guillaume savaton - au mouvant sillage

Simulating digital circuits in Racket

A RISC-V core in Racket

Guillaume Savaton

Let’s try to simulate a non-trivial circuit in Racket using the techniques proposed in the previous post.

Virgule is a 32-bit RISC processor core that supports most of the base instruction set of the RISC-V specification (RV32I). It was initially designed and implemented in VHDL to serve as an illustration for the digital electronics course that I teach. The VHDL source code is not publicly available yet but you can get an overview of what Virgule is by using its web-based simulator emulsiV and reading its documentation.

I have written two implementations of Virgule: one uses a finite state machine as a sequencer; the other is organized as a five-stage pipeline. Both implementations use the same set of components in their datapaths.

The architecture of Virgule favours simplicity over completeness, speed or size. If you are looking for an optimized, production-ready RISC-V core, there are plenty of other implementations to choose from.


The pipelined version could be the topic of another post. In this post, I will focus on the state-based implementation because it is easier to understand. Here is an overview of its internal architecture with a state diagram of its sequencer:

Architecture of the slow, state-based implementation

Since the architecture is fully synchronous, the clock signal is not represented to avoid cluttering the block diagram.

Virgule uses a similar bus interface as the PicoRV32. The same interface is used for fetching instructions and for load/store operations. Here is a description of Virgule’s I/O ports:

Signal Direction Size (bits) Role
reset Input 1 Forces the processor to restart in its initial state.
valid Output 1 When asserted, the processor initiates a data transfer.
ready Input 1 Indicates that the current responder is ready for a new data transfer.
address Output 32 The address where to read or write.
wstrobe Output 4 Write enables for each byte of wdata; 0000 for a read transfer.
wdata Output 32 The data to write.
rdata Input 32 The data read from the current responder.
irq Input 1 Interrupt request.

The processor asserts its output valid to indicate that address, wstrobe and wdata are all valid and stable. If a memory or peripheral device is mapped to the given address, it responds by assigning rdata and asserting ready. A data transfer is considered complete when valid and ready are both high on the same clock edge.

In the following sections, I will detail the internal operation of the processor and show the Racket code that implements it. But before that, let’s have a look at the Racket forms that we will need.

Circuit description facilities and conventions

My previous blog post, Simulating digital circuits in Racket, introduced several constructs to represent and manipulate hardware signals in Racket. This section explains the choices that I have made, and the syntactic sugar that I have added since that post was written.

Combinational components

A combinational component can be written as a function. The form define-signal automatically lifts a Racket function that operates on values into a function that operates on signals. The instruction decoder and the arithmetic and logic unit are defined like this:

(define-signal (decoder data)

(define-signal (arith-logic-unit instr a b)

In the previous blog post, my implementation of define-signal could only define functions with a single output value. It is an error to return (values ...) as the result of such a function.

In decoder, I work around this limitation by returning a struct value of type:

(struct instruction (...))

To address other situations, when creating a struct type is not relevant, I have added a #:returns clause to signal-λ, define-signal and for/signal. It is used in load-store-unit like this:

(define-signal (load-store-unit #:instr instr #:address address
                                #:store-enable store-enable #:store-data store-data)
                                #:rdata rdata
  #:returns (wstrobe wdata load-data)
  (define wstrobe   ...)
  (define wdata     ...)
  (define load-data ...))

Internally, load-store-unit will bundle load-data, wstrobe and wdata into a signal of lists. When calling load-store-unit, this signal will be unbundled into three separate signals:

(define-values (wstrobe wdata load-data)
  (load-store-unit #:instr        ...
                   #:address      ...
                   #:store-enable ...
                   #:store-data   ...
                   #:rdata        ...))

If you like to use named associations in your VHDL or Verilog instantiation statements, you will appreciate the addition of keyword arguments to define-signal.

Sequential components

Sequential components such as register-unit or branch-unit are represented by ordinary functions using define. As a consequence, if a component has several outputs, the corresponding Racket function can use (values ...) to return the output signals. virgule itself is defined like this:

(define (virgule #:reset reset #:rdata rdata #:ready ready #:irq irq)
  (values valid address wstrobe wdata))

In the function body, we can create sequential signals with register, or any of its variants, and combinational signals with for/signal.

