clash-prelude-0.11.2: CAES Language for Synchronous Hardware - Prelude library

CLaSH.Tutorial

Description

Synopsis

# Introduction

CλaSH (pronounced ‘clash’) is a functional hardware description language that borrows both its syntax and semantics from the functional programming language Haskell. It provides a familiar structural design approach to both combination and synchronous sequential circuits. The CλaSH compiler transforms these high-level descriptions to low-level synthesizable VHDL, Verilog, or SystemVerilog.

Features of CλaSH:

• Strongly typed, but with a very high degree of type inference, enabling both safe and fast prototyping using concise descriptions.
• Interactive REPL: load your designs in an interpreter and easily test all your component without needing to setup a test bench.
• Compile your designs for fast simulation.
• Higher-order functions, in combination with type inference, result in designs that are fully parametric by default.
• Synchronous sequential circuit design based on streams of values, called Signals, lead to natural descriptions of feedback loops.
• Multiple clock domains, with type safe clock domain crossing.
• Template language for introducing new VHDL/(System)Verilog primitives.

Although we say that CλaSH borrows the semantics of Haskell, that statement should be taken with a grain of salt. What we mean to say is that the CλaSH compiler views a circuit description as structural description. This means, in an academic handwavy way, that every function denotes a component and every function application denotes an instantiation of said component. Now, this has consequences on how we view recursively defined functions: structurally, a recursively defined function would denote an infinitely deep / structured component, something that cannot be turned into an actual circuit (See also Limitations of CλaSH).

On the other hand, Haskell's by-default non-strict evaluation works very well for the simulation of the feedback loops, which are ubiquitous in digital circuits. That is, when we take our structural view to circuit descriptions, value-recursion corresponds directly to a feedback loop:

counter = s
where
s = register 0 (s + 1)


The above definition, which uses value-recursion, can be synthesized to a circuit by the CλaSH compiler.

Over time, you will get a better feeling for the consequences of taking a structural view on circuit descriptions. What is always important to remember is that every applied functions results in an instantiated component, and also that the compiler will never infer / invent more logic than what is specified in the circuit description.

With that out of the way, let us continue with installing CλaSH and building our first circuit.

# Installation

The CλaSH compiler and Prelude library for circuit design only work with the GHC Haskell compiler version 8.0 (lower versions of GHC are not supported).

1. Install GHC 8.0

• Download and install GHC for your platform. Unix user can use ./configure prefix=<LOCATION> to set the installation location.
• Make sure that the bin directory of GHC is in your PATH.

In case you cannot find what you are looking for on https://www.haskell.org/ghc/download_ghc_8_0_2, you can, alternatively, use the following instructions:

• Ubuntu:

• Run: sudo add-apt-repository -y ppa:hvr/ghc
• Run: sudo apt-get update
• Run: sudo apt-get install cabal-install-1.24 ghc-8.0.2 libtinfo-dev
• Update your PATH with: /opt/ghc/8.0.2/bin, /opt/cabal/1.24/bin, and $HOME/.cabal/bin • Run: cabal update • Skip step 2. • OS X: • Follow the instructions on: Haskell Platform Mac OS X to install the minimal Haskell platform • Run: cabal update • Skip step 2. • Windows: • Follow the instructions on: Haskell Platform Windows to install the minimal Haskell platform • Run: cabal update • Skip step 2. 1. Install Cabal (version 1.24 or higher) • Binary, when available: • Download the binary for cabal-install • Put the binary in a location mentioned in your PATH • Add cabal's bin directory to your PATH: • Windows: %appdata%\cabal\bin • Unix: $HOME/.cabal/bin
• Source:

• Unpack (tar xf) the archive and cd to the directory
• Run: sh bootstrap.sh
• Follow the instructions to add cabal to your PATH
• Run cabal update
2. Install CλaSH

• Run:

• i386 Linux: cabal install clash-ghc --enable-documentation --enable-executable-dynamic
• Other: cabal install clash-ghc --enable-documentation
• This is going to take awhile, so have a refreshment
3. Verify that everything is working by:

• Run: clash --interactive FIR.hs
• Execute, in the interpreter, the :vhdl command
• Execute, in the interpreter, the :verilog command
• Execute, in the interpreter, the :systemverilog command
• Exit the interpreter using :q
• Examine the VHDL code in the vhdl directory
• Examine the Verilog code in the verilog directory
• Examine the SystemVerilog code in the systemverilog directory

# Working with this tutorial

This tutorial can be followed best whilst having the CλaSH interpreter running at the same time. If you followed the installation instructions, you already know how to start the CλaSH compiler in interpretive mode:

clash --interactive


For those familiar with Haskell/GHC, this is indeed just GHCi, with three added commands (:vhdl, :verilog, and :systemverilog). You can load files into the interpreter using the :l <FILENAME> command. Now, depending on your choice in editor, the following edit-load-run cycle probably work best for you:

• Commandline (e.g. emacs, vim):

• You can run system commands using :!, for example :! touch <FILENAME>
• Set the editor mode to your favourite editor using: :set editor <EDITOR>
• You can load files using :l as noted above.
• You can go into editor mode using: :e
• Leave the editor mode by quitting the editor (e.g. :wq in vim)

• Just create new files in your editor.
• Load the files using :l as noted above.
• Once a file has been edited and saved, type :r to reload the files in the interpreter

You are of course free to deviate from these suggestions as you see fit :-) It is just recommended that you have the CλaSH interpreter open during this tutorial.

The very first circuit that we will build is the "classic" multiply-and-accumulate (MAC) circuit. This circuit is as simple as it sounds, it multiplies its inputs and accumulates them. Before we describe any logic, we must first create the file we will be working on and input some preliminaries:

• Create the file:

MAC.hs

• Write on the first line the module header:

module MAC where


Module names must always start with a Capital letter. Also make sure that the file name corresponds to the module name.

• Add the import statement for the CλaSH prelude library:

import CLaSH.Prelude


This imports all the necessary functions and datatypes for circuit description.

We can now finally start describing the logic of our circuit, starting with just the multiplication and addition:

ma acc (x,y) = acc + x * y


If you followed the instructions of running the interpreter side-by-side, you can already test this function:

>>> ma 4 (8,9)
76
>>> ma 2 (3,4)
14


We can also examine the inferred type of ma in the interpreter:

>>> :t ma
ma :: Num a => a -> (a, a) -> a


Talking about types also brings us to one of the most important parts of this tutorial: types and synchronous sequential logic. Especially how we can always determine, through the types of a specification, if it describes combinational logic or (synchronous) sequential logic. We do this by examining the type of one of the sequential primitives, the register function:

register :: a -> Signal a -> Signal a
register i s = ...


Where we see that the second argument and the result are not just of the polymorphic a type, but of the type: Signal a. All (synchronous) sequential circuits work on values of type Signal a. Combinational circuits always work on values of, well, not of type Signal a. A Signal is an (infinite) list of samples, where the samples correspond to the values of the Signal at discrete, consecutive, ticks of the clock. All (sequential) components in the circuit are synchronized to this global clock. For the rest of this tutorial, and probably at any moment where you will be working with CλaSH, you should probably not actively think about Signals as infinite lists of samples, but just as values that are manipulated by sequential circuits. To make this even easier, it actually not possible to manipulate the underlying representation directly: you can only modify Signal values through a set of primitives such as the register function above.

