width\n# (ex 32 for A100, 16 for MI 210)\nper_sublane_control_transistor_count = 996200\nnvidia_per_sublane_control_transistor_count = 725650\namd_per_sublane_control_transistor_count = 1534500\n\nper_sublane_control_dict = {'nvidia':per_sublane_control_transistor_count, \\\n                            'amd':per_sublane_control_transistor_count}\n\nper_core_comm_transistor_count = 44300000\nnvidia_per_core_comm_transistor_count = 55000000\namd_per_core_comm_transistor_count = 33600000\n\nper_core_comm_dict = {'nvidia':per_core_comm_transistor_count, \\\n                      'amd':per_core_comm_transistor_count}\n\n\n# memory controllers scale with process node, but PHYs do not\n# pcie, ddr, hbm\n# note: DDR link unit is 32 bits\npcie5_phy_mm2_per_lane = 0.64\npcie4_phy_mm2_per_lane = 0.48\nddr5_phy_mm2_per_link_unit = 1.45\nhbm2e_phy_mm2_per_link_unit = 10.45\nnvlink3_phy_mm2_per_link_unit = 1.888\nnvlink4_phy_mm2_per_link_unit = 0.965\ninfinity_fabric_phy_mm2_per_link_unit = 5.69\n\npcie5_ctrl_transistors_per_lane = 5372100\npcie4_ctrl_transistors_per_lane = 3962500\nddr5_ctrl_transistors_per_link_unit = 90446400\nhbm2e_ctrl_transistors_per_link_unit = 552743000\nnvlink3_ctrl_transistors_per_link_unit = 74632000\nnvlink4_ctrl_transistors_per_link_unit = 86628000\ninfinity_fabric_ctrl_transistors_per_link_unit = 348148000\n\n# mem tech keywords\nPCIE5 = 'PCIe5'\nPCIE4 = 'PCIe4'\nDDR5 = 'DDR5'\nHBM = 'HBM2e'\nNVLINK3 = 'NVLink3'\nNVLINK4 = 'NVLink4'\nINFINITYFABRIC = 'InfinityFabric'\n\n# average via dramexchange spot price, Oct 2023\nddr5_cost_per_gb = 2.4\nhbm_cost_per_gb = 7\n\n# return die area for a dimension x dimension SA with a\n# give bitwidth FPU at a given process node\n# right now, we model each PE's MAC as a FPU\ndef calc_systolic_array_area_mm2(dimension_x, dimension_y, bitwidth, transistor_density_mil_mm2):\n    if bitwidth == 'fp64':\n        total_transistor_count = fpu64_transistor_count * dimension_x * dimension_y\n    elif bitwidth == 'fp32':\n        total_transistor_count = fpu32_transistor_count * dimension_x * dimension_y\n    elif bitwidth == 'fp16':\n        total_transistor_count = fpu16_transistor_count * dimension_x * dimension_y\n\n    return total_transistor_count / 1e6 / transistor_density_mil_mm2\n\n# vector width corresponds to number of FPUs you have\ndef calc_vector_area_mm2(int32_count, fp16_count, fp32_count, fp64_count, transistor_density_mil_mm2):\n    total_transistor_count = 0\n    total_transistor_count += int32_count * int32_transistor_count\n    total_transistor_count += fp16_count * fpu16_transistor_count\n    total_transistor_count += fp32_count * fpu32_transistor_count\n    total_transistor_count += fp64_count * fpu64_transistor_count\n    \n    return total_transistor_count / 1e6 / transistor_density_mil_mm2\n\n# for cache designs, if the desired capacity is larger than the max cache unit\n# split them up into multiple units of the max capacity\n# min cache size is 4096 bytes\ndef calc_cache_sram_area_mm2(capacity_bytes, sram_bitcell_area_mm2, max_cache_unit_bytes=(2**19)):\n    if capacity_bytes > max_cache_unit_bytes:\n        num_cache_units = math.ceil(capacity_bytes / max_cache_unit_bytes)\n        unit_size_bytes = max_cache_unit_bytes\n    else:\n        num_cache_units = 1\n        unit_size_bytes = capacity_bytes\n\n    # cache size model is for capacity of 4096 bytes to 1 MB\n    if unit_size_bytes < 2 ** 12:\n        unit_size_bytes = 2 ** 12\n\n    area_efficiency_index = math.ceil(math.log(unit_size_bytes, 2)) - 12\n    area_efficiency_factor = cache_area_efficiency_arr[area_efficiency_index]\n    unit_cache_area = unit_size_bytes * 8 * sram_bitcell_area_mm2 / area_efficiency_factor\n    cache_area = num_cache_units * unit_cache_area\n    return cache_area\n\n# area model comes from EMPIRE\n# num_reg_files: how many distinct register files each sublanes has\n# D: how many registers there are in each RF\n# W: bits per register\n# P: number of read/write ports\ndef calc_reg_file_area(num_reg_files, D, W, P, transistor_density_mil_mm2):\n    area_90nm_um2 = (3.29 * 10**4) - (1.09 * 10**3 * D) - (8.83 * 10**2 * W) - (5.55 * 10**3 * P) \\\n           + (5.35 * 10**1 * D * W) + (1.50 * 10**-2 * D**2) + (1.08 * 10**-2 * W**2) \\\n           + (5.86 * 10**-1 * P**2) + (1.42 * 10**2 * D * P) + (3.68 * 10**2 * W * P)\n    \n    # need to convert um2 to mm2, convert to 7nm\n    area_90nm_mm2 = area_90nm_um2 / 1e6\n    area_mm2 =  area_90nm_mm2 * (scm.transistor_density_arr[scm.PN_90_INDEX] / transistor_density_mil_mm2)\n    total_reg_file_area = num_reg_files * area_mm2\n    return total_reg_file_area\n\n# for width, for PCIe and NVLink, it is the whole lane\n# for DDR and HBM, it's 128 bits and 1024 bits respectively\ndef calc_mem_controller_area_mm2(mem_tech, width, transistor_density_mil_mm2):\n    controller_transistor_count = -1\n\n    if mem_tech == PCIE5:\n        controller_transistor_count = pcie5_ctrl_transistors_per_lane * width\n    elif mem_tech == PCIE4:\n        controller_transistor_count = pcie4_ctrl_transistors_per_lane * width\n    elif mem_tech == DDR5:\n        controller_transistor_count = ddr5_ctrl_transistors_per_link_unit * width\n    elif mem_tech == HBM:\n        controller_transistor_count = hbm2e_ctrl_transistors_per_link_unit * width\n    elif mem_tech == NVLINK3:\n        controller_transistor_count = nvlink3_ctrl_transistors_per_link_unit * width\n    elif mem_tech == NVLINK4:\n        controller_transistor_count = nvlink4_ctrl_transistors_per_link_unit * width\n    elif mem_tech == INFINITYFABRIC:\n        controller_transistor_count = infinity_fabric_ctrl_transistors_per_link_unit * width\n\n    return (controller_transistor_count / 1e6) / transistor_density_mil_mm2\n\ndef calc_mem_phy_area_mm2(mem_tech, width):\n    if mem_tech == PCIE5:\n        return pcie5_phy_mm2_per_lane * width\n    elif mem_tech == PCIE4:\n        return pcie4_phy_mm2_per_lane * width\n    elif mem_tech == DDR5:\n        return ddr5_phy_mm2_per_link_unit * width\n    elif mem_tech == HBM:\n        return hbm2e_phy_mm2_per_link_unit * width\n    elif mem_tech == NVLINK3:\n        return nvlink3_phy_mm2_per_link_unit * width\n    elif mem_tech == NVLINK4:\n        return nvlink4_phy_mm2_per_link_unit * width\n    elif mem_tech == INFINITYFABRIC:\n        return infinity_fabric_phy_mm2_per_link_unit * width\n    else:\n        return -1\n\ndef find_logic_sram_transistor_density(process_node):\n    if '7' in process_node:\n        return transistor_density_7nm, sram_bit_cell_density_7nm\n    elif '6' in process_node:\n        return transistor_density_6nm, sram_bit_cell_density_6nm\n    elif '5' in process_node:\n        return transistor_density_5nm, sram_bit_cell_density_5nm\n\n    raise Exception(\"Invalid Process Node\")\n\n\n# a compute core consists of a fixed control overhead\n# a specified width fp32 vector engine\n# a specified dimmension fp16 systolic array\n# a specified L1 cache\n# at a specified process node\n# NB: you can fit multiple cores onto a single die for chiplet systems\ndef calc_compute_chiplet_area_mm2(configs_dict, verbose=False):\n    total_die_map = {}\n    core_breakdown_map = {}\n    device_name = configs_dict['name']\n    device_brand = 'nvidia' if 'nvidia' in device_name.lower() else 'amd'\n    vector_width = configs_dict['device']['compute_chiplet']['core']['vector_unit']['vector_width']\n    vector_int32_count = configs_dict['device']['compute_chiplet']['core']['vector_unit']['int32_count']\n    vector_fp16_count = configs_dict['device']['compute_chiplet']['core']['vector_unit']['fp16_count']\n    vector_fp32_count = configs_dict['device']['compute_chiplet']['core']['vector_unit']['fp32_count']\n    vector_fp64_count = configs_dict['device']['compute_chiplet']['core']['vector_unit']['fp64_count']\n    sa_dim_x = configs_dict['device']['compute_chiplet']['core']['systolic_array']['array_width']\n    sa_dim_y = configs_dict['device']['compute_chiplet']['core']['systolic_array']['array_height']\n    sa_bitwidth = configs_dict['device']['compute_chiplet']['core']['systolic_array']['data_type']\n    num_reg_files = configs_dict['device']['compute_chiplet']['core']['register_file']['num_reg_files']\n    num_registers = configs_dict['device']['compute_chiplet']['core']['register_file']['num_registers']\n    register_bitwidth = configs_dict['device']['compute_chiplet']['core']['register_file']['register_bitwidth']\n    num_rdwr_ports = configs_dict['device']['compute_chiplet']['core']['register_file']['num_rdwr_ports']\n    sublane_count = configs_dict['device']['compute_chiplet']['core']['sublane_count']\n    cache_size_bytes = configs_dict['device']['compute_chiplet']['core']['SRAM_KB'] * (2 ** 10)\n    process_node = configs_dict['device']['compute_chiplet']['process_node']\n    cores_per_chiplet = configs_dict['device']['compute_chiplet']['physical_core_count']\n\n    # each sublane has a SA and vector unit. a core is made up of sublanes. a chiplet has multiple cores\n    transistor_density_mil_mm2, sram_density_bitcell_mm2 = find_logic_sram_transistor_density(process_node)\n    per_sublane_area_mm2 = 0\n    per_sublane_control_area_mm2 = per_sublane_control_dict[device_brand] / 1e6 / transistor_density_mil_mm2\n    per_sublane_area_mm2 += (vector_width * per_sublane_control_area_mm2)\n    control_logic_area = per_sublane_area_mm2 * sublane_count\n\n    per_lane_vector_area = calc_vector_area_mm2(vector_int32_count, vector_fp16_count, vector_fp32_count, vector_fp64_count, transistor_density_mil_mm2)\n    per_sublane_area_mm2 += per_lane_vector_area\n\n    per_lane_sa_area = calc_systolic_array_area_mm2(sa_dim_x, sa_dim_y, sa_bitwidth, transistor_density_mil_mm2)\n    per_sublane_area_mm2 += per_lane_sa_area\n\n    per_lane_regfile_area = calc_reg_file_area(num_reg_files, num_registers, register_bitwidth, num_rdwr_ports, transistor_density_mil_mm2)\n    per_sublane_area_mm2 += per_lane_regfile_area\n\n    per_core_compute_area_mm2 = per_sublane_area_mm2 * sublane_count\n    cache_area_mm2 = calc_cache_sram_area_mm2(cache_size_bytes, sram_density_bitcell_mm2)\n    per_core_area_mm2 = per_core_compute_area_mm2 + cache_area_mm2\n\n    core_breakdown_map['total_core_area'] = per_core_area_mm2\n    core_breakdown_map['control_area'] = control_logic_area\n    core_breakdown_map['alu_area'] = per_lane_vector_area * sublane_count\n    core_breakdown_map['sa_area'] = per_lane_sa_area * sublane_count\n    core_breakdown_map['regfile_area'] = per_lane_regfile_area * sublane_count\n    core_breakdown_map['local_buffer_area'] = cache_area_mm2\n\n    total_cores_area = per_core_area_mm2 * cores_per_chiplet\n    total_crossbar_area = (per_core_comm_dict[device_brand] / 1e6 / transistor_density_mil_mm2) * cores_per_chiplet\n    # each core has an area overhead to connect to the xbar\n    compute_chiplet_area_mm2 = total_cores_area + total_crossbar_area\n\n    total_die_map['total_area'] = compute_chiplet_area_mm2\n    total_die_map['cores_area'] = total_cores_area\n    total_die_map['crossbar_area'] = total_crossbar_area\n    if verbose:\n        return compute_chiplet_area_mm2, core_breakdown_map, total_die_map\n    else:\n        return compute_chiplet_area_mm2\n\n\n# NB: for mem_tech, if you are using DDR or HBM, it will be 128 bits and 1024 bits respectively per lane\n# for PCIe and NVLink, specify the number of lanes (128bits per lane)\n# def calc_io_die_area_mm2(cache_size_bytes, mem_tech, mem_tech_width, num_nvlink_phys, \\\n#                          transistor_density_mil_mm2, sram_density_bitcell_mm2):\ndef calc_io_die_area_mm2(config_dict, verbose=False):\n    total_die_map = {}\n\n    cache_size_bytes = config_dict['device']['io']['physical_global_buffer_MB'] * (2 ** 20)\n    mem_tech = config_dict['device']['memory_protocol']\n    num_mem_tech_units = config_dict['device']['io']['memory_channel_physical_count']\n    gpu_gpu_comm_tech = config_dict['interconnect']['link']['name']\n    num_gpu_gpu_comm_phy = config_dict['interconnect']['link_count_per_device']\n    process_node = config_dict['device']['io']['process_node']\n\n    transistor_density_mil_mm2, sram_density_bitcell_mm2 = find_logic_sram_transistor_density(process_node)\n    io_die_area_mm2 = 0\n    io_die_area_mm2 += calc_cache_sram_area_mm2(cache_size_bytes, sram_density_bitcell_mm2)\n    global_buffer_area = io_die_area_mm2\n\n    # mem tech for communicating to off chip memory\n    mem_phy_area = calc_mem_phy_area_mm2(mem_tech, num_mem_tech_units)\n    mem_controller_area = calc_mem_controller_area_mm2(mem_tech, num_mem_tech_units, transistor_density_mil_mm2)\n    io_die_area_mm2 += mem_phy_area\n    io_die_area_mm2 += mem_controller_area\n\n    # every  IO die has a few NV links for chip to chip communication\n    device_phy_area = calc_mem_phy_area_mm2(gpu_gpu_comm_tech, num_gpu_gpu_comm_phy)\n    device_controller_area = calc_mem_controller_area_mm2(gpu_gpu_comm_tech, num_gpu_gpu_comm_phy, transistor_density_mil_mm2)\n    io_die_area_mm2 += device_phy_area\n    io_die_area_mm2 += device_controller_area\n\n    total_die_map['total_die_area'] = io_die_area_mm2\n    total_die_map['global_buffer_area'] = global_buffer_area\n    total_die_map['mem_phy_area'] = mem_phy_area\n    total_die_map['mem_controller_area'] = mem_controller_area\n    total_die_map['device_phy_area'] = device_phy_area\n    total_die_map['device_controller_area'] = device_controller_area\n\n    if verbose:\n        return io_die_area_mm2, total_die_map\n    else:\n        return io_die_area_mm2\n"
  },
  {
    "path": "cost_model/regfile_area.py",
    "content": "def calculate_regfile_area(D, W, P):\n    area_90nm_um2 = (3.29 * 10**4) - (1.09 * 10**3 * D) - (8.83 * 10**2 * W) - (5.55 * 10**3 * P) \\\n           + (5.35 * 10**1 * D * W) + (1.50 * 10**-2 * D**2) + (1.08 * 10**-2 * W**2) \\\n           + (5.86 * 10**-1 * P**2) + (1.42 * 10**2 * D * P) + (3.68 * 10**2 * W * P)\n    \n    # need to convert um2 to mm2, convert to 7nm\n    area_90nm_mm2 = area_90nm_um2 / 1e6\n    area_7nm_mm2 =  area_90nm_mm2 * (1.6 / 96.3)\n    return area_7nm_mm2\n\nreg_area = calculate_regfile_area(16384, 32, 4)\nprint(reg_area)\n\nreg_area = 64 * calculate_regfile_area(512, 32, 4)\nprint(reg_area)\n\nreg_area = calculate_regfile_area(800, 32, 4)\nprint(reg_area)"
  },
  {
    "path": "design_space_exploration/__init__.py",
    "content": ""
  },
  {
    "path": "design_space_exploration/dse.py",
    "content": "import json, re\nfrom hardware_model.compute_module import (\n    VectorUnit,\n    SystolicArray,\n    Core,\n    ComputeModule,\n    overhead_dict,\n)\nfrom hardware_model.io_module import IOModule\nfrom hardware_model.memory_module import MemoryModule\nfrom hardware_model.device import Device\nfrom hardware_model.interconnect import LinkModule, InterConnectModule, TopologyType\nfrom hardware_model.system import System\nfrom software_model.transformer import (\n    TransformerBlockInitComputationTP,\n    TransformerBlockAutoRegressionTP,\n)\nfrom software_model.utils import data_type_dict, Tensor\n# from cost_model.cost_model import calc_compute_chiplet_area_mm2, calc_io_die_area_mm2\nfrom math import ceil\n\ndef read_architecture_template(file_path):\n    with open(file_path, \"r\") as f:\n        arch_specs = json.load(f)\n    return arch_specs\n\n\ndef template_to_system(arch_specs):\n    device_specs = arch_specs[\"device\"]\n    compute_chiplet_specs = device_specs[\"compute_chiplet\"]\n    io_specs = device_specs[\"io\"]\n    core_specs = compute_chiplet_specs[\"core\"]\n    sublane_count = core_specs[\"sublane_count\"]\n    # vector unit\n    vector_unit_specs = core_specs[\"vector_unit\"]\n    vector_unit = VectorUnit(\n        sublane_count\n        * vector_unit_specs[\"vector_width\"]\n        * vector_unit_specs[\"flop_per_cycle\"],\n        int(re.search(r\"(\\d+)\", vector_unit_specs[\"data_type\"]).group(1)) // 8,\n        35,\n        vector_unit_specs[\"vector_width\"],\n        sublane_count,\n    )\n    # systolic array\n    systolic_array_specs = core_specs[\"systolic_array\"]\n    systolic_array = SystolicArray(\n        systolic_array_specs[\"array_height\"],\n        systolic_array_specs[\"array_width\"],\n        systolic_array_specs[\"mac_per_cycle\"],\n        int(re.search(r\"(\\d+)\", systolic_array_specs[\"data_type\"]).group(1)) // 8,\n        int(re.search(r\"(\\d+)\", systolic_array_specs[\"data_type\"]).group(1)) // 8,\n    )\n    # core\n    core = Core(\n        vector_unit,\n        systolic_array,\n        sublane_count,\n        core_specs[\"SRAM_KB\"] * 1024,\n    )\n    # compute module\n    compute_module = ComputeModule(\n        core,\n        compute_chiplet_specs[\"core_count\"] * device_specs[\"compute_chiplet_count\"],\n        device_specs[\"frequency_Hz\"],\n        io_specs[\"global_buffer_MB\"] * 1024 * 1024,\n        io_specs[\"global_buffer_bandwidth_per_cycle_byte\"],\n        overhead_dict[\"A100\"],\n    )\n    # io module\n    io_module = IOModule(\n        io_specs[\"memory_channel_active_count\"]\n        * io_specs[\"pin_count_per_channel\"]\n        * io_specs[\"bandwidth_per_pin_bit\"]\n        // 8,\n        1e-6,\n    )\n    # memory module\n    memory_module = MemoryModule(\n        device_specs[\"memory\"][\"total_capacity_GB\"] * 1024 * 1024 * 1024\n    )\n    # device\n    device = Device(compute_module, io_module, memory_module)\n    # interconnect\n    interconnect_specs = arch_specs[\"interconnect\"]\n    link_specs = interconnect_specs[\"link\"]\n    link_module = LinkModule(\n        link_specs[\"bandwidth_per_direction_byte\"],\n        link_specs[\"bandwidth_both_directions_byte\"],\n        link_specs[\"latency_second\"],\n        link_specs[\"flit_size_byte\"],\n        link_specs[\"max_payload_size_byte\"],\n        link_specs[\"header_size_byte\"],\n    )\n    interconnect_module = InterConnectModule(\n        arch_specs[\"device_count\"],\n        TopologyType.FC\n        if interconnect_specs[\"topology\"] == \"FC\"\n        else TopologyType.RING,\n        link_module,\n        interconnect_specs[\"link_count_per_device\"],\n    )\n\n    # system\n    system = System(device, interconnect_module)\n\n    return system\n\n\ndef test_template_to_system():\n    arch_specs = read_architecture_template(\"configs/template.json\")\n    A100_system = template_to_system(arch_specs)\n    bs = 8\n    s = 2048\n    model = TransformerBlockInitComputationTP(\n        d_model=12288,\n        n_heads=96,\n        device_count=4,\n        data_type=data_type_dict[\"fp16\"],\n    )\n    _ = model(Tensor([bs, s, 12288], data_type_dict[\"fp16\"]))\n    model.roofline_model(A100_system)\n\n\ndef find_cheapest_design(\n    d_model,\n    n_heads,\n    n_layers,\n    batch_size,\n    input_seq_length,\n    init_latency,\n    output_seq_length,\n    auto_regression_latency,\n    \n):\n    i=0\n    smallest_total_area_mm2=float('inf')\n    best_arch_specs=None\n    arch_specs = read_architecture_template(\"configs/template.json\")\n    for device_count in [4, 8, 12, 16]:\n        model_init = TransformerBlockInitComputationTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=device_count,\n                data_type=data_type_dict[\"fp16\"],\n            )\n        model_auto_regression = TransformerBlockAutoRegressionTP(\n                d_model=12288,\n                n_heads=96,\n                device_count=device_count,\n                data_type=data_type_dict[\"fp16\"],)\n        _ = model_init(Tensor([batch_size, input_seq_length, model_init.d_model], data_type_dict[\"fp16\"]))\n        _ = model_auto_regression(Tensor([batch_size, 1, model_init.d_model],data_type_dict[\"fp16\"]), input_seq_length+output_seq_length)\n        arch_specs[\"device_count\"] = device_count\n        if device_count <= 4:\n            topology = \"FC\"\n        else:\n            topology = \"RING\"\n        arch_specs[\"interconnect\"][\"topology\"] = topology\n        for link_count_per_device in [6, 12, 18, 24]:\n            arch_specs[\"interconnect\"][\"link_count_per_device\"] = link_count_per_device\n            # device\n            for core_count in [32, 64, 128, 256]:\n                arch_specs[\"device\"][\"compute_chiplet\"][\"core_count\"] = core_count\n                # core\n                for sublane_count in [1, 2, 4, 8]:\n                    arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\n                        \"sublane_count\"\n                    ] = sublane_count\n                    # systolic array\n                    for array_height in [16, 32, 64, 128]:\n                        arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\n                            \"systolic_array\"\n                        ][\"array_height\"] = array_height\n                        arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\n                            \"systolic_array\"\n                        ][\"array_width\"] = array_height\n                        # vector unit\n                        for vector_width in [16, 32, 64, 128]:\n                            arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\n                                \"vector_unit\"\n                            ][\"vector_width\"] = vector_width\n                            for SRAM_KB in [64, 128, 256, 512, 1024]:\n                                arch_specs[\"device\"][\"compute_chiplet\"][\"core\"][\n                                    \"SRAM_KB\"\n                                ] = SRAM_KB\n                                # global buffer\n                                for total_global_buffer_MB in [\n                                    80,\n                                    160,\n                                    240,\n                                    320,\n                                    400,\n                                    480,\n                                    640,\n                                    800,\n                                    960,\n                                ]:\n                                    global_buffer_MB = (\n                                        total_global_buffer_MB // device_count\n                                    )\n                                    global_buffer_bandwidth_per_cycle_byte = (\n                                        5120 * global_buffer_MB // 40\n                                    )\n                                    arch_specs[\"device\"][\"io\"][\n                                        \"global_buffer_MB\"\n                                    ] = global_buffer_MB\n                                    arch_specs[\"device\"][\"io\"][\n                                        \"global_buffer_bandwidth_per_cycle_byte\"\n                                    ] = global_buffer_bandwidth_per_cycle_byte\n                                    # memory\n                                    memory_capacity_requirement_GB = ceil(model_auto_regression.memory_requirement*n_layers/1e9/16)*16\n                                    # print(f\"memory_capacity_requirement_GB={model_auto_regression.memory_requirement*n_layers/1e9}\")\n                                    # exit()\n                                    for memory_protocol in [\n                                        \"HBM2e\",\n                                        \"DDR5\",\n                                        \"PCIe5\",\n                                        # \"GDDR6X\"\n                                    ]:\n                                        arch_specs['device']['memory_protocol']=memory_protocol\n                                        if memory_protocol == \"HBM2e\":\n                                            # 400 GB/s per channel, 16 GB\n                                            channel_count=memory_capacity_requirement_GB // 16\n                                            if channel_count>8:\n                                                continue\n                                            channel_count_list = [channel_count]\n                                            pin_count_per_channel=1024\n                                            bandwidth_per_pin_bit=3.2e9\n                                        elif memory_protocol == \"DDR5\":\n                                            # 19.2 GB/s per channel, 2 channel per dimm\n                                            channel_count_list = [16, 24, 32]\n                                            pin_count_per_channel=32\n                                            bandwidth_per_pin_bit=4.8e9\n                                        elif memory_protocol == \"PCIe5\":\n                                            # 4 GB/s per channel\n                                            channel_count_list = [64, 96, 128]\n                                            pin_count_per_channel=1\n                                            bandwidth_per_pin_bit=32e9\n                                        # elif memory_protocol == \"GDDR6X\":\n                                        #     # 84 GB/s per channel, 2 GB\n                                        #     channel_count_list= memo\n                                        for channel_count in channel_count_list:\n                                            arch_specs['device']['memory']['total_capacity_GB'] = memory_capacity_requirement_GB\n                                            arch_specs['device']['io']['memory_channel_active_count'] = channel_count\n                                            arch_specs['device']['io']['memory_channel_physical_count'] = channel_count\n                                            arch_specs['device']['io']['pin_count_per_channel'] = pin_count_per_channel\n                                            arch_specs['device']['io']['bandwidth_per_pin_bit'] = bandwidth_per_pin_bit\n                                            \n                                            total_area_mm2=calc_compute_chiplet_area_mm2(arch_specs)+calc_io_die_area_mm2(arch_specs)\n                                            # print(f\"channel_count={arch_specs['device']['io']['memory_channel_active_count']},total area={total_area_mm2}\")\n                                            if total_area_mm2>900:\n                                                continue\n                                            system=template_to_system(arch_specs)\n                                            init_roofline_latency=model_init.roofline_model(system)*n_layers\n                                            if init_roofline_latency>init_latency:\n                                                continue\n                        \n                                            auto_regression_roofline_latency=model_auto_regression.roofline_model(system)*n_layers\n                                            if auto_regression_roofline_latency>auto_regression_latency:\n                                                continue\n                                            auto_regression_latency_simulated = model_auto_regression.compile_and_simulate(system, 'heuristic-GPU')\n                                            if auto_regression_latency_simulated>auto_regression_latency:\n                                                continue\n                                            init_latency_simulated = model_init.compile_and_simulate(system, 'heuristic-GPU')\n                                            if init_latency_simulated>init_latency:\n                                                continue\n                                            if total_area_mm2*device_count<smallest_total_area_mm2:\n                                                smallest_total_area_mm2=total_area_mm2*device_count\n                                                best_arch_specs=arch_specs\n                                                best_arch_specs['area_per_device_mm2']=total_area_mm2\n                                                # print(f\"best_arch_specs={best_arch_specs}\")\n                                                # print(f\"smallest_total_area_mm2={smallest_total_area_mm2}\")\n                                            i=i+1\n                                            if i%100==0:\n                                                print(f'i={i}')\n    print(f'number of potential designs={i}')\n    with open(\"configs/best_arch_specs.json\", \"w\") as f:\n        json.dump(best_arch_specs, f, indent=4)\n                                            \n\nif __name__ == \"__main__\":\n    # test_template_to_system()\n    find_cheapest_design(12288, 96, 96, 8, 2048, 5, 1024, 0.1)\n    \n    \n"
  },
  {
    "path": "docs/run.md",
