Abnormal normalizations?

[uunet!cwi.nl!Dik.Winter]

 > My question was simply whether or not such a normalization could or might
 > occur... an issue which (I believe) is essentially independent of the
 > comparison of NaNs, and also totally independent of the knothole effect.

Can normalizations occur that cut off bits and precision on assignment?
I think yes.  On the machines I know/have known there are two kinds of
normalization:
1.  A number is normalized if the most significant machine-radix digit
    of the mantissa is non-zero.  This is the most standard way of
    normalization; it shifts to the left the mantissa, decreasing the
    exponent, until that digit is non-zero.  This *can* result in
    underflow which can be rewritten as zero.  This could happen on
    CDC Cybers and can happen on Cray's for instance.
2.  A number is normalized if the absolute value of the exponent is
    minimal.  (A.A. Gray representation, makes conversion to/from
    integer easier.)  In this case normalization shifts the mantissa
    to the right or left at the same time increasing or decreasing the
    exponent; depending on the size of the exponent.  But the machines
    I know that implemented this representation stopped shifting as soon
    as non-zero bits would shift out or if a shift would result in
    over- or underflow.
IEEE machines do not allow this because the leading mantissa bit is hidden,
so on assignment no normalization takes place.  The Gray representation
machines I know also do not allow this.  It can take place on machines
where assignment does normalize and the leading mantissa bit is not hidden.

I do not know off-hand the situation on Cray's, but I know that on the
Cyber it was possible to get an unnormalized result from an operation
which would be normalized on assignment to another variable; losing
precision due to underflow.