Now, let us get back to the functionality of the register function: it is a simple latch that only changes state at the tick of the global clock, and it has an initial value a which is its output at time 0. We can further examine the register function by taking a look at the first 4 samples of the register functions applied to a constant signal with the value 8:

>>> sampleN 4 (register 0 (signal 8))
[0,8,8,8]


Where we see that the initial value of the signal is the specified 0 value, followed by 8's.

### Sequential circuit

The register function is our primary sequential building block to capture state. It is used internally by one of the CLaSH.Prelude function that we will use to describe our MAC circuit. Note that the following paragraphs will only show one of many ways to specify a sequential circuit, at the section we will show a couple more.

A principled way to describe a sequential circuit is to use one of the classic machine models, within the CλaSH prelude library offer standard function to support the Mealy machine. To improve sharing, we will combine the transition function and output function into one. This gives rise to the following Mealy specification of the MAC circuit:

macT acc (x,y) = (acc',o)
where
acc' = ma acc (x,y)
o    = acc


Note that the where clause and explicit tuple are just for demonstrative purposes, without loss of sharing we could've also written:

macT acc inp = (ma acc inp,acc)


Going back to the original specification we note the following:

• acc is the current state of the circuit.
• '(x,y)' is its input.
• acc' is the updated, or next, state.
• o is the output.

When we examine the type of macT we see that is still completely combinational:

>>> :t macT
macT :: Num t => t -> (t, t) -> (t, t)


The CLaSH.Prelude library contains a function that creates a sequential circuit from a combinational circuit that has the same Mealy machine type / shape of macT:

mealy :: (s -> i -> (s,o))
-> s
-> (Signal i -> Signal o)
mealy f initS = ...


The complete sequential MAC circuit can now be specified as:

mac = mealy macT 0


Where the first argument of mealy is our macT function, and the second argument is the initial state, in this case 0. We can see it is functioning correctly in our interpreter:

>>> import qualified Data.List as L
>>> L.take 4 $simulate mac [(1,1),(2,2),(3,3),(4,4)] [0,1,5,14]  Where we simulate our sequential circuit over a list of input samples and take the first 4 output samples. We have now completed our first sequential circuit and have made an initial confirmation that it is working as expected. ### Generating VHDL We are now almost at the point that we can create actual hardware, in the form of a VHDL netlist, from our sequential circuit specification. The first thing we have to do is create a function called topEntity and ensure that it has a monomorphic type. In our case that means that we have to give it an explicit type annotation. It might not always be needed, you can always check the type with the :t command and see if the function is monomorphic: topEntity :: Signal (Signed 9, Signed 9) -> Signal (Signed 9) topEntity = mac  Which makes our circuit work on 9-bit signed integers. Including the above definition, our complete MAC.hs should now have the following content: module MAC where import CLaSH.Prelude ma acc (x,y) = acc + x * y macT acc (x,y) = (acc',o) where acc' = ma acc (x,y) o = acc mac = mealy macT 0 topEntity :: Signal (Signed 9, Signed 9) -> Signal (Signed 9) topEntity = mac  The topEntity function is the starting point for the CλaSH compiler to transform your circuit description into a VHDL netlist. It must meet the following restrictions in order for the CλaSH compiler to work: • It must be completely monomorphic • It must be completely first-order Our topEntity meets those restrictions, and so we can convert it successfully to VHDL by executing the :vhdl command in the interpreter. This will create a directory called vhdl, which contains a directory called MAC, which ultimately contains all the generated VHDL files. You can now load these files into your favourite VHDL synthesis tool, marking MAC_topEntity.vhdl as the file containing the top level entity. ### Circuit testbench There are multiple reasons as to why might you want to create a so-called testbench for the VHDL: • You want to compare post-synthesis / post-place&route behaviour to that of the behaviour of the original VHDL. • Need representative stimuli for your dynamic power calculations • Verify that the VHDL output of the CλaSH compiler has the same behaviour as the Haskell / CλaSH specification. For these purposes, you can have CλaSH compiler generate a MAC_testbench.vhdl file which contains a stimulus generator and an expected output verifier. The CλaSH compiler looks for the following functions to generate these to aspects: 1. testInput for the stimulus generator. 2. expectedOutput for the output verification. Given a topEntity with the type: topEntity :: Signal a -> Signal b  Where a and b are placeholders for monomorphic types: the topEntity is not allowed to be polymorphic. So given the above type for the topEntity, the type of testInput should be: testInput :: Signal a  And the type of expectedOutput should be: expectedOutput :: Signal b -> Signal Bool  Where the expectedOutput function should assert to True once it has verified all expected values. The CLaSH.Prelude module contains two standard functions to serve the above purpose, but a user is free to use any CλaSH specification to describe these two functions. For this tutorial we will be using the functions specified in the CLaSH.Prelude module, which are stimuliGenerator and outputVerifier: testInput :: Signal (Signed 9,Signed 9) testInput = stimuliGenerator$(listToVecTH [(1,1) :: (Signed 9,Signed 9),(2,2),(3,3),(4,4)])

expectedOutput :: Signal (Signed 9) -> Signal Bool
expectedOutput = outputVerifier $(listToVecTH [0 :: Signed 9,1,5,14])  This will create a stimulus generator that creates the same inputs as we used earlier for the simulation of the circuit, and creates an output verifier that compares against the results we got from our earlier simulation. We can even simulate the behaviour of the testbench: >>> sampleN 7$ expectedOutput (topEntity testInput)
[False,False,False,False
cycle(system1000): 4, outputVerifier
expected value: 14, not equal to actual value: 30
,True
cycle(system1000): 5, outputVerifier
expected value: 14, not equal to actual value: 46
,True
cycle(system1000): 6, outputVerifier
expected value: 14, not equal to actual value: 62
,True]


We can see that for the first 4 samples, everything is working as expected, after which warnings are being reported. The reason is that stimuliGenerator will keep on producing the last sample, (4,4), while the outputVerifier will keep on expecting the last sample, 14. In the VHDL testbench these errors won't show, as the the global clock will be stopped after 4 ticks.

You should now again run :vhdl in the interpreter; this time the compiler will take a bit longer to generate all the circuits. After it is finished you can load all the files in your favourite VHDL simulation tool. Once all files are loaded into the VHDL simulator, run the simulation on the testbench entity. On questasim / modelsim: doing a run -all will finish once the output verifier will assert its output to true. The generated testbench, modulo the clock signal generator(s), is completely synthesizable. This means that if you want to test your circuit on an FPGA, you will only have to replace the clock signal generator(s) by actual clock sources, such as an onboard PLL.

### Generating Verilog and SystemVerilog

Aside from being to generate VHDL, the CλaSH compiler can also generate Verilog and SystemVerilog. You can repeat the previous two parts of the tutorial, but instead of executing the :vhdl command, you execute the :verilog or :sytemverilog command in the interpreter. This will create a directory called verilog, respectively systemverilog, which contains a directory called MAC, which ultimately contains all the generated Verilog and SystemVerilog files. Verilog files end in the file extension v, while SystemVerilog files end in the file extension sv.

This concludes the main part of this section on "Your first circuit", read on for alternative specifications for the same mac circuit, or just skip to the next section where we will describe another DSP classic: an FIR filter structure.