    "content": "# User Guide: How to Run a LLMCompass Simulation\n\n## Step 1: Build a Hardware Configuration\n\nFollow the [NVIDIA GA100 example](../configs/GA100.json). This is a 4-GA100 node connected with NVLinks.\n\n### Explanations on the Knobs\nMost of the attributes are self-explained:\n\n```json\n{\n    \"name\": \"NVIDIA A100(80GB)x4\", \n    \"device_count\": 4, # how many devices in a node\n    \"interconnect\": {\n        \"link\": {\n            \"name\": \"NVLink3\",\n            \"bandwidth_per_direction_byte\": 25e9,\n            \"bandwidth_both_directions_byte\": 50e9,\n            \"latency_second\": 8.92e-6,\n            \"flit_size_byte\": 16,\n            \"header_size_byte\": 16,\n            \"max_payload_size_byte\": 256\n        },\n        \"link_count_per_device\": 12,\n        \"topology\": \"FC\" # currently support FC (fully-connected) and RING\n    },\n    \"device\": {\n        \"frequency_Hz\": 1410e6,\n        \"compute_chiplet_count\": 1,\n        \"compute_chiplet\": {\n            \"physical_core_count\": 128, # used for area model\n            \"core_count\": 128, # used for performance model\n            \"process_node\": \"7nm\", # currently support 7nm, 6nm, 5nm\n            \"core\": {\n                \"sublane_count\": 4,\n                \"systolic_array\": {\n                    \"array_width\": 16,\n                    \"array_height\": 16,\n                    \"data_type\": \"fp16\",\n                    \"mac_per_cycle\": 1\n                },\n                \"vector_unit\": {\n                    \"vector_width\": 32,\n                    \"flop_per_cycle\": 4, # 32*4=128 flops per cycle per vector unit\n                    \"data_type\": \"fp16\",\n                    \"int32_count\": 16, # the number of int32 ALUs, used for area model\n                    \"fp16_count\": 0,\n                    \"fp32_count\": 16,\n                    \"fp64_count\": 8\n                },\n                \"register_file\": {\n                    \"num_reg_files\": 1,\n                    \"num_registers\": 16384,\n                    \"register_bitwidth\":32,\n                    \"num_rdwr_ports\":4\n                },\n                \"SRAM_KB\": 192\n            }\n        },\n        \"memory_protocol\": \"HBM2e\",\n        \"_memory_protocol_list\": [\n            \"HBM2e\",\n            \"DDR4\",\n            \"DDR5\",\n            \"PCIe4\",\n            \"PCIe5\"\n        ],\n        \"io\": {\n            \"process_node\": \"7nm\",\n            \"global_buffer_MB\": 48,\n            \"physical_global_buffer_MB\": 48,\n            \"global_buffer_bandwidth_per_cycle_byte\": 5120,\n            \"memory_channel_physical_count\": 6, # used for area model\n            \"memory_channel_active_count\": 5, # used for performance model\n            \"pin_count_per_channel\": 1024,\n            \"bandwidth_per_pin_bit\": 3.2e9\n        },\n        \"memory\": {\n            \"total_capacity_GB\": 80\n        }\n    }\n}\n\n```\n\n## Step 2: Build a LLM Computational Graph\n\nTransformer blocks have been provided as in [`transformer.py`](../software_model/transformer.py), including Initial Computation (also called Prefill or Context stage) and Auto Regression (also called Decoding or Generation stage), with Tensor Parallelism support (automatically turned of if the system only has 1 device).\n\nThe user needs to provide these parameter:\n* `d_model`: the hidden dimension, 12288 for GPT3\n* `n_heads`: the number of heads, 96 for GPT3\n* `device_count`: tensor parallelism\n* `data_type`: `int8`, `fp16`, or `fp32`\n\n### Build Your Own LLM\n\nThe user can also build their own computational graph following the [`transformer.py`](../software_model/transformer.py) example using provided operators: [`matmul`](../software_model/matmul.py), [`softmax`](../software_model/softmax.py), [`layernorm`](../software_model/layernorm.py), [`gelu`](../software_model/gelu.py), and [`allreduce`](../software_model/communication_primitives.py).\n\nThe user needs to define a new `class` by inheriting `Operator` the class and configure these fields:\n* `__init__`: define the needed operators in the initial function\n* `__call__`: build the computational graph. The shape of Tensors will be automatically calculated and used for simulation.\n* `compile_and_simulate`: simulate all the operators and get the total latency as well as other runtimes.\n* `roofline_model` (optional): a roofline model analysis.\n* `run_on_gpu` (optional): run the computational graph on real-world GPUs with PyTorch.\n\n## Step 3: Run a LLMCompass Simulation\n\nFirst, read the hardware configuration and parse it to LLMCompass:\n```python\nfrom design_space_exploration.dse import template_to_system, read_architecture_template\n\nspecs = read_architecture_template(\"PATH/TO/YOUR/JSON\")\nsystem = template_to_system(specs)\n\n```\n\nNext, initiate and instantiate an LLM as in this example:\n```python\nmodel_auto_regression = TransformerBlockAutoRegressionTP(\n        d_model=12288,\n        n_heads=96,\n        device_count=1,\n        data_type=data_type_dict[\"fp16\"],\n    )\n_ = model_auto_regression(\n\tTensor([bs, 1, 12288], data_type_dict[\"fp16\"]),\n\tseq_len,\n)\n\n```\n\nFinally, run the simulation\n```\nauto_regression_latency_simulated = model_auto_regression.compile_and_simulate(\n\tsystem, \"heuristic-GPU\"\n)\n```\n"
  },
  {
    "path": "environment.yml",
    "content": "name: llmcompass_ae\nchannels:\n  - pytorch\n  - defaults\ndependencies:\n  - python=3.9\n  - pytorch\n  - pip:\n    - scalesim\n    - matplotlib\n    - seaborn\n    - scipy"
  },
  {
    "path": "hardware_model/__init__.py",
    "content": "# from compute_module import *\n# from io_module import *\n# from memory_module import *\n# from chiplet import *\n# from interconnect import *\n# from pcb import *\n"
  },
  {
    "path": "hardware_model/arch_template.py",
    "content": "class ArchitectureTemplate:\n    def __init__(self, \n                 # ve\n                 ):"
  },
  {
    "path": "hardware_model/compute_module.py",
    "content": "from math import ceil\nfrom software_model.utils import DataType, data_type_dict\n\n\nclass VectorUnit:\n    def __init__(\n        self,\n        total_vector_flops_per_cycle,\n        word_size,\n        flops_per_exp,\n        vector_width,\n        vector_count,\n        data_type=data_type_dict[\"fp16\"],\n    ):\n        self.total_vector_flops_per_cycle = total_vector_flops_per_cycle\n        self.word_size = word_size  # Byte\n        self.flops_per_exp = flops_per_exp  # flops per exp instruction\n        self.vector_width = vector_width\n        self.vector_count = vector_count\n        self.flops_per_cycle = ceil(\n            total_vector_flops_per_cycle / vector_width / vector_count\n        )\n        self.data_type = data_type\n\n\nvector_unit_dict = {\n    \"A100_fp16\": VectorUnit(512, 2, 35, 32, 4),\n    \"TPUv3_fp32\": VectorUnit(128 * 8, 4, 15, 128, 8, data_type_dict[\"fp32\"]),\n    \"MI210_fp32\": VectorUnit(128, 4, 18, 16, 4, data_type_dict[\"fp32\"]),\n    \"TPUv3_new\": VectorUnit(128 * 4, 4, 15, 128, 4, data_type_dict[\"fp32\"]),\n}\n\n\nclass SystolicArray:\n    def __init__(\n        self,\n        array_height,\n        array_width,\n        mac_per_cycle,\n        input_word_size,\n        output_word_size,\n    ):\n        self.array_height = array_height\n        self.array_width = array_width\n        self.mac_per_cycle = mac_per_cycle\n        self.input_word_size = input_word_size\n        self.output_word_size = output_word_size\n\n\nsystolic_array_dict = {\n    \"A100_fp16\": SystolicArray(16, 16, 1, 2, 2),\n    \"A100_int8\": SystolicArray(16, 16, 2, 1, 4),\n    \"TPUv3_bf16\": SystolicArray(128, 128, 1, 2, 4),\n    \"MI210_fp16\": SystolicArray(16, 16, 0.5, 2, 2),\n    \"TPUv3_new\": SystolicArray(128, 128, 1, 2, 4),\n}\n\n\nclass Core:\n    def __init__(\n        self,\n        vector_unit: VectorUnit,\n        systolic_array: SystolicArray,\n        systolic_array_count,\n        SRAM_size,\n    ):\n        self.vector_unit = vector_unit\n        self.systolic_array = systolic_array\n        self.systolic_array_count = systolic_array_count\n        self.SRAM_size = SRAM_size  # Byte\n        # assert(vector_unit.word_size==systolic_array.word_size)\n        self.vector_word_size = vector_unit.word_size\n\n\ncore_dict = {\n    \"SM_A100_fp16\": Core(\n        vector_unit_dict[\"A100_fp16\"], systolic_array_dict[\"A100_fp16\"], 4, 192 * 1024\n    ),\n    \"SM_A100_int8\": Core(\n        vector_unit_dict[\"A100_fp16\"], systolic_array_dict[\"A100_int8\"], 4, 192 * 1024\n    ),\n    \"Core_TPUv3_bf16\": Core(\n        vector_unit_dict[\"TPUv3_fp32\"],\n        systolic_array_dict[\"TPUv3_bf16\"],\n        2,\n        16 * 1024 * 1024,\n    ),\n    \"CU_MI210_fp16\": Core(\n        vector_unit_dict[\"MI210_fp32\"], systolic_array_dict[\"MI210_fp16\"], 4, 128 * 1024\n    ),\n    \"Core_TPUv3_new\": Core(\n        vector_unit_dict[\"TPUv3_new\"],\n        systolic_array_dict[\"TPUv3_new\"],\n        1,\n        8 * 1024 * 1024,\n    ),\n}\n# compute_tile_dict={'SM_A100_int8':ComputeTile(512, 4096, 192*1024*8,3.41, 'TSMC N7', 128*8),'SM_A100_fp16':ComputeTile(512, 2048, 192*1024*8,3.41, 'TSMC N7', 128),}\n# flops: https://docs.nvidia.com/deeplearning/performance/dl-performance-gpu-background/index.html#gpu-arch__fig2\n# area: https://pbs.twimg.com/media/FOT_-NJWUAARrtB?format=jpg&name=large\n\n\nclass Overhead:\n    def __init__(self, matmul, softmax, layernorm, gelu):\n        self.matmul = matmul\n        self.softmax = softmax\n        self.layernorm = layernorm\n        self.gelu = gelu\n\n\noverhead_dict = {\n    \"A100\": Overhead(2.1e-5, 1.2e-5, 4.5e-5, 4.5e-5),\n    \"TPUv3\": Overhead(11e-5, 30e-5, 14e-5, 10e-5),\n    \"MI210\": Overhead(3.4e-5, 2.2e-5, 2.8e-5, 2.1e-5),\n}\n\n\nclass ComputeModule:\n    def __init__(\n        self,\n        core: Core,\n        core_count,\n        clock_freq,\n        l2_size,\n        l2_bandwidth_per_cycle,\n        overhead: Overhead = overhead_dict[\"A100\"],\n    ):\n        self.core = core\n        self.core_count = core_count\n        self.clock_freq = clock_freq\n        self.l2_size = int(l2_size)  # Byte\n        self.l2_bandwidth_per_cycle = l2_bandwidth_per_cycle  # Byte/clock\n        self.total_vector_flops_per_cycle = (\n            core.vector_unit.total_vector_flops_per_cycle * core_count\n        )\n        self.total_vector_flops = self.total_vector_flops_per_cycle * clock_freq\n        self.total_systolic_array_flops = (\n            core_count\n            * core.systolic_array_count\n            * core.systolic_array.mac_per_cycle\n            * 2\n            * core.systolic_array.array_height\n            * core.systolic_array.array_width\n            * clock_freq\n        )\n        self.overhead = overhead\n\n\ncompute_module_dict = {\n    \"A100_fp16\": ComputeModule(\n        core_dict[\"SM_A100_fp16\"],\n        108,\n        1.41e9,\n        40 * 1024**2,\n        5120,\n        overhead_dict[\"A100\"],\n    ),\n    \"A100_int8\": ComputeModule(\n        core_dict[\"SM_A100_int8\"],\n        108,\n        1.41e9,\n        40 * 1024**2,\n        5120,\n        overhead_dict[\"A100\"],\n    ),\n    \"TPUv3_bf16\": ComputeModule(\n        core_dict[\"Core_TPUv3_bf16\"],\n        1,\n        940e6,\n        16 * 1024**3,\n        490,\n        overhead_dict[\"TPUv3\"],\n    ),\n    \"MI210_fp16\": ComputeModule(\n        core_dict[\"CU_MI210_fp16\"],\n        104,\n        1.4e9,\n        8 * 1024**2,\n        4096,\n        overhead_dict[\"MI210\"],\n    ),\n    \"TPUv3_new\": ComputeModule(\n        core_dict[\"Core_TPUv3_new\"],\n        2,\n        940e6,\n        16 * 1024**3,\n        490,\n        overhead_dict[\"TPUv3\"],\n    ),\n}\n"
  },
  {
    "path": "hardware_model/device.py",
    "content": "from hardware_model.compute_module import ComputeModule, compute_module_dict\nfrom hardware_model.io_module import IOModule, IO_module_dict\nfrom hardware_model.memory_module import MemoryModule, memory_module_dict\n\n\nclass Device:\n    def __init__(\n        self,\n        compute_module: ComputeModule,\n        io_module: IOModule,\n        memory_module: MemoryModule,\n    ) -> None:\n        self.compute_module = compute_module\n        self.io_module = io_module\n        self.memory_module = memory_module\n\n\ndevice_dict = {\n    \"A100_80GB_fp16\": Device(\n        compute_module_dict[\"A100_fp16\"],\n        IO_module_dict[\"A100\"],\n        memory_module_dict[\"A100_80GB\"],\n    ),\n    \"TPUv3\": Device(\n        compute_module_dict[\"TPUv3_bf16\"],\n        IO_module_dict[\"TPUv3\"],\n        memory_module_dict[\"TPUv3\"],\n    ),\n    \"MI210\": Device(\n        compute_module_dict[\"MI210_fp16\"],\n        IO_module_dict[\"MI210\"],\n        memory_module_dict[\"MI210\"],\n    ),\n    \"TPUv3_new\": Device(\n        compute_module_dict[\"TPUv3_new\"],\n        IO_module_dict[\"TPUv3\"],\n        memory_module_dict[\"TPUv3\"],\n    ),\n}\n"
  },
  {
    "path": "hardware_model/interconnect.py",
    "content": "from enum import Enum, auto\nfrom math import ceil\n\n\nclass TopologyType(Enum):\n    RING = auto()\n    FC = auto()\n\n\nclass LinkModule:\n    def __init__(\n        self,\n        bandwidth_per_direction: float,  # B/s\n        bandwidth_both_direction: float,  # B/s\n        latency: float,  # s\n        flit_size: int,  # B\n        max_payload_size: int,  # B\n        header_size: int,  # B\n    ) -> None:\n        self.bandwidth_per_direction = bandwidth_per_direction\n        self.bandwidth_both_direction = bandwidth_both_direction\n        self.latency = latency\n        self.flit_size = flit_size\n        self.max_payload_size = max_payload_size\n        self.header_size = ceil(header_size / flit_size) * flit_size\n\n\nlink_module_dict = {\n    \"NVLinkV3\": LinkModule(25e9, 50e9, 8.92e-6, 16, 256, 16),\n    \"TPUv3Link\": LinkModule(81.25e9 / 2, 81.25e9, 150e-6, 16, 256, 16),\n}\n# we cannot find a way to measure TPU p2p latency, we also don't know TPU packet format\n\n\nclass InterConnectModule:\n    def __init__(\n        self,\n        device_count: int,\n        topology,\n        link_module: LinkModule,\n        link_count_per_device: int,\n        internal_link_bandwidth_per_direction: float = float(\"inf\"),\n    ) -> None:\n        self.device_count = device_count\n        self.topology = topology\n        self.link_module = link_module\n        self.link_count_per_device = link_count_per_device\n        self.internal_link_bandwidth_per_direction = (\n            internal_link_bandwidth_per_direction\n        )\n        pass\n\n\n# we treat the 2D torus interconnect of 8 TPU cores as 2 rings + internal link\ninterconnect_module_dict = {\n    \"NVLinkV3_FC_4\": InterConnectModule(\n        4, TopologyType.FC, link_module_dict[\"NVLinkV3\"], 12\n    ),\n    \"TPUv3Link_8\": InterConnectModule(\n        4, TopologyType.RING, link_module_dict[\"TPUv3Link\"], 2, 162.5e9\n    ),\n}\n\n# class InterConnectTorusModule:\n#     def __init__(self) -> None:\n#         pass\n\n\n# class InterConnectUniRingModule:\n#     def __init__(\n#         self,\n#         device_count,\n#         link: LinkModule,\n#     ) -> None:\n#         pass\n\n\n# class InterConnectMeshModule:\n#     def __init__(self) -> None:\n#         pass\n\n\n# class InterConnectFCModule:\n#     def __init__(self) -> None:\n#         pass\n"
  },
  {
    "path": "hardware_model/io_module.py",
    "content": "class IOModule:\n    def __init__(self, bandwidth, latency):\n        self.bandwidth = bandwidth\n        self.latency = latency\n\n\nIO_module_dict = {\n    \"A100\": IOModule(2039e9, 1e-6),\n    \"TPUv3\": IOModule(float(\"inf\"), 1e-6),\n    \"MI210\": IOModule(1.6e12, 1e-6)\n}\n"
  },
  {
    "path": "hardware_model/memory_module.py",
    "content": "class MemoryModule:\n    def __init__(self, memory_capacity):\n        self.memory_capacity = memory_capacity\n\nmemory_module_dict = {'A100_80GB': MemoryModule(80e9),'TPUv3': MemoryModule(float('inf')),'MI210': MemoryModule(64e9)}\n"
  },
  {
    "path": "hardware_model/system.py",
    "content": "from hardware_model.device import Device, device_dict\nfrom hardware_model.interconnect import InterConnectModule, interconnect_module_dict\nfrom typing import List\n\n\nclass System:\n    def __init__(self, pcb_module: Device, interconnect: InterConnectModule) -> None:\n        self.device = pcb_module\n        self.interconnect = interconnect\n\n\nsystem_dict = {\n    \"A100_4_fp16\": System(\n        device_dict[\"A100_80GB_fp16\"],\n        interconnect_module_dict[\"NVLinkV3_FC_4\"],\n    ),\n    \"TPUv3_8\": System(device_dict[\"TPUv3\"], interconnect_module_dict[\"TPUv3Link_8\"])    \n}\n"
  },
  {
    "path": "software_model/__init__.py",
    "content": ""
  },
  {
    "path": "software_model/communication_primitives.py",
    "content": "from hardware_model.device import Device\nfrom hardware_model.interconnect import (\n    LinkModule,\n    InterConnectModule,\n    TopologyType,\n    interconnect_module_dict,\n)\nfrom software_model.utils import Tensor, DataType\nfrom typing import Any, List\nfrom utils import size\nfrom math import ceil\n\n\nclass CommunicationPrimitive:\n    def __init__(self, data_type: DataType) -> None:\n        self.data_type = data_type\n        # simulation results\n        self.latency = None\n\n\nclass AllReduceMultiPCB(CommunicationPrimitive):\n    def __init__(self, data_type: DataType) -> None:\n        super().__init__(data_type)\n\n    def __call__(self, tensor: Tensor) -> Any:\n        assert tensor.data_type == self.data_type\n        self.input_shape = tensor.shape\n        return tensor\n\n    def simulate(self, interconnect_module: InterConnectModule) -> None:\n        device_count = interconnect_module.device_count\n        link_bandwidth_per_direction = (\n            interconnect_module.link_module.bandwidth_per_direction\n        )\n        link_bandwidth_both_direction = (\n            interconnect_module.link_module.bandwidth_both_direction\n        )\n        link_latency = interconnect_module.link_module.latency\n        flit_size = interconnect_module.link_module.flit_size\n        header_size = interconnect_module.link_module.header_size\n        max_payload_size = interconnect_module.link_module.max_payload_size\n        link_count_per_device = interconnect_module.link_count_per_device\n        data_size = size(self.input_shape) * self.data_type.word_size\n        if interconnect_module.topology == TopologyType.FC:\n            edge_bandwidth_per_direction = (\n                link_bandwidth_per_direction\n                * link_count_per_device\n                / (device_count - 1)\n            )\n            edge_bandwidth_both_direction = (\n                link_bandwidth_both_direction\n                * link_count_per_device\n                / (device_count - 1)\n            )\n            edge_latency = link_latency\n            data_size_per_device = data_size / device_count\n            effective_data_size_per_device = (\n                header_size\n                + ceil(data_size_per_device / max_payload_size) * header_size\n                + data_size_per_device\n            )\n            # stage 1: ring reduce\n            latency = (\n                edge_latency\n                + effective_data_size_per_device / edge_bandwidth_both_direction\n            ) * (device_count - 1)\n            # stage 2: broadcast\n            latency += effective_data_size_per_device / edge_bandwidth_per_direction\n            latency += (\n                data_size / interconnect_module.internal_link_bandwidth_per_direction\n            )\n            self.latency = latency\n            return latency\n        elif interconnect_module.topology == TopologyType.RING:\n            edge_bandwidth = link_bandwidth_per_direction * link_count_per_device\n            edge_latency = link_latency\n            data_size_per_device = data_size / device_count\n            effective_data_size_per_device = (\n                header_size\n                + ceil(data_size_per_device / max_payload_size) * header_size\n                + data_size_per_device\n            )\n            per_transmission_latency = effective_data_size_per_device / edge_bandwidth\n            latency = (edge_latency + per_transmission_latency) * (\n                (device_count - 1) * 2\n            )\n            latency += (\n                data_size / interconnect_module.internal_link_bandwidth_per_direction\n            )\n            self.latency = latency\n        else:\n            raise NotImplementedError\n        return self.latency\n\n\n# class P2P:\n#     def __init__(self):\n#         self.src = None\n#         self.dst = None\n#         self.tensor = None\n\n#     def __call__(self, src: int, dst: int, tensor: Tensor):\n#         self.src = src\n#         self.dst = dst\n#         self.tensor = tensor\n\n#     def __simulate__(self, src: ChipletModule, dst: ChipletModule, link: LinkModule):\n#         pass\n\n\nclass Broadcast:\n    def __init__(self):\n        self.src = None\n        self.tensor = None\n\n    def __call__(self, src: int, tensor: Tensor):\n        self.src = src\n        self.tensor = tensor\n\n"
  },
  {
    "path": "software_model/gelu.py",
    "content": "from utils import size\nfrom typing import List, Tuple\nfrom hardware_model.device import Device\nfrom software_model.operators import Operator\nfrom software_model.utils import Tensor, DataType\nfrom math import ceil, log2, log\nimport time\nimport statistics\nimport numpy as np\nimport torch\n\n\n@torch.compile\ndef gelu_gpu(input: torch.Tensor) -> torch.Tensor:\n    return torch.nn.functional.gelu(input, approximate=\"tanh\")\n\n\n# x * 0.5 * (1.0 + torch.tanh(0.79788456 * x * (1 + 0.044715 * x * x)))\nclass GeLU(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.shape = None\n\n    def __call__(self, input: Tensor) -> Tensor:\n        assert self.data_type == input.data_type\n        self.shape = input.shape\n        self.M = size(input.shape[:])\n        self.computational_graph = self.ComputationalGraph(self.M, self.data_type)\n        return input\n\n    def roofline_model(self, pcb_module: Device):\n        self.computational_graph.data_type = (\n            pcb_module.compute_module.core.vector_unit.data_type\n        )\n        M = self.M\n        data_type = self.computational_graph.data_type\n        total_io_count = M * 2 * data_type.word_size\n        io_latency = (\n            total_io_count / min(pcb_module.io_module.bandwidth\n            , pcb_module.compute_module.l2_bandwidth_per_cycle\n            * pcb_module.compute_module.clock_freq)\n        )\n        total_flop_count = M * (\n            10 + pcb_module.compute_module.core.vector_unit.flops_per_exp\n        )\n        compute_latency = (\n            total_flop_count\n            / pcb_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n            / pcb_module.compute_module.core_count\n            / pcb_module.compute_module.clock_freq\n        )\n        self.roofline_latency = max(compute_latency, io_latency)\n        return self.roofline_latency\n\n    def print_latency(self):\n        print(f\"{self.shape}, {self.latency_on_gpu*1e6}us\")\n\n    class ComputationalGraph:\n        def __init__(self, M: int, data_type: DataType):            \n            self.M = M\n            self.data_type = data_type\n\n    def compile_and_simulate(self, pcb_module: Device, compile_mode: str):\n        self.computational_graph.data_type = (\n            pcb_module.compute_module.core.vector_unit.data_type\n        )\n        parallelism = (\n            pcb_module.compute_module.core_count\n            * pcb_module.compute_module.core.vector_unit.vector_width\n            * pcb_module.compute_module.core.vector_unit.vector_count\n        )\n        M = ceil(self.computational_graph.M / parallelism) * parallelism\n        data_type = self.computational_graph.data_type\n        total_io_count = M * 2 * data_type.word_size\n        io_latency = (\n            total_io_count / pcb_module.io_module.bandwidth\n            + total_io_count\n            / pcb_module.compute_module.l2_bandwidth_per_cycle\n            / pcb_module.compute_module.clock_freq\n        )\n        total_flop_count = M * (\n            10 + pcb_module.compute_module.core.vector_unit.flops_per_exp\n        )\n        compute_latency = (\n            total_flop_count\n            / pcb_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n            / pcb_module.compute_module.core_count\n            / pcb_module.compute_module.clock_freq\n        )\n\n        return max(compute_latency, io_latency)\n\n    def run_on_gpu(self):\n        assert self.shape is not None\n        input = torch.randn(self.shape, dtype=torch.float16, device=\"cuda\")\n        latencies = []\n\n        # warmup\n        for _ in range(3):\n            _ = gelu_gpu(input)\n            torch.cuda.synchronize()\n        for _ in range(self.iterations):\n            start = time.time()\n            output = gelu_gpu(input)\n            torch.cuda.synchronize()\n            end = time.time()\n            assert output.shape == input.shape\n            latencies.append(end - start)\n        # print(latencies)\n        self.latency_on_gpu = statistics.median(latencies)\n        return self.latency_on_gpu\n\n    @staticmethod\n    def gpu_kernel_launch_overhead():\n        import torch\n\n        size = 1\n        latencies = []\n        for _ in range(50):\n            a = torch.randn(size, size, device=\"cuda\")\n            torch.cuda.synchronize()\n            start = time.time()\n            c = gelu_gpu(a)\n            torch.cuda.synchronize()\n            end = time.time()\n            latencies.append(end - start)\n        avg_overhead = statistics.median(latencies)\n        # print('GPU kernel launch overhead: ', avg_overhead*1e3, 'ms')\n        print(latencies)\n        return avg_overhead\n"
  },
  {
    "path": "software_model/layernorm.py",
    "content": "from utils import size\nfrom typing import List, Tuple\nfrom hardware_model.device import Device\nfrom software_model.operators import Operator\nfrom software_model.utils import Tensor, DataType\nfrom math import ceil, log2, log\nimport time\nimport statistics\nimport numpy as np\nimport torch\n\n\n@torch.compile\ndef layernorm_gpu(input: torch.Tensor) -> torch.Tensor:\n    return torch.layer_norm(input, [input.shape[-1]])\n\n\nclass LayerNorm(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.shape = None\n\n    def __call__(self, input: Tensor) -> Tensor:\n        assert self.data_type == input.data_type\n        self.shape = input.shape\n        self.M = size(input.shape[:-1])\n        self.N = input.shape[-1]\n        self.computational_graph = self.ComputationalGraph(\n            self.M, self.N, self.data_type\n        )\n        return input\n\n    def roofline_model(self, pcb_module: Device):\n        self.io_count = self.M * self.N * self.data_type.word_size * 2\n        self.flop_count = self.M * self.N * 7\n        self.roofline_latency = max(\n            self.io_count\n            / min(\n                pcb_module.io_module.bandwidth,\n                pcb_module.compute_module.l2_bandwidth_per_cycle\n                * pcb_module.compute_module.clock_freq,\n            ),\n            self.flop_count / pcb_module.compute_module.total_vector_flops,\n        )\n        return self.roofline_latency\n\n    def print_latency(self):\n        print(f\"{self.shape}, {self.latency_on_gpu*1e6}us\")\n\n    class ComputationalGraph:\n        def __init__(self, M: int, N: int, data_type: DataType):\n            self.M = M\n            self.N = N\n            self.data_type = data_type\n\n    class Mapping:\n        def __init__(\n            self,\n            l2_tile_M: int,\n            l2_tile_N: int,\n            l1_tile_M: int,\n            l1_tile_N: int,\n        ):\n            self.l2_tile_M = l2_tile_M\n            self.l2_tile_N = l2_tile_N\n            self.l1_tile_M = l1_tile_M\n            self.l1_tile_N = l1_tile_N\n\n        def display(self):\n            print(\"-\" * 20)\n            print(\n                f\"l2_tile_M: {self.l2_tile_M}, l1_tile_M: {self.l1_tile_M}, l1_tile_N: {self.l1_tile_N}\"\n            )\n\n    def compile_and_simulate(self, pcb_module: Device, compile_mode: str):\n        self.computational_graph.data_type = (\n            pcb_module.compute_module.core.vector_unit.data_type\n        )\n        min_cycle_count = float(\"inf\")\n        best_mapping = None\n        M = self.computational_graph.M\n        N = self.computational_graph.N\n        data_type = self.computational_graph.data_type\n        l2_tile_N = N\n        l2_tile_M = (\n            pcb_module.compute_module.l2_size // (l2_tile_N * data_type.word_size) // 2\n        )\n        l2_tile_M = min(l2_tile_M, M)\n        if compile_mode == \"heuristic-GPU\" or compile_mode == \"heuristic-our-throughput\":\n            # if N <= 1024:\n            l1_tile_N = N\n            l1_tile_M = (\n                pcb_module.compute_module.core.SRAM_size\n                // (l1_tile_N * data_type.word_size)\n                // 2\n            )\n            while l1_tile_M < pcb_module.compute_module.core.vector_unit.vector_count:\n                l1_tile_N = l1_tile_N // 2\n                l1_tile_M = (\n                    pcb_module.compute_module.core.SRAM_size\n                    // (l1_tile_N * data_type.word_size)\n                    // 2\n                )\n            l1_tile_M = min(l1_tile_M, l2_tile_M)\n        elif compile_mode == \"heuristic-TPU\":\n            l1_tile_N = N\n            l1_tile_M = pcb_module.compute_module.core.SRAM_size // (\n                2 * l1_tile_N * data_type.word_size\n            )\n            l1_tile_M = min(l1_tile_M, M)\n        mapping = self.Mapping(\n            l2_tile_M,\n            l2_tile_N,\n            l1_tile_M,\n            l1_tile_N,\n        )\n        cycle_count = self.simulate(self.computational_graph, mapping, pcb_module)\n        if cycle_count < min_cycle_count:\n            min_cycle_count = cycle_count\n            best_mapping = mapping\n        self.best_mapping = best_mapping\n        self.best_cycle_count = min_cycle_count\n        self.best_latency = min_cycle_count / pcb_module.compute_module.clock_freq\n        self.latency = self.best_latency\n        # self.best_mapping.display()\n        return self.latency\n\n    def simulate(\n        self,\n        computational_graph: ComputationalGraph,\n        mapping: Mapping,\n        pcb_module: Device,\n    ) -> int:\n        M = computational_graph.M\n        N = computational_graph.N\n        data_type = computational_graph.data_type\n        l2_tile_M = mapping.l2_tile_M\n\n        M_l2_t = M // l2_tile_M\n        M_remain = M % l2_tile_M\n\n        l2_tiles = np.empty([ceil(M / l2_tile_M)], dtype=self.L2TileSimulator)\n\n        if M_l2_t != 0:\n            l2_tiles[:M_l2_t] = self.L2TileSimulator(\n                l2_tile_M,\n                N,\n                data_type,\n                mapping,\n                pcb_module,\n            )\n        if M_remain != 0:\n            l2_tiles[-1] = self.L2TileSimulator(\n                M_remain,\n                N,\n                data_type,\n                mapping,\n                pcb_module,\n            )\n\n        total_cycle_count = 0\n        l2_tile_count = ceil(M / l2_tile_M)\n        for m in range(l2_tile_count):\n            total_cycle_count += l2_tiles[m].read_cycle_count\n            total_cycle_count += l2_tiles[m].compute_cycle_count\n            total_cycle_count += l2_tiles[m].write_cycle_count\n        return total_cycle_count\n\n    class L2TileSimulator:\n        def __init__(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"LayerNorm.Mapping\",\n            pcb_module: Device,\n        ):\n            self.M = M\n            self.N = N\n            self.read_cycle_count = self.simulate_l2_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.write_cycle_count = self.simulate_l2_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.compute_cycle_count = self.simulate_l2_tile_compute_cycle_count(\n                M, N, data_type, mapping, pcb_module\n            )\n\n        def simulate_l2_tile_io_cycle_count(\n            self, M: int, N: int, data_type: DataType, chiplet_module: Device\n        ):\n            return ceil(\n                