| // Licensed under the Apache License, Version 2.0, see LICENSE for details. |
| // SPDX-License-Identifier: Apache-2.0 |
| // |
| // This module implements different LFSR types: |
| // |
| // 0) Galois XOR type LFSR ([1], internal XOR gates, very fast). |
| // Parameterizable width from 4 to 64 bits. |
| // Coefficients obtained from [2]. |
| // |
| // 1) Fibonacci XNOR type LFSR, parameterizable from 3 to 168 bits. |
| // Coefficients obtained from [3]. |
| // |
| // All flavors have an additional entropy input and lockup protection, which |
| // reseeds the state once it has accidentally fallen into the all-zero (XOR) or |
| // all-one (XNOR) state. |
| // |
| // Refs: [1] https://en.wikipedia.org/wiki/Linear-feedback_shift_register |
| // [2] https://users.ece.cmu.edu/~koopman/lfsr/ |
| // [3] https://www.xilinx.com/support/documentation/application_notes/xapp052.pdf |
| |
| module prim_lfsr #( |
| // Lfsr Type, can be FIB_XNOR or GAL_XOR |
| parameter LfsrType = "GAL_XOR", |
| // Lfsr width |
| parameter int unsigned LfsrDw = 32, |
| // Width of input to be XOR'd into state (lfsr_q[InDw-1:0]) |
| parameter int unsigned InDw = 8, |
| // Width of output tap (from lfsr_q[OutDw-1:0]) |
| parameter int unsigned OutDw = 8, |
| // Lfsr reset state, must be nonzero! |
| parameter logic [LfsrDw-1:0] Seed = LfsrDw'(1), |
| // Custom polynomial coeffs |
| parameter logic [LfsrDw-1:0] Custom = '0, |
| // Enable this for DV, disable this for long LFSRs in FPV |
| parameter bit MaxLenSVA = 1'b1 |
| ) ( |
| input clk_i, |
| input rst_ni, |
| input en_i, |
| input [InDw-1:0] data_i, |
| output logic [OutDw-1:0] data_o |
| ); |
| |
| // automatically generated with get-lfsr-coeffs.py script |
| localparam int unsigned GAL_XOR_LUT_OFF = 4; |
| localparam logic [63:0] GAL_XOR_COEFFS [0:60] = |
| '{ 64'h9, |
| 64'h12, |
| 64'h21, |
| 64'h41, |
| 64'h8E, |
| 64'h108, |
| 64'h204, |
| 64'h402, |
| 64'h829, |
| 64'h100D, |
| 64'h2015, |
| 64'h4001, |
| 64'h8016, |
| 64'h10004, |
| 64'h20013, |
| 64'h40013, |
| 64'h80004, |
| 64'h100002, |
| 64'h200001, |
| 64'h400010, |
| 64'h80000D, |
| 64'h1000004, |
| 64'h2000023, |
| 64'h4000013, |
| 64'h8000004, |
| 64'h10000002, |
| 64'h20000029, |
| 64'h40000004, |
| 64'h80000057, |
| 64'h100000029, |
| 64'h200000073, |
| 64'h400000002, |
| 64'h80000003B, |
| 64'h100000001F, |
| 64'h2000000031, |
| 64'h4000000008, |
| 64'h800000001C, |
| 64'h10000000004, |
| 64'h2000000001F, |
| 64'h4000000002C, |
| 64'h80000000032, |
| 64'h10000000000D, |
| 64'h200000000097, |
| 64'h400000000010, |
| 64'h80000000005B, |
| 64'h1000000000038, |
| 64'h200000000000E, |
| 64'h4000000000025, |
| 64'h8000000000004, |
| 64'h10000000000023, |
| 64'h2000000000003E, |
| 64'h40000000000023, |
| 64'h8000000000004A, |
| 64'h100000000000016, |
| 64'h200000000000031, |
| 64'h40000000000003D, |
| 64'h800000000000001, |
| 64'h1000000000000013, |
| 64'h2000000000000034, |
| 64'h4000000000000001, |
| 64'h800000000000000D }; |
| |
| // automatically generated with get-lfsr-coeffs.py script |
| localparam int unsigned FIB_XNOR_LUT_OFF = 3; |
| localparam logic [167:0] FIB_XNOR_COEFFS [0:165] = |
| '{ 168'h6, |
| 168'hC, |
| 168'h14, |
| 168'h30, |
| 168'h60, |
| 168'hB8, |
| 168'h110, |
| 168'h240, |
| 168'h500, |
| 168'h829, |
| 168'h100D, |
| 168'h2015, |
| 168'h6000, |
| 168'hD008, |
| 168'h12000, |
| 168'h20400, |
| 168'h40023, |
| 168'h90000, |
| 168'h140000, |
| 168'h300000, |
| 168'h420000, |
| 168'hE10000, |
| 168'h1200000, |
