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taxi/src/lfsr/rtl/taxi_lfsr.sv

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// SPDX-License-Identifier: CERN-OHL-S-2.0
/*
Copyright (c) 2016-2025 FPGA Ninja, LLC
Authors:
- Alex Forencich
*/
`resetall
`timescale 1ns / 1ps
`default_nettype none
/*
* Parametrizable combinatorial parallel LFSR/CRC
*/
module taxi_lfsr #
(
// width of LFSR
parameter LFSR_W = 31,
// LFSR polynomial
parameter logic [LFSR_W-1:0] LFSR_POLY = 31'h10000001,
// LFSR configuration: 0 for Fibonacci (PRBS), 1 for Galois (CRC)
parameter logic LFSR_GALOIS = 1'b0,
// LFSR feed forward enable
parameter logic LFSR_FEED_FORWARD = 1'b0,
// bit-reverse input and output
parameter logic REVERSE = 1'b0,
// width of data ports
parameter DATA_W = 8,
// enable data input and output
parameter logic DATA_IN_EN = 1'b1,
parameter logic DATA_OUT_EN = 1'b1
)
(
input wire logic [DATA_W-1:0] data_in,
input wire logic [LFSR_W-1:0] state_in,
output wire logic [DATA_W-1:0] data_out,
output wire logic [LFSR_W-1:0] state_out
);
/*
Fully parametrizable combinatorial parallel LFSR/CRC module. Implements an unrolled LFSR
next state computation, shifting DATA_W bits per pass through the module. Input data
is XORed with LFSR feedback path, tie data_in to zero if this is not required.
Works in two parts: statically computes a set of bit masks, then uses these bit masks to
select bits for XORing to compute the next state.
Ports:
data_in
Data bits to be shifted through the LFSR (DATA_W bits)
state_in
LFSR/CRC current state input (LFSR_W bits)
data_out
Data bits shifted out of LFSR (DATA_W bits)
state_out
LFSR/CRC next state output (LFSR_W bits)
Parameters:
LFSR_W
Specify width of LFSR/CRC register
LFSR_POLY
Specify the LFSR/CRC polynomial in hex format. For example, the polynomial
x^32 + x^26 + x^23 + x^22 + x^16 + x^12 + x^11 + x^10 + x^8 + x^7 + x^5 + x^4 + x^2 + x + 1
would be represented as
32'h04c11db7
Note that the largest term (x^32) is suppressed. This term is generated automatically based
on LFSR_W.
LFSR_GALOIS
Specify the LFSR configuration, either Fibonacci (0) or Galois (1). Fibonacci is generally used
for linear-feedback shift registers (LFSR) for pseudorandom binary sequence (PRBS) generators,
scramblers, and descrambers, while Galois is generally used for cyclic redundancy check
generators and checkers.
Fibonacci style (example for 64b66b scrambler, 0x8000000001)
DIN (LSB first)
|
V
(+)<---------------------------(+)<-----------------------------.
| ^ |
| .----. .----. .----. | .----. .----. .----. |
+->| 0 |->| 1 |->...->| 38 |-+->| 39 |->...->| 56 |->| 57 |--'
| '----' '----' '----' '----' '----' '----'
V
DOUT
Galois style (example for CRC16, 0x8005)
,-------------------+-------------------------+----------(+)<-- DIN (MSB first)
| | | ^
| .----. .----. V .----. .----. V .----. |
`->| 0 |->| 1 |->(+)->| 2 |->...->| 14 |->(+)->| 15 |--+---> DOUT
'----' '----' '----' '----' '----'
LFSR_FEED_FORWARD
Generate feed forward instead of feed back LFSR. Enable this for PRBS checking and self-
synchronous descrambling.
Fibonacci feed-forward style (example for 64b66b descrambler, 0x8000000001)
DIN (LSB first)
|
| .----. .----. .----. .----. .----. .----.
+->| 0 |->| 1 |->...->| 38 |-+->| 39 |->...->| 56 |->| 57 |--.
| '----' '----' '----' | '----' '----' '----' |
| V |
(+)<---------------------------(+)------------------------------'
|
V
DOUT
Galois feed-forward style
,-------------------+-------------------------+------------+--- DIN (MSB first)
| | | |
| .----. .----. V .----. .----. V .----. V
`->| 0 |->| 1 |->(+)->| 2 |->...->| 14 |->(+)->| 15 |->(+)-> DOUT
'----' '----' '----' '----' '----'
REVERSE
Bit-reverse LFSR input and output. Shifts MSB first by default, set REVERSE for LSB first.
