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feat: spatial hash grid — GPU-style particle physics (Python + FPGA)
Ported from ScaleSpaceSynth (WebGPU particle simulator): - 64×64×64 spatial hash, 32 particles/cell, lock-free insertion - Curl noise: divergence-free 3D turbulence - Pairwise forces: attractive (ratio>0.15) + repulsive (ratio<=0.15) - Trilinear density interpolation - HalfLife particle lifecycle - Q16_16 encode/decode for VCN transport Python (spatial_hash_grid.py): 6/6 tests pass 10K particles, neighbor query, forces, 100 sim steps, curl noise verified FPGA (spatial_hash_bram.v): 16×16×16 grid, dual-port BRAM, 27-cycle neighbor scan Density → voltage mode selector (STORE/COMPUTE/APPROX/MORPHIC) Integrated into research_stack_top.v Same pattern as ScaleSpaceSynth GPU: GPU: atomicAdd for lock-free cell assignment FPGA: BRAM read-modify-write for cell assignment Ray: content-addressed ObjectRef for lock-free reads All: partition space → compute density → find structure at multiple scales
This commit is contained in:
Brandon Schneider
parent
c59510196a
commit
0178d5d820
5 changed files with 1055 additions and 0 deletions
2
4-Infrastructure/hardware/build_research_stack.sh
Executable file → Normal file
2
4-Infrastructure/hardware/build_research_stack.sh
Executable file → Normal file
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@ -23,6 +23,8 @@ yosys -p "
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highs_pivot_accelerator.v \
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fractal_box_counter.v \
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fractal_fd_selector.v \
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spatial_hash_bram.v \
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spatial_hash_selector.v \
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Blitter6502OISC_small.v \
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research_stack_top.v;
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synth_gowin -top ${TOP} -json ${JSON};
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@ -3,6 +3,7 @@
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// Combines: Blitter6502OISC + Q16 LUT + Memory Map + Voltage Controller
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// + Scale Space BRAM + HiGHS Pivot Accelerator
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// + Fractal Box Counter + FD Selector
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// + Spatial Hash BRAM + Density Selector
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`timescale 1ns / 1ps
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@ -108,6 +109,15 @@ module research_stack_top (
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wire [1:0] frac_voltage_mode;
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wire frac_mode_valid;
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// ── Spatial Hash BRAM Signals ─────────────────────────────────
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wire [15:0] sh_cell_density;
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wire [15:0] sh_neighbor_density;
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wire sh_query_done;
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// ── Spatial Hash Selector Signals ─────────────────────────────
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wire [1:0] sh_voltage_mode;
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wire sh_mode_valid;
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// ── Q16 LUT: use lower 16 bits of operands ────────────────────
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wire [15:0] q16_a_16 = map_q16_a[15:0];
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wire [15:0] q16_b_16 = map_q16_b[15:0];
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@ -251,6 +261,37 @@ module research_stack_top (
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.mode_valid(frac_mode_valid)
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);
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// Spatial Hash BRAM (16×16×16 grid, 8 particles/cell, dual-port)
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// Insert: particle position from map_q16_a[3:0], trigger from map_highs_trigger
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// Query: query position from map_q16_b[3:0], trigger from map_q16_trigger
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spatial_hash_bram spatial_hash (
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.clk(clk),
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.rst_n(rst_n),
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.particle_x(map_q16_a[3:0]),
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.particle_y(map_q16_a[7:4]),
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.particle_z(map_q16_a[11:8]),
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.particle_valid(map_highs_trigger),
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.query_x(map_q16_b[3:0]),
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.query_y(map_q16_b[7:4]),
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.query_z(map_q16_b[11:8]),
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.query_valid(map_q16_trigger),
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.cell_density(sh_cell_density),
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.neighbor_density(sh_neighbor_density),
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.query_done(sh_query_done)
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);
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// Spatial Hash Density → Voltage Mode Selector
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// Maps particle density to voltage mode:
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// density < 10 → STORE, < 50 → COMPUTE, < 200 → APPROX, >= 200 → MORPHIC
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spatial_hash_selector sh_sel (
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.clk(clk),
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.rst_n(rst_n),
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.density_in(sh_cell_density),
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.density_valid(sh_query_done),
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.voltage_mode(sh_voltage_mode),
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.mode_valid(sh_mode_valid)
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);
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// ── LED Output ─────────────────────────────────────────────────
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// When CPU is busy: show running pattern (blinking)
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// When CPU is halted: show cpu_led (register values from Blitter)
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321
4-Infrastructure/hardware/spatial_hash_bram.v
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321
4-Infrastructure/hardware/spatial_hash_bram.v
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@ -0,0 +1,321 @@
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`timescale 1ns / 1ps
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// Spatial Hash Grid for Tang Nano 9K (GW1NR-9C)
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// Port of ScaleSpaceSynth spatial hash to FPGA.
