On Saturday, May 22, 2021 at 4:34:08 AM UTC-6, Bob Eager wrote:
> The more expensive machines had hardware implementation of that same
Yes. Compatibility between hardware and software is a big reason why
a format of a type usually used with one is also used with the other.
Basically, what I'm noting is that after looking at the floating-point formats
of a large number of historical machines, I found that most fell into one
of two categories:
the sign of the floating-point number as a whole
the exponent (including sign), most often as excess-n
- this format best preserves the ordering of floating-point numbers; if
the exponent and mantissa are inverted for negative numbers (as done
on the PDP-10 and the Sigma) floating-point numbers can have the
same ordering as two's complement integers
(I called this Group I)
the exponent as one integer, and
the sign of the floating-point number together with the mantissa
as another integer (although usually also normalilzed)
This is the easiest and most convenient format for software,
since you have two integers. The RECOMP II, with hardware
floating-point, used a version of this format to simplify the
hardware drastically, and the floating-point hardware add-on
for the PDP-8 also used it, as just two examples of it also
being used in hardware.
(I called this Group II)
And I found one variant of that to be worthy of mention in
its own right.
This is where:
- the mantissa+sign comes first;
- the format occupies two machine words;
- the first bit of the second machine word is either
a copy of the sign or unused.
The rationale behind that format was, in my opinion,
to allow efficient operation on a machine which
had hardware multiply for integers, but not floating-point
hardware... set up so that arithmetic on double-length
integers would be easy to do _if_ you didn't try to use
_all_ the bits, including the first bit, of the integer with
the less significant part, but instead allowed the sign to
be indicated in both halves.
(This is what I called Group III)
And so my point is that by having both the exponent and
mantissa in sign-magnitude form, putting the exponent
first, and putting the sign of the exponent at the end,
rather than the beginning of the exponent...
the Model 709 and TC-16 computers from the People's
Republic of China kept both sign bits together, just as they
are together (if the exponent were sign-magnitude, at least)
in Group I,
and yet both the bits of the exponent and the bits of the mantissa
are contiguous as they are in Group II...
thus making a unique format that doesn't really fit into any
of the categories that I found applied to all the other computers
I had seen.