code: def lentz_thompson_barnett_algorithm(
      *,
      num_iterations,
      small,
      threshold,
      nth_partial_numerator,
      nth_partial_denominator,
      inputs,
  ):
      # Position in the evaluation.
      kIterationIdx = 0
      # Whether or not we have reached the desired tolerance.
      kValuesUnconvergedIdx = 1
      # Ratio between nth canonical numerator and the nth-1 canonical numerator.
      kCIdx = 2
      # Ratio between nth-1 canonical denominator and the nth canonical denominator.
      kDIdx = 3
      # Computed approximant in the evaluation.
      kHIdx = 4
  
      def while_cond_fn(values):
          iteration = values[kIterationIdx]
          iterations_remain_cond = lt(iteration, num_iterations)
          values_unconverged_cond = values[kValuesUnconvergedIdx]
          return bitwise_and(
              iterations_remain_cond, values_unconverged_cond
          )
  
      def while_body_fn(values):
          iteration = values[kIterationIdx]
          partial_numerator = nth_partial_numerator(iteration, *inputs)
          partial_denominator = nth_partial_denominator(
              iteration, *inputs
          )
  
          c = add(
              partial_denominator, div(partial_numerator, values[kCIdx])
          )
          small_constant = full_like(c, small)
          c = select(lt(abs(c), small_constant), small_constant, c)
          d = add(
              partial_denominator, mul(partial_numerator, values[kDIdx])
          )
          d = select(lt(abs(d), small_constant), small_constant, d)
          d = reciprocal(d)
          delta = mul(c, d)
          h = mul(values[kHIdx], delta)
  
          # Update values
          values[kIterationIdx] = iteration + 1
          values[kCIdx] = c
          values[kDIdx] = d
          values[kHIdx] = h
          # If any values are greater than the tolerance, we have not converged.
          tolerance_comparison = ge(
              abs(sub(delta, _const(delta, 1.0))), threshold
          )
          values[kValuesUnconvergedIdx] = _any(tolerance_comparison)
          return values
  
      partial_denominator = nth_partial_denominator(0, *inputs)
      h = select(
          lt(abs(partial_denominator), small),
          broadcast_in_dim(small, partial_denominator.shape, ()),
          partial_denominator,
      )
      values = [1, True, h, full_like(h, 0), h]
      values = while_loop(while_cond_fn, while_body_fn, values)
      return values[kHIdx]
  
imports: from enum import Enum
  import numpy
  from functools import partial
  from jax._src.lax.lax import add, bitwise_and, bitwise_not, bitwise_or, broadcast_in_dim, broadcast_shapes, convert_element_type, div, eq, exp, full_like, ge, gt, le, log, log1p, lt, mul, ne, neg, reciprocal, reduce, select, sign, sqrt, square, standard_naryop, standard_unop, sub, _const, _dtype, _float, _nary_lower_hlo, _ones, _isnan, _reduce
  from jax._src.lax.control_flow import while_loop
  from jax._src import dtypes
  from jax._src.interpreters import ad
  from jax._src.interpreters import mlir
  from jax._src.lib.mlir.dialects import chlo
  from jax._src.typing import Array, ArrayLike
label_desc: Use image node_id 23 for calling a global function with example usage: lentz_thompson_barnett_algorithm() and returns: values, bitwise_and, values