M\n                * N\n                * data_type.word_size\n                / (\n                    chiplet_module.io_module.bandwidth\n                    / chiplet_module.compute_module.clock_freq\n                )\n            )\n\n        def simulate_l2_tile_compute_cycle_count(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"LayerNorm.Mapping\",\n            pcb_module: Device,\n        ):\n            l1_tile_M = mapping.l1_tile_M\n            l1_tile_N = mapping.l1_tile_N\n\n            l1_tile = LayerNorm.L1TileSimulator(\n                l1_tile_M,\n                l1_tile_N,\n                data_type,\n                mapping,\n                pcb_module,\n            )\n            l1_tile_count = ceil(M / l1_tile_M) * ceil(N / l1_tile_N)\n            l1_tile_cycle_count = (\n                l1_tile.read_cycle_count * 3\n                + l1_tile.write_cycle_count\n                + l1_tile.compute_cycle_count\n            )\n            total_cycle_count = (\n                ceil(l1_tile_count / pcb_module.compute_module.core_count)\n            ) * (\n                l1_tile_cycle_count\n                + (ceil(N / l1_tile_N) - 1) * (l1_tile.reduction_cycle_count)\n            )\n            return total_cycle_count\n\n    class L1TileSimulator:\n        def __init__(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"LayerNorm.Mapping\",\n            pcb_module: Device,\n        ):\n            self.M = M\n            self.N = N\n            self.read_cycle_count = self.simulate_l1_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.compute_cycle_count = self.simulate_l1_tile_compute_cycle_count(\n                M, N, data_type, mapping, pcb_module\n            )\n            self.write_cycle_count = self.simulate_l1_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.reduction_cycle_count = (\n                M\n                * N\n                / pcb_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n                + M\n                * N\n                * data_type.word_size\n                * 2\n                / (\n                    pcb_module.compute_module.l2_bandwidth_per_cycle\n                    / pcb_module.compute_module.core_count\n                )\n            )\n\n        def simulate_l1_tile_io_cycle_count(\n            self, M: int, N: int, data_type: DataType, pcb_module: Device\n        ):\n            return ceil(\n                M\n                * N\n                * data_type.word_size\n                / (pcb_module.compute_module.l2_bandwidth_per_cycle)\n            )\n\n        def simulate_l1_tile_compute_cycle_count(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"LayerNorm.Mapping\",\n            pcb_module: Device,\n        ):\n            M_per_vector_count = ceil(\n                M / pcb_module.compute_module.core.vector_unit.vector_count\n            )\n            N_per_vector_count = N\n            M_per_vector_lane = M_per_vector_count\n            N_per_vector_lane = ceil(\n                N_per_vector_count\n                / pcb_module.compute_module.core.vector_unit.vector_width\n            )\n\n            # each lane computes it own mean\n            total_cycle_count = ceil(\n                N_per_vector_lane\n                * M_per_vector_lane\n                / pcb_module.compute_module.core.vector_unit.flops_per_cycle\n            )\n            # the whole vector reduce to one mean\n            total_cycle_count += log2(\n                pcb_module.compute_module.core.vector_unit.vector_width\n            )\n            # each lane computes it own variance\n            total_cycle_count += (\n                ceil(\n                    N_per_vector_lane\n                    * M_per_vector_lane\n                    / pcb_module.compute_module.core.vector_unit.flops_per_cycle\n                )\n                * 2\n            )\n            # the whole vector reduce to one variance\n            total_cycle_count += log2(\n                pcb_module.compute_module.core.vector_unit.vector_width\n            )\n            # calculate normalized output\n            total_cycle_count += (\n                ceil(\n                    N_per_vector_lane\n                    * M_per_vector_lane\n                    / pcb_module.compute_module.core.vector_unit.flops_per_cycle\n                )\n                * 4\n            )  # division is heavy\n\n            return total_cycle_count\n\n    def run_on_gpu(self):\n        # import torch\n        # from apex.normalization.fused_layer_norm import FusedLayerNorm\n        # from apex.contrib.layer_norm import FastLayerNorm\n        assert self.shape is not None\n        input = torch.randn(self.shape, dtype=torch.float16, device=\"cuda\")\n        latencies = []\n\n        # warmup\n        for _ in range(3):\n            _ = layernorm_gpu(input)\n\n            torch.cuda.synchronize()\n        for _ in range(self.iterations):\n            start = time.time()\n            output = layernorm_gpu(input)\n            torch.cuda.synchronize()\n            end = time.time()\n            assert output.shape == input.shape\n            latencies.append(end - start)\n        # print(latencies)\n        self.latency_on_gpu = statistics.median(latencies)\n        return self.latency_on_gpu\n\n    @staticmethod\n    def gpu_kernel_launch_overhead():\n        import torch\n\n        size = 1\n        latencies = []\n        a = torch.randn(1, 1, 1, device=\"cuda\")\n        for _ in range(50):\n            start = time.time()\n            c = layernorm_gpu(a)\n            torch.cuda.synchronize()\n            end = time.time()\n            latencies.append(end - start)\n        avg_overhead = statistics.median(latencies)\n        # print('GPU kernel launch overhead: ', avg_overhead*1e3, 'ms')\n        print(latencies)\n        return avg_overhead\n"
  },
  {
    "path": "software_model/matmul.py",
    "content": "from utils import size\nfrom typing import List, Tuple\nfrom hardware_model.device import Device\nfrom software_model.operators import Operator\nfrom software_model.utils import Tensor, DataType\nfrom math import ceil, log2, floor\nimport torch\nimport time\nimport statistics\nimport numpy as np\nimport pandas as pd\nimport os\nfrom scalesim.scale_sim import scalesim\nimport copy\n\n\nclass BatchedMatmul(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.input1_shape = None\n        self.input2_shape = None\n        self.output_shape = None\n\n    def __call__(self, input1: Tensor, input2: Tensor) -> Tensor:\n        # [b, M, K] * [b, K, N] = [b, M, N]\n        assert self.data_type == input1.data_type\n        assert self.data_type == input2.data_type\n        self.input1_shape = input1.shape\n        self.input2_shape = input2.shape\n        assert size(self.input1_shape[:-2]) == size(self.input2_shape[:-2])\n        self.bs = size(self.input1_shape[:-2])\n        self.M = self.input1_shape[-2]\n        self.K = self.input1_shape[-1]\n        assert self.input2_shape[-2] == self.K\n        self.N = self.input2_shape[-1]\n        self.output_shape = self.input1_shape[:-2] + [self.M, self.N]\n        output = Tensor(self.output_shape, self.data_type)\n        return output\n\n    def roofline_model(self, pcb_module: Device):\n        matmul = Matmul(self.data_type)\n        _ = matmul(Tensor([self.M, self.K]), Tensor([self.K, self.N]))\n        matmul_latency = matmul.roofline_model(pcb_module)\n        self.roofline_latency = matmul_latency * self.bs\n        return self.roofline_latency\n\n    # def compile_and_simulate(self, pcb_module: Device, compile_mode: str):\n    #     matmul = Matmul(self.data_type)\n    #     _ = matmul(Tensor([self.M, self.K]), Tensor([self.K, self.N]))\n    #     matmul_latency = (\n    #         matmul.compile_and_simulate(pcb_module, compile_mode)\n    #         # - pcb_module.io_module.latency * 2\n    #     )\n    #     self.latency = matmul_latency * self.bs  # + pcb_module.io_module.latency * 2\n    #     return self.latency\n\n    def compile_and_simulate(self, pcb_module: Device, compile_mode: str):\n        matmul = Matmul(self.data_type)\n        _ = matmul(Tensor([self.M, self.K]), Tensor([self.K, self.N]))\n        matmul_latency1 = (\n            matmul.compile_and_simulate(pcb_module, compile_mode) * self.bs\n        )\n\n        matmul = Matmul(self.data_type)\n        _ = matmul(\n            Tensor([self.M, self.K * self.bs]), Tensor([self.K * self.bs, self.N])\n        )\n        matmul_latency2 = (\n            matmul.compile_and_simulate(pcb_module, compile_mode)\n            + (self.bs - 1)\n            * self.M\n            * self.N\n            * self.data_type.word_size\n            / pcb_module.io_module.bandwidth\n        )\n        self.latency = min(matmul_latency1, matmul_latency2)\n        return self.latency\n\n    def run_on_gpu(\n        self,\n    ):\n        input1 = torch.randn(self.bs, self.M, self.K, dtype=torch.float16).cuda()\n        input2 = torch.randn(self.bs, self.K, self.N, dtype=torch.float16).cuda()\n        latencies = []\n        # warmup\n        for _ in range(3):\n            _ = torch.bmm(input1, input2)\n            torch.cuda.synchronize()\n        for _ in range(self.iterations):\n            start = time.time()\n            output = torch.bmm(input1, input2)\n            torch.cuda.synchronize()\n            end = time.time()\n            latencies.append(end - start)\n\n        self.latency_on_gpu = (\n            statistics.median(latencies)\n            # - self.gpu_kernel_launch_overhead()\n            # - 4e-5\n            # min(latencies) - 8e-6\n        )  # GPU launch kernel overhead and PyTorch overhead\n        return self.latency_on_gpu\n\n    @staticmethod\n    def gpu_kernel_launch_overhead():\n        latencies = []\n        for _ in range(50):\n            a = torch.randn(1, 1, 1, device=\"cuda\")\n            b = torch.randn(1, 1, 1, device=\"cuda\")\n            torch.cuda.synchronize()\n            start = time.time()\n            c = torch.bmm(a, b)\n            torch.cuda.synchronize()\n            end = time.time()\n            latencies.append(end - start)\n        avg_overhead = statistics.median(latencies)\n        # print('GPU kernel launch overhead: ', avg_overhead*1e3, 'ms')\n        # print(latencies)\n        return avg_overhead\n\n\nclass Matmul(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.input1_shape = None\n        self.input2_shape = None\n        self.output_shape = None\n        self.look_up_table = None\n        self.best_mapping = None\n\n    def __call__(self, input1: Tensor, input2: Tensor) -> Tensor:\n        # [bs, M, K] * [K, N] = [bs, M, N]\n        assert self.data_type == input1.data_type\n        assert self.data_type == input2.data_type\n        self.input1_shape = input1.shape\n        self.input2_shape = input2.shape\n        self.M = size(self.input1_shape[:-1])\n        self.K = self.input1_shape[-1]\n        assert self.input2_shape[-2] == self.K\n        self.N = self.input2_shape[-1]\n        if len(self.input1_shape) == 2:\n            self.output_shape = [self.M, self.N]\n        else:\n            self.output_shape = self.input1_shape[:-1] + [self.N]\n        output = Tensor(self.output_shape, self.data_type)\n        self.computational_graph = self.ComputationalGraph(\n            self.M, self.N, self.K, self.data_type\n        )\n        self.flop_count = 2 * self.M * self.K * self.N\n        self.io_count = self.M * self.K + self.K * self.N + self.M * self.N\n        # print(f'{self.M}, {self.N}, {self.K}')\n        return output\n\n    def roofline_model(self, pcb_module: Device):\n        self.roofline_latency = max(\n            self.flop_count / pcb_module.compute_module.total_systolic_array_flops,\n            self.io_count\n            / min(\n                pcb_module.io_module.bandwidth,\n                pcb_module.compute_module.l2_bandwidth_per_cycle\n                * pcb_module.compute_module.clock_freq,\n            ),\n        )\n        return self.roofline_latency\n\n    def print_latency(self):\n        print(\n            f\"{self.computational_graph.M}, {self.computational_graph.N}, {self.computational_graph.K}, {self.best_latency*1e3:.4f}ms, {self.latency_on_gpu*1e3:.4f}ms, {self.best_latency/self.latency_on_gpu*100:.2f}%\",\n            flush=True,\n        )\n\n    @staticmethod\n    def generate_tile_loops(loop_M: int, loop_N: int, loop_K: int, loop_order: str):\n        assert loop_order in [\"mkn\", \"mnk\", \"nkm\", \"nmk\", \"knm\", \"kmn\"]\n        if loop_order == \"mnk\":\n            for m in range(loop_M):\n                for n in range(loop_N):\n                    for k in range(loop_K):\n                        yield m, n, k\n        elif loop_order == \"mkn\":\n            for m in range(loop_M):\n                for k in range(loop_K):\n                    for n in range(loop_N):\n                        yield m, n, k\n        elif loop_order == \"nmk\":\n            for n in range(loop_N):\n                for m in range(loop_M):\n                    for k in range(loop_K):\n                        yield m, n, k\n        elif loop_order == \"nkm\":\n            for n in range(loop_N):\n                for k in range(loop_K):\n                    for m in range(loop_M):\n                        yield m, n, k\n        elif loop_order == \"knm\":\n            for k in range(loop_K):\n                for n in range(loop_N):\n                    for m in range(loop_M):\n                        yield m, n, k\n        elif loop_order == \"kmn\":\n            for k in range(loop_K):\n                for m in range(loop_M):\n                    for n in range(loop_N):\n                        yield m, n, k\n\n    class ComputationalGraph:\n        def __init__(self, M: int, N: int, K: int, data_type: DataType):\n            self.M = M\n            self.N = N\n            self.K = K\n            self.data_type = data_type\n\n        def display(self):\n            print(\"-\" * 10 + \" Computational Graph \" + \"-\" * 10)\n            print(\n                f\"M: {self.M}, N: {self.N}, K: {self.K}, word_size(B): {self.data_type.word_size}\"\n            )\n\n    class Mapping:\n        def __init__(\n            self,\n            l2_tile_M: int,\n            l2_tile_N: int,\n            l2_tile_K: int,\n            is_l2_double_buffering: bool,\n            l1_tile_M: int,\n            l1_tile_N: int,\n            l1_tile_K: int,\n            l2_loop_order: str,\n            l1_loop_order: str,\n            l0_M_tiling_factor: int,\n            l0_N_tiling_factor: int,\n            l0_K_tiling_factor: int,\n            dataflow: str = \"os\",\n        ):\n            self.l2_tile_M = l2_tile_M\n            self.l2_tile_N = l2_tile_N\n            self.l2_tile_K = l2_tile_K\n            self.is_l2_double_buffering = is_l2_double_buffering\n            self.l1_tile_M = l1_tile_M\n            self.l1_tile_N = l1_tile_N\n            self.l1_tile_K = l1_tile_K\n            self.l2_loop_order = l2_loop_order\n            self.l1_loop_order = l1_loop_order\n            self.l0_M_tiling_factor = l0_M_tiling_factor\n            self.l0_N_tiling_factor = l0_N_tiling_factor\n            self.l0_K_tiling_factor = l0_K_tiling_factor\n            self.dataflow = dataflow\n\n        def display(self):\n            print(f'{\"-\"*10} Mapping {\"-\"*10}')\n            print(\n                f\"l2_tile_M: {self.l2_tile_M}, l2_tile_N: {self.l2_tile_N}, l2_tile_K: {self.l2_tile_K}, is_l2_double_buffering: {self.is_l2_double_buffering}, l2_loop_order: {self.l2_loop_order}\"\n            )\n            print(\n                f\"l1_tile_M: {self.l1_tile_M}, l1_tile_N: {self.l1_tile_N}, l1_tile_K: {self.l1_tile_K}, l1_loop_order: {self.l1_loop_order}\"\n            )\n            print(\n                f\"l0_M_tiling_factor: {self.l0_M_tiling_factor}, l0_N_tiling_factor: {self.l0_N_tiling_factor}, l0_K_tiling_factor: {self.l0_K_tiling_factor}\"\n            )\n\n    @staticmethod\n    def find_permutations(n):\n        permutations = set()\n\n        for i in range(1, n + 1):\n            if n % i == 0:\n                for j in range(1, n + 1):\n                    if (n // i) % j == 0:\n                        k = n // (i * j)\n                        permutations.add((i, j, k))\n\n        return list(permutations)\n\n    def compile_and_simulate(\n        self,\n        pcb_module: Device,\n        compile_mode: str = \"exhaustive\",\n    ):\n        min_cycle_count = 2**63 - 1\n        best_mapping = None\n        M = self.computational_graph.M\n        N = self.computational_graph.N\n        K = self.computational_graph.K\n        if (M == 1 or N == 1) and (\n            compile_mode == \"heuristic-GPU\"\n            or compile_mode == \"heuristic-our-throughput\"\n        ):\n            working_set_size = M * K + N * K + M * N\n            total_io_count = working_set_size * self.data_type.word_size\n            io_latency = total_io_count / pcb_module.io_module.bandwidth\n            total_flop_count = 2 * M * N * K\n            compute_latency = (\n                total_flop_count\n                / pcb_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n                / pcb_module.compute_module.core_count\n                / pcb_module.compute_module.clock_freq\n            )\n            self.latency = max(\n                compute_latency, io_latency\n            )  # + pcb_module.io_module.latency * 2\n            return self.latency\n        if compile_mode == \"exhaustive\":\n            for l2_tile_M_log2 in range(5, ceil(log2(self.computational_graph.M)) + 1):\n                l2_tile_M = 2**l2_tile_M_log2\n                for l2_tile_N_log2 in range(\n                    5, ceil(log2(self.computational_graph.N)) + 1\n                ):\n                    l2_tile_N = 2**l2_tile_N_log2\n                    for l2_tile_K_log2 in range(\n                        5, ceil(log2(self.computational_graph.K)) + 1\n                    ):\n                        l2_tile_K = 2**l2_tile_K_log2\n                        working_set_size = (\n                            l2_tile_N * l2_tile_K\n                            + l2_tile_M * l2_tile_K\n                            + l2_tile_M * l2_tile_N\n                        )\n                        if (\n                            working_set_size\n                            > pcb_module.compute_module.l2_size\n                            // self.data_type.word_size\n                        ):\n                            continue\n                        elif (\n                            working_set_size\n                            <= pcb_module.compute_module.l2_size\n                            // self.data_type.word_size\n                            // 2\n                        ):\n                            is_l2_double_buffering = True\n                        else:\n                            is_l2_double_buffering = False\n                        for l1_tile_M_log2 in range(5, l2_tile_M_log2 + 1):\n                            l1_tile_M = 2**l1_tile_M_log2\n                            for l1_tile_N_log2 in range(5, l2_tile_N_log2 + 1):\n                                l1_tile_N = 2**l1_tile_N_log2\n                                for l1_tile_K_log2 in range(5, l2_tile_K_log2 + 1):\n                                    l1_tile_K = 2**l1_tile_K_log2\n                                    if (\n                                        l1_tile_M * l1_tile_N\n                                        + l1_tile_N * l1_tile_K\n                                        + l1_tile_M * l1_tile_K\n                                        > pcb_module.compute_module.core.SRAM_size\n                                        // self.data_type.word_size\n                                        // 2\n                                    ):\n                                        continue\n                                    for l2_loop_order in [\n                                        \"mkn\",\n                                        \"mnk\",\n                                        \"nkm\",\n                                        \"nmk\",\n                                        \"knm\",\n                                        \"kmn\",\n                                    ]:\n                                        for l1_loop_order in [\n                                            \"mkn\",\n                                            \"mnk\",\n                                            \"nkm\",\n                                            \"nmk\",\n                                            \"knm\",\n                                            \"kmn\",\n                                        ]:\n                                            for (\n                                                l0_M_tiling_factor,\n                                                l0_N_tiling_factor,\n                                                l0_K_tiling_factor,\n                                            ) in self.find_permutations(\n                                                pcb_module.compute_module.core.systolic_array_count\n                                            ):\n                                                mapping = self.Mapping(\n                                                    l2_tile_M,\n                                                    l2_tile_N,\n                                                    l2_tile_K,\n                                                    is_l2_double_buffering,\n                                                    l1_tile_M,\n                                                    l1_tile_N,\n                                                    l1_tile_K,\n                                                    l2_loop_order,\n                                                    l1_loop_order,\n                                                    l0_M_tiling_factor,\n                                                    l0_N_tiling_factor,\n                                                    l0_K_tiling_factor,\n                                                )\n                                                cycle_count = self.simulate(\n                                                    self.computational_graph,\n                                                    mapping,\n                                                    pcb_module,\n                                                )\n                                                if cycle_count < min_cycle_count:\n                                                    min_cycle_count = cycle_count\n                                                    best_mapping = mapping\n        elif compile_mode == \"heuristic-our-throughput\":\n            i = 0\n            for l2_tile_M in [32, 64, 128, 256, 512, 1024, 2048, 4096]:\n                for l2_tile_N in [\n                    l2_tile_M // 4,\n                    l2_tile_M // 2,\n                    l2_tile_M,\n                    l2_tile_M * 2,\n                    l2_tile_M * 4,\n                    l2_tile_M * 8,\n                    l2_tile_M * 16,\n                    l2_tile_M * 32,\n                    \n                ]:\n                    l2_tile_K_max = (\n                        pcb_module.compute_module.l2_size\n                        // self.data_type.word_size\n                        // 2\n                        - l2_tile_M * l2_tile_N\n                    ) // (l2_tile_M + l2_tile_N)\n                    if l2_tile_K_max < 1:\n                        continue\n                    l2_tile_K = min(l2_tile_K_max, K)\n                    l2_tile_K = floor(log2(l2_tile_K))\n                    l2_tile_K = 2**l2_tile_K\n                    working_set_size = (\n                        l2_tile_N * l2_tile_K\n                        + l2_tile_M * l2_tile_K\n                        + l2_tile_M * l2_tile_N\n                    )\n                    if (\n                        working_set_size\n                        > pcb_module.compute_module.l2_size // self.data_type.word_size\n                    ):\n                        continue\n                    elif (\n                        working_set_size\n                        <= pcb_module.compute_module.l2_size\n                        // self.data_type.word_size\n                        // 2\n                    ):\n                        is_l2_double_buffering = True\n                    else:\n                        is_l2_double_buffering = False\n\n                    assert is_l2_double_buffering\n\n                    for l1_tile_M in [32, 64, 128, 256]:\n                        l1_tile_M = min(l1_tile_M, l2_tile_M, l2_tile_N)\n                        # if l1_tile_M > min(l2_tile_M, l2_tile_N):\n                        #     continue\n                        l1_tile_N = l1_tile_M\n                        l1_tile_K_max = (\n                            pcb_module.compute_module.core.SRAM_size\n                            // self.data_type.word_size\n                            // 2\n                            - l1_tile_M * l1_tile_N\n                        ) // (l1_tile_M + l1_tile_N)\n                        if l1_tile_K_max < 1:\n                            continue\n                        l1_tile_K = min(l1_tile_K_max, l2_tile_K)\n                        l1_tile_K = floor(log2(l1_tile_K))\n                        l1_tile_K = 2**l1_tile_K\n\n                        if (\n                            l1_tile_M * l1_tile_N\n                            + l1_tile_N * l1_tile_K\n                            + l1_tile_M * l1_tile_K\n                            > pcb_module.compute_module.core.SRAM_size\n                            // self.data_type.word_size\n                            // 2\n                        ):\n                            continue\n                        l2_loop_order = \"knm\"\n                        l1_loop_order = \"knm\"\n                        for (\n                            l0_M_tiling_factor,\n                            l0_N_tiling_factor,\n                            l0_K_tiling_factor,\n                        ) in [(2, 2, 1)]:\n                            # self.find_permutations(\n                            #     pcb_module.compute_module.core.systolic_array_count\n                            # ):\n                            i += 1\n                            # start = time.time()\n                            mapping = self.Mapping(\n                                l2_tile_M,\n                                l2_tile_N,\n                                l2_tile_K,\n                                is_l2_double_buffering,\n                                l1_tile_M,\n                                l1_tile_N,\n                                l1_tile_K,\n                                l2_loop_order,\n                                l1_loop_order,\n                                l0_M_tiling_factor,\n                                l0_N_tiling_factor,\n                                l0_K_tiling_factor,\n                            )\n                            cycle_count = self.simulate(\n                                self.computational_graph,\n                                mapping,\n                                pcb_module,\n                            )\n                            # end = time.time()\n                            # if i % 1000 == 0:\n                            #     print(f\"{i} simulation time: {end-start}\")\n                            if cycle_count < min_cycle_count:\n                                min_cycle_count = cycle_count\n                                best_mapping = mapping\n        elif compile_mode == \"heuristic-GPU\":\n            i = 0\n            for l2_tile_M in [64, 128, 256, 512, 1024, 2048]:\n                for l2_tile_N in [l2_tile_M // 2, l2_tile_M, l2_tile_M * 2]:\n                    if K <= 12288:\n                        l2_K_tiling_factor_list = [1, 2, 4, 8]\n                    else:\n                        l2_K_tiling_factor_list = [\n                            K // 1024,\n                            K // 2048,\n                            K // 4096,\n                            K // 8192,\n                        ]\n                    for l2_K_tiling_factor in l2_K_tiling_factor_list:\n                        l2_tile_K = ceil(\n                            self.computational_graph.K / l2_K_tiling_factor\n                        )\n                        l2_tile_K = 2 ** floor(log2(l2_tile_K))\n                        working_set_size = (\n                            l2_tile_N * l2_tile_K\n                            + l2_tile_M * l2_tile_K\n                            + l2_tile_M * l2_tile_N\n                        )\n                        if (\n                            working_set_size\n                            > pcb_module.compute_module.l2_size\n                            // self.data_type.word_size\n                        ):\n                            continue\n                        elif (\n                            working_set_size\n                            <= pcb_module.compute_module.l2_size\n                            // self.data_type.word_size\n                            // 2\n                        ):\n                            is_l2_double_buffering = True\n                        else:\n                            is_l2_double_buffering = False\n\n                        for l1_tile_M in [32, 64, 128, 256]:\n                            if l1_tile_M > min(l2_tile_M, l2_tile_N):\n                                continue\n                            l1_tile_N = l1_tile_M\n                            for l1_K_tiling_factor in [1, 2, 4, 8, 16, 32]:\n                                l1_tile_K = ceil(l2_tile_K / l1_K_tiling_factor)\n                                if (\n                                    l1_tile_M * l1_tile_N\n                                    + l1_tile_N * l1_tile_K\n                                    + l1_tile_M * l1_tile_K\n                                    > pcb_module.compute_module.core.SRAM_size\n                                    // self.data_type.word_size\n                                    // 2\n                                ):\n                                    continue\n                                l2_loop_order = \"knm\"\n                                l1_loop_order = \"knm\"\n                                for (\n                                    l0_M_tiling_factor,\n                                    