Burst-Mode Asynchronous Controllers on FPGA

FPGAs have been mainly used to design synchronous circuits. Asynchronous design on FPGAs is di ﬃ cult because the resulting circuit may su ﬀ er from hazard problems. We propose a method that implements a popular class of asynchronous circuits, known as burst mode, on FPGAs based on look-up table architectures. We present two conditions that, if satisﬁed, guarantee essential hazard-free implementation on any LUT-based FPGA. By doing that, besides all the intrinsic advantages of asynchronous over synchronous circuits, they also take advantage of the shorter design time and lower cost associated with FPGA designs.


Introduction
Due to the increasing complexity of digital systems combined with the market drive for higher performance, there has been an increased interest about asynchronous circuits [1,2].Asynchronous circuits do not present clock distribution related problems like clock skew.The circuits have low power consumption, better modularity, robustness toward variations in temperature, and low emission of electromagnetic radiation [3].One known weakness of asynchronous circuits has been the difficulty to design hazard-free circuits and to solve the critical races [3].Furthermore, asynchronous circuits frequently cannot benefit from the use of FPGAs due to the extra difficulty imposed by their fixed architecture to deal with hazards [4].
Burst-mode asynchronous controllers proposed by Nowick [9,10] are a popular class of finite state machines.They allow multiple inputs changes.They operate according to the GFM, meaning that a new state transition may only start when the whole circuit (gates and lines) is stable.This paper addresses burst-mode asynchronous controllers.Their advantages are the use of basic gates, similarity with synchronous design.These controllers have been adopted in important industrial and academic designs [11][12][13].
FPGAs are popular components for prototyping and production of digital circuits due to their low cost and short design time.Their focus has been on synchronous digital circuits.There have been some recent efforts to prototype asynchronous circuits on both commercial [14][15][16][17] and academic FPGAs [4,[18][19][20].
Burst-mode controllers are usually designed using a logic-driven design methodology [21].There are two reasons why off-the-shelf FPGAs are not fit for burst-mode asynchronous controllers [4,14,22].(1) The mapping process of burst-mode Booleans functions (equations of next state-controllers) to logic blocks (macrocells) may introduce logic hazards.
(2) The internal routing among logic blocks may introduce significant delays that may result in essential hazards.

Avoiding Logic Hazards in Burst-Mode Controllers
The burst-mode specification proposed by Nowick is functional-hazard free [23].Nowick also proposed a method to produce logic-hazard free burst-mode Boolean functions [24].Furthermore, Siegel et al. [25] proposed a technique to decompose large fan-in burst-mode Boolean functions without introducing logic-hazards.Finally, Maheswaran and Akella [15] and Hauck et al. [4] showed that if Booleans functions are functional-hazard free then they can be mapped on ordinary LUT-based FPGAs without presenting logic hazards [26].

Avoiding Essential Hazards in Burst-Mode Controllers
Yun and Dill [27] and Nowick and Coates [10] proposed the insertion of delay elements on the feedback wires to avoid essential hazards in burst-mode controllers.However, this solution is not adequate for FPGAs because these components are not designed to ease the insertion of delay elements.Furthermore, delay elements degrade the circuit cycle time, area, and reliability.
In this paper, we demonstrated a sufficient condition that guarantees essential hazard-free operation of any type of burstmode controller when mapped on any type of LUT-based FPGA component without the need of extra delay elements.The proof is based on two new concepts: (1) essential signals; (2) essential super states.The essential hazard-free operation is guaranteed if the following conditions are satisfied: (1) essential hazard-free specification: for all state transitions in a burst-mode specification, if the label contains a nonempty output burst, it must also contain at least one essential input signal; (2) essential hazard-free implementation: starting from an essential hazard-free specification, while building the burst-mode flow map, all single states whose incident state transitions are labeled with nonempty output bursts must be transformed into essential super states.
Furthermore, whenever a burst-mode specification does not satisfy the first condition, we present two functional transformations that create essential input signals without altering the original functionality: (1) reduction of input concurrency: transforms concurrent transitions into sequential transitions whenever acceptable (but there is a latency penalty); (2) addition of dummy input signals (but there is an area penalty).

