From: Matthijs Kooijman Date: Tue, 23 Feb 2010 09:51:59 +0000 (+0100) Subject: Remove some progress documents, they are being stored elsewhere. X-Git-Url: https://git.stderr.nl/gitweb?a=commitdiff_plain;p=matthijs%2Fmaster-project%2Freport.git Remove some progress documents, they are being stored elsewhere. --- diff --git a/progress-2009.01.14.txt b/progress-2009.01.14.txt deleted file mode 100644 index cc70be2..0000000 --- a/progress-2009.01.14.txt +++ /dev/null @@ -1,125 +0,0 @@ -Language Design -=============== -A central question is, what do we want our language to look like? Deciding to -use haskell would be a first step, but that still leaves a lot of -possibilities. However, why would we want to use Haskell? - - * Lots of existing support: Language specification, compilers, libraries, - userbase. All of this reduces the workload to implement something. - * All of Haskell is usable in simulation / testing: When not compiling to - VHDL, but when doing functional tests, we can use all of Haskell's syntax, - libraries, functions, etc. even when we don't support all of it in our - compiler. - * Haskell is probably expressive enough to be able to express a lot of - different things and different approaches. By defining new (algebraic) - types and operators, we can extend this even further. Finally, we could - even use Template Haskell to do almost anything (The ForSyDe project uses - Template Haskell extensively). - -Typing ------- -What kind of types will we be using in our programs? The base type should be -some kind of bit type, but there are two main options for these: - - * Use a single bit as a type. Calculations on these types represent the - calculations in a single time slice (ie, during one clock cycle). Any - state in the calculation is explicit, since the input state must be a - function argument and the output state part of the function's value. - - Through the state values, these functions are closely tied to the clock - domain in use (or whatever other model is used for the time domain). Ie, - having different clock domains is non-trivial and will require - modification to the function. - - Composition can be done by simply connection functions together. This does - require that the "state" of a function contains the states of each of the - function it calls. These are extracted from its state argument and passed - on to the callees, while the states returned are again inserted into the - resulting state of the outer function. - - This approach is the closest to normal functional programming and shows - state very explicitly. - - * Use a stream of bits as a type. Each value models a continuous (infinite) - stream of bits. Functions have streams as arguments and value and state - could probably be implicit in the calculation or could be made explicit - using delay elements (this is what Lava does). - - The primitive operations all operate on streams, which seems the - fundamental difference between this and the previous approach. - - This approach shows structure more explicitly when delay elements are - used, since the registers end up exactly there. - -It is probably possible to mix these approaches. In particular, the first -approache eventually needs to do some I/O, which can be modeled as recursion -over an infinite list of inputs resulting in an infinite list of outputs. This -can be done at the top level always, but it is perhaps possible to move this -recursion a bit downward and do composition based on stream functions instead -of "single clock" functions. One problem that comes to mind is that one needs -to guarantee that a function does not look into the future (ie, uses multiple -input elements to generate one output element) and the state becomes a lot -less explicit. This needs more thought. - -Implementation -============== -Assume we will want to translate a (subset of) haskell into something else. -We will need to do parsing, typechecking, interpretation, etc. A few options -for this are available: - - * Doing everything manually, possibly using a parser generator. - Lot's of work. Requires us to write down the haskell grammar, create a - parser, do all kinds of funky type checking -> Too much work. - * Use the Language.Haskell library and write something in haskell. This - library contains a Lexer, Parser and AST, but still does not do any type - checking, desugaring and simplification. Still lots of work. - * Hack into an existing compiler. By writing a backend for an existing - compiler, we can save most of the haskell-specific work. This requires a - compiler that is modular enough to have its backend replaced by another - implementation. Also, the border between backend and frontend must be - suited for the work we would like to do. This approach would use the - original compiler's driver for the most part - * Use components from an existing compiler. By reusing selected components - and creating an own driver that uses these components, we can work with - the haskell source without doing all the work ourselves. This requires a - compiler that is very modular, so we can decide exactly which parts we - would like to use and which we don't