Re: Arithmetics with carry

Hi Kevin

I would recommend you to search and study the instruction set of a
microprocessor
with the support you're trying to implement in your processor.

Many processors have two different add instruccions (with and without carry)
to support large integer arithmetic. The simplest I know of is the 8031
8-bit microcontroller
from Intel, Infineon, Dallas and many other manufacturers.

The first hit I found in google points to the page
http://www.rehn.org/YAM51/51set/instruction.shtml
It contains the description and some numeric examples for arithmetic
operations.

Of interest are:
    ADD   (A =A +x, carry is not used)
    ADDC (A=A+x+carry)
    SUBB (A = A-x-carry)


"Kevin Becker" <[EMAIL PROTECTED]> escribió en el mensaje
news:[EMAIL PROTECTED]
> Francisco Rodriguez wrote:
> > As your numbers are 32-bit wide, and overflow condition is a flag
> > about the result of the _whole_ v := v + i operation, it can be
determined
> > by the MSB bits only (that is, from columns 31 and 30 of the addition).
>
> Thank you! I think I used the wrong word "underflow". What I mean is:
> if "i" is negative, it might be that abs(lo(i)) is greater than lo(v).
> What happens then? An example:
>
> v = 1234 0100 hex
> i = 0000 0101 hex
>
> The operation for the lo bits will result in FFFF and the carry will
> be set. Then when I add the high bits, it will be 1235 when it should
> actually be 1233. How do I save that the first operation was not an


No.
I assume you're substracting the numbers, as i is positive and the
result you mention is v-i. Then, take into account that substraction
is performed by an adder in 2's complement arithmetic as follows:

v - i = v + 2's complement(i) = v + not(i) + 1

So v-i operation is converted to 12340100 + FFFFFEFE + 1 = 1233FFFF

The low part is 0100 + FEFF = FFFF,
the carry from the low part is _not_ set, so the high part is 1234 + FFFF =
1233

> overflow but a borrow? (I don't know how to call this. That's what I
> mistakenly called underflow).

Go to the mentioned page, you'll see the different descriptions for carry
(or borrow)
and the overflow.
Carry/borrow is the cy-16 out of the add operation (remember there's no
substraction
circuit). It is the overflow flag if and only if you're using unsigned
arithmetic
Overflow for signed arithmetic is cy-16 xor cy-15. When this xor gives you 1
means you've obtained a positive result adding two negative numbers, or a
negative result
adding two positives.

>
> Glen Herrmannsfeld wrote:
> > After the high halfword add, you compare the carry out to the carry out
of
> > the sign bit to the carry in of the sign bit.  If they are different
then it
> > is overflow or underflow.  The value of such bit tells you which one.
>
> So does that mean I have to modify my architecture and set TWO flags?
> A carry flag and a negative flag (if sign of last operation was
> negative), and then the Add-With-Carry instruction would look at both?

Never look at both.
Your ALU must provide two flags, carry and overflow, and two different add
instructions
x+y and x+y+carry. Of course, every add must update both flags.
If you also provide set-carry/clear-carry instructions, the pseudocode of
the 32-bit operations would be

for 32-bit additions:
    add x-low, y-low
    addc x-high, y-high

for 32-bit substractions:
    set carry
    addc x-low, not(y-low)
    addc x-high, not(y-high)

When the whole operation is finished, check carry/borrow if the 32-bit
numbers are unsigned,
or the overflow flag if the 32-bit numbers are signed. But no both.
Don't check the flags after the low part.

>
> Thanks a lot!

Best regards
    Francisco