Research-Stack/4-Infrastructure/hardware/s3c_manifold_fpga.v

346 lines
13 KiB
Verilog

// S3C Manifold FPGA Implementation
// Derived from Lean: Semantics/S3C.lean
// Target: Gowin GW1NR-9 (Tang Nano 9K)
// Q16.16 fixed-point arithmetic
// Implements genus-3 topological manifold for audio processing
`timescale 1ns / 1ps
// ═══════════════════════════════════════════════════════════════════════════
// S3C Shell Decomposition: n = k^2 + a
// Computes shell coordinates for integer decomposition
// ═══════════════════════════════════════════════════════════════════════════
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))
// OPTIMIZATION: Use lookup table for sqrt (smaller than hardware sqrt)
// For 16-bit input, we can use a 256-entry lookup table for sqrt of 0-65535
// Simplified sqrt approximation using binary search
reg [15:0] sqrt_result;
reg [15:0] sqrt_low;
reg [15:0] sqrt_high;
reg [15:0] sqrt_mid;
reg [15:0] sqrt_sq;
integer i;
always @(*) begin
sqrt_low = 0;
sqrt_high = 16'd256; // sqrt(65536) = 256
sqrt_result = 0;
// Binary search for sqrt
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-Handle Manifold
// Maps audio sample to 3-handle manifold structure
// ═══════════════════════════════════════════════════════════════════════════
module s3c_manifold_handle (
input wire [15:0] sample,
output wire [15:0] handleK, // Coarse handle (amplitude envelope)
output wire [15:0] handleA, // Medium handle (spectral content)
output wire [15:0] handleB // Fine handle (phase information)
);
wire [15:0] k, a, b;
wire [31:0] mass;
wire [15:0] width;
s3c_shell_decomposition shell_inst (
.n(sample),
.k(k),
.a(a),
.b(b),
.mass(mass),
.width(width)
);
assign handleK = k;
assign handleA = a;
assign handleB = b;
endmodule
// ═══════════════════════════════════════════════════════════════════════════
// S3C 3-Point Contact Detection
// Detects 3-point contact from manifold handles
// ═══════════════════════════════════════════════════════════════════════════
module s3c_three_point_contact (
input wire [15:0] handleK,
input wire [15:0] handleA,
input wire [15:0] handleB,
output wire kappaA, // Forward spectral prediction
output wire kappaB, // Temporal midpoint
output wire kappaC // Backward phase correction
);
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, // ab*F_m
output wire [31:0] mirrorResonance, // (a-b)*F_p
output wire [31:0] spectralCoupling, // <chi, F_c>
output wire [31:0] total // J(n)
);
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
// Emit only if kappa_A AND kappa_C AND J > 0
// ═══════════════════════════════════════════════════════════════════════════
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
// Complete S3C manifold processing for audio samples
// ═══════════════════════════════════════════════════════════════════════════
module s3c_audio_processor (
input wire clk,
input wire rst_n,
input wire [15:0] audio_sample, // Unsigned 16-bit audio sample
output reg [15:0] handleK,
output reg [15:0] handleA,
output reg [15:0] handleB,
output reg [31:0] massResonance,
output reg [31:0] mirrorResonance,
output reg [31:0] spectralCoupling,
output reg [31:0] jScore,
output reg emit
);
// Pipeline Stage 1: Manifold handles
wire [15:0] handleK_stage1, handleA_stage1, handleB_stage1;
reg [15:0] handleK_stage1_reg, handleA_stage1_reg, handleB_stage1_reg;
s3c_manifold_handle manifold_inst (
.sample(audio_sample),
.handleK(handleK_stage1),
.handleA(handleA_stage1),
.handleB(handleB_stage1)
);
always @(posedge clk or negedge rst_n) begin
if (!rst_n) begin
