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// formal: prove 4 expect pass slang top rr_arbiter
`define FORMAL
// rr_arbiter: 4-requester round-robin arbiter. The grant is combinational from req and the 2-bit
// pointer last (the index granted most recently). The search starts at last + 1 and wraps. A grant is
// given in the cycle a request is seen and lasts one cycle (no lock). Synchronous active-high reset:
// last = 3, so requester 0 has priority first. BUG selects a variant (0 is the design as specified);
// HELPER=0 removes the helper assertions.
module rr_arbiter #(parameter BUG = 0, parameter HELPER = 1) (
  input  wire       clk,
  input  wire       rst,
  input  wire [3:0] req,
  output wire [3:0] grant
);
  reg [1:0] last;

  wire [3:0] hi_mask = (last == 2'd0) ? 4'b1110 :
                       (last == 2'd1) ? 4'b1100 :
                       (last == 2'd2) ? 4'b1000 : 4'b0000;
  wire [3:0] hi_req  = req & hi_mask;
  wire [3:0] lo_req  = (BUG == 3) ? (req | (4'b0001 << last)) : req;

  function [3:0] lowest;           // lowest set bit, one-hot (0 if none)
    input [3:0] v;
    lowest = v & (~v + 4'd1);
  endfunction

  wire [3:0] g_hi = lowest(hi_req);
  wire [3:0] g_lo = lowest(lo_req) & {4{(hi_req == 4'b0) || (BUG == 2)}};
  assign grant = g_hi | g_lo;

  wire [1:0] gidx = grant[0] ? 2'd0 : grant[1] ? 2'd1 : grant[2] ? 2'd2 : 2'd3;

  always @(posedge clk) begin
    if (rst) last <= 2'd3;
    else if (|grant && !(BUG == 1 && grant[0])) last <= gidx;
  end

`ifdef FORMAL
  reg init = 1'b1;
  always @(posedge clk) init <= 1'b0;
  always @(*) if (init) assume (rst);

  // wt[i]: consecutive cycles requester i has requested without being granted
  reg [2:0] wt0, wt1, wt2, wt3;
  always @(posedge clk) begin
    if (rst) begin wt0 <= 3'd0; wt1 <= 3'd0; wt2 <= 3'd0; wt3 <= 3'd0; end
    else begin
      wt0 <= (req[0] && !grant[0]) ? wt0 + 3'd1 : 3'd0;
      wt1 <= (req[1] && !grant[1]) ? wt1 + 3'd1 : 3'd0;
      wt2 <= (req[2] && !grant[2]) ? wt2 + 3'd1 : 3'd0;
      wt3 <= (req[3] && !grant[3]) ? wt3 + 3'd1 : 3'd0;
    end
  end

  always @(*) if (!init) begin
    a_onehot0:  assert ((grant & (grant - 4'd1)) == 4'd0);
    a_no_phantom: assert ((grant & ~req) == 4'd0);
    a_work_cons:  assert (!(|req) || (|grant));
    // bounded response (safety form of starvation freedom): nobody waits more than 3 cycles
    a_wt0: assert (wt0 <= 3'd3);
    a_wt1: assert (wt1 <= 3'd3);
    a_wt2: assert (wt2 <= 3'd3);
    a_wt3: assert (wt3 <= 3'd3);
  end

  // helper invariants for the induction step of the wait bounds
  function [1:0] ahead;             // how many grants can still precede requester i
    input [1:0] i;
    ahead = i - last - 2'd1;        // 0..3 (mod 4)
  endfunction
  generate if (HELPER) begin : g_helper
    always @(*) if (!init) begin
      h_wt0: assert (wt0 + {1'b0, ahead(2'd0)} <= 3'd3);
      h_wt1: assert (wt1 + {1'b0, ahead(2'd1)} <= 3'd3);
      h_wt2: assert (wt2 + {1'b0, ahead(2'd2)} <= 3'd3);
      h_wt3: assert (wt3 + {1'b0, ahead(2'd3)} <= 3'd3);
    end
  end endgenerate

  // covers
  always @(*) if (!init) begin
    c_g0: cover (grant[0]);
    c_g1: cover (grant[1]);
    c_g2: cover (grant[2]);
    c_g3: cover (grant[3]);
    c_contend: cover (req == 4'b1111 && wt3 == 3'd3);
    c_idle: cover (req == 4'b0000 && grant == 4'd0);
  end
`endif
endmodule