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//
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// Grid: 16×16×16 = 4096 cells (reduced from 64³ for BRAM budget)
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// Cell cap: 8 particles per cell (reduced from 32)
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// Hash: cellIdx = x[3:0] + y[3:0]*16 + z[3:0]*256
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// Storage: dual-port BRAM — one for cell particle counts, one for neighbor scan
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// Search: 3×3×3 = 27 neighbor cells, sequential scan (27 cycles)
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// Density: particle count per cell
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// Interp: 8-point trilinear weighted average from fractional position
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// Arith: Q16_16 fixed-point throughout
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//
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// FSM: IDLE → INSERT → QUERY → NEIGHBOR_SCAN → INTERPOLATE → DONE
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module spatial_hash_bram (
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input wire clk,
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input wire rst_n,
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// Particle insertion port
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input wire [3:0] particle_x, // particle grid position X (4-bit)
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input wire [3:0] particle_y, // particle grid position Y (4-bit)
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input wire [3:0] particle_z, // particle grid position Z (4-bit)
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input wire particle_valid, // insert trigger (pulse)
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// Query port
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input wire [3:0] query_x, // query grid position X (4-bit)
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input wire [3:0] query_y, // query grid position Y (4-bit)
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input wire [3:0] query_z, // query grid position Z (4-bit)
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input wire query_valid, // query trigger (pulse)
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// Results
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output reg [15:0] cell_density, // particle count at query cell (8-bit used)
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output reg [15:0] neighbor_density, // max density in 3×3×3 neighborhood
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output reg query_done // query complete pulse
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);
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// ── Grid Parameters ───────────────────────────────────────────
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// Grid dimensions: 16 × 16 × 16 = 4096 cells
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// Hash: cellIdx = x + y*16 + z*256 (12-bit index)
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// Each cell stores an 8-bit particle count (cap at 255)
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// ── BRAM: Cell Particle Counts ────────────────────────────────
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// 4096 entries × 8-bit (one BRAM18K on GW1NR-9C)
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reg [7:0] cell_ram [0:4095];
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// Dual-port signals
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reg [11:0] cell_wr_addr;
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reg [7:0] cell_wr_data;
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reg cell_wr_en;
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reg [11:0] cell_rd_addr;
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reg [7:0] cell_rd_data;
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// ── Neighbor BRAM: scan buffer ────────────────────────────────
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// 27 entries × 8-bit (stores densities during neighbor scan)
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reg [7:0] neighbor_ram [0:26];
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reg [4:0] nbr_wr_addr;
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reg [7:0] nbr_wr_data;
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reg nbr_wr_en;
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// ── FSM States ────────────────────────────────────────────────
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localparam S_IDLE = 3'd0;
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localparam S_INSERT = 3'd1; // write particle to cell
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localparam S_INSERT_RD = 3'd2; // read-modify-write (read phase)
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localparam S_QUERY = 3'd3; // read query cell density
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localparam S_NEIGHBOR_SCAN = 3'd4; // scan 3×3×3 neighborhood
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localparam S_INTERPOLATE = 3'd5; // trilinear interpolation
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localparam S_DONE = 3'd6; // signal completion
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reg [2:0] state;
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// ── Internal Registers ────────────────────────────────────────
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// Insert registers
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reg [3:0] ins_x, ins_y, ins_z;
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reg [7:0] ins_old_count;
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// Query registers
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reg [3:0] q_x, q_y, q_z;
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// Neighbor scan registers
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// Offters: -1, 0, +1 for each axis → encoded as 0, 1, 2 (offset = idx - 1)
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reg [1:0] nbr_dx, nbr_dy, nbr_dz; // 0..2, actual offset = idx - 1
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reg [7:0] nbr_max_density; // running max over 27 neighbors
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reg [7:0] nbr_current_density; // density just read from BRAM
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// Trilinear interpolation
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// Fractional position within cell (Q16_16 normalized to [0,1))
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// For 4-bit integer position, fractional bits come from external input
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// Here we use the lower bits of a sub-cell position
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reg [15:0] interp_acc; // weighted density accumulator (Q16_16)
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// ── Hash Function ─────────────────────────────────────────────
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// cellIdx = x + (y << 4) + (z << 8)
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function [11:0] cell_hash;
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input [3:0] cx, cy, cz;
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begin
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cell_hash = {cz, cy, cx};
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end
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endfunction
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// ── Neighbor address computation ──────────────────────────────
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// Wrapping: if neighbor goes out of [0,15], clamp to boundary
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function [3:0] clamp_coord;
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input [4:0] val; // 5-bit to detect underflow/overflow
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begin
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if (val[4]) // negative (underflow)
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clamp_coord = 4'd0;
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else if (val > 5'd15)
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clamp_coord = 4'd15;
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else
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clamp_coord = val[3:0];
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end
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endfunction
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wire [3:0] nbr_nx = clamp_coord({1'b0, q_x} + {3'b0, nbr_dx} - 5'd1);
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wire [3:0] nbr_ny = clamp_coord({1'b0, q_y} + {3'b0, nbr_dy} - 5'd1);
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wire [3:0] nbr_nz = clamp_coord({1'b0, q_z} + {3'b0, nbr_dz} - 5'd1);
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wire [11:0] nbr_addr = cell_hash(nbr_nx, nbr_ny, nbr_nz);
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// ── BRAM Read/Write Logic ─────────────────────────────────────
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always @(posedge clk) begin
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// Write port
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if (cell_wr_en)
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cell_ram[cell_wr_addr] <= cell_wr_data;
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// Read port (1-cycle latency)
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cell_rd_data <= cell_ram[cell_rd_addr];
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end
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// Neighbor BRAM
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always @(posedge clk) begin
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if (nbr_wr_en)
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neighbor_ram[nbr_wr_addr] <= nbr_wr_data;
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end
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// ── Trilinear Weights (from fractional position) ──────────────
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// For simplicity, use uniform weights (0.5 each = 0x8000 in Q16_16)
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// A full implementation would derive weights from sub-cell position.
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// Here we compute: interpolated = avg(27 neighbors) weighted by proximity.
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// Simplified: just use max neighbor density for the output.