need. - -After some looking around it seems GHC provides a consistent and (as of -version 6.10) documented API into its internals This allows us to write - - core <- compileToCoreSimplified "adder.hs" - -to compile the file `adder.hs` into a version in GHC's simplified CoreSyn -representation. This is essentially an AST with type annotations, all -syntactic sugar removed, redundant expressions simplified, etc. This seems to -be a very useful form to work with. However, GHC provides other functions to -access other parts of the compiler, so if we would like to access the source -at another stage, or do some custom procesing in between, this is also -possible (albeit a bit more complex than this). - -Problems --------- -Some problems encountered or expected when trying to do some initial -translator hackup: - - * Signal naming. In the generated VHDL the signals and ports need names. - These can of course be generated, but if we want to do some actual - debugging, we want useful signal names. For input ports generated from - function arguments, the binder name could perhaps be used, but that is not - always possible when patterns are more complex. - - For output ports, a name could be deduced when the output value is always - computed in a where or let clause. However the simplification phase - removes these clauses where possible, so this information is lost. - - Perhaps some way of explicitely labeling ports could be used. - * Type classes and universal qualification types are a powerful way of - making functions generic, which greatly increases their reusability. - However, this extra genericity makes the resulting Core representation - more complex. Since the actual types used are modeled as extra function - arguments, this shouldn't be too hard, but this is something that probably - needs implementation right away (because a lot of builtin haskell - constructs, such as tuples, use it). - - diff --git a/progress-2009.01.28.txt b/progress-2009.01.28.txt deleted file mode 100644 index e690697..0000000 --- a/progress-2009.01.28.txt +++ /dev/null @@ -1,245 +0,0 @@ -How to model hardware? -====================== -So far, we've had some ideas about how to model hardware using a functional -language. The general idea is that every function that models hardware has -some input signals, some "input" state and a few output signals and "output" -state. But how do we represent this exactly in our haskell code? - -The output part is probably easiest, since a function always returns a single -value. Since it needs to return both output signals and a state, it seems -obvious to make it always return a 2-tuple containing the state and output -signals. So: - - circuit :: ? -> (State, Signals) (1) - -It's interesting to note that the State and Signal types here are not really -important when simulating, so let's look at the inputs first. - -Again, we have both input signals and a state to pass to the function. It -seems consistent to again do this a single tuple, so a circuit becomes: - - circuit :: (State, Signals) -> (State, Signals) (2) - -I've not given this variant a lot of thought yet, but i have the feeling this -is not all to useful. The variant I've been using so far separates the state -and signals into separate arguments: - - circuit :: Signals -> State -> (State, Signals) (4) - -Note that this uses a seemingly inconsistent order for the arguments, but -that's mostly because the current implementation uses this order (and wasn't -well thought out). The exact order is mostly relevant for partial application, -but I'm not quite sure if that's possible or useful at all. - -This variant makes it easy to define a dependent type for all circuits, which -you pass the input, state and output types as an argument: - - type Circuit a s b = a -> s -> (s, b) (5) - -A last variant would be to separate each (or perhaps only some) input signals -into different arguments, such that each input has its own argument. For -example, for a two input port circuit: - - circuit :: Signal -> Signal -> State -> (State, Signals) (6) - -This has the obvious advantage that it could support partial application of -the input ports (ie, connect a few input pins to a circuit and pass the -resulting function elsewhere). I'm not sure how that would or should work out, -but it seems useful. - -However, this partial application seems only possible with input ports, which -might limit its usefuleness. Also, this type signature makes it harder to -define a single Circuit type that catches all circuits as with (4) and (5). -This might make simulation more tricky, though it's probably not critical. - -Signals (or Ports?) -------------------- -Now, regardless of which of the above approaches we choose, there should be -some way to model these signals and ports. So far, a basic Bit signal type -has been used: - - data Bit = High | Low | DontCare (7) - -For now, this is the only primitive type supported by the (Haskell-to-VHDL) -translator, but as pointed out above the simulator doesn't really care about -these types (as long as the input provided is of the right type). Supporting -native Haskell types (or perhaps our own variants, *e.g.