### Alternative specifications

• Num instance for Signal:

Signal a is also also considered a Numeric type as long as the value type a is also Numeric. This means that we can also use the standard numeric operators, such as (*) and (+), directly on signals. An alternative specification of the mac circuit will also use the register function directly:

macN (x,y) = acc
where
acc = register 0 (acc + x * y)

• Applicative instance for Signal:

We can also mix the combinational ma function, with the sequential register function, by lifting the ma function to the sequential Signal domain using the operators (<$> and <*>) of the Applicative type class: macA (x,y) = acc where acc = register 0 acc' acc' = ma <$> acc <*> bundle (x,y)

• State Monad

We can also implement the original macT function as a State monadic computation. First we must an extra import statement, right after the import of CLaSH.Prelude:

import Control.Monad.State


We can then implement macT as follows:

macTS (x,y) = do
acc <- get
put (acc + x * y)
return acc


We can use the mealy function again, although we will have to change position of the arguments and result:

asStateM :: (i -> State s o)
-> s
-> (Signal i -> Signal o)
asStateM f i = mealy g i
where
g s x = let (o,s') = runState (f x) s
in  (s',o)


We can then create the complete mac circuit as:

macS = asStateM macTS 0


# Higher-order functions

An FIR filter is defined as: the dot-product of a set of filter coefficients and a window over the input, where the size of the window matches the number of coefficients.

dotp as bs = sum (zipWith (*) as bs)

fir coeffs x_t = y_t
where
y_t = dotp coeffs xs
xs  = window x_t

topEntity :: Signal (Signed 16) -> Signal (Signed 16)
topEntity = fir (0 :> 1 :> 2 :> 3 :> Nil)


Here we can see that, although the CλaSH compiler handles recursive function definitions poorly, many of the regular patterns that we often encounter in circuit design are already captured by the higher-order functions that are present for the Vector type.

# Composition of sequential circuits

Given a function f of type:

f :: Int -> (Bool, Int) -> (Int, (Int, Bool))


When we want to make compositions of f in g using mealy, we have to write:

g a b c = (b1,b2,i2)
where
(i1,b1) = unbundle (mealy f 0 (bundle (a,b)))
(i2,b2) = unbundle (mealy f 3 (bundle (i1,c)))


Why do we need these bundle, and unbundle functions you might ask? When we look at the type of mealy:

mealy :: (s -> i -> (s,o))
-> s
-> (Signal i -> Signal o)


we see that the resulting function has an input of type Signal i, and an output of Signal o. However, the type of (a,b) in the definition of g is: (Signal Bool, Signal Int). And the type of (i1,b1) is of type (Signal Int, Signal Bool).

Syntactically, Signal (Bool,Int) and (Signal Bool, Signal Int) are unequal. So we need to make a conversion between the two, that is what bundle and unbundle are for. In the above case bundle gets the type:

bundle :: (Signal Bool, Signal Int) -> Signal (Bool,Int)


and unbundle:

unbundle :: Signal (Int,Bool) -> (Signal Int, Signal Bool)


The true types of these two functions are, however:

bundle   :: Bundle a => Unbundled a -> Signal a
unbundle :: Bundle a => Signal a -> Unbundled a


Unbundled is an associated type family belonging to the Bundle type class, which, together with bundle and unbundle defines the isomorphism between a product type of Signals and a Signal of a product type. That is, while (Signal a, Signal b) and Signal (a,b) are not equal, they are isomorphic and can be converted from, or to, the other using bundle and unbundle.

Instances of this Bundle type-class are defined as isomorphisms for:

• All tuples until and including 8-tuples
• The Vector type

But they are defined as identities for:

• All elementary / primitive types such as: Bit, Bool, Signed n, etc.

That is:

instance Bundle (a,b) where
type Unbundled' clk (a,b) = (Signal' clk a, Signal' clk b)
bundle   (a,b) = (,) <$> a <*> b unbundle tup = (fst <$> tup, snd <*> tup)


but,

instance Bundle Bool where
type Unbundled' clk Bool = Signal' clk Bool
bundle   s = s
unbundle s = s


What you need take away from the above is that a product type (e.g. a tuple) of Signals is not syntactically equal to a Signal of a product type, but that the functions of the Bundle type class allow easy conversion between the two.

As a final note on this section we also want to mention the mealyB function, which does the bundling and unbundling for us:

mealyB :: (Bundle i, Bundle o)
=> (s -> i -> (s,o))
-> s
-> (Unbundled i -> Unbundled o)


Using mealyB we can define g as:

g a b c = (b1,b2,i2)
where
(i1,b1) = mealyB f 0 (a,b)
(i2,b2) = mealyB f 3 (i1,c)


The general rule of thumb is: always use mealy, unless you do pattern matching or construction of product types, then use mealyB.

# TopEntity annotations: controlling the VHDL/(System)Verilog generation.

The TopEntity annotations described in this section make it easier to put your CλaSH design on an FPGA.

We can exert some control how the top level function is created by the CλaSH compiler by annotating the topEntity function with a TopEntity annotation. You apply these annotations using the ANN pragma like so:

{-# ANN topEntity (TopEntity {t_name = ..., ...  }) #-}
topEntity x = ...


For example, given the following specification:

topEntity :: Signal Bit -> Signal (BitVector 8)
topEntity key1 = leds
where
key1R = isRising 1 key1
leds  = mealy blinkerT (1,False,0) key1R

where
-- clock frequency = 50e6   (50 MHz)
-- led update rate = 333e-3 (every 333ms)
cnt_max = 16650000 -- 50e6 * 333e-3

cntr' | cntr == cnt_max = 0
| otherwise       = cntr + 1

mode' | key1R     = not mode
| otherwise = mode

leds' | cntr == 0 = if mode then complement leds
else rotateL leds 1
| otherwise = leds


The CλaSH compiler will normally generate the following Blinker_topEntity.vhdl file:

-- Automatically generated VHDL
library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;
use IEEE.MATH_REAL.ALL;
use work.all;

port(input_0         : in std_logic_vector(0 downto 0);
-- clock
system1000      : in std_logic;
-- asynchronous reset: active low
system1000_rstn : in std_logic;
output_0        : out std_logic_vector(7 downto 0));
end;

begin
port map
(key1_i1         => input_0
,system1000      => system1000
,system1000_rstn => system1000_rstn
,topLet_o        => output_0);
end;


However, if we add the following TopEntity annotation in the file:

{-# ANN topEntity
(defTop
, t_inputs   = ["KEY1"]
, t_outputs  = ["LED"]
, t_extraIn  = [ ("CLOCK_50", 1)
, ("KEY0"    , 1)
]
, t_clocks   = [ altpll "altpll50" "CLOCK_50(0)" "not KEY0(0)" ]
}) #-}


The CλaSH compiler will generate the following blinker.vhdl file instead:

-- Automatically generated VHDL
library IEEE;
use IEEE.STD_LOGIC_1164.ALL;
use IEEE.NUMERIC_STD.ALL;
use IEEE.MATH_REAL.ALL;
use work.all;

port(KEY1     : in std_logic_vector(0 downto 0);
CLOCK_50 : in std_logic_vector(0 downto 0);
KEY0     : in std_logic_vector(0 downto 0);
LED      : out std_logic_vector(7 downto 0));
end;

signal system1000      : std_logic;
signal system1000_rstn : std_logic;
signal altpll50_locked : std_logic;
begin
altpll50_inst : entity altpll50
port map
(inclk0 => CLOCK_50(0)
,c0     => system1000
,areset => not KEY0(0)
,locked => altpll50_locked);

-- reset system1000_rstn is asynchronously asserted, but synchronously de-asserted
resetSync_n_0 : block
signal n_1 : std_logic;
signal n_2 : std_logic;
begin
process(system1000,altpll50_locked)
begin
if altpll50_locked = '0' then
n_1 <= '0';
n_2 <= '0';
elsif rising_edge(system1000) then
n_1 <= '1';
n_2 <= n_1;
end if;
end process;

system1000_rstn <= n_2;
end block;

port map
(key1_i1         => KEY1
,system1000      => system1000
,system1000_rstn => system1000_rstn
,topLet_o        => LED);
end;


Where we now have:

• A top-level component that is called blinker.
• Inputs and outputs that have a user-chosen name: KEY1, LED, etc.
• An instantiated PLL component providing a stable clock signal from the free-running clock pin CLOCK_50.
• A reset that is asynchronously asserted by the lock signal originating from the PLL, meaning that your design is kept in reset until the PLL is providing a stable clock. The reset is additionally synchronously de-asserted to prevent metastability of your design due to unlucky timing of the de-assertion of the reset.