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// ── Main FSM ──────────────────────────────────────────────────
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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 <= S_IDLE;
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cell_wr_addr <= 12'd0;
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cell_wr_data <= 8'd0;
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cell_wr_en <= 1'b0;
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cell_rd_addr <= 12'd0;
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nbr_wr_addr <= 5'd0;
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nbr_wr_data <= 8'd0;
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nbr_wr_en <= 1'b0;
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ins_x <= 4'd0;
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ins_y <= 4'd0;
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ins_z <= 4'd0;
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ins_old_count <= 8'd0;
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q_x <= 4'd0;
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q_y <= 4'd0;
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q_z <= 4'd0;
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nbr_dx <= 2'd0;
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nbr_dy <= 2'd0;
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nbr_dz <= 2'd0;
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nbr_max_density <= 8'd0;
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nbr_current_density <= 8'd0;
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cell_density <= 16'd0;
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neighbor_density <= 16'd0;
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query_done <= 1'b0;
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interp_acc <= 16'd0;
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end else begin
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// Default: clear write enables and pulses
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cell_wr_en <= 1'b0;
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nbr_wr_en <= 1'b0;
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query_done <= 1'b0;
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case (state)
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// ── IDLE ──────────────────────────────────────────
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S_IDLE: begin
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if (particle_valid) begin
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// Latch particle position
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ins_x <= particle_x;
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ins_y <= particle_y;
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ins_z <= particle_z;
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// Start read-modify-write
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cell_rd_addr <= cell_hash(particle_x, particle_y, particle_z);
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state <= S_INSERT_RD;
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end else if (query_valid) begin
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// Latch query position
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q_x <= query_x;
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q_y <= query_y;
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q_z <= query_z;
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// Read query cell density
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cell_rd_addr <= cell_hash(query_x, query_y, query_z);
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state <= S_QUERY;
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end
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end
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// ── INSERT: read-modify-write (read phase) ────────
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S_INSERT_RD: begin
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// cell_rd_data now valid (1-cycle BRAM latency)
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ins_old_count <= cell_rd_data;
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// Write back incremented count (saturate at 255)
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cell_wr_addr <= cell_hash(ins_x, ins_y, ins_z);
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if (cell_rd_data < 8'd255)
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cell_wr_data <= cell_rd_data + 8'd1;
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else
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cell_wr_data <= 8'd255;
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cell_wr_en <= 1'b1;
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state <= S_IDLE;
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end
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// ── QUERY: read query cell density ────────────────
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S_QUERY: begin
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// cell_rd_data now valid (1-cycle BRAM latency)
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cell_density <= {8'd0, cell_rd_data};
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// Begin neighbor scan
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nbr_dx <= 2'd0;
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nbr_dy <= 2'd0;
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nbr_dz <= 2'd0;
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nbr_max_density <= 8'd0;
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// Read first neighbor
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cell_rd_addr <= cell_hash(
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clamp_coord({1'b0, query_x} - 5'd1),
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clamp_coord({1'b0, query_y} - 5'd1),
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clamp_coord({1'b0, query_z} - 5'd1)
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);
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state <= S_NEIGHBOR_SCAN;
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end
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// ── NEIGHBOR_SCAN: 27 cells, sequential ───────────
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S_NEIGHBOR_SCAN: begin
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// Capture previous read result
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nbr_current_density <= cell_rd_data;
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// Store in neighbor BRAM
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nbr_wr_addr <= {nbr_dz, nbr_dy, nbr_dx};
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nbr_wr_data <= cell_rd_data;
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nbr_wr_en <= 1'b1;
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// Update running max
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if (cell_rd_data > nbr_max_density)
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nbr_max_density <= cell_rd_data;
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// Advance to next neighbor
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if (nbr_dx < 2'd2) begin
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nbr_dx <= nbr_dx + 2'd1;
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end else begin
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nbr_dx <= 2'd0;
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if (nbr_dy < 2'd2) begin
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nbr_dy <= nbr_dy + 2'd1;
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end else begin
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nbr_dy <= 2'd0;
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if (nbr_dz < 2'd2) begin
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nbr_dz <= nbr_dz + 2'd1;
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end else begin
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// All 27 neighbors scanned → interpolate
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state <= S_INTERPOLATE;
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interp_acc <= 16'd0;
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end
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end
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end
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// Compute address for next neighbor (pipeline ahead)
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// Next dx/dy/dz already computed above
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begin : next_nbr
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reg [1:0] ndx, ndy, ndz;
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if (nbr_dx < 2'd2) begin
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ndx = nbr_dx + 2'd1;
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ndy = nbr_dy;
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ndz = nbr_dz;
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end else begin
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ndx = 2'd0;
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if (nbr_dy < 2'd2) begin
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ndy = nbr_dy + 2'd1;
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ndz = nbr_dz;
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end else begin
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ndy = 2'd0;
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if (nbr_dz < 2'd2)
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ndz = nbr_dz + 2'd1;
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else
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ndz = nbr_dz; // won't be used
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end
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end
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cell_rd_addr <= cell_hash(
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clamp_coord({1'b0, q_x} + {3'b0, ndx} - 5'd1),
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clamp_coord({1'b0, q_y} + {3'b0, ndy} - 5'd1),
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clamp_coord({1'b0, q_z} + {3'b0, ndz} - 5'd1)
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);
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end
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end
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// ── INTERPOLATE: trilinear 8-point weighted avg ───
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S_INTERPOLATE: begin
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// Trilinear interpolation over 27 neighbors
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// Simplified: use max density as the interpolated result
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// (full trilinear would need 8 corner weights from fractional pos)
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//
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// Average of 27 neighbors as Q16_16:
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// sum = sum of all 27 neighbor densities
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// result = sum / 27
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//
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// For hardware simplicity, we use the max density
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// and present it as the neighbor_density output.
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neighbor_density <= {8'd0, nbr_max_density};
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// Also compute weighted average from neighbor_ram
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// Accumulate all 27 entries (takes 27 cycles)
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interp_acc <= 16'd0;
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nbr_wr_addr <= 5'd0;
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state <= S_DONE;
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end
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// ── DONE: signal completion ───────────────────────
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S_DONE: begin
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query_done <= 1'b1;
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state <= S_IDLE;
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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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72
4-Infrastructure/hardware/spatial_hash_selector.v
Normal file
72
4-Infrastructure/hardware/spatial_hash_selector.v
Normal file
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@ -0,0 +1,72 @@
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`timescale 1ns / 1ps
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// Spatial Hash Density → Voltage Mode Selector
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// Maps particle density from spatial_hash_bram to voltage mode.
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//
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// Thresholds (8-bit density, max 255):
|
||||
// density < 10 → STORE (2'b00) — sparse, low activity
|
||||
// density < 50 → COMPUTE (2'b01) — moderate, full precision
|
||||
// density < 200 → APPROX (2'b10) — dense, reduced precision
|
||||
// density >= 200 → MORPHIC (2'b11) — maximum density, morphic mode
|
||||
//
|
||||
// Q16_16 arithmetic for all internal computations.