Hazard-Free BM Conditions
This paper is divided in four sections.Section 3 briefly explains the burst-mode specifications.Section 2 presents the essential signal and essential super-state concepts and explains the two functional transformations.Section 4 presents our method and illustrated with an example.Section 5 shows our experimental results presenting the latency and area penalties found on nine known and one homemade benchmark.Section 6 presents our conclusions and future work.

Burst-Mode Specification
The BM specification is represented as a state transition diagram.Each transition is triggered by an input burst (single-or multiple-input changes) causing the occurrence of an output burst (that may be empty or nonempty).It is necessary to define an initial state.State transitions are represented by arcs, which are labeled with their corresponding input/output bursts.The signals are always transition sensitive (0 → 1, or 1 → 0).Input bursts may not be empty.The input signals are monotonic, changing only once during each state transition.The BM specification has to obey the polarity property, the unique entry point and the maximal set property [23].
Figure 1 shows a BM specification.The input signals are a, b, and c while the output signals are x and y.For example, state transition 7 [a+ b−/x+] → 2 means that if a changes from 0 to 1 and b changes from 1 to 0, the output x will change from 0 to 1. State 0 is the initial state.Figure 2 shows the corresponding burst-mode flow map (2D map) [27].Several tools, like Minimalist [28], 3D [27], and ATACS [29] have been proposed to synthesize controllers from a textual description of the burst-mode specification.These International Journal of Reconfigurable Computing tools generate an independent netlist of the technology (nextstate equations of the type sum of products).
BM asynchronous controllers may be subject to sequential hazards.Essential hazards, like transient essential hazard or steady-state essential hazard, are inherent to the sequential function and are not necessarily associated to a particular implementation of the circuit.The concept of essential hazard has been originally defined by Unger [30] in connection with fundamental-mode controllers.
This concept has been generalized for BM controllers and may be explained using the total state concept.A total state A(I, O) is a vector composed of all the input (I) and output (O) signal values in the specification.A total state corresponds to one single cube (cell) on a burst-mode flow map (see Figure 2).For example, the total state 2 of the Figure 2 is (a, b, c, x, y  A potential essential hazard can be detected applying the GUR rule from any initial state.For example, Figures 3(a As the final total state (11001) after the last activation (T3) is different from the final total state (11010) after the first activation (T1), then a steady-state essential hazard has occurred.Figure 3(a) shows the path T2 and Figure 3(b) shows the path T3.

BM-EHF Condition
An input signal in a BM specification is a context signal in an A → B transition if it does not change during this transition (it is not on the label) while it is a trigger signal if it is labeled during this transition.The input burst of each state transition can be represented by an input transition cube (ITC).For example, the ITC for state transition 7 → 2 on Figure 1 is abc = 220 (2 means do not care).In this example a and b are trigger signals while c is a context signal (whose value is 0).Definition 3. Let A and B be a pair of total states in a BM specification and I b /O b be the input/output burst for the A → B transition.Let E s be one input signal (E s ∈ I b ).E s is an essential signal if it is a context signal on all transitions incident on state A and is a trigger signal on the transition For instance (see Figure 1), a, b, c are not essential on transitions 4 → 0, 1 → 2, and 2 → 3 because they are trigger Proof.Let T1(A → B) and T2(B → C) be two sequential state transitions of a BM-EHF specification.ITC T1 and ITC T2 are their respective input transition cubes.Suppose that the transition T2 input burst does not contain as essential signal.
Then ITC T1 ⊆ ITC T2 , which means that the C final total state belongs to a path on ITC T1 .This fact violates Definitions 1 or 2.
Figure 4 shows the HP-mp-for-pkt benchmark [12,13].On all transition labels there is at least one essential signal.Therefore, it is a BM-EHF specification.
There are two ways to transform nonessential hazard-free BM specifications into a BM-EHF specification.

Reduction of Input Burst Concurrency
The transformation consists of decomposing the input burst labeled on a state transition generating two-state transitions.For example, Figure 5 shows a reduced concurrency BM-EHF specification equivalent to the BM specification in Figure 1

Insertion of Essential Signals
This transformation consists of inserting the smallest number of dummy essential signals in all state transitions without essential signal.For example, Figure 6 shows an BM-EHF specification equivalent to the specification in Figure 1 in which adummy essential signal d has been added to state transitions 1 → 2 and 2 → 3.This transformation has a higher cost than the previous one because it increases the number of input signals (I b ), modifying the interaction with the external environment.
If one observes the 2 → 3 state transition in Figure 6, the conclusion is that a is essential on transitions 1 → 2 → 3, while d is essential on transitions 7 → 2 → 3.

