code: def _exp_sinch(a, x):
      """
      Stably evaluate exp(a)*sinh(x)/x
  
      Notes
      -----
      The strategy of falling back to a sixth order Taylor expansion
      was suggested by the Spallation Neutron Source docs
      which was found on the internet by google search.
      http://www.ornl.gov/~t6p/resources/xal/javadoc/gov/sns/tools/math/ElementaryFunction.html
      The details of the cutoff point and the Horner-like evaluation
      was picked without reference to anything in particular.
  
      Note that sinch is not currently implemented in scipy.special,
      whereas the "engineer's" definition of sinc is implemented.
      The implementation of sinc involves a scaling factor of pi
      that distinguishes it from the "mathematician's" version of sinc.
  
      """
  
      # If x is small then use sixth order Taylor expansion.
      # How small is small? I am using the point where the relative error
      # of the approximation is less than 1e-14.
      # If x is large then directly evaluate sinh(x) / x.
      if abs(x) < 0.0135:
          x2 = x * x
          return np.exp(a) * (
              1 + (x2 / 6.0) * (1 + (x2 / 20.0) * (1 + (x2 / 42.0)))
          )
      else:
          return (np.exp(a + x) - np.exp(a - x)) / (2 * x)
  
imports: import numpy
  from scipy.linalg._basic import solve, solve_triangular
  from scipy.sparse._base import issparse
  from scipy.sparse.linalg import spsolve
  from scipy.sparse._sputils import is_pydata_spmatrix, isintlike
  import scipy.sparse
  import scipy.sparse.linalg
  from scipy.sparse.linalg._interface import LinearOperator
  from scipy.sparse._construct import eye
  from ._expm_multiply import _ident_like, _exact_1_norm
label_desc: Use image node_id 10 for calling a global function with example usage: _exp_sinch(a, x) and returns: unknown, unknown