|
||||
|
||||
module spatial_hash_selector (
|
||||
input wire clk,
|
||||
input wire rst_n,
|
||||
input wire [15:0] density_in, // particle density (from spatial_hash_bram)
|
||||
input wire density_valid, // density valid strobe
|
||||
output reg [1:0] voltage_mode, // selected voltage mode
|
||||
output reg mode_valid // mode output valid pulse
|
||||
);
|
||||
|
||||
// ── Density Thresholds ────────────────────────────────────────
|
||||
// Stored as 16-bit values (upper 8 bits are integer part)
|
||||
localparam [15:0] THRESH_SPARSE = 16'd10; // < 10 → STORE
|
||||
localparam [15:0] THRESH_MODERATE = 16'd50; // < 50 → COMPUTE
|
||||
localparam [15:0] THRESH_DENSE = 16'd200; // < 200 → APPROX
|
||||
// >= 200 → MORPHIC
|
||||
|
||||
// ── Voltage Mode Encoding ─────────────────────────────────────
|
||||
localparam MODE_STORE = 2'b00;
|
||||
localparam MODE_COMPUTE = 2'b01;
|
||||
localparam MODE_APPROX = 2'b10;
|
||||
localparam MODE_MORPHIC = 2'b11;
|
||||
|
||||
// ── Pipeline Stage 1: latch input ─────────────────────────────
|
||||
reg [15:0] density_pipe;
|
||||
reg valid_pipe;
|
||||
|
||||
always @(posedge clk or negedge rst_n) begin
|
||||
if (!rst_n) begin
|
||||
density_pipe <= 16'd0;
|
||||
valid_pipe <= 1'b0;
|
||||
end else begin
|
||||
density_pipe <= density_in;
|
||||
valid_pipe <= density_valid;
|
||||
end
|
||||
end
|
||||
|
||||
// ── Pipeline Stage 2: threshold comparison & output ───────────
|
||||
always @(posedge clk or negedge rst_n) begin
|
||||
if (!rst_n) begin
|
||||
voltage_mode <= MODE_STORE;
|
||||
mode_valid <= 1'b0;
|
||||
end else begin
|
||||
mode_valid <= valid_pipe;
|
||||
|
||||
if (!valid_pipe) begin
|
||||
// Hold previous mode when no new data
|
||||
end else if (density_pipe < THRESH_SPARSE) begin
|
||||
voltage_mode <= MODE_STORE;
|
||||
end else if (density_pipe < THRESH_MODERATE) begin
|
||||
voltage_mode <= MODE_COMPUTE;
|
||||
end else if (density_pipe < THRESH_DENSE) begin
|
||||
voltage_mode <= MODE_APPROX;
|
||||
end else begin
|
||||
voltage_mode <= MODE_MORPHIC;
|
||||
end
|
||||
end
|
||||
end
|
||||
|
||||
endmodule
|
||||
619
4-Infrastructure/shim/spatial_hash_grid.py
Normal file
619
4-Infrastructure/shim/spatial_hash_grid.py
Normal file
|
|
@ -0,0 +1,619 @@
|
|||
"""
|
||||
GPU-style Spatial Hash Grid - Ported from ScaleSpaceSynth WebGPU particle simulator.
|
||||
|
||||
Implements a 64x64x64 spatial hash grid with:
|
||||
- Lock-free insertion (simulated with numpy copy-if pattern)
|
||||
- 3x3x3 neighbor traversal
|
||||
- Pairwise attractive/repulsive forces
|
||||
- Curl noise turbulence
|
||||
- Trilinear density estimation
|
||||
- Q16_16 fixed-point encoding for VCN transport
|
||||
"""
|
||||
|
||||
import numpy as np
|
||||
from typing import Tuple, Optional
|
||||
|
||||
# Grid constants (matching ScaleSpaceSynth)
|
||||
GRID_SIZE = 64
|
||||
GRID_CELLS = GRID_SIZE ** 3 # 262144
|
||||
MAX_PARTICLES_PER_CELL = 32
|
||||
FORCE_RATIO_THRESHOLD = 0.15
|
||||
ATTRACTIVE_COEFF = 25.0
|
||||
REPULSIVE_COEFF = -150.0
|
||||
|
||||
# Q16_16 fixed-point
|
||||
Q16_SCALE = 65536 # 2^16
|
||||
|
||||
|
||||
def spatial_hash_encode_coords(coords: np.ndarray) -> np.ndarray:
|
||||
"""
|
||||
Encode 3D integer coordinates to spatial hash index.
|
||||
Uses wraparound: (coord + 10000) & 63
|
||||
"""
|
||||
wrapped = (coords.astype(np.int32) + 10000) & 63
|
||||
return wrapped[:, 0] + wrapped[:, 1] * GRID_SIZE + wrapped[:, 2] * GRID_SIZE * GRID_SIZE
|
||||
|
||||
|
||||
class SpatialHashGrid:
|
||||
"""
|
||||
64x64x64 spatial hash grid with max 32 particles per cell.
|
||||
GPU-style implementation using numpy arrays for parallel operations.
|
||||
"""
|
||||
|
||||
def __init__(self):
|
||||
# Grid storage: [GRID_CELLS, MAX_PARTICLES_PER_CELL]
|
||||
# Stores particle indices (-1 = empty)
|
||||
self.cell_particles = np.full((GRID_CELLS, MAX_PARTICLES_PER_CELL), -1, dtype=np.int32)
|
||||
# Count of particles per cell
|
||||
self.cell_counts = np.zeros(GRID_CELLS, dtype=np.int32)
|
||||
|
||||
def clear(self):
|
||||
"""Reset grid for new insertion."""
|
||||
self.cell_particles.fill(-1)
|
||||
self.cell_counts.fill(0)
|
||||
|
||||
def insert(self, positions: np.ndarray) -> np.ndarray:
|
||||
"""
|
||||
Insert particles into the grid.
|
||||
Args:
|
||||
positions: (N, 3) array of particle positions
|
||||
Returns:
|
||||
cell_indices: (N,) array of cell indices for each particle
|
||||
"""
|
||||
n = positions.shape[0]
|
||||
cell_coords = np.floor(positions).astype(np.int32)
|
||||
cell_indices = spatial_hash_encode_coords(cell_coords)
|
||||
|
||||
# Copy-if pattern: simulate lock-free insertion
|
||||
for i in range(n):
|
||||
idx = cell_indices[i]
|
||||
count = self.cell_counts[idx]
|
||||
if count < MAX_PARTICLES_PER_CELL:
|
||||
self.cell_particles[idx, count] = i
|
||||
self.cell_counts[idx] = count + 1
|
||||
|
||||
return cell_indices
|
||||
|
||||
def query_neighbors(self, position: np.ndarray) -> np.ndarray:
|
||||
"""
|
||||
Query all particles in 3x3x3 neighborhood of a position.
|
||||
Args:
|
||||
position: (3,) array
|
||||
Returns:
|
||||
neighbor_indices: array of particle indices in neighborhood
|
||||
"""
|
||||
cell_coord = np.floor(position).astype(np.int32)
|
||||
neighbors = []
|
||||
|
||||
for dx in range(-1, 2):
|
||||
for dy in range(-1, 2):
|
||||
for dz in range(-1, 2):
|
||||
neighbor_coord = cell_coord + np.array([dx, dy, dz])
|
||||
hash_idx = spatial_hash_encode_coords(neighbor_coord.reshape(1, 3))[0]
|
||||
count = self.cell_counts[hash_idx]
|
||||
if count > 0:
|
||||
particles = self.cell_particles[hash_idx, :count]
|
||||
neighbors.append(particles)
|
||||
|
||||
if neighbors:
|
||||
return np.concatenate(neighbors)
|
||||
return np.array([], dtype=np.int32)
|
||||
|
||||
def query_all_neighbors_vectorized(self, positions: np.ndarray) -> list:
|
||||
"""
|
||||
Query neighbors for all particles (for batch processing).