See the documentation of TopEntity for the meaning of all its fields.

# Multiple clock domains

CλaSH supports multi-clock designs, though perhaps in a slightly limited form. What is possible is:

• Explicitly assign clocks to memory primitives.

What is not possible is:

• Generate a clock signal in module A, and assign this clock signal to a memory primitive in module B.

What this means is that when CλaSH converts your design to VHDL/(System)Verilog, you end up with a top-level module/entity with multiple clock and reset ports for the different clock domains. If you're targeting an FPGA, you can use e.g. a PPL or MMCM to provide the clock signals.

## Building a FIFO synchroniser

This part of the tutorial assumes you know what metastability is, and how it can never truly be avoided in any asynchronous circuit. Also it assumes that you are familiar with the design of synchronizer circuits, and why a dual flip-flop synchroniser only works for bit-synchronisation and not word-synchronisation. The explicitly clocked versions of all synchronous functions and primitives can be found in CLaSH.Prelude.Explicit, which also re-exports the functions in CLaSH.Signal.Explicit. We will use those functions to create a FIFO where the read and write port are synchronised to different clocks. Below you can find the code to build the FIFO synchroniser based on the design described in: http://www.sunburst-design.com/papers/CummingsSNUG2002SJ_FIFO1.pdf

We start with enable a few options that will make writing the type-signatures for our components a bit easier. We'll also import the standard CLaSH.Prelude module, and the CLaSH.Prelude.Explicit module for our explicitly clocked synchronous functions:

{-# LANGUAGE PartialTypeSignatures #-}
{-# OPTIONS_GHC -fno-warn-partial-type-signatures #-}
module MultiClockFifo where

import CLaSH.Prelude
import CLaSH.Prelude.Explicit
import Data.Maybe             (isJust)


Then we'll start with the heart of the FIFO synchroniser, an asynchronous RAM in the form of asyncRam'. It's called an asynchronous RAM because the read port is not synchronised to any clock (though the write port is). Note that in CλaSH we don't really have asynchronous logic, there is only combinational and synchronous logic. As a consequence, we see in the type signature of asyncRam':

asyncRam'
:: _
=> SClock wclk                   -- ^ Clock to which to synchronise the write port of the RAM
-> SClock rclk                   -- ^ Clock to which the read address signal r is synchronised
-> SNat n                        -- ^ Size n of the RAM
-> Signal' wclk (Maybe (addr,a)) -- ^ (write address w, value to write)
-> Signal' rclk a                -- ^ Value of the RAM at address r


that the signal containing the read address r is synchronised to a different clock. That is, there is no such thing as an AsyncSignal in CλaSH.

We continue by instantiating the asyncRam':

fifoMem wclk rclk addrSize wfull raddr wdataM =
asyncRam' wclk rclk
(pow2SNat addrSize)
(mux (not <$> wfull) wdataM (pure Nothing))  We see that we give it 2^addrSize elements, where addrSize is the bit-size of the address. Also, we only write new values to the RAM when a new write is requested, indicated by wdataM having a$Just$value, and the buffer is not full, indicated by wfull. The next part of the design calculates the read and write address for the asynchronous RAM, and creates the flags indicating whether the FIFO is full or empty. The address and flag generator is given in mealy machine style: ptrCompareT addrSize flagGen (bin,ptr,flag) (s_ptr,inc) = ((bin',ptr',flag') ,(flag,addr,ptr)) where -- GRAYSTYLE2 pointer bin' = bin + boolToBV (inc && not flag) ptr' = (bin' shiftR 1) xor bin' addr = slice (addrSize subSNat d1) d0 bin flag' = flagGen ptr' s_ptr  It is parametrised in both address size, addrSize, and status flag generator, flagGen. It has two inputs, s_ptr, the synchronised pointer from the other clock domain, and inc, which indicates we want to perform a write or read of the FIFO. It creates three outputs: flag, the full or empty flag, addr, the read or write address into the RAM, and ptr, the Gray-encoded version of the read or write address which will be synchronised between the two clock domains. Next follow the initial states of address generators, and the flag generators for the empty and full flags: -- FIFO empty: when next pntr == synchronized wptr or on reset isEmpty = (==) rptrEmptyInit = (0,0,True) -- FIFO full: when next pntr == synchronized {~wptr[addrSize:addrSize-1],wptr[addrSize-2:0]} isFull addrSize ptr s_ptr = ptr == complement (slice addrSize (addrSize subSNat d1) s_ptr) ++# slice (addrSize subSNat d2) d0 s_ptr wptrFullInit = (0,0,False)  We create a dual flip-flop synchroniser to be used to synchronise the Gray-encoded pointers between the two clock domains: ptrSync clk1 clk2 = register' clk2 0 . register' clk2 0 . unsafeSynchronizer clk1 clk2  It uses the unsafeSynchroniser primitive, which is needed to go from one clock domain to the other. All synchronizers are specified in terms of unsafeSynchronizer (see for example the source of asyncRam#). The unsafeSynchronizer primitive is turned into a (bundle of) wire(s) by the CλaSH compiler, so developers must ensure that it is only used as part of a proper synchronizer. Finally we combine all the component in: fifo :: _ => SNat (addrSize + 2) -> SClock wclk -> SClock rclk -> Signal' rclk Bool -> Signal' wclk (Maybe a) -> (Signal' rclk a, Signal' rclk Bool, Signal' wclk Bool) fifo addrSize wclk rclk rinc wdataM = (rdata,rempty,wfull) where s_rptr = ptrSync rclk wclk rptr s_wptr = ptrSync wclk rclk wptr rdata = fifoMem wclk rclk addrSize wfull raddr (liftA2 (,) <$> (Just <$> waddr) <*> wdataM) (rempty,raddr,rptr) = mealyB' rclk (ptrCompareT addrSize isEmpty) rptrEmptyInit (s_wptr,rinc) (wfull,waddr,wptr) = mealyB' wclk (ptrCompareT addrSize (isFull addrSize)) wptrFullInit (s_rptr,isJust <$> wdataM)


where we first specify the synchronisation of the read and the write pointers, instantiate the asynchronous RAM, and instantiate the read address / pointer / flag generator and write address / pointer / flag generator.

