[gpsim-devel] overflow flag

[Eric S. <er...@br...>]

In searching the archives for messages regarding LCDs, I see that there
was some discussion of the overflow flag not too long ago.  Perhaps
this has already been resolved, but in case it hasn't...

I don't know how Microchip has implemented this, and have not tried
writing a test program, but I do know what most if not all other
microprocessors do.

Suppose you're doing an eight-bit add, so your operands are a7..a0 (MSB
through LSB), b7..b0, and c0 (carry in).  Your result is r7..r0 and
c8 (carry out).  Inside the adder, there is a carry from each stage to
the next.  (Assume a ripple carry adder; the actual implementation may be
different but the principle is the same.)  So the carry from stage 6 to
stage 7 is c7.

The overflow is c7 xor c8.

In C this can be done with two additions, some masking and shifting,
and an xor:

sum = a + b + c0;
r = sum & 0xff;
c8 = sum >> 8;
v = (c8 ^ ((((a & 0x7f) + (b & 0x7f) + c0) & 0x80) >> 7)) & 1;

This can be extended in the obvious way for longer (or shorter)
word lengths.  Replace 8, 7, 0x80, and 0x7f with wsize, (wsize-1),
(1<<(wsize-1)), and ((1<<(wsize-1))-1).

For subtraction, the same thing applies.  The carry in and out are
considered to be "not borrow".  The b operand is inverted (ones
complement), and an add is performed.  For subtract without a borrow
input, set the carry input of the adder to one (no borrow).

Some microprocessors implement a "true borrow"; this is done by
having the hardware invert the carry in and carry out during a
subtract instruction.  The PIC does not do this, because it would
take two extra exclusive OR gates, and provide no real benefit.

Eric