DATA_W
Specify width of input and output data bus. The module will perform one shift per input
data bit, so if the input data bus is not required tie data_in to zero and set DATA_W
to the required number of shifts per clock cycle.
Settings for common LFSR/CRC implementations:
Name Configuration Length Polynomial Initial value Notes
CRC16-IBM Galois, bit-reverse 16 16'h8005 16'hffff
CRC16-CCITT Galois 16 16'h1021 16'h1d0f
CRC32 Galois, bit-reverse 32 32'h04c11db7 32'hffffffff Ethernet FCS; invert final output
CRC32C Galois, bit-reverse 32 32'h1edc6f41 32'hffffffff iSCSI, Intel CRC32 instruction; invert final output
PRBS6 Fibonacci 6 6'h21 any
PRBS7 Fibonacci 7 7'h41 any
PRBS9 Fibonacci 9 9'h021 any ITU V.52
PRBS10 Fibonacci 10 10'h081 any ITU
PRBS11 Fibonacci 11 11'h201 any ITU O.152
PRBS15 Fibonacci, inverted 15 15'h4001 any ITU O.152
PRBS17 Fibonacci 17 17'h04001 any
PRBS20 Fibonacci 20 20'h00009 any ITU V.57
PRBS23 Fibonacci, inverted 23 23'h040001 any ITU O.151
PRBS29 Fibonacci, inverted 29 29'h08000001 any
PRBS31 Fibonacci, inverted 31 31'h10000001 any
64b66b Fibonacci, bit-reverse 58 58'h8000000001 any 10G Ethernet
pcie Galois, bit-reverse 16 16'h0039 16'hffff PCIe gen 1/2
128b130b Galois, bit-reverse 23 23'h210125 any PCIe gen 3
*/
localparam IN_W = LFSR_W+(DATA_IN_EN ? DATA_W : 0);
localparam OUT_W = LFSR_W+(DATA_OUT_EN ? DATA_W : 0);
function [OUT_W-1:0][IN_W-1:0] lfsr_mask();
logic [LFSR_W-1:0] lfsr_mask_state[LFSR_W-1:0];
logic [DATA_W-1:0] lfsr_mask_data[LFSR_W-1:0];
logic [LFSR_W-1:0] output_mask_state[DATA_W-1:0];
logic [DATA_W-1:0] output_mask_data[DATA_W-1:0];
logic [LFSR_W-1:0] state_val;
logic [DATA_W-1:0] data_val;
logic [DATA_W-1:0] data_mask;
// init bit masks
for (integer i = 0; i < LFSR_W; i = i + 1) begin
lfsr_mask_state[i] = '0;
lfsr_mask_state[i][i] = 1'b1;
lfsr_mask_data[i] = '0;
end
for (integer i = 0; i < DATA_W; i = i + 1) begin
output_mask_state[i] = '0;
if (i < LFSR_W) begin
output_mask_state[i][i] = 1'b1;
end
output_mask_data[i] = '0;
end
// simulate shift register
if (LFSR_GALOIS) begin
// Galois configuration
for (data_mask = {1'b1, {DATA_W-1{1'b0}}}; data_mask != 0; data_mask = data_mask >> 1) begin
// determine shift in value
// current value in last FF, XOR with input data bit (MSB first)
state_val = lfsr_mask_state[LFSR_W-1];
data_val = lfsr_mask_data[LFSR_W-1];
data_val = data_val ^ data_mask;
// shift
for (integer j = LFSR_W-1; j > 0; j = j - 1) begin
lfsr_mask_state[j] = lfsr_mask_state[j-1];
lfsr_mask_data[j] = lfsr_mask_data[j-1];
end
for (integer j = DATA_W-1; j > 0; j = j - 1) begin
output_mask_state[j] = output_mask_state[j-1];
output_mask_data[j] = output_mask_data[j-1];
end
output_mask_state[0] = state_val;
output_mask_data[0] = data_val;
if (LFSR_FEED_FORWARD) begin
// only shift in new input data
state_val = '0;
data_val = data_mask;
end
lfsr_mask_state[0] = state_val;
lfsr_mask_data[0] = data_val;
// add XOR inputs at correct indicies
for (integer j = 1; j < LFSR_W; j = j + 1) begin
if (LFSR_POLY[j]) begin