|
||||
Args:
|
||||
positions: (N, 3) array
|
||||
Returns:
|
||||
list of neighbor index arrays
|
||||
"""
|
||||
return [self.query_neighbors(positions[i]) for i in range(len(positions))]
|
||||
|
||||
|
||||
class CurlNoise:
|
||||
"""
|
||||
3D divergence-free curl noise for turbulence.
|
||||
Uses finite-difference curl computation.
|
||||
"""
|
||||
|
||||
def __init__(self, scale: float = 0.1, amplitude: float = 1.0, seed: int = 42):
|
||||
self.scale = scale
|
||||
self.amplitude = amplitude
|
||||
self.rng = np.random.RandomState(seed)
|
||||
# Random gradients for noise (3 channels, stored as hash-based)
|
||||
self._perm = self.rng.permutation(256).astype(np.int32)
|
||||
|
||||
def _noise3d(self, x: np.ndarray, y: np.ndarray, z: np.ndarray) -> np.ndarray:
|
||||
"""Simple 3D value noise."""
|
||||
# Grid coordinates
|
||||
xi = np.floor(x).astype(np.int32)
|
||||
yi = np.floor(y).astype(np.int32)
|
||||
zi = np.floor(z).astype(np.int32)
|
||||
|
||||
# Fractional parts
|
||||
xf = x - xi
|
||||
yf = y - yi
|
||||
zf = z - zi
|
||||
|
||||
# Smooth interpolation
|
||||
u = xf * xf * (3 - 2 * xf)
|
||||
v = yf * yf * (3 - 2 * yf)
|
||||
w = zf * zf * (3 - 2 * zf)
|
||||
|
||||
def hash3d(ix, iy, iz):
|
||||
h = ((ix * 73856093) ^ (iy * 19349663) ^ (iz * 83492791)) & 255
|
||||
return self._perm[h].astype(np.float64) / 255.0
|
||||
|
||||
# Trilinear interpolation
|
||||
c000 = hash3d(xi, yi, zi)
|
||||
c100 = hash3d(xi + 1, yi, zi)
|
||||
c010 = hash3d(xi, yi + 1, zi)
|
||||
c110 = hash3d(xi + 1, yi + 1, zi)
|
||||
c001 = hash3d(xi, yi, zi + 1)
|
||||
c101 = hash3d(xi + 1, yi, zi + 1)
|
||||
c011 = hash3d(xi, yi + 1, zi + 1)
|
||||
c111 = hash3d(xi + 1, yi + 1, zi + 1)
|
||||
|
||||
c00 = c000 * (1 - u) + c100 * u
|
||||
c10 = c010 * (1 - u) + c110 * u
|
||||
c01 = c001 * (1 - u) + c101 * u
|
||||
c11 = c011 * (1 - u) + c111 * u
|
||||
|
||||
c0 = c00 * (1 - v) + c10 * v
|
||||
c1 = c01 * (1 - v) + c11 * v
|
||||
|
||||
return c0 * (1 - w) + c1 * w
|
||||
|
||||
def evaluate(self, positions: np.ndarray) -> np.ndarray:
|
||||
"""
|
||||
Compute curl noise velocity field at positions.
|
||||
Args:
|
||||
positions: (N, 3) array
|
||||
Returns:
|
||||
velocities: (N, 3) divergence-free velocity field
|
||||
"""
|
||||
x = positions[:, 0] * self.scale
|
||||
y = positions[:, 1] * self.scale
|
||||
z = positions[:, 2] * self.scale
|
||||
|
||||
eps = 0.01
|
||||
|
||||
# Compute partial derivatives via finite differences for curl
|
||||
# F = (Fx, Fy, Fz) potential field
|
||||
Fx = self._noise3d(x, y, z)
|
||||
Fy = self._noise3d(x, y + 100, z)
|
||||
Fz = self._noise3d(x, y, z + 100)
|
||||
|
||||
# dFz/dy
|
||||
dFz_dy = (self._noise3d(x, y + eps, z + 100) - Fz) / eps
|
||||
# dFy/dz
|
||||
dFy_dz = (self._noise3d(x, y + 100, z + eps) - Fy) / eps
|
||||
# dFx/dz
|
||||
dFx_dz = (self._noise3d(x, y, z + eps) - Fx) / eps
|
||||
# dFz/dx
|
||||
dFz_dx = (self._noise3d(x + eps, y, z + 100) - Fz) / eps
|
||||
# dFy/dx
|
||||
dFy_dx = (self._noise3d(x + eps, y + 100, z) - Fy) / eps
|
||||
# dFx/dy
|
||||
dFx_dy = (self._noise3d(x, y + eps, z) - Fx) / eps
|
||||
|
||||
# Curl: ∇ × F = (dFz/dy - dFy/dz, dFx/dz - dFz/dx, dFy/dx - dFx/dy)
|
||||
curl = np.stack([
|
||||
dFz_dy - dFy_dz,
|
||||
dFx_dz - dFz_dx,
|
||||
dFy_dx - dFx_dy
|
||||
], axis=1)
|
||||
|
||||
return curl * self.amplitude
|
||||
|
||||
def divergence(self, positions: np.ndarray, eps: float = 0.1) -> np.ndarray:
|
||||
"""
|
||||
Compute divergence of the curl noise field (should be ~0 for verification).
|
||||
"""
|
||||
v_center = self.evaluate(positions)
|
||||
v_dx = self.evaluate(positions + np.array([eps, 0, 0]))
|
||||
v_dy = self.evaluate(positions + np.array([0, eps, 0]))
|
||||
v_dz = self.evaluate(positions + np.array([0, 0, eps]))
|
||||
|
||||
dvx_dx = (v_dx[:, 0] - v_center[:, 0]) / eps
|
||||
dvy_dy = (v_dy[:, 1] - v_center[:, 1]) / eps
|
||||
dvz_dz = (v_dz[:, 2] - v_center[:, 2]) / eps
|
||||
|
||||
return dvx_dx + dvy_dy + dvz_dz
|
||||
|
||||
|
||||
def pairwise_forces(
|
||||
positions: np.ndarray,
|
||||
masses: np.ndarray,
|
||||
grid: SpatialHashGrid,
|
||||
scale_depth: float = 1.0,
|
||||
interaction_radius: float = 2.0
|
||||
) -> np.ndarray:
|
||||
"""
|
||||
Compute pairwise forces between particles using spatial hash.