(define (register-unit #:reset reset #:enable enable
                       #:src-instr src-instr #:dest-instr dest-instr #:xd xd)
  (define x-reg (register/r ... reset
                  (for/signal (enable dest-instr xd this-reg)
  (for/signal (src-instr x-reg) #:returns (xs1 xs2)
    (define xs1 ...)
    (define xs2 ...)))

To make the code easier to read, I have modified for/signal so that the following forms are equivalent:

; This form:
(for/signal (src-instr x-reg) ...)
; ... is short for:
(for/signal ([src-instr src-instr] [x-reg x-reg]) ...)

Referring to a signal that is defined later

In a circuit that contains circular dependencies, a signal can appear in an expression before it is assigned. signal-defer is a macro that delays the evaluation of a Racket variable containing a signal. It could be defined like this:

(define-simple-macro (signal-defer sig)
  (signal-delay (signal-force sig)))

If I write:

(define x (signal-defer y))

the value of y will not be read until x is forced. Forcing x will also automatically force y.

However, since we know that signal-delay creates a function, and considering that we do not need an extra level of memoization, we can replace it by a simple lambda:

(define-simple-macro (signal-defer sig)
  (λ ()
    (signal-force sig)))

Logic values and logic vectors

Hardware description languages usually have special support for binary data types of arbitrary width. Before writing Virgule, my first impulse was to create a Racket module that would provide data types and operations in the spirit of VHDL packages std_logic_1164 and numeric_std.

Such a module would be useful if my intent was to use Racket as a hardware description language. But you might remember that my ultimate goal is to use Racket as a platform for a hardware description DSL. While I expect this DSL to come with data types for logic vectors, I am not convinced that we need sophisticated abstractions for these types at runtime.

For this reason, the implementation of Virgule in Racket uses built-in types for logic values and logic vectors: booleans for flags and control signals, integers for general-purpose data and numbers. In fact, Racket integers already provide all the facilities that I need to represent logic vectors at runtime:

  • They can be arbitrarily large.
  • They support all the bitwise operations needed for logic vectors.
  • And obviously, they support integer arithmetic operations.

The missing features are: the ability to restrict the width of an integer, sign extension of an integer with a given width, and vector concatenation. For this reason, I have written the following helpers:

(unsigned-slice   v left right)
(signed-slice     v left right)
(unsigned         v width)
(signed           v width)
(unsigned-concat [v left right] ...)
(signed-concat   [v left right] ...)
  • unsigned-slice and signed-slice take a slice of a vector v. left is the index of the most significant bit and right is the index of the least significant bit. right defaults to left if omitted. The signed version sign-extends the result starting from index left.
  • unsigned and signed are shorthands to take a right-aligned slice of a given width.
  • unsigned-concat and signed-concat are macros that concatenate slices from one or more logic vectors. right can be omitted like in unsigned-slice and signed-slice.

You can find the complete source code of these functions and macros in module logic.rkt.

There is no support for uninitialized or indeterminate binary values, such as 'U' and 'X' in VHDL’s std_logic type, or x in Verilog.

Virgule implementation walkthrough

There is a lot of Racket code in this section. The biggest code snippets are collapsed so you are not obliged to scroll through them if you are only interested in the explanations.


The sequencer is a Moore machine where each state activates a boolean command signal (fetch-en, decode-en, etc).

In states fetch, load and store, the sequencer waits for a data transfer to complete (ready). In the execute state, the sequencer uses information from the current decoded instruction (load?, store?, has-rd?) to decide where to go next.

Virgule sequencer state machine

In Racket, the state machine is composed of a register/r form that stores the current state, a match expression that computes the next state, and one combinational signal for each action. I chose to represent states as symbols. In VHDL, I would declare an enumerated type.

Click on the snippet to expand it.