l0_N_tiling_factor,\n                                    l0_K_tiling_factor,\n                                ) in self.find_permutations(\n                                    pcb_module.compute_module.core.systolic_array_count\n                                ):\n                                    i += 1\n                                    start = time.time()\n                                    mapping = self.Mapping(\n                                        l2_tile_M,\n                                        l2_tile_N,\n                                        l2_tile_K,\n                                        is_l2_double_buffering,\n                                        l1_tile_M,\n                                        l1_tile_N,\n                                        l1_tile_K,\n                                        l2_loop_order,\n                                        l1_loop_order,\n                                        l0_M_tiling_factor,\n                                        l0_N_tiling_factor,\n                                        l0_K_tiling_factor,\n                                    )\n                                    cycle_count = self.simulate(\n                                        self.computational_graph,\n                                        mapping,\n                                        pcb_module,\n                                    )\n                                    end = time.time()\n                                    # if i % 1000 == 0:\n                                    #     print(f\"{i} simulation time: {end-start}\")\n                                    if cycle_count < min_cycle_count:\n                                        min_cycle_count = cycle_count\n                                        best_mapping = mapping\n            # print(\"total dse times:\", i)\n        elif compile_mode == \"heuristic-TPU\":\n            l2_tile_M = self.computational_graph.M\n            l2_tile_N = self.computational_graph.N\n            l2_tile_K = self.computational_graph.K\n\n            is_l2_double_buffering = True\n            for l1_tile_M in [l2_tile_M, 64, 128, 256, 512, 1024, 2048, 4096, 8192]:\n                if l1_tile_M > l2_tile_M * 2:\n                    continue\n                for l1_tile_N in [\n                    l1_tile_M // 2,\n                    l1_tile_M,\n                    l1_tile_M * 2,\n                    l1_tile_M * 8,\n                    l1_tile_M * 16,\n                    l1_tile_M * 64,\n                    l1_tile_M * 128,\n                    l1_tile_M * 256,\n                ]:\n                    if l1_tile_N > l2_tile_N:\n                        continue\n                    if l1_tile_N <= 0:\n                        continue\n                    l1_tile_K_max = (\n                        pcb_module.compute_module.core.SRAM_size\n                        // self.data_type.word_size\n                        // 2\n                        - l1_tile_M * l1_tile_N\n                    ) // (l1_tile_M + l1_tile_N)\n                    if l1_tile_K_max < 1:\n                        continue\n                    l1_tile_K = min(l1_tile_K_max, l2_tile_K)\n                    l1_tile_K = floor(log2(l1_tile_K))\n                    l1_tile_K = 2**l1_tile_K\n\n                    l2_loop_order = \"knm\"\n                    l1_loop_order = \"knm\"\n                    for (\n                        l0_M_tiling_factor,\n                        l0_N_tiling_factor,\n                        l0_K_tiling_factor,\n                    ) in [(1, 2, 1)]:\n                        mapping = self.Mapping(\n                            l2_tile_M,\n                            l2_tile_N,\n                            l2_tile_K,\n                            is_l2_double_buffering,\n                            l1_tile_M,\n                            l1_tile_N,\n                            l1_tile_K,\n                            l2_loop_order,\n                            l1_loop_order,\n                            l0_M_tiling_factor,\n                            l0_N_tiling_factor,\n                            l0_K_tiling_factor,\n                        )\n                        # mapping.display()\n                        # start=time.time()\n                        cycle_count = self.simulate(\n                            self.computational_graph,\n                            mapping,\n                            pcb_module,\n                        )\n                        # end=time.time()\n                        # print(f'simulation time: {end-start}')\n                        if cycle_count < min_cycle_count:\n                            min_cycle_count = cycle_count\n                            best_mapping = mapping\n        elif compile_mode == \"heuristic-TPU-new\":\n            l2_tile_M = self.computational_graph.M\n            l2_tile_N = self.computational_graph.N\n            l2_tile_K = self.computational_graph.K\n\n            is_l2_double_buffering = True\n            for l1_tile_M in [l2_tile_M, 32, 64, 128, 256, 512, 1024, 2048, 4096, 8192]:\n                if l1_tile_M > l2_tile_M * 2:\n                    continue\n                for l1_tile_N in [\n                    l1_tile_M // 2,\n                    l1_tile_M,\n                    l1_tile_M * 2,\n                    l1_tile_M * 8,\n                    l1_tile_M * 16,\n                    l1_tile_M * 64,\n                    l1_tile_M * 128,\n                    l1_tile_M * 256,\n                ]:\n                    if l1_tile_N > l2_tile_N:\n                        continue\n                    if l1_tile_N <= 0:\n                        continue\n                    l1_tile_K_max = (\n                        pcb_module.compute_module.core.SRAM_size\n                        // self.data_type.word_size\n                        // 2\n                        - l1_tile_M * l1_tile_N\n                    ) // (l1_tile_M + l1_tile_N)\n                    if l1_tile_K_max < 1:\n                        continue\n                    l1_tile_K = min(l1_tile_K_max, l2_tile_K)\n                    l1_tile_K = floor(log2(l1_tile_K))\n                    l1_tile_K = 2**l1_tile_K\n\n                    l2_loop_order = \"knm\"\n                    l1_loop_order = \"knm\"\n                    for (\n                        l0_M_tiling_factor,\n                        l0_N_tiling_factor,\n                        l0_K_tiling_factor,\n                    ) in [(1, 1, 1)]:\n                        mapping = self.Mapping(\n                            l2_tile_M,\n                            l2_tile_N,\n                            l2_tile_K,\n                            is_l2_double_buffering,\n                            l1_tile_M,\n                            l1_tile_N,\n                            l1_tile_K,\n                            l2_loop_order,\n                            l1_loop_order,\n                            l0_M_tiling_factor,\n                            l0_N_tiling_factor,\n                            l0_K_tiling_factor,\n                        )\n                        # mapping.display()\n                        # start=time.time()\n                        cycle_count = self.simulate(\n                            self.computational_graph,\n                            mapping,\n                            pcb_module,\n                        )\n                        # end=time.time()\n                        # print(f'simulation time: {end-start}')\n                        if cycle_count < min_cycle_count:\n                            min_cycle_count = cycle_count\n                            best_mapping = mapping\n        else:\n            raise ValueError(f\"compile_mode {compile_mode} not supported\")\n        self.best_mapping = best_mapping\n        # if self.best_mapping is not None:\n        #     self.best_mapping.display()\n        self.best_cycle_count = min_cycle_count\n        self.best_latency = min_cycle_count / pcb_module.compute_module.clock_freq\n        self.latency = self.best_latency\n        # self.best_mapping.display()\n        return self.latency\n\n    def simulate(\n        self,\n        computational_graph: ComputationalGraph,\n        mapping: Mapping,\n        pcb_module: Device,\n    ) -> int:\n        if self.look_up_table is None:\n            self.look_up_table = pd.read_csv(\n                f\"./systolic_array_model/look_up_table_{pcb_module.compute_module.core.systolic_array.array_height}_{pcb_module.compute_module.core.systolic_array.array_width}.csv\",\n                header=None,\n                names=[\n                    \"M\",\n                    \"N\",\n                    \"K\",\n                    \"ArrayHeight\",\n                    \"ArrayWidth\",\n                    \"Dataflow\",\n                    \"cycle_count\",\n                    \"util_rate\",\n                ],\n            )\n            self.look_up_table.drop_duplicates(\n                inplace=True,\n                subset=[\"M\", \"N\", \"K\", \"ArrayHeight\", \"ArrayWidth\", \"Dataflow\"],\n            )\n            # self.look_up_table.reset_index(drop=True, inplace=True)\n            # self.look_up_table.to_csv(\n            #     f\"./systolic_array_model/look_up_table_{pcb_module.compute_module.core.systolic_array.array_height}_{pcb_module.compute_module.core.systolic_array.array_width}.csv\",\n            #     header=False,\n            #     index=False,\n            # )\n            self.look_up_table.set_index(\n                [\"M\", \"N\", \"K\", \"ArrayHeight\", \"ArrayWidth\", \"Dataflow\"],\n                inplace=True,\n            )\n        # print(self.look_up_table)\n        # print(self.look_up_table.loc[(32, 16, 256, 16, 16, 'os'), \"cycle_count\"\n        #                              ].item())\n        # print('sdfsdfsdfsd')\n        # exit()\n        M = computational_graph.M\n        N = computational_graph.N\n        K = computational_graph.K\n        data_type = computational_graph.data_type\n\n        l2_tile_M = mapping.l2_tile_M\n        l2_tile_N = mapping.l2_tile_N\n        l2_tile_K = mapping.l2_tile_K\n\n        if mapping.is_l2_double_buffering:\n            assert (\n                l2_tile_M * l2_tile_N + l2_tile_N * l2_tile_K + l2_tile_M * l2_tile_K\n                <= pcb_module.compute_module.l2_size // self.data_type.word_size // 2\n            )\n        else:\n            assert (\n                l2_tile_M * l2_tile_N + l2_tile_N * l2_tile_K + l2_tile_M * l2_tile_K\n                <= pcb_module.compute_module.l2_size // self.data_type.word_size\n            )\n\n        M_l2_t = M // l2_tile_M\n        N_l2_t = N // l2_tile_N\n        K_l2_t = K // l2_tile_K\n        M_remain = M % l2_tile_M\n        N_remain = N % l2_tile_N\n        K_remain = K % l2_tile_K\n\n        l2_tiles = np.empty(\n            [ceil(M / l2_tile_M), ceil(N / l2_tile_N), ceil(K / l2_tile_K)],\n            dtype=self.L2TileSimulator,\n        )\n        # print('-'*20)\n        # print(l2_tiles.shape)\n        if M_l2_t * N_l2_t * K_l2_t != 0:\n            l2_tiles[:M_l2_t, :N_l2_t, :K_l2_t] = self.L2TileSimulator(\n                l2_tile_M,\n                l2_tile_N,\n                l2_tile_K,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n        if M_remain != 0:\n            l2_tiles[-1, :N_l2_t, :K_l2_t] = self.L2TileSimulator(\n                M_remain,\n                l2_tile_N,\n                l2_tile_K,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n        if N_remain != 0:\n            l2_tiles[:M_l2_t, -1, :K_l2_t] = self.L2TileSimulator(\n                l2_tile_M,\n                N_remain,\n                l2_tile_K,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n        if K_remain != 0:\n            l2_tiles[:M_l2_t, :N_l2_t, -1] = self.L2TileSimulator(\n                l2_tile_M,\n                l2_tile_N,\n                K_remain,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n        if M_remain * N_remain != 0:\n            l2_tiles[-1, -1, :K_l2_t] = self.L2TileSimulator(\n                M_remain,\n                N_remain,\n                l2_tile_K,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n        if M_remain * K_remain != 0:\n            l2_tiles[-1, :N_l2_t, -1] = self.L2TileSimulator(\n                M_remain,\n                l2_tile_N,\n                K_remain,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n        if N_remain * K_remain != 0:\n            l2_tiles[:M_l2_t, -1, -1] = self.L2TileSimulator(\n                l2_tile_M,\n                N_remain,\n                K_remain,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n        if M_remain * N_remain * K_remain != 0:\n            l2_tiles[-1, -1, -1] = self.L2TileSimulator(\n                M_remain,\n                N_remain,\n                K_remain,\n                data_type,\n                mapping,\n                pcb_module,\n                self.look_up_table,\n            )\n\n        total_cycle_count = 0\n        total_cycle_count += (\n            l2_tiles[0, 0, 0].M_K_io_cycle_count + l2_tiles[0, 0, 0].K_N_io_cycle_count\n        )\n\n        previous_m = 0\n        previous_n = 0\n        previous_k = 0\n\n        for m, n, k in self.generate_tile_loops(\n            ceil(M / l2_tile_M),\n            ceil(N / l2_tile_N),\n            ceil(K / l2_tile_K),\n            mapping.l2_loop_order,\n        ):\n            if m == 0 and n == 0 and k == 0:\n                continue\n\n            l2_tile = l2_tiles[m, n, k]\n            previous_l2_tile = l2_tiles[previous_m, previous_n, previous_k]\n\n            # current tile read latency\n            if m == previous_m and k == previous_k:\n                current_tile_read_cycle_count = l2_tile.K_N_io_cycle_count\n            elif n == previous_n and k == previous_k:\n                current_tile_read_cycle_count = l2_tile.M_K_io_cycle_count\n            else:\n                current_tile_read_cycle_count = (\n                    l2_tile.M_K_io_cycle_count + l2_tile.K_N_io_cycle_count\n                )\n            if k > 0 and not (m == previous_m and n == previous_n):\n                current_tile_read_cycle_count += l2_tile.M_N_io_cycle_count\n            # previous tile compute latency\n            previous_tile_compute_cycle_count = previous_l2_tile.compute_cycle_count\n            if k > 0:\n                previous_tile_compute_cycle_count += (\n                    previous_l2_tile.K_reduction_cycle_count\n                )\n            # previous tile write latency\n            if m == previous_m and n == previous_n:\n                previous_tile_write_cycle_count = 0\n            else:\n                previous_tile_write_cycle_count = previous_l2_tile.M_N_io_cycle_count\n\n            # read current tile, compute previous tile, write previous tile\n            if mapping.is_l2_double_buffering:  # pipelined\n                total_cycle_count += (\n                    max(\n                        current_tile_read_cycle_count, previous_tile_compute_cycle_count\n                    )\n                    + previous_tile_write_cycle_count\n                )\n            else:  # non-pipelined\n                total_cycle_count += (\n                    current_tile_read_cycle_count\n                    + previous_tile_compute_cycle_count\n                    + previous_tile_write_cycle_count\n                )\n\n            previous_m = m\n            previous_n = n\n            previous_k = k\n\n        # compute and write last tile\n        total_cycle_count += (\n            l2_tiles[-1, -1, -1].M_N_io_cycle_count\n            + l2_tiles[-1, -1, -1].compute_cycle_count\n        )\n\n        if previous_k > 0:\n            total_cycle_count += ceil(l2_tiles[-1, -1, -1].K_reduction_cycle_count)\n\n        return total_cycle_count #+ ceil(\n        # pcb_module.io_module.latency * 2 * pcb_module.compute_module.clock_freq\n        # )\n\n    class L2TileSimulator:\n        def __init__(\n            self,\n            M: int,\n            N: int,\n            K: int,\n            data_type: DataType,\n            mapping: \"Matmul.Mapping\",\n            pcb_module: Device,\n            look_up_table: pd.DataFrame,\n        ):\n            # print(f'L2 tile: {M} {N} {K}')\n            self.M = M\n            self.N = N\n            self.K = K\n            self.K_reduction_cycle_count = ceil(\n                M * N / pcb_module.compute_module.total_vector_flops_per_cycle\n            ) + 2 * ceil(\n                M\n                * N\n                * data_type.word_size\n                / pcb_module.compute_module.l2_bandwidth_per_cycle\n            )\n            self.K_reduction_io_count = 2 * M * N * data_type.word_size\n            self.M_K_io_cycle_count = self.simulate_l2_tile_io_cycle_count(\n                M, K, data_type, pcb_module\n            )\n            self.K_N_io_cycle_count = self.simulate_l2_tile_io_cycle_count(\n                K, N, data_type, pcb_module\n            )\n            self.M_N_io_cycle_count = self.simulate_l2_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.compute_cycle_count = self.simulate_l2_tile_compute_cycle_count(\n                M, N, K, data_type, mapping, pcb_module, look_up_table\n            )\n\n        def simulate_l2_tile_io_cycle_count(\n            self, M: int, N: int, data_type: DataType, chiplet_module: Device\n        ):\n            return ceil(\n                M\n                * N\n                * data_type.word_size\n                / (\n                    chiplet_module.io_module.bandwidth\n                    / chiplet_module.compute_module.clock_freq\n                )\n            )\n\n        def simulate_l2_tile_compute_cycle_count(\n            self,\n            M: int,\n            N: int,\n            K: int,\n            data_type: DataType,\n            mapping: \"Matmul.Mapping\",\n            chiplet_module: Device,\n            look_up_table: pd.DataFrame,\n        ) -> int:\n            l1_tile_M = mapping.l1_tile_M\n            l1_tile_N = mapping.l1_tile_N\n            l1_tile_K = mapping.l1_tile_K\n\n            M_l1_t = M // l1_tile_M\n            N_l1_t = N // l1_tile_N\n            K_l1_t = K // l1_tile_K\n            M_remain = M % l1_tile_M\n            N_remain = N % l1_tile_N\n            K_remain = K % l1_tile_K\n\n            l1_tiles = np.empty(\n                [ceil(M / l1_tile_M), ceil(N / l1_tile_N), ceil(K / l1_tile_K)],\n                dtype=Matmul.L1TileSimulator,\n            )\n            if M_l1_t * N_l1_t * K_l1_t != 0:\n                l1_tiles[:M_l1_t, :N_l1_t, :K_l1_t] = Matmul.L1TileSimulator(\n                    l1_tile_M,\n                    l1_tile_N,\n                    l1_tile_K,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n            if M_remain != 0:\n                l1_tiles[-1, :N_l1_t, :K_l1_t] = Matmul.L1TileSimulator(\n                    M_remain,\n                    l1_tile_N,\n                    l1_tile_K,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n            if N_remain != 0:\n                l1_tiles[:M_l1_t, -1, :K_l1_t] = Matmul.L1TileSimulator(\n                    l1_tile_M,\n                    N_remain,\n                    l1_tile_K,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n            if K_remain != 0:\n                l1_tiles[:M_l1_t, :N_l1_t, -1] = Matmul.L1TileSimulator(\n                    l1_tile_M,\n                    l1_tile_N,\n                    K_remain,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n            if M_remain * N_remain != 0:\n                l1_tiles[-1, -1, :K_l1_t] = Matmul.L1TileSimulator(\n                    M_remain,\n                    N_remain,\n                    l1_tile_K,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n            if M_remain * K_remain != 0:\n                l1_tiles[-1, :N_l1_t, -1] = Matmul.L1TileSimulator(\n                    M_remain,\n                    l1_tile_N,\n                    K_remain,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n            if N_remain * K_remain != 0:\n                l1_tiles[:M_l1_t, -1, -1] = Matmul.L1TileSimulator(\n                    l1_tile_M,\n                    N_remain,\n                    K_remain,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n            if M_remain * N_remain * K_remain != 0:\n                l1_tiles[-1, -1, -1] = Matmul.L1TileSimulator(\n                    M_remain,\n                    N_remain,\n                    K_remain,\n                    data_type,\n                    mapping,\n                    chiplet_module,\n                    look_up_table,\n                )\n\n            M_K_tile_size = np.zeros(\n                [ceil(M / l1_tile_M), ceil(K / l1_tile_K)], dtype=int\n            )\n            M_K_tile_size[:M_l1_t, :K_l1_t] = l1_tile_M * l1_tile_K\n            if M_remain > 0:\n                M_K_tile_size[-1, :K_l1_t] = M_remain * l1_tile_K\n            if K_remain > 0:\n                M_K_tile_size[:M_l1_t, -1] = l1_tile_M * K_remain\n            if M_remain > 0 and K_remain > 0:\n                M_K_tile_size[-1, -1] = M_remain * K_remain\n\n            K_N_tile_size = np.zeros(\n                [ceil(K / l1_tile_K), ceil(N / l1_tile_N)], dtype=int\n            )\n            K_N_tile_size[:K_l1_t, :N_l1_t] = l1_tile_K * l1_tile_N\n            if K_remain > 0:\n                K_N_tile_size[-1, :N_l1_t] = K_remain * l1_tile_N\n            if N_remain > 0:\n                K_N_tile_size[:K_l1_t, -1] = l1_tile_K * N_remain\n            if K_remain > 0 and N_remain > 0:\n                K_N_tile_size[-1, -1] = K_remain * N_remain\n\n            M_N_tile_size = np.zeros(\n                [ceil(M / l1_tile_M), ceil(N / l1_tile_N)], dtype=int\n            )\n            M_N_tile_size[:M_l1_t, :N_l1_t] = l1_tile_M * l1_tile_N\n            if M_remain > 0:\n                M_N_tile_size[-1, :N_l1_t] = M_remain * l1_tile_N\n            if N_remain > 0:\n                M_N_tile_size[:M_l1_t, -1] = l1_tile_M * N_remain\n            if M_remain > 0 and N_remain > 0:\n                M_N_tile_size[-1, -1] = M_remain * N_remain\n\n            total_cycle_count = 0\n            previous_batch_Read_M_K = np.zeros(\n                [ceil(M / l1_tile_M), ceil(K / l1_tile_K)], dtype=bool\n            )\n            previous_batch_Read_K_N = np.zeros(\n                [ceil(K / l1_tile_K), ceil(N / l1_tile_N)], dtype=bool\n            )\n            previous_batch_Read_M_N = np.zeros(\n                [ceil(M / l1_tile_M), ceil(N / l1_tile_N)], dtype=bool\n            )\n            previous_batch_Write_M_N = np.zeros(\n                [ceil(M / l1_tile_M), ceil(N / l1_tile_N)], dtype=bool\n            )\n            previous_batch_compute_cycle_count = 0\n            active_l1_tile_list = []\n            for m, n, k in Matmul.generate_tile_loops(\n                ceil(M / l1_tile_M),\n                ceil(N / l1_tile_N),\n                ceil(K / l1_tile_K),\n                mapping.l1_loop_order,\n            ):\n                active_l1_tile_list.append((m, n, k, l1_tiles[m, n, k]))\n                if (\n                    m == ceil(M / l1_tile_M) - 1\n                    and n == ceil(N / l1_tile_N) - 1\n                    and k == ceil(K / l1_tile_K) - 1\n                ):\n                    pass\n                elif (\n                    len(active_l1_tile_list) < chiplet_module.compute_module.core_count\n                ):\n                    continue\n\n                assert (\n                    len(active_l1_tile_list) <= chiplet_module.compute_module.core_count\n                )\n                current_batch_Read_M_K = np.zeros(\n                    [ceil(M / l1_tile_M), ceil(K / l1_tile_K)], dtype=bool\n                )\n                current_batch_Read_K_N = np.zeros(\n                    [ceil(K / l1_tile_K), ceil(N / l1_tile_N)], dtype=bool\n                )\n                current_batch_Read_M_N = np.zeros(\n                    [ceil(M / l1_tile_M), ceil(N / l1_tile_N)], dtype=bool\n                )\n                current_batch_Write_M_N = np.zeros(\n                    [ceil(M / l1_tile_M), ceil(N / l1_tile_N)], dtype=bool\n                )\n\n                current_batch_compute_cycle_count = 0\n                for i in range(len(active_l1_tile_list)):\n                    temp_m, temp_n, temp_k, temp_l1_tile = active_l1_tile_list[i]\n                    current_batch_Read_M_K[temp_m, temp_k] = 1\n                    current_batch_Read_K_N[temp_k, temp_n] = 1\n                    current_batch_Read_M_N[temp_m, temp_n] = temp_k > 0\n                    current_batch_Write_M_N[temp_m, temp_n] = 1\n                    temp_l1_tile_compute_cycle_count = temp_l1_tile.compute_cycle_count\n                    if temp_k > 0:\n                        temp_l1_tile_compute_cycle_count += ceil(\n                            temp_l1_tile.M\n                            * temp_l1_tile.N\n                            / chiplet_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n                        )\n                    current_batch_compute_cycle_count = max(\n                        current_batch_compute_cycle_count,\n                        temp_l1_tile_compute_cycle_count,\n                    )\n\n                # if one output tile in this batch shares input/output with another output tile in the previous batch, assign them to the same core to avoid data movement\n                # note that of the three input matrix mk, kn, mn, at most one of them can be the same if we change m,n,k\n                current_batch_M_K_read_count = np.sum(\n                    (current_batch_Read_M_K * (~previous_batch_Read_M_K))\n                    * M_K_tile_size\n                )\n                current_batch_K_N_read_count = np.sum(\n                    (current_batch_Read_K_N * (~previous_batch_Read_K_N))\n                    * K_N_tile_size\n                )\n                current_batch_M_N_read_count = np.sum(\n                    (\n                        current_batch_Read_M_N\n                        * (~(previous_batch_Read_M_N + previous_batch_Write_M_N))\n                    )\n                    * M_N_tile_size\n                )\n                previous_batch_M_N_write_count = np.sum(\n                    (previous_batch_Write_M_N * (~current_batch_Read_M_N))\n                    * M_N_tile_size\n                )\n\n                # read current batch while compute and write previous batch\n                current_batch_read_count = (\n                    current_batch_M_K_read_count\n                    + current_batch_K_N_read_count\n                    + current_batch_M_N_read_count\n                )\n                current_batch_read_cycle_count = ceil(\n                    current_batch_read_count\n                    * chiplet_module.compute_module.core.systolic_array.input_word_size\n                    / chiplet_module.compute_module.l2_bandwidth_per_cycle\n                )\n                prvious_batch_write_cycle_count = ceil(\n                    previous_batch_M_N_write_count\n                    * chiplet_module.compute_module.core.systolic_array.output_word_size\n                    / chiplet_module.compute_module.l2_bandwidth_per_cycle\n                )\n\n                total_cycle_count += (\n                    max(\n                        current_batch_read_cycle_count,\n                        previous_batch_compute_cycle_count,\n                    )\n                    + prvious_batch_write_cycle_count\n                )\n\n                previous_batch_compute_cycle_count = current_batch_compute_cycle_count\n                previous_batch_Read_M_K = copy.deepcopy(current_batch_Read_M_K)\n                previous_batch_Read_K_N = copy.deepcopy(current_batch_Read_K_N)\n                previous_batch_Read_M_N = copy.deepcopy(current_batch_Read_M_N)\n                previous_batch_Write_M_N = copy.deepcopy(current_batch_Write_M_N)\n\n                active_l1_tile_list = []\n\n            # last batch's compute and write\n            total_cycle_count += previous_batch_compute_cycle_count + ceil(\n                np.sum(previous_batch_Write_M_N * M_N_tile_size)\n                * data_type.word_size\n                / chiplet_module.compute_module.l2_bandwidth_per_cycle\n            )\n\n            return total_cycle_count\n\n    class L1TileSimulator:\n        def __init__(\n            self,\n            M: int,\n            N: int,\n            K: int,\n            data_type: DataType,\n            mapping: \"Matmul.Mapping\",\n            chiplet_module: Device,\n            look_up_table: pd.DataFrame,\n        ):\n            # print(f'L1 tile: {M} {N} {K}')\n            self.M = M\n            self.N = N\n            self.K = K\n            self.compute_cycle_count = self.simulate_l1_tile_compute_cycle_count(\n                M, N, K, data_type, mapping, chiplet_module, look_up_table\n            )\n\n        def simulate_l1_tile_compute_cycle_count(\n            self,\n            M: int,\n            N: int,\n            K: int,\n            data_type: DataType,\n            mapping: \"Matmul.Mapping\",\n            chiplet_module: Device,\n            look_up_table: pd.DataFrame,\n        ):\n            assert (\n                M * K + K * N + M * N\n                <= chiplet_module.compute_module.core.SRAM_size\n                // data_type.word_size\n                // 2\n            )\n\n            M_tiling_factor = mapping.l0_M_tiling_factor\n            N_tiling_factor = mapping.l0_N_tiling_factor\n            K_tiling_factor = mapping.l0_K_tiling_factor\n            assert (\n                M_tiling_factor * K_tiling_factor * N_tiling_factor\n                <= chiplet_module.compute_module.core.systolic_array_count\n            )\n\n            compute_cycle_count = ceil(\n                Matmul.simulate_systolic_array_cycle_count(\n                    look_up_table,\n                    ceil(M / M_tiling_factor),\n                    ceil(N / N_tiling_factor),\n                    ceil(K / K_tiling_factor),\n                    chiplet_module.compute_module.core.systolic_array.array_height,\n                    chiplet_module.compute_module.core.systolic_array.array_width,\n                    chiplet_module.compute_module.core.systolic_array.mac_per_cycle,\n                    mapping.dataflow,\n                )\n                + (K_tiling_factor - 1)\n                * M\n                * N\n                / chiplet_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n            )\n\n            return compute_cycle_count\n\n    @staticmethod\n    def simulate_systolic_array_cycle_count(\n        look_up_table: pd.DataFrame,\n        M,\n        N,\n        K,\n        array_height,\n        array_width,\n        mac_per_clock,\n        dataflow=\"os\",\n    ):\n        # print(f'start: {M} {N} {K} {array_height} {array_width} {mac_per_clock} {dataflow}')\n        assert M * N * K * array_height * array_width * mac_per_clock != 0\n        if M >= array_height and N >= array_width:\n            if (\n                M * N * K / array_height / array_width / max(array_height, array_width)\n                >= 128\n            ):\n                return ceil(\n                    M * N * K / array_height / array_width / mac_per_clock / 0.99\n                )\n            elif (\n                M * N * K / array_height / array_width / max(array_height, array_width)\n                >= 64\n            ):\n                return ceil(\n                    M * N * K / array_height / array_width / mac_per_clock / 0.98\n                )\n        elif M >= array_height and N < array_width:\n            if K * M / array_height / max(array_height, array_width) >= 64:\n                util_rate = N / array_width / 0.98\n                return ceil(\n                    M * N * K / array_height / array_width / mac_per_clock / util_rate\n                )\n        elif M < array_height and N >= array_width:\n            if K * N / array_width / max(array_height, array_width) >= 64:\n                util_rate = M / array_height / 0.98\n                return ceil(\n                    M * N * K / array_height / array_width / mac_per_clock / util_rate\n                )\n        else:\n            assert M < array_height and N < array_width\n            if K / max(array_height, array_width) >= 64:\n                util_rate = M / array_height * N / array_width / 0.98\n                return ceil(\n                    M * N * K / array_height / array_width / mac_per_clock / util_rate\n                )\n        # print('start look up table')\n        try:\n            cycle_count = look_up_table.loc[\n                (M, N, K, array_height, array_width, dataflow), \"cycle_count\"\n            ].item()\n        except KeyError:\n            try:\n                cycle_count = look_up_table.loc[\n                    (N, M, K, array_height, array_width, dataflow), \"cycle_count\"\n                ].item()\n            except KeyError:\n                # print('not found in look up table')\n                config = f\"./systolic_array_model/temp/systolic_array_{os.getpid()}.cfg\"\n                with open(config, \"w\") as f:\n                    f.writelines(\"[general]\\n\")\n                    f.writelines(\"run_name = systolic_array\\n\\n\")\n                    f.writelines(\"[architecture_presets]\\n\")\n                    f.writelines(\"ArrayHeight:    \" + str(array_height) + \"\\n\")\n                    f.writelines(\"ArrayWidth:     \" + str(array_width) + \"\\n\")\n                    f.writelines(\"IfmapSramSzkB:    \" + str(1024) + \"\\n\")\n                    f.writelines(\"FilterSramSzkB:   \" + str(1024) + \"\\n\")\n                    f.writelines(\"OfmapSramSzkB:    \" + str(1024) + \"\\n\")\n                    f.writelines(\"IfmapOffset:    0\\n\")\n                    f.writelines(\"FilterOffset:   10000000\\n\")\n                    f.writelines(\"OfmapOffset:    20000000\\n\")\n                    f.writelines(\"Dataflow : \" + dataflow + \"\\n\")\n                    f.writelines(\"Bandwidth : \" + \"100\" + \"\\n\")\n                    f.writelines(\"MemoryBanks: 1\\n\\n\")\n                    f.writelines(\"[run_presets]\\n\")\n                    f.writelines(\"InterfaceBandwidth: CALC\\n\")\n\n                topology = f\"./systolic_array_model/temp/matmul_{os.getpid()}.csv\"\n                with open(topology, \"w\") as f:\n                    f.writelines(\"Layer, M, N, K\\n\")\n                    f.writelines(f\"matmul1, {M}, {N}, {K},\\n\")\n\n                logpath = f\"./systolic_array_model/temp/\"\n                s = scalesim(\n                    save_disk_space=True,\n                    verbose=False,\n                    config=config,\n                    topology=topology,\n                    input_type_gemm=True,\n                )\n                s.run_scale(top_path=logpath)\n\n                cycle_count = s.runner.single_layer_sim_object_list[0].total_cycles\n                util_rate = s.runner.single_layer_sim_object_list[0].overall_util\n                with open(\n                    f\"./systolic_array_model/look_up_table_{array_height}_{array_width}.csv\",\n                    \"a\",\n                ) as f:\n                    f.writelines(\n                        f\"{M},{N},{K},{array_height},{array_width},{dataflow},{cycle_count},{util_rate:.3f}\\n\"\n                    )\n                look_up_table.loc[(M, N, K, array_height, array_width, dataflow), :] = [\n                    cycle_count,\n                    util_rate,\n                ]\n                if len(look_up_table) % 10 == 0:\n                    look_up_table.sort_index(inplace=True)\n        # if (\n        #     dataflow == \"os\"\n        # ):  # scalesim assumes collecting output is not on critical path in os\n        #     cycle_count += min(array_height, array_width, M, N)\n        # if True:\n        #     print(f\"{M}x{N}x{K}x{array_height}x{array_width}x{dataflow}: {cycle_count}\")\n        # new_table = look_up_table[~look_up_table.index.duplicated(keep='first')]\n        # if look_up_table.shape[0]-new_table.shape[0]>=1:\n        #     print(look_up_table)\n        #     print(look_up_table.duplicated(keep=False))\n        #     exit()\n        # print(f'end: {M} {N} {K} {array_height} {array_width} {mac_per_clock} {dataflow}')\n        # assert isinstance(cycle_count, float), f\"cycle_count: {cycle_count}\"\n        return ceil(cycle_count / mac_per_clock)\n\n    def run_on_gpu(\n        self,\n    ):\n        # import subprocess\n        # subprocess.run(['nvidia-smi', '-q', '–d', 'CLOCK'])\n        input1 = torch.randn(\n            self.computational_graph.M,\n            self.computational_graph.K,\n            dtype=torch.bfloat16,\n            device=\"cuda:0\",\n        )\n        input2 = torch.randn(\n            self.computational_graph.K,\n            self.computational_graph.N,\n            dtype=torch.bfloat16,\n            device=\"cuda:0\",\n        )\n        latencies = []\n        input1_dummy = torch.ones(4096, 4096).cuda()\n        input2_dummy = torch.ones(4096, 4096).cuda()\n        # warmup\n        for _ in range(3):\n            torch.matmul(input1_dummy, input2_dummy)\n            torch.cuda.synchronize()\n            time.sleep(1)\n        for _ in range(self.iterations):\n            # x = torch.matmul(input1_dummy, input2_dummy)  # flush the cache\n            # torch.cuda.synchronize()\n            start = time.time()\n            output = torch.matmul(input1, input2)\n            torch.cuda.synchronize()\n            end = time.time()\n            assert list(output.shape) == [\n                self.computational_graph.M,\n                self.computational_graph.N,\n            ]\n            latencies.append(end - start)\n            # time.sleep(1)\n\n        self.latency_on_gpu = (\n            statistics.median(latencies)\n            # min(latencies)\n            # - self.gpu_kernel_launch_overhead()\n            # - 4e-5\n            # min(latencies) - 8e-6\n        )  # GPU launch kernel overhead and PyTorch overhead\n        return self.latency_on_gpu\n\n    @staticmethod\n    def gpu_kernel_launch_overhead():\n        size = 1\n        latencies = []\n        for _ in range(50):\n            a = torch.randn(size, size, device=\"cuda\")\n            b = torch.randn(size, size, device=\"cuda\")\n            torch.cuda.synchronize()\n            start = time.time()\n            c = torch.matmul(a, b)\n            torch.cuda.synchronize()\n            end = time.time()\n            latencies.append(end - start)\n        avg_overhead = statistics.median(latencies)\n        print(\"GPU kernel launch overhead: \", avg_overhead * 1e3, \"ms\")\n        print(latencies)\n        return avg_overhead\n"
  },
  {
    "path": "software_model/operators.py",
    "content": "from utils import size, closest_factors\nfrom typing import List, Tuple, Union\nfrom hardware_model.device import Device\nfrom software_model.utils import Tensor, DataType\n\n\nclass Operator:\n    def __init__(\n        self,\n        flop_count,\n        load_count,\n        store_count,\n        peak_memory_usage,\n        data_type: DataType,\n        gpu_device=None,\n        verbose=True,\n    ):\n        self.flop_count = flop_count\n        self.load_count = load_count\n        self.store_count = store_count\n        self.io_count = load_count + store_count\n        self.peak_memory_usage = peak_memory_usage\n        self.data_type = data_type\n        self.gpu_device = gpu_device\n        self.verbose = verbose\n        self.log = \"\"\n        self.comment = \"\"\n        # simulation results\n        self.latency = 0\n        self.latency_on_gpu = 1\n        self.is_io_bound = None\n        # run on gpu\n        self.iterations = 50\n\n    class mapping:\n        pass\n\n\n# auxilary functions\n\n\nclass Reshape(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.input_shape = None\n        self.output_shape = None\n\n    def __call__(self, input: Tensor, output_shape: List[int]) -> Tensor:\n        assert input.size == size(output_shape)\n        self.flop_count = 0\n        self.load_count = 0\n        self.store_count = 0\n        self.io_count = 0\n        self.peak_memory_usage = 0\n        self.input_shape = input.shape\n        self.output_shape = output_shape\n        output = Tensor(output_shape, self.data_type)\n        return output\n\n\nclass Concat(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.input1_shape = None\n        self.input2_shape = None\n        self.concat_dim = None\n        self.output_shape = None\n\n    def __call__(self, input1: Tensor, input2: Tensor, concat_dim: int) -> Tensor:\n        assert len(input1.shape) == len(input2.shape)\n        for i in range(len(input1.shape)):\n            if i != concat_dim:\n                assert input1.shape[i] == input2.shape[i]\n        self.input1_shape = input1.shape\n        self.input2_shape = input2.shape\n        self.concat_dim = concat_dim\n        self.flop_count = 0\n        self.load_count = input1.size + input2.size\n        self.store_count = input1.size + input2.size\n        self.io_count = self.load_count + self.store_count\n        self.peak_memory_usage = (input1.size + input2.size) * 2\n        self.output_shape = (\n            input1.shape[:concat_dim]\n            + [input1.shape[concat_dim] + input2.shape[concat_dim]]\n            + input1.shape[concat_dim + 1 :]\n        )\n        output = Tensor(self.output_shape, self.data_type)\n        return output\n\n\nclass Transpose(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.input_shape = None\n        self.output_shape = None\n\n    def __call__(self, input: Tensor, permute: List[int]) -> Tensor:\n        assert len(input.shape) == len(permute)\n        self.input_shape = input.shape\n        self.permute = permute\n\n        self.flop_count = 0\n        self.load_count = size(input.shape)\n        self.store_count = self.load_count\n        self.io_count = self.load_count + self.store_count\n        self.peak_memory_usage = input.size * 2\n\n        self.output_shape = [self.input_shape[i] for i in permute]\n        output = Tensor(self.output_shape, self.data_type)\n        return output\n"
  },
  {
    "path": "software_model/softmax.py",
    "content": "from utils import size\nfrom typing import List, Tuple\nfrom hardware_model.device import Device\nfrom software_model.operators import Operator\nfrom software_model.utils import Tensor, DataType\nfrom math import ceil, log2\nimport torch\nimport time\nimport statistics\nimport numpy as np\n\n\nclass Softmax(Operator):\n    def __init__(self, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.shape = None\n\n    def __call__(self, input: Tensor) -> Tensor:\n        assert self.data_type == input.data_type\n        self.shape = input.shape\n        self.M = size(input.shape[:-1])\n        self.N = input.shape[-1]\n        self.computational_graph = self.ComputationalGraph(\n            self.M, self.N, self.data_type\n        )\n        return input\n\n    def print_latency(self):\n        print(f\"{self.shape}, {self.latency_on_gpu*1e6}us\")\n\n    class ComputationalGraph:\n        def __init__(self, M: int, N: int, data_type: DataType):\n            self.M = M\n            self.N = N\n            self.data_type = data_type\n\n    class Mapping:\n        def __init__(\n            self,\n            l2_tile_M: int,\n            l2_tile_N: int,\n            is_l2_double_buffering: bool,\n            l1_tile_M: int,\n            l1_tile_N: int,\n            is_l1_double_buffering: bool = False,\n        ):\n            self.l2_tile_M = l2_tile_M\n            self.l2_tile_N = l2_tile_N\n            self.is_l2_double_buffering = is_l2_double_buffering\n            self.l1_tile_M = l1_tile_M\n            self.l1_tile_N = l1_tile_N\n            self.is_l1_double_buffering = is_l1_double_buffering\n\n        def display(self):\n            print(\"-\" * 20)\n            print(\n                f\"l2_tile_M: {self.l2_tile_M}, is_l2_double_buffering: {self.is_l2_double_buffering}, l1_tile_M: {self.l1_tile_M}, l1_tile_N: {self.l1_tile_N}, is_l1_double_buffering: {self.is_l1_double_buffering}\"\n            )\n    \n    def roofline_model(self, pcb_module: Device):\n        self.io_count = self.M * self.N * self.data_type.word_size * 3\n        self.flop_count = self.M * self.N * (pcb_module.compute_module.core.vector_unit.flops_per_exp * 3 + 7)\n        self.roofline_latency=max(self.io_count/min(pcb_module.io_module.bandwidth, pcb_module.compute_module.l2_bandwidth_per_cycle*pcb_module.compute_module.clock_freq), self.flop_count/pcb_module.compute_module.total_vector_flops)\n        return self.roofline_latency\n\n    def compile_and_simulate(self, pcb_module: Device, compile_mode=None):\n        self.computational_graph.data_type = pcb_module.compute_module.core.vector_unit.data_type\n        min_cycle_count = float(\"inf\")\n        best_mapping = None\n        M = self.computational_graph.M\n        N = self.computational_graph.N\n        data_type = self.computational_graph.data_type\n        l2_tile_N = N\n        l2_tile_M = (\n            pcb_module.compute_module.l2_size // (l2_tile_N * data_type.word_size)\n        )\n        l2_tile_M = min(l2_tile_M, M)\n        is_l2_double_buffering = False\n        for l1_N_tiling_factor in [1, 2, 4, 8, 16, 32]:\n            l1_tile_N = ceil(l2_tile_N / l1_N_tiling_factor)\n            for l1_tile_M in [1, 2, 4, 8, 16, 32, 64, 128, 256]:\n                for is_l1_double_buffering in [True, False]:\n                    if is_l1_double_buffering:\n                        if (\n                            l1_tile_M * l1_tile_N * data_type.word_size\n                            > pcb_module.compute_module.core.SRAM_size // 2\n                        ):\n                            continue\n                    else:\n                        if (\n                            l1_tile_M * l1_tile_N * data_type.word_size\n                            > pcb_module.compute_module.core.SRAM_size\n                        ):\n                            continue\n                    mapping = self.Mapping(\n                        l2_tile_M,\n                        l2_tile_N,\n                        is_l2_double_buffering,\n                        l1_tile_M,\n                        l1_tile_N,\n                        is_l1_double_buffering,\n                    )\n                    cycle_count = self.simulate(\n                        self.computational_graph, mapping, pcb_module\n                    )\n                    if cycle_count < min_cycle_count:\n                        min_cycle_count = cycle_count\n                        best_mapping = mapping\n        self.best_mapping = best_mapping\n        self.best_cycle_count = min_cycle_count\n        self.best_latency = min_cycle_count / pcb_module.compute_module.clock_freq\n        self.latency = self.best_latency\n        # self.best_mapping.display()\n        return self.latency\n\n    def simulate(\n        self,\n        computational_graph: ComputationalGraph,\n        mapping: Mapping,\n        pcb_module: Device,\n    ) -> int:\n        M = computational_graph.M\n        N = computational_graph.N\n        data_type = computational_graph.data_type\n        l2_tile_M = mapping.l2_tile_M\n\n        if mapping.is_l2_double_buffering:\n            assert (\n                l2_tile_M * N * data_type.word_size * 2\n                <= pcb_module.compute_module.l2_size\n            )\n        else:\n            assert (\n                l2_tile_M * N * data_type.word_size <= pcb_module.compute_module.l2_size\n            )\n\n        M_l2_t = M // l2_tile_M\n        M_remain = M % l2_tile_M\n\n        l2_tiles = np.empty([ceil(M / l2_tile_M)], dtype=self.L2TileSimulator)\n\n        if M_l2_t != 0:\n            l2_tiles[:M_l2_t] = self.L2TileSimulator(\n                l2_tile_M,\n                N,\n                data_type,\n                mapping,\n                pcb_module,\n            )\n        if M_remain != 0:\n            l2_tiles[-1] = self.L2TileSimulator(\n                M_remain,\n                N,\n                data_type,\n                mapping,\n                pcb_module,\n            )\n\n        total_cycle_count = 0\n        l2_tile_count = ceil(M / l2_tile_M)\n        for m in range(l2_tile_count):\n            total_cycle_count += l2_tiles[m].read_cycle_count\n            total_cycle_count += l2_tiles[m].compute_cycle_count\n            total_cycle_count += l2_tiles[m].write_cycle_count\n        return total_cycle_count\n\n    class L2TileSimulator:\n        def __init__(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"Softmax.Mapping\",\n            pcb_module: Device,\n        ):\n            self.M = M\n            self.N = N\n            self.read_cycle_count = self.simulate_l2_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.write_cycle_count = self.simulate_l2_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.compute_cycle_count = self.simulate_l2_tile_compute_cycle_count(\n                M, N, data_type, mapping, pcb_module\n            )\n\n        def simulate_l2_tile_io_cycle_count(\n            self, M: int, N: int, data_type: DataType, chiplet_module: Device\n        ):\n            return ceil(\n                M\n                * N\n                * data_type.word_size\n                / (\n                    chiplet_module.io_module.bandwidth\n                    / chiplet_module.compute_module.clock_freq\n                )\n            )\n\n        def simulate_l2_tile_compute_cycle_count(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"Softmax.Mapping\",\n            pcb_module: Device,\n        ):\n            l1_tile_M = mapping.l1_tile_M\n            l1_tile_N = mapping.l1_tile_N\n\n            l1_tile = Softmax.L1TileSimulator(\n                l1_tile_M,\n                l1_tile_N,\n                data_type,\n                mapping,\n                pcb_module,\n            )\n            l1_tile_count = ceil(M / l1_tile_M) * ceil(N / l1_tile_N)           \n            l1_tile_cycle_count = (\n                l1_tile.read_cycle_count\n                + l1_tile.write_cycle_count\n                + l1_tile.compute_cycle_count\n            )\n            total_cycle_count = (\n                ceil(l1_tile_count / pcb_module.compute_module.core_count) + 1\n            ) * (\n                l1_tile_cycle_count\n                + log2(ceil(N / l1_tile_N)) * l1_tile.reduction_cycle_count\n            )\n            return total_cycle_count\n\n\n    class L1TileSimulator:\n        def __init__(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"Softmax.Mapping\",\n            pcb_module: Device,\n        ):\n            self.M = M\n            self.N = N\n            self.flops_per_exp = (\n                pcb_module.compute_module.core.vector_unit.flops_per_exp\n            )\n            self.read_cycle_count = self.simulate_l1_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.compute_cycle_count = self.simulate_l1_tile_compute_cycle_count(\n                M, N, data_type, mapping, pcb_module\n            )\n            self.write_cycle_count = self.simulate_l1_tile_io_cycle_count(\n                M, N, data_type, pcb_module\n            )\n            self.reduction_cycle_count = (\n                M\n                * N\n                * (self.flops_per_exp + 2)\n                / pcb_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n                + M\n                * N\n                * data_type.word_size\n                * 2\n                / (pcb_module.compute_module.l2_bandwidth_per_cycle/pcb_module.compute_module.core_count)\n            )\n\n        def simulate_l1_tile_io_cycle_count(\n            self, M: int, N: int, data_type: DataType, pcb_module: Device\n        ):\n            return ceil(\n                M\n                * N\n                * data_type.word_size\n                / (pcb_module.compute_module.l2_bandwidth_per_cycle)\n            )\n\n        def simulate_l1_tile_compute_cycle_count(\n            self,\n            M: int,\n            N: int,\n            data_type: DataType,\n            mapping: \"Softmax.Mapping\",\n            pcb_module: Device,\n        ):\n            # online softmax\n            total_flop_count = M * N * (self.flops_per_exp * 3 + 7)\n            return ceil(\n                total_flop_count\n                / pcb_module.compute_module.core.vector_unit.total_vector_flops_per_cycle\n            )\n\n    def run_on_gpu(self):\n        assert self.shape is not None\n        input = torch.randn(self.shape, dtype=torch.float16, device=\"cuda\")\n        latencies = []\n        # warmup\n        for _ in range(3):\n            _ = torch.softmax(input, dim=-1)\n            torch.cuda.synchronize()\n        for _ in range(self.iterations):\n            start = time.time()\n            output = torch.softmax(input, dim=-1)\n            torch.cuda.synchronize()\n            end = time.time()\n            assert output.shape == input.shape\n            latencies.append(end - start)\n        self.latency_on_gpu = statistics.median(latencies)\n        return self.latency_on_gpu\n\n    @staticmethod\n    def gpu_kernel_launch_overhead():\n        size = 1\n        latencies = []\n        for _ in range(50):\n            a = torch.randn(size, size, device=\"cuda\")\n            torch.cuda.synchronize()\n            start = time.time()\n            c = torch.softmax(a, dim=-1)\n            torch.cuda.synchronize()\n            end = time.time()\n            latencies.append(end - start)\n        avg_overhead = statistics.median(latencies)\n        print('GPU kernel launch overhead: ', avg_overhead*1e3, 'ms')\n        print(latencies)\n        return avg_overhead"
  },
  {
    "path": "software_model/transformer.py",
    "content": "from software_model.operators import (\n    Operator,\n    Reshape,\n    Concat,\n    Transpose,\n)\nfrom software_model.matmul import Matmul, BatchedMatmul\nfrom software_model.softmax import Softmax\nfrom software_model.layernorm import LayerNorm\nfrom software_model.gelu import GeLU\n\n\nfrom software_model.utils import Tensor, DataType\nfrom software_model.communication_primitives import AllReduceMultiPCB\nfrom math import ceil\nfrom typing import List\nfrom hardware_model.system import System\n\n\nclass TransformerBlockInitComputationTP(Operator):\n    def __init__(self, d_model, n_heads, device_count, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.d_model = d_model\n        self.n_heads = n_heads\n        self.device_count = device_count\n        # parameters per device\n        d = d_model\n        self.Wq = Tensor([d, d // device_count], data_type)\n        self.Wk = Tensor([d, d // device_count], data_type)\n        self.Wv = Tensor([d, d // device_count], data_type)\n        self.W0 = Tensor([d // device_count, d], data_type)\n        self.W1 = Tensor([d, 4 * d // device_count], data_type)\n        self.W2 = Tensor([4 * d // device_count, d], data_type)\n        # operators per device\n        # # multi-head attention\n        self.Q_proj = Matmul(data_type)\n        self.K_proj = Matmul(data_type)\n        self.V_proj = Matmul(data_type)\n        self.Q_reshape = Reshape(data_type)\n        self.K_reshape = Reshape(data_type)\n        self.V_reshape = Reshape(data_type)\n        self.Q_transpose = Transpose(data_type)\n        self.K_transpose = Transpose(data_type)\n        self.V_transpose = Transpose(data_type)\n        self.Q_mul_K = BatchedMatmul(data_type)\n        self.A_softmax = Softmax(data_type)\n        self.A_mul_V = BatchedMatmul(data_type)\n        self.H_transpose = Transpose(data_type)\n        self.H_reshape = Reshape(data_type)\n        self.H_matmul0 = Matmul(data_type)\n        self.layer_norm0 = LayerNorm(data_type)\n        self.allreduce_mha = AllReduceMultiPCB(data_type)\n        # # feed-forward network\n        self.H_matmul1 = Matmul(data_type)\n        self.H_gelu = GeLU(data_type)\n        self.H_matmul2 = Matmul(data_type)\n        self.layer_norm1 = LayerNorm(data_type)\n        self.allreduce_ffn = AllReduceMultiPCB(data_type)\n\n    def __call__(self, X: Tensor) -> Tensor:\n        # b: batch size\n        # s: sequence length\n        # d: hidden dimension\n        # d_h: dimension per head\n        b, s, d = X.shape\n        assert d == self.d_model\n        h = self.n_heads\n        dev_cnt = self.device_count\n        d_h = d // h\n\n        # multi-head attention\n        Q = self.Q_proj(X, self.Wq)  # [b, s, d / dev_cnt]\n        assert Q.shape == [b, s, d // dev_cnt]\n        K = self.K_proj(X, self.Wk)  # [b, s, d / dev_cnt]\n        V = self.V_proj(X, self.Wv)  # [b, s, d / dev_cnt]\n        Q = self.Q_reshape(Q, [b, s, h // dev_cnt, d_h])\n        K = self.K_reshape(K, [b, s, h // dev_cnt, d_h])\n        V = self.V_reshape(V, [b, s, h // dev_cnt, d_h])\n        Q_T = self.Q_transpose(Q, [0, 2, 1, 3])  # [b, h / dev_cnt, s, d_h]\n        assert Q_T.shape == [b, h // dev_cnt, s, d_h]\n        K_T = self.K_transpose(K, [0, 2, 3, 1])  # [b, h / dev_cnt, d_h, s]\n        assert K_T.shape == [b, h // dev_cnt, d_h, s]\n        V_T = self.V_transpose(V, [0, 2, 1, 3])  # [b, h / dev_cnt, s, d_h]\n        assert V_T.shape == [b, h // dev_cnt, s, d_h]\n        A = self.Q_mul_K(Q_T, K_T)  # [b, h / dev_cnt, s, s]\n        assert A.shape == [b, h // dev_cnt, s, s]\n        A_prob = self.A_softmax(A)\n        H = self.A_mul_V(A_prob, V_T)  #  [b, h / dev_cnt, s, d_h]\n        assert H.shape == [b, h // dev_cnt, s, d_h]\n        H = self.H_transpose(H, [0, 2, 1, 3])  #  [b, s, h / dev_cnt, d_h]\n        assert H.shape == [b, s, h // dev_cnt, d_h]\n        H = self.H_reshape(H, [b, s, d // dev_cnt])\n        assert H.shape == [b, s, d // dev_cnt]\n        H0 = self.H_matmul0(H, self.W0)  #  [b, s, d]\n        assert H0.shape == [b, s, d]\n        H0 = self.layer_norm0(H0)\n        assert H0.shape == [b, s, d]\n        if dev_cnt > 1:\n            H0 = self.allreduce_mha(H0)\n\n        # feed-forward network\n        H1 = self.H_matmul1(H0, self.W1)  # [b, s, 4 * d / dev_cnt]\n        assert H1.shape == [b, s, 4 * d // dev_cnt]\n        H1 = self.H_gelu(H1)\n        H2 = self.H_matmul2(H1, self.W2)  #  [b, s, d]\n        assert H2.shape == [b, s, d]\n        H2 = self.layer_norm1(H2)\n        if dev_cnt > 1:\n            H2 = self.allreduce_ffn(H2)\n\n        assert H2.shape == [b, s, d]\n        return H2\n\n    def roofline_model(self, system: System):\n        device = system.device\n        interconnect = system.interconnect\n\n        qkv_latency = 3 * (\n            self.Q_proj.roofline_model(device) + device.compute_module.overhead.matmul\n        )\n        q_mul_k_latency = (\n            self.Q_mul_K.roofline_model(device) + device.compute_module.overhead.matmul\n        )\n        a_mul_v_latency = (\n            self.A_mul_V.roofline_model(device) + device.compute_module.overhead.matmul\n        )\n        h_matmul0_latency = (\n            self.H_matmul0.roofline_model(device)\n            + device.compute_module.overhead.matmul\n        )\n        h1_matmul1_latency = (\n            self.H_matmul1.roofline_model(device)\n            + device.compute_module.overhead.matmul\n        )\n        h2_matmul2_latency = (\n            self.H_matmul2.roofline_model(device)\n            + device.compute_module.overhead.matmul\n        )\n\n        matmul_total_latency = (\n            qkv_latency\n            + q_mul_k_latency\n            + a_mul_v_latency\n            + h_matmul0_latency\n            + h1_matmul1_latency\n            + h2_matmul2_latency\n        )\n\n        # normalization\n        softmax_latency = (\n            self.A_softmax.roofline_model(device)\n            + device.compute_module.overhead.softmax\n        )\n        layernorm_latency = (\n            self.layer_norm0.roofline_model(device)\n            + device.compute_module.overhead.layernorm\n        )\n\n        normlization_total_latency = softmax_latency + layernorm_latency * 2\n\n        # gelu\n        gelu_latency = (\n            self.H_gelu.roofline_model(device) + device.compute_module.overhead.gelu\n        )\n\n        # allreduce\n        if self.device_count > 1:\n            allreduce_latency = self.allreduce_mha.simulate(interconnect)\n            allreduce_total_latency = allreduce_latency * 2\n        else:\n            allreduce_total_latency = 0\n            allreduce_total_latency = 0\n\n        # others\n\n        # print\n        print(\"Roofline breakdown:\")\n        print(\n            f\"{qkv_latency}\\n{q_mul_k_latency}\\n{a_mul_v_latency}\\n{h_matmul0_latency}\\n{h1_matmul1_latency}\\n{h2_matmul2_latency}\\n{softmax_latency}\\n{layernorm_latency}\\n{layernorm_latency}\\n{gelu_latency}\\n{allreduce_latency}\\n{allreduce_latency}\\n\"\n        )\n        self.roofline_log = f\"{qkv_latency}, {q_mul_k_latency}, {a_mul_v_latency}, {h_matmul0_latency}, {h1_matmul1_latency}, {h2_matmul2_latency}, {softmax_latency}, {layernorm_latency}, {layernorm_latency}, {gelu_latency}, {allreduce_latency}, {allreduce_latency}\"\n        print(\"total:\")\n        print(\n            f\"{matmul_total_latency}\\n{normlization_total_latency}\\n{gelu_latency}\\n{allreduce_total_latency}\\n\"\n        )\n        self.roofline_latency = (\n            matmul_total_latency\n            + normlization_total_latency\n            + gelu_latency\n            + allreduce_total_latency\n        )\n        return self.roofline_latency\n\n    def compile_and_simulate(self, system: System, compile_mode: str):\n        device = system.device\n        interconnect = system.interconnect\n\n        # matmul\n        print(\"simulating qkv\")\n        qkv_latency = 3 * (\n            self.Q_proj.