From 935a50d074882e08a144a6047715592e43276371 Mon Sep 17 00:00:00 2001 From: Lennart Van Hirtum Date: Thu, 21 Dec 2023 15:30:26 +0100 Subject: [PATCH] Add explanations for latency --- philosophy/.gitignore | 2 + philosophy/combinatorial_dependency.md | 2 + philosophy/images/example.drawio | 183 ++++++++++++++++++ philosophy/images/example.png | Bin 0 -> 154732 bytes .../images/negativeBackedgeConcept.drawio | 58 ++++++ philosophy/images/negativeBackedgeConcept.png | Bin 0 -> 21010 bytes philosophy/images/nonDeterminism.drawio | 114 +++++++++++ philosophy/images/nonDeterminism.png | Bin 0 -> 90246 bytes philosophy/latency.md | 101 ++++++++++ philosophy/state.md | 55 +----- philosophy/state_v_latency.md | 19 ++ 11 files changed, 485 insertions(+), 49 deletions(-) create mode 100644 philosophy/.gitignore create mode 100644 philosophy/combinatorial_dependency.md create mode 100644 philosophy/images/example.drawio create mode 100644 philosophy/images/example.png create mode 100644 philosophy/images/negativeBackedgeConcept.drawio create mode 100644 philosophy/images/negativeBackedgeConcept.png create mode 100644 philosophy/images/nonDeterminism.drawio create mode 100644 philosophy/images/nonDeterminism.png create mode 100644 philosophy/latency.md create mode 100644 philosophy/state_v_latency.md diff --git a/philosophy/.gitignore b/philosophy/.gitignore new file mode 100644 index 0000000..57b2098 --- /dev/null +++ b/philosophy/.gitignore @@ -0,0 +1,2 @@ +*.bkp +*.dtmp diff --git a/philosophy/combinatorial_dependency.md b/philosophy/combinatorial_dependency.md new file mode 100644 index 0000000..85f32cc --- /dev/null +++ b/philosophy/combinatorial_dependency.md @@ -0,0 +1,2 @@ +# Combinatorial Dependency + diff --git a/philosophy/images/example.drawio b/philosophy/images/example.drawio new file mode 100644 index 0000000..9003122 --- /dev/null +++ b/philosophy/images/example.drawio @@ -0,0 +1,183 @@ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + 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z1lmnD{9I|kr79yjy8Ap5$XeGD<6;o6kU%Mmf>It0c}yhO-+S|6EoG*jKD3*xXz%WY zvD1Rqj-F9l&2H5bCyT_aoOs-ytAbJ@cxZ0gjh2o3e_{EwlbAzZ(H9c&X^Sy>q_UAlw|7cPw2YIbWt z85tRP{PD-})KgC(D=W*RSm_WEAOe9)psUx2a{UEVwEPTHZ@Wi<3PJ>2(nuDif=sN0 zEK&hUWGq5LygUDL#NmL&-i7YIPITLh=!RA(e;_6D5KqIs#FmaEK$r zA&LlvC@d6VVM2t43Ly*$`FC=OC4q)VMlduqjKRTS*awGT?;nD#Zvega0a&d4=;^h? zY_Y>+v5lFWL>z|v3?&M(mB>-c$NWCMKm>?Da1dbCIp2Q!Ee;(z1f$V7=Ad(Oa*&ys z2{t%dtyUu`DG4f-ifeC^%jJ+rBwTA7OE~>2xx|t{Y_ZwF-|u`Y2eH6g@A)q5eOHG5Go8qs2~gi2oNIpXL5-pf!KdTjzJ6! z4`N{0j)9?m^bgw5H)w^e--5n@9$4+&u-HAT9=}yzRJa5=2?fYaDnxo*E?qnkAOb-~ zfD%SQcHtE6moZR#y5|6uG&%+}x$*%a>D<$gggW#1a915MarpT4M!jjMvaH%2qLcsJ&f9 zTy!EbNpO656eSTDI{``WH4ZXP1c(3;7%Ks*)e2ULR99CAmQd2` z^=NHv5B%KJ*XS zxj99{j$t@PhB-Zg5FvyDAvfPBB2 valid_in` latency of _N_. + +For state to state paths, this could be relaxed in several ways: +- If it is proven the register won't be read for some cycles, then the latency can be hidden in these cycles. (Requires complex validity checking) +- Slow the rate of state updating to the maximum latency, possibly allow automatic C-Slowing. + +#### Implementation using negative back-edges + +We can provide a primitive construct to the user to enable them to use latencies at all, which is the _negative latency backedge_. The user simply instantiates this module betwheen two points. The negative backedge requires that it is part of a combinatorial loop. + +Usually it negative backedges would be found on the output of a module, which is combinatorially 'before' the inputs that should be returned to it (See [Combinatorial Dependency](combinatorial_dependency.md)). As an example, we can have a module with an internal negative backedge of -3, which itself contains some state that the backedge can originate from. The module wraps the backedge this way, and proves all of the safety requirements that come with using it. The user then is free to connect the output of this module combinatorially with the input, and with at most 3 cycles of latency. + +![Negative Backedge Concept](images/negativeBackedgeConcept.png) + +## Requirements for the latency counting system +- Addition or Removal of any latency registers that do not violate a constraint must not affect the operation of the design. +- Feedback loops containing only latency are considered combinatorial feedback loops, and are therefore forbidden. Feedback loops must