(define (virgule #:reset reset #:rdata rdata #:ready ready #:irq irq)

  (define state-reg (register/r 'state-fetch reset
                      (for/signal (instr ready [state this-reg])
                        (match state
                          ['state-fetch     (if ready 'state-decode state)]
                          ['state-decode    'state-execute]
                          ['state-execute   (cond [(instruction-load?   instr) 'state-load]
                                                   [(instruction-store?  instr) 'state-store]
                                                   [(instruction-has-rd? instr) 'state-writeback]
                                                   [else                        'state-fetch])]
                          ['state-load      (if ready 'state-writeback state)]
                          ['state-store     (if ready 'state-fetch state)]
                          ['state-writeback 'state-fetch]))))

  (define (state-equal? sym)
    (for/signal (state-reg)
      (equal? state-reg sym)))

  (define fetch-en     (state-equal? 'state-fetch))
  (define decode-en    (state-equal? 'state-decode))
  (define execute-en   (state-equal? 'state-execute))
  (define load-en      (state-equal? 'state-load))
  (define store-en     (state-equal? 'state-store))
  (define writeback-en (state-equal? 'state-writeback))


Fetching instructions

In the fetch state, the processor copies the program counter register pc-reg to the address bus and asserts the valid output. At the end of the memory transfer (valid and ready), the input data bus rdata is copied to register rdata-reg.

Fetching instructions

This is the complete definition of signals rdata-reg, valid and ready. In function virgule, they are part of the code that manages all memory accesses.

(define rdata-reg (register/e 0 (signal-and valid ready) rdata))
(define valid     (signal-or fetch-en store-en load-en))
(define address   (signal-if fetch-en pc-reg alu-result-reg))

Decoding instructions

The decoder function extracts information from the instruction word in rdata-reg, producing the instr signal of type:

(struct instruction (rd funct3 rs1 rs2 imm
                     alu-fn use-pc? use-imm? has-rd?
                     load? store? jump? branch? mret?))
Field Type Role
rd 5-bit unsigned The index of the destination register.
funct3 3-bit unsigned The funct3 field of the instruction, encodes branch, load and store operations.
rs1 5-bit unsigned The index of the first source register.
rs2 5-bit unsigned The index of the second source register.
imm 32-bit signed The immediate value encoded in the instruction.
alu-fn symbol The arithmetic or logic operation to execute.
use-pc? boolean Does this instruction use the program counter as the first ALU operand?
use-imm? boolean Does this instruction use an immediate as the second ALU operand?
has-rd? boolean Does this instruction write a result to a destination register?
load? boolean Is this instruction a memory load?
store? boolean Is this instruction a memory store?
jump? boolean Is this instruction a jump (JAL, JALR)?
branch? boolean Is this instruction a conditional branch?
mret? boolean Is this instruction a return from an interrupt handler?

Decoding instructions

Several other operations happen in the decode state:

  • register-unit reads the source registers needed by the instruction, and outputs their values to xs1 and xs2.
  • Two multiplexers select the operands for the arithmetic and logic unit. The first operand (alu-a) can be either the current value of the program counter (pc-reg) or xs1. The second operand (alu-b) can be either an immediate value or xs2.
  • At the end of the clock cycle, alu-a, alu-b, xs1, xs2 and instr are stored to registers.
(define instr (decoder (signal-defer rdata-reg)))
(define instr-reg (register/e instr-nop decode-en instr))

; Full version in section "Register writeback".
(define-values (xs1 xs2) (register-unit ...
                                        #:src-instr instr

(define xs1-reg (register/e 0 decode-en xs1))
(define xs2-reg (register/e 0 decode-en xs2))

(define alu-a-reg (register/e 0 decode-en
                    (for/signal (instr xs1 [pc (signal-defer pc-reg)])
                      (if (instruction-use-pc? instr)
(define alu-b-reg (register/e 0 decode-en
                    (for/signal (instr xs2)
                      (if (instruction-use-imm? instr)
                        (instruction-imm instr)

decoder is defined in datapath-components.rkt It uses constants and functions defined in module opcodes.rkt.

  • instruction-fmt identifies the format of an instruction.
  • word->fields extracts the fields from the instruction word.
  • decode-alu-fn identifies the arithmetic or logic operation to execute.
(define (instruction-fmt opcode)
  (match opcode
    [(== opcode-op)                         'fmt-r]
    [(== opcode-store)                      'fmt-s]
    [(== opcode-branch)                     'fmt-b]
    [(or (== opcode-lui) (== opcode-auipc)) 'fmt-u]
    [(== opcode-jal)                        'fmt-j]
    [_                                      'fmt-i]))

