// Morphic Scalar FPGA with S3C Manifold Integration
// Derived from Lean: Semantics/S3C.lean + Semantics/MorphicScalar.lean
// Target: Gowin GW1NR-9 (Tang Nano 9K)
// Q16.16 fixed-point arithmetic with S3C genus-3 manifold processing
// Corrections per expansion paths document: I2S (not PDM) for SPH0645

`timescale 1ns / 1ps

// ═══════════════════════════════════════════════════════════════════════════
// Scalar State Encoding (4-bit state ID)
// ═══════════════════════════════════════════════════════════════════════════
localparam STATE_SUPERPOSED           = 4'd0;
localparam STATE_SCOUTING             = 4'd1;
localparam STATE_MEASURE_LOCAL_NEED   = 4'd2;
localparam STATE_COLLAPSED_PROFILE     = 4'd3;
localparam STATE_EXECUTE              = 4'd4;
localparam STATE_RECEIPT              = 4'd5;
localparam STATE_AMPLITUDE_UPDATE     = 4'd6;
localparam STATE_QUERY_COLLECTIVE     = 4'd7;
localparam STATE_COLLECTIVE_RESPONSE  = 4'd8;
localparam STATE_QUERY_LLM            = 4'd9;
localparam STATE_DIRECTED             = 4'd10;
localparam STATE_HOLD                 = 4'd11;
localparam STATE_OPERATOR_ALERT       = 4'd12;
localparam STATE_LOW_POWER_PASSIVE    = 4'd13;
localparam STATE_QUARANTINE           = 4'd14;
localparam STATE_MIGRATE              = 4'd15;

// ═══════════════════════════════════════════════════════════════════════════
// S3C Shell Decomposition: n = k^2 + a
// ═══════════════════════════════════════════════════════════════════════════
module s3c_shell_decomposition (
    input  wire [15:0] n,          // Input sample (unsigned 16-bit)
    output reg  [15:0] k,          // Shell index (coarse handle)
    output reg  [15:0] a,          // Lower offset (medium handle)
    output reg  [15:0] b,          // Upper offset (fine handle)
    output reg  [31:0] mass,       // Intersection form a*b
    output reg  [15:0] width       // Shell width = 2k+1 = a+b+1
);
    // Compute k = floor(sqrt(n)) using binary search
    reg [15:0] sqrt_result;
    reg [15:0] sqrt_low;
    reg [15:0] sqrt_high;
    reg [15:0] sqrt_mid;
    reg [31:0] sqrt_sq;
    
    integer i;
    
    always @(*) begin
        sqrt_low = 0;
        sqrt_high = 16'd256;
        sqrt_result = 0;
        
        for (i = 0; i < 8; i = i + 1) begin
            sqrt_mid = (sqrt_low + sqrt_high) >> 1;
            sqrt_sq = sqrt_mid * sqrt_mid;
            if (sqrt_sq < n) begin
                sqrt_low = sqrt_mid + 1;
            end else begin
                sqrt_high = sqrt_mid;
            end
        end
        sqrt_result = sqrt_low - 1;
        if (sqrt_result > 255) sqrt_result = 255;
    end
    
    // Compute k, a, b, mass, width
    reg [31:0] k_sq;
    reg [31:0] k1_sq;
    
    always @(*) begin
        k = sqrt_result;
        k_sq = k * k;
        a = n - k_sq[15:0];
        k1_sq = (k + 1) * (k + 1);
        b = k1_sq[15:0] - n;
        mass = a * b;
        width = a + b + 1;
    end
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C 3-Point Contact Detection
// ═══════════════════════════════════════════════════════════════════════════
module s3c_three_point_contact (
    input  wire [15:0] handleK,
    input  wire [15:0] handleA,
    input  wire [15:0] handleB,
    output wire        kappaA,
    output wire        kappaB,
    output wire        kappaC
);
    assign kappaA = (handleA > 0);
    assign kappaB = (handleK > 0);
    assign kappaC = (handleB > 0);
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C J-Score Calculation
// J(n) = ab*F_m + (a-b)*F_p + <chi, F_c>
// ═══════════════════════════════════════════════════════════════════════════
module s3c_j_score (
    input  wire [15:0] handleK,
    input  wire [15:0] handleA,
    input  wire [15:0] handleB,
    output wire [31:0] massResonance,
    output wire [31:0] mirrorResonance,
    output wire [31:0] spectralCoupling,
    output wire [31:0] total
);
    wire [31:0] ab;
    wire [15:0] a_minus_b;
    wire [31:0] abs_a_minus_b;
    