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.matmul\n        )\n        print(\"simulating q_mul_k\")\n        q_mul_k_latency = (\n            self.Q_mul_K.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.matmul\n        )\n        print(\"simulating a_mul_v\")\n        a_mul_v_latency = (\n            self.A_mul_V.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.matmul\n        )\n        print(\"simulating h_matmul0\")\n        h_matmul0_latency = (\n            self.H_matmul0.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.matmul\n        )\n        print(\"simulating h1_matmul1\")\n        h1_matmul1_latency = (\n            self.H_matmul1.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.matmul\n        )\n        print(\"simulating h2_matmul2\")\n        h2_matmul2_latency = (\n            self.H_matmul2.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.matmul\n        )\n        print(\"finish matmul simulation\")\n\n        matmul_total_latency = (\n            qkv_latency\n            + q_mul_k_latency\n            + a_mul_v_latency\n            + h_matmul0_latency\n            + h1_matmul1_latency\n            + h2_matmul2_latency\n        )\n\n        # normalization\n        softmax_latency = (\n            self.A_softmax.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.softmax\n        )\n        layernorm_latency = (\n            self.layer_norm0.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.layernorm\n        )\n\n        normlization_total_latency = softmax_latency + layernorm_latency * 2\n\n        # gelu\n        gelu_latency = (\n            self.H_gelu.compile_and_simulate(device, compile_mode)\n            + device.compute_module.overhead.gelu\n        )\n\n        # allreduce\n        if self.device_count > 1:\n            allreduce_latency = self.allreduce_mha.simulate(interconnect)\n            allreduce_total_latency = allreduce_latency * 2\n        else:\n            allreduce_latency = 0\n            allreduce_total_latency = 0\n\n        # others\n\n        # print\n        # print(\"breakdown:\")\n        # print(\n        #     f\"{qkv_latency}\\n{q_mul_k_latency}\\n{a_mul_v_latency}\\n{h_matmul0_latency}\\n{h1_matmul1_latency}\\n{h2_matmul2_latency}\\n{softmax_latency}\\n{layernorm_latency}\\n{layernorm_latency}\\n{gelu_latency}\\n{allreduce_latency}\\n{allreduce_latency}\\n\"\n        # )\n        # print(\"total:\")\n        # print(\n        #     f\"{matmul_total_latency}\\n{normlization_total_latency}\\n{gelu_latency}\\n{allreduce_total_latency}\\n\"\n        # )\n        self.latency = (\n            matmul_total_latency\n            + normlization_total_latency\n            + gelu_latency\n            + allreduce_total_latency\n        )\n        self.simluate_log = f\"{qkv_latency}, {q_mul_k_latency}, {a_mul_v_latency}, {h_matmul0_latency}, {h1_matmul1_latency}, {h2_matmul2_latency}, {softmax_latency}, {layernorm_latency}, {layernorm_latency}, {gelu_latency}, {allreduce_latency}, {allreduce_latency}\"\n        return self.latency\n\n    def run_on_gpu(self):\n        # matmul\n        qkv_latency = (\n            self.Q_proj.run_on_gpu()  # - self.Q_proj.gpu_kernel_launch_overhead()\n        ) * 3\n        q_mul_k_latency = (\n            self.Q_mul_K.run_on_gpu()  # - self.Q_mul_K.gpu_kernel_launch_overhead()\n        )\n        a_mul_v_latency = (\n            self.A_mul_V.run_on_gpu()  # - self.A_mul_V.gpu_kernel_launch_overhead()\n        )\n        h_matmul0_latency = (\n            self.H_matmul0.run_on_gpu()  # - self.H_matmul0.gpu_kernel_launch_overhead()\n        )\n        h1_matmul1_latency = (\n            self.H_matmul1.run_on_gpu()  # - self.H_matmul1.gpu_kernel_launch_overhead()\n        )\n        h2_matmul2_latency = (\n            self.H_matmul2.run_on_gpu()  # - self.H_matmul2.gpu_kernel_launch_overhead()\n        )\n\n        matmul_total_latency = (\n            qkv_latency\n            + q_mul_k_latency\n            + a_mul_v_latency\n            + h_matmul0_latency\n            + h1_matmul1_latency\n            + h2_matmul2_latency\n        )\n\n        # normalization\n        softmax_latency = (\n            self.A_softmax.run_on_gpu()  # - self.A_softmax.gpu_kernel_launch_overhead()\n        )\n        layernorm_latency = (\n            self.layer_norm0.run_on_gpu()\n            - self.layer_norm0.gpu_kernel_launch_overhead()\n        )\n\n        normlization_total_latency = softmax_latency + layernorm_latency * 2\n\n        # gelu\n        gelu_latency = (\n            self.H_gelu.run_on_gpu()  # - self.H_gelu.gpu_kernel_launch_overhead()\n        )\n\n        # allreduce\n        allreduce_total_latency = 0\n\n        # others\n\n        # print\n        print(\"breakdown:\")\n        print(\n            f\"{qkv_latency}\\n{q_mul_k_latency}\\n{a_mul_v_latency}\\n{h_matmul0_latency}\\n{h1_matmul1_latency}\\n{h2_matmul2_latency}\\n{softmax_latency}\\n{layernorm_latency}\\n{layernorm_latency}\\n{gelu_latency}\\n\"\n        )\n        print(\"total:\")\n        print(\n            f\"{matmul_total_latency}\\n{normlization_total_latency}\\n{gelu_latency}\\n{allreduce_total_latency}\\n\"\n        )\n        self.latency_on_gpu = (\n            matmul_total_latency\n            + normlization_total_latency\n            + gelu_latency\n            + allreduce_total_latency\n        )\n        return self.latency_on_gpu\n\n\nclass TransformerBlockAutoRegressionTP(Operator):\n    def __init__(self, d_model, n_heads, device_count, data_type: DataType):\n        super().__init__(0, 0, 0, 0, data_type)\n        self.d_model = d_model\n        self.n_heads = n_heads\n        self.device_count = device_count\n        # parameters per device\n        d = d_model\n        self.Wq = Tensor([d, d // device_count], data_type)\n        self.Wk = Tensor([d, d // device_count], data_type)\n        self.Wv = Tensor([d, d // device_count], data_type)\n        self.W0 = Tensor([d // device_count, d], data_type)\n        self.W1 = Tensor([d, 4 * d // device_count], data_type)\n        self.W2 = Tensor([4 * d // device_count, d], data_type)\n        # operators per device\n        # # multi-head attention\n        self.Q_proj = Matmul(data_type)\n        self.K_proj = Matmul(data_type)\n        self.V_proj = Matmul(data_type)\n        self.Q_reshape = Reshape(data_type)\n        self.K_reshape = Reshape(data_type)\n        self.V_reshape = Reshape(data_type)\n        self.Q_transpose = Transpose(data_type)\n        self.K_transpose = Transpose(data_type)\n        self.V_transpose = Transpose(data_type)\n        self.K_concat = Concat(data_type)\n        self.V_concat = Concat(data_type)\n        self.Q_mul_K = BatchedMatmul(data_type)\n        self.A_softmax = Softmax(data_type)\n        self.A_mul_V = BatchedMatmul(data_type)\n        self.H_transpose = Transpose(data_type)\n        self.H_reshape = Reshape(data_type)\n        self.H_matmul0 = Matmul(data_type)\n        self.layer_norm0 = LayerNorm(data_type)\n        self.allreduce_mha = AllReduceMultiPCB(data_type)\n        # # feed-forward network\n        self.H_matmul1 = Matmul(data_type)\n        self.H_gelu = GeLU(data_type)\n        self.H_matmul2 = Matmul(data_type)\n        self.layer_norm1 = LayerNorm(data_type)\n        self.allreduce_ffn = AllReduceMultiPCB(data_type)\n\n    def __call__(self, x: Tensor, seq_len: int) -> Tensor:\n        # b: batch size\n        # s: sequence length\n        # d: hidden dimension\n        # d_h: dimension per head\n        b, _, d = x.shape\n        assert d == self.d_model\n        s = seq_len\n        h = self.n_heads\n        dev_cnt = self.device_count\n        d_h = d // h\n\n        # KV cache\n        K_cache = Tensor([b, h // dev_cnt, d_h, s], self.data_type)\n        V_cache = Tensor([b, h // dev_cnt, s, d_h], self.data_type)\n\n        # multi-head attention\n        q = self.Q_proj(x, self.Wq)  # [b, 1, d / dev_cnt]\n        assert q.shape == [b, 1, d // dev_cnt]\n        k = self.K_proj(x, self.Wk)  # [b, 1, d / dev_cnt]\n        v = self.V_proj(x, self.Wv)  # [b, 1, d / dev_cnt]\n        q = self.Q_reshape(q, [b, 1, h // dev_cnt, d_h])\n        k = self.K_reshape(k, [b, 1, h // dev_cnt, d_h])\n        v = self.V_reshape(v, [b, 1, h // dev_cnt, d_h])\n        q_T = self.Q_transpose(q, [0, 2, 1, 3])  # [b, h / dev_cnt, 1, d_h]\n        assert q_T.shape == [b, h // dev_cnt, 1, d_h]\n        k_T = self.K_transpose(k, [0, 2, 3, 1])  # [b, h / dev_cnt, d_h, 1]\n        assert k_T.shape == [b, h // dev_cnt, d_h, 1]\n        v_T = self.V_transpose(v, [0, 2, 1, 3])  # [b, h / dev_cnt, 1, d_h]\n        assert v_T.shape == [b, h // dev_cnt, 1, d_h]\n        K_T = self.K_concat(K_cache, k_T, 3)  # [b, h / dev_cnt, d_h, s+1]\n        assert K_T.shape == [b, h // dev_cnt, d_h, s + 1]\n        V_T = self.V_concat(V_cache, v_T, 2)  # [b, h / dev_cnt, s+1, d_h]\n        assert V_T.shape == [b, h // dev_cnt, s + 1, d_h]\n        a = self.Q_mul_K(q_T, K_T)  # [b, h / dev_cnt, 1, s+1]\n        assert a.shape == [b, h // dev_cnt, 1, s + 1]\n        a_prob = self.A_softmax(a)\n        h0 = self.A_mul_V(a_prob, V_T)  #  [b, h / dev_cnt, 1, d_h]\n        assert h0.shape == [b, h // dev_cnt, 1, d_h]\n        h0 = self.H_transpose(h0, [0, 2, 1, 3])  #  [b, 1, h / dev_cnt, d_h]\n        assert h0.shape == [b, 1, h // dev_cnt, d_h]\n        h0 = self.H_reshape(h0, [b, 1, d // dev_cnt])\n        assert h0.shape == [b, 1, d // dev_cnt]\n        h0 = self.H_matmul0(h0, self.W0)  #  [b, 1, d]\n        assert h0.shape == [b, 1, d]\n        h0 = self.layer_norm0(h0)\n        assert h0.shape == [b, 1, d]\n        if dev_cnt > 1:\n            h0 = self.allreduce_mha(h0)\n\n        # feed-forward network\n        h1 = self.H_matmul1(h0, self.W1)  # [b, 1, 4 * d / dev_cnt]\n        assert h1.shape == [b, 1, 4 * d // dev_cnt]\n        h1 = self.H_gelu(h1)\n        h2 = self.H_matmul2(h1, self.W2)  #  [b, 1, d]\n        assert h2.shape == [b, 1, d]\n        h2 = self.layer_norm1(h2)\n        if dev_cnt > 1:\n            h2 = self.allreduce_ffn(h2)\n\n        assert h2.shape == [b, 1, d]\n        self.memory_requirement = (\n            self.Wq.size * self.Wq.data_type.word_size\n            + self.Wk.size * self.Wk.data_type.word_size\n            + self.Wv.size * self.Wv.data_type.word_size\n            + self.W0.size * self.W0.data_type.word_size\n            + self.W1.size * self.W1.data_type.word_size\n            + self.W2.size * self.W2.data_type.word_size\n            + K_cache.size * K_cache.data_type.word_size\n            + V_cache.size * V_cache.data_type.word_size\n        )\n        return h2\n\n    def roofline_model(self, system: System):\n        device = system.device\n        interconnect = system.interconnect\n\n        qkv_latency = 3 * (\n            self.Q_proj.roofline_model(device) + device.compute_module.overhead.matmul\n        )\n        q_mul_k_latency = (\n            self.Q_mul_K.roofline_model(device) + device.compute_module.overhead.matmul\n        )\n        a_mul_v_latency = (\n            self.A_mul_V.roofline_model(device) + device.compute_module.overhead.matmul\n        )\n        h_matmul0_latency = (\n            self.H_matmul0.roofline_model(device)\n            + device.compute_module.overhead.matmul\n        )\n        h1_matmul1_latency = (\n            self.H_matmul1.roofline_model(device)\n            + device.compute_module.overhead.matmul\n        )\n        h2_matmul2_latency = (\n            self.H_matmul2.roofline_model(device)\n            + device.compute_module.overhead.matmul\n        )\n\n        matmul_total_latency = (\n            qkv_latency\n            + q_mul_k_latency\n            + a_mul_v_latency\n            + h_matmul0_latency\n            + h1_matmul1_latency\n            + h2_matmul2_latency\n        )\n\n        # normalization\n        softmax_latency = (\n            self.A_softmax.roofline_model(device)\n            + device.compute_module.overhead.softmax\n        )\n        layernorm_latency = (\n            self.layer_norm0.roofline_model(device)\n            + device.compute_module.overhead.layernorm\n        )\n\n        normlization_total_latency = softmax_latency + layernorm_latency * 2\n\n        # gelu\n        gelu_latency = (\n            self.H_gelu.roofline_model(device) + device.compute_module.overhead.gelu\n        )\n\n        # allreduce\n        if self.device_count > 1:\n            allreduce_latency = self.allreduce_mha.simulate(interconnect)\n            allreduce_total_latency = allreduce_latency * 2\n        else:\n            allreduce_latency = 0\n            allreduce_total_latency = 0\n\n        # others\n\n        # print\n        print(\"Roofline breakdown:\")\n        print(\n            f\"{qkv_latency}\\n{q_mul_k_latency}\\n{a_mul_v_latency}\\n{h_matmul0_latency}\\n{h1_matmul1_latency}\\n{h2_matmul2_latency}\\n{softmax_latency}\\n{layernorm_latency}\\n{layernorm_latency}\\n{gelu_latency}\\n{allreduce_latency}\\n{allreduce_latency}\\n\"\n        )\n        print(\"total:\")\n        print(\n            f\"{matmul_total_latency}\\n{normlization_total_latency}\\n{gelu_latency}\\n{allreduce_total_latency}\\n\"\n        )\n        self.roofline_latency = (\n            matmul_total_latency\n            + normlization_total_latency\n            + gelu_latency\n            + allreduce_total_latency\n        )\n        # print(f'memory requirement: {self.memory_requirement/1e9*96}GB')\n        self.roofline_log = f\"{qkv_latency}, {q_mul_k_latency}, {a_mul_v_latency}, {h_matmul0_latency}, {h1_matmul1_latency}, {h2_matmul2_latency}, {softmax_latency}, {layernorm_latency}, {layernorm_latency}, {gelu_latency}, {allreduce_latency}, {allreduce_latency}\"\n        return self.roofline_latency\n\n    def compile_and_simulate(self, system: System, compile_mode: str):\n        pcb = system.device\n        interconnect = system.interconnect\n\n        # matmul\n        # print(\"simulating qkv\")\n        qkv_latency = 3 * (\n            self.Q_proj.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.matmul\n        )\n        # print(\"simulating q_mul_k\")\n        q_mul_k_latency = (\n            self.Q_mul_K.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.matmul\n        )\n        # print(\"simulating a_mul_v\")\n        a_mul_v_latency = (\n            self.A_mul_V.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.matmul\n        )\n        # print(\"simulating h_matmul0\")\n        h_matmul0_latency = (\n            self.H_matmul0.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.matmul\n        )\n        # print(\"simulating h1_matmul1\")\n        h1_matmul1_latency = (\n            self.H_matmul1.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.matmul\n        )\n        # print(\"simulating h2_matmul2\")\n        h2_matmul2_latency = (\n            self.H_matmul2.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.matmul\n        )\n\n        matmul_total_latency = (\n            qkv_latency\n            + q_mul_k_latency\n            + a_mul_v_latency\n            + h_matmul0_latency\n            + h1_matmul1_latency\n            + h2_matmul2_latency\n        )\n\n        # normalization\n        softmax_latency = (\n            self.A_softmax.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.softmax\n        )\n        layernorm_latency = (\n            self.layer_norm0.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.layernorm\n        )\n\n        normlization_total_latency = softmax_latency + layernorm_latency * 2\n\n        # gelu\n        gelu_latency = (\n            self.H_gelu.compile_and_simulate(pcb, compile_mode)\n            + pcb.compute_module.overhead.gelu\n        )\n\n        # allreduce\n        if self.device_count > 1:\n            allreduce_latency = self.allreduce_mha.simulate(interconnect)\n            allreduce_total_latency = allreduce_latency * 2\n        else:\n            allreduce_latency = 0\n            allreduce_total_latency = 0\n\n        # others\n\n        # print\n        # print(\"breakdown:\")\n        # print(\n        #     f\"{qkv_latency}\\n{q_mul_k_latency}\\n{a_mul_v_latency}\\n{h_matmul0_latency}\\n{h1_matmul1_latency}\\n{h2_matmul2_latency}\\n{softmax_latency}\\n{layernorm_latency}\\n{layernorm_latency}\\n{gelu_latency}\\n{allreduce_latency}\\n{allreduce_latency}\\n\"\n        # )\n        # print(\"total:\")\n        # print(\n        #     f\"{matmul_total_latency}\\n{normlization_total_latency}\\n{gelu_latency}\\n{allreduce_total_latency}\\n\"\n        # )\n        self.latency = (\n            matmul_total_latency\n            + normlization_total_latency\n            + gelu_latency\n            + allreduce_total_latency\n        )\n        self.simluate_log = f\"{qkv_latency}, {q_mul_k_latency}, {a_mul_v_latency}, {h_matmul0_latency}, {h1_matmul1_latency}, {h2_matmul2_latency}, {softmax_latency}, {layernorm_latency}, {layernorm_latency}, {gelu_latency}, {allreduce_latency}, {allreduce_latency}\"\n        return self.latency\n\n    def run_on_gpu(self):\n        # matmul\n        qkv_latency = (\n            self.Q_proj.run_on_gpu()  # - self.Q_proj.gpu_kernel_launch_overhead()\n        ) * 3\n        q_mul_k_latency = (\n            self.Q_mul_K.run_on_gpu()  # - self.Q_mul_K.gpu_kernel_launch_overhead()\n        )\n        a_mul_v_latency = (\n            self.A_mul_V.run_on_gpu()  # - self.A_mul_V.gpu_kernel_launch_overhead()\n        )\n        h_matmul0_latency = (\n            self.H_matmul0.run_on_gpu()  # - self.H_matmul0.gpu_kernel_launch_overhead()\n        )\n        h1_matmul1_latency = (\n            self.H_matmul1.run_on_gpu()  # - self.H_matmul1.gpu_kernel_launch_overhead()\n        )\n        h2_matmul2_latency = (\n            self.H_matmul2.run_on_gpu()  # - self.H_matmul2.gpu_kernel_launch_overhead()\n        )\n\n        matmul_total_latency = (\n            qkv_latency\n            + q_mul_k_latency\n            + a_mul_v_latency\n            + h_matmul0_latency\n            + h1_matmul1_latency\n            + h2_matmul2_latency\n        )\n\n        # normalization\n        softmax_latency = (\n            self.A_softmax.run_on_gpu()  # - self.A_softmax.gpu_kernel_launch_overhead()\n        )\n        layernorm_latency = (\n            self.layer_norm0.run_on_gpu()\n            - self.layer_norm0.gpu_kernel_launch_overhead()\n        )\n\n        normlization_total_latency = softmax_latency + layernorm_latency * 2\n\n        # gelu\n        gelu_latency = (\n            self.H_gelu.run_on_gpu()  # - self.H_gelu.gpu_kernel_launch_overhead()\n        )\n        # gelu_latency = max(gelu_latency, 1e-7)\n\n        # allreduce\n        allreduce_total_latency = 0\n\n        # others\n\n        # print\n        print(\"breakdown:\")\n        print(\n            f\"{qkv_latency}\\n{q_mul_k_latency}\\n{a_mul_v_latency}\\n{h_matmul0_latency}\\n{h1_matmul1_latency}\\n{h2_matmul2_latency}\\n{softmax_latency}\\n{layernorm_latency}\\n{layernorm_latency}\\n{gelu_latency}\\n\"\n        )\n        print(\"total:\")\n        print(\n            f\"{matmul_total_latency}\\n{normlization_total_latency}\\n{gelu_latency}\\n{allreduce_total_latency}\\n\"\n        )\n        self.latency_on_gpu = (\n            matmul_total_latency\n            + normlization_total_latency\n            + gelu_latency\n            + allreduce_total_latency\n        )\n        return self.latency_on_gpu\n\n\nclass LLMInitComputationTP:\n    def __init__(\n        self,\n        d_model,\n        n_heads,\n        n_layers,\n        device_count,\n    ) -> None:\n        pass\n"
  },
  {
    "path": "software_model/utils.py",
    "content": "from typing import List\nfrom utils import size\n\n\nclass DataType:\n    def __init__(self, name: str, word_size: int) -> None:\n        self.name = name\n        self.word_size:int = word_size\n\ndata_type_dict = {\"int8\": DataType(\"int8\", 1), \"fp16\": DataType(\"fp16\", 2), \"fp32\": DataType(\"fp32\", 4)}\n\nclass Tensor:\n    def __init__(\n        self, shape: List, data_type=data_type_dict[\"fp16\"]\n    ) -> None:\n        self.shape = shape\n        self.size = size(shape)\n        self.data_type = data_type\n        \n"
  },
  {
    "path": "systolic_array_model/look_up_table.csv",
    "content": "64,16,4096,128,128,os,4349,5.886\n32,32,4096,128,128,os,4349,5.886\n64,32,4096,128,128,os,4349,11.773\n64,32,2048,128,128,os,2301,11.126\n64,16,2048,128,128,os,2301,5.563\n32,32,2048,128,128,os,2301,5.563\n64,32,1024,128,128,os,1277,10.023\n64,16,1024,128,128,os,1277,5.012\n32,32,1024,128,128,os,1277,5.012\n64,32,512,128,128,os,765,8.366\n64,16,512,128,128,os,765,4.183\n32,32,512,128,128,os,765,4.183\n64,32,256,128,128,os,509,6.287\n64,16,256,128,128,os,509,3.143\n32,32,256,128,128,os,509,3.143\n64,32,128,128,128,os,381,4.199\n64,64,4096,128,128,os,4349,23.546\n64,64,2048,128,128,os,2301,22.251\n64,64,1024,128,128,os,1277,20.047\n64,64,512,128,128,os,765,16.732\n64,64,256,128,128,os,509,12.574\n64,64,128,128,128,os,381,8.399\n32,128,4096,128,128,os,4349,23.546\n64,128,4096,128,128,os,4349,47.091\n64,128,2048,128,128,os,2301,44.502\n32,128,2048,128,128,os,2301,22.251\n64,128,1024,128,128,os,1277,40.094\n32,128,1024,128,128,os,1277,20.047\n64,128,512,128,128,os,765,33.464\n32,128,512,128,128,os,765,16.732\n64,128,256,128,128,os,509,25.147\n32,128,256,128,128,os,509,12.574\n64,128,128,128,128,os,381,16.798\n128,128,4096,128,128,os,4349,94.183\n128,128,2048,128,128,os,2301,89.005\n128,128,1024,128,128,os,1277,80.188\n128,128,512,128,128,os,765,66.928\n128,128,256,128,128,os,509,50.295\n128,128,128,128,128,os,381,33.596\n128,256,2048,128,128,os,4603,88.985\n64,256,2048,128,128,os,4603,44.493\n128,256,1024,128,128,os,2555,80.157\n64,256,1024,128,128,os,2555,40.078\n128,256,512,128,128,os,1531,66.884\n64,256,512,128,128,os,1531,33.442\n128,256,256,128,128,os,1019,50.245\n64,256,256,128,128,os,1019,25.123\n128,256,128,128,128,os,763,33.552\n256,256,1024,128,128,os,5111,80.141\n256,256,512,128,128,os,3063,66.863\n256,256,256,128,128,os,2039,50.221\n256,256,128,128,128,os,1527,33.53\n128,512,1024,128,128,os,5111,80.141\n256,512,512,128,128,os,6127,66.852\n128,512,512,128,128,os,3063,66.863\n256,512,256,128,128,os,4079,50.208\n128,512,256,128,128,os,2039,50.221\n256,512,128,128,128,os,3055,33.519\n512,512,256,128,128,os,8159,50.202\n512,512,128,128,128,os,6111,33.513\n256,1024,256,128,128,os,8159,50.202\n512,1024,128,128,128,os,12223,33.511\n"
  },
  {
    "path": "systolic_array_model/look_up_table_128_128.csv",
    "content": 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os,765,0.004\n1,1,256,128,128,os,509,0.003\n32,32,192,128,128,os,445,2.697\n1,32,192,128,128,os,445,0.084\n64,64,192,128,128,os,445,10.787\n1,64,192,128,128,os,445,0.169\n128,128,192,128,128,os,445,43.146\n1,128,192,128,128,os,445,0.337\n256,256,192,128,128,os,1783,43.073\n1,256,192,128,128,os,891,0.337\n256,128,192,128,128,os,891,43.098\n"
  },
  {
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    "content": 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079\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n3,64,8,16,16,os,151,3.974\n22,128,2,16,16,os,511,4.305\n6,128,16,16,16,os,367,13.079\n11,128,4,16,16,os,271,8.118\n6,128,16,16,16,os,367,13.079\n12,64,4,16,16,os,135,8.889\n22,128,2,16,16,os,511,4.305\n3,64,16,16,16,os,183,6.557\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n12,64,4,16,16,os,135,8.889\n3,64,16,16,16,os,183,6.557\n3,64,8,16,16,os,151,3.974\n22,128,4,16,16,os,543,8.103\n11,128,8,16,16,os,303,14.521\n11,128,4,16,16,os,271,8.118\n6,128,16,16,16,os,367,13.079\n6,128,8,16,16,os,303,7.921\n22,128,4,16,16,os,543,8.103\n6,128,16,16,16,os,367,13.079\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n22,128,4,16,16,os,543,8.103\n6,128,16,16,16,os,367,13.079\n12,64,4,16,16,os,135,8.889\n3,64,8,16,16,os,151,3.974\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n6,128,16,16,16,os,367,13.079\n11,128,8,16,16,os,303,14.521\n11,128,8,16,16,os,303,14.521\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n12,64,4,16,16,os,135,8.889\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n6,128,8,16,16,os,303,7.921\n11,128,8,16,16,os,303,14.521\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n3,64,8,16,16,os,151,3.974\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n12,64,4,16,16,os,135,8.889\n11,128,8,16,16,os,303,14.521\n11,128,4,16,16,os,271,8.118\n6,64,4,16,16,os,135,4.444\n6,128,16,16,16,os,367,13.079\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n6,64,4,16,16,os,135,4.444\n6,64,4,16,16,os,135,4.444\n11,128,4,16,16,os,271,8.118\n12,64,4,16,16,os,135,8.889\n6,128,16,16,16,os,367,13.079\n3,64,8,16,16,os,151,3.974\n11,128,8,16,16,os,303,14.521\n11,128,8,16,16,os,303,14.521\n6,128,8,16,16,os,303,7.921\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n12,64,4,16,16,os,135,8.889\n6,128,16,16,16,os,367,13.079\n6,128,8,16,16,os,303,7.921\n3,64,8,16,16,os,151,3.974\n3,64,16,16,16,os,183,6.557\n6,128,16,16,16,os,367,13.079\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n6,128,16,16,16,os,367,13.079\n12,64,4,16,16,os,135,8.889\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n11,128,8,16,16,os,303,14.521\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n6,128,16,16,16,os,367,13.079\n12,64,4,16,16,os,135,8.889\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n22,128,2,16,16,os,511,4.305\n6,128,16,16,16,os,367,13.079\n6,128,16,16,16,os,367,13.079\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n3,64,16,16,16,os,183,6.557\n6,64,4,16,16,os,135,4.444\n6,128,8,16,16,os,303,7.921\n6,64,4,16,16,os,135,4.444\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n11,128,8,16,16,os,303,14.521\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n6,64,4,16,16,os,135,4.444\n6,128,16,16,16,os,367,13.079\n12,64,4,16,16,os,135,8.889\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n3,64,8,16,16,os,151,3.974\n6,64,4,16,16,os,135,4.444\n6,128,8,16,16,os,303,7.921\n22,128,4,16,16,os,543,8.103\n6,128,8,16,16,os,303,7.921\n3,64,8,16,16,os,151,3.974\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n11,128,8,16,16,os,303,14.521\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n3,64,8,16,16,os,151,3.974\n6,64,4,16,16,os,135,4.444\n3,64,8,16,16,os,151,3.974\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n11,128,8,16,16,os,303,14.521\n6,64,4,16,16,os,135,4.444\n6,64,4,16,16,os,135,4.444\n6,128,16,16,16,os,367,13.079\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n12,64,2,16,16,os,127,4.724\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n12,64,2,16,16,os,127,4.724\n22,128,4,16,16,os,543,8.103\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n11,128,8,16,16,os,303,14.521\n22,128,4,16,16,os,543,8.103\n11,128,8,16,16,os,303,14.521\n22,128,4,16,16,os,543,8.103\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n6,64,4,16,16,os,135,4.444\n12,64,4,16,16,os,135,8.889\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n11,128,8,16,16,os,303,14.521\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n11,128,8,16,16,os,303,14.521\n6,64,8,16,16,os,151,7.947\n12,64,2,16,16,os,127,4.724\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n3,64,8,16,16,os,151,3.974\n11,128,8,16,16,os,303,14.521\n3,64,8,16,16,os,151,3.974\n3,64,16,16,16,os,183,6.557\n11,128,4,16,16,os,271,8.118\n11,128,8,16,16,os,303,14.521\n6,128,16,16,16,os,367,13.079\n12,8,8,16,16,os,37,8.108\n6,128,16,16,16,os,367,13.079\n22,128,4,16,16,os,543,8.103\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n6,128,8,16,16,os,303,7.921\n6,64,4,16,16,os,135,4.444\n12,64,2,16,16,os,127,4.724\n3,64,16,16,16,os,183,6.557\n11,128,8,16,16,os,303,14.521\n22,128,4,16,16,os,543,8.103\n3,64,8,16,16,os,151,3.974\n6,64,4,16,16,os,135,4.444\n11,128,8,16,16,os,303,14.521\n12,64,2,16,16,os,127,4.724\n22,128,4,16,16,os,543,8.103\n6,64,4,16,16,os,135,4.444\n22,128,4,16,16,os,543,8.103\n11,128,4,16,16,os,271,8.118\n6,64,4,16,16,os,135,4.444\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n11,128,8,16,16,os,303,14.521\n22,128,4,16,16,os,543,8.103\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n11,128,8,16,16,os,303,14.521\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n12,64,2,16,16,os,127,4.724\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n12,64,4,16,16,os,135,8.889\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n11,128,4,16,16,os,271,8.118\n12,64,2,16,16,os,127,4.724\n22,128,4,16,16,os,543,8.103\n6,128,8,16,16,os,303,7.921\n22,128,4,16,16,os,543,8.103\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n6,128,16,16,16,os,367,13.079\n22,128,4,16,16,os,543,8.103\n3,64,8,16,16,os,151,3.974\n12,64,2,16,16,os,127,4.724\n22,128,4,16,16,os,543,8.103\n6,64,4,16,16,os,135,4.444\n12,64,2,16,16,os,127,4.724\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n22,128,4,16,16,os,543,8.103\n11,128,8,16,16,os,303,14.521\n6,64,4,16,16,os,135,4.444\n12,64,4,16,16,os,135,8.889\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n22,128,4,16,16,os,543,8.103\n22,128,4,16,16,os,543,8.103\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n12,64,4,16,16,os,135,8.889\n6,128,16,16,16,os,367,13.079\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n6,128,16,16,16,os,367,13.079\n11,128,8,16,16,os,303,14.521\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n6,128,16,16,16,os,367,13.079\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n11,128,8,16,16,os,303,14.521\n22,128,2,16,16,os,511,4.305\n6,128,16,16,16,os,367,13.079\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n22,128,4,16,16,os,543,8.103\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n6,64,4,16,16,os,135,4.444\n22,128,4,16,16,os,543,8.103\n11,128,8,16,16,os,303,14.521\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