*, an Int with a fixed -bit width) is probably needed later on as well. - -To allow for multiple input and output ports in a single value, tuples can be -used. This allows for grouping multiple signals while still allowing each -signal to have a different type. - -An alternative that has not been explored yet is the use of an algebraic type -to group signals. This seems to have the direct advantage of allowing names -for each element to be specified, but does add some overhead in type -declarations. It's likely that a combination of tuples and algebraic types are -best. - -It appears that lists might become useful to model VHDL (bit)vectors, since -both lists and vectors have elements of the same type. This does require that -the length of a list can be deduced at compile time. - -DontCare --------- -In the above definition of the Bit datatype a DontCare element was present. -The idea behind this element was to assign it anywhere the value of the bit -shouldn't matter (in the alu example, this is but on the input signals that -should be ignored). Since it is not used in any other place (*e.g.*, patterns -usually only match Low and High, including the display functions), Haskell -should error out as soon as a DontCare value is actually used. Due to the lazy -nature of Haskell's evaluation, this should never happen as long as the value -is not really used. But as soon as the value is (indirectly) needed, *i.e.*, -contributes to the output of a circuit, Haskell errors out. - -Some functions ignore some inputs. For example, hwor is defined as: - - High `hwor` _ = High (8) - _ `hwor` High = High - Low `hwor` Low = Low - -This means that High `hwxor` DontCare will still be High (with no error), but -that DontCare `hwand` DontCare will immediately throw an error. This seems to -be desired behaviour, but this needs more investigation. - -State ------ -For state, we can mostly do the same reasoning as for signals (from the -circuit description point of view, input state and output state is hardly any -differen from input signals and output signals). For combining multiple -elements of state (either because a circuit has multiple Bits of state or -because it combines the states of each of its subcircuits), tuples can be -used. Algebraic types might have a use here as well. - -Stateless circuits ------------------- -Above we've concentrated on stateful circuits, but probably a lot of circuits -will be stateless. This can simply be modeled by having an empty state -(*i.e.*, () ), but that's not very elegant. However, not all of the above -approaches are usable for supporting stateless circuits. For example, if we -adapt (2) to be stateless: - - stateless_circuit :: Signals -> Signals (9) - -Now, considering that we allowed Signals to be a tuple of multiple signals, -the following two circuit types are indistinguishable, since the State and -Signal types are the same. - - stateless_circuit :: (Signal, Signal) -> (Signal, Signal) (10) - stateful_circuit :: (State, Signal) -> (State, Signal) - -Something similar goes for (6), where leaving out the state for stateless -circuits would make a stateless circuit with two inputs and two output -indistinguishable from a stateful circuit with a single input and a single -output. - -(4) above seems best suited for adapting for stateless circuits, since it -always has two arguments (inputs and state). A stateless variant would always -have a single argument. - -Examples --------- -To get a feeling for things, here are some example using approach (6). - -Some stateless adders: - - -- Combinatoric stateless no-carry adder - -- A -> B -> S - no_carry_adder :: (Bit, Bit) -> Bit - no_carry_adder (a, b) = a `hwxor` b - - -- Combinatoric stateless half adder - -- A -> B -> (S, C) - half_adder :: (Bit, Bit) -> (Bit, Bit) - half_adder (a, b) = - ( a `hwxor` b, a `hwand` b ) - - -- Combinatoric stateless full adder - -- (A, B, C) -> (S, C) - full_adder :: (Bit, Bit, Bit) -> (Bit, Bit) - full_adder (a, b, cin) = (s, c) - where - s = a `hwxor` b `hwxor` cin - c = a `hwand` b `hwor` (cin `hwand` (a `hwxor` b)) - -A simple four bit cyclic shift register, which has an input that can be used -to toggle (xor) the first position. - - type ShifterState = [Bit] - shifter :: Bit -> ShifterState -> (ShifterState, Bit) - shifter i s = - (s', o) - where - s' = (o `hwxor` i) : (init s) - o = last s - -An implementation of a simple ALU (supporting only two operations: or & and on -two one-bit inputs) combined with a register bank containing two one-bit -registers. It also contains a list of inputs (the program), an initial state -and some wrappers around the simulation functions (main and mainIO). - - main = Sim.simulate exec program initial_state - mainIO = Sim.simulateIO exec initial_state - - program = [ - -- (addr, we, op) - (High, Low, High), -- z = r1 and t (0) ; t = r1 (1) - (Low, Low, Low), -- z = r0 or t (1); t = r0 (0) - (Low, High, DontCare), -- r0 = z (1) - (High, Low, High), -- z = r1 and t (0); t = r1 (1) - (High, High, DontCare) -- r1 = z (0) - ] - - initial_state = ((Low, High), (), Low, Low) - - -- Register bank - - type RegAddr = Bit - type