Blue-CRC

Overview

Cyclic Redundancy Check(CRC) is an error-detection mechanism widely used in communication systems. The CRC algorithm behaves like a hash function, specifically, it calculates an unique identifier(checksum) for original data, and then uses this identifier to determine whether the data has changed after transmission. For a specific system, CRC can be implemented either through software codes or hardware circuit. And this repo provides a highly parameterized, parallel, pipelined and high-throughput hardware implementation of CRC algorithm using Bluespec SystemVerilog.

Main Features

The main features of the implemented CRC circuit are listed as follows:

• Complete CRC Configuration: The circuit supports complete CRC configuration parameters including polynomial, initVal(the initial CRC value), finalXor(the result is xor’d with this value if desired), reverseOutput(if True, reverse the input bit order), reverseInput(if True, reverse the result bit order).
• Standard I/O Interface: The input interface supports AXI-Stream protocol whose data width is parameterized. And CRC result is transmitted following the basic valid-ready handshake protocol.
• Parallel and Pipelined: The circuit is designed to process multiple bytes per cycle, and can reach the working frequency of 500MHz on Xilinx xcvu9p FPGA.
• High Throughput: The circuit configured with 256-bit input and 32-bit CRC output reaches at most throughput of 128Gb/s.
• Two computing modes: The circuit supports both CRC generation mode for the sender and CRC verification mode for the receiver.

Algorithm Theory

The idea of our parallel and high-performance CRC implementation comes from the paper and its corresponding open-source implementation. And main contributions of this repo compared to the existing work include:

• Parameterize the original design and provide a standard interface;
• Refine the logic implementation to improve the working frequency.
• Support both generation and verification modes for CRC calculation.

The calculation of CRC is basically a division operation on two polynomials based on modulo-2 arithmetic and the remainder of this division is just the checksum we wanted. Consider a m-bit original data $b_{m-1}b_{m-2}b_{m-3}...b_{1}b_{0}$ can be represented as the polynomial $M(x)$:

$$ M(x)=b_{m-1}x^{m-1}+b_{m-2}x^{m-2}+...+b_{1}x+b_{0} $$

And a predetermined (n+1)-bit generator polynomial can be represented as $G(x)$:

$$ G(x)=b_{n}x^{n}+b_{n-1}x^{n-1}+...+b_{1}x^{1}+b_{0} $$

And the CRC is derived following the equation below:

$$ CRC[M(x)]=remainder(\frac{M(x)x^{n}}{G(x)}) $$

More detailed introduction of CRC can be accessed via this link. Based on the characteristics of modulo-2 arithmetic, CRC calculation can be easily implemented using a LFSR register as the figure shown below:

This circuit is one of the most classic hardware implementations of CRC algorithm, which only needs few hardware resources and can reach high working frequency. However, the LFSR implementation takes in only 1-bit per cycle, which provides a poor throughput. In order to get a parallel and high-performance CRC design, the serial implementation demonstrated above should be rearranged into a parallel architecture. And in blue-crc, the following two theorems is used to achieve parallelism in CRC computation.

• Theorem 1:

$$ CRC[A(x)]=CRC(\sum_{i=1}^{n}A_{i})=\sum_{i=1}^{n}CRC(A_{i}) $$

• Theorem 2:

$$ CRC[A(x)x^k] = CRC[CRC[A(x)]x^k] $$

Theorem 1 indicates that original data of any length can be split into multiple pieces and CRC checksum of each piece can be calculated in parallel and then add up to get the CRC result of complete data. In our designed, the length of one piece is 8-bit and it’s assumed that the length of original data is multiples of bytes. For example, a N-bit original data, represented as polynomial $A(x)$, can be divided into n bytes, i.e. $N=8\times n$, each byte of original data is represented as the polynomial $A_{i}(x)$, and $A(x)$ can be expressed as:

$$ A(x)=\sum_{i=0}^{n-1}A_i(x)\ x^{8i} $$

And the CRC of A(x) is derived as below:

$$ CRC(A(x))=CRC[A_{n-1}(x)x^{8(n-1)}]+CRC[A_{n-2}(x)x^{8(n-2)}]+... +CRC[A_{1}(x)x^8]+ CRC[A_{0}(x)] $$

To calculate the CRC of each 8-bit piece, we don't have to implement real circuit instead it' more efficient to precompute the CRC results of all possible values of 8-bit data and store them in hardware lookup table. When we need to compute CRC, we can just search the precomputed table using the input data as index.

