Case 1 arises in arithmetic that flushes underflows to zero. The comment explains that the underflow threshold is backed up to the next power of B if the computation of add_sub_hi cannot be reproduced, indicating some anomaly.
The call to test_tiny_differences() explores whether the differences between unequal values are zero. It applies to all of cases 1-3.
else:
# Case 1
underflow_threshold = base_tiny # Safe value computed above
# A sanity check determines that the result from
# tiny_x_and_difference() matches expectation, based on the
# loop on powers of B. The factor one_plus_safe accounts for
# the difference between the tiny_B and tiny_x loops.
# h_fact accounts for the case that what ought to be the
# tiniest power of B in the representation is given the value
# zero. If these don't match, the threshold is backed up a
# factor of B.
if ((ONE_OVER_C * add_sub_hi)
!= ((ONE_OVER_C * less_tiny_B) * one_plus_safe * h_fact)):
underflow_threshold = less_tiny_B
bad_cond(err_failure,
"Either accuracy deteriorates as numbers\n")
print("approach a threshold = {:0.17e}"
.format(underflow_threshold))
print(" coming down from {:0.17e}".format(C))
print(" or else multiplication gets too many ", end="")
print("last digits wrong.")
pause()
# Cases 1-3 fall through to a final test for zero differences.
test_tiny_differences()