(define (word->fields w)
  (define opcode (unsigned-slice w 6 0))
  (define imm (match (instruction-fmt opcode)
                ['fmt-i (signed-concat [w 31 20])]
                ['fmt-s (signed-concat [w 31 25] [w 11 7])]
                ['fmt-b (signed-concat [w 31] [w 7] [w 30 25] [w 11 8] [0 0])]
                ['fmt-u (signed-concat [w 31 12] [0 11 0])]
                ['fmt-j (signed-concat [w 31] [w 19 12] [w 20] [w 30 21] [0 0])]
                [_      0]))
  (values opcode
          (unsigned-slice w 11  7) ; rd
          (unsigned-slice w 14 12) ; funct3
          (unsigned-slice w 19 15) ; rs1
          (unsigned-slice w 24 20) ; rs2
          (unsigned-slice w 31 25) ; funct7

(define (decode-alu-fn opcode funct3 funct7)
  (match (list     opcode                             funct3              funct7)
    [(list     (== opcode-lui)                        _                   _              ) 'alu-nop]
    [(list     (== opcode-op)                     (== funct3-add-sub) (== funct7-sub-sra)) 'alu-sub]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-slt)         _              ) 'alu-slt]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-sltu)        _              ) 'alu-sltu]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-xor)         _              ) 'alu-xor]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-or)          _              ) 'alu-or]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-and)         _              ) 'alu-and]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-sll)         _              ) 'alu-sll]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-srl-sra) (== funct7-sub-sra)) 'alu-sra]
    [(list (or (== opcode-op-imm) (== opcode-op)) (== funct3-srl-sra)     _              ) 'alu-srl]
    [_                                                                                     'alu-add]))

(define-signal (decoder data)
  (define-values (opcode rd funct3 rs1 rs2 funct7 imm)
    (word->fields data))
  (define use-pc?  (in? opcode (opcode-auipc opcode-jal opcode-branch)))
  (define use-imm? (not (= opcode opcode-op)))
  (define load?    (= opcode opcode-load))
  (define store?   (= opcode opcode-store))
  (define mret?    (and (= opcode opcode-system) (= funct3 funct3-mret) (= imm imm-mret)))
  (define jump?    (in? opcode (opcode-jal opcode-jalr)))
  (define branch?  (= opcode opcode-branch))
  (define has-rd?  (nor branch? store? (zero? rd)))
  (define alu-fn   (decode-alu-fn opcode funct3 funct7))
  (instruction rd funct3 rs1 rs2 imm
               alu-fn use-pc? use-imm? has-rd?
               load? store? jump? branch? mret?))

Arithmetic and logic operations, branches

In the execute state, arith-logic-unit performs an arithmetic or logic operation and branch-unit computes the address of the next instruction. The signal pc+4 receives the address of the next instruction in memory. It is stored in a register (pc+4-reg) for later use in the writeback state.

Executing instructions

In branch and jump instructions, the target address is the result of an addition performed by the arithmetic and logic unit. If the instruction is a conditional branch, branch-unit will compare the values of two source registers, available in xs1-reg and xs2-reg, and decide whether the branch is taken or not.

(define alu-result     (arith-logic-unit instr-reg alu-a-reg alu-b-reg))
(define alu-result-reg (register/e 0 execute-en alu-result))

(define pc-reg (register/re 0 reset execute-en
                 (branch-unit #:reset   reset
                              #:enable  execute-en
                              #:irq     irq
                              #:instr   instr-reg
                              #:xs1     xs1-reg
                              #:xs2     xs2-reg
                              #:address alu-result
                              #:pc+4    (signal-defer pc+4))))
(define pc+4 (for/signal (pc-reg)
               (word (+ 4 pc-reg))))
(define pc+4-reg (register/e 0 execute-en pc+4))

branch-unit also handles interrupts. When irq is asserted, and when the processor is not already serving an interrupt request, it will:

  • switch to a non-interruptible state,
  • save the address of the next instruction to an internal register (mepc-reg),
  • branch to the interrupt service routine at address 4.

If the current instruction is mret, branch-unit will:

  • switch back to the interruptible state,
  • branch to the address saved in mepc-reg.

Functions arith-logic-unit and branch-unit are defined in module datapath-components.rkt.