n12,64,2,16,16,os,127,4.724\n12,64,2,16,16,os,127,4.724\n22,128,4,16,16,os,543,8.103\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n6,128,16,16,16,os,367,13.079\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n6,64,4,16,16,os,135,4.444\n22,128,4,16,16,os,543,8.103\n11,128,8,16,16,os,303,14.521\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n6,128,8,16,16,os,303,7.921\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n22,128,4,16,16,os,543,8.103\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n3,64,16,16,16,os,183,6.557\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n11,128,8,16,16,os,303,14.521\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n12,64,4,16,16,os,135,8.889\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n6,64,4,16,16,os,135,4.444\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n22,128,2,16,16,os,511,4.305\n22,128,4,16,16,os,543,8.103\n12,64,2,16,16,os,127,4.724\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n11,128,8,16,16,os,303,14.521\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n6,64,4,16,16,os,135,4.444\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n12,64,2,16,16,os,127,4.724\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n3,64,8,16,16,os,151,3.974\n6,128,8,16,16,os,303,7.921\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n3,64,8,16,16,os,151,3.974\n3,64,8,16,16,os,151,3.974\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n3,64,8,16,16,os,151,3.974\n22,128,2,16,16,os,511,4.305\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n6,64,4,16,16,os,135,4.444\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n6,64,4,16,16,os,135,4.444\n6,128,16,16,16,os,367,13.079\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n3,64,16,16,16,os,183,6.557\n6,64,4,16,16,os,135,4.444\n11,128,4,16,16,os,271,8.118\n11,128,8,16,16,os,303,14.521\n6,128,8,16,16,os,303,7.921\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n12,64,2,16,16,os,127,4.724\n6,128,8,16,16,os,303,7.921\n22,128,2,16,16,os,511,4.305\n3,64,8,16,16,os,151,3.974\n22,128,2,16,16,os,511,4.305\n12,64,4,16,16,os,135,8.889\n12,64,2,16,16,os,127,4.724\n11,128,4,16,16,os,271,8.118\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n11,128,4,16,16,os,271,8.118\n12,64,2,16,16,os,127,4.724\n12,64,2,16,16,os,127,4.724\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n11,128,4,16,16,os,271,8.118\n22,128,4,16,16,os,543,8.103\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n12,64,2,16,16,os,127,4.724\n12,64,4,16,16,os,135,8.889\n12,64,4,16,16,os,135,8.889\n12,64,4,16,16,os,135,8.889\n22,128,2,16,16,os,511,4.305\n19,128,16,16,16,os,735,20.680\n3,64,16,16,16,os,183,6.557\n3,64,16,16,16,os,183,6.557\n12,64,4,16,16,os,135,8.889\n12,64,4,16,16,os,135,8.889\n3,64,16,16,16,os,183,6.557\n76,64,8,16,16,os,759,20.026\n3,64,8,16,16,os,151,3.974\n12,64,4,16,16,os,135,8.889\n3,64,8,16,16,os,151,3.974\n3,64,8,16,16,os,151,3.974\n6,64,4,16,16,os,135,4.444\n6,128,8,16,16,os,303,7.921\n6,64,4,16,16,os,135,4.444\n6,64,4,16,16,os,135,4.444\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n12,64,2,16,16,os,127,4.724\n12,64,2,16,16,os,127,4.724\n12,64,2,16,16,os,127,4.724\n38,128,8,16,16,os,911,16.685\n11,128,4,16,16,os,271,8.118\n22,128,2,16,16,os,511,4.305\n12,64,4,16,16,os,135,8.889\n22,128,2,16,16,os,511,4.305\n3,64,8,16,16,os,151,3.974\n76,128,4,16,16,os,1359,11.185\n3,64,8,16,16,os,151,3.974\n3,64,8,16,16,os,151,3.974\n6,64,4,16,16,os,135,4.444\n76,64,8,16,16,os,759,20.026\n6,64,4,16,16,os,135,4.444\n76,32,16,16,16,os,459,33.115\n6,64,4,16,16,os,135,4.444\n19,128,16,16,16,os,735,20.680\n12,64,2,16,16,os,127,4.724\n12,64,2,16,16,os,127,4.724\n12,64,2,16,16,os,127,4.724\n76,64,8,16,16,os,759,20.026\n76,64,8,16,16,os,759,20.026\n3,64,8,16,16,os,151,3.974\n76,128,4,16,16,os,1359,11.185\n38,128,8,16,16,os,911,16.685\n6,64,4,16,16,os,135,4.444\n76,32,16,16,16,os,459,33.115\n12,64,2,16,16,os,127,4.724\n76,128,4,16,16,os,1359,11.185\n6,128,8,16,16,os,303,7.921\n76,128,4,16,16,os,1359,11.185\n19,128,8,16,16,os,607,12.521\n76,32,16,16,16,os,459,33.115\n3,64,8,16,16,os,151,3.974\n11,128,4,16,16,os,271,8.118\n3,64,8,16,16,os,151,3.974\n76,32,16,16,16,os,459,33.115\n22,128,2,16,16,os,511,4.305\n6,64,4,16,16,os,135,4.444\n6,64,4,16,16,os,135,4.444\n3,64,8,16,16,os,151,3.974\n76,64,4,16,16,os,679,11.193\n76,64,8,16,16,os,759,20.026\n76,64,8,16,16,os,759,20.026\n12,64,2,16,16,os,127,4.724\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n76,128,4,16,16,os,1359,11.185\n38,128,4,16,16,os,815,9.325\n38,128,8,16,16,os,911,16.685\n12,64,2,16,16,os,127,4.724\n76,64,8,16,16,os,759,20.026\n76,32,16,16,16,os,459,33.115\n76,64,8,16,16,os,759,20.026\n19,128,8,16,16,os,607,12.521\n76,128,4,16,16,os,1359,11.185\n3,64,8,16,16,os,151,3.974\n3,64,8,16,16,os,151,3.974\n76,64,8,16,16,os,759,20.026\n76,64,8,16,16,os,759,20.026\n76,32,16,16,16,os,459,33.115\n76,128,4,16,16,os,1359,11.185\n76,64,4,16,16,os,679,11.193\n3,64,8,16,16,os,151,3.974\n76,128,2,16,16,os,1279,5.942\n6,64,4,16,16,os,135,4.444\n76,64,8,16,16,os,759,20.026\n76,32,16,16,16,os,459,33.115\n19,128,16,16,16,os,735,20.680\n6,64,4,16,16,os,135,4.444\n76,128,4,16,16,os,1359,11.185\n38,128,4,16,16,os,815,9.325\n12,64,2,16,16,os,127,4.724\n6,64,4,16,16,os,135,4.444\n76,32,8,16,16,os,379,20.053\n12,64,2,16,16,os,127,4.724\n19,128,8,16,16,os,607,12.521\n76,128,4,16,16,os,1359,11.185\n76,64,8,16,16,os,759,20.026\n12,64,2,16,16,os,127,4.724\n76,32,16,16,16,os,459,33.115\n76,64,8,16,16,os,759,20.026\n3,64,8,16,16,os,151,3.974\n76,32,16,16,16,os,459,33.115\n76,128,4,16,16,os,1359,11.185\n76,64,8,16,16,os,759,20.026\n76,128,4,16,16,os,1359,11.185\n19,128,8,16,16,os,607,12.521\n76,64,4,16,16,os,679,11.193\n6,64,4,16,16,os,135,4.444\n38,128,8,16,16,os,911,16.685\n76,64,8,16,16,os,759,20.026\n38,128,4,16,16,os,815,9.325\n76,128,2,16,16,os,1279,5.942\n76,32,16,16,16,os,459,33.115\n76,128,4,16,16,os,1359,11.185\n76,128,4,16,16,os,1359,11.185\n76,64,4,16,16,os,679,11.193\n76,128,2,16,16,os,1279,5.942\n76,64,8,16,16,os,759,20.026\n76,32,16,16,16,os,459,33.115\n76,32,8,16,16,os,379,20.053\n12,64,2,16,16,os,127,4.724\n76,128,4,16,16,os,1359,11.185\n76,32,16,16,16,os,459,33.115\n76,32,16,16,16,os,459,33.115\n76,128,4,16,16,os,1359,11.185\n38,128,4,16,16,os,815,9.325\n38,128,8,16,16,os,911,16.685\n76,64,8,16,16,os,759,20.026\n76,32,8,16,16,os,379,20.053\n19,128,16,16,16,os,735,20.680\n76,32,16,16,16,os,459,33.115\n76,32,16,16,16,os,459,33.115\n76,64,8,16,16,os,759,20.026\n19,128,8,16,16,os,607,12.521\n22,128,4,16,16,os,543,8.103\n76,128,2,16,16,os,1279,5.942\n76,64,4,16,16,os,679,11.193\n76,64,8,16,16,os,759,20.026\n76,128,4,16,16,os,1359,11.185\n76,128,4,16,16,os,1359,11.185\n76,32,8,16,16,os,379,20.053\n76,32,16,16,16,os,459,33.115\n76,32,16,16,16,os,459,33.115\n76,128,4,16,16,os,1359,11.185\n38,128,4,16,16,os,815,9.325\n3,64,8,16,16,os,151,3.974\n38,128,8,16,16,os,911,16.685\n6,128,8,16,16,os,303,7.921\n11,128,4,16,16,os,271,8.118\n6,64,4,16,16,os,135,4.444\n19,128,16,16,16,os,735,20.680\n76,32,16,16,16,os,459,33.115\n22,128,2,16,16,os,511,4.305\n19,128,8,16,16,os,607,12.521\n19,128,8,16,16,os,607,12.521\n76,64,8,16,16,os,759,20.026\n76,128,4,16,16,os,1359,11.185\n76,32,16,16,16,os,459,33.115\n3,64,8,16,16,os,151,3.974\n38,128,8,16,16,os,911,16.685\n12,64,2,16,16,os,127,4.724\n76,128,2,16,16,os,1279,5.942\n76,64,4,16,16,os,679,11.193\n6,64,4,16,16,os,135,4.444\n19,128,8,16,16,os,607,12.521\n76,64,4,16,16,os,679,11.193\n76,64,8,16,16,os,759,20.026\n19,128,8,16,16,os,607,12.521\n12,64,2,16,16,os,127,4.724\n76,64,4,16,16,os,679,11.193\n19,128,8,16,16,os,607,12.521\n76,32,8,16,16,os,379,20.053\n76,128,4,16,16,os,1359,11.185\n38,128,4,16,16,os,8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4.954\n10,128,8,16,16,os,303,13.201\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n38,128,2,16,16,os,767,4.954\n10,128,16,16,16,os,367,21.798\n10,128,16,16,16,os,367,21.798\n10,128,16,16,16,os,367,21.798\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n10,128,16,16,16,os,367,21.798\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n10,128,16,16,16,os,367,21.798\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n10,128,8,16,16,os,303,13.201\n38,128,2,16,16,os,767,4.954\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n38,128,2,16,16,os,767,4.954\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n38,128,2,16,16,os,767,4.954\n10,128,8,16,16,os,303,13.201\n19,128,4,16,16,os,543,6.998\n38,128,2,16,16,os,767,4.954\n4,4,128,16,16,os,157,5.096\n1,32,128,16,16,os,315,5.079\n8,1,128,16,16,os,157,2.548\n1,1,128,16,16,os,157,0.318\n1,16,64,16,16,os,93,4.301\n32,1,64,16,16,os,187,4.278\n1,1,64,16,16,os,93,0.269\n1,16,128,16,16,os,157,5.096\n1,32,32,16,16,os,123,3.252\n1,1,32,16,16,os,61,0.205\n8,1,64,16,16,os,93,2.151\n1,16,32,16,16,os,61,3.279\n1,32,16,16,16,os,91,2.198\n1,1,16,16,16,os,45,0.139\n8,1,32,16,16,os,61,1.639\n1,16,16,16,16,os,45,2.222\n1,32,8,16,16,os,75,1.333\n1,1,8,16,16,os,37,0.084\n8,1,16,16,16,os,45,1.111\n1,16,8,16,16,os,37,1.351\n1,32,4,16,16,os,67,0.746\n1,1,4,16,16,os,33,0.047\n8,1,8,16,16,os,37,0.676\n1,16,4,16,16,os,33,0.758\n1,32,2,16,16,os,63,0.397\n1,1,2,16,16,os,31,0.025\n8,1,4,16,16,os,33,0.379\n1,16,2,16,16,os,31,0.403\n1,32,1,16,16,os,61,0.205\n1,1,1,16,16,os,30,0.013\n8,1,2,16,16,os,31,0.202\n1,16,1,16,16,os,30,0.208\n8,1,1,16,16,os,30,0.104\n1,64,128,16,16,os,631,5.071\n64,1,64,16,16,os,375,4.267\n1,64,32,16,16,os,247,3.239\n1,64,16,16,16,os,183,2.186\n1,64,8,16,16,os,151,1.325\n1,64,4,16,16,os,135,0.741\n1,64,2,16,16,os,127,0.394\n1,64,1,16,16,os,123,0.203\n128,1,64,16,16,os,751,4.261\n1,128,32,16,16,os,495,3.232\n1,128,16,16,16,os,367,2.180\n1,128,8,16,16,os,303,1.320\n1,128,4,16,16,os,271,0.738\n1,128,2,16,16,os,255,0.392\n1,128,1,16,16,os,247,0.202\n8,1,512,16,16,os,541,2.957\n1,1,512,16,16,os,541,0.370\n1,16,256,16,16,os,285,5.614\n32,1,256,16,16,os,571,5.604\n1,1,256,16,16,os,285,0.351\n1,16,512,16,16,os,541,5.915\n8,1,256,16,16,os,285,2.807\n8,32,192,16,16,os,443,43.341\n1,32,192,16,16,os,443,5.418\n32,16,96,16,16,os,251,76.494\n1,16,96,16,16,os,125,4.800\n1,32,96,16,16,os,251,4.781\n16,16,192,16,16,os,221,86.878\n1,16,192,16,16,os,221,5.430\n32,32,48,16,16,os,311,61.736\n1,32,48,16,16,os,155,3.871\n1,8,192,16,16,os,221,2.715\n16,64,192,16,16,os,887,86.584\n1,64,192,16,16,os,887,5.411\n64,32,96,16,16,os,1007,76.266\n1,64,96,16,16,os,503,4.771\n32,32,192,16,16,os,887,86.584\n64,64,48,16,16,os,1247,61.588\n1,64,48,16,16,os,311,3.859\n8,16,512,16,16,os,541,47.320\n8,16,512,16,16,os,541,47.320\n8,256,32,16,16,os,991,25.832\n4,256,32,16,16,os,991,12.916\n8,256,32,16,16,os,991,25.832\n8,256,16,16,16,os,735,17.415\n4,256,32,16,16,os,991,12.916\n2,256,32,16,16,os,991,6.458\n8,256,16,16,16,os,735,17.415\n4,256,16,16,16,os,735,8.707\n8,256,8,16,16,os,607,10.544\n2,256,32,16,16,os,991,6.458\n4,256,16,16,16,os,735,8.707\n8,256,8,16,16,os,607,10.544\n1,256,32,16,16,os,991,3.229\n1,256,16,16,16,os,735,2.177\n1,256,8,16,16,os,607,1.318\n1,256,4,16,16,os,543,0.737\n1,256,2,16,16,os,511,0.391\n1,256,1,16,16,os,495,0.202\n1,256,32,16,16,os,991,3.229\n1,256,16,16,16,os,735,2.177\n1,256,8,16,16,os,607,1.318\n1,256,4,16,16,os,543,0.737\n1,256,2,16,16,os,511,0.391\n1,256,1,16,16,os,495,0.202\n64,256,8,16,16,os,2431,21.061\n256,128,4,16,16,os,4351,11.767\n64,256,8,16,16,os,2431,21.061\n256,256,2,16,16,os,8191,6.251\n64,256,4,16,16,os,2175,11.770\n256,128,4,16,16,os,4351,11.767\n256,128,2,16,16,os,4095,6.252\n256,256,2,16,16,os,8191,6.251\n64,256,4,16,16,os,2175,11.770\n256,256,1,16,16,os,7935,3.226\n256,128,2,16,16,os,4095,6.252\n256,256,1,16,16,os,7935,3.226\n64,256,2,16,16,os,2047,6.253\n256,128,1,16,16,os,3967,3.227\n64,256,2,16,16,os,2047,6.253\n256,128,1,16,16,os,3967,3.227\n64,256,1,16,16,os,1983,3.227\n64,256,1,16,16,os,1983,3.227\n1,16,513,16,16,os,542,5.916\n1,32,257,16,16,os,573,5.606\n256,32,1,16,16,os,991,3.229\n256,32,16,16,16,os,1471,34.806\n256,32,1,16,16,os,991,3.229\n256,32,8,16,16,os,1215,21.070\n256,32,16,16,16,os,1471,34.806\n256,32,8,16,16,os,1215,21.070\n2,256,16,16,16,os,735,4.354\n4,256,8,16,16,os,607,5.272\n8,256,4,16,16,os,543,5.893\n2,256,8,16,16,os,607,2.636\n4,256,4,16,16,os,543,2.947\n8,256,2,16,16,os,511,3.131\n2,256,16,16,16,os,735,4.354\n4,256,8,16,16,os,607,5.272\n8,256,4,16,16,os,543,5.893\n2,256,8,16,16,os,607,2.636\n4,256,4,16,16,os,543,2.947\n8,256,2,16,16,os,511,3.131\n1,65,128,16,16,os,789,4.119\n1,33,64,16,16,os,281,2.936\n1,65,128,16,16,os,789,4.119\n1,65,64,16,16,os,469,3.465\n1,33,64,16,16,os,281,2.936\n1,33,128,16,16,os,473,3.488\n1,65,64,16,16,os,469,3.465\n1,65,32,16,16,os,309,2.629\n1,33,128,16,16,os,473,3.488\n1,17,128,16,16,os,315,2.698\n1,65,32,16,16,os,309,2.629\n1,65,128,16,16,os,789,4.119\n1,65,128,16,16,os,789,4.119\n1,17,128,16,16,os,315,2.698\n1,33,64,16,16,os,281,2.936\n32,65,64,16,16,os,939,55.378\n1,33,64,16,16,os,281,2.936\n1,65,64,16,16,os,469,3.465\n1,65,64,16,16,os,469,3.465\n32,65,64,16,16,os,939,55.378\n1,33,128,16,16,os,473,3.488\n1,33,128,16,16,os,473,3.488\n1,65,128,16,16,os,789,4.119\n128,33,32,16,16,os,1487,35.508\n1,65,32,16,16,os,309,2.629\n128,33,32,16,16,os,1487,35.508\n1,33,64,16,16,os,281,2.936\n1,65,32,16,16,os,309,2.629\n1,33,32,16,16,os,185,2.230\n1,17,128,16,16,os,315,2.698\n1,33,32,16,16,os,185,2.230\n1,17,128,16,16,os,315,2.698\n1,65,64,16,16,os,469,3.465\n64,65,32,16,16,os,1239,41.969\n32,65,64,16,16,os,939,55.378\n1,33,128,16,16,os,473,3.488\n32,65,64,16,16,os,939,55.378\n64,65,32,16,16,os,1239,41.969\n64,33,64,16,16,os,1127,46.850\n1,65,128,16,16,os,789,4.119\n1,65,32,16,16,os,309,2.629\n1,65,32,16,16,os,309,2.629\n128,33,32,16,16,os,1487,35.508\n1,33,64,16,16,os,281,2.936\n128,33,32,16,16,os,1487,35.508\n64,33,64,16,16,os,1127,46.850\n1,65,32,16,16,os,309,2.629\n1,17,128,16,16,os,315,2.698\n1,33,32,16,16,os,185,2.230\n1,17,128,16,16,os,315,2.698\n1,33,32,16,16,os,185,2.230\n128,65,16,16,16,os,1839,28.276\n1,65,64,16,16,os,469,3.465\n1,17,128,16,16,os,315,2.698\n1,65,128,16,16,os,789,4.119\n32,65,64,16,16,os,939,55.378\n128,65,16,16,16,os,1839,28.276\n1,65,16,16,16,os,229,1.774\n1,33,128,16,16,os,473,3.488\n32,65,64,16,16,os,939,55.378\n64,65,32,16,16,os,1239,41.969\n64,65,32,16,16,os,1239,41.969\n1,33,64,16,16,os,281,2.936\n32,65,64,16,16,os,939,55.378\n1,65,16,16,16,os,229,1.774\n128,33,32,16,16,os,1487,35.508\n1,65,32,16,16,os,309,2.629\n1,65,64,16,16,os,469,3.465\n64,33,64,16,16,os,1127,46.850\n1,33,32,16,16,os,185,2.230\n128,17,64,16,16,os,1503,36.194\n128,33,32,16,16,os,1487,35.508\n1,17,128,16,16,os,315,2.698\n1,17,128,16,16,os,315,2.698\n1,33,32,16,16,os,185,2.230\n64,33,64,16,16,os,1127,46.850\n1,65,64,16,16,os,469,3.465\n1,33,128,16,16,os,473,3.488\n128,17,64,16,16,os,1503,36.194\n128,33,32,16,16,os,1487,35.508\n1,33,32,16,16,os,185,2.230\n1,17,64,16,16,os,187,2.273\n64,65,32,16,16,os,1239,41.969\n128,65,16,16,16,os,1839,28.276\n32,65,64,16,16,os,939,55.378\n32,65,64,16,16,os,939,55.378\n128,65,16,16,16,os,1839,28.276\n1,65,32,16,16,os,309,2.629\n1,17,64,16,16,os,187,2.273\n1,33,32,16,16,os,185,2.230\n32,65,32,16,16,os,619,42.003\n64,65,32,16,16,os,1239,41.969\n1,33,128,16,16,os,473,3.488\n1,65,16,16,16,os,229,1.774\n1,65,16,16,16,os,229,1.774\n128,65,16,16,16,os,1839,28.276\n64,65,32,16,16,os,1239,41.969\n64,33,64,16,16,os,1127,46.850\n1,17,128,16,16,os,315,2.698\n32,65,32,16,16,os,619,42.003\n64,65,32,16,16,os,1239,41.969\n1,65,32,16,16,os,309,2.629\n128,33,32,16,16,os,1487,35.508\n64,33,64,16,16,os,1127,46.850\n32,65,64,16,16,os,939,55.378\n64,65,32,16,16,os,1239,41.969\n1,65,16,16,16,os,229,1.774\n128,33,32,16,16,os,1487,35.508\n128,33,16,16,16,os,1103,23.935\n128,17,64,16,16,os,1503,36.194\n1,17,128,16,16,os,315,2.698\n32,65,64,16,16,os,939,55.378\n64,33,64,16,16,os,1127,46.850\n128,33,32,16,16,os,1487,35.508\n64,33,64,16,16,os,1127,46.850\n1,33,32,16,16,os,185,2.230\n128,33,16,16,16,os,1103,23.935\n1,33,16,16,16,os,137,1.505\n128,65,16,16,16,os,1839,28.276\n1,17,64,16,16,os,187,2.273\n128,65,16,16,16,os,1839,28.276\n1,33,32,16,16,os,185,2.230\n64,33,64,16,16,os,1127,46.850\n128,17,64,16,16,os,1503,36.194\n128,33,32,16,16,os,1487,35.508\n1,33,32,16,16,os,185,2.230\n1,33,16,16,16,os,137,1.505\n64,33,64,16,16,os,1127,46.850\n32,65,64,16,16,os,939,55.378\n64,65,32,16,16,os,1239,41.969\n128,17,64,16,16,os,1503,36.194\n32,65,32,16,16,os,619,42.003\n128,65,16,16,16,os,1839,28.276\n1,65,16,16,16,os,229,1.774\n64,65,16,16,16,os,919,28.292\n1,65,16,16,16,os,229,1.774\n128,65,16,16,16,os,1839,28.276\n1,17,64,16,16,os,187,2.273\n128,65,16,16,16,os,1839,28.276\n64,65,32,16,16,os,1239,41.969\n64,65,16,16,16,os,919,28.292\n1,33,32,16,16,os,185,2.230\n1,65,16,16,16,os,229,1.774\n64,33,64,16,16,os,1127,46.850\n1,17,64,16,16,os,187,2.273\n64,65,32,16,16,os,1239,41.969\n128,33,16,16,16,os,1103,23.935\n1,65,16,16,16,os,229,1.774\n128,33,32,16,16,os,1487,35.508\n128,65,16,16,16,os,1839,28.276\n1,17,64,16,16,os,187,2.273\n1,65,16,16,16,os,229,1.774\n64,33,64,16,16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16,16,os,1279,5.082\n1,65,2,16,16,os,159,0.319\n64,33,8,16,16,os,455,14.505\n1,17,8,16,16,os,75,0.708\n1,17,8,16,16,os,75,0.708\n1,33,4,16,16,os,101,0.511\n128,33,2,16,16,os,767,4.302\n64,33,4,16,16,os,407,8.108\n64,33,4,16,16,os,407,8.108\n64,65,2,16,16,os,639,5.086\n1,65,2,16,16,os,159,0.319\n128,33,2,16,16,os,767,4.302\n1,33,2,16,16,os,95,0.271\n64,65,2,16,16,os,639,5.086\n64,65,4,16,16,os,679,9.573\n1,65,1,16,16,os,154,0.165\n1,17,8,16,16,os,75,0.708\n64,65,2,16,16,os,639,5.086\n32,65,4,16,16,os,339,9.587\n1,33,2,16,16,os,95,0.271\n64,33,8,16,16,os,455,14.505\n64,65,2,16,16,os,639,5.086\n128,17,8,16,16,os,607,11.203\n64,33,4,16,16,os,407,8.108\n32,65,4,16,16,os,339,9.587\n64,33,8,16,16,os,455,14.505\n1,33,2,16,16,os,95,0.271\n64,33,4,16,16,os,407,8.108\n128,17,8,16,16,os,607,11.203\n128,33,2,16,16,os,767,4.302\n1,33,2,16,16,os,95,0.271\n1,65,2,16,16,os,159,0.319\n64,65,2,16,16,os,639,5.086\n64,65,2,16,16,os,639,5.086\n128,17,8,16,16,os,607,11.203\n1,65,1,16,16,os,154,0.165\n128,17,8,16,16,os,607,11.203\n32,65,4,16,16,os,339,9.587\n32,65,4,16,16,os,339,9.587\n64,33,8,16,16,os,455,14.505\n128,65,2,16,16,os,1279,5.082\n1,65,1,16,16,os,154,0.165\n1,33,2,16,16,os,95,0.271\n1,17,8,16,16,os,75,0.708\n1,33,2,16,16,os,95,0.271\n64,65,4,16,16,os,679,9.573\n128,17,8,16,16,os,607,11.203\n128,17,8,16,16,os,607,11.203\n1,33,2,16,16,os,95,0.271\n128,17,8,16,16,os,607,11.203\n64,65,2,16,16,os,639,5.086\n32,65,4,16,16,os,339,9.587\n128,17,4,16,16,os,543,6.262\n1,17,4,16,16,os,67,0.396\n32,65,2,16,16,os,319,5.094\n128,17,4,16,16,os,543,6.262\n128,33,1,16,16,os,743,2.221\n1,17,4,16,16,os,67,0.396\n1,33,1,16,16,os,92,0.140\n64,65,1,16,16,os,619,2.625\n32,65,2,16,16,os,319,5.094\n64,33,2,16,16,os,383,4.308\n128,17,4,16,16,os,543,6.262\n128,33,1,16,16,os,743,2.221\n128,17,2,16,16,os,511,3.327\n1,17,4,16,16,os,67,0.396\n1,33,1,16,16,os,92,0.140\n1,17,2,16,16,os,63,0.211\n64,65,1,16,16,os,619,2.625\n64,33,2,16,16,os,383,4.308\n32,65,1,16,16,os,309,2.629\n32,65,2,16,16,os,319,5.094\n128,17,4,16,16,os,543,6.262\n64,33,1,16,16,os,371,2.224\n1,17,4,16,16,os,67,0.396\n128,17,2,16,16,os,511,3.327\n128,33,1,16,16,os,743,2.221\n1,17,2,16,16,os,63,0.211\n128,17,1,16,16,os,495,1.717\n1,33,1,16,16,os,92,0.140\n32,65,2,16,16,os,319,5.094\n1,17,1,16,16,os,61,0.109\n64,65,1,16,16,os,619,2.625\n128,33,1,16,16,os,743,2.221\n64,33,2,16,16,os,383,4.308\n32,65,1,16,16,os,309,2.629\n1,33,1,16,16,os,92,0.140\n128,17,2,16,16,os,511,3.327\n128,17,2,16,16,os,511,3.327\n128,17,4,16,16,os,543,6.262\n64,33,1,16,16,os,371,2.224\n64,65,1,16,16,os,619,2.625\n64,65,1,16,16,os,619,2.625\n1,17,2,16,16,os,63,0.211\n1,17,4,16,16,os,67,0.396\n1,17,2,16,16,os,63,0.211\n64,33,2,16,16,os,383,4.308\n128,17,1,16,16,os,495,1.717\n128,33,1,16,16,os,743,2.221\n64,33,2,16,16,os,383,4.308\n32,65,1,16,16,os,309,2.629\n32,65,1,16,16,os,309,2.629\n1,17,1,16,16,os,61,0.109\n32,65,2,16,16,os,319,5.094\n32,65,2,16,16,os,319,5.094\n128,17,2,16,16,os,511,3.327\n128,17,2,16,16,os,511,3.327\n64,33,1,16,16,os,371,2.224\n32,65,1,16,16,os,309,2.629\n1,33,1,16,16,os,92,0.140\n64,33,1,16,16,os,371,2.224\n128,33,1,16,16,os,743,2.221\n1,17,2,16,16,os,63,0.211\n1,17,2,16,16,os,63,0.211\n128,33,1,16,16,os,743,2.221\n128,17,1,16,16,os,495,1.717\n128,33,1,16,16,os,743,2.221\n1,33,1,16,16,os,92,0.140\n64,33,1,16,16,os,371,2.224\n64,65,1,16,16,os,619,2.625\n128,17,1,16,16,os,495,1.717\n1,33,1,16,16,os,92,0.140\n1,17,1,16,16,os,61,0.109\n1,33,1,16,16,os,92,0.140\n64,33,2,16,16,os,383,4.308\n1,17,1,16,16,os,61,0.109\n128,17,1,16,16,os,495,1.717\n64,65,1,16,16,os,619,2.625\n32,65,1,16,16,os,309,2.629\n64,65,1,16,16,os,619,2.625\n64,65,1,16,16,os,619,2.625\n32,65,1,16,16,os,309,2.629\n128,17,2,16,16,os,511,3.327\n1,17,1,16,16,os,61,0.109\n64,33,2,16,16,os,383,4.308\n64,33,2,16,16,os,383,4.308\n64,33,2,16,16,os,383,4.308\n1,17,2,16,16,os,63,0.211\n64,33,1,16,16,os,371,2.224\n64,33,1,16,16,os,371,2.224\n128,17,2,16,16,os,511,3.327\n128,17,2,16,16,os,511,3.327\n128,17,2,16,16,os,511,3.327\n128,17,1,16,16,os,495,1.717\n1,17,2,16,16,os,63,0.211\n128,17,1,16,16,os,495,1.717\n32,65,1,16,16,os,309,2.629\n1,17,2,16,16,os,63,0.211\n1,17,2,16,16,os,63,0.211\n1,17,1,16,16,os,61,0.109\n1,17,1,16,16,os,61,0.109\n64,33,1,16,16,os,371,2.224\n32,65,1,16,16,os,309,2.629\n32,65,1,16,16,os,309,2.629\n128,17,1,16,16,os,495,1.717\n64,33,1,16,16,os,371,2.224\n1,17,2,16,16,os,63,0.211\n1,17,1,16,16,os,61,0.109\n64,33,1,16,16,os,371,2.224\n32,65,1,16,16,os,309,2.629\n32,65,1,16,16,os,309,2.629\n128,17,1,16,16,os,495,1.717\n64,33,1,16,16,os,371,2.224\n128,17,1,16,16,os,495,1.717\n64,33,1,16,16,os,371,2.224\n128,17,1,16,16,os,495,1.717\n64,33,1,16,16,os,371,2.224\n32,65,1,16,16,os,309,2.629\n1,17,1,16,16,os,61,0.109\n1,17,1,16,16,os,61,0.109\n1,17,1,16,16,os,61,0.109\n128,17,1,16,16,os,495,1.717\n128,17,1,16,16,os,495,1.717\n128,17,1,16,16,os,495,1.717\n64,33,1,16,16,os,371,2.224\n1,17,1,16,16,os,61,0.109\n1,17,1,16,16,os,61,0.109\n1,17,1,16,16,os,61,0.109\n128,17,1,16,16,os,495,1.717\n1,17,1,16,16,os,61,0.109\n8,32,129,16,1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n29,32,128,16,16,os,631,73.534\n12,128,32,16,16,os,495,38.788\n13,8,512,16,16,os,541,38.447\n12,16,512,16,16,os,541,70.980\n29,32,128,16,16,os,631,73.534\n7,16,512,16,16,os,541,41.405\n12,128,32,16,16,os,495,38.788\n20,16,128,16,16,os,315,50.794\n29,8,512,16,16,os,1083,42.844\n18,32,128,16,16,os,631,45.642\n12,128,32,16,16,os,495,38.788\n18,32,128,16,16,os,631,45.642\n23,32,128,16,16,os,631,58.320\n2,16,64,16,16,os,93,8.602\n23,32,128,16,16,os,631,58.320\n29,32,128,16,16,os,631,73.534\n2,8,256,16,16,os,285,5.614\n9,32,256,16,16,os,571,50.438\n10,16,256,16,16,os,285,56.140\n29,32,128,16,16,os,631,73.534\n20,16,128,16,16,os,315,50.794\n17,32,128,16,16,os,631,43.106\n17,32,128,16,16,os,631,43.106\n23,8,512,16,16,os,1083,33.980\n2,8,256,16,16,os,285,5.614\n13,8,512,16,16,os,541,38.447\n2,8,256,16,16,os,285,5.614\n17,8,512,16,16,os,1083,25.115\n17,32,128,16,16,os,631,43.106\n17,32,128,16,16,os,631,43.106\n23,8,512,16,16,os,1083,33.980\n17,32,128,16,16,os,631,43.106\n9,32,256,16,16,os,571,50.438\n23,8,512,16,16,os,1083,33.980\n10,32,128,16,16,os,315,50.794\n23,8,512,16,16,os,1083,33.980\n17,8,512,16,16,os,1083,25.115\n13,8,512,16,16,os,541,38.447\n23,8,512,16,16,os,1083,33.980\n29,32,128,16,16,os,631,73.534\n13,8,512,16,16,os,541,38.447\n29,32,128,16,16,os,631,73.534\n19,16,128,16,16,os,315,48.254\n9,32,256,16,16,os,571,50.438\n23,32,128,16,16,os,631,58.320\n9,32,256,16,16,os,571,50.438\n29,32,128,16,16,os,631,73.534\n10,32,128,16,16,os,315,50.794\n23,8,512,16,16,os,1083,33.980\n23,8,512,16,16,os,1083,33.980\n9,32,256,16,16,os,571,50.438\n9,8,512,16,16,os,541,26.617\n23,8,512,16,16,os,1083,33.980\n23,8,512,16,16,os,1083,33.980\n23,8,512,16,16,os,1083,33.980\n23,8,512,16,16,os,1083,33.980\n23,16,128,16,16,os,315,58.413\n9,8,512,16,16,os,541,26.617\n7,16,512,16,16,os,541,41.405\n20,8,512,16,16,os,1083,29.548\n9,16,128,16,16,os,157,45.860\n20,8,512,16,16,os,1083,29.548\n23,32,128,16,16,os,631,58.320\n29,8,512,16,16,os,1083,42.844\n13,8,512,16,16,os,541,38.447\n20,16,128,16,16,os,315,50.794\n29,8,512,16,16,os,1083,42.844\n15,32,128,16,16,os,315,76.190\n20,16,128,16,16,os,315,50.794\n20,8,512,16,16,os,1083,29.548\n23,8,512,16,16,os,1083,33.980\n9,32,128,16,16,os,315,45.714\n12,16,512,16,16,os,541,70.980\n20,8,512,16,16,os,1083,29.548\n7,16,512,16,16,os,541,41.405\n9,8,512,16,16,os,541,26.617\n12,16,512,16,16,os,541,70.980\n20,8,512,16,16,os,1083,29.548\n29,8,512,16,16,os,1083,42.844\n20,8,512,16,16,os,1083,29.548\n2,16,64,16,16,os,93,8.602\n15,32,128,16,16,os,315,76.190\n29,8,512,16,16,os,1083,42.844\n9,32,256,16,16,os,571,50.438\n9,16,128,16,16,os,157,45.860\n9,32,128,16,16,os,315,45.714\n23,16,128,16,16,os,315,58.413\n2,16,32,16,16,os,61,6.557\n17,32,128,16,16,os,631,43.106\n29,32,128,16,16,os,631,73.534\n20,16,128,16,16,os,315,50.794\n12,16,512,16,16,os,541,70.980\n12,16,512,16,16,os,541,70.980\n9,16,512,16,16,os,541,53.235\n5,32,256,16,16,os,571,28.021\n23,32,128,16,16,os,631,58.320\n9,16,512,16,16,os,541,53.235\n23,32,128,16,16,os,631,58.320\n23,32,128,16,16,os,631,58.320\n29,32,128,16,16,os,631,73.534\n20,16,128,16,16,os,315,50.794\n9,16,512,16,16,os,541,53.235\n9,16,128,16,16,os,157,45.860\n5,16,64,16,16,os,93,21.505\n29,32,128,16,16,os,631,73.534\n15,32,128,16,16,os,315,76.190\n12,16,512,16,16,os,541,70.980\n2,8,256,16,16,os,285,5.614\n2,8,256,16,16,os,285,5.614\n5,16,64,16,16,os,93,21.505\n17,32,128,16,16,os,631,43.106\n20,8,512,16,16,os,1083,29.548\n20,8,512,16,16,os,1083,29.548\n17,32,128,16,16,os,631,43.106\n20,8,512,16,16,os,1083,29.548\n9,16,512,16,16,os,541,53.235\n23,16,128,16,16,os,315,58.413\n2,8,128,16,16,os,157,5.096\n23,8,512,16,16,os,1083,33.980\n12,16,512,16,16,os,541,70.980\n20,8,512,16,16,os,1083,29.548\n29,8,512,16,16,os,1083,42.844\n9,16,128,16,16,os,157,45.860\n3,128,64,16,16,os,751,12.783\n2,16,64,16,16,os,93,8.602\n15,32,128,16,16,os,315,76.190\n7,16,512,16,16,os,541,41.405\n23,32,128,16,16,os,631,58.320\n29,8,512,16,16,os,1083,42.844\n18,32,128,16,16,os,631,45.642\n29,32,128,16,16,os,631,73.534\n3,128,64,16,16,os,751,12.783\n20,8,512,16,16,os,1083,29.548\n29,8,512,16,16,os,1083,42.844\n20,8,512,16,16,os,1083,29.548\n20,8,512,16,16,os,1083,29.548\n12,16,512,16,16,os,541,70.980\n20,16,128,16,16,os,315,50.794\n29,8,512,16,16,os,1083,42.844\n23,8,512,16,16,os,1083,33.980\n3,128,64,16,16,os,751,12.783\n15,32,128,16,16,os,315,76.190\n18,32,128,16,16,os,631,45.642\n29,32,128,16,16,os,631,73.534\n3,128,64,16,16,os,751,12.783\n29,8,512,16,16,os,1083,42.844\n18,32,128,16,16,os,631,45.642\n29,32,128,16,16,os,631,73.534\n17,32,128,16,16,os,631,43.106\n18,32,128,16,16,os,631,45.642\n5,16,64,16,16,os,93,21.505\n23,32,64,16,16,os,375,49.067\n17,32,128,16,16,os,631,43.106\n12,16,512,16,16,os,541,70.980\n2,8,256,16,16,os,285,5.614\n18,8,512,16,16,os,1083,26.593\n29,8,512,16,16,os,1083,42.844\n23,8,512,16,16,os,1083,33.980\n18,8,512,16,16,os,1083,26.593\n5,16,64,16,16,os,93,21.505\n23,8,512,16,16,os,1083,33.980\n29,32,128,16,16,os,631,73.534\n9,16,512,16,16,os,541,53.235\n23,8,512,16,16,os,1083,33.980\n23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607,19.110\n51,16,32,16,16,os,247,41.296\n5,128,64,16,16,os,751,21.305\n5,128,64,16,16,os,751,21.305\n51,16,32,16,16,os,247,41.296\n41,128,16,16,16,os,1103,29.737\n9,128,32,16,16,os,495,29.091\n51,16,32,16,16,os,247,41.296\n29,128,8,16,16,os,607,19.110\n51,64,8,16,16,os,607,16.804\n18,128,8,16,16,os,607,11.862\n5,128,32,16,16,os,495,16.162\n5,128,32,16,16,os,495,16.162\n18,128,32,16,16,os,991,29.062\n5,128,64,16,16,os,751,21.305\n9,128,32,16,16,os,495,29.091\n15,128,16,16,16,os,367,32.698\n5,128,64,16,16,os,751,21.305\n18,128,32,16,16,os,991,29.062\n15,128,16,16,16,os,367,32.698\n5,128,64,16,16,os,751,21.305\n29,128,8,16,16,os,607,19.110\n9,128,16,16,16,os,367,19.619\n41,128,16,16,16,os,1103,29.737\n41,128,16,16,16,os,1103,29.737\n21,128,64,16,16,os,1503,44.711\n21,128,64,16,16,os,1503,44.711\n5,128,64,16,16,os,751,21.305\n21,128,64,16,16,os,1503,44.711\n9,128,16,16,16,os,367,19.619\n51,128,32,16,16,os,1983,41.150\n9,128,32,16,16,os,495,29.091\n18,128,16,16,16,os,735,19.592\n26,128,64,16,16,os,1503,55.356\n5,128,64,16,16,os,751,21.305\n9,128,32,16,16,os,495,29.091\n34,128,8,16,16,os,911,14.929\n9,128,16,16,16,os,367,19.619\n21,128,64,16,16,os,1503,44.711\n9,128,16,16,16,os,367,19.619\n9,128,32,16,16,os,495,29.091\n9,128,16,16,16,os,367,19.619\n5,128,32,16,16,os,495,16.162\n9,128,64,16,16,os,751,38.349\n21,128,64,16,16,os,1503,44.711\n5,128,32,16,16,os,495,16.162\n18,128,16,16,16,os,735,19.592\n9,128,32,16,16,os,495,29.091\n26,128,64,16,16,os,1503,55.356\n5,128,32,16,16,os,495,16.162\n18,128,16,16,16,os,735,19.592\n9,128,64,16,16,os,751,38.349\n29,128,8,16,16,os,607,19.110\n26,128,64,16,16,os,1503,55.356\n9,128,32,16,16,os,495,29.091\n5,128,32,16,16,os,495,16.162\n9,128,16,16,16,os,367,19.619\n5,128,32,16,16,os,495,16.162\n41,128,32,16,16,os,1487,44.116\n9,128,16,16,16,os,367,19.619\n5,128,64,16,16,os,751,21.305\n18,128,16,16,16,os,735,19.592\n41,128,16,16,16,os,1103,29.737\n9,128,32,16,16,os,495,29.091\n41,128,32,16,16,os,1487,44.116\n18,128,32,16,16,os,991,29.062\n29,128,8,16,16,os,607,19.110\n51,128,32,16,16,os,1983,41.150\n21,128,32,16,16,os,991,33.905\n9,128,32,16,16,os,495,29.091\n29,128,8,16,16,os,607,19.110\n41,128,16,16,16,os,1103,29.737\n9,128,16,16,16,os,367,19.619\n9,128,16,16,16,os,367,19.619\n5,128,64,16,16,os,751,21.305\n5,128,32,16,16,os,495,16.162\n51,16,32,16,16,os,247,41.296\n18,128,32,16,16,os,991,29.062\n21,128,32,16,16,os,991,33.905\n9,128,32,16,16,os,495,29.091\n29,128,8,16,16,os,607,19.110\n26,128,64,16,16,os,1503,55.356\n9,128,32,16,16,os,495,29.091\n9,128,16,16,16,os,367,19.619\n51,64,8,16,16,os,607,16.804\n26,128,64,16,16,os,1503,55.356\n9,128,32,16,16,os,495,29.091\n26,128,64,16,16,os,1503,55.356\n51,16,32,16,16,os,247,41.296\n18,128,32,16,16,os,991,29.062\n21,128,64,16,16,os,1503,44.711\n5,128,64,16,16,os,751,21.305\n9,128,16,16,16,os,367,19.619\n5,128,64,16,16,os,751,21.305\n18,128,32,16,16,os,991,29.062\n21,128,64,16,16,os,1503,44.711\n9,128,32,16,16,os,495,29.091\n26,128,64,16,16,os,1503,55.356\n9,128,16,16,16,os,367,19.619\n5,128,32,16,16,os,495,16.162\n9,128,32,16,16,os,495,29.091\n9,128,32,16,16,os,495,29.091\n18,128,16,16,16,os,735,19.592\n5,128,32,16,16,os,495,16.162\n5,128,32,16,16,os,495,16.162\n9,128,16,16,16,os,367,19.619\n18,128,16,16,16,os,735,19.592\n9,128,32,16,16,os,495,29.091\n5,128,64,16,16,os,751,21.305\n29,128,8,16,16,os,607,19.110\n41,128,32,16,16,os,1487,44.116\n5,128,64,16,16,os,751,21.305\n41,128,8,16,16,os,911,18.002\n5,128,64,16,16,os,751,21.305\n9,128,32,16,16,os,495,29.091\n9,128,32,16,16,os,495,29.091\n9,128,32,16,16,os,495,29.091\n9,128,32,16,16,os,495,29.091\n9,128,16,16,16,os,367,19.619\n5,128,32,16,16,os,495,16.162\n21,128,32,16,16,os,991,33.905\n9,128,16,16,16,os,367,19.619\n41,128,32,16,16,os,1487,44.116\n9,128,32,16,16,os,495,29.091\n21,128,64,16,16,os,1503,44.711\n29,128,8,16,16,os,607,19.110\n18,128,16,16,16,os,735,19.592\n5,128,32,16,16,os,495,16.162\n5,128,32,16,16,os,495,16.162\n9,128,32,16,16,os,495,29.091\n9,128,32,16,16,os,495,29.091\n29,128,8,16,16,os,607,19.110\n18,128,16,16,16,os,735,19.592\n5,128,32,16,16,os,495,16.162\n5,128,32,16,16,os,495,16.162\n21,128,64,16,16,os,1503,44.711\n9,128,16,16,16,os,367,19.619\n21,128,64,16,16,os,1503,44.711\n21,128,64,16,16,os,1503,44.711\n5,128,64,16,16,os,751,21.305\n5,128,32,16,16,os,495,16.162\n5,128,32,16,16,os,495,16.162\n41,128,32,16,16,os,1487,44.116\n5,128,32,16,16,os,495,16.162\n5,128,32,16,16,os,495,16.162\n21,128,16,16,16,os,735,22.857\n5,128,32,16,16,os,495,16.162\n9,128,32,16,16,os,495,29.091\n41,128,32,16,16,os,1487,44.116\n21,128,64,16,16,os,1503,44.711\n9,128,16,16,16,os,367,19.619\n9,128,16,16,16,os,367,19.619\n5,128,64,16,16,os,751,21.305\n26,128,32,16,16,os,991,41.978\n5,128,32,16,16,os,495,16.162\n18,128,16,16,16,os,735,19.592\n5,128,64,16,16,os,751,21.305\n9,128,16,16,16,os,367,19.619\n9,128,16,16,16,os,367,19.619\n9,128,16,16,16,os,367,19.619\n26,128,64,16,16,os,1503,55.356\n26,128,64,16,16,os,1503,55.356\n41,128,32,16,16,os,1487,44.116\n21,128,64,16,16,os,1503,44.711\n9,128,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  {