Super-State Condition
Lemma 1 is a necessary and sufficient condition for an essential hazard free specification but not for hazard-free implementation.The super-state concept will guarantee the latter condition.
Definition 4 (super-state).Consider an input burst I b (a, b, . . ., n) and an output burst O b (x, y, . . ., m).We call a super-state the set of single total states defined by all 0/1 combinations of a subset S Ib of the input burst signals, keeping fixed the remaining input signals and all the output signals.
Definition 5 (essential super-state).Consider a BM-EHF specification in which a total state F is reached by a set of N incident transitions {I t i } i = 1, . . ., N. Each incident transition I t i is activated by an input burst I b i .Each input burst is labeled with a subset of the input signals set   S ∪Ib = ∪{I b i } of all input signals active on the incident transitions set {I t i }, labeled with nonempty output bursts.
An essential super-state BM flow map is derived from a BM-EHF specification by applying Definition 5 to all total states.Figure 7 is such a map for the specification in Figure 6.Cells in red are used to compose essential super-states.For example, the 0 [a+b+/x+] → 1 transition creates essential super-state 1 composed of four total states: abcdxy = [000010, 010010, 100010, 110010].State 110010 is the final total state.Total state 2 may be reached from either state 1 or state 7. Applying Definition 5, we find that it must be composed of six total states (essential super-state 2): abcdxy = [000111, 010111,100111,110111,100011,110011].This set of total states can be described by a cube (super-state transition cube-SSTC).Figure 8 shows the description in states transition diagram of the BM-ESS flow map.

Proposition 1. If a total state F in a BM-EHF specification is reached by one or more incident transitions labeled with empty output bursts, then F is an essential super-state.
Proof.Let T1(A → F) be a state transition with an empty output burst.SSTC A and SSTC F are super-state transition cubes for final total states A and F. As A must be essential, and as SSTC A [output] = SSTC F [output] because both output bursts are empty, then F is also an essential super-state.

Lemma 2. The BM-EHF specification has an EHF implementation if and only if for
Proof.Let T1(B → A) and T2(A → C) be state transitions with output bursts.SSTC A and SSTC C are the superstate transition cubes of final total states A and C. Suppose that the T2(A → C) input burst does not contain an essential signal.Then SSTC . This means that A cannot be an essential super-state because this would violate Definition 5.

Metodolology
Our method begins from the BM specification and implements the asynchronous controllers in the architecture of Huffman with feedback output.The synthesis procedure has five steps.

International Journal of Reconfigurable Computing
(3) Generate the BM-EHF specification with essential super-states (BM-ESS) according to Section 3.5 (applying Definition 5).(4) Use the Minimalist tool that starts from the BM-ESS specification and produces the equations of next-state hazard-free (sum of products-netlist).
(5) Use the Quartus tool [31] that starts from the netlist in structural VHDL.
The BM specification shown in Figure 1 has been used to illustrate our method.Figure 5 shows BM-EHF specification (Steps (1) and ( 2)). Figure 9 shows the BM-ESS specification (Step (3)).Steps ( 4) and ( 5  synthesis.One-state variable y0 was required to solve the existing conflicts (see Figure 10) [28].Figure 11 shows logic circuit (RTL view-Altera).Figure 12 shows result of simulation of the circuit that was obtained by our method (hazard-free waveforms).

Discussion
Figures 13 and 14 show, respectively, the simulation results and the logic circuit of the mp-for-pkt benchmark whose specification is shown in Figure 4.The synthesis was performed using the Minimalist tool followed by the Quartus tool. Figure 13 shows two glitches, one on the Allocoutbound output and one on the AllocPB output.For example, the glitch on signal Allocoutbound occurs on state transition 1 [Ackout−Req+/TRS−AllocPB+] → 2. Figure 14 shows the behavior in the logic circuit of the state transition 1 → 2. The reason of the glitch: input signal Req+ acts in the paths 1 and 2, where the change in the path 1 arrives first in LUT-5 (see Figure 14).This glitche can also be identified in the BM flow map.Thespecification is EHF (Lemma 1 is satisfied) but the implementation is not (Lemma 2 is not satisfied), causing a transient essential hazard shown in Figure 15 (to apply GUR rule-T2: 2 The result of simulation of the circuit that was obtained by our method shows that the glitches have been eliminated (see Figure 16).The area penalty was 8 LUTs against 5 LUTs in the first solution.The latency penalty was 2,2%.

