feat(poly_arith): implement synchronous PolyAdd/PolySub streaming module

Phase 2.3: Polynomial modular addition and subtraction.
- poly_arith_sync.v: mode=0 add (a+b mod Q), mode=1 sub (a-b mod Q)
- Pure streaming (1 coeff/cycle, no BRAM needed)
- Uses pipeline_reg for valid/ready handshake

Verified: 10/10 vectors bit-exact vs Python reference

sync_rtl/poly_arith/TB/tb_poly_arith.cpp

@@ -0,0 +1,175 @@
+// tb_poly_arith.cpp - Verilator C++ testbench for poly_arith_sync
+//
+// Reads test vectors from a hex file specified by +VECTOR_FILE= plusarg.
+// Each line: "MODE A0 A1 ... A255 B0 B1 ... B255"
+//   MODE: 'A' for add, 'S' for sub
+//   A0..A255: 256 hex coefficients (12-bit, 3 hex digits each)
+//   B0..B255: 256 hex coefficients
+//
+// Feeds 256 (A, B) pairs through the DUT, collects 256 output coeffs,
+// prints one "RESULT: C0 C1 ... C255" line per vector.
+//
+// Clock: 10 ns period (100 MHz).
+// Reset: 2 cycles low, then high.
+// Timeout: 100,000 cycles.
+
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <sstream>
+#include <cstdlib>
+#include <vector>
+#include "Vpoly_arith_sync.h"
+#include "verilated.h"
+
+#define CLK_PERIOD_NS    10.0
+#define TIMEOUT_CYCLES   100000
+
+static vluint64_t main_time = 0;
+
+double sc_time_stamp() {
+    return main_time;
+}
+
+// Helper: toggle clock (full cycle: low->high->low) with eval
+static void posedge(Vpoly_arith_sync* dut) {
+    dut->clk = !dut->clk;
+    main_time += (vluint64_t)(CLK_PERIOD_NS / 2.0);
+    dut->eval();
+    dut->clk = !dut->clk;
+    main_time += (vluint64_t)(CLK_PERIOD_NS / 2.0);
+    dut->eval();
+}
+
+int main(int argc, char** argv) {
+    Verilated::commandArgs(argc, argv);
+
+    // Parse +VECTOR_FILE= plusarg
+    const char* vector_file = NULL;
+    for (int i = 1; i < argc; i++) {
+        std::string arg(argv[i]);
+        if (arg.rfind("+VECTOR_FILE=", 0) == 0) {
+            vector_file = argv[i] + 13;
+        }
+    }
+
+    if (!vector_file) {
+        std::cerr << "ERROR: +VECTOR_FILE= not specified" << std::endl;
+        return 1;
+    }
+
+    std::ifstream infile(vector_file);
+    if (!infile.is_open()) {
+        std::cerr << "ERROR: Cannot open vector file: " << vector_file << std::endl;
+        return 1;
+    }
+
+    // Instantiate DUT
+    Vpoly_arith_sync* dut = new Vpoly_arith_sync;
+
+    // Initialize
+    dut->clk         = 0;
+    dut->rst_n       = 0;
+    dut->coeff_a_in  = 0;
+    dut->coeff_b_in  = 0;
+    dut->mode        = 0;
+    dut->valid_i     = 0;
+    dut->ready_i     = 0;
+
+    // Reset: 2 cycles low
+    for (int i = 0; i < 4; i++) {
+        dut->clk = !dut->clk;
+        main_time += (vluint64_t)(CLK_PERIOD_NS / 2.0);
+        dut->eval();
+        dut->clk = !dut->clk;
+        main_time += (vluint64_t)(CLK_PERIOD_NS / 2.0);
+        dut->eval();
+    }
+    dut->rst_n = 1;
+
+    // Always ready to receive results
+    dut->ready_i = 1;
+
+    std::string line;
+    vluint64_t cycle = 0;
+
+    while (std::getline(infile, line)) {
+        // Skip empty lines and comments
+        if (line.empty() || line[0] == '#') continue;
+
+        // Parse: MODE A0..A255 B0..B255 (513 values on one line)
+        std::istringstream iss(line);
+        std::string mode_str;
+        if (!(iss >> mode_str)) continue;
+
+        // Determine mode
+        bool mode_val;
+        if (mode_str == "A" || mode_str == "a") {
+            mode_val = false;
+        } else if (mode_str == "S" || mode_str == "s") {
+            mode_val = true;
+        } else {
+            std::cerr << "ERROR: Unknown mode: " << mode_str << std::endl;
+            continue;
+        }
+
+        dut->mode = mode_val ? 1 : 0;
+
+        // Read 256 A coeffs
+        unsigned int coeff;
+        std::vector<unsigned int> a_coeffs, b_coeffs;
+        for (int i = 0; i < 256; i++) {
+            if (!(iss >> std::hex >> coeff)) {
+                std::cerr << "ERROR: Missing A coeff at index " << i << std::endl;
+                return 1;
+            }
+            a_coeffs.push_back(coeff & 0xFFF);
+        }
+
+        // Read 256 B coeffs
+        for (int i = 0; i < 256; i++) {
+            if (!(iss >> std::hex >> coeff)) {
+                std::cerr << "ERROR: Missing B coeff at index " << i << std::endl;
+                return 1;
+            }
+            b_coeffs.push_back(coeff & 0xFFF);
+        }
+
+        // Feed 256 coefficient pairs and collect results
+        std::vector<unsigned int> results;
+        for (int i = 0; i < 256; i++) {
+            // Drive inputs
+            dut->coeff_a_in = a_coeffs[i];
+            dut->coeff_b_in = b_coeffs[i];
+            dut->valid_i    = 1;
+
+            // Posedge: DUT samples input, pipeline_reg captures data, valid_o→1
+            posedge(dut);
+            dut->valid_i = 0;
+
+            // Read result now (valid_o is high, coeff_out is valid)
+            // Posedge: pipeline_reg clears valid_o (ready_i=1), but result
+            // is available on coeff_out port (combinational from data_r)
+            posedge(dut);
+
+            results.push_back(dut->coeff_out & 0xFFF);
+
+            cycle += 2;
+            if (cycle > TIMEOUT_CYCLES) {
+                std::cerr << "ERROR: Timeout after " << cycle << " cycles" << std::endl;
+                return 1;
+            }
+        }
+
+        // Print result as one space-separated hex line
+        printf("RESULT:");
+        for (int i = 0; i < 256; i++) {
+            printf(" %03X", results[i]);
+        }
+        printf("\n");
+    }
+
+    infile.close();
+    delete dut;
+    return 0;
+}