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// formal: cover 6 expect reached slang top rr_arbiter
`define FORMAL
// rr_arbiter: 4-requester round-robin arbiter. The grant is combinational from req and the 2-bit
// pointer last (the index granted most recently). The search starts at last + 1 and wraps. A grant is
// given in the cycle a request is seen and lasts one cycle (no lock). Synchronous active-high reset:
// last = 3, so requester 0 has priority first. BUG selects a variant (0 is the design as specified);
// HELPER=0 removes the helper assertions.
module rr_arbiter #(parameter BUG = 0, parameter HELPER = 1) (
  input  wire       clk,
  input  wire       rst,
  input  wire [3:0] req,
  output wire [3:0] grant
);
  reg [1:0] last;

  wire [3:0] hi_mask = (last == 2'd0) ? 4'b1110 :
                       (last == 2'd1) ? 4'b1100 :
                       (last == 2'd2) ? 4'b1000 : 4'b0000;
  wire [3:0] hi_req  = req & hi_mask;
  wire [3:0] lo_req  = (BUG == 3) ? (req | (4'b0001 << last)) : req;

  function [3:0] lowest;           // lowest set bit, one-hot (0 if none)
    input [3:0] v;
    lowest = v & (~v + 4'd1);
  endfunction

  wire [3:0] g_hi = lowest(hi_req);
  wire [3:0] g_lo = lowest(lo_req) & {4{(hi_req == 4'b0) || (BUG == 2)}};
  assign grant = g_hi | g_lo;

  wire [1:0] gidx = grant[0] ? 2'd0 : grant[1] ? 2'd1 : grant[2] ? 2'd2 : 2'd3;

  always @(posedge clk) begin
    if (rst) last <= 2'd3;
    else if (|grant && !(BUG == 1 && grant[0])) last <= gidx;
  end

`ifdef FORMAL
  reg init = 1'b1;
  always @(posedge clk) init <= 1'b0;
  always @(*) if (init) assume (rst);

  // wt[i]: consecutive cycles requester i has requested without being granted
  reg [2:0] wt0, wt1, wt2, wt3;
  always @(posedge clk) begin
    if (rst) begin wt0 <= 3'd0; wt1 <= 3'd0; wt2 <= 3'd0; wt3 <= 3'd0; end
    else begin
      wt0 <= (req[0] && !grant[0]) ? wt0 + 3'd1 : 3'd0;
      wt1 <= (req[1] && !grant[1]) ? wt1 + 3'd1 : 3'd0;
      wt2 <= (req[2] && !grant[2]) ? wt2 + 3'd1 : 3'd0;
      wt3 <= (req[3] && !grant[3]) ? wt3 + 3'd1 : 3'd0;
    end
  end

  always @(*) if (!init) begin
    a_onehot0:  assert ((grant & (grant - 4'd1)) == 4'd0);
    a_no_phantom: assert ((grant & ~req) == 4'd0);
    a_work_cons:  assert (!(|req) || (|grant));
    // bounded response (safety form of starvation freedom): nobody waits more than 3 cycles
    a_wt0: assert (wt0 <= 3'd3);
    a_wt1: assert (wt1 <= 3'd3);
    a_wt2: assert (wt2 <= 3'd3);
    a_wt3: assert (wt3 <= 3'd3);
  end

  // helper invariants for the induction step of the wait bounds
  function [1:0] ahead;             // how many grants can still precede requester i
    input [1:0] i;
    ahead = i - last - 2'd1;        // 0..3 (mod 4)
  endfunction
  generate if (HELPER) begin : g_helper
    always @(*) if (!init) begin
      h_wt0: assert (wt0 + {1'b0, ahead(2'd0)} <= 3'd3);
      h_wt1: assert (wt1 + {1'b0, ahead(2'd1)} <= 3'd3);
      h_wt2: assert (wt2 + {1'b0, ahead(2'd2)} <= 3'd3);
      h_wt3: assert (wt3 + {1'b0, ahead(2'd3)} <= 3'd3);
    end
  end endgenerate

  // covers
  always @(*) if (!init) begin
    c_g0: cover (grant[0]);
    c_g1: cover (grant[1]);
    c_g2: cover (grant[2]);
    c_g3: cover (grant[3]);
    c_contend: cover (req == 4'b1111 && wt3 == 3'd3);
    c_idle: cover (req == 4'b0000 && grant == 4'd0);
  end
`endif
endmodule

