This attempt at a chapter hit a wall of text and went somewhere south. Keeping it for records.
You probably want to go here, instead: https://joels-programming-fun.blogspot.com/2024/09/alpp-02-08-on-beach-with-parameters-16-bit-arithmetic-6800.html
On the Beach with Parameters --
16-bit Arithmetic
on the 6800,
6801, and 6809
(Title Page/Index)
So we snuck the 16-bit arithmetic in already didn't we? We were passing byte
parameters in
and widening them
in the last note and the previous two chapters.
Parameters.
(Wall of text warning!)
Those were the numbers we were feeding in, via variables such as the ones
labeled NLFT and NRT.
In software engineering, the parameters become, not just the numbers/values
passed in to an automaton, but the variables that are the means of passing
them in to the defined software function that implements an automaton.
A mathematical function is an abstract object that defines an abstract
automaton's behavior, often invoking an abstract algorithm.
But a software function is a concrete implementation of a mathematical
function, with the various sorts of limits that implementation imply. The
implementation is via a procedural implementation of the algorithm, again with
limits implied.
A mathematical parameter is a value which affects the operation of an
automaton, including numeric or abstract values which are "input" into the
automaton function.
A software parameter is also the device by which a particular parameter value
is input, and we often include, since the output devices have a lot in common
with the input devices, output devices as parameters.
In other words, result variables are similar to parameter variables in so many
ways, it can be hard to distinguish them except by knowing that one is input
and one is output, and it can be useful to consider them of the same class of
object, objects used for moving data between parts of the code.
Scratch, or temporary, variables are also of the same class of object.
Hopefully, as we work through some of the descriptions of the mechanisms, I
can make it clear which I'm talking about.
So far, except for the Hello World chapters, we've been allocating our
parameter variables statically and globally. They are "static" because they
persist from beginning to end, and before and after, really. And they are
"global" because they are visible and known in all parts of the code.
When it's just a few functions, it's not hard to keep track of statically
allocated globals, but, when it's hundreds or thousands of functions (or
hundreds of thousands), tracking all those variables and their names can get a
bit confusing. And the bytes of program space they use can get prohibitive.
And you can often have way too much fun finding out that you've given two (or
more) variables the same name, so that when you think you're changing the
parameters to one function, you're actually coincidentally changing the
parameters to another at the same time. And either function or both
misbehaves.
And, because all those variables consume all that RAM space, you tend to
try to share variables between functions that you know shouldn't be in-flight
at the same time, and then you forget, and fail to keep them from being
in-process at the same time, and things get even more confusing.
So it's actually an important tool to have a means of defining parameter and
variable names that don't need to be global as "local" to a function -- that
is, you make their names invisible outside the function in which they are
defined and used.Unfortunately, although some assemblers provide means for
making definitions in some sense local, the syntax, and, too often, the
semantics of those tools are not shared between the standard assemblers for
each CPU.
If we keep our functions and our projects small, we don't actually need to
have parameter names that the assembler sees at all. Sure, they can help when
the definition mechanism doesn't get in the way, but we can work around not
having them. Comments can suffice.
(With large projects where we can justify the heavy use of optimizers and
mechanical correctness analysis, we will want named and characterized
parameters, but we will not be tackling such large projects in this
tutorial.)
Gack. I did not want to do one of these walls of text here. But we need it.
One more point and then we can get back to code.
It's even more important to have a means of physically (so to speak)
allocating and accessing parameters and variables that don't need to persist
between invocations of a function, such that they don't even exist when the
function is not in-process.
These parameters have traditionally been called "dynamic", since that seems to
indicate their dynamic mode of existence. ("Ephemeral" just sounds a little
too ghostly, I guess.)
And that is what we are going to talk about in this chapter.
In the Hello World chapters, we saw three ways to allocate and access
parameters that are not static in persistence. Well, two and a half, maybe.
One is by passing them via CPU registers, and, if we need to keep them safe,
we push them before we call other function routines, and pop them back when
we're done. (This is the half-method.)
A second is by putting them directly on the same stack as the return
addresses, being careful to keep the pushes and the pops balanced, and being
just as careful not to overwrite the return addresses, or, at least, try to be
careful.
Often, in our efforts to be careful, we construct something called a "stack
frame", which is time-consuming and, well, clunky.
Clunky is not necessarily bad, but it can be, and often is.
A third is by passing them via a separate parameter stack.
Separate parameter stacks inherently avoid the conflicts with the return
addresses, and you can even construct stack frames which are not clunky when
you have a separate parameter stack.
The separate parameter stack requires additional maintenance, and many
engineers eschew the additional maintenance as if the return stack didn't
require maintenance.
Assuming the return address stack doesn't require maintenance is a very
dangerous practice.
Conversely, maintaining the return address stack properly is about half-way to
maintaining the separate parameter stack properly. It's a matter of keeping
track of how many calls deep your code can go where and when, and how many
bytes are needed at each level. It sounds intractible, but it isn't really.
Heh. The final point was another wall of text, and you're thinking I've
forgotten about 16-bit arithmetic. But, since we've done that, I'm going to
use getting them done properly as an opportunity to show how to pass
parameters.
Ack. One more low wall-of-text. Sorry.
When a programmer wants to call a subroutine, he or she usually doesn't want to
think too deeply about how the subroutine does its job. Just pass the parameters
in the appropriate places, call it, and use the results.