lfsr_mask_state[j] = lfsr_mask_state[j] ^ state_val;
lfsr_mask_data[j] = lfsr_mask_data[j] ^ data_val;
end
end
end
end else begin
// Fibonacci configuration
for (data_mask = {1'b1, {DATA_W-1{1'b0}}}; data_mask != 0; data_mask = data_mask >> 1) begin
// determine shift in value
// current value in last FF, XOR with input data bit (MSB first)
state_val = lfsr_mask_state[LFSR_W-1];
data_val = lfsr_mask_data[LFSR_W-1];
data_val = data_val ^ data_mask;
// add XOR inputs from correct indicies
for (integer j = 1; j < LFSR_W; j = j + 1) begin
if (LFSR_POLY[j]) begin
state_val = lfsr_mask_state[j-1] ^ state_val;
data_val = lfsr_mask_data[j-1] ^ data_val;
end
end
// shift
for (integer j = LFSR_W-1; j > 0; j = j - 1) begin
lfsr_mask_state[j] = lfsr_mask_state[j-1];
lfsr_mask_data[j] = lfsr_mask_data[j-1];
end
for (integer j = DATA_W-1; j > 0; j = j - 1) begin
output_mask_state[j] = output_mask_state[j-1];
output_mask_data[j] = output_mask_data[j-1];
end
output_mask_state[0] = state_val;
output_mask_data[0] = data_val;
if (LFSR_FEED_FORWARD) begin
// only shift in new input data
state_val = '0;
data_val = data_mask;
end
lfsr_mask_state[0] = state_val;
lfsr_mask_data[0] = data_val;
end
end
// disable broken linter
/* verilator lint_off WIDTH */
if (REVERSE) begin
// output reversed
for (integer i = 0; i < LFSR_W; i = i + 1) begin
for (integer j = 0; j < LFSR_W; j = j + 1) begin
lfsr_mask[i][j] = lfsr_mask_state[LFSR_W-i-1][LFSR_W-j-1];
end
if (DATA_IN_EN) begin
for (integer j = 0; j < DATA_W; j = j + 1) begin
lfsr_mask[i][j+LFSR_W] = lfsr_mask_data[LFSR_W-i-1][DATA_W-j-1];
end
end
end
if (DATA_OUT_EN) begin
for (integer i = 0; i < DATA_W; i = i + 1) begin
for (integer j = 0; j < LFSR_W; j = j + 1) begin
lfsr_mask[i+LFSR_W][j] = output_mask_state[DATA_W-i-1][LFSR_W-j-1];
end
if (DATA_IN_EN) begin
for (integer j = 0; j < DATA_W; j = j + 1) begin
lfsr_mask[i+LFSR_W][j+LFSR_W] = output_mask_data[DATA_W-i-1][DATA_W-j-1];
end
end
end
end
end else begin
// output normal
for (integer i = 0; i < LFSR_W; i = i + 1) begin
if (DATA_IN_EN) begin
lfsr_mask[i] = {lfsr_mask_data[i], lfsr_mask_state[i]};
end else begin
lfsr_mask[i] = lfsr_mask_state[i];
end
end
if (DATA_OUT_EN) begin
for (integer i = 0; i < DATA_W; i = i + 1) begin
if (DATA_IN_EN) begin
lfsr_mask[i+LFSR_W] = {output_mask_data[i], output_mask_state[i]};
end else begin
lfsr_mask[i+LFSR_W] = output_mask_state[i];
end
end
end
end
/* verilator lint_on WIDTH */
endfunction
wire [OUT_W-1:0][IN_W-1:0] mask = lfsr_mask();
for (genvar n = 0; n < LFSR_W; n = n + 1) begin : lfsr_state
if (DATA_IN_EN) begin
assign state_out[n] = ^({data_in, state_in} & mask[n]);
end else begin
assign state_out[n] = ^(state_in & mask[n]);
end
end
if (DATA_OUT_EN) begin
for (genvar n = 0; n < DATA_W; n = n + 1) begin : lfsr_data
if (DATA_IN_EN) begin
assign data_out[n] = ^({data_in, state_in} & mask[n+LFSR_W]);
end else begin
assign data_out[n] = ^(state_in & mask[n+LFSR_W]);
end
end
end else begin
assign data_out = '0;
end
endmodule
`resetall
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