Results
We applied our theory to 9 known [8,9,12,13] and one homemade benchmark.Table 1 presents the number of input and output signals, states, and transitions for each benchmark.Table 2 presents the area and timing results for these benchmarks synthesized as Huffman machines (with feedback output) before applying our theory.Syntheses performed using Minimalist followed by Quartus.The area was measured in terms of the number of LUTs while the latency was derived from simulations of the circuits already fitted on an EP2C35F672C7 device from Altera (Cyclone II family).required to satisfy Lemmas 1 and 2. Table 4 shows the same results for the benchmarks after adhering to Lemmas 1 and 2.
As expected we found an area penalty (average of 54%), a latency penalty (average of 4,8%), and a state variables penalty (average of 75%).The call-proc benchmark showed a smaller area (less LUTs) and the rev-setup benchmark showed a reduced latency time.However, the area penalties did not impact significantly the FPGA usage ( ∼ =1%) still leaving enough free space for a datapath and other components that could be placed on the same device.

Conclusions
This work presented two conditions that, if satisfied, guarantee that burst-mode asynchronous controllers can be mapped on any commercial LUT-based FPGA without incurring in essential hazards.
When these conditions are not satisfied, we presented functional transformations that may be used to solve the problem.In this case, there is an area (mainly are added state variables-75%) and a latency penalty.However, our experimental results on a set of known benchmark showed low latency penalty (4,8%) and low FPGA occupation overhead ( ∼ =1%).This type of burst-mode controllers may be combined with a self-timed datapath that have already been successfully synthesized on commercial FPGAs, in order to create fully asynchronous processor on FPGAs.
) = 10011.There may be n! paths on the BM flow map corresponding to the transition from total state A(I 1 , O 1 ) to total state B(I 2 , O 2 ) (labeled with an input/output burst I b /O b ), n being the number input signals in I b .These paths cover the set {A, B, C, . . ., N}, where A is the initial total state, B is the final total state, and C, . . ., N are intermediary total states.

Let A(I 1 ,Definition 2 .
O 1 ) and B(I 2 , O 2 ) be two total states in the BM flow map and I b /O b the input/output burst that activates the transition A → B. Let N be the number of the input burst signals.Consider the following transitions sequence: T1: A [Ib] → B; (transition 1 is A → B activated by I b ) T2: B [Ib inverted polarity] → C i (i = 1, . . ., k are possible final states); T3: C [Ib] → D j (i = 1, . . ., n are possible initial states), ( j = 1, . . ., m are possible final states).Definition 1.There is a potential steady-state essential hazard in the A → B transition if, applying the GUR rule, any final total state D j ( j = 1, . . ., m) / = B.There is a potential transient essential hazard in the A → B transition if, applying the GUR rule, there is a total state I ( / = A and / = B) on any path of transitions B → C i or C i → D j that produces an output signal different from any value occurring on any path of transition A → B.

International
{I s }.An essential super-state is the super-state defined by the union

Figure 12 :
Figure 12: Simulation of the logic circuit of Figure 5.

Figure 13 :
Figure 13: Simulation of the mp-for-pkt: with transient essential hazard.

Figure 15 :
Figure 15: BM flow map showing a transient essential hazard.

Figure 16 :
Figure 16: Simulation of the EHF version of the mp-for-pkt.

Table 1 :
BM specifications show data.

Table 2 :
Experimental Results to Huffman Machine The column State vars shows the variables of state.

Table 3 :
BM-ESS specifications lead to the following data.

Table 4 :
Experimental results show Huffman machine-EHF ( * Minimalist Tool did not complete the synthesis).
Table 3 presents the number of inputs and output signals, states, transitions, and dummy signals for the same benchmarks after applying the functional transformations