


import mpmath  # for roots of unity
import numpy as np


class 	_a							:

							def __init__(							self:     Optional[Any]   ,						UpperCamelCase_:     List[Any]=None   ,						UpperCamelCase_:     str=None							)      ->       str:





									"""simple docstring"""







									lowercase__						=				list(poly_a or [0]							)[:]
									lowercase__						=				list(poly_b or [0]							)[:]

									# Remove leading zero coefficients
									while self.polyA[-1] == 0:
											self.polyA.pop()
									lowercase__						=				len(self.polyA							)

									while self.polyB[-1] == 0:
											self.polyB.pop()
									lowercase__						=				len(self.polyB							)

									# Add 0 to make lengths equal a power of 2
									lowercase__						=				int(
									    2 ** np.ceil(np.loga(len(self.polyA							) + len(self.polyB							) - 1							)							)							)

									while len(self.polyA							) < self.c_max_length:
											self.polyA.append(0							)
									while len(self.polyB							) < self.c_max_length:
											self.polyB.append(0							)
									# A complex root used for the fourier transform
									lowercase__						=				complex(mpmath.root(x=1   ,						n=self.c_max_length   ,						k=1							)							)

									# The product
									lowercase__						=				self.__multiply()

							def 				lowerCamelCase_			(							self:     str   ,						UpperCamelCase_:     Any							)      ->       Any:





									"""simple docstring"""







									lowercase__						=				[[x] for x in self.polyA] if which == 'A' else [[x] for x in self.polyB]
									# Corner case
									if len(__snake_case							) <= 1:
											return dft[0]
									#
									lowercase__						=				self.c_max_length // 2
									while next_ncol > 0:
											lowercase__						=				[[] for i in range(__snake_case							)]
											lowercase__						=				self.root**next_ncol

											# First half of next step
											lowercase__						=				1
											for j in range(self.c_max_length // (next_ncol * 2)							):
													for i in range(__snake_case							):
															new_dft[i].append(dft[i][j] + current_root * dft[i + next_ncol][j]							)
													current_root *= root
											# Second half of next step
											lowercase__						=				1
											for j in range(self.c_max_length // (next_ncol * 2)							):
													for i in range(__snake_case							):
															new_dft[i].append(dft[i][j] - current_root * dft[i + next_ncol][j]							)
													current_root *= root
											# Update
											lowercase__						=				new_dft
											lowercase__						=				next_ncol // 2
									return dft[0]

							def 				lowerCamelCase_			(							self:     str							)      ->       Union[str, Any]:





									"""simple docstring"""







									lowercase__						=				self.__dft('''A'''							)
									lowercase__						=				self.__dft('''B'''							)
									lowercase__						=				[[dft_a[i] * dft_b[i] for i in range(self.c_max_length							)]]
									del dft_a
									del dft_b

									# Corner Case
									if len(inverce_c[0]							) <= 1:
											return inverce_c[0]
									# Inverse DFT
									lowercase__						=				2
									while next_ncol <= self.c_max_length:
											lowercase__						=				[[] for i in range(__snake_case							)]
											lowercase__						=				self.root ** (next_ncol // 2)
											lowercase__						=				1
											# First half of next step
											for j in range(self.c_max_length // next_ncol							):
													for i in range(next_ncol // 2							):
															# Even positions
															new_inverse_c[i].append(
															    (
															        inverce_c[i][j]
															        + inverce_c[i][j + self.c_max_length // next_ncol]
															    )
															    / 2							)
															# Odd positions
															new_inverse_c[i + next_ncol // 2].append(
															    (
															        inverce_c[i][j]
															        - inverce_c[i][j + self.c_max_length // next_ncol]
															    )
															    / (2 * current_root)							)
													current_root *= root
											# Update
											lowercase__						=				new_inverse_c
											next_ncol *= 2
									# Unpack
									lowercase__						=				[round(x[0].real   ,						8							) + round(x[0].imag   ,						8							) * 1J for x in inverce_c]

									# Remove leading 0's
									while inverce_c[-1] == 0:
											inverce_c.pop()
									return inverce_c


							def __str__(							self:     Optional[int]							)      ->       List[Any]:





									"""simple docstring"""







									lowercase__						=				'A = ' + ' + '.join(
									    f'{coef}*x^{i}' for coef, i in enumerate(self.polyA[: self.len_A]							)							)
									lowercase__						=				'B = ' + ' + '.join(
									    f'{coef}*x^{i}' for coef, i in enumerate(self.polyB[: self.len_B]							)							)
									lowercase__						=				'A*B = ' + ' + '.join(
									    f'{coef}*x^{i}' for coef, i in enumerate(self.product							)							)

									return f'{a}\n{b}\n{c}'


# Unit tests
if __name__ == "__main__":
			import doctest

			doctest.testmod()






import json
import logging
import os
import socket

import git
import numpy as np
import torch


logging.basicConfig(
    format='%(asctime)s - %(levelname)s - %(name)s - PID: %(process)d -  %(message)s',
    datefmt='%m/%d/%Y %H:%M:%S',
    level=logging.INFO,
)
lowerCAmelCase	=							logging.getLogger(__name__)
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		lowercase__						=				git.Repo(search_parent_directories=SCREAMING_SNAKE_CASE					)
		lowercase__						=				{
		    '''repo_id''': str(SCREAMING_SNAKE_CASE					),
		    '''repo_sha''': str(repo.head.object.hexsha					),
		    '''repo_branch''': str(repo.active_branch					),
		}

		with open(os.path.join(SCREAMING_SNAKE_CASE						,    '''git_log.json'''					)						,    '''w'''					) as f:
				json.dump(SCREAMING_SNAKE_CASE						,    SCREAMING_SNAKE_CASE						,    indent=4					)
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		if params.n_gpu <= 0:
				lowercase__						=				0
				lowercase__						=				-1
				lowercase__						=				True
				lowercase__						=				False
				return

		assert torch.cuda.is_available()

		logger.info('''Initializing GPUs'''					)
		if params.n_gpu > 1:
				assert params.local_rank != -1

				lowercase__						=				int(os.environ['''WORLD_SIZE''']					)
				lowercase__						=				int(os.environ['''N_GPU_NODE''']					)
				lowercase__						=				int(os.environ['''RANK''']					)

				# number of nodes / node ID
				lowercase__						=				params.world_size // params.n_gpu_per_node
				lowercase__						=				params.global_rank // params.n_gpu_per_node
				lowercase__						=				True

				assert params.n_nodes == int(os.environ['''N_NODES''']					)
				assert params.node_id == int(os.environ['''NODE_RANK''']					)

		# local job (single GPU)
		else:
				assert params.local_rank == -1

				lowercase__						=				1
				lowercase__						=				0
				lowercase__						=				0
				lowercase__						=				0
				lowercase__						=				1
				lowercase__						=				1
				lowercase__						=				False

		# sanity checks
		assert params.n_nodes >= 1
		assert 0 <= params.node_id < params.n_nodes
		assert 0 <= params.local_rank <= params.global_rank < params.world_size
		assert params.world_size == params.n_nodes * params.n_gpu_per_node

		# define whether this is the master process / if we are in multi-node distributed mode
		lowercase__						=				params.node_id == 0 and params.local_rank == 0
		lowercase__						=				params.n_nodes > 1

		# summary
		lowercase__						=				f'--- Global rank: {params.global_rank} - '
		logger.info(PREFIX + '''Number of nodes: %i''' % params.n_nodes					)
		logger.info(PREFIX + '''Node ID        : %i''' % params.node_id					)
		logger.info(PREFIX + '''Local rank     : %i''' % params.local_rank					)
		logger.info(PREFIX + '''World size     : %i''' % params.world_size					)
		logger.info(PREFIX + '''GPUs per node  : %i''' % params.n_gpu_per_node					)
		logger.info(PREFIX + '''Master         : %s''' % str(params.is_master					)					)
		logger.info(PREFIX + '''Multi-node     : %s''' % str(params.multi_node					)					)
		logger.info(PREFIX + '''Multi-GPU      : %s''' % str(params.multi_gpu					)					)
		logger.info(PREFIX + '''Hostname       : %s''' % socket.gethostname()					)

		# set GPU device
		torch.cuda.set_device(params.local_rank					)

		# initialize multi-GPU
		if params.multi_gpu:
				logger.info('''Initializing PyTorch distributed'''					)
				torch.distributed.init_process_group(
				    init_method='''env://'''						,    backend='''nccl'''						,    )
def       _a			(				SCREAMING_SNAKE_CASE					):


		"""simple docstring"""




		np.random.seed(args.seed					)
		torch.manual_seed(args.seed					)
		if args.n_gpu > 0:
				torch.cuda.manual_seed_all(args.seed					)