However, the parallel scheme proposed above is still impractical for hardware implementation. For real circuit design, the width of input data bus is usually fixed and original data is split into multiple frames and sent into the component serially. So the hardware needs to compute the CRC result in an accumulative manner. In each cycle, the circuit calculates CRC checksum of input frame based on Theorem 1, and then adds it to the intermediate CRC result of former frames.

The addition of CRC result of current input frame and the intermediate CRC result is based on Theorem 2. Assume that original data is transmitted in big-endian byte order, the width of the input bus is 256-bit, $A(x)$ represents data received in this cycle and $A'(x)$ represents data received in former cycles. And we need to add $CRC[A(x)]$ to the intermediate result $CRC[A'(x)]$ to get $CRC[A'(x)x^{256} + A(x)]$. Based on Theorem 2, we can derive the equation below: $$CRC[A'(x)x^{256}+A(x)]=CRC[A'(x)x^{256}]+CRC[A(x)]=CRC[CRC[A'(x)]\times x^{256}]+CRC[A(x)]$$ The equation shows that we need to shift the intermediate CRC result left, perform CRC calculation on it again and then add it with the CRC result of current frame. And the CRC calculation of the intermediate checksum can also be implemented using hardware lookup tables. For accumulation, there's one more case to consider, that is, the width of raw data may not just be multiples of 256-bit, so you cannot directly use the above formula for accumulation when processing the last input frame. Instead we need to dynamically calculate the width of valid data in the last frame of original data. Assume that the valid width of the last frame data is m, the accumulation is done following the equation below: $$CRC[A'(x)x^m+A(x)]=CRC[CRC[A'(x)]\times x^m]+CRC[A(x)]$$

Hardware Architecture

The diagram below shows the hardware implementation of the parallel CRC algorithm introduced above. To improve the working frequency and throughput, the circuit design adopts an eight-stage pipelined architecture. The first five stages calculate the checksum of the input data and add it to the intermediate CRC result. The last three stages is used to handle the accumulation of the last frame of one packet, in which the width of valid data may be less than the width of bus.

Area Usage and Frequency

The actual performance and hardware resources utilization of CRC circuits depend on the specific configuration parameters. In most cases, the throughput of the hardware circuit increases with the width of input data bus, and the hardware resources utilization is related to both data bus width and checksum width. Taking the 32-bit CRC checksum specified by the IEEE 802-3 protocol as an example, CRC circuit with input bus configured at 256-bit can reach the working frequency of 500MHz on Xilinx xcvu9p FPGA device, and the maximum throughput can reach 128Gb/s. The detailed utilization of different hardware resources is as follows:

CLB Logic:
+----------------------------+-------+-------+------------+-----------+-------+
|          Site Type         |  Used | Fixed | Prohibited | Available | Util% |
+----------------------------+-------+-------+------------+-----------+-------+
| CLB LUTs                   | 21584 |     0 |          0 |   1182240 |  1.83 |
|   LUT as Logic             | 10636 |     0 |          0 |   1182240 |  0.90 |
|   LUT as Memory            | 10948 |     0 |          0 |    591840 |  1.85 |
|     LUT as Distributed RAM | 10948 |     0 |            |           |       |
|     LUT as Shift Register  |     0 |     0 |            |           |       |
| CLB Registers              |  9647 |     0 |          0 |   2364480 |  0.41 |
|   Register as Flip Flop    |  9647 |     0 |          0 |   2364480 |  0.41 |
|   Register as Latch        |     0 |     0 |          0 |   2364480 |  0.00 |
| CARRY8                     |     0 |     0 |          0 |    147780 |  0.00 |
| F7 Muxes                   |     0 |     0 |          0 |    591120 |  0.00 |
| F8 Muxes                   |     0 |     0 |          0 |    295560 |  0.00 |
| F9 Muxes                   |     0 |     0 |          0 |    147780 |  0.00 |
+----------------------------+-------+-------+------------+-----------+-------+

