Какой тип данных в Verilog эквивалентен переменной в VHDL?

Как написать эквивалентный код Verilog для приведенного ниже кода VHDL? Я показываю свой код Verilog за кодом VHDL. Код Verilog компилируется, но aux недействителен в течение всей симуляции.

VHDL: (classic_multiplier_parameters.vhd определяет m = 8)

library ieee; 
use ieee.std_logic_1164.all;
use ieee.std_logic_arith.all;
use ieee.std_logic_unsigned.all;
use work.classic_multiplier_parameters.all;

entity poly_multiplier is
port (
  a, b: in std_logic_vector(M-1 downto 0);
  d: out std_logic_vector(2*M-2 downto 0)
);
end poly_multiplier;


architecture simple of poly_multiplier is
  type matrix_ands is array (0 to 2*M-2) of STD_LOGIC_VECTOR(2*M-2 downto 0);
  signal a_by_b: matrix_ands;
  signal c: std_logic_vector(2*M-2 downto 0);
begin

  gen_ands: for k in 0 to M-1 generate
    l1: for i in 0 to k generate
       a_by_b(k)(i) <= A(i) and B(k-i);
    end generate;
  end generate;

  gen_ands2: for k in M to 2*M-2 generate
    l2: for i in k to 2*M-2 generate
       a_by_b(k)(i) <= A(k-i+(M-1)) and B(i-(M-1));
    end generate;
  end generate;

  d(0) <= a_by_b(0)(0);
  gen_xors: for k in 1 to 2*M-2 generate
    l3: process(a_by_b(k),c(k)) 
        variable aux: std_logic;
        begin
        if (k < M) then
          aux := a_by_b(k)(0);
          for i in 1 to k loop aux := a_by_b(k)(i) xor aux; end loop;
        else
          aux := a_by_b(k)(k);
          for i in k+1 to 2*M-2 loop aux := a_by_b(k)(i) xor aux; end loop;
        end if;
        d(k) <= aux;
    end process;
  end generate;

end simple;

Верилог:

module mul(
    a, b,
    d);
parameter M = 8;

input [M-1:0] a, b;
output [2*M-2:0] d;

wire [2*M-2:0] a_by_b [2*M-2:0];
wire aux;
//`UNPACK_ARRAY(2*M-2, 2*M-2, pack_a_by_b, a_by_b)

    //the first and
    genvar i, k;
    generate 
    for(k=0; k<=M-1; k=k+1) begin: for1_outer
        for(i=0; i<=k; i=i+1) begin: for1_inner
            assign a_by_b[k][i] = a[i] & b[k-i];
        end
    end
    endgenerate

    //second and
    generate 
    for(k=M; k<=2*M-2; k=k+1) begin: for2_outer
        for(i=k; i<=2*M-2; i=i+1) begin: for2_inner
            assign a_by_b[k][i] = a[k-i+(M-1)] & b[i-(M-1)];
        end 
    end
    endgenerate

    assign d[0] = a_by_b[0][0];
    // xors
    generate
    for(k=1; k<=2*M-2; k=k+1) begin: for3_outer
        if(k < M) begin
            assign aux = a_by_b[k][0];
            for(i=1; i<=k; i=i+1) begin: for3_inner1
                assign aux = a_by_b[k][i] ^ aux;
            end
        end
        else begin
            assign aux = a_by_b[k][k];
            for(i=k+1; i<=2*M-2; i=i+1) begin: for3_inner2
                assign aux = a_by_b[k][i] ^ aux;
            end
        end
        assign d[k] = aux;
    end
    endgenerate
endmodule

Verilog: (дополнительно как тип регистра)

module mul(
    a, b,
    d);
parameter M = 3;

input [M-1:0] a, b;
output [2*M-2:0] d;

wire [2*M-2:0] a_by_b [2*M-2:0];
reg aux = 1'b1;
//`UNPACK_ARRAY(2*M-2, 2*M-2, pack_a_by_b, a_by_b)

    //the first and
    genvar i, k;
    generate 
    for(k=0; k<=M-1; k=k+1) begin: for1_outer
        for(i=0; i<=k; i=i+1) begin: for1_inner
            assign a_by_b[k][i] = a[i] & b[k-i];
        end
    end
    endgenerate

    //second and
    generate 
    for(k=M; k<=2*M-2; k=k+1) begin: for2_outer
        for(i=k; i<=2*M-2; i=i+1) begin: for2_inner
            assign a_by_b[k][i] = a[k-i+(M-1)] & b[i-(M-1)];
        end 
    end
    endgenerate

    assign d[0] = a_by_b[0][0];
    // xors
    generate
    for(k=1; k<=2*M-2; k=k+1) begin: for3_outer
        if(k < M) begin
            always @(*) begin 
                aux = a_by_b[k][0];
            end
            for(i=1; i<=k; i=i+1) begin: for3_inner1

            always @(*) begin 
                aux <= a_by_b[k][i] ^ aux;
            end
            end
        end
        else begin

            always @(*) begin 
            aux <= a_by_b[k][k];
            end
            for(i=k+1; i<=2*M-2; i=i+1) begin: for3_inner2

            always @(*) begin 
                aux <= a_by_b[k][i] ^ aux;
            end
            end
        end
        assign d[k] = aux;
    end
    endgenerate
endmodule