Ultimately, the whole file containing our FIFO design will look like this:

{-# LANGUAGE PartialTypeSignatures #-}
{-# OPTIONS_GHC -fno-warn-partial-type-signatures #-}
module MultiClockFifo where

import CLaSH.Prelude
import CLaSH.Prelude.Explicit
import Data.Maybe             (isJust)

asyncRam' wclk rclk
(pow2SNat addrSize)
(mux (not <$> wfull) wdataM (pure Nothing)) ptrCompareT addrSize flagGen (bin,ptr,flag) (s_ptr,inc) = ((bin',ptr',flag') ,(flag,addr,ptr)) where -- GRAYSTYLE2 pointer bin' = bin + boolToBV (inc && not flag) ptr' = (bin' shiftR 1) xor bin' addr = slice (addrSize subSNat d1) d0 bin flag' = flagGen ptr' s_ptr -- FIFO empty: when next pntr == synchronized wptr or on reset isEmpty = (==) rptrEmptyInit = (0,0,True) -- FIFO full: when next pntr == synchronized {~wptr[addrSize:addrSize-1],wptr[addrSize-2:0]} isFull addrSize ptr s_ptr = ptr == complement (slice addrSize (addrSize subSNat d1) s_ptr) ++# slice (addrSize subSNat d2) d0 s_ptr wptrFullInit = (0,0,False) -- Dual flip-flop synchroniser ptrSync clk1 clk2 = register' clk2 0 . register' clk2 0 . unsafeSynchronizer clk1 clk2 -- Async FIFO synchroniser fifo :: _ => SNat (addrSize + 2) -> SClock wclk -> SClock rclk -> Signal' rclk Bool -> Signal' wclk (Maybe a) -> (Signal' rclk a, Signal' rclk Bool, Signal' wclk Bool) fifo addrSize wclk rclk rinc wdataM = (rdata,rempty,wfull) where s_rptr = ptrSync rclk wclk rptr s_wptr = ptrSync wclk rclk wptr rdata = fifoMem wclk rclk addrSize wfull raddr (liftA2 (,) <$> (Just <$> waddr) <*> wdataM) (rempty,raddr,rptr) = mealyB' rclk (ptrCompareT addrSize isEmpty) rptrEmptyInit (s_wptr,rinc) (wfull,waddr,wptr) = mealyB' wclk (ptrCompareT addrSize (isFull addrSize)) wptrFullInit (s_rptr,isJust <$> wdataM)


## Instantiating a FIFO synchroniser

Having finished our FIFO synchroniser it's time to instantiate with concrete clock domains. Let us assume we have part of our system connected to an ADC which runs at 20 MHz, and we have created an FFT component running at only 9 MHz, while the rest of our system runs at 50 MHz. What we want to do connect part of our design connected to the ADC, and running at 20 MHz, to part of our design connected to the FFT running at 9 MHz.

First, we must calculate the relative clock periods using freqCalc:

>>> freqCalc [20,9,50]
[45,100,18]


We can then create the clocks:

type ClkADC = 'Clk "ADC"    45
type ClkFFT = 'Clk "FFT"    100
type ClkSys = 'Clk "System" 18

clkFFT :: SClock ClkFFT
clkFFT = sclock

clkSys :: SClock ClkSys
clkSys = sclock


and subsequently a 256-space FIFO synchroniser that safely bridges the ADC clock domain and to the FFT clock domain:

adcToFFT
:: Signal' ClkFFT Bool
-> Signal' ClkADC (Maybe (SFixed 8 8))
-> (Signal' ClkFFT (SFixed 8 8), Signal' ClkFFT Bool, Signal' ClkADC Bool)


There are times when you already have an existing piece of IP, or there are times where you need the VHDL to have a specific shape so that the VHDL synthesis tool can infer a specific component. In these specific cases you can resort to defining your own VHDL primitives. Actually, most of the primitives in CλaSH are specified in the same way as you will read about in this section. There are perhaps 10 (at most) functions which are truly hard-coded into the CλaSH compiler. You can take a look at the files in https://github.com/clash-lang/clash-compiler/tree/master/clash-vhdl/primitives (or https://github.com/clash-lang/clash-compiler/tree/master/clash-verilog/primitives for the Verilog primitives or https://github.com/clash-lang/clash-compiler/tree/master/clash-systemverilog/primitives for the SystemVerilog primitives) if you want to know which functions are defined as "regular" primitives. The compiler looks for primitives in two locations:

• The official install location: e.g.
• $CABAL_DIR/share/<GHC_VERSION>/clash-vhdl-<VERSION>/primitives • $CABAL_DIR/share/<GHC_VERSION>/clash-verilog-<VERSION>/primitives
• $CABAL_DIR/share/<GHC_VERSION>/clash-systemverilog-<VERSION>/primitives • The current directory (the location given by pwd) Where redefined primitives in the current directory will overwrite those in the official install location. For now, files containing primitive definitions must end in the .json file-extension. CλaSH differentiates between two types of primitives, expression primitives and declaration primitives, corresponding to whether the primitive is a VHDL expression or a VHDL declaration. We will first explore expression primitives, using Signed multiplication (*) as an example. The CLaSH.Sized.Internal.Signed module specifies multiplication as follows: (*#) :: KnownNat n => Signed n -> Signed n -> Signed n (S a) *# (S b) = fromInteger_INLINE (a * b) {-# NOINLINE (*#) #-}  For which the VHDL expression primitive is: { "BlackBox" : { "name" : "CLaSH.Sized.Internal.Signed.*#" , "templateE" : "resize(~ARG[1] * ~ARG[2], ~LIT[0])" } }  The name of the primitive is the fully qualified name of the function you are creating the primitive for. Because we are creating an expression primitive we define a templateE field. As the name suggest, it is a VHDL template, meaning that the compiler must fill in the holes heralded by the tilde (~). Here: • ~ARG[1] denotes the second argument given to the (*#) function, which corresponds to the LHS of the (*) operator. • ~ARG[2] denotes the third argument given to the (*#) function, which corresponds to the RHS of the (*) operator. • ~LIT[0] denotes the first argument given to the (*#) function, with the extra condition that it must be a LITeral. If for some reason this first argument does not turn out to be a literal then the compiler will raise an error. This first arguments corresponds to the "KnownNat n" class constraint. An extensive list with all of the template holes will be given the end of this section. What we immediately notice is that class constraints are counted as normal arguments in the primitive definition. This is because these class constraints are actually represented by ordinary record types, with fields corresponding to the methods of the type class. In the above case, KnownNat is actually just like a newtype wrapper for Integer. The second kind of primitive that we will explore is the declaration primitive. We will use blockRam# as an example, for which the Haskell/CλaSH code is: -- | blockRAM primitive blockRam# :: KnownNat n => SClock clk -- ^ Clock to synchronize to -> Vec n a -- ^ Initial content of the BRAM, also -- determines the size, n, of the BRAM. -- -- NB: MUST be a constant. -> Signal' clk Int -- ^ Read address r -> Signal' clk Bool -- ^ Write enable -> Signal' clk Int -- ^ Write address w -> Signal' clk a -- ^ Value to write (at address w) -> Signal' clk a -- ^ Value of the blockRAM at address r from the previous clock -- cycle blockRam# clk content rd en wr din = register' clk (errorX "blockRam#: intial value undefined") dout where szI = length content dout = runST$ do
arr <- newListArray (0,szI-1) (toList content)
traverse (ramT arr) (bundle (rd,en,wr,din))

ramT :: STArray s Int e -> (Int,Bool,Int,e) -> ST s e
ramT ram (r,e,w,d) = do
-- reading from address using an X exception results in an X result
r' <- unsafeIOToST \$
catch (evaluate r >>= (return . Right))
((err :: XException) -> return (Left (throw err)))
d' <- case r' of
Right r2 -> readArray ram r2
Left err -> return err
-- writing to an address using an X exception makes everything X
when e (writeArray ram w d)
return d'
{-# NOINLINE blockRam# #-}


