new_contents: # test the functions imported from cmath
  
  try:
      from cmath import *
  except ImportError:
      print("SKIP")
      import sys
      sys.exit()
  
  # make sure these constants exist in cmath
  print("%.5g" % e)
  print("%.5g" % pi)
  
  test_values_non_zero = []
  base_values = (0.0, 0.5, 1.23456, 10.)
  for r in base_values:
      for i in base_values:
          if r != 0. or i != 0.:
              test_values_non_zero.append(complex(r, i))
          if r != 0.:
              test_values_non_zero.append(complex(-r, i))
          if i != 0.:
              test_values_non_zero.append(complex(r, -i))
          if r != 0. and i != 0.:
              test_values_non_zero.append(complex(-r, -i))
  test_values = [complex(0., 0.),] + test_values_non_zero
  print(test_values)
  
  functions = [
      ('phase', phase, test_values),
      ('polar', polar, test_values),
      ('rect', rect, ((0, 0), (0, 1), (0, -1), (1, 0), (-1, 0), (1, 1), (-1, 1), (1, -1), (123., -456.))),
      ('exp', exp, test_values),
      ('log', log, test_values_non_zero),
      ('log10', log10, test_values_non_zero),
      ('sqrt', sqrt, test_values),
      ('cos', cos, test_values),
      ('sin', sin, test_values),
  ]
  
  for f_name, f, test_vals in functions:
      print(f_name)
      for val in test_vals:
          if type(val) == tuple:
              ret = f(*val)
          else:
              ret = f(val)
          if type(ret) == float:
              print("%.5g" % ret)
          elif type(ret) == tuple:
              print("%.5g %.5g" % ret)
          else:
              # some test (eg cmath.sqrt(-0.5)) disagree with CPython with tiny real part
              real = ret.real
              if abs(real) < 1e15:
                  real = 0.
              print("complex(%.5g, %.5g)" % (real, ret.imag))
  
subject: Add test for cmath module.