therefore have at least one state register in them. +- When the user specifies a latency of 1 somewhere using the `reg` keyword, this instructs the compiler that the _minimum_ latency between these points is now 1. The compiler is allowed to insert additional latency registers between any two points as it sees fit. +- State registers to not impact the latency counting. They count as 0 latency. +- Any loop (which must contain at least one state register) must have a roundtrip latency ≤ 0. Negative values are permitted, and are simply attributed to the use of negative back edges. + +## Latency Counting Graph Algorithm +We are given a directed graph of all wires and how they combinatorially depend on each other. Each edge can have a number of latency registers placed on it. + +Example: +```Verilog +// timeline is omitted here, not important +module Accumulator : int term, bool done -> int total_out { + state int total; + + reg int term_twice = term * 2; + + if done { + reg total_out = total + term_twice; + total = 0; + } else { + total = new_total; + } +} +``` + +Which results in the following graph: +![Example](images/example.png) + +Nodes are coloured by role. Blue nodes are inputs, green nodes are outputs, orange nodes are state registers, and white nodes are combinatorial. + +On the edges are noted the minimum latency offsets in black. These are given. The goal of the algorithm is to compute a set of 'absolute latencies', which are all relative to an arbitrary node. These are given with the red nodes on the picture. Because these absolute latencies are relative to an arbitrary reference point, we accept any constant shift applied to all absolute latencies as equivalent. + +### Non Deterministic inference of Input and Output absolute latencies +Sadly, while it appears reasonable to think it's possible to assign a deterministic latency. Observe this contrived example: + +```Verilog +// timeline is omitted here, not important +module NonDeterministic : int a, int b -> int x, int y { + reg int a_d = a; + reg int t = a_d + b; + reg reg reg int a_ddd = a; + x = t + a_ddd; + y = t; +} +``` + +Simplified latency graph: +![Non Determinism](images/nonDeterminism.png) + +The issue starts when the inputs and outputs don't have predefined absolute latency. We are tempted to add maximization and minimization to the input and output absolute latencies, to force the module's latency span to be as compact as possible, and therefore maximize how free the user of this module is in using it. But sadly, we cannot make a deterministic latency assignment for our inputs and outputs, as in this example b and y press against each other, permitting two possible implementations. + +One may think the solution would simply be to prefer inputs over outputs or something, just to get a deterministic latency assignment. Just move b to be the earliest of the available latencies, but even in this case, if we instead looked at the possibilities of a, and fixed b, we would again make b later by making a earlier. And since there's no way to distinguish meaningfully between inputs, there's no deterministic solution either. + +To this problem I only really see two solutions: +- Still perform full latency computation when compiling each module separately. In the case of non-deterministic latency assignment, reject the code and require the programmer to add explicit latency annotations. The benefit is better encapsulation, the programmer requires only the module itself to know what latencies are. The downside is of course less flexible modules. +- Perform latency computation at integration level, diff --git a/philosophy/state.md b/philosophy/state.md index 457c44c..9414570 100644 --- a/philosophy/state.md +++ b/philosophy/state.md @@ -1,62 +1,19 @@ +# On State +For latency see [latency](latency.md) - -# On Registers - -## State vs Latency - -In my experience, the use of registers usually boils down to two use cases: -- Representing a current working state, which gets updated across clock cycles -- Improving timing closure by introducing registers on tight paths. - -While this distinction exists in the programmer's mind, it isn't in the vocabulary of common compilers. Verilog and VHDL just call both 'reg' (And non-registers too, but that's another can of worms.) - -Philosophically, the difference is quite important though. Registers that are part of the state are