And for which the declaration primitive is:

{ "BlackBox" :
{ "name" : "CLaSH.Prelude.BlockRam.blockRam#"
, "type" :
"blockRam# :: KnownNat n       -- ARG[0]
=> SClock clk       -- clk,  ARG[1]
-> Vec n a          -- init, ARG[2]
-> Signal' clk Int  -- rd,   ARG[3]
-> Signal' clk Bool -- wren, ARG[4]
-> Signal' clk Int  -- wr,   ARG[5]
-> Signal' clk a    -- din,  ARG[6]
-> Signal' clk a"
, "templateD" :
"-- blockRam begin
~GENSYM[~COMPNAME_blockRam][0] : block
signal ~GENSYM[RAM][1] : ~TYP[2] := ~LIT[2];~IF ~VIVADO ~THEN
signal ~GENSYM[dout][2] : std_logic_vector(~SIZE[~TYP[6]]-1 downto 0);~ELSE
signal ~SYM[2] : ~TYP[6];~FI
signal ~GENSYM[rd][3] : integer range 0 to ~LIT[0] - 1;
signal ~GENSYM[wr][4] : integer range 0 to ~LIT[0] - 1;
begin
~SYM[3] <= to_integer(~ARG[3])
-- pragma translate_off
mod ~LIT[0]
-- pragma translate_on
;

~SYM[4] <= to_integer(~ARG[5])
-- pragma translate_off
mod ~LIT[0]
-- pragma translate_on
;

~GENSYM[blockRam_sync][5] : process(~CLK[1])
begin
if rising_edge(~CLK[1]) then
~SYM[1](~SYM[4]) <= ~TOBV[~ARG[6]][~TYP[6]];~ELSE
~SYM[1](~SYM[4]) <= ~ARG[6];~FI
end if;
~SYM[2] <= ~SYM[1](~SYM[3]);
end if;
~RESULT <= ~FROMBV[~SYM[2]][~TYPO];~ELSE
~RESULT <= ~SYM[2];~FI
end block;
-- blockRam end"
}
}


Again, the name of the primitive is the fully qualified name of the function you are creating the primitive for. Because we are creating a declaration primitive we define a templateD field. Instead of discussing what the individual template holes mean in the above context, we will instead just give a general listing of the available template holes:

• ~RESULT: VHDL signal to which the result of a primitive must be assigned to. NB: Only used in a declaration primitive.
• ~ARG[N]: (N+1)'th argument to the function.
• ~LIT[N]: (N+1)'th argument to the function An extra condition that must hold is that this (N+1)'th argument is an (integer) literal.
• ~CLK[N]: Clock signal to which the (N+1)'th argument is synchronized to.
• ~CLKO: Clock signal to which the result is synchronized to.
• ~RST[N]: Asynchronous reset signal to the clock to which the (N+1)'th argument is synchronized to.
• ~RSTO: Asynchronous reset signal to the clock to which the result is synchronized to.
• ~TYP[N]: VHDL type of the (N+1)'th argument.
• ~TYPO: VHDL type of the result.
• ~TYPM[N]: VHDL typename of the (N+1)'th argument; used in type qualification.
• ~TYPM: VHDL typename of the result; used in type qualification.
• ~ERROR[N]: Error value for the VHDL type of the (N+1)'th argument.
• ~ERRORO: Error value for the VHDL type of the result.
• ~GENSYM[<NAME>][N]: Create a unique name, trying to stay as close to the given <NAME> as possible. This unique symbol can be referred to in other places using ~SYM[N].
• ~SYM[N]: a reference to the unique symbol created by ~GENSYM[<NAME>][N].
• ~SIGD[<HOLE>][N]: Create a signal declaration, using <HOLE> as the name of the signal, and the type of the (N+1)'th argument.
• ~SIGDO[<HOLE>]: Create a signal declaration, using <HOLE> as the name of the signal, and the type of the result.
• ~TYPELEM[<HOLE>]: The element type of the vector type represented by <HOLE>. The content of <HOLE> must either be: TYPM[N], TYPO, or TYPELEM[<HOLE>].
• ~COMPNAME: The name of the component in which the primitive is instantiated.
• ~LENGTH[<HOLE>]: The vector length of the type represented by <HOLE>.
• ~DEPTH[<HOLE>]: The tree depth of the type represented by <HOLE>. The content of <HOLE> must either be: TYPM[N], TYPO, or TYPELEM[<HOLE>].
• ~SIZE[<HOLE>]: The number of bits needed to encode the type represented by <HOLE>. The content of <HOLE> must either be: TYPM[N], TYPO, or TYPELEM[<HOLE>].
• ~IF <CONDITION> ~THEN <THEN> ~ELSE <ELSE> ~FI: renders the <ELSE> part when <CONDITION> evaluates to 0, and renders the <THEN> in all other cases. Valid <CONDITION>s are ~LENGTH[<HOLE>], ~SIZE[<HOLE>], ~DEPTH[<HOLE>], and ~VIVADO.
• ~VIVADO: 1 when CλaSH compiler is invoked with the -clash-xilinx or -clash-vivado flag. To be used with in an ~IF .. ~THEN .. ~ElSE .. ~FI statement.
• ~FROMBV[<HOLE>][<TYPE>]: create conversion code that so that the expression in <HOLE> is converted to a bit vector (std_logic_vector). The <TYPE> hole indicates the type of the expression and must be either ~TYP[N], ~TYPO, or ~TYPELEM[<HOLE>].
• ~TOBV[<HOLE>][<TYPE>]: create conversion code that so that the expression in <HOLE>, which has a bit vector (std_logic_vector) type, is converted to type indicated by <TYPE>. The <TYPE> hole indicates the must be either ~TYP[N], ~TYPO, or ~TYPELEM[<HOLE>].

Some final remarks to end this section: VHDL primitives are there to instruct the CλaSH compiler to use the given VHDL template, instead of trying to do normal synthesis. As a consequence you can use constructs inside the Haskell definitions that are normally not synthesizable by the CλaSH compiler. However, VHDL primitives do not give us co-simulation: where you would be able to simulate VHDL and Haskell in a single environment. If you still want to simulate your design in Haskell, you will have to describe, in a cycle- and bit-accurate way, the behaviour of that (potentially complex) IP you are trying to include in your design.

Perhaps in the future, someone will figure out how to connect the two simulation worlds, using e.g. VHDL's foreign function interface VHPI.

