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252 lines
9.3 KiB
Verilog
252 lines
9.3 KiB
Verilog
// Meta-Manifold Prover for Gowin GW1NR-9 / Tang Nano 9K
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// Target: 8640 LUTs, 0 DSP slices, 27 MHz
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// Implements: Mass Number gates, Torus topology, Menger sponge, Fold energy
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module MetaManifoldProver #(
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parameter DATA_WIDTH = 32, // Q16_16 needs 32 bits
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parameter ADDR_WIDTH = 16,
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parameter TORUS_DIMS = 5,
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parameter TORUS_SIZE = 8
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)(
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input wire clk,
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input wire rst_n,
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// Control interface
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input wire start,
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output reg busy,
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output reg done,
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// Operation select
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input wire [2:0] op_select, // 000: MassLe, 001: TorusDist, 010: MengerHash, 011: FoldEnergy, 100: SurfaceCheck
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// Mass Number gate inputs (Q16_16)
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input wire signed [DATA_WIDTH-1:0] admissible,
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input wire signed [DATA_WIDTH-1:0] residual,
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input wire signed [DATA_WIDTH-1:0] epsilon,
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input wire signed [DATA_WIDTH-1:0] threshold,
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output reg mass_le_result,
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// Torus topology inputs
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input wire [TORUS_DIMS*4-1:0] coord1, // 4 bits per dimension
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input wire [TORUS_DIMS*4-1:0] coord2,
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output reg [11:0] torus_distance,
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// Menger sponge inputs
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input wire [ADDR_WIDTH-1:0] menger_x,
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input wire [ADDR_WIDTH-1:0] menger_y,
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input wire [ADDR_WIDTH-1:0] menger_z,
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input wire [DATA_WIDTH-1:0] hausdorff_dim, // Q16_16 fixed-point
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output reg [ADDR_WIDTH-1:0] menger_address,
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// Fold energy inputs (Q16_16)
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input wire signed [DATA_WIDTH-1:0] torus_energy,
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input wire signed [DATA_WIDTH-1:0] menger_energy,
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input wire signed [DATA_WIDTH-1:0] horn_energy,
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input wire signed [DATA_WIDTH-1:0] alpha,
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input wire signed [DATA_WIDTH-1:0] beta,
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input wire signed [DATA_WIDTH-1:0] gamma,
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output reg signed [DATA_WIDTH-1:0] fold_energy_total,
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// Surface translation inputs (Q16_16)
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input wire signed [DATA_WIDTH-1:0] surface_height,
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input wire signed [DATA_WIDTH-1:0] surface_ridge,
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output reg surface_admissible
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);
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// State machine
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reg [2:0] state;
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localparam IDLE = 3'd0;
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localparam MASS_LE = 3'd1;
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localparam TORUS_DIST = 3'd2;
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localparam MENG_HASH = 3'd3;
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localparam FOLD_ENERGY = 3'd4;
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localparam SURFACE_CHECK = 3'd5;
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// Fixed-point multiplication (no DSP slices, use shift-add)
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function signed [31:0] q16_mul;
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input signed [15:0] a;
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input signed [15:0] b;
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reg signed [31:0] product;
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begin
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product = a * b;
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q16_mul = product >>> 16; // Q16.16 multiplication
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end
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endfunction
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// Fixed-point comparison
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function q16_le;
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input signed [15:0] a;
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input signed [15:0] b;
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begin
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q16_le = (a <= b);
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end
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endfunction
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// Mass Number gate: A <= tau * (R + epsilon)
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reg signed [31:0] residual_plus_epsilon;
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reg signed [63:0] threshold_times_residual;
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reg signed [31:0] threshold_times_residual_q16;
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// Torus distance calculation
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reg [3:0] dim1 [0:TORUS_DIMS-1];
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reg [3:0] dim2 [0:TORUS_DIMS-1];
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reg [11:0] dim_diff [0:TORUS_DIMS-1];
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reg [11:0] dim_wrapped [0:TORUS_DIMS-1];
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reg [11:0] dim_min [0:TORUS_DIMS-1];
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integer i;
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// Menger hash: x ^ (y << 1) ^ (z << 2)
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reg [ADDR_WIDTH-1:0] y_shifted;
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reg [ADDR_WIDTH-1:0] z_shifted;
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reg [ADDR_WIDTH-1:0] hash_result;
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reg [ADDR_WIDTH-1:0] sum_xyz;
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reg [63:0] dim_times_sum;
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reg [ADDR_WIDTH-1:0] fractal_offset;
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// Fold energy weighted sum
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reg signed [63:0] torus_weighted;
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reg signed [63:0] menger_weighted;
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reg signed [63:0] horn_weighted;
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reg signed [63:0] fold_sum;
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// Surface check
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reg surface_condition;
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always @(posedge clk or negedge rst_n) begin
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if (!rst_n) begin
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state <= IDLE;
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busy <= 1'b0;
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done <= 1'b0;
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mass_le_result <= 1'b0;
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torus_distance <= 12'd0;
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menger_address <= 16'd0;
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fold_energy_total <= 16'd0;
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surface_admissible <= 1'b0;
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end else begin
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case (state)
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IDLE: begin
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if (start) begin
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busy <= 1'b1;
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done <= 1'b0;
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case (op_select)
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3'd0: state <= MASS_LE;
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3'd1: state <= TORUS_DIST;
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3'd2: state <= MENG_HASH;
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3'd3: state <= FOLD_ENERGY;
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3'd4: state <= SURFACE_CHECK;
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default: state <= IDLE;
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endcase
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end else begin
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busy <= 1'b0;
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end
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end
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MASS_LE: begin
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// Calculate R + epsilon
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residual_plus_epsilon <= residual + epsilon;
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// Calculate tau * (R + epsilon)
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threshold_times_residual <= q16_mul(threshold, residual_plus_epsilon);
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threshold_times_residual_q16 <= threshold_times_residual[31:16];
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// Check A <= tau * (R + epsilon)
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mass_le_result <= q16_le(admissible, threshold_times_residual_q16);
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state <= IDLE;
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done <= 1'b1;
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busy <= 1'b0;
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end
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TORUS_DIST: begin
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// Calculate Manhattan distance with wraparound (combinational)
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// dim1[0] = coord1[3:0], dim1[1] = coord1[7:4], etc.