    assign ab = handleA * handleB;
    assign a_minus_b = (handleA >= handleB) ? (handleA - handleB) : (handleB - handleA);
    assign abs_a_minus_b = {16'b0, a_minus_b};
    
    assign massResonance = ab;
    assign mirrorResonance = abs_a_minus_b;
    assign spectralCoupling = {16'b0, handleK};
    assign total = massResonance + mirrorResonance + spectralCoupling;
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C Emission Gate
// ═══════════════════════════════════════════════════════════════════════════
module s3c_emission_gate (
    input  wire        kappaA,
    input  wire        kappaC,
    input  wire [31:0] jScore,
    output wire        emit
);
    assign emit = kappaA && kappaC && (jScore > 0);
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// S3C Audio Processing Pipeline (Integrated with Morphic Scalar)
// ═══════════════════════════════════════════════════════════════════════════
module s3c_morphic_processor (
    input  wire        clk,
    input  wire        rst_n,
    input  wire [15:0] audio_sample,  // Unsigned 16-bit audio sample (from I2S)
    output reg  [3:0]  scalar_state,
    output reg         s3c_emit,
    output reg  [31:0] s3c_j_score,
    output reg  [31:0] s3c_mass,
    output reg  [15:0] handleK,
    output reg  [15:0] handleA,
    output reg  [15:0] handleB
);
    // Pipeline Stage 1: Shell decomposition
    wire [15:0] k_stage1, a_stage1, b_stage1;
    wire [31:0] mass_stage1;
    wire [15:0] width_stage1;
    reg [15:0] k_stage1_reg, a_stage1_reg, b_stage1_reg;
    reg [31:0] mass_stage1_reg;
    
    s3c_shell_decomposition shell_inst (
        .n(audio_sample),
        .k(k_stage1),
        .a(a_stage1),
        .b(b_stage1),
        .mass(mass_stage1),
        .width(width_stage1)
    );
    
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            k_stage1_reg <= 16'd0;
            a_stage1_reg <= 16'd0;
            b_stage1_reg <= 16'd0;
            mass_stage1_reg <= 32'd0;
        end else begin
            k_stage1_reg <= k_stage1;
            a_stage1_reg <= a_stage1;
            b_stage1_reg <= b_stage1;
            mass_stage1_reg <= mass_stage1;
        end
    end
    
    // Pipeline Stage 2: Contact detection + J-score
    wire kappaA_stage2, kappaB_stage2, kappaC_stage2;
    wire [31:0] massResonance_stage2, mirrorResonance_stage2, spectralCoupling_stage2, jScore_stage2;
    reg kappaA_stage2_reg, kappaC_stage2_reg;
    reg [31:0] jScore_stage2_reg;
    reg [31:0] massResonance_stage2_reg;
    
    s3c_three_point_contact contact_inst (
        .handleK(k_stage1_reg),
        .handleA(a_stage1_reg),
        .handleB(b_stage1_reg),
        .kappaA(kappaA_stage2),
        .kappaB(kappaB_stage2),
        .kappaC(kappaC_stage2)
    );
    
    s3c_j_score jscore_inst (
        .handleK(k_stage1_reg),
        .handleA(a_stage1_reg),
        .handleB(b_stage1_reg),
        .massResonance(massResonance_stage2),
        .mirrorResonance(mirrorResonance_stage2),
        .spectralCoupling(spectralCoupling_stage2),
        .total(jScore_stage2)
    );
    
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            kappaA_stage2_reg <= 1'b0;
            kappaC_stage2_reg <= 1'b0;
            jScore_stage2_reg <= 32'd0;
            massResonance_stage2_reg <= 32'd0;
        end else begin
            kappaA_stage2_reg <= kappaA_stage2;
            kappaC_stage2_reg <= kappaC_stage2;
            jScore_stage2_reg <= jScore_stage2;
            massResonance_stage2_reg <= massResonance_stage2;
        end
    end
    
    // Pipeline Stage 3: Emission gate + State mapping
    wire emit_stage3;
    
    s3c_emission_gate emission_inst (
        .kappaA(kappaA_stage2_reg),
        .kappaC(kappaC_stage2_reg),
        .jScore(jScore_stage2_reg),
        .emit(emit_stage3)
    );
    
