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| # Copyright 2019 Google LLC | ||
| # | ||
| # | ||
| # Licensed under the Apache License, Version 2.0 (the "License"); | ||
| # you may not use this file except in compliance with the License. | ||
| # You may obtain a copy of the License at | ||
| # | ||
| # http://www.apache.org/licenses/LICENSE-2.0 | ||
| # | ||
| # Unless required by applicable law or agreed to in writing, software | ||
| # distributed under the License is distributed on an "AS IS" BASIS, | ||
| # WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. | ||
| # See the License for the specific language governing permissions and | ||
| # limitations under the License. | ||
| # ============================================================================== | ||
|
|
||
| """divide_and_conquer per layer cost modeling using ACE and data fitting. | ||
| For a given layer with its hardware design params, predict its cost | ||
| in actual ASIC implementation using ACE metric and actual MAC gates data points. | ||
| """ | ||
|
|
||
| import io | ||
| import pandas as pd | ||
| import numpy as np | ||
| import matplotlib.pyplot as plt | ||
| from scipy.optimize import curve_fit | ||
|
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||
|
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| # Rule-of-thumb mapping between bits and gates in memory area estimate. | ||
| MemoryGatesPerBit = { | ||
| 'Register': 10.0, | ||
| 'SRAM': 1.0, | ||
| 'ROM': 0.1, | ||
| } | ||
|
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| # Previously calculated 3D polynomial coefficients with relative MAE<5%. | ||
| MAC_POLY3D_PARAMS = np.array([7.70469119, 13.76199652, -92.15756665]) | ||
|
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| # MAC area data points generated from go/mac_vs_area. | ||
| MAC24 = pd.read_csv(io.StringIO(''' | ||
| 283,280,286,313,325,336,356,, | ||
| 274,290,325,372,401,428,485,, | ||
| 285,325,388,510,568,614,713,, | ||
| 308,372,509,750,865,1002,1167,, | ||
| 336,427,617,1003,1151,1309,,, | ||
| 356,480,722,1165,,,,, | ||
| '''), header=None) | ||
|
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||
| MAC32 = pd.read_csv(io.StringIO(''' | ||
| 391,365,377,410,453,433,458,507, | ||
| 364,382,418,466,497,521,578,685, | ||
| 378,418,485,594,659,721,832,1035, | ||
| 408,466,596,843,1029,1151,1321,1642, | ||
| 432,521,724,1153,1363,1512,1797,, | ||
| 457,578,830,1330,1551,1782,2273,, | ||
| '''), header=None) | ||
|
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||
| MAC40 = pd.read_csv(io.StringIO(''' | ||
| 458,457,470,500,522,527,551,605,664 | ||
| 457,475,513,561,597,616,670,782,888 | ||
| 470,513,579,699,766,816,928,1150,1358 | ||
| 499,561,699,996,1161,1273,1499,1850,2189 | ||
| 527,612,818,1275,1545,1691,2054,2516, | ||
| 549,670,927,1496,1798,2035,2490,3294, | ||
| '''), header=None) | ||
|
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||
| MAC48 = pd.read_csv(io.StringIO(''' | ||
| 595,550,566,594,659,624,642,694,745 | ||
| 551,566,607,654,727,707,763,881,984 | ||
| 566,607,679,794,871,921,1017,1270,1489 | ||
| 594,655,793,1097,1285,1401,1668,2101,2378 | ||
| 624,711,921,1397,1816,1950,2277,2763,3301 | ||
| 642,762,1015,1669,1974,2264,2718,3631,4415 | ||
| '''), header=None) | ||
|
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|
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||
| def mac_gates_polynomial_3d(xyz, a, b, c): | ||
| """Using a 3d polynomial function to model MAC area. | ||
| This function models the MAC area to be the sum of multipler, accumulator | ||
| and a constant shift. Particularly, multiplier area is modeled to be linear | ||
| # to input_bits * weight_bits, per ACE rule. | ||
| Args: | ||
| xyz: tuple includes input, weight and accumulator bits. | ||
| a: polynomial coefficient 0. | ||
| b: polynomial coefficient 1. | ||
| c: polynomial coefficient 2. | ||
| Returns: | ||
| MAC area predicted by the function. | ||
| """ | ||
| x, y, z = xyz | ||
| return a * x * y + b * z + c | ||
|
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|
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| def gen_mac_gate_model(do_plot=False): | ||
| """Generate the polynomial cost model coefficients using given data. | ||
| Args: | ||
| do_plot: Bool indicates whether plot the raw data and the fitted curve. | ||
| Returns: | ||
| params: The esitimated params of the polynomical function. | ||
| mae_predict: Calculate the mean absolute error of the predictions. | ||
| parameter_std_deviation: one standard deviation errors on the parameters, | ||
| indicating the uncertainties of the params. | ||
| """ | ||
| # acc bits, 1st index | ||
| abit = np.array([24, 32, 40, 48]) | ||
| abit = np.repeat(abit, 54) | ||
|
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||
| # weight bits, 2nd index | ||
| wbit = np.array([1, 2, 4, 8, 12, 16]) | ||
| wbit = np.tile(np.repeat(wbit, 9), 4) | ||
|