| 168'h2000023, |
| 168'h4000013, |
| 168'h9000000, |
| 168'h14000000, |
| 168'h20000029, |
| 168'h48000000, |
| 168'h80200003, |
| 168'h100080000, |
| 168'h204000003, |
| 168'h500000000, |
| 168'h801000000, |
| 168'h100000001F, |
| 168'h2000000031, |
| 168'h4400000000, |
| 168'hA000140000, |
| 168'h12000000000, |
| 168'h300000C0000, |
| 168'h63000000000, |
| 168'hC0000030000, |
| 168'h1B0000000000, |
| 168'h300003000000, |
| 168'h420000000000, |
| 168'hC00000180000, |
| 168'h1008000000000, |
| 168'h3000000C00000, |
| 168'h6000C00000000, |
| 168'h9000000000000, |
| 168'h18003000000000, |
| 168'h30000000030000, |
| 168'h40000040000000, |
| 168'hC0000600000000, |
| 168'h102000000000000, |
| 168'h200004000000000, |
| 168'h600003000000000, |
| 168'hC00000000000000, |
| 168'h1800300000000000, |
| 168'h3000000000000030, |
| 168'h6000000000000000, |
| 168'hD800000000000000, |
| 168'h10000400000000000, |
| 168'h30180000000000000, |
| 168'h60300000000000000, |
| 168'h80400000000000000, |
| 168'h140000028000000000, |
| 168'h300060000000000000, |
| 168'h410000000000000000, |
| 168'h820000000001040000, |
| 168'h1000000800000000000, |
| 168'h3000600000000000000, |
| 168'h6018000000000000000, |
| 168'hC000000018000000000, |
| 168'h18000000600000000000, |
| 168'h30000600000000000000, |
| 168'h40200000000000000000, |
| 168'hC0000000060000000000, |
| 168'h110000000000000000000, |
| 168'h240000000480000000000, |
| 168'h600000000003000000000, |
| 168'h800400000000000000000, |
| 168'h1800000300000000000000, |
| 168'h3003000000000000000000, |
| 168'h4002000000000000000000, |
| 168'hC000000000000000018000, |
| 168'h10000000004000000000000, |
| 168'h30000C00000000000000000, |
| 168'h600000000000000000000C0, |
| 168'hC00C0000000000000000000, |
| 168'h140000000000000000000000, |
| 168'h200001000000000000000000, |
| 168'h400800000000000000000000, |
| 168'hA00000000001400000000000, |
| 168'h1040000000000000000000000, |
| 168'h2004000000000000000000000, |
| 168'h5000000000028000000000000, |
| 168'h8000000004000000000000000, |
| 168'h18600000000000000000000000, |
| 168'h30000000000000000C00000000, |
| 168'h40200000000000000000000000, |
| 168'hC0300000000000000000000000, |
| 168'h100010000000000000000000000, |
| 168'h200040000000000000000000000, |
| 168'h5000000000000000A0000000000, |
| 168'h800000010000000000000000000, |
| 168'h1860000000000000000000000000, |
| 168'h3003000000000000000000000000, |
| 168'h4010000000000000000000000000, |
| 168'hA000000000140000000000000000, |
| 168'h10080000000000000000000000000, |
| 168'h30000000000000000000180000000, |
| 168'h60018000000000000000000000000, |
| 168'hC0000000000000000300000000000, |
| 168'h140005000000000000000000000000, |
| 168'h200000001000000000000000000000, |
| 168'h404000000000000000000000000000, |
| 168'h810000000000000000000000000102, |
| 168'h1000040000000000000000000000000, |
| 168'h3000000000000006000000000000000, |
| 168'h5000000000000000000000000000000, |
| 168'h8000000004000000000000000000000, |
| 168'h18000000000000000000000000030000, |
| 168'h30000000030000000000000000000000, |
| 168'h60000000000000000000000000000000, |
| 168'hA0000014000000000000000000000000, |
| 168'h108000000000000000000000000000000, |
| 168'h240000000000000000000000000000000, |
| 168'h600000000000C00000000000000000000, |
| 168'h800000040000000000000000000000000, |
| 168'h1800000000000300000000000000000000, |
| 168'h2000000000000010000000000000000000, |
| 168'h4008000000000000000000000000000000, |
