



"""simple docstring"""







from math import factorial, radians

def       _lowerCamelCase				(							UpperCAmelCase_ :       Dict,	UpperCAmelCase_ :       List[Any] = 18,	UpperCAmelCase_ :       Tuple = 10     )	-> Dict:






	"""simple docstring"""





	A__											=					angle_in_degrees - ((angle_in_degrees // 360.0) * 360.0)

	# Converting from degrees to radians
	A__											=					radians(_lowerCAmelCase     )

	A__											=					angle_in_radians
	A__											=					3
	A__											=					-1

	for _ in range(_lowerCAmelCase     ):
		result += (b * (angle_in_radians**a)) / factorial(_lowerCAmelCase     )

		A__											=					-b  # One positive term and the next will be negative and so on...
		a += 2  # Increased by 2 for every term.

	return round(_lowerCAmelCase,	_lowerCAmelCase     )


if __name__ == "__main__":
			__import__("""doctest""").testmod()






"""simple docstring"""
import operator as op


SCREAMING_SNAKE_CASE_					     =	'''scaler.pt'''
SCREAMING_SNAKE_CASE_					     =	'''pytorch_model'''
SCREAMING_SNAKE_CASE_					     =	'''random_states'''
SCREAMING_SNAKE_CASE_					     =	'''optimizer'''
SCREAMING_SNAKE_CASE_					     =	'''scheduler'''
SCREAMING_SNAKE_CASE_					     =	'''pytorch_model.bin'''
SCREAMING_SNAKE_CASE_					     =	'''pytorch_model.bin.index.json'''
SCREAMING_SNAKE_CASE_					     =	'''model.safetensors'''
SCREAMING_SNAKE_CASE_					     =	'''model.safetensors.index.json'''
SCREAMING_SNAKE_CASE_					     =	'''1.10.2'''
SCREAMING_SNAKE_CASE_					     =	'''py38'''
SCREAMING_SNAKE_CASE_					     =	'''4.17.0'''
SCREAMING_SNAKE_CASE_					     =	['''ml.p3.16xlarge''', '''ml.p3dn.24xlarge''', '''ml.p4dn.24xlarge''']
SCREAMING_SNAKE_CASE_					     =	['''FULL_SHARD''', '''SHARD_GRAD_OP''', '''NO_SHARD''', '''HYBRID_SHARD''', '''HYBRID_SHARD_ZERO2''']
SCREAMING_SNAKE_CASE_					     =	['''TRANSFORMER_BASED_WRAP''', '''SIZE_BASED_WRAP''', '''NO_WRAP''']
SCREAMING_SNAKE_CASE_					     =	['''BACKWARD_PRE''', '''BACKWARD_POST''', '''NO_PREFETCH''']
SCREAMING_SNAKE_CASE_					     =	['''FULL_STATE_DICT''', '''LOCAL_STATE_DICT''', '''SHARDED_STATE_DICT''']
SCREAMING_SNAKE_CASE_					     =	'''2.0.1'''
SCREAMING_SNAKE_CASE_					     =	['''pdsh''', '''standard''', '''openmpi''', '''mvapich''']
SCREAMING_SNAKE_CASE_					     =	['''default''', '''reduce-overhead''', '''max-autotune''']

SCREAMING_SNAKE_CASE_					     =	{'''>''': op.gt, '''>=''': op.ge, '''==''': op.eq, '''!=''': op.ne, '''<=''': op.le, '''<''': op.lt}

# These are the args for `torch.distributed.launch` for pytorch < 1.9
SCREAMING_SNAKE_CASE_					     =	[
    '''nnodes''',
    '''nproc_per_node''',
    '''rdzv_backend''',
    '''rdzv_endpoint''',
    '''rdzv_id''',
    '''rdzv_conf''',
    '''standalone''',
    '''max_restarts''',
    '''monitor_interval''',
    '''start_method''',
    '''role''',
    '''module''',
    '''m''',
    '''no_python''',
    '''run_path''',
    '''log_dir''',
    '''r''',
    '''redirects''',
    '''t''',
    '''tee''',
    '''node_rank''',
    '''master_addr''',
    '''master_port''',
]

SCREAMING_SNAKE_CASE_					     =	['''DEEPSPEED''', '''MULTI_GPU''', '''FSDP''', '''MEGATRON_LM''']
SCREAMING_SNAKE_CASE_					     =	['''DEEPSPEED''', '''MULTI_XPU''', '''FSDP''']