(define-signal (arith-logic-unit instr a b)
  (define sa (signed-word a))
  (define sb (signed-word b))
  (define sh (unsigned-slice b 5 0))
  (word (match (instruction-alu-fn instr)
          ['alu-nop  b]
          ['alu-add  (+ a b)]
          ['alu-sub  (- a b)]
          ['alu-slt  (if (< sa sb) 1 0)]
          ['alu-sltu (if (< a  b)  1 0)]
          ['alu-xor  (bitwise-xor a b)]
          ['alu-or   (bitwise-ior a b)]
          ['alu-and  (bitwise-and a b)]
          ['alu-sll  (arithmetic-shift a     sh)]
          ['alu-srl  (arithmetic-shift a  (- sh))]
          ['alu-sra  (arithmetic-shift sa (- sh))])))

(define (branch-taken? instr a b)
  (and (instruction-branch? instr)
       (let ([sa (signed-word a)]
             [sb (signed-word b)])
         (match (instruction-funct3 instr)
           [(== funct3-beq)  (=      a  b)]
           [(== funct3-bne)  (not (= a  b))]
           [(== funct3-blt)  (<      sa sb)]
           [(== funct3-bge)  (>=     sa sb)]
           [(== funct3-bltu) (<      a  b)]
           [(== funct3-bgeu) (>=     a  b)]
           [_                #f]))))

(define (branch-unit #:reset reset #:enable enable #:irq irq
                     #:instr instr #:xs1 xs1 #:xs2 xs2 #:address address #:pc+4 pc+4)
  (define pc-target (for/signal (instr xs1 xs2 address pc+4 [mepc (signal-defer mepc-reg)])
                      (define aligned-address (unsigned-concat [address 31 2] [0 1 0]))
                      (cond [(instruction-mret? instr)     mepc]
                            [(instruction-jump? instr)     aligned-address]
                            [(branch-taken? instr xs1 xs2) aligned-address]
                            [else                          pc+4])))
  (define irq-state-reg (register/re #f reset enable
                          (for/signal (instr irq [state this-reg])
                            (cond [(instruction-mret? instr) #f]
                                  [irq                       #t]
                                  [else                      state]))))
  (define accept-irq (signal-and-not irq irq-state-reg))
  (define mepc-reg (register/re 0 reset (signal-and enable accept-irq)
  (signal-if accept-irq
             (signal irq-addr)

Memory operations

In load and store operations, the address is always the result of an addition performed by the arithmetic and logic unit. The valid output is asserted in the load and store states. At the end of the memory transfer (valid and ready), the input data bus rdata is copied to register rdata-reg.

Memory transfers

In the store state, the role of load-store-unit consists in copying the data from xs2-reg to wdata, ensuring that it is properly aligned with respect to the target address and data size. load-store-unit also sets the wstrobe output.

(define rdata-reg (register/e 0 (signal-and valid ready) rdata))
(define valid     (signal-or fetch-en store-en load-en))
(define address   (signal-if fetch-en pc-reg alu-result-reg))

; Full version in section "Register writeback".
(define-values (wstrobe wdata ...)
  (load-store-unit #:instr        instr-reg
                   #:address      alu-result-reg
                   #:store-enable store-en
                   #:store-data   xs2-reg

Here is the part of load-store-unit that handles store operations:

(define-signal (load-store-unit #:instr instr #:address address
                                #:store-enable store-enable #:store-data store-data
                                #:rdata rdata)
  #:returns (wstrobe wdata load-data)
  (define align         (unsigned-slice address 1 0))
  (define wdata (match (instruction-funct3 instr)
                  [(== funct3-lb-sb) (unsigned-concat [store-data  7 0] [store-data  7 0]
                                                      [store-data  7 0] [store-data  7 0])]
                  [(== funct3-lh-sh) (unsigned-concat [store-data 15 0] [store-data 15 0])]
                  [_                 store-data]))
  (define wstrobe (if store-enable
                    (match (instruction-funct3 instr)
                      [(or (== funct3-lb-sb) (== funct3-lbu)) (arithmetic-shift #b0001 align)]
                      [(or (== funct3-lh-sh) (== funct3-lhu)) (arithmetic-shift #b0011 align)]
                      [(== funct3-lw-sw)                      #b1111]
                      [_                                      #b0000])

Register writeback

Finally, in the writeback state, the processor stores the result of the current instruction into a destination register. The register index is available in the rd field of instr-reg.