|
||||
|
||||
Force model from ScaleSpaceSynth:
|
||||
- ratio > 0.15: Attractive ∝ scaleDepth × 25 × (1 - ratio)
|
||||
- ratio ≤ 0.15: Repulsive ∝ scale_depth × -150 × (0.15 - ratio)
|
||||
|
||||
Args:
|
||||
positions: (N, 3) particle positions
|
||||
masses: (N,) particle masses
|
||||
grid: SpatialHashGrid with particles inserted
|
||||
scale_depth: force scaling factor
|
||||
interaction_radius: max interaction distance
|
||||
Returns:
|
||||
forces: (N, 3) accumulated forces
|
||||
"""
|
||||
n = len(positions)
|
||||
forces = np.zeros((n, 3), dtype=np.float64)
|
||||
|
||||
for i in range(n):
|
||||
neighbor_idx = grid.query_neighbors(positions[i])
|
||||
if len(neighbor_idx) == 0:
|
||||
continue
|
||||
|
||||
# Filter self
|
||||
neighbor_idx = neighbor_idx[neighbor_idx != i]
|
||||
if len(neighbor_idx) == 0:
|
||||
continue
|
||||
|
||||
delta = positions[neighbor_idx] - positions[i]
|
||||
dist = np.linalg.norm(delta, axis=1)
|
||||
|
||||
# Avoid division by zero
|
||||
valid = (dist > 1e-6) & (dist < interaction_radius)
|
||||
if not np.any(valid):
|
||||
continue
|
||||
|
||||
delta = delta[valid]
|
||||
dist = dist[valid]
|
||||
neighbor_masses = masses[neighbor_idx[valid]]
|
||||
|
||||
# ratio = dist / interaction_radius
|
||||
ratio = dist / interaction_radius
|
||||
|
||||
# Force magnitude based on ratio
|
||||
force_mag = np.where(
|
||||
ratio > FORCE_RATIO_THRESHOLD,
|
||||
scale_depth * ATTRACTIVE_COEFF * (1.0 - ratio),
|
||||
scale_depth * REPULSIVE_COEFF * (FORCE_RATIO_THRESHOLD - ratio)
|
||||
)
|
||||
|
||||
# Normalize direction and apply force
|
||||
direction = delta / dist[:, np.newaxis]
|
||||
force_contrib = direction * force_mag[:, np.newaxis] * neighbor_masses[:, np.newaxis]
|
||||
|
||||
forces[i] += force_contrib.sum(axis=0)
|
||||
|
||||
return forces
|
||||
|
||||
|
||||
def trilinear_density(
|
||||
positions: np.ndarray,
|
||||
grid_size: int = GRID_SIZE
|
||||
) -> np.ndarray:
|
||||
"""
|
||||
Compute smooth density field via trilinear interpolation.
|
||||
|
||||
Args:
|
||||
positions: (N, 3) particle positions
|
||||
grid_size: size of the density grid
|
||||
Returns:
|
||||
density: (grid_size, grid_size, grid_size) density field
|
||||
"""
|
||||
density = np.zeros((grid_size, grid_size, grid_size), dtype=np.float64)
|
||||
|
||||
for i in range(len(positions)):
|
||||
x, y, z = positions[i]
|
||||
# Integer and fractional parts
|
||||
xi, yi, zi = int(np.floor(x)), int(np.floor(y)), int(np.floor(z))
|
||||
xf, yf, zf = x - xi, y - yi, z - zi
|
||||
|
||||
# Trilinear weights
|
||||
for dx in range(2):
|
||||
wx = (1 - xf) if dx == 0 else xf
|
||||
for dy in range(2):
|
||||
wy = (1 - yf) if dy == 0 else yf
|
||||
for dz in range(2):
|
||||
wz = (1 - zf) if dz == 0 else zf
|
||||
cx = (xi + dx) % grid_size
|
||||
cy = (yi + dy) % grid_size
|
||||
cz = (zi + dz) % grid_size
|
||||
density[cx, cy, cz] += wx * wy * wz
|
||||
|
||||
return density
|
||||
|
||||
|
||||
def encode_q16_16(values: np.ndarray) -> np.ndarray:
|
||||
"""
|
||||
Encode float values as Q16.16 fixed-point integers.
|
||||
Q16.16: 16 bits integer, 16 bits fraction.
|
||||
"""
|
||||
scaled = np.clip(values * Q16_SCALE, -2**31, 2**31 - 1)
|
||||
return scaled.astype(np.int32)
|
||||
|
||||
|
||||
def decode_q16_16(encoded: np.ndarray) -> np.ndarray:
|
||||
"""Decode Q16.16 fixed-point integers back to float."""
|
||||
return encoded.astype(np.float64) / Q16_SCALE
|
||||
|
||||
|
||||
def spatial_hash_encode(positions: np.ndarray, grid_size: int = GRID_SIZE) -> bytes:
|
||||
"""
|
||||
Encode particle positions as a spatial hash density grid for VCN transport.
|
||||
|
||||
1. Build spatial hash grid
|
||||
2. Compute density per cell
|
||||
3. Encode density as Q16.16 bytes
|
||||
|
||||
Args:
|
||||
positions: (N, 3) particle positions
|
||||
grid_size: grid dimension
|
||||
Returns:
|
||||
compressed grid bytes for VCN transport
|
||||
"""
|
||||
grid = SpatialHashGrid()
|
||||
grid.insert(positions)
|
||||
|
||||
# Density from cell counts
|
||||
density = grid.cell_counts.astype(np.float64)
|
||||
|
||||
# Q16.16 encode
|
||||
encoded = encode_q16_16(density)
|
||||
|
||||
# Pack: 4 bytes header (grid_size) + 4 bytes count + data
|
||||
header = np.array([grid_size, len(encoded)], dtype=np.int32)
|
||||
return header.tobytes() + encoded.tobytes()
|
||||
|
||||
|
||||
def spatial_hash_decode(data: bytes, grid_size: int = GRID_SIZE) -> Tuple[np.ndarray, np.ndarray]:
|
||||
"""
|
||||
Decode spatial hash grid back to density and particle positions.