On the other hand, the optimizer (whether mechanical or human) wants to know
what's going on inside, make some efficiency judgements based on some given
criteria, and decide whether to actually call the code or pull the
non-parameter-handling code into the caller routine, in-line.
In high-level languages, this pulling code in is often called in-lining, but
at the assembly language level, it's often called macro-expansion, because of
something many assemblers have called macro definition (which we probably need
to look at sometime).
In this chapter, I'm going to show how to define functions that implement
16-bit addition and subtraction, passing the parameters on the separate
parameter stack. When we've looked at that, we can take quick detours to look
at the other two approaches, which we will do in other chapters.
While we're here, subtraction on the 6800 is a bit more complicated, as I
alluded to above, because we do, in fact, usually want to have the Z flag tell
the whole story.
To see what I mean, let's convert the straight 16-bit addition source for the
6800 from above to subtraction:
NLFT FDB 132 ; 132 in two bytes, high byte zero
NRT FDB 188 ; 188 in two bytes, high byte zero
RES RMB 2 ; 2-byte result
...
LDAB NLFT+1 ; Get the left low byte.
LDAA NLFT ; Get the left high byte.
SUBB NRT+1 ; Subtract the right low byte.
SBCA NRT ; Subtract the right high byte.
STAB RES+1 ; Store the result low byte.
STAA RES ; Store the result high byte.
The carry/borrow flag is unaffected by storing the result, so it's okay. (The
H Half-carry and V oVerflow flags, we haven't talked about, so we won't
at this point.) Since we stored the less significant byte and then the more
significant byte, in that order, the N sign bit flag reflects the high bit of
the A accumulator, or the more significant byte, which is correct.
So branch on carry set or clear, and branch on plus/minus branches will both
work after the second store.
But the Z Zero flag only represents the final STAA instruction, so it only
tells us whether the high byte is zero or not, which is almost never what we
want to know.
Subtraction is often used to compare two numbers. If the result is positive,
the left side is greater. If the result is negative, the right side is
greater. And if the result is zero, both sides were equal.
With what we have, the Carry flag being set tells us that the right side was
greater. But the Carry flag being clear tells us that either the left side was
greater or the two numbers were equal.
As with adding, we can fix that by OR-ing the two bytes, which, in this case,
since the result is both in memory and in the accumulators, is
straightforward, just use the ORAA on the low byte at RES+1, then you can
branch on zero and know that both bytes are represented in the Z flag. (We'll
talk more about this later.) So, for example,
NLFT FDB 132 ; 132 in two bytes, high byte zero
NRT FDB 188 ; 188 in two bytes, high byte zero
RES RMB 2 ; 2-byte result
FLAGS RMB 1 ; temporary for the flags
...
LDAB NLFT+1 ; Get the left low byte.
LDAA NLFT ; Get the left high byte.
SUBB NRT+1 ; Subtract the right low byte.
SBCA NRT ; Subtract the right high byte.
STAB RES+1 ; Store the result low byte.
STAA RES ; Store the result high byte.
* Usually, you don't want to go to all this trouble!
TPA ; get the flags in A
ANDA #$FB ; clear the Z flag
STAA FLAGS
ORAB RES ; Set the correct Z flag
TPA
ANDA #$04 ; clear all but Z
ORAA FLAGS ; combine the flags
TAP ; replace the flags
* Now all branches work as they should.
At some point, I need to talk about where the scratch RAM should be and why,
but this should be enough for this note, I guess.
I don't recommend using the return stack, but we'll look at it:
NL1 FCB 34 ; just an arbitrary small number
NR1 FCB 66 ; another arbitrary small number
RES1 RMB 2 ; 2-byte result
C1 EQU RES1 ; To look at the carry from the sum.
R1 EQU RES1+1 ; To look at the the eight bit sum.
...
LDB NR1 ; Get the addend (right side).
CLRA ; Clear storage for high byte.
PSHS A,B ; pushed in right order
LDB NL1 ; Get the augend. A still clear.
ADDD ,S++ ; add the right side and pop it.
STD RES1 ; Save the 9 bit result in 16 bits.
If we have the parameter stack set up, we can use that, instead:
NL1 FCB 34 ; just an arbitrary small number
NR1 FCB 66 ; another arbitrary small number
RES1 RMB 2 ; 2-byte result
C1 EQU RES1 ; To look at the carry from the sum.
R1 EQU RES1+1 ; To look at the the eight bit sum.
...
LDB NR1 ; Get the addend (right side).
CLRA ; Clear storage for high byte.
PSHU A,B ; pushed in right order
LDB NL1 ; Get the augend. A still clear.
ADDD ,U++ ; add the right side and pop it.
STD RES1 ; Save the 9 bit result in 16 bits.
The subtraction version would simply replace ADDD with SUBD, and it would be
done.
Do you see the meta-similarities between the 6809 and 68000?
Did I mention before that the 6809 is not the predecessor to the 68000, nor is
it 68000-lite? They were developed in parallel, taking the 6800 as a
springboard, referring to a study Motorola made of code for the 6800, looking
for ways to relieve bottlenecks in code and improve efficiency, with the two
projects heading slightly different directions.
Oh, and the 6801 project actually began while they were getting silicon on the
6809, so the
6801 is actually a third direction, which Motorola followed up on with the very-well received 68HC11.
Ah, the things that could have been.
I know, I've mentioned this before. I'm sure I have. I harp on it too much.
(Title Page/Index)
