hw/ip/prim/rtl/prim_lfsr.sv

// Copyright lowRISC contributors.
// 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. Further, an external seed can be loaded into the LFSR
// state at runtime. If that seed is all-zero (XOR case) or all-one (XNOR case),
// the state will be reseeded in the next cycle using the lockup protection mechanism.
// Note that the external seed input takes precedence over internal state updates.
//
// All polynomials up to 34 bit in length have been verified in simulation.
//
// 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

`include "prim_assert.sv"

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 the entropy input to be XOR'd into state (lfsr_q[EntropyDw-1:0])
  parameter int unsigned       EntropyDw    =  8,
  // Width of output tap (from lfsr_q[StateOutDw-1:0])
  parameter int unsigned       StateOutDw   =  8,
  // Lfsr reset state, must be nonzero!
  parameter logic [LfsrDw-1:0] DefaultSeed  = LfsrDw'(1),
  // Custom polynomial coeffs
  parameter logic [LfsrDw-1:0] CustomCoeffs = '0,
  // If StatePermEn is set to 1, the custom permutation specified via StatePerm is applied
  // to the state output, in order to break linear shifting patterns of the LFSR.
  parameter bit                      StatePermEn = 1'b0,
  parameter logic [LfsrDw-1:0][$clog2(LfsrDw)-1:0] StatePerm = '0,
  // Enable this for DV, disable this for long LFSRs in FPV
  parameter bit                MaxLenSVA    = 1'b1,
  // Can be disabled in cases where seed and entropy
  // inputs are unused in order to not distort coverage
  // (the SVA will be unreachable in such cases)
  parameter bit                LockupSVA    = 1'b1,
  parameter bit                ExtSeedSVA   = 1'b1
) (
  input                         clk_i,
  input                         rst_ni,
  input                         seed_en_i, // load external seed into the state (takes precedence)
  input        [LfsrDw-1:0]     seed_i,    // external seed input
  input                         lfsr_en_i, // enables the LFSR
  input        [EntropyDw-1:0]  entropy_i, // additional entropy to be XOR'ed into the state
  output logic [StateOutDw-1:0] state_o    // (partial) LFSR state output
);

  // automatically generated with util/design/get-lfsr-coeffs.py script
  localparam int unsigned GAL_XOR_LUT_OFF = 4;
  localparam logic [63:0] GAL_XOR_COEFFS [61] =
    '{ 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 [166] =
    '{ 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 (64'(LfsrType) == 64'("GAL_XOR")) begin : gen_gal_xor

    // if custom polynomial is provided
    if (CustomCoeffs > 0) begin : gen_custom
      assign coeffs = CustomCoeffs[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'(entropy_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(DefaultSeedNzCheck_A, |DefaultSeed)


  ////////////////////
  // Fibonacci XNOR //
  ////////////////////
  end else if (64'(LfsrType) == "FIB_XNOR") begin : gen_fib_xnor

    // if custom polynomial is provided
    if (CustomCoeffs > 0) begin : gen_custom
      assign coeffs = CustomCoeffs[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'(entropy_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(DefaultSeedNzCheck_A, !(&DefaultSeed))


  /////////////
  // Unknown //
  /////////////
  end else begin : gen_unknown_type
    `ASSERT_INIT(UnknownLfsrType_A, 0)
  end


  //////////////////
  // Shared logic //
  //////////////////

  assign lfsr_d = (seed_en_i)           ? seed_i          :
                  (lfsr_en_i && lockup) ? DefaultSeed     :
                  (lfsr_en_i)           ? next_lfsr_state :
                                          lfsr_q;

  if (StatePermEn) begin : gen_state_perm
    for (genvar k = 0; k < StateOutDw; k++) begin : gen_perm_loop
      assign state_o[k] = lfsr_q[StatePerm[k]];
    end
  end else begin : gen_no_state_perm
    assign state_o  = lfsr_q[StateOutDw-1:0];
  end

  always_ff @(posedge clk_i or negedge rst_ni) begin : p_reg
    if (!rst_ni) begin
      lfsr_q <= DefaultSeed;
    end else begin
      lfsr_q <= lfsr_d;
    end
  end


  ///////////////////////
  // shared assertions //
  ///////////////////////

  `ASSERT_KNOWN(DataKnownO_A, state_o)

// the code below is not meant to be synthesized,
// but it is intended to be used in simulation and FPV
`ifndef SYNTHESIS
  function automatic logic[LfsrDw-1:0] compute_next_state(logic[LfsrDw-1:0]    lfsrcoeffs,
                                                          logic[EntropyDw-1:0] entropy,
                                                          logic[LfsrDw-1:0]    state);
    logic state0;