### Verilog primitives

For those who are interested, the equivalent Verilog primitives are:

{ "BlackBox" :
{ "name"      : "CLaSH.Sized.Internal.Signed.*#"
, "templateE" : "~ARG[1] * ~ARG[2]"
}
}


and

{ "BlackBox" :
{ "name" : "CLaSH.Prelude.BlockRam.blockRam#"
, "type" :
"blockRam# :: KnownNat n       -- ARG[0]
=> SClock clk       -- clk,  ARG[1]
-> Vec n a          -- init, ARG[2]
-> Signal' clk Int  -- rd,   ARG[3]
-> Signal' clk Bool -- wren, ARG[4]
-> Signal' clk Int  -- wr,   ARG[5]
-> Signal' clk a    -- din,  ARG[6]
-> Signal' clk a"
, "templateD" :
"// blockRam begin
reg ~TYPO ~GENSYM[RAM][0] [0:~LIT[0]-1];
reg ~TYPO ~GENSYM[dout][1];

reg ~TYP[2] ~GENSYM[ram_init][2];
integer ~GENSYM[i][3];
initial begin
~SYM[2] = ~ARG[2];
for (~SYM[3]=0; ~SYM[3] < ~LIT[0]; ~SYM[3] = ~SYM[3] + 1) begin
~SYM[0][~LIT[0]-1-~SYM[3]] = ~SYM[2][~SYM[3]*~SIZE[~TYPO]+:~SIZE[~TYPO]];
end
end

always @(posedge ~CLK[1]) begin : ~GENSYM[~COMPNAME_blockRam][4]
if (~ARG[4]) begin
~SYM[0][~ARG[5]] <= ~ARG[6];
end
~SYM[1] <= ~SYM[0][~ARG[3]];
end

assign ~RESULT = ~SYM[1];
// blockRam end"
}
}


### SystemVerilog primitives

And the equivalent SystemVerilog primitives are:

{ "BlackBox" :
{ "name"      : "CLaSH.Sized.Internal.Signed.*#"
, "templateE" : "~ARG[1] * ~ARG[2]"
}
}


and

{ "BlackBox" :
{ "name" : "CLaSH.Prelude.BlockRam.blockRam#"
, "type" :
"blockRam# :: KnownNat n       -- ARG[0]
=> SClock clk       -- clk,  ARG[1]
-> Vec n a          -- init, ARG[2]
-> Signal' clk Int  -- rd,   ARG[3]
-> Signal' clk Bool -- wren, ARG[4]
-> Signal' clk Int  -- wr,   ARG[5]
-> Signal' clk a    -- din,  ARG[6]
-> Signal' clk a"
, "templateD" :
"// blockRam begin
~SIGD[~GENSYM[RAM][0]][2];
logic [~SIZE[~TYP[6]]-1:0] ~GENSYM[dout][1];
initial begin
~SYM[0] = ~LIT[2];
end
always @(posedge ~CLK[1]) begin : ~GENSYM[~COMPNAME_blockRam][2]
if (~ARG[4]) begin
~SYM[0][~ARG[5]] <= ~TOBV[~ARG[6]][~TYP[6]];
end
~SYM[1] <= ~SYM[0][~ARG[3]];
end
assign ~RESULT = ~FROMBV[~SYM[1]][~TYP[6]];
// blockRam end"
}
}


# Conclusion

For now, this is the end of this tutorial. We will be adding updates over time, so check back from time to time. For now, we recommend that you continue with exploring the CLaSH.Prelude module, and get a better understanding of the capabilities of CλaSH in the process.

# Troubleshooting

A list of often encountered errors and their solutions:

• Type error: Couldn't match expected type Signal (a,b) with actual type (Signal a, Signal b):

Signals of product types and product types (to which tuples belong) of signals are isomorphic due to synchronisity principle, but are not (structurally) equal. Use the bundle function to convert from a product type to the signal type. So if your code which gives the error looks like:

... = f a b (c,d)


add the bundle' function like so:

... = f a b (bundle (c,d))


Product types supported by bundle are:

• All tuples until and including 8-tuples
• The Vector type

NB: Use bundle' when you are using explicitly clocked Signal's

• Type error: Couldn't match expected type (Signal a, Signal b) with actual type Signal (a,b):

Product types (to which tuples belong) of signals and signals of product types are isomorphic due to synchronicity principle, but are not (structurally) equal. Use the unbundle function to convert from a signal type to the product type. So if your code which gives the error looks like:

(c,d) = f a b


add the unbundle function like so:

(c,d) = unbundle (f a b)


Product types supported by unbundle are:

• All tuples until and including 8-tuples
• The Vector type

NB: Use unbundle' when you are using explicitly clocked Signal's

• CLaSH.Netlist(..): Not in normal form: <REASON>: <EXPR>:

A function could not be transformed into the expected normal form. This usually means one of the following:

• The topEntity has residual polymorphism.
• The topEntity has higher-order arguments, or a higher-order result.
• You are using types which cannot be represented in hardware.

The solution for all the above listed reasons is quite simple: remove them. That is, make sure that the topEntity is completely monomorphic and first-order. Also remove any variables and constants/literals that have a non-representable type, see Unsupported Haskell features to find out which types are not representable.

• CLaSH.Normalize(94): Expr belonging to bndr: <FUNCTION> remains recursive after normalization:

• If you actually wrote a recursive function, rewrite it to a non-recursive one using e.g. one of the higher-order functions in CLaSH.Sized.Vector :-)
• You defined a recursively defined value, but left it polymorphic:
topEntity x y = acc
where
acc = register 3 (acc + x * y)


The above function, works for any number-like type. This means that acc is a recursively defined polymorphic value. Adding a monomorphic type annotation makes the error go away:

topEntity :: Signal (Signed 8) -> Signal (Signed 8) -> Signal (Signed 8)
topEntity x y = acc
where
acc = register 3 (acc + x * y)


Or, alternatively:

topEntity x y = acc
where
acc = register (3 :: Signed 8) (acc + x * y)

• CLaSH.Normalize.Transformations(155): InlineNonRep: <FUNCTION> already inlined 100 times in:<FUNCTION>, <TYPE>:

You left the topEntity function polymorphic or higher-order: use :t topEntity to check if the type is indeed polymorphic or higher-order. If it is, add a monomorphic type signature, and / or supply higher-order arguments.

• Can't make testbench for: <LONG_VERBATIM_COMPONENT_DESCRIPTION>:

• Don't worry, it's actually only a warning.
• The topEntity function does not have exactly 1 argument. If your topEntity has no arguments, you're out of luck for now. If it has multiple arguments, consider bundling them in a tuple.
• <*** Exception: <<loop>> or "blinking cursor"

You are using value-recursion, but one of the Vector functions that you are using is too strict in one of the recursive arguments. For example:

-- Bubble sort for 1 iteration
sortV xs = map fst sorted :< (snd (last sorted))
where
lefts  = head xs :> map snd (init sorted)
rights = tail xs
sorted = zipWith compareSwapL lefts rights

-- Compare and swap
compareSwapL a b = if a < b then (a,b)
else (b,a)


Will not terminate because zipWith is too strict in its second argument.

In this case, adding lazyV on zipWiths second argument:

sortVL xs = map fst sorted :< (snd (last sorted))
where
lefts  = head xs :> map snd (init sorted)
rights = tail xs
sorted = zipWith compareSwapL (lazyV lefts) rights


Results in a successful computation:

>>> sortVL (4 :> 1 :> 2 :> 3 :> Nil)
<1,2,3,4>


# Limitations of CλaSH

Here is a list of Haskell features for which the CλaSH compiler has only limited support (for now):

• Recursively defined functions

At first hand, it seems rather bad that a compiler for a functional language cannot synthesize recursively defined functions to circuits. However, when viewing your functions as a structural specification of a circuit, this feature of the CλaSH compiler makes sense. Also, only certain types of recursion are considered non-synthesisable; recursively defined values are for example synthesisable: they are (often) synthesized to feedback loops.

Let us distinguish between three variants of recursion:

• Dynamic data-dependent recursion

As demonstrated in this definition of a function that calculates the n'th Fibbonacci number:

fibR 0 = 0
fibR 1 = 1
fibR n = fibR (n-1) + fibR (n-2)


To get the first 10 numbers, we do the following:

>>> import qualified Data.List as L
>>> L.map fibR [0..9]
[0,1,1,2,3,5,8,13,21,34]


The fibR function is not synthesizable by the CλaSH compiler, because, when we take a structural view, fibR describes an infinitely deep structure.