    // Map S3C emission to morphic scalar state
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            scalar_state <= STATE_SUPERPOSED;
            s3c_emit <= 1'b0;
            s3c_j_score <= 32'd0;
            s3c_mass <= 32'd0;
            handleK <= 16'd0;
            handleA <= 16'd0;
            handleB <= 16'd0;
        end else begin
            // S3C emit triggers state transition
            if (emit_stage3) begin
                scalar_state <= STATE_EXECUTE;
            end else begin
                scalar_state <= STATE_SUPERPOSED;
            end
            
            s3c_emit <= emit_stage3;
            s3c_j_score <= jScore_stage2_reg;
            s3c_mass <= massResonance_stage2_reg;
            handleK <= k_stage1_reg;
            handleA <= a_stage1_reg;
            handleB <= b_stage1_reg;
        end
    end
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// I2S Receiver for SPH0645 (Correction per expansion paths: I2S, not PDM)
// ═══════════════════════════════════════════════════════════════════════════
module i2s_receiver (
    input  wire        clk,
    input  wire        rst_n,
    input  wire        sclk,      // I2S bit clock
    input  wire        ws,        // Word select (LRCK)
    input  wire        sd,        // Serial data
    output reg  [15:0] left_sample,
    output reg  [15:0] right_sample,
    output reg         sample_valid
);
    reg [3:0] bit_count;
    reg [15:0] shift_reg;
    reg ws_prev;
    
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            bit_count <= 4'd0;
            shift_reg <= 16'd0;
            left_sample <= 16'd0;
            right_sample <= 16'd0;
            sample_valid <= 1'b0;
            ws_prev <= 1'b0;
        end else begin
            ws_prev <= ws;
            
            // Detect WS transition (start of new word)
            if (ws != ws_prev) begin
                bit_count <= 4'd0;
                sample_valid <= 1'b0;
            end
            
            // Sample on falling edge of SCLK (I2S standard)
            if (sclk == 1'b0) begin
                if (bit_count < 16) begin
                    shift_reg <= {shift_reg[14:0], sd};
                    bit_count <= bit_count + 1'b1;
                end else begin
                    // Word complete
                    if (ws_prev == 1'b0) begin
                        left_sample <= {shift_reg[14:0], sd};  // MSB first
                    end else begin
                        right_sample <= {shift_reg[14:0], sd};
                        sample_valid <= 1'b1;
                    end
                end
            end
        end
    end
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// Top-Level: Morphic Scalar with S3C Integration
// ═══════════════════════════════════════════════════════════════════════════
module morphic_scalar_s3c_top (
    // Clock and reset
    input  wire        clk,           // Pin 52 (27MHz)
    input  wire        rst_n,         // Pin 4 (Reset_Button)
    
    // User input
    input  wire        user_btn,      // Pin 3 (User_Button)
    
    // LED outputs
    output wire [5:0]  led,           // Pins 10,11,13,14,15,16
    
    // UART
    output wire        uart_tx,       // Pin 17
    input  wire        uart_rx,       // Pin 18
    
    // I2S Microphone (SPH0645 - corrected per expansion paths)
    input  wire        i2s_sclk,      // I2S bit clock
    input  wire        i2s_ws,        // Word select (LRCK)
    input  wire        i2s_sd,        // Serial data
    
    // State machine control
    input  wire        state_transition,
    input  wire [3:0]  target_state,
    input  wire        operator_available,
    
    // Outputs
    output reg  [3:0]  scalar_state,
    output reg         s3c_emit,
    output reg  [31:0] s3c_j_score,
    output reg  [31:0] s3c_mass,
    output reg  [15:0] handleK,
    output reg  [15:0] handleA,
    output reg  [15:0] handleB
);
    // I2S receiver
    wire [15:0] left_sample, right_sample;
    wire sample_valid;
    
    i2s_receiver i2s_inst (
        .clk(clk),
        .rst_n(rst_n),
        .sclk(i2s_sclk),
        .ws(i2s_ws),
        .sd(i2s_sd),
        .left_sample(left_sample),
        .right_sample(right_sample),
        .sample_valid(sample_valid)
    );
    
    // Convert signed I2S to unsigned for S3C
    wire [15:0] audio_sample_unsigned;
    assign audio_sample_unsigned = left_sample + 16'sd8000;
    
    // S3C morphic processor
    s3c_morphic_processor s3c_inst (
        .clk(clk),
        .rst_n(rst_n),
        .audio_sample(audio_sample_unsigned),
        .scalar_state(scalar_state),
        .s3c_emit(s3c_emit),
        .s3c_j_score(s3c_j_score),
        .s3c_mass(s3c_mass),
        .handleK(handleK),
        .handleA(handleA),
        .handleB(handleB)
    );
    