| 168'hC000000000000000000000000000000600, |
| 168'h10000080000000000000000000000000000, |
| 168'h30600000000000000000000000000000000, |
| 168'h4A400000000000000000000000000000000, |
| 168'h80000004000000000000000000000000000, |
| 168'h180000003000000000000000000000000000, |
| 168'h200001000000000000000000000000000000, |
| 168'h600006000000000000000000000000000000, |
| 168'hC00000000000000006000000000000000000, |
| 168'h1000000000000100000000000000000000000, |
| 168'h3000000000000006000000000000000000000, |
| 168'h6000000003000000000000000000000000000, |
| 168'h8000001000000000000000000000000000000, |
| 168'h1800000000000000000000000000C000000000, |
| 168'h20000000000001000000000000000000000000, |
| 168'h48000000000000000000000000000000000000, |
| 168'hC0000000000000006000000000000000000000, |
| 168'h180000000000000000000000000000000000000, |
| 168'h280000000000000000000000000000005000000, |
| 168'h60000000C000000000000000000000000000000, |
| 168'hC00000000000000000000000000018000000000, |
| 168'h1800000600000000000000000000000000000000, |
| 168'h3000000C00000000000000000000000000000000, |
| 168'h4000000080000000000000000000000000000000, |
| 168'hC000300000000000000000000000000000000000, |
| 168'h10000400000000000000000000000000000000000, |
| 168'h30000000000000000000006000000000000000000, |
| 168'h600000000000000C0000000000000000000000000, |
| 168'hC0060000000000000000000000000000000000000, |
| 168'h180000006000000000000000000000000000000000, |
| 168'h3000000000C0000000000000000000000000000000, |
| 168'h410000000000000000000000000000000000000000, |
| 168'hA00140000000000000000000000000000000000000 }; |
| |
| logic lockup; |
| logic [LfsrDw-1:0] lfsr_d, lfsr_q; |
| logic [LfsrDw-1:0] next_lfsr_state, coeffs; |
| |
| ////////////////////////////////////////////////////// |
| // Galois XOR |
| if (LfsrType == "GAL_XOR") begin : gen_gal_xor |
| |
| // if custom polynomial is provided |
| if (Custom) begin : gen_custom |
| assign coeffs = Custom[LfsrDw-1:0]; |
| end else begin : gen_lut |
| assign coeffs = GAL_XOR_COEFFS[LfsrDw-GAL_XOR_LUT_OFF][LfsrDw-1:0]; |
| // check that the most significant bit of polynomial is 1 |
| `ASSERT_INIT(MinLfsrWidth_A, LfsrDw >= $low(GAL_XOR_COEFFS)+GAL_XOR_LUT_OFF) |
| `ASSERT_INIT(MaxLfsrWidth_A, LfsrDw <= $high(GAL_XOR_COEFFS)+GAL_XOR_LUT_OFF) |
| end |
| |
| // calculate next state using internal XOR feedback and entropy input |
| assign next_lfsr_state = LfsrDw'(data_i) ^ ({LfsrDw{lfsr_q[0]}} & coeffs) ^ (lfsr_q >> 1); |
| |
| // lockup condition is all-zero |
| assign lockup = ~(|lfsr_q); |
| |
| // check that seed is not all-zero |
| `ASSERT_INIT(SeedNzCheck_A, |Seed) |
| |
| ////////////////////////////////////////////////////// |
| // Fibonacci XNOR |
| end else if (LfsrType == "FIB_XNOR") begin : gen_fib_xnor |
| |
| // if custom polynomial is provided |
| if (Custom) begin : gen_custom |
| assign coeffs = Custom[LfsrDw-1:0]; |
| end else begin : gen_lut |
| assign coeffs = FIB_XNOR_COEFFS[LfsrDw-FIB_XNOR_LUT_OFF][LfsrDw-1:0]; |
| // check that the most significant bit of polynomial is 1 |
| `ASSERT_INIT(MinLfsrWidth_A, LfsrDw >= $low(FIB_XNOR_COEFFS)+FIB_XNOR_LUT_OFF) |
| `ASSERT_INIT(MaxLfsrWidth_A, LfsrDw <= $high(FIB_XNOR_COEFFS)+FIB_XNOR_LUT_OFF) |
| end |
| |
| // calculate next state using external XNOR feedback and entropy input |
| assign next_lfsr_state = LfsrDw'(data_i) ^ {lfsr_q[LfsrDw-2:0], ~(^(lfsr_q & coeffs))}; |
| |
| // lockup condition is all-ones |
