+++ /dev/null
-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).
-
-<!-- vim: set sw=2 sts=2 ts=8: -->
+++ /dev/null
-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)
+++ /dev/null
-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.
projects / matthijs / master-project / report.git / commitdiff