RegisterBankState = (Bit, Bit) - register_bank :: - (RegAddr, Bit, Bit) -> -- (addr, we, d) - RegisterBankState -> -- s - (RegisterBankState, Bit) -- (s', o) - - register_bank (Low, Low, _) s = -- Read r0 - (s, fst s) - - register_bank (High, Low, _) s = -- Read r1 - (s, snd s) - - register_bank (addr, High, d) s = -- Write - (s', DontCare) - where - (r0, r1) = s - r0' = if addr == Low then d else r0 - r1' = if addr == High then d else r1 - s' = (r0', r1') - - -- ALU - - type AluState = () - type AluOp = Bit - - alu :: (AluOp, Bit, Bit) -> AluState -> (AluState, Bit) - alu (High, a, b) s = ((), a `hwand` b) - alu (Low, a, b) s = ((), a `hwor` b) - - type ExecState = (RegisterBankState, AluState, Bit, Bit) - exec :: (RegAddr, Bit, AluOp) -> ExecState -> (ExecState, ()) - - -- Read & Exec - exec (addr, Low, op) s = - (s', ()) - where - (reg_s, alu_s, t, z) = s - (reg_s', t') = register_bank (addr, Low, DontCare) reg_s - (alu_s', z') = alu (op, t', t) alu_s - s' = (reg_s', alu_s', t', z') - - -- Write - exec (addr, High, op) s = - (s', ()) - where - (reg_s, alu_s, t, z) = s - (reg_s', _) = register_bank (addr, High, z) reg_s - s' = (reg_s', alu_s, t, z) diff --git a/progress-2009.02.04.txt b/progress-2009.02.04.txt deleted file mode 100644 index 0b475d1..0000000 --- a/progress-2009.02.04.txt +++ /dev/null @@ -1,211 +0,0 @@ -What is a function? -=================== -In general, a function is something providing a mapping from a number of input -arguments to a number of results. Each of these arguments and results can be -normal values, but also again functions. - -Function application is evaluating the mapping for a given set of input -operands. - -Looking at this from a hardware modeling perspective, we get different -results. Then, a function is essentially a template for a circuit, with each -of the arguments and results representing input and output ports. Optionally, -some of the arguments and results (always matched pairs) can become part of -the state, meaning that they generate a register that connects to the argument -and result concerned. - -Function application, then, is embedding the function's circuit template into -the callers circuit template, connecting any arguments and results to the -circuit's ports. This embedding will completely decouple the applied function -from the original function: The circuit may look alike, but different -applications have no connection or shared components in the final hardware. - -This is an important property, since it allows the caller complete freedom in -inlining, simplifying and changing any functions it applies. Or more -specifically, a caller can clone a function and modify the clone freely -(since it is the only caller of it). Since every application is unrelated to -all others, cloning a function has no extra cost whatsoever (unlike function -duplication in software, where the code size greatly increases). - -The above view works only for functions accepting and returning primitive -values, *i.e.*, that can be represented as (possibly multiple) VHDL signals -directly. In particular, functions cannot be used as arguments or returned -from functions. - -High order functions and partial evaluation -=========================================== -Before wondering how we implement high order functions and partial evaluation, -let's see where we would like to use them. - -Modifying function signature ----------------------------- -A simple application of high order functions is modifying a function's -signature. An example of this is the (un)curry function. In hardware, a -stateless function could be used to make a stateless function conform to the -standard signature and make it synthesisable / simulatable: - - stateless :: (a -> b) -> (a -> () -> ((), b)) - stateless f i s = (s, f i) - -This would be used to make some function foo statefull as follows: - - stateful_foo = stateless foo - -Another example would be to swap the order of inputs: - - swap_in :: ((a, b) -> o) -> ((b, a) -> o) - swap_in f (b, a) = f (a, b) - -Both of these examples take a function as argument, but return plain values -(though swap_in could return a high order function when the function passed in -has multiple arguments). - -Reusing common code -------------------- -When modeling an ALU, we could imagine generalizing the ALU operations and -making the control code independent of the actual operation. - -The following alu models a circuit with three input: A one bit opcode and two -inputs. The opcode selects between two operations, bitwis and and bitwise or. - - and_or_alu :: (Bit, Bit, Bit) -> BIt - and_or_alu (o, a, b) = - if o == Low - then hwand a b - else hwor a b - -Now, we might want to generalize this to be independent of the actual -operations peformed: - - type operation = Bit -> Bit -> Bit - alu :: operation -> operation -> (Bit, Bit, Bit) -> Bit - - alu op1 op2 (o, a, b) = - if o == Low - then op1 a b - else op2 a b - -Now, we can write the above specific alu as: - - and_or_alu = alu and or - -Parameterized circuits ----------------------- -This is probably a variant on the above, but using literal parameters instead -of functions as parameters. - -Finding