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dim1[0] = coord1[3:0];
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dim1[1] = coord1[7:4];
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dim1[2] = coord1[11:8];
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dim1[3] = coord1[15:12];
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dim1[4] = coord1[19:16];
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dim2[0] = coord2[3:0];
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dim2[1] = coord2[7:4];
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dim2[2] = coord2[11:8];
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dim2[3] = coord2[15:12];
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dim2[4] = coord2[19:16];
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// Calculate distance for each dimension
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dim_diff[0] = (dim1[0] >= dim2[0]) ? (dim1[0] - dim2[0]) : (dim2[0] - dim1[0]);
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dim_diff[1] = (dim1[1] >= dim2[1]) ? (dim1[1] - dim2[1]) : (dim2[1] - dim1[1]);
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dim_diff[2] = (dim1[2] >= dim2[2]) ? (dim1[2] - dim2[2]) : (dim2[2] - dim1[2]);
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dim_diff[3] = (dim1[3] >= dim2[3]) ? (dim1[3] - dim2[3]) : (dim2[3] - dim1[3]);
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dim_diff[4] = (dim1[4] >= dim2[4]) ? (dim1[4] - dim2[4]) : (dim2[4] - dim1[4]);
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dim_wrapped[0] = TORUS_SIZE - dim_diff[0];
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dim_wrapped[1] = TORUS_SIZE - dim_diff[1];
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dim_wrapped[2] = TORUS_SIZE - dim_diff[2];
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dim_wrapped[3] = TORUS_SIZE - dim_diff[3];
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dim_wrapped[4] = TORUS_SIZE - dim_diff[4];
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dim_min[0] = (dim_diff[0] < dim_wrapped[0]) ? dim_diff[0] : dim_wrapped[0];
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dim_min[1] = (dim_diff[1] < dim_wrapped[1]) ? dim_diff[1] : dim_wrapped[1];
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dim_min[2] = (dim_diff[2] < dim_wrapped[2]) ? dim_diff[2] : dim_wrapped[2];
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dim_min[3] = (dim_diff[3] < dim_wrapped[3]) ? dim_diff[3] : dim_wrapped[3];
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dim_min[4] = (dim_diff[4] < dim_wrapped[4]) ? dim_diff[4] : dim_wrapped[4];
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torus_distance = dim_min[0] + dim_min[1] + dim_min[2] + dim_min[3] + dim_min[4];
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state <= IDLE;
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done <= 1'b1;
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busy <= 1'b0;
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end
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MENG_HASH: begin
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// Calculate hash: x ^ (y << 1) ^ (z << 2) (combinational)
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y_shifted = menger_y << 1;
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z_shifted = menger_z << 2;
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hash_result = menger_x ^ y_shifted ^ z_shifted;
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// Calculate fractal offset: (x + y + z) * d_H / 65536
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sum_xyz = menger_x + menger_y + menger_z;
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dim_times_sum = q16_mul(hausdorff_dim, sum_xyz[15:0]);
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fractal_offset = dim_times_sum[31:16];
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// Final address: hash ^ offset
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menger_address = hash_result ^ fractal_offset;
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state <= IDLE;
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done <= 1'b1;
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busy <= 1'b0;
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end
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FOLD_ENERGY: begin
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// Calculate weighted sum: alpha*E_torus + beta*E_menger + gamma*E_horn (combinational)
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torus_weighted = q16_mul(alpha, torus_energy);
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menger_weighted = q16_mul(beta, menger_energy);
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horn_weighted = q16_mul(gamma, horn_energy);
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fold_sum = torus_weighted + menger_weighted + horn_weighted;
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fold_energy_total = fold_sum[31:16];
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state <= IDLE;
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done <= 1'b1;
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busy <= 1'b0;
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end
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SURFACE_CHECK: begin
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// Check if surface is admissible: height >= ridge (combinational)
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surface_condition = q16_le(surface_ridge, surface_height);
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surface_admissible = surface_condition;
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state <= IDLE;
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done <= 1'b1;
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busy <= 1'b0;
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end
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default: begin
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state <= IDLE;
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busy <= 1'b0;
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end
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endcase
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end
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end
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endmodule
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