BLOCKRAM:
+----------------+------+-------+------------+-----------+-------+
|    Site Type   | Used | Fixed | Prohibited | Available | Util% |
+----------------+------+-------+------------+-----------+-------+
| Block RAM Tile |    0 |     0 |          0 |      2160 |  0.00 |
|   RAMB36/FIFO* |    0 |     0 |          0 |      2160 |  0.00 |
|   RAMB18       |    0 |     0 |          0 |      4320 |  0.00 |
| URAM           |    0 |     0 |          0 |       960 |  0.00 |
+----------------+------+-------+------------+-----------+-------+

User Guide

Configuration Parameters

The following table lists complete configuration parameters of CRC hardware:

Name	Description	Requirement
crc_width	The width of CRC checksum	The width needs to be multiples of 8-bit
axi_keep_width	The width of tkeep field in AXI-Stream protocol	/
polynomial	The value of generator polynomial	The value should be in the range restricted by crc_width
init_value	The initial value for CRC calculation	The value should be in the range restricted by crc_width
final_xor	The final result is xor’d with this value	The value should be in the range restricted by crc_width
reverse_input	if True, reverse the bit order of each input byte	Two available options: reverse or not_reverse
reverse_output	if True, reverse the bit order of final result	Two available options: reverse or not_reverse
mem_file_prefix	The name prefix of files containing lookup tables	/
crc_mode	The computation mode of CRC circuit	Two available modes: (1) SEND: appends zeros after raw data automatically and is used for CRC generation in the sender; (2) RECV: calculates the division of raw data by polynominal without appending zeros and is used for CRC verification in the receiver;

Input Format

CRC hardware receives input data from the upstream module based on the AXI-Stream bus protocol. And the output port of final result uses the valid-ready handshake mechanism to interact with the downstream module. The Verilog ports generated from the top-level module of BSV designs are as follows:

module mkCrcRawAxiStreamCustom(
    input CLK,
    input RST_N,
    
    input s_axis_tvalid,
    input s_axis_tdata,
    input s_axis_tkeep,
    input s_axis_tlast,
    input s_axis_tuser,
    output s_axis_tready,
    
    output m_crc_stream_data,
    output m_crc_stream_valid,
    input  m_crc_stream_ready
);

When initiating CRC computation, the original data must be transmitted in big-endian byte order, that is, higher bytes need to be transmitted before lower bytes. Assuming that the width of the input AXI-Stream bus of CRC circuit is 32-bit(4-byte) and the width of raw data is 80-bit(10-byte), the transmission needs three cycles to complete and the AXI-Stream frames transmitted in each cycle is shown below:

BSV Interface

The blue-crc is based on Bluespec SystemVerilog hardware description language, so for designers using BSV, CRC module can be used directly through instantiation. Detailed steps required to use it are as follows:

1. Get source codes: blue-crc uses the AXI-Stream interface provided by the blue-wrapper project, so you need to add --recursive option to get its codes when cloning:

git clone --recursive https://github.com/datenlord/blue-crc.git

2. Import modules:

import CrcDefines :: *;
import CrcAxiStream :: *;
import AxiStreamTypes :: *;