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  },
  {
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32,128,60,16,16,is,1391,69.015\n32,32,536,16,16,is,5303,40.43\n16,64,536,16,16,is,3739,57.342\n64,64,136,16,16,is,3959,54.963\n32,128,136,16,16,is,3131,69.499\n64,128,72,16,16,is,3479,66.226\n32,256,72,16,16,is,3019,76.317\n32,32,268,16,16,is,2651,40.438\n16,64,268,16,16,is,1869,57.357\n64,64,68,16,16,is,2199,49.477\n32,128,68,16,16,is,1739,62.565\n64,128,36,16,16,is,2087,55.199\n32,256,36,16,16,is,1811,63.611\n128,64,72,16,16,is,4399,52.376\n128,64,36,16,16,is,2639,43.653\n64,64,152,16,16,is,4399,55.285\n32,128,152,16,16,is,3479,69.905\n64,64,76,16,16,is,2199,55.298\n32,128,76,16,16,is,1739,69.925\n32,32,760,16,16,is,7487,40.604\n16,64,760,16,16,is,5279,57.587\n32,32,380,16,16,is,3743,40.609\n16,64,380,16,16,is,2639,57.598\n64,64,232,16,16,is,6599,56.251\n32,128,232,16,16,is,5219,71.125\n64,64,116,16,16,is,3519,52.742\n32,128,116,16,16,is,2783,66.691\n16,16,2124,16,16,is,8245,25.761\n32,32,532,16,16,is,5303,40.128\n16,64,532,16,16,is,3739,56.914\n16,16,2428,16,16,is,9423,25.767\n16,16,3036,16,16,is,11779,25.775\n16,16,3644,16,16,is,14135,25.78\n64,64,228,16,16,is,6599,55.281\n32,128,228,16,16,is,5219,69.898\n1,1,1,16,16,os,30,0.013\n1,1,2,16,16,os,31,0.025\n1,1,4,16,16,os,33,0.047\n1,1,8,16,16,os,37,0.084\n1,1,16,16,16,os,45,0.139\n1,1,32,16,16,os,61,0.205\n1,2,1,16,16,os,30,0.026\n1,2,2,16,16,os,31,0.05\n1,2,4,16,16,os,33,0.095\n1,2,8,16,16,os,37,0.169\n1,2,16,16,16,os,45,0.278\n1,2,32,16,16,os,61,0.41\n1,4,1,16,16,os,30,0.052\n1,4,2,16,16,os,31,0.101\n1,4,4,16,16,os,33,0.189\n1,4,8,16,16,os,37,0.338\n1,4,16,16,16,os,45,0.556\n8,512,32,16,16,os,1983,25.819\n16,512,16,16,16,os,1471,34.806\n32,512,8,16,16,os,2431,21.061\n512,16,16,16,16,os,1471,34.806\n512,32,8,16,16,os,2431,21.061\n512,8,32,16,16,os,1983,25.819\n8,32,384,16,16,os,827,46.433\n32,8,384,16,16,os,827,46.433\n8,32,192,16,16,os,443,43.341\n32,8,192,16,16,os,443,43.341\n8,64,192,16,16,os,887,43.292\n64,8,192,16,16,os,887,43.292\n8,32,96,16,16,os,251,38.247\n32,8,96,16,16,os,251,38.247\n8,64,96,16,16,os,503,38.171\n64,8,96,16,16,os,503,38.171\n8,128,96,16,16,os,1007,38.133\n128,8,96,16,16,os,1007,38.133\n8,32,48,16,16,os,155,30.968\n32,8,48,16,16,os,155,30.968\n8,64,48,16,16,os,311,30.868\n64,8,48,16,16,os,311,30.868\n8,128,48,16,16,os,623,30.819\n128,8,48,16,16,os,623,30.819\n8,32,24,16,16,os,107,22.43\n32,8,24,16,16,os,107,22.43\n8,64,24,16,16,os,215,22.326\n64,8,24,16,16,os,215,22.326\n8,128,24,16,16,os,431,22.274\n128,8,24,16,16,os,431,22.274\n8,32,12,16,16,os,83,14.458\n32,8,12,16,16,os,83,14.458\n8,64,12,16,16,os,167,14.371\n64,8,12,16,16,os,167,14.371\n8,128,12,16,16,os,335,14.328\n128,8,12,16,16,os,335,14.328\n128,128,24,16,16,os,3455,44.457\n128,128,12,16,16,os,2687,28.582\n128,128,6,16,16,os,2303,16.674\n128,128,3,16,16,os,2111,9.095\n32,16,12288,128,128,os,12541,3.062\n16,32,12288,128,128,os,12541,3.062\n32,32,6144,128,128,os,6397,6.003\n32,16,6144,128,128,os,6397,3.001\n16,32,6144,128,128,os,6397,3.001\n32,32,3072,128,128,os,3325,5.774\n32,16,3072,128,128,os,3325,2.887\n16,32,3072,128,128,os,3325,2.887\n32,32,1536,128,128,os,1789,5.366\n32,16,1536,128,128,os,1789,2.683\n16,32,1536,128,128,os,1789,2.683\n32,32,768,128,128,os,1021,4.701\n32,16,768,128,128,os,1021,2.351\n16,32,768,128,128,os,1021,2.351\n32,32,384,128,128,os,637,3.768\n32,16,384,128,128,os,637,1.884\n16,32,384,128,128,os,637,1.884\n32,32,192,128,128,os,445,2.697\n32,32,12288,128,128,os,12541,6.124\n64,16,12288,128,128,os,12541,6.124\n16,64,12288,128,128,os,12541,6.124\n32,64,6144,128,128,os,6397,12.006\n64,32,6144,128,128,os,6397,12.006\n64,16,6144,128,128,os,6397,6.003\n16,64,6144,128,128,os,6397,6.003\n32,64,3072,128,128,os,3325,11.549\n64,32,3072,128,128,os,3325,11.549\n64,16,3072,128,128,os,3325,5.774\n32,128,6144,128,128,os,6397,24.011\n256,16,6144,128,128,os,12795,12.005\n16,256,6144,128,128,os,12795,12.005\n128,32,6144,128,128,os,6397,24.011\n32,256,3072,128,128,os,6651,23.094\n256,32,3072,128,128,os,6651,23.094\n32,128,3072,128,128,os,3325,23.098\n256,16,3072,128,128,os,6651,11.547\n16,256,3072,128,128,os,6651,11.547\n128,32,3072,128,128,os,3325,23.098\n32,256,1536,128,128,os,3579,21.459\n256,32,1536,128,128,os,3579,21.459\n32,128,1536,128,128,os,1789,21.465\n256,16,1536,128,128,os,3579,10.729\n16,256,1536,128,128,os,3579,10.729\n128,32,1536,128,128,os,1789,21.465\n32,256,768,128,128,os,2043,18.796\n256,32,768,128,128,os,2043,18.796\n32,128,768,128,128,os,1021,18.805\n256,16,768,128,128,os,2043,9.398\n16,256,768,128,128,os,2043,9.398\n128,32,768,128,128,os,1021,18.805\n32,256,384,128,128,os,1275,15.059\n256,32,384,128,128,os,1275,15.059\n32,128,384,128,128,os,637,15.071\n256,16,384,128,128,os,1275,7.529\n16,256,384,128,128,os,1275,7.529\n128,32,384,128,128,os,637,15.071\n32,256,192,128,128,os,891,10.774\n256,32,192,128,128,os,891,10.774\n512,16,3072,128,128,os,13303,11.546\n16,512,3072,128,128,os,13303,11.546\n32,512,1536,128,128,os,7159,21.456\n512,32,1536,128,128,os,7159,21.456\n512,16,1536,128,128,os,7159,10.728\n16,512,1536,128,128,os,7159,10.728\n64,128,6144,128,128,os,6397,48.023\n256,32,6144,128,128,os,12795,24.009\n32,256,6144,128,128,os,12795,24.009\n128,64,6144,128,128,os,6397,48.023\n64,256,3072,128,128,os,6651,46.189\n256,64,3072,128,128,os,6651,46.189\n64,64,3072,128,128,os,3325,23.098\n64,128,3072,128,128,os,3325,46.195\n128,64,3072,128,128,os,3325,46.195\n64,256,1536,128,128,os,3579,42.917\n256,64,1536,128,128,os,3579,42.917\n64,64,1536,128,128,os,1789,21.465\n64,128,1536,128,128,os,1789,42.929\n64,32,1536,128,128,os,1789,10.732\n128,64,1536,128,128,os,1789,42.929\n32,64,1536,128,128,os,1789,10.732\n64,256,768,128,128,os,2043,37.592\n256,64,768,128,128,os,2043,37.592\n64,64,768,128,128,os,1021,18.805\n64,128,768,128,128,os,1021,37.61\n64,32,768,128,128,os,1021,9.403\n128,64,768,128,128,os,1021,37.61\n32,64,768,128,128,os,1021,9.403\n64,256,384,128,128,os,1275,30.118\n256,64,384,128,128,os,1275,30.118\n64,64,384,128,128,os,637,15.071\n64,128,384,128,128,os,637,30.141\n64,32,384,128,128,os,637,7.535\n128,64,384,128,128,os,637,30.141\n32,64,384,128,128,os,637,7.535\n64,256,192,128,128,os,891,21.549\n256,64,192,128,128,os,891,21.549\n64,64,192,128,128,os,445,10.787\n512,32,3072,128,128,os,13303,23.093\n32,512,3072,128,128,os,13303,23.093\n64,512,1536,128,128,os,7159,42.911\n512,64,1536,128,128,os,7159,42.911\n64,512,768,128,128,os,4087,37.583\n512,64,768,128,128,os,4087,37.583\n512,32,768,128,128,os,4087,18.791\n32,512,768,128,128,os,4087,18.791\n64,512,384,128,128,os,2551,30.106\n512,64,384,128,128,os,2551,30.106\n512,32,384,128,128,os,2551,15.053\n32,512,384,128,128,os,2551,15.053\n64,512,192,128,128,os,1783,21.537\n512,64,192,128,128,os,1783,21.537\n1024,32,1536,128,128,os,14319,21.454\n32,1024,1536,128,128,os,14319,21.454\n64,1024,768,128,128,os,8175,37.578\n1024,64,768,128,128,os,8175,37.578\n1024,32,768,128,128,os,8175,18.789\n32,1024,768,128,128,os,8175,18.789\n64,1024,384,128,128,os,5103,30.1\n1024,64,384,128,128,os,5103,30.1\n1024,32,384,128,128,os,5103,15.05\n32,1024,384,128,128,os,5103,15.05\n64,1024,192,128,128,os,3567,21.531\n1024,64,192,128,128,os,3567,21.531\n256,64,6144,128,128,os,12795,48.019\n64,256,6144,128,128,os,12795,48.019\n128,128,3072,128,128,os,3325,92.391\n128,256,1536,128,128,os,3579,85.834\n256,128,1536,128,128,os,3579,85.834\n128,128,1536,128,128,os,1789,85.858\n128,256,768,128,128,os,2043,75.184\n256,128,768,128,128,os,2043,75.184\n128,128,768,128,128,os,1021,75.22\n128,256,384,128,128,os,1275,60.235\n256,128,384,128,128,os,1275,60.235\n128,128,384,128,128,os,637,60.283\n128,256,192,128,128,os,891,43.098\n256,128,192,128,128,os,891,43.098\n128,128,192,128,128,os,445,43.146\n512,64,3072,128,128,os,13303,46.185\n64,512,3072,128,128,os,13303,46.185\n128,512,768,128,128,os,4087,75.165\n512,128,768,128,128,os,4087,75.165\n128,512,384,128,128,os,2551,60.212\n512,128,384,128,128,os,2551,60.212\n128,512,192,128,128,os,1783,43.073\n512,128,192,128,128,os,1783,43.073\n1024,64,1536,128,128,os,14319,42.908\n64,1024,1536,128,128,os,14319,42.908\n128,1024,384,128,128,os,5103,60.2\n1024,128,384,128,128,os,5103,60.2\n128,1024,192,128,128,os,3567,43.061\n1024,128,192,128,128,os,3567,43.061\n256,256,768,128,128,os,4087,75.165\n256,256,384,128,128,os,2551,60.212\n256,256,192,128,128,os,1783,43.073\n256,512,384,128,128,os,5103,60.2\n512,256,384,128,128,os,5103,60.2\n256,512,192,128,128,os,3567,43.061\n512,256,192,128,128,os,3567,43.061\n256,1024,192,128,128,os,7135,43.055\n1024,256,192,128,128,os,7135,43.055\n512,512,192,128,128,os,7135,43.055\n256,128,64,128,128,os,635,20.157\n128,256,64,128,128,os,635,20.157\n256,256,32,128,128,os,1143,11.199\n256,128,32,128,128,os,571,11.208\n128,256,32,128,128,os,571,11.208\n256,256,16,128,128,os,1079,5.931\n256,128,16,128,128,os,539,5.937\n128,256,16,128,128,os,539,5.937\n256,256,8,128,128,os,1047,3.056\n256,128,8,128,128,os,523,3.059\n128,256,8,128,128,os,523,3.059\n256,256,4,128,128,os,1031,1.552\n256,128,4,128,128,os,515,1.553\n128,256,4,128,128,os,515,1.553\n256,256,2,128,128,os,1023,0.782\n256,128,2,128,128,os,511,0.783\n128,256,2,128,128,os,511,0.783\n256,256,1,128,128,os,1019,0.393\n512,256,64,128,128,os,2543,20.134\n256,512,64,128,128,os,2543,20.134\n512,512,32,128,128,os,4575,11.191\n512,256,32,128,128,os,2287,11.194\n256,512,32,128,128,os,2287,11.194\n512,512,16,128,128,os,4319,5.927\n512,256,16,128,128,os,2159,5.929\n256,512,16,128,128,os,2159,5.929\n512,512,8,128,128,os,4191,3.054\n512,256,8,128,128,os,2095,3.055\n256,512,8,128,128,os,2095,3.055\n512,512,4,128,128,os,4127,1.551\n512,256,4,128,128,os,2063,1.551\n256,512,4,128,128,os,2063,1.551\n512,512,2,128,128,os,4095,0.781\n512,256,2,128,128,os,2047,0.782\n256,512,2,128,128,os,2047,0.782\n512,512,1,128,128,os,4079,0.392\n1024,512,64,128,128,os,10175,20.128\n512,1024,64,128,128,os,10175,20.128\n1024,1024,32,128,128,os,18303,11.189\n1024,512,32,128,128,os,9151,11.19\n512,1024,32,128,128,os,9151,11.19\n1024,1024,16,128,128,os,17279,5.926\n1024,512,16,128,128,os,8639,5.927\n512,1024,16,128,128,os,8639,5.927\n1024,1024,8,128,128,os,16767,3.054\n1024,512,8,128,128,os,8383,3.054\n512,1024,8,128,128,os,8383,3.054\n1024,1024,4,128,128,os,16511,1.55\n1024,512,4,128,128,os,8255,1.551\n512,1024,4,128,128,os,8255,1.551\n1024,1024,2,128,128,os,16383,0.781\n1024,512,2,128,128,os,8191,0.781\n512,1024,2,128,128,os,8191,0.781\n1024,1024,1,128,128,os,16319,0.392\n256,128,128,128,128,os,763,33.552\n128,256,128,128,128,os,763,33.552\n256,256,64,128,128,os,1271,20.142\n512,256,128,128,128,os,3055,33.519\n256,512,128,128,128,os,3055,33.519\n512,512,64,128,128,os,5087,20.13\n256,128,256,128,128,os,1019,50.245\n128,256,256,128,128,os,1019,50.245\n256,256,128,128,128,os,1527,33.53\n512,256,256,128,128,os,4079,50.208\n256,512,256,128,128,os,4079,50.208\n512,512,128,128,128,os,6111,33.513\n256,128,512,128,128,os,1531,66.884\n128,256,512,128,128,os,1531,66.884\n256,256,256,128,128,os,2039,50.221\n256,128,1024,128,128,os,2555,80.157\n128,256,1024,128,128,os,2555,80.157\n256,256,512,128,128,os,3063,66.863\n64,128,192,128,128,os,445,21.573\n64,32,192,128,128,os,445,5.393\n128,64,192,128,128,os,445,21.573\n32,64,192,128,128,os,445,5.393\n64,256,96,128,128,os,699,13.734\n256,64,96,128,128,os,699,13.734\n64,64,96,128,128,os,349,6.877\n32,512,192,128,128,os,1783,10.768\n64,512,96,128,128,os,1399,13.724\n32,1024,3072,128,128,os,26607,23.092\n32,1024,192,128,128,os,3567,10.765\n64,1024,96,128,128,os,2799,13.719\n32,2048,1536,128,128,os,28639,21.453\n64,2048,768,128,128,os,16351,37.576\n32,2048,768,128,128,os,16351,18.788\n64,2048,384,128,128,os,10207,30.097\n32,2048,384,128,128,os,10207,15.048\n64,2048,192,128,128,os,7135,21.528\n32,2048,192,128,128,os,7135,10.764\n64,2048,96,128,128,os,5599,13.717\n32,4096,384,128,128,os,20415,15.048\n64,4096,192,128,128,os,14271,21.526\n32,4096,192,128,128,os,14271,10.763\n64,4096,96,128,128,os,11199,13.716\n32,8192,192,128,128,os,28543,10.763\n64,8192,96,128,128,os,22399,13.715\n512,32,192,128,128,os,1783,10.768\n512,64,96,128,128,os,1399,13.724\n1024,32,3072,128,128,os,26607,23.092\n1024,32,192,128,128,os,3567,10.765\n1024,64,96,128,128,os,2799,13.719\n2048,32,1536,128,128,os,28639,21.453\n2048,64,768,128,128,os,16351,37.576\n2048,32,768,128,128,os,16351,18.788\n2048,64,384,128,128,os,10207,30.097\n2048,32,384,128,128,os,10207,15.048\n2048,64,192,128,128,os,7135,21.528\n2048,32,192,128,128,os,7135,10.764\n2048,64,96,128,128,os,5599,13.717\n64,128,64,128,128,os,317,10.095\n256,32,64,128,128,os,635,5.039\n64,32,64,128,128,os,317,2.524\n32,256,64,128,128,os,635,5.039\n128,64,64,128,128,os,317,10.095\n32,64,64,128,128,os,317,2.524\n64,256,32,128,128,os,571,5.604\n256,64,32,128,128,os,571,5.604\n64,64,32,128,128,os,285,2.807\n64,128,128,128,128,os,381,16.798\n256,32,128,128,128,os,763,8.388\n64,32,128,128,128,os,381,4.199\n32,256,128,128,128,os,763,8.388\n128,64,128,128,128,os,381,16.798\n32,64,128,128,128,os,381,4.199\n64,256,64,128,128,os,635,10.079\n256,64,64,128,128,os,635,10.079\n64,64,64,128,128,os,317,5.047\n64,128,256,128,128,os,509,25.147\n256,32,256,128,128,os,1019,12.561\n64,32,256,128,128,os,509,6.287\n32,256,256,128,128,os,1019,12.561\n128,64,256,128,128,os,509,25.147\n32,64,256,128,128,os,509,6.287\n64,256,128,128,128,os,763,16.776\n256,64,128,128,128,os,763,16.776\n64,64,128,128,128,os,381,8.399\n64,128,512,128,128,os,765,33.464\n256,32,512,128,128,os,1531,16.721\n64,32,512,128,128,os,765,8.366\n32,256,512,128,128,os,1531,16.721\n128,64,512,128,128,os,765,33.464\n32,64,512,128,128,os,765,8.366\n64,256,256,128,128,os,1019,25.123\n256,64,256,128,128,os,1019,25.123\n64,64,256,128,128,os,509,12.574\n64,128,1024,128,128,os,1277,40.094\n256,32,1024,128,128,os,2555,20.039\n64,32,1024,128,128,os,1277,10.023\n32,256,1024,128,128,os,2555,20.039\n128,64,1024,128,128,os,1277,40.094\n32,64,1024,128,128,os,1277,10.023\n64,256,512,128,128,os,1531,33.442\n256,64,512,128,128,os,1531,33.442\n64,64,512,128,128,os,765,16.732\n64,128,2048,128,128,os,2301,44.502\n256,32,2048,128,128,os,4603,22.246\n64,32,2048,128,128,os,2301,11.126\n32,256,2048,128,128,os,4603,22.246\n128,64,2048,128,128,os,2301,44.502\n32,64,2048,128,128,os,2301,11.126\n64,256,1024,128,128,os,2555,40.078\n256,64,1024,128,128,os,2555,40.078\n64,64,1024,128,128,os,1277,20.047\n64,128,4096,128,128,os,4349,47.091\n256,32,4096,128,128,os,8699,23.543\n64,32,4096,128,128,os,4349,11.773\n32,256,4096,128,128,os,8699,23.543\n128,64,4096,128,128,os,4349,47.091\n32,64,4096,128,128,os,4349,11.773\n64,256,2048,128,128,os,4603,44.493\n256,64,2048,128,128,os,4603,44.493\n64,64,2048,128,128,os,2301,22.251\n32,512,64,128,128,os,1271,5.035\n64,512,32,128,128,os,1143,5.599\n32,512,128,128,128,os,1527,8.382\n64,512,64,128,128,os,1271,10.071\n4096,32,384,128,128,os,20415,15.048\n64,64,6144,128,128,os,6397,24.011\n32,128,192,128,128,os,445,10.787\n64,128,96,128,128,os,349,13.754\n128,128,96,128,128,os,349,27.507\n128,256,96,128,128,os,699,27.468\n256,128,96,128,128,os,699,27.468\n128,512,96,128,128,os,1399,27.448\n512,128,96,128,128,os,1399,27.448\n128,1024,96,128,128,os,2799,27.438\n1024,128,96,128,128,os,2799,27.438\n128,2048,192,128,128,os,7135,43.055\n128,2048,96,128,128,os,5599,27.433\n2048,128,192,128,128,os,7135,43.055\n2048,128,96,128,128,os,5599,27.433\n256,256,96,128,128,os,1399,27.448\n256,512,96,128,128,os,2799,27.438\n512,256,96,128,128,os,2799,27.438\n256,1024,96,128,128,os,5599,27.433\n1024,256,96,128,128,os,5599,27.433\n256,2048,96,128,128,os,11199,27.431\n2048,256,96,128,128,os,11199,27.431\n512,512,96,128,128,os,5599,27.433\n512,1024,96,128,128,os,11199,27.431\n1024,512,96,128,128,os,11199,27.431\n128,128,64,128,128,os,317,20.189\n128,128,32,128,128,os,285,11.228\n256,64,16,128,128,os,539,2.968\n128,128,16,128,128,os,269,5.948\n256,64,8,128,128,os,523,1.53\n128,128,8,128,128,os,261,3.065\n256,64,4,128,128,os,515,0.777\n128,128,4,128,128,os,257,1.556\n256,64,2,128,128,os,511,0.391\n128,128,2,128,128,os,255,0.784\n256,128,1,128,128,os,509,0.393\n256,64,1,128,128,os,509,0.196\n128,128,1,128,128,os,254,0.394\n128,256,1,128,128,os,509,0.393\n128,512,64,128,128,os,1271,20.142\n128,512,32,128,128,os,1143,11.199\n128,512,16,128,128,os,1079,5.931\n128,512,8,128,128,os,1047,3.056\n128,512,4,128,128,os,1031,1.552\n128,512,2,128,128,os,1023,0.782\n256,512,1,128,128,os,2039,0.392\n128,512,1,128,128,os,1019,0.393\n512,128,64,128,128,os,1271,20.142\n512,128,32,128,128,os,1143,11.199\n512,128,16,128,128,os,1079,5.931\n512,128,8,128,128,os,1047,3.056\n512,128,4,128,128,os,1031,1.552\n512,128,2,128,128,os,1023,0.782\n512,256,1,128,128,os,2039,0.392\n512,128,1,128,128,os,1019,0.393\n256,1024,64,128,128,os,5087,20.13\n256,1024,32,128,128,os,4575,11.191\n256,1024,16,128,128,os,4319,5.927\n256,1024,8,128,128,os,4191,3.054\n256,1024,4,128,128,os,4127,1.551\n256,1024,2,128,128,os,4095,0.781\n512,1024,1,128,128,os,8159,0.392\n256,1024,1,128,128,os,4079,0.392\n1024,256,64,128,128,os,5087,20.13\n1024,256,32,128,128,os,4575,11.191\n1024,256,16,128,128,os,4319,5.927\n1024,256,8,128,128,os,4191,3.054\n1024,256,4,128,128,os,4127,1.551\n1024,256,2,128,128,os,4095,0.781\n1024,512,1,128,128,os,8159,0.392\n1024,256,1,128,128,os,4079,0.392\n512,2048,32,128,128,os,18303,11.189\n1024,2048,16,128,128,os,34559,5.926\n512,2048,16,128,128,os,17279,5.926\n1024,2048,8,128,128,os,33535,3.054\n512,2048,8,128,128,os,16767,3.054\n1024,2048,4,128,128,os,33023,1.55\n512,2048,4,128,128,os,16511,1.55\n1024,2048,2,128,128,os,32767,0.781\n512,2048,2,128,128,os,16383,0.781\n1024,2048,1,128,128,os,32639,0.392\n512,2048,1,128,128,os,16319,0.392\n2048,512,32,128,128,os,18303,11.189\n2048,1024,16,128,128,os,34559,5.926\n2048,512,16,128,128,os,17279,5.926\n2048,1024,8,128,128,os,33535,3.054\n2048,512,8,128,128,os,16767,3.054\n2048,1024,4,128,128,os,33023,1.55\n2048,512,4,128,128,os,16511,1.55\n2048,1024,2,128,128,os,32767,0.781\n2048,512,2,128,128,os,16383,0.781\n2048,1024,1,128,128,os,32639,0.392\n2048,512,1,128,128,os,16319,0.392\n128,128,128,128,128,os,381,33.596\n128,512,128,128,128,os,1527,33.53\n512,128,128,128,128,os,1527,33.53\n256,1024,128,128,128,os,6111,33.513\n1024,256,128,128,128,os,6111,33.513\n128,128,256,128,128,os,509,50.295\n128,512,256,128,128,os,2039,50.221\n512,128,256,128,128,os,2039,50.221\n128,128,512,128,128,os,765,66.928\n128,512,512,128,128,os,3063,66.863\n512,128,512,128,128,os,3063,66.863\n128,128,1024,128,128,os,1277,80.188\n128,128,2048,128,128,os,2301,89.005\n256,64,4096,128,128,os,8699,47.086\n256,64,8192,128,128,os,16891,48.499\n64,16,1536,128,128,os,1789,5.366\n64,16,768,128,128,os,1021,4.701\n64,16,384,128,128,os,637,3.768\n64,32,12288,128,128,os,12541,12.248\n32,64,12288,128,128,os,12541,12.248\n64,64,12288,128,128,os,12541,24.496\n128,32,12288,128,128,os,12541,24.496\n32,128,12288,128,128,os,12541,24.496\n128,64,12288,128,128,os,12541,48.991\n64,128,12288,128,128,os,12541,48.991\n64,16,12288,128,128,ws,42815,1.794\n32,32,12288,128,128,ws,39743,1.932\n64,32,6144,128,128,ws,21407,3.588\n64,16,64,128,128,os,317,1.262\n32,32,64,128,128,os,317,1.262\n64,32,32,128,128,os,285,1.404\n64,16,128,128,128,os,381,2.1\n32,32,128,128,128,os,381,2.1\n64,16,256,128,128,os,509,3.143\n32,32,256,128,128,os,509,3.143\n64,16,512,128,128,os,765,4.183\n32,32,512,128,128,os,765,4.183\n64,16,1024,128,128,os,1277,5.012\n32,32,1024,128,128,os,1277,5.012\n64,16,2048,128,128,os,2301,5.563\n32,32,2048,128,128,os,2301,5.563\n64,16,4096,128,128,os,4349,5.886\n32,32,4096,128,128,os,4349,5.886\n64,16,8192,128,128,os,8445,6.063\n32,32,8192,128,128,os,8445,6.063\n64,32,8192,128,128,os,8445,12.126\n32,64,8192,128,128,os,8445,12.126\n64,64,4096,128,128,os,4349,23.546\n32,128,4096,128,128,os,4349,23.546\n128,32,4096,128,128,os,4349,23.546\n128,32,64,128,128,os,317,5.047\n32,128,64,128,128,os,317,5.047\n64,128,32,128,128,os,285,5.614\n128,64,32,128,128,os,285,5.614\n128,32,128,128,128,os,381,8.399\n32,128,128,128,128,os,381,8.399\n128,32,256,128,128,os,509,12.574\n32,128,256,128,128,os,509,12.574\n128,32,512,128,128,os,765,16.732\n32,128,512,128,128,os,765,16.732\n128,32,1024,128,128,os,1277,20.047\n32,128,1024,128,128,os,1277,20.047\n128,32,2048,128,128,os,2301,22.251\n32,128,2048,128,128,os,2301,22.251\n64,64,8192,128,128,os,8445,24.251\n128,32,8192,128,128,os,8445,24.251\n32,128,8192,128,128,os,8445,24.251\n64,32,16384,128,128,os,16637,12.31\n32,64,16384,128,128,os,16637,12.31\n64,128,8192,128,128,os,8445,48.502\n32,256,8192,128,128,os,16891,24.25\n64,256,4096,128,128,os,8699,47.086\n256,32,8192,128,128,os,16891,24.25\n128,64,8192,128,128,os,8445,48.502\n32,512,4096,128,128,os,17399,23.542\n64,512,2048,128,128,os,9207,44.488\n512,32,4096,128,128,os,17399,23.542\n512,64,2048,128,128,os,9207,44.488\n512,32,2048,128,128,os,9207,22.244\n32,512,2048,128,128,os,9207,22.244\n64,512,1024,128,128,os,5111,40.07\n512,64,1024,128,128,os,5111,40.07\n32,1024,2048,128,128,os,18415,22.243\n64,1024,1024,128,128,os,10223,40.067\n1024,32,2048,128,128,os,18415,22.243\n1024,64,1024,128,128,os,10223,40.067\n1024,32,1024,128,128,os,10223,20.033\n32,1024,1024,128,128,os,10223,20.033\n64,1024,512,128,128,os,6127,33.426\n1024,64,512,128,128,os,6127,33.426\n1024,32,512,128,128,os,6127,16.713\n32,2048,512,128,128,os,12255,16.712\n512,64,512,128,128,os,3063,33.431\n64,2048,256,128,128,os,8159,25.101\n1024,64,256,128,128,os,4079,25.104\n64,512,512,128,128,os,3063,33.431\n2048,32,512,128,128,os,12255,16.712\n64,1024,256,128,128,os,4079,25.104\n2048,64,256,128,128,os,8159,25.101\n64,512,4096,128,128,os,17399,47.083\n512,64,4096,128,128,os,17399,47.083\n64,1024,2048,128,128,os,18415,44.485\n1024,64,2048,128,128,os,18415,44.485\n64,2048,512,128,128,os,12255,33.423\n1024,128,256,128,128,os,4079,50.208\n2048,64,512,128,128,os,12255,33.423\n128,1024,256,128,128,os,4079,50.208\n128,128,4096,128,128,os,4349,94.183\n128,256,2048,128,128,os,4603,88.985\n256,128,2048,128,128,os,4603,88.985\n128,256,4096,128,128,os,8699,94.172\n128,512,2048,128,128,os,9207,88.976\n256,128,4096,128,128,os,8699,94.172\n512,128,2048,128,128,os,9207,88.976\n128,512,1024,128,128,os,5111,80.141\n512,128,1024,128,128,os,5111,80.141\n128,1024,1024,128,128,os,10223,80.133\n1024,128,1024,128,128,os,10223,80.133\n128,1024,512,128,128,os,6127,66.852\n1024,128,512,128,128,os,6127,66.852\n128,2048,256,128,128,os,8159,50.202\n2048,128,256,128,128,os,8159,50.202\n128,128,8192,128,128,os,8445,97.004\n256,256,2048,128,128,os,9207,88.976\n256,512,1024,128,128,os,10223,80.133\n256,256,1024,128,128,os,5111,80.141\n256,512,2048,128,128,os,18415,88.971\n128,1024,2048,128,128,os,18415,88.971\n256,1024,1024,128,128,os,20447,80.129\n1024,128,2048,128,128,os,18415,88.971\n512,256,2048,128,128,os,18415,88.971\n1024,256,1024,128,128,os,20447,80.129\n256,1024,512,128,128,os,12255,66.846\n1024,256,512,128,128,os,12255,66.846\n128,2048,512,128,128,os,12255,66.846\n512,256,512,128,128,os,6127,66.852\n256,2048,256,128,128,os,16319,50.199\n1024,256,256,128,128,os,8159,50.202\n256,512,512,128,128,os,6127,66.852\n256,256,4096,128,128,os,17399,94.166\n128,512,4096,128,128,os,17399,94.166\n512,128,4096,128,128,os,17399,94.166\n512,512,1024,128,128,os,20447,80.129\n512,1024,512,128,128,os,24511,66.843\n1024,512,512,128,128,os,24511,66.843\n512,512,512,128,128,os,12255,66.846\n256,2048,512,128,128,os,24511,66.843\n512,2048,256,128,128,os,32639,50.198\n1024,512,256,128,128,os,16319,50.199\n512,512,256,128,128,os,8159,50.202\n512,512,2048,128,128,os,36831,88.969\n256,1024,2048,128,128,os,36831,88.969\n512,1024,1024,128,128,os,40895,80.127\n1024,256,2048,128,128,os,36831,88.969\n1024,512,1024,128,128,os,40895,80.127\n1024,1024,512,128,128,os,49023,66.842\n512,2048,512,128,128,os,49023,66.842\n1024,2048,256,128,128,os,65279,50.197\n2048,1024,256,128,128,os,65279,50.197\n1024,1024,64,128,128,os,20351,20.127\n512,2048,64,128,128,os,20351,20.127\n1024,2048,32,128,128,os,36607,11.189\n2048,512,64,128,128,os,20351,20.127\n2048,1024,32,128,128,os,36607,11.189\n1024,512,128,128,128,os,12223,33.511\n512,1024,128,128,128,os,12223,33.511\n1024,1024,128,128,128,os,24447,33.509\n512,2048,128,128,128,os,24447,33.509\n1024,2048,64,128,128,os,40703,20.126\n2048,512,128,128,128,os,24447,33.509\n2048,1024,64,128,128,os,40703,20.126\n1024,1024,256,128,128,os,32639,50.198\n64,32,12288,128,128,ws,42815,3.588\n32,64,12288,128,128,ws,39743,3.865\n64,64,6144,128,128,ws,21407,7.175\n64,64,12288,128,128,ws,42815,7.175\n32,128,12288,128,128,ws,39743,7.73\n64,128,6144,128,128,ws,21407,14.35\n128,32,12288,128,128,ws,48959,6.275\n128,64,6144,128,128,ws,24479,12.55\n128,64,8192,128,128,ws,32639,12.549\n128,64,4096,128,128,ws,16319,12.55\n64,128,8192,128,128,ws,28543,14.35\n64,128,4096,128,128,ws,14271,14.351\n128,128,4096,128,128,ws,16319,25.1\n128,128,2048,128,128,ws,8159,25.101\n128,128,8192,128,128,ws,32639,25.099\n64,256,8192,128,128,ws,57087,14.35\n64,256,4096,128,128,ws,28543,14.35\n128,256,4096,128,128,ws,32639,25.099\n128,256,2048,128,128,ws,16319,25.1\n256,64,8192,128,128,ws,40831,20.063\n256,64,4096,128,128,ws,20415,20.064\n256,128,4096,128,128,ws,20415,40.127\n256,128,2048,128,128,ws,10207,40.129\n256,256,2048,128,128,ws,20415,40.127\n256,256,4096,128,128,ws,40831,40.126\n128,512,4096,128,128,ws,65279,25.098\n256,512,2048,128,128,ws,40831,40.126\n512,128,4096,128,128,ws,28607,57.273\n512,256,2048,128,128,ws,28607,57.273\n512,512,1024,128,128,ws,28607,57.273\n512,512,2048,128,128,ws,57215,57.272\n256,1024,2048,128,128,ws,81663,40.126\n512,1024,1024,128,128,ws,57215,57.272\n1024,256,2048,128,128,ws,44991,72.832\n1024,512,1024,128,128,ws,44991,72.832\n1024,1024,512,128,128,ws,44991,72.832\n512,2048,512,128,128,ws,57215,57.272\n64,16,12288,128,128,is,38207,2.01\n32,32,12288,128,128,is,39743,1.932\n64,32,6144,128,128,is,19871,3.865\n64,32,12288,128,128,is,39743,3.865\n32,64,12288,128,128,is,42815,3.588\n64,64,6144,128,128,is,21407,7.175\n64,64,12288,128,128,is,42815,7.175\n32,128,12288,128,128,is,48959,6.275\n64,128,6144,128,128,is,24479,12.55\n128,32,12288,128,128,is,39743,7.73\n128,64,6144,128,128,is,21407,14.35\n128,64,8192,128,128,is,28543,14.35\n128,64,4096,128,128,is,14271,14.351\n64,128,8192,128,128,is,32639,12.549\n64,128,4096,128,128,is,16319,12.55\n128,128,4096,128,128,is,16319,25.1\n128,128,2048,128,128,is,8159,25.101\n128,128,8192,128,128,is,32639,25.099\n64,256,8192,128,128,is,40831,20.063\n64,256,4096,128,128,is,20415,20.064\n128,256,4096,128,128,is,20415,40.127\n128,256,2048,128,128,is,10207,40.129\n256,64,8192,128,128,is,57087,14.35\n256,64,4096,128,128,is,28543,14.35\n256,128,4096,128,128,is,32639,25.099\n256,128,2048,128,128,is,16319,25.1\n256,256,2048,128,128,is,20415,40.127\n256,256,4096,128,128,is,40831,40.126\n128,512,4096,128,128,is,28607,57.273\n256,512,2048,128,128,is,28607,57.273\n512,128,4096,128,128,is,65279,25.098\n512,256,2048,128,128,is,40831,40.126\n512,512,1024,128,128,is,28607,57.273\n512,512,2048,128,128,is,57215,57.272\n256,1024,2048,128,128,is,44991,72.832\n512,1024,1024,128,128,is,44991,72.832\n1024,256,2048,128,128,is,81663,40.126\n1024,512,1024,128,128,is,57215,57.272\n1024,2048,128,128,128,os,48895,33.509\n2048,1024,128,128,128,os,48895,33.509\n64,16,16384,128,128,os,16637,6.155\n32,32,16384,128,128,os,16637,6.155\n1024,256,512,128,128,ws,11247,72.837\n512,512,512,128,128,ws,14303,57.275\n1024,512,256,128,128,ws,11247,72.837\n2048,1024,256,128,128,ws,38879,84.282\n64,64,16384,128,128,os,16637,24.62\n32,128,16384,128,128,os,16637,24.62\n128,32,16384,128,128,os,16637,24.62\n8,16,256,16,16,os,285,44.912\n16,8,256,16,16,os,285,44.912\n32,4,256,16,16,os,571,22.417\n8,16,128,16,16,os,157,40.764\n16,8,128,16,16,os,157,40.764\n32,4,128,16,16,os,315,20.317\n8,16,32,16,16,os,61,26.23\n16,8,32,16,16,os,61,26.23\n32,4,32,16,16,os,123,13.008\n32,512,1024,128,128,os,5111,20.035\n32,512,512,128,128,os,3063,16.716\n64,512,256,128,128,os,2039,25.11\n32,512,256,128,128,os,2039,12.555\n64,512,128,128,128,os,1527,16.765\n32,1024,256,128,128,os,4079,12.552\n64,1024,128,128,128,os,3055,16.759\n64,16,32,128,128,os,285,0.702\n32,32,32,128,128,os,285,0.702\n64,32,16,128,128,os,269,0.743\n64,16,16,128,128,os,269,0.372\n32,32,16,128,128,os,269,0.372\n64,32,8,128,128,os,261,0.383\n64,16,8,128,128,os,261,0.192\n32,32,8,128,128,os,261,0.192\n64,32,4,128,128,os,257,0.195\n64,16,4,128,128,os,257,0.097\n32,32,4,128,128,os,257,0.097\n64,32,2,128,128,os,255,0.098\n64,16,2,128,128,os,255,0.049\n32,32,2,128,128,os,255,0.049\n64,32,1,128,128,os,254,0.049\n64,64,16,128,128,os,269,1.487\n32,64,16,128,128,os,269,0.743\n64,64,8,128,128,os,261,0.766\n32,64,8,128,128,os,261,0.383\n64,64,4,128,128,os,257,0.389\n32,64,4,128,128,os,257,0.195\n64,64,2,128,128,os,255,0.196\n32,64,2,128,128,os,255,0.098\n64,64,1,128,128,os,254,0.098\n128,32,32,128,128,os,285,2.807\n128,64,16,128,128,os,269,2.974\n128,32,16,128,128,os,269,1.487\n128,64,8,128,128,os,261,1.533\n128,32,8,128,128,os,261,0.766\n128,64,4,128,128,os,257,0.778\n128,32,4,128,128,os,257,0.389\n128,64,2,128,128,os,255,0.392\n128,32,2,128,128,os,255,0.196\n128,64,1,128,128,os,254,0.197\n"
  },
  {
    "path": "utils.py",
    "content": "from typing import List\n\ndef size_of_list(list: List):\n    result = 1\n    for i in list:\n        result *= i\n    return result\n\ndef size(list):\n    if isinstance(list, List):     \n        return size_of_list(list)\n    else:\n        return list.size\n\ndef closest_factors(n):\n    x = int(n**0.5)\n    while x >= 1:\n        if n % x == 0:\n            return x, n // x\n        x -= 1\n    return 0,0"
  }
]