In principal, descriptions like the above could be synthesized to a circuit, but it would have to be a sequential circuit. Where the most general synthesis would then require a stack. Such a synthesis approach is also known as behavioural synthesis, something which the CλaSH compiler simply does not do. One reason that CλaSH does not do this is because it does not fit the paradigm that only functions working on values of type Signal result in sequential circuits, and all other (non higher-order) functions result in combinational circuits. This paradigm gives the designer the most straightforward mapping from the original Haskell description to generated circuit, and thus the greatest control over the eventual size of the circuit and longest propagation delay.

• Value-recursion

As demonstrated in this definition of a function that calculates the n'th Fibbonaci number on the n'th clock cycle:

fibS = r
where r = register 0 r + register 0 (register 1 r)


To get the first 10 numbers, we do the following:

>>> sampleN 10 fibS
[0,1,1,2,3,5,8,13,21,34]


Unlike the fibR function, the above fibS function is synthesisable by the CλaSH compiler. Where the recursively defined (non-function) value r is synthesized to a feedback loop containing three registers and one adder.

Note that not all recursively defined values result in a feedback loop. An example that uses recursively defined values which does not result in a feedback loop is the following function that performs one iteration of bubble sort:

sortV xs = map fst sorted :< (snd (last sorted))
where
lefts  = head xs :> map snd (init sorted)
rights = tail xs
sorted = zipWith compareSwapL lefts rights


Where we can clearly see that lefts and sorted are defined in terms of each other. Also the above sortV function is synthesisable.

• Static/Structure-dependent recursion

Static, or, structure-dependent recursion is a rather vague concept. What we mean by this concept are recursive definitions where a user can sensibly imagine that the recursive definition can be completely unfolded (all recursion is eliminated) at compile-time in a finite amount of time.

Such definitions would e.g. be:

mapV :: (a -> b) -> Vec n a -> Vec n b
mapV _ Nil         = Nil
mapV f (Cons x xs) = Cons (f x) (mapV f xs)

topEntity :: Vec 4 Int -> Vec 4 Int
topEntity = mapV (+1)


Where one can imagine that a compiler can unroll the definition of mapV four times, knowing that the topEntity function applies mapV to a Vec of length 4. Sadly, the compile-time evaluation mechanisms in the CλaSH compiler are very poor, and a user-defined function such as the mapV function defined above, is currently not synthesisable. We do plan to add support for this in the future. In the mean time, this poor support for user-defined recursive functions is amortized by the fact that the CλaSH compiler has built-in support for the higher-order functions defined in CLaSH.Sized.Vector. Most regular design patterns often encountered in circuit design are captured by the higher-order functions in CLaSH.Sized.Vector.

• Recursive datatypes

The CλaSH compiler needs to be able to determine a bit-size for any value that will be represented in the eventual circuit. More specifically, we need to know the maximum number of bits needed to represent a value. While this is trivial for values of the elementary types, sum types, and product types, putting a fixed upper bound on recursive types is not (always) feasible. This means that the ubiquitous list type is unsupported! The only recursive type that is currently supported by the CλaSH compiler is the Vector type, for which the compiler has hard-coded knowledge.

For "easy" Vector literals you should use Template Haskell splices and the listToVecTH meta-function that as we have seen earlier in this tutorial.

While pattern matching for regular ADTs is supported, pattern matching for GADTs is not. The constructors Cons and Nil of the Vector type, which is also a GADT, are no exception! However, you can use the convenient :> pattern synonym.

• Floating point types

There is no support for the Float and Double types, if you need numbers with a fractional part you can use the Fixed point type.

As to why there is no support for these floating point types:

1. In order to achieve reasonable operating frequencies, arithmetic circuits for floating point data types must be pipelined.
2. Haskell's primitive arithmetic operators on floating point data types, such as plusFloat#

plusFloat# :: Float# -> Float# -> Float#


which underlie Float's Num instance, must be implemented as purely combinational circuits according to their type. Remember, sequential circuits operate on values of type "Signal a".

Although it is possible to implement purely combinational (not pipelined) arithmetic circuits for floating point data types, the circuit would be unreasonable slow. And so, without synthesis possibilities for the basic arithmetic operations, there is no point in supporting the floating point data types.

Only the following primitive Haskell types are supported:

• Integer
• Int
• Int8
• Int16
• Int32
• Int64 (not available when compiling with -clash-intwidth=32 on a 64-bit machine)
• Word
• Word8
• Word16
• Word32
• Word64 (not available when compiling with -clash-intwidth=32 on a 64-bit machine)
• Char

There are several aspects of which you should take note:

• Int and Word are represented by the same number of bits as is native for the architecture of the computer on which the CλaSH compiler is executed. This means that if you are working on a 64-bit machine, Int and Word will be 64-bit. This might be problematic when you are working in a team, and one designer has a 32-bit machine, and the other has a 64-bit machine. In general, you should be avoiding Int in such cases, but as a band-aid solution, you can force the CλaSH compiler to use a specific bit-width for Int and Word using the -clash-intwidth=N flag, where N must either be 32 or 64.
• When you use the -clash-intwidth=32 flag on a 64-bit machine, the Word64 and Int64 types cannot be translated. This restriction does not apply to the other three combinations of -clash-intwidth flag and machine type.
• The translation of Integer is not meaning-preserving. Integer in Haskell is an arbitrary precision integer, something that cannot be represented in a statically known number of bits. In the CλaSH compiler, we chose to represent Integer by the same number of bits as we do for Int and Word. As you have read in a previous bullet point, this number of bits is either 32 or 64, depending on the architecture of the machine the CλaSH compiler is running on, or the setting of the -clash-intwidth flag.

Consequently, you should use Integer with due diligence; be especially careful when using fromIntegral as it does a conversion via Integer. For example:

signedToUnsigned :: Signed 128 -> Unsigned 128
signedToUnsigned = fromIntegral

can either lose the top 64 or 96 bits depending on whether Integer is represented by 64 or 32 bits. Instead, when doing such conversions, you should use bitCoerce:

signedToUnsigned :: Signed 128 -> Unsigned 128
signedToUnsigned = bitCoerce
• Side-effects: IO, ST, etc.

There is no support for side-effecting computations such as those in the IO or ST monad. There is also no support for Haskell's FFI.

# CλaSH vs Lava

In Haskell land the most well-known way of describing digital circuits is the Lava family of languages:

The big difference between CλaSH and Lava is that CλaSH uses a "standard" compiler (static analysis) approach towards synthesis, where Lava is an embedded domain specific language. One downside of static analysis vs. the embedded language approach is already clearly visible: synthesis of recursive descriptions does not come for "free". This will be implemented in CλaSH in due time, but that doesn't help the circuit designer right now. As already mentioned earlier, the poor support for recursive functions is amortized by the built-in support for the higher-order in CLaSH.Sized.Vector.

The big upside of CλaSH and its static analysis approach is that CλaSH can do synthesis of "normal" functions: there is no forced encasing datatype (often called Signal in Lava) on all the arguments and results of a synthesizable function. This enables the following features not available to Lava:

• Automatic synthesis for user-defined ADTs
• Synthesis of all choice constructs (pattern matching, guards, etc.)
• Applicative instance for the Signal type
• Working with "normal" functions permits the use of e.g. the State monad to describe the functionality of a circuit.

Although there are Lava alternatives to some of the above features (e.g. first-class patterns to replace pattern matching) they are not as "beautiful" and / or easy to use as the standard Haskell features.