3. Specify Configuration Parameters: The CrcConfig struct encapsulates configuration parameters for CRC hardware circuits. The definition of CrcConfig struct is as follows:

typedef struct {
    Bit#(crcWidth) polynominal;
    Bit#(crcWidth) initVal;
    Bit#(crcWidth) finalXor;
    IsReverseBitOrder revInput;
    IsReverseBitOrder revOutput;
    String memFilePrefix;
    CrcMode crcMode;
} CrcConfig#(numeric type crcWidth) deriving(Eq, FShow);

typedef enum {
    CRC_MODE_RECV,
    CRC_MODE_SEND
} CrcMode deriving(Eq, FShow);

typedef enum {
    BIT_ORDER_REVERSE,
    BIT_ORDER_NOT_REVERSE
} IsReverseBitOrder deriving(Eq, FShow);

4. Instantiate CrcAxiStream: The top-level interface CrcAxiStream is defined as follows:

typedef Bit#(width) CrcResult#(numeric type width);
typedef Get#(CrcResult#(crcWidth)) CrcResultGet#(numeric type crcWidth);
typedef Put#(AxiStream#(keepWidth, AXIS_USER_WIDTH)) AxiStreamPut#(numeric type keepWidth);

interface CrcAxiStream#(numeric type crcWidth, numeric type axiKeepWidth);
    interface AxiStreamPut#(axiKeepWidth) crcReq;
    interface CrcResultGet#(crcWidth) crcResp;
endinterface

Take the 32-bit CRC specified in the IEEE 802-3 protocol as an example, if you want to get CRC circuit with 256-bit input data bus, the detailed instantiation code is as follows:

CrcConfig#(32) conf = CrcConfig {
    polynominal: 32'h04C11DB7,
    initVal    : 32'hFFFFFFFF,
    finalXor   : 32'hFFFFFFFF,
    revInput   : BIT_ORDER_REVERSE,
    revOutput  : BIT_ORDER_REVERSE,
    memFilePrefix: "mem_tab",
    crcMode: CRC_MODE_SEND
};
CrcAxiStream#(32, 256) crc <- mkCrcAxiStream(conf);

5. Generate lookup table files: The script for generating lookup table files is scripts/gen_crc_tab.py. Before using this script, you need to specify CRC configuration in .json file, whose content must be consistent with the configuration in BSV code:

{
    "crc_width": 32,
    "axi_keep_width": 32,
    "polynomial": "0x04C11DB7",
    "init_value": "0xFFFFFFFF",
    "final_xor": "0xFFFFFFFF",
    "reverse_input": true,
    "reverse_output": true,
    "mem_file_prefix": "crc_tab",
    "crc_mode": "CRC_MODE_SEND"
}

6. Once .json file is configured, run the script using python (you need to specify the path of JSON configuration file and output directory) to get lookup table files:

python3 gen_crc_tab.py JSON_FILE_PATH OUTPUT_DIR

7. When compiling the project, it is necessary to add the path of blue-crc source code to compile options. Assuming that the root directory of blue-crc is $(ROOT):

bsc -p +:$(BLUE_CRC)/src:$(ROOT)/lib/blue-wrapper/src

8. When generating Verilog codes of your project for simulating or synthesizing using other EDA tools, you need to copy an additional Verilog file LookupTable.v so that it can be read by your tools. This file implements the CRC lookup table using reg array and $readmemh system calls so you need to ensure that your simulation or synthesis tools support these Verilog grammers.

Verilog Interface

Although the blue-crc project is implemented using BSV, it also provides script scripts/gen_crc.py to generate configurable Verilog codes. The script needs to be executed in the root directory of blue-crc project, and the path of CRC configuration file in .json format needs to be specified:

python3 scripts/gen_crc.py JSON_FILE_PATH [OUTPUT_VERILOG_DIR] [OUTPUT_TABLE_DIR]

If the output directories of Verilog codes and lookup tables are not configured when executing the script, these files will be generated to verilog folder under the root directory by default. Generating Verilog codes requires BSV compiler, so you need to ensure that the compiler is installed and configured before executing the script.