ReWire by Example

Pipelined Versions of doubleround

Naive Approach

We can write perfectly valid ReWire code for in the same style as the first carry-save adder from (Section 2.3). That is, as a simple loop that takes an input, applies dr10, and signals the output:

type HxW32 = Hex (W 32)

dr10 :: HxW32 -> HxW32
dr10 = doubleround . doubleround . doubleround . doubleround . doubleround .
       doubleround . doubleround . doubleround . doubleround . doubleround 

loop :: Maybe HxW32 -> ReacT (Maybe HxW32) (Maybe HxW32) Identity ()
loop (Just hxw32) = signal (Just (dr10 hxw32)) >>= loop
loop Nothing      = signal Nothing >>= loop

start :: ReacT (Maybe HxW32) (Maybe HxW32) Identity ()
start = loop Nothing

The full code is available here: Naive_DR10.hs. If the loop function is passed a valid input (i.e., (Just hxw32)), then dr10 is applied to it. In each cycle, dr10 hxw32 is calculated.

Why is this naive? If you look at the code for doubleround, there are a lot of operations going on in dr10. Pure functions like these are compiled to combinational logic, and, the combinational logic for ten doublerounds is substantial. It would be better to pipeline calls to doubleround to avoid this.

There’s another way that this is naive in that inputs and outputs include Hex (W 32) which is \(16 \times 32 = 512\) bits. This means that, on an FGPA, one would need 1024 input and output ports and that is (I believe) beyond what’s currently available. We’ll come back to this issue later on.

The Plan

• Using the doubleround function, I’ll demonstrate 2- and 5-stage pipelines of dr10.
• I.e., ReWire versions of:

	pipe2 = [doubleround . doubleround . doubleround . doubleround . doubleround] .
               [doubleround . doubleround . doubleround . doubleround . doubleround]
	pipe5 = [doubleround . doubleround] . [doubleround . doubleround] . [doubleround .
               doubleround] . [doubleround . doubleround] . [doubleround . doubleround]

λ> :t ins
ins :: [W 8]
λ> pretty ins
0x01 : 0x02 : 0x03 : 0x04 : 0x05 : 0x06 : 0x07 : 0x08 : 0x09 : 0x0A : 0x0B : 0x0C : 0x0D : 0x0E : 0x0F : []
λ> 
λ> pretty $ map (three . two . one) ins
0x07 : 0x08 : 0x09 : 0x0A : 0x0B : 0x0C : 0x0D : 0x0E : 0x0F : 0x10 : 0x11 : 0x12 : 0x13 : 0x14 : 0x15 : []
λ> pretty $ runP start (Stall , DC) (map Arg ins)
(Stall,DC) :> (Arg 0x01,DC) :> (Arg 0x02,DC) :> (Arg 0x03,DC) :> (Arg 0x04,Val 0x07) :> (Arg 0x05,Val 0x08) :> (Arg 0x06,Val 0x09) :> (Arg 0x07,Val 0x0A) :> (Arg 0x08,Val 0x0B) :> (Arg 0x09,Val 0x0C) :> (Arg 0x0A,Val 0x0D) :> (Arg 0x0B,Val 0x0E) :> (Arg 0x0C,Val 0x0F) :> (Arg 0x0D,Val 0x10) :> (Arg 0x0E,Val 0x11) :> (Arg 0x0F,Val 0x12) :+> Nothing
λ>