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# ---- formal lab results ledger, engine v2: every row cites a typed run (kind, depth, outcome[, design]) ----
STATUS = ("proven", "bounded", "cex", "cover-reached", "inconclusive")
FROM_RUN = {"proven": {("prove", "proved")},
            "bounded": {("bmc", "bounded")},
            "cex": {("bmc", "counterexample"), ("prove", "counterexample")},
            "cover-reached": {("cover", "reached")},
            "inconclusive": {("prove", "unproven"), ("cover", "not-reached")}}
NEED = {"sync_fifo": 9, "rr_arbiter": 5, "hs_bridge": 4, "csr_block": 3,
        "pipe3": 5, "pipe3_eq": 5, "mod10_counter": 15, "toggle_demo": 4}
KEYS = ("property", "design", "status", "bound", "why", "run", "assumes", "cover", "kills", "rev")
REV = 3
ALWAYS = "reset-at-step-0"
TRACKED = "tracked-constant-stable"
def row_problems(e, runs, tracked):
    n = e.get("property", "?")
    miss = [k for k in KEYS if k not in e]
    if miss:
        return ["missing-field:%s:%s" % (n, ",".join(miss))]
    if e["status"] not in STATUS:
        return ["bad-status:" + n]
    p = []
    if e["rev"] != REV:
        p.append("stale:" + n)
    if e["run"] not in runs:
        return p + ["no-such-run:" + n]
    kind, depth, outcome = runs[e["run"]][:3]
    if len(runs[e["run"]]) > 3 and runs[e["run"]][3] != e["design"]:
        p.append("run-of-another-design:" + n)         # a run typed with its design may be cited only by that design's rows
    if (kind, outcome) not in FROM_RUN[e["status"]]:
        p.append("status-not-from-run:" + n)
    if e["bound"] != depth:
        p.append("bound-not-run-depth:" + n)
    has_cover = bool(str(e["cover"]).strip())
    if e["status"] in ("proven", "bounded") and not (has_cover and e["kills"]):
        p.append("no-evidence:" + n)
    if e["status"] == "cover-reached" and not has_cover:
        p.append("no-evidence:" + n)
    if e["status"] == "cex" and not e["kills"]:
        p.append("no-evidence:" + n)
    if e["status"] == "bounded":
        if e["design"] not in NEED:
            p.append("unknown-design:" + n)
        elif depth < NEED[e["design"]]:
            p.append("short-bound:" + n)
        if len(str(e["why"]).strip()) < 12:
            p.append("unjustified:" + n)
    if ALWAYS not in e["assumes"]:
        p.append("hidden-assume:%s:%s" % (n, ALWAYS))
    if n in tracked and TRACKED not in e["assumes"]:
        p.append("hidden-assume:%s:%s" % (n, TRACKED))
    return p
def ledger_ok(ledger, runs, required, mutants, register, tracked, final=True):
    names = [e.get("property") for e in ledger]
    bad = ["duplicate:" + n for n in sorted({n for n in names if names.count(n) > 1})]
    bad += ["missing-row:" + r for r in sorted(set(required) - set(names))]
    bad += [q for e in ledger for q in row_problems(e, runs, tracked)]
    good = [e for e in ledger if not row_problems(e, runs, tracked)]      # only a row without complaints counts as evidence
    solid = {e["property"] for e in good if e["status"] in ("proven", "cover-reached")}
    for a, rows in sorted(register.items()):
        if rows is None:
            if final:
                bad.append("deferred-assume:" + a)      # a stage may defer a discharge; a final package may not
        elif not (rows and all(r in solid for r in rows)):
            bad.append("open-assume:" + a)
    bad += ["unregistered-assume:%s:%s" % (e.get("property"), a) for e in ledger
            for a in e.get("assumes", []) if a not in register]
    killed = {m for e in good if e["status"] == "cex" for m in e["kills"]}
    bad += ["survivor:" + m for m in sorted(set(mutants) - killed)]
    bad += ["unsupported-kill:%s:%s" % (e.get("property"), m) for e in ledger
            if e.get("status") in ("proven", "bounded") for m in e.get("kills", []) if m not in killed]
    return bad
def mutation_score(ledger, mutants):
    assert mutants, "no mutants registered"
    killed = {m for e in ledger if e.get("status") == "cex" for m in e.get("kills", [])}
    return len(killed & set(mutants)) / len(mutants)

RUNS = {
    "arb-prove": ("prove", 4, "proved"),
    "arb-cover": ("cover", 6, "reached"),
}
REQUIRED = ["arbiter-structural", "arbiter-wait-bound", "arbiter-covers"]
MUTANTS = ["arb-W%d" % i for i in range(1, 4)]
REGISTER = {"reset-at-step-0": None}                 # discharged by the pair rows of lesson 3
YOUR_ROWS = []          # fill from your own runs
bad = ledger_ok(YOUR_ROWS, RUNS, REQUIRED, MUTANTS, REGISTER, set(), final=False)
if YOUR_ROWS:
    assert bad == [], bad
    print("PASS: stage 2 arbiter package consistent")
else:
    expected = ["missing-row:" + r for r in REQUIRED] + ["survivor:" + m for m in MUTANTS]
    assert sorted(bad) == sorted(expected), bad
    print("PASS: the empty package is rejected with %d complaints" % len(bad))