| assign lockup = &lfsr_q; |
| |
| // check that seed is not all-ones |
| `ASSERT_INIT(SeedNzCheck_A, !(&Seed)) |
| |
| ////////////////////////////////////////////////////// |
| // Unknown |
| end else begin : gen_unknown_type |
| `ASSERT_INIT(UnknownLfsrType_A, 0) |
| end |
| |
| ////////////////////////////////////////////////////// |
| // Shared logic |
| ////////////////////////////////////////////////////// |
| |
| assign lfsr_d = (en_i && lockup) ? Seed : |
| (en_i) ? next_lfsr_state : |
| lfsr_q; |
| |
| assign data_o = lfsr_q[OutDw-1:0]; |
| |
| always_ff @(posedge clk_i or negedge rst_ni) begin : p_reg |
| if (!rst_ni) begin |
| lfsr_q <= Seed; |
| end else begin |
| lfsr_q <= lfsr_d; |
| end |
| end |
| |
| |
| ////////////////////////////////////////////////////// |
| // shared assertions |
| ////////////////////////////////////////////////////// |
| |
| function automatic logic[LfsrDw-1:0] compute_next_state(logic[LfsrDw-1:0] coeffs, |
| logic[InDw-1:0] data, |
| logic[LfsrDw-1:0] state); |
| logic state0; |
| |
| // Galois XOR |
| if (LfsrType == "GAL_XOR") begin |
| if (!state) begin |
| state = Seed; |
| end else begin |
| state0 = state[0]; |
| state = state >> 1; |
| if (state0) state ^= coeffs; |
| state ^= LfsrDw'(data); |
| end |
| // Fibonacci XNOR |
| end else if (LfsrType == "FIB_XNOR") begin |
| if (&state) begin |
| state = Seed; |
| end else begin |
| state0 = ~(^(state & coeffs)); |
| state = state << 1; |
| state[0] = state0; |
| state ^= LfsrDw'(data); |
| end |
| end else begin |
| $error("unknown lfsr type"); |
| end |
| |
| return state; |
| endfunction : compute_next_state |
| |
| `ASSERT_INIT(InputWidth_A, LfsrDw >= InDw) |
| `ASSERT_INIT(OutputWidth_A, LfsrDw >= OutDw) |
| // check that a stuck LFSR is correctly reseeded |
| `ASSERT(LfsrLockupCheck_A, en_i && lockup |=> !lockup, clk_i, !rst_ni) |
| // MSB must be one in any case |
| `ASSERT(CoeffCheck_A, coeffs[LfsrDw-1], clk_i, !rst_ni) |
| |
| // check whether next state is computed correctly |
| `ASSERT(NextStateCheck_A, en_i |=> lfsr_q == |
| compute_next_state(coeffs, $past(data_i,1), $past(lfsr_q,1)), |
| clk_i, !rst_ni ) |
| |
| // the code below is not meant to be synthesized, |
| // but it is intended to be used in simulation and FPV |
| // the formal tool defines SYNTHESIS, hence this workaround |
| `ifdef FPV_ON |
| `define MAX_LEN_SVA |
| `endif |
| `ifndef SYNTHESIS |
| `define MAX_LEN_SVA |
| `endif |
| |
| if (MaxLenSVA) begin : gen_max_len_sva |
| `ifdef MAX_LEN_SVA |
| // the code below is a workaround to enable long sequences to be checked. |
| // some simulators do not support SVA sequences longer than 2**32-1. |
| logic [LfsrDw-1:0] cnt_d, cnt_q; |
| logic data_set_d, data_set_q; |
| logic [LfsrDw-1:0] cmp_val; |
| |
| assign cmp_val = {{(LfsrDw-1){1'b1}}, 1'b0}; // 2**LfsrDw-2 |
| assign cnt_d = (en_i && lockup) ? '0 : |
| (en_i && (cnt_q == cmp_val)) ? '0 : |
| (en_i) ? cnt_q + 1'b1 : |
| cnt_q; |
| |
| assign data_set_d = data_set_q | (|data_i); |
| |
| always_ff @(posedge clk_i or negedge rst_ni) begin : p_max_len |
| if (!rst_ni) begin |
| cnt_q <= '0; |
| data_set_q <= 1'b0; |
| end else begin |
| cnt_q <= cnt_d; |
| data_set_q <= data_set_d; |
| end |
| end |
| |
| `ASSERT(MaximalLengthCheck0_A, cnt_q == 0 |-> lfsr_q == Seed, clk_i, !rst_ni || data_set_q) |
| `ASSERT(MaximalLengthCheck1_A, cnt_q != 0 |-> lfsr_q != Seed, clk_i, !rst_ni || data_set_q) |
| `endif |
| end |
| `undef MAX_LEN_SVA |
| |
| endmodule |
