Tiny values with nonzero low-order digits

Powers of the radix don’t tell the whole story, so Paranoia computes a parallel set of tiny values with nonzero low-order digits. Just adding a useful number of units in the last place is a challenge, so read about SAFE_ULPS_OF_ONE in the section on constants. The function tiny_values_and_difference(), returns seven values to be used in the following tests. They are explained in the discussion of the function.

# Constant SAFE_ULPS_OF_ONE = B OR 1 * ULP_OF_ONE_PLUS should have
# enough units in the last place of 1 to leave something nonzero
# in multiplication, even if there's no guard digit.
one_plus_safe = ONE + SAFE_ULPS_OF_ONE

# Compute a rich set of values analogous to the tiniest powers of B, but with
# nonzero low-order bits and attention to the differences of small values.
(less_tiny_x, tiny_x, too_tiny_x, underflow_threshold, add_sub_tiny,
 add_sub_hi, add_sub_lo) = tiny_values_and_difference(one_plus_safe)
print("***less_tiny_x, tiny_x, too_tiny_x = {:.7e} {:.7e} {:.7e}"
      .format(less_tiny_x, tiny_x, too_tiny_x))
print("***underflow_threshold, add_sub_tiny, add_sub_hi = {:.7e} {:.7e} {:.7e}"
      .format(underflow_threshold, add_sub_tiny, add_sub_hi))