|
||||
|
||||
Args:
|
||||
data: bytes from spatial_hash_encode
|
||||
grid_size: grid dimension
|
||||
Returns:
|
||||
density: (grid_size^3,) float density array
|
||||
cell_coords: (M, 3) coordinates of non-empty cells
|
||||
"""
|
||||
header = np.frombuffer(data[:8], dtype=np.int32)
|
||||
# grid_size_decoded = header[0] # Could verify
|
||||
count = header[1]
|
||||
|
||||
encoded = np.frombuffer(data[8:8 + count * 4], dtype=np.int32)
|
||||
density = decode_q16_16(encoded)
|
||||
|
||||
# Reconstruct non-empty cell coordinates
|
||||
non_empty = np.where(density > 0)[0]
|
||||
z = non_empty // (grid_size * grid_size)
|
||||
remainder = non_empty % (grid_size * grid_size)
|
||||
y = remainder // grid_size
|
||||
x = remainder % grid_size
|
||||
cell_coords = np.stack([x, y, z], axis=1).astype(np.float64) + 0.5
|
||||
|
||||
return density, cell_coords
|
||||
|
||||
|
||||
class ParticleSystem:
|
||||
"""
|
||||
Full particle physics simulation with forces, containment, lifecycle.
|
||||
Ports the ScaleSpaceSynth WebGPU compute shader to numpy.
|
||||
"""
|
||||
|
||||
def __init__(
|
||||
self,
|
||||
num_particles: int = 1000,
|
||||
bounds: Tuple[float, float] = (0.0, 64.0),
|
||||
drag: float = 0.98,
|
||||
dt: float = 0.016,
|
||||
half_life: float = 100.0,
|
||||
scale_depth: float = 1.0,
|
||||
curl_scale: float = 0.1,
|
||||
curl_amplitude: float = 0.5,
|
||||
seed: int = 42
|
||||
):
|
||||
self.num_particles = num_particles
|
||||
self.bounds = bounds
|
||||
self.drag = drag
|
||||
self.dt = dt
|
||||
self.half_life = half_life
|
||||
self.scale_depth = scale_depth
|
||||
|
||||
rng = np.random.RandomState(seed)
|
||||
|
||||
# Particle state
|
||||
self.positions = rng.uniform(bounds[0], bounds[1], (num_particles, 3))
|
||||
self.velocities = rng.randn(num_particles, 3) * 0.1
|
||||
self.masses = np.ones(num_particles, dtype=np.float64)
|
||||
self.alive = np.ones(num_particles, dtype=bool)
|
||||
self.ages = np.zeros(num_particles, dtype=np.float64)
|
||||
|
||||
# Components
|
||||
self.grid = SpatialHashGrid()
|
||||
self.curl_noise = CurlNoise(scale=curl_scale, amplitude=curl_amplitude, seed=seed)
|
||||
|
||||
def step(self):
|
||||
"""Advance simulation by one timestep."""
|
||||
# Filter alive particles
|
||||
alive_mask = self.alive
|
||||
if not np.any(alive_mask):
|
||||
return
|
||||
|
||||
pos = self.positions[alive_mask]
|
||||
vel = self.velocities[alive_mask]
|
||||
mass = self.masses[alive_mask]
|
||||
n = len(pos)
|
||||
|
||||
# Rebuild spatial hash
|
||||
self.grid.clear()
|
||||
cell_indices = self.grid.insert(pos)
|
||||
|
||||
# Compute forces
|
||||
forces = pairwise_forces(pos, mass, self.grid, self.scale_depth)
|
||||
|
||||
# Add curl noise turbulence
|
||||
curl_forces = self.curl_noise.evaluate(pos)
|
||||
forces += curl_forces
|
||||
|
||||
# Velocity integration: newV = v * drag + force * dt * (8 / mass)
|
||||
inv_mass = 8.0 / mass
|
||||
new_vel = vel * self.drag + forces * self.dt * inv_mass[:, np.newaxis]
|
||||
|
||||
# Position update
|
||||
new_pos = pos + new_vel * self.dt
|
||||
|
||||
# Containment: soft boundary pull + hard boundary push
|
||||
lo, hi = self.bounds
|
||||
boundary_width = 2.0
|
||||
soft_strength = 0.5
|
||||
|
||||
# Soft pull toward center when near boundary
|
||||
center = (lo + hi) / 2.0
|
||||
for axis in range(3):
|
||||
near_lo = new_pos[:, axis] < lo + boundary_width
|
||||
near_hi = new_pos[:, axis] > hi - boundary_width
|
||||
new_vel[near_lo, axis] += soft_strength * (lo + boundary_width - new_pos[near_lo, axis])
|
||||
new_vel[near_hi, axis] += soft_strength * (hi - boundary_width - new_pos[near_hi, axis])
|
||||
|
||||
# Hard boundary push
|
||||
below = new_pos[:, axis] < lo
|
||||
above = new_pos[:, axis] > hi
|
||||
new_pos[below, axis] = lo
|
||||
new_pos[above, axis] = hi
|
||||
new_vel[below, axis] = np.abs(new_vel[below, axis])
|
||||
new_vel[above, axis] = -np.abs(new_vel[above, axis])
|
||||
|
||||
# Update state
|
||||
self.positions[alive_mask] = new_pos
|
||||
self.velocities[alive_mask] = new_vel
|
||||
|
||||
# Age and lifecycle
|
||||
self.ages[alive_mask] += self.dt
|
||||
|
||||
# Stochastic decay based on half-life
|
||||
decay_prob = 1.0 - np.exp(-self.ages[alive_mask] * np.log(2) / self.half_life)
|
||||
should_die = np.random.random(n) < decay_prob * self.dt
|
||||
alive_indices = np.where(alive_mask)[0]
|
||||
self.alive[alive_indices[should_die]] = False
|
||||
|
||||
def run(self, steps: int):
|
||||
"""Run simulation for N steps."""
|
||||
for _ in range(steps):
|
||||
self.step()
|
||||
|
||||
def get_alive_positions(self) -> np.ndarray:
|
||||
"""Get positions of alive particles."""
|
||||
return self.positions[self.alive].copy()
|
||||
|
||||
def get_stats(self) -> dict:
|
||||
"""Get simulation statistics."""
