init: initial commit of the Scarlett framework

- Initialize Rust project configuration (Cargo) and .gitignore
- Implement core Intermediate Representation (IR), printer, and builder
utilities
- Add IR validation module for type checking and constraint verification
- Introduce optimization passes: Mem2Reg, Constant Folding, Copy
Propagation, Dead Code Elimination, and SSA Destruction
- Implement x86_64 backend for assembly code generation
- Add a C test harness and main entry point to generate, compile, and
test a GCD assembly function

harness.c

@@ -0,0 +1,46 @@
+#include <stdio.h>
+#include <stdint.h>
+#include <inttypes.h>
+
+// Declare the external assembly function generated by the Rust backend
+extern uint64_t gcd(uint64_t a, uint64_t b);
+
+int main() {
+    // Define an array of test cases: {a, b, expected_result}
+    uint64_t test_cases[][3] = {
+        {48, 18, 6},
+        {54, 24, 6},
+        {7, 13, 1},             // Prime numbers
+        {100, 10, 10},          // One is a multiple of the other
+        {2740, 1760, 20},       // Larger random numbers
+        {1234567890, 90, 90},   // Testing 64-bit bounds
+        {5, 0, 5}               // Edge case: b is 0 (Your IR handles this perfectly!)
+    };
+
+    int num_cases = sizeof(test_cases) / sizeof(test_cases[0]);
+    int passed = 0;
+
+    printf("Running GCD Assembly Tests...\n");
+    printf("-----------------------------\n");
+
+    for (int i = 0; i < num_cases; i++) {
+        uint64_t a = test_cases[i][0];
+        uint64_t b = test_cases[i][1];
+        uint64_t expected = test_cases[i][2];
+
+        // Call out into your compiled assembly!
+        uint64_t result = gcd(a, b);
+
+        if (result == expected) {
+            printf("[PASS] gcd(%" PRIu64 ", %" PRIu64 ") = %" PRIu64 "\n", a, b, result);
+            passed++;
+        } else {
+            printf("[FAIL] gcd(%" PRIu64 ", %" PRIu64 ") = %" PRIu64 " (Expected: %" PRIu64 ")\n", a, b, result, expected);
+        }
+    }
+
+    printf("-----------------------------\n");
+    printf("Results: %d/%d passed.\n", passed, num_cases);
+
+    return (passed == num_cases) ? 0 : 1;
+}