  • If the instruction is a load, the result is taken from rdata-reg via load-store-unit, ensuring that it is properly aligned and sign-extended.
  • If the instruction is a jump, the destination register receives a return address (pc+4-reg).
  • In other cases, the destination register receives the result from arith-logic-unit (alu-result-reg).

Register writeback

(define-values (xs1 xs2) (register-unit #:reset      reset
                                        #:enable     writeback-en
                                        #:src-instr  instr
                                        #:dest-instr instr-reg
                                        #:xd         (signal-defer xd)))

(define-values (wstrobe wdata load-data)
  (load-store-unit #:instr        instr-reg
                   #:address      alu-result-reg
                   #:store-enable store-en
                   #:store-data   xs2-reg
                   #:rdata        rdata-reg))

(define xd (for/signal (instr-reg load-data pc+4-reg alu-result-reg)
             (cond [(instruction-load? instr-reg) load-data]
                   [(instruction-jump? instr-reg) pc+4-reg]
                   [else                          alu-result-reg])))

Here is the code for register-unit. It uses a persistent vector (pvector) to store register values. You will find an explanation of this implementation choice in section Performance considerations.

(define (register-unit #:reset reset #:enable enable
                       #:src-instr src-instr #:dest-instr dest-instr #:xd xd)
  (define x-reg (register/r (make-pvector reg-count 0) reset
                  (for/signal (enable dest-instr xd this-reg)
                    (if (and enable (instruction-has-rd? dest-instr))
                      (set-nth this-reg (instruction-rd dest-instr) xd)
  (for/signal (src-instr x-reg) #:returns (xs1 xs2)
    (define xs1 (nth x-reg (instruction-rs1 src-instr)))
    (define xs2 (nth x-reg (instruction-rs2 src-instr)))))

And this is the part of load-store-unit that handles load operations:

(define-signal (load-store-unit #:instr instr #:address address
                                #:store-enable store-enable #:store-data store-data
                                #:rdata rdata)
  #:returns (wstrobe wdata load-data)
  (define align         (unsigned-slice address 1 0))
  (define aligned-rdata (unsigned-slice rdata 31 (* 8 align)))
  (define load-data (word (match (instruction-funct3 instr)
                            [(== funct3-lb-sb) (signed-slice   aligned-rdata  7 0)]
                            [(== funct3-lh-sh) (signed-slice   aligned-rdata 15 0)]
                            [(== funct3-lbu)   (unsigned-slice aligned-rdata  7 0)]
                            [(== funct3-lhu)   (unsigned-slice aligned-rdata 15 0)]
                            [_                                 aligned-rdata]))))

Simulating a computer system

The repository contains several modules that can help simulate a system with a processor core, memory and peripheral devices:

Example programs for a simple system with a fake text output device are available in the examples folder.

Performance considerations

While writing the register unit and the memory components, I had to choose between two structures for the memory cells: they could be defined as a signal of vectors, or as a vector of signals.

In VHDL, such a choice does not exist: if I declare a signal with an array type, I am allowed to manipulate it as a whole, or I can reference each array element as if it were a separate signal.

My first impression was that a signal of vectors would be less efficient because each write operation would create a new vector. But using a vector of signals turned out to be far worse, because the cost of reading at any arbitrary location outweighed the benefits.

The benchmarks folder contains five programs that compare the speed an memory usage of various memory implementations. The following choices are evaluated:

  • Using a signal of vectors vs a vector of signals.
  • Using built-in Racket vectors vs persistent vectors.
  • Using register/e vs register.

The third item compares the use of these patterns:

(register/e q0 e
  (for/signal (...)

(register q0
  (for/signal (this-reg ...)
    (if e

In the first case, the register is updated only when e is true, but the expression in for/signal is evaluated even when e is false. In the second case, the register is updated in every clock cycle, but expr is evaluated only when e is true. Both produce signals with the same values, but are not equivalent in terms of operations and intermediate data.

The results below have been obtained for a memory containing 1000 integers, a simulation duration of 10000 clock cycles with one write every two clock cycles. All memory cells are written and read in turns.

They show that the most efficient combination is to use a signal of persistent vectors with register.

Storage Register type Time (ms) Memory use (MB)
vector of signals register/e 21000 2000
Signal of vectors register/e 110 86
Signal of vectors register 58 45
Signal of pvectors register/e 39 14
Signal of pvectors register 28 10