handleK_stage1_reg <= 16'd0;
handleA_stage1_reg <= 16'd0;
handleB_stage1_reg <= 16'd0;
end else begin
handleK_stage1_reg <= handleK_stage1;
handleA_stage1_reg <= handleA_stage1;
handleB_stage1_reg <= handleB_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] massResonance_stage2_reg, mirrorResonance_stage2_reg, spectralCoupling_stage2_reg, jScore_stage2_reg;
s3c_three_point_contact contact_inst (
.handleK(handleK_stage1_reg),
.handleA(handleA_stage1_reg),
.handleB(handleB_stage1_reg),
.kappaA(kappaA_stage2),
.kappaB(kappaB_stage2),
.kappaC(kappaC_stage2)
);
s3c_j_score jscore_inst (
.handleK(handleK_stage1_reg),
.handleA(handleA_stage1_reg),
.handleB(handleB_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;
massResonance_stage2_reg <= 32'd0;
mirrorResonance_stage2_reg <= 32'd0;
spectralCoupling_stage2_reg <= 32'd0;
jScore_stage2_reg <= 32'd0;
end else begin
kappaA_stage2_reg <= kappaA_stage2;
kappaC_stage2_reg <= kappaC_stage2;
massResonance_stage2_reg <= massResonance_stage2;
mirrorResonance_stage2_reg <= mirrorResonance_stage2;
spectralCoupling_stage2_reg <= spectralCoupling_stage2;
jScore_stage2_reg <= jScore_stage2;
end
end
// Pipeline Stage 3: Emission gate
wire emit_stage3;
s3c_emission_gate emission_inst (
.kappaA(kappaA_stage2_reg),
.kappaC(kappaC_stage2_reg),
.jScore(jScore_stage2_reg),
.emit(emit_stage3)
);
// Output registers
always @(posedge clk or negedge rst_n) begin
if (!rst_n) begin
handleK <= 16'd0;
handleA <= 16'd0;
handleB <= 16'd0;
massResonance <= 32'd0;
mirrorResonance <= 32'd0;
spectralCoupling <= 32'd0;
jScore <= 32'd0;
emit <= 1'b0;
end else begin
handleK <= handleK_stage1_reg;
handleA <= handleA_stage1_reg;
handleB <= handleB_stage1_reg;
massResonance <= massResonance_stage2_reg;
mirrorResonance <= mirrorResonance_stage2_reg;
spectralCoupling <= spectralCoupling_stage2_reg;
jScore <= jScore_stage2_reg;
emit <= emit_stage3;
end
end
endmodule
// ═══════════════════════════════════════════════════════════════════════════
// S3C Testbench
// ═══════════════════════════════════════════════════════════════════════════
module s3c_audio_processor_tb;
reg clk;
reg rst_n;
reg [15:0] audio_sample;
wire [15:0] handleK;
wire [15:0] handleA;
wire [15:0] handleB;
wire [31:0] massResonance;
wire [31:0] mirrorResonance;
wire [31:0] spectralCoupling;
wire [31:0] jScore;
wire emit;
// Instantiate DUT
s3c_audio_processor dut (
.clk(clk),
.rst_n(rst_n),
.audio_sample(audio_sample),
.handleK(handleK),
.handleA(handleA),
.handleB(handleB),
.massResonance(massResonance),
.mirrorResonance(mirrorResonance),
.spectralCoupling(spectralCoupling),
.jScore(jScore),
.emit(emit)
);
// Clock generation
initial clk = 0;
always #18.5185 clk = ~clk; // 27MHz
// Test stimulus
initial begin
// Initialize
rst_n = 0;
audio_sample = 16'd0;
#100;
rst_n = 1;
#100;
// Test samples (matching Python test)
audio_sample = 16'd100;
#100;
$display("Sample 100: k=%d, a=%d, b=%d, mass=%d, emit=%b",
handleK, handleA, handleB, massResonance, emit);
audio_sample = 16'd256;
#100;
$display("Sample 256: k=%d, a=%d, b=%d, mass=%d, emit=%b",
handleK, handleA, handleB, massResonance, emit);
audio_sample = 16'd1000;
#100;
$display("Sample 1000: k=%d, a=%d, b=%d, mass=%d, emit=%b",
handleK, handleA, handleB, massResonance, emit);
audio_sample = 16'd5000;
#100;
$display("Sample 5000: k=%d, a=%d, b=%d, mass=%d, emit=%b",
handleK, handleA, handleB, massResonance, emit);
audio_sample = 16'd10000;
#100;
$display("Sample 10000: k=%d, a=%d, b=%d, mass=%d, emit=%b",
handleK, handleA, handleB, massResonance, emit);
#100;
$finish;
end
endmodule