    // LED status indicator
    wire pattern_match_detected;
    led_status_opt led_inst (
        .scalar_state(scalar_state),
        .s3c_emit(s3c_emit),
        .s3c_j_score(s3c_j_score),
        .pattern_match(pattern_match_detected),
        .led(led)
    );
    
    // UART debug output
    reg uart_tx_start;
    reg [7:0] uart_tx_data;
    wire uart_tx_busy;
    
    uart_tx_opt uart_inst (
        .clk(clk),
        .rst_n(rst_n),
        .tx_start(uart_tx_start),
        .tx_data(uart_tx_data),
        .uart_tx(uart_tx),
        .tx_busy(uart_tx_busy)
    );
    
    // Simple UART transmission for state monitoring
    reg [3:0] prev_state;
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            prev_state <= 4'd0;
            uart_tx_start <= 1'b0;
            uart_tx_data <= 8'd0;
        end else begin
            if (scalar_state != prev_state && !uart_tx_busy) begin
                prev_state <= scalar_state;
                uart_tx_data <= {4'h5, scalar_state};  // state frame: high nibble tag + state
                uart_tx_start <= 1'b1;
            end else begin
                uart_tx_start <= 1'b0;
            end
        end
    end
    
    // User button integration
    reg user_btn_prev;
    wire user_btn_pressed = (user_btn && !user_btn_prev);
    
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            user_btn_prev <= 1'b0;
        end else begin
            user_btn_prev <= user_btn;
        end
    end
    
    // Override state transition when button pressed
    wire effective_state_transition = state_transition || user_btn_pressed;
    wire [3:0] effective_target_state = user_btn_pressed ? STATE_MEASURE_LOCAL_NEED : target_state;
    
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// LED Status Indicator Module
// ═══════════════════════════════════════════════════════════════════════════
module led_status_opt (
    input  wire [3:0]  scalar_state,
    input  wire        s3c_emit,
    input  wire [31:0] s3c_j_score,
    input  wire        pattern_match,
    output reg  [5:0]  led
);
    always @(*) begin
        led[5] = scalar_state[3];
        led[4] = scalar_state[2];
        led[3] = (s3c_j_score > 32'd1000);  // High J-score threshold
        led[2] = s3c_emit;
        led[1] = (scalar_state == STATE_EXECUTE);
        led[0] = pattern_match;
    end
endmodule

// ═══════════════════════════════════════════════════════════════════════════
// UART Debug Module (115200 baud @ 27MHz)
// ═══════════════════════════════════════════════════════════════════════════
module uart_tx_opt (
    input  wire        clk,
    input  wire        rst_n,
    input  wire        tx_start,
    input  wire [7:0]  tx_data,
    output reg         uart_tx,
    output reg         tx_busy
);
    localparam BAUD_DIV = 16'd234;
    reg [15:0] baud_counter;
    reg [2:0]  bit_counter;
    reg [7:0]  tx_shift;
    reg [3:0]  state;
    
    always @(posedge clk or negedge rst_n) begin
        if (!rst_n) begin
            state <= 4'd0;
            baud_counter <= 16'd0;
            bit_counter <= 3'd0;
            tx_shift <= 8'd0;
            uart_tx <= 1'b1;
            tx_busy <= 1'b0;
        end else begin
            case (state)
                4'd0: begin
                    uart_tx <= 1'b1;
                    tx_busy <= 1'b0;
                    if (tx_start) begin
                        tx_shift <= tx_data;
                        bit_counter <= 3'd0;
                        baud_counter <= 16'd0;
                        state <= 4'd1;
                        tx_busy <= 1'b1;
                    end
                end
                4'd1: begin
                    uart_tx <= 1'b0;
                    if (baud_counter == BAUD_DIV) begin
                        baud_counter <= 16'd0;
                        state <= 4'd2;
                    end else begin
                        baud_counter <= baud_counter + 1'b1;
                    end
                end
                4'd2, 4'd3, 4'd4, 4'd5, 4'd6, 4'd7, 4'd8, 4'd9: begin
                    uart_tx <= tx_shift[bit_counter];
                    if (baud_counter == BAUD_DIV) begin
                        baud_counter <= 16'd0;
                        if (bit_counter == 3'd7) begin
                            state <= 4'd10;
                        end else begin
                            bit_counter <= bit_counter + 1'b1;
                        end
                    end else begin
                        baud_counter <= baud_counter + 1'b1;
                    end
                end
                4'd10: begin
                    uart_tx <= 1'b1;
                    if (baud_counter == BAUD_DIV) begin
                        state <= 4'd0;
                    end else begin
                        baud_counter <= baud_counter + 1'b1;
                    end
                end
            endcase
        end
    end
endmodule