The next big comment puts the two sets of tiny values in context. Paranoia introduces the concept of pseudo zero, for values that compare unequal to zero yet may behave like zero in some operations. The Control Data CDC 6000 series of machines had such tiny, seemingly nonzero values that infallibly behaved like zero in multiplication and division. They were encoded with the smallest representable exponent – the same exponent as true zero – so the designers saved a bit of hardware by simply treating all such numbers as zero during multiplication and division. They behaved correctly in addition and subtraction. This flaw lived on into Cray supercomputers, too.
[Insert Jamie Sethian example. Ponder whether to libel Seymour Cray here, evenœpolitely.]
After the comment, the call to test_for_pseudo_zero() is made strictly for the side effect.
# The two sets of tiny values characterize the underflow behavior.
# The following comments mirror BASIC comments 4530-4560. The relational ">~"
# may be loosely read "greater than or kind of equal to". It refers to the odd
# behavior of some arithmetics near 0, where some "pseudo zero" values behave
# like zero in some contexts and nonzero in others.
#
# 1 >> C = 1/B^k >= less_tiny_B > tiny_B >~ too_tiny_B >~ 0
# where the tiny values differ by a factor of H
#
# 1 >> d = (1+SAFE_ULPS_OF_ONE)*C >= underflow_threshold
# >= add_sub_hi >= less_tiny_x > tiny_x >~ too_tiny_x >~ 0
# where underflow_threshold = d * H^k is the first NONZERO value to
# violate (x*H)/H = x else underflow_threshold = 0
# and where add_sub_hi = underflow_threshold * H^k is the first to satisfy
# add_sub_tiny <- |(x*H)/H - x| > 0 else add_sub_hi = less_tiny_x
test_for_pseudo_zero(too_tiny_x)