"""simple docstring"""







def       A__    (	lowercase_     :	int      , lowercase_     :	int = 1000						)  ->							str:
   if (not isinstance(lowercase_      , lowercase_						)) or (digit_position <= 0):
      raise ValueError('Digit position must be a positive integer'						)
   elif (not isinstance(lowercase_      , lowercase_						)) or (precision < 0):
      raise ValueError('Precision must be a nonnegative integer'						)

   # compute an approximation of (16 ** (n - 1)) * pi whose fractional part is mostly
   # accurate
   __lowerCamelCase    		=					(
       4 * _subsum(lowercase_      , 1      , lowercase_						)
       - 2 * _subsum(lowercase_      , 4      , lowercase_						)
       - _subsum(lowercase_      , 5      , lowercase_						)
       - _subsum(lowercase_      , 6      , lowercase_						)
   )

   # return the first hex digit of the fractional part of the result
   return hex(int((sum_result % 1) * 16						)						)[2:]



def       A__    (	lowercase_     :	int      , lowercase_     :	int      , lowercase_     :	int						)  ->							float:
   __lowerCamelCase    		=					0.0
   for sum_index in range(digit_pos_to_extract + precision						):
      __lowerCamelCase    		=					8 * sum_index + denominator_addend
      if sum_index < digit_pos_to_extract:
         # if the exponential term is an integer and we mod it by the denominator
         # before dividing, only the integer part of the sum will change;
         # the fractional part will not
         __lowerCamelCase    		=					pow(
             16      , digit_pos_to_extract - 1 - sum_index      , lowercase_						)
      else:
         __lowerCamelCase    		=					pow(16      , digit_pos_to_extract - 1 - sum_index						)
      total += exponential_term / denominator
   return total


if __name__ == "__main__":
     import doctest

     doctest.testmod()







import os
from dataclasses import replace

import jax
import wandb
from bigbird_flax import Args, DataCollator, FlaxBigBirdForNaturalQuestions, Trainer, build_tx, train_step, val_step
from datasets import load_dataset
from flax import jax_utils

from transformers import BigBirdTokenizerFast


if __name__ == "__main__":
      print('''#################### AVAILABLE DEVICES ####################''')
      print(jax.devices())
      print('''###########################################################''')

      # setup for wandb sweep
      UpperCAmelCase_    		=				Args()
      UpperCAmelCase_    		=				wandb.init(project='''bigbird-natural-questions''', config=args.__dict__)
      UpperCAmelCase_    		=				dict(logger.config)
      del wandb_args["batch_size"]
      UpperCAmelCase_    		=				replace(args, **wandb_args)
      UpperCAmelCase_    		=				args.base_dir + '''-''' + wandb.run.id
      UpperCAmelCase_    		=				replace(args, base_dir=base_dir)
      print(args)

      UpperCAmelCase_    		=				load_dataset('''json''', data_files=args.tr_data_path)['''train''']
      UpperCAmelCase_    		=				load_dataset('''json''', data_files=args.val_data_path)['''train''']

      # drop extra batch for now
      UpperCAmelCase_    		=				range(len(tr_dataset) - len(tr_dataset) % args.batch_size)
      UpperCAmelCase_    		=				tr_dataset.shuffle().select(indices)
      UpperCAmelCase_    		=				range(len(val_dataset) - len(val_dataset) % args.batch_size)
      UpperCAmelCase_    		=				val_dataset.shuffle().select(indices)

      if os.environ.get('''TRAIN_ON_SMALL''', '''false''') == "true":
            UpperCAmelCase_    		=				tr_dataset.shuffle().select(range(80_000))
            UpperCAmelCase_    		=				val_dataset.shuffle().select(range(8_000))

      print(tr_dataset)
      print(val_dataset)

      UpperCAmelCase_    		=				FlaxBigBirdForNaturalQuestions.from_pretrained(
          args.model_id, block_size=args.block_size, num_random_blocks=args.num_random_blocks
      )
      UpperCAmelCase_    		=				BigBirdTokenizerFast.from_pretrained(args.model_id)
      UpperCAmelCase_    		=				DataCollator(pad_id=tokenizer.pad_token_id, max_length=4_096)

      UpperCAmelCase_    		=				{
          '''lr''': args.lr,
          '''init_lr''': args.init_lr,
          '''warmup_steps''': args.warmup_steps,
          '''num_train_steps''': args.max_epochs * (len(tr_dataset) // args.batch_size),
          '''weight_decay''': args.weight_decay,
      }
      UpperCAmelCase_		,     UpperCAmelCase_    		=				build_tx(**tx_args)

      UpperCAmelCase_    		=				Trainer(
          args=args,
          data_collator=data_collator,
          model_save_fn=model.save_pretrained,
          train_step_fn=train_step,
          val_step_fn=val_step,
          logger=logger,
          scheduler_fn=lr,
      )

      UpperCAmelCase_    		=				None
      UpperCAmelCase_    		=				trainer.create_state(model, tx, num_train_steps=tx_args['''num_train_steps'''], ckpt_dir=ckpt_dir)
      try:
            trainer.train(state, tr_dataset, val_dataset)
      except KeyboardInterrupt:
            print('''Oooops; TRAINING STOPPED UNFORTUNATELY''')

      print('''SAVING WEIGHTS IN `final-weights`''')
      UpperCAmelCase_    		=				jax_utils.unreplicate(state.params)
      model.save_pretrained(os.path.join(args.base_dir, '''final-weights'''), params=params)