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||
| # input bits, 3rd index | ||
| xbit = np.array([1, 2, 4, 8, 10, 12, 16, 24, 32]) | ||
| xbit = np.tile(xbit, 24) | ||
|
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||
| # Record all mac area data points associated with each accumulator bitwidth | ||
| mac_arrs = [] | ||
| # Record the start and end index of the mac area data points | ||
| # associated with each accumulator bitwidth | ||
| mac_arrs_index = {} | ||
| # Record index of all valid data points | ||
| valid_index = [] | ||
| start_pos = 0 | ||
|
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||
| for (mac_acc, acc_bits) in zip( | ||
| [MAC24, MAC32, MAC40, MAC48], [24, 32, 40, 48]): | ||
| cur_mac = mac_acc.to_numpy().reshape(-1) | ||
| # Filter out nan data points | ||
| cur_valid_index = ~np.isnan(cur_mac) | ||
| cur_valid_mac = cur_mac[cur_valid_index] | ||
| # Record the data length for each accumulator bits | ||
| end_pos = start_pos + len(cur_valid_mac) | ||
| mac_arrs_index[acc_bits] = (start_pos, end_pos) | ||
| # Append mac areas of each accumulator bits to a list | ||
| mac_arrs += list(cur_valid_mac) | ||
| start_pos = end_pos | ||
| valid_index += list(cur_valid_index) | ||
|
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||
| # Filter out invalid data | ||
| xbit = xbit[valid_index] | ||
| wbit = wbit[valid_index] | ||
| abit = abit[valid_index] | ||
|
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| # curve fitting for all data points | ||
| params, covariance = curve_fit( | ||
| mac_gates_polynomial_3d, (xbit, wbit, abit), mac_arrs) | ||
|
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||
| # Compute one standard deviation errors on the parameters. | ||
| parameter_std_deviation = np.sqrt(np.diag(covariance)) | ||
|
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| # Calculate the mean absolute error between prediction and given data. | ||
| mac_predict = mac_gates_polynomial_3d((xbit, wbit, abit), *params) | ||
| mae = np.mean(np.abs(mac_predict - mac_arrs)) | ||
| mae_predict = mae / np.mean(mac_arrs) | ||
|
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||
| if do_plot: | ||
| # Plot all raw data points | ||
| fig = plt.figure(figsize=(10, 10)) | ||
| ax = fig.add_subplot(111, projection='3d') | ||
|
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||
| ax.scatter(xbit, wbit, mac_arrs, label='Data') | ||
|
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| ax.set_xlabel('X_bits') | ||
| ax.set_ylabel('W_bits') | ||
| ax.set_zlabel('MAC') | ||
|
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| plt.title('MAC area data points') | ||
| plt.show() | ||
|
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||
| # Generate a mesh grid for plotting. | ||
| x_fit = np.linspace(min(xbit), max(xbit), 50) | ||
| w_fit = np.linspace(min(wbit), max(wbit), 50) | ||
| xmesh, wmesh = np.meshgrid(x_fit, w_fit) | ||
|
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| fig = plt.figure(figsize=(16, 16)) | ||
| index = 1 | ||
|
|
||
| # Plotting 3D fitting curve for each accumulator bitwidth | ||
| for acc_bits in [24, 32, 40, 48]: | ||
| ax = fig.add_subplot(2, 2, index, projection='3d') | ||
|
|
||
| start_pos = mac_arrs_index[acc_bits][0] | ||
| end_pos = mac_arrs_index[acc_bits][1] | ||
| ax.scatter(xbit[start_pos:end_pos], wbit[start_pos:end_pos], | ||
| mac_arrs[start_pos:end_pos], label='Data') | ||
|
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| amesh = np.full(shape=(50, 50), fill_value=acc_bits) | ||
| poly_fit = mac_gates_polynomial_3d((xmesh, wmesh, amesh), *params) | ||
|
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||
| ax.plot_surface( | ||
| xmesh, wmesh, poly_fit, cmap='viridis', alpha=0.8, | ||
| label=f'Fitted Surface | acc_bits={acc_bits}') | ||
|
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||
| ax.set_xlabel('X') | ||
| ax.set_ylabel('W') | ||
| ax.set_zlabel('MAC') | ||
| ax.set_title(f'accumulator bitwidth: {acc_bits}') | ||
| index += 1 | ||
|
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| plt.show() | ||
|
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| return params, mae_predict, parameter_std_deviation | ||
|
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| def get_ace_mac_gates(xbit, wbit, abit, regen_params=False): | ||
| """Function to estimate MAC area, including 1 multipler and 1 accumulator. | ||
| Args: | ||
| xbit: int. input bits. | ||
| wbit: int. weight bits. | ||
| abit: int. accumulator bits. | ||
| regen_params: Bool. If True, regenerate the MAC cost model coefficients. | ||
| If False, reuse the previously generated model coefficients. | ||
| Returns: | ||
| Estimated MAC gates. | ||
| """ | ||
| if regen_params: | ||
| mac_params, _, _ = gen_mac_gate_model(do_plot=True) | ||
| else: | ||
| mac_params = MAC_POLY3D_PARAMS | ||
|
|
||
| return mac_gates_polynomial_3d((xbit, wbit, abit), *mac_params) |
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