    // Galois XOR
    if (64'(LfsrType) == 64'("GAL_XOR")) begin
      if (state == 0) begin
        state = DefaultSeed;
      end else begin
        state0 = state[0];
        state = state >> 1;
        if (state0) state ^= lfsrcoeffs;
        state ^= LfsrDw'(entropy);
      end
    // Fibonacci XNOR
    end else if (64'(LfsrType) == "FIB_XNOR") begin
      if (&state) begin
        state = DefaultSeed;
      end else begin
        state0 = ~(^(state & lfsrcoeffs));
        state = state << 1;
        state[0] = state0;
        state ^= LfsrDw'(entropy);
      end
    end else begin
      $error("unknown lfsr type");
    end

    return state;
  endfunction : compute_next_state

  // check whether next state is computed correctly
  `ASSERT(NextStateCheck_A, lfsr_en_i && !seed_en_i |=> lfsr_q ==
    compute_next_state(coeffs, $past(entropy_i,1), $past(lfsr_q,1)))

  // Only check this if enabled.
  if (StatePermEn) begin : gen_perm_check
    // Check that the supplied permutation is valid.
    logic [LfsrDw-1:0] lfsr_perm_test;
    initial begin : p_perm_check
      lfsr_perm_test = '0;
      for (int k = 0; k < LfsrDw; k++) begin
        lfsr_perm_test[StatePerm[k]] = 1'b1;
      end
      // All bit positions must be marked with 1.
      `ASSERT_I(PermutationCheck_A, &lfsr_perm_test)
    end
  end

`endif

  `ASSERT_INIT(InputWidth_A, LfsrDw >= EntropyDw)
  `ASSERT_INIT(OutputWidth_A, LfsrDw >= StateOutDw)

  // MSB must be one in any case
  `ASSERT(CoeffCheck_A, coeffs[LfsrDw-1])

  // output check
  `ASSERT_KNOWN(OutputKnown_A, state_o)
  if (!StatePermEn) begin : gen_output_sva
    `ASSERT(OutputCheck_A, state_o == StateOutDw'(lfsr_q))
  end
  // if no external input changes the lfsr state, a lockup must not occur (by design)
  //`ASSERT(NoLockups_A, (!entropy_i) && (!seed_en_i) |=> !lockup, clk_i, !rst_ni)
  `ASSERT(NoLockups_A, lfsr_en_i && !entropy_i && !seed_en_i |=> !lockup)

  // this can be disabled if unused in order to not distort coverage
  if (ExtSeedSVA) begin : gen_ext_seed_sva
    // check that external seed is correctly loaded into the state
    // rst_ni is used directly as part of the pre-condition since the usage of rst_ni
    // in disable_iff is unsampled.  See #1985 for more details
    `ASSERT(ExtDefaultSeedInputCheck_A, (seed_en_i && rst_ni) |=> lfsr_q == $past(seed_i))
  end

  // if the external seed mechanism is not used,
  // there is theoretically no way we end up in a lockup condition
  // in order to not distort coverage, this SVA can be disabled in such cases
  if (LockupSVA) begin : gen_lockup_mechanism_sva
    // check that a stuck LFSR is correctly reseeded
    `ASSERT(LfsrLockupCheck_A, lfsr_en_i && lockup && !seed_en_i |=> !lockup)
  end

  if (MaxLenSVA) begin : gen_max_len_sva

`ifndef SYNTHESIS
    // 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 perturbed_d, perturbed_q;
    logic [LfsrDw-1:0] cmp_val;

    assign cmp_val = {{(LfsrDw-1){1'b1}}, 1'b0}; // 2**LfsrDw-2
    assign cnt_d = (lfsr_en_i && lockup)             ? '0           :
                   (lfsr_en_i && (cnt_q == cmp_val)) ? '0           :
                   (lfsr_en_i)                       ? cnt_q + 1'b1 :
                                                       cnt_q;

    assign perturbed_d = perturbed_q | (|entropy_i) | seed_en_i;

    always_ff @(posedge clk_i or negedge rst_ni) begin : p_max_len
      if (!rst_ni) begin
        cnt_q       <= '0;
        perturbed_q <= 1'b0;
      end else begin
        cnt_q       <= cnt_d;
        perturbed_q <= perturbed_d;
      end
    end

    `ASSERT(MaximalLengthCheck0_A, cnt_q == 0 |-> lfsr_q == DefaultSeed,
        clk_i, !rst_ni || perturbed_q)
    `ASSERT(MaximalLengthCheck1_A, cnt_q != 0 |-> lfsr_q != DefaultSeed,
        clk_i, !rst_ni || perturbed_q)
`endif
  end

endmodule