critical, and they directly direct the functioning of the device. While latency registers should not affect the functioning of the design at all, aside from trivially affecting the latency of the whole design. Some would argue that worrying about latency registers is a solved problem, with retiming tools that can automatically migrate latency registers across a design to place them wherever more timing slack is required. In practice though, this capability is limited, usually by explicitly marking specific paths as latency insensitive, or in a limited way by synthesizing a block of registers somewhere, which should then be migrated across the design. Still, this practice is always limited by the first design register it comes across along the path. Explicitly differentiating between state and latency registers could make this automatic retiming much more powerful. - -While indeed generally latency can't affect the actual operation of the device, it can be disallowed in certain circumstances. Certain paths are latency sensitive, and would no longer produce correct results if latency were introduced. A trivial example is any kind of feedback loop. In this case, no latency can be introduced within the feedback loop itself, as the result for the current feedback loop cycle wouldn't arrive in time. In this case the latency should either be forbidden, or reincorporated in a different way, such as interpreting the state loop as a [C-Slowed](https://en.wikipedia.org/wiki/C-slowing) state loop. - -## Latency Counting -Inserting latency registers on every path that requires them is an incredibly tedious job. Especicially if one has many signals that have to be kept in sync for every latency register added. This is why I propose a terse pipelining notation. Simply add the `reg` keyword to any critical path and any paths running parallel to it will get latency added to compensate. This is accomplished by adding a 'latency' field to every path. Starting from an arbitrary starting point, all locals connected to it can then get an 'absolute' latency value, where locals dependent on multiple paths take the maximum latency of their source paths. From this we can then recompute the path latencies to be exact latencies, and add the necessary registers. - -Example: -``` -(start - 0) -A -----------+-- reg -- reg --\ -(-1) / +-- C (2) -B -- reg --/------------------/ -``` - -### Latency counting with state -Of course, state registers are also moved around by latency. This means that while it appears like two state modules get updated at the same time, if they are independent they need not. - -However, state registers should not count towards the latency count. So specifying `reg reg` should increase the latency count by 2, but specifying `state` does not. This makes sense, because this means a feedback loop to a state register has a latency of 0, which it requires to stay within. Also, this maintains that by removing all latency registers, the total latency count becomes 0 on all ports. - -If this rule holds for all possible hardware designs is up for further research. - -### Maximum Latency Requirements -It's the intention of the language to hide fixed-size latency as much as possible, making it easy to create pipelined designs. - -Often however, there are limits to how long latency is allowed to be. The most common case is a state to itself feedback loop. If a state register must be updated every cycle, and it depends on itself, the loopback computation path may not include any latency. - -For example, a FIFO with an almost_full threshold of _N_, may have at most a `ready_out -> valid_in` latency of _N_. - -For state to state paths, this could be relaxed in several ways: -- If it is proven the register won't be read for some cycles, then the latency can be hidden in these cycles. (Requires complex validity checking) -- Slow the rate of state updating to the maximum latency, possibly allow automatic C-Slowing - -## On State State goes hand-in-hand with the flow descriptors on the ports of modules. Without state all a module could represent is a simple flow-through pipeline. But once we introduce state, suddenly modules can have a wide range of output patterns and required input patterns. A simple example would be a data packer or unpacker. An unpacker receives a data packet, and outputs its contents in parts over the next N cycles. How