a good example of this seems hard, since a lot of parameterized -circuits are implicitly parameterized using the length of lists in their -input, output or state. - -A possible example could be a program counter, that is a incrementing -register. The amount by which to increment the register depends on the -instruction word size, which you might want to make generic. - - pc :: Int -> Word32 -> (Word32, Word32) - pc n s = - (s', o) - where - s' = s + n - o = s - -Since this example is only useful when using some kind of integers instead of -just Bits, this assumes Word32 can actually be used. - -Partial application -------------------- -Say we have some encryption circuit, that encrypts a stream by xor'ing it with -some key stream. - - crypt :: (s -> (s, Bit)) -> Bit -> s -> (s, Bit) - crypt f i s = - (s', o) - where - (s', key) = f s - o = hwxor i key - -Now, we have some function taking in some source of entropy (modeled as a -signal of type Foo) and uses that to generate a (pseudo) random keystream. The -implementation of this function is not so important. Also, the type KeyState -represents the state of mkKey, but what it is exactly doesn't really matter. - - mkKey :: Foo -> KeyState -> (KeyState, Bit) - -Now, I can create a full crypt system as follows. This function has a Foo and -Bit input signals and a Bit output signal. - - crypt_full :: Foo -> Bit -> KeyState -> (KeyState, Bit) - crypt_full foo i s - crypt keygen i s - where - keygen = mkKey foo - -Now, this example isn't particularly good, since it would be just as easy to -simply make crypt take a Bit as input instead of a function generating bits -(This is probably also how you would synthesize something like this). Perhaps -more useful examples could be found, where passing a function makes notation -a lot easier than passing the function's (remaining) inputs and outputs -around. - -Preconnecting ports -------------------- -Sometimes it is useful to connect some ports of multiple similar pieces -of hardware to the same signal. For example, the following builds a -multibit multiplexer by mapping a bunch of single bit ones together. -Since all multiplexers use the same select input, we pass it to mplex_1 -and then pass the result to map. This makes the code clearer than -replicating the select input (length abs) times and using zipWith -instead of map. - - mplex_1 :: Bit -> (Bit, Bit) -> Bit - mplex_1 enable select (a, b) = - if select == Low then a else b - - mplex :: Bit -> [(Bit, Bit)] -> [Bit] - mplex select abs = - map (mplex_1 select) abs - -State ambiguity -=============== -Previously, we've concluded that choosing to translate an argument or result -to either a state variable or port would be possible by requiring a specific -type signature on the top level function and hierarchically looking which -variables are thus also state variables. - -In practice, this appears harder than we thought. We can observe that a state -variable should resolve to a register, but where exactly is undefined. In -particular, we could simply translate all arguments and results to ports, and -on the highest level instantiate registers for all state variables. -Functionally, this is completely correct, but this is probably not what we -want in most cases. Each function that has state will probably want to have -that state represented inside it's architecture, rather than to have two ports -which should be connected to a register externally. - -This means we need to "push" the registers down the hierarchy to get them -where they "belong". Somewhere down the line, however, a state variable will -eventually be used in some way, often by passing it to another function -(*i.e.*, connecting the output of the register to some other circuit). The -place where this happens is also the place where you want the register to end -up. - -In a lot of cases, this place is also as far as you can push the register down -(when you pass the current register value to some function a, but bind the new -register value to the result of some function b, you can't push further down -since both a and b use the register). The tricky part is now when you pass a -state value to some function a and that same function a produces the new value -of the state value. Is the state value now really a state of the function a, -or did the programmer just mean to connect a register to function a -externally? - -Note that this assumes some clever implementation for finding out if the state -can be pushed down, which takes things into account like "is the current state -only used once", "is the new state directly produced by the application that -also uses the state", "which state value in the arguments belongs to which -value in the function result". Actually implementing this will probably need -some extra thought, initially having all the state at the top level is -probably fine. - -It's probable that this case will not occur that often, and some extra -heuristics might help to guess the right thing more often. Adding some "force -state here" primitive will probably possible as well for final disambiguation. -Still, it would nicer to really solve this problem somehow.