some new things, mostly not working or finished

fib/fib.c

@@ -0,0 +1,46 @@
+#include <stdio.h>
+#include <stdint.h>
+
+// tiny struct to hold a 2x2 matrix
+typedef struct {
+    uint64_t m00, m01, m10, m11;
+} Matrix2x2;
+
+// multiply two 2x2 matrices together
+Matrix2x2 multiply(Matrix2x2 a, Matrix2x2 b) {
+    // standard 2x2 matrix multiplication
+    return (Matrix2x2) {
+        a.m00* b.m00 + a.m01 * b.m10, // top-left
+            a.m00* b.m01 + a.m01 * b.m11, // top-right
+            a.m10* b.m00 + a.m11 * b.m10, // bottom-left
+            a.m10* b.m01 + a.m11 * b.m11  // bottom-right
+    };
+}
+
+// raise a matrix to the power n using binary exponentiation
+Matrix2x2 matrix_pow(Matrix2x2 base, int n) {
+    Matrix2x2 result = { 1, 0, 0, 1 }; // start with identity
+    while (n > 0) {
+        if (n % 2 == 1) result = multiply(result, base); // if odd, multiply once
+        base = multiply(base, base); // square the base
+        n /= 2; // integer divide n by 2
+    }
+    return result;
+}
+
+// get nth fibonacci number using matrix exponentiation
+uint64_t fibonacci_matrix(int n) {
+    if (n == 0) return 0; // edge case
+    Matrix2x2 base = { 1, 1, 1, 0 }; // Fibonacci Q-matrix
+    Matrix2x2 result = matrix_pow(base, n - 1); // raise to (n-1)
+    return result.m00; // top-left is F(n)
+}
+
+int main() {
+    int n = 50; // how many numbers to print
+    for (int i = 0; i < n; i++) {
+        printf("%