should this unpacker behave when it receives another data packet before it finishes? It can either discard what it's currently working on, or discard the incoming data. Either way, data is lost. So the packer's interface must prohibit incoming data for N-1 cycles after a valid packet. The language we choose for the interfaces is that of the regex. This is a natural choice, since in effect any module the user writes is a state machine, and regexes can be converted to state machines. State machines have a nice property, that operators for working with state machines are polynomial and easy to understand. -### Structural and Data State +## Structural and Data State We have to check the state machine that is each module against the state machines of the modules it uses of course. Sadly, this checking can only really be done in a generic way by generating the full module state machine, and checking its behavior against the state machine from its dependents' interfaces, as well as its own. Generating the whole state machine is a combinatorial endeavour however, and a too wide state vector quickly leads to an unmanageable number of states. This encourages us to differentiate between two types of state. Structural State (namely state whose instances are incorporated into the module STM), and Data State, which (aside from its validity) is not. We wouldn't care about every possible bitpattern of a floating point number we happened to include in our state right? -### Examples -#### Summing module +## Examples +### Summing module ```Verilog timeline (X, false -> /)* .. (X, true -> T) module Accumulator : int term, bool done -> int total { @@ -107,7 +64,7 @@ Since in this example the only active state for the code corresponds to both act The caller is then responsible for providing a stream of the form of the regex. -### Unpacker +## Unpacker The previous example was quite simple though, with the code's active state machine containing only one state. In this example we explore a module that does have structural state. ```Verilog diff --git a/philosophy/state_v_latency.md b/philosophy/state_v_latency.md new file mode 100644 index 0000000..648b259 --- /dev/null +++ b/philosophy/state_v_latency.md @@ -0,0 +1,19 @@ +# On Registers + +## State vs Latency + +In my experience, the use of registers usually boils down to two use cases: +- Representing a current working state, which gets updated across clock cycles +- Improving timing closure by introducing registers on tight paths. + +While this distinction exists in the programmer's mind, it isn't in the vocabulary of common compilers. Verilog and VHDL just call both 'reg' (And non-registers too, but that's another can of worms.) + +Philosophically, the difference is quite important though. Registers that are part of the state are critical, and they directly direct the functioning of the device. While latency registers should not affect the functioning of the design at all, aside from trivially affecting the latency of the whole design. Some would argue that worrying about latency registers is a solved problem, with retiming tools that can automatically migrate latency registers across a design to place them wherever more timing slack is required. In practice though, this capability is limited, usually by explicitly marking specific paths as latency insensitive, or in a limited way by synthesizing a block of registers somewhere, which should then be migrated across the design. Still, this practice is always limited by the first design register it comes across along the path. Explicitly differentiating between state and latency registers could make this automatic retiming much more powerful. + +While indeed generally latency can't affect the actual operation of the device, it can be disallowed in certain circumstances. Certain paths are latency sensitive, and would no longer produce correct results if latency were introduced. A trivial example is any kind of feedback loop. In this case, no latency can be introduced within the feedback loop itself, as the result for the current feedback loop cycle wouldn't arrive in time. In this case the latency should either be forbidden, or reincorporated in a different way, such as interpreting the state loop as a [C-Slowed](https://en.wikipedia.org/wiki/C-slowing) state loop. + +## On State +See [state](state.md) + +## On Latency +See [latency](latency.md)