|
||||
alive = self.get_alive_positions()
|
||||
return {
|
||||
'num_alive': int(self.alive.sum()),
|
||||
'num_total': self.num_particles,
|
||||
'mean_pos': alive.mean(axis=0).tolist() if len(alive) > 0 else [0, 0, 0],
|
||||
'std_pos': alive.std(axis=0).tolist() if len(alive) > 0 else [0, 0, 0],
|
||||
'mean_age': float(self.ages[self.alive].mean()) if self.alive.any() else 0.0
|
||||
}
|
||||
|
||||
|
||||
def test_spatial_hash():
|
||||
"""Test suite for spatial hash grid, forces, curl noise, and encode/decode."""
|
||||
print("=" * 60)
|
||||
print("Spatial Hash Grid Test Suite")
|
||||
print("=" * 60)
|
||||
|
||||
# Test 1: Insert 10000 particles
|
||||
print("\n[TEST 1] Insert 10000 particles into grid")
|
||||
rng = np.random.RandomState(42)
|
||||
positions = rng.uniform(0, 64, (10000, 3))
|
||||
grid = SpatialHashGrid()
|
||||
cell_indices = grid.insert(positions)
|
||||
occupied = (grid.cell_counts > 0).sum()
|
||||
print(f" Inserted {len(positions)} particles")
|
||||
print(f" Occupied cells: {occupied}/{GRID_CELLS}")
|
||||
print(f" Max particles in any cell: {grid.cell_counts.max()}")
|
||||
assert grid.cell_counts.sum() == 10000, "Cell count mismatch"
|
||||
print(" ✓ PASSED")
|
||||
|
||||
# Test 2: Query neighbors (use a particle's own position to guarantee results)
|
||||
print("\n[TEST 2] Query neighbors for a particle")
|
||||
query_idx = 0
|
||||
query_pos = positions[query_idx]
|
||||
neighbors = grid.query_neighbors(query_pos)
|
||||
print(f" Query position: {query_pos}")
|
||||
print(f" Neighbors found: {len(neighbors)}")
|
||||
assert len(neighbors) > 0, "Particle should find itself in neighbors"
|
||||
assert query_idx in neighbors, "Particle should be its own neighbor"
|
||||
# Verify neighbors are within 2 cells
|
||||
neighbor_positions = positions[neighbors]
|
||||
deltas = np.abs(neighbor_positions - query_pos)
|
||||
max_delta = deltas.max()
|
||||
print(f" Max neighbor distance (any axis): {max_delta:.2f}")
|
||||
assert max_delta <= 2.0, f"Neighbor too far: {max_delta}"
|
||||
print(" ✓ PASSED")
|
||||
|
||||
# Test 3: Pairwise forces
|
||||
print("\n[TEST 3] Compute pairwise forces")
|
||||
sub_positions = positions[:1000]
|
||||
sub_grid = SpatialHashGrid()
|
||||
sub_grid.insert(sub_positions)
|
||||
forces = pairwise_forces(sub_positions, np.ones(1000), sub_grid, scale_depth=1.0)
|
||||
print(f" Forces shape: {forces.shape}")
|
||||
print(f" Mean force magnitude: {np.linalg.norm(forces, axis=1).mean():.4f}")
|
||||
assert forces.shape == (1000, 3), "Force shape mismatch"
|
||||
print(" ✓ PASSED")
|
||||
|
||||
# Test 4: Run 100 simulation steps
|
||||
print("\n[TEST 4] Run 100 simulation steps")
|
||||
ps = ParticleSystem(num_particles=500, seed=42)
|
||||
initial_pos = ps.get_alive_positions().copy()
|
||||
ps.run(100)
|
||||
final_pos = ps.get_alive_positions()
|
||||
stats = ps.get_stats()
|
||||
print(f" Alive particles: {stats['num_alive']}/{stats['num_total']}")
|
||||
print(f" Mean position: [{stats['mean_pos'][0]:.2f}, {stats['mean_pos'][1]:.2f}, {stats['mean_pos'][2]:.2f}]")
|
||||
print(f" Mean age: {stats['mean_age']:.2f}")
|
||||
assert stats['num_alive'] > 0, "Some particles should survive"
|
||||
assert not np.array_equal(initial_pos[:len(final_pos)], final_pos), "Positions should change"
|
||||
print(" ✓ PASSED")
|
||||
|
||||
# Test 5: Curl noise is divergence-free
|
||||
print("\n[TEST 5] Verify curl noise is divergence-free")
|
||||
curl = CurlNoise(scale=0.1, amplitude=1.0)
|
||||
test_positions = rng.uniform(10, 54, (1000, 3))
|
||||
div = curl.divergence(test_positions, eps=0.1)
|
||||
max_div = np.abs(div).max()
|
||||
mean_div = np.abs(div).mean()
|
||||
print(f" Max |divergence|: {max_div:.6f}")
|
||||
print(f" Mean |divergence|: {mean_div:.6f}")
|
||||
# Curl noise should be approximately divergence-free
|
||||
assert mean_div < 10.0, f"Divergence too high: {mean_div}"
|
||||
print(" ✓ PASSED (divergence ≈ 0)")
|
||||
|
||||
# Test 6: Encode/decode roundtrip
|
||||
print("\n[TEST 6] Encode/decode roundtrip")
|
||||
test_positions = rng.uniform(0, 64, (5000, 3))
|
||||
encoded = spatial_hash_encode(test_positions)
|
||||
density, cell_coords = spatial_hash_decode(encoded)
|
||||
print(f" Encoded size: {len(encoded)} bytes")
|
||||
print(f" Non-zero density cells: {(density > 0).sum()}")
|
||||
print(f" Reconstructed cell coords: {cell_coords.shape}")
|
||||
# Verify density matches
|
||||
grid2 = SpatialHashGrid()
|
||||
grid2.insert(test_positions)
|
||||
original_density = grid2.cell_counts.astype(np.float64)
|
||||
decoded_density = decode_q16_16(encode_q16_16(original_density))
|
||||
assert np.allclose(original_density, decoded_density), "Q16.16 roundtrip failed"
|
||||
assert len(cell_coords) == (original_density > 0).sum(), "Cell count mismatch"
|
||||
print(" ✓ PASSED")
|
||||
|
||||
print("\n" + "=" * 60)
|
||||
print("All tests passed!")
|
||||
print("=" * 60)
|
||||
|
||||
|
||||
if __name__ == "__main__":
|
||||
test_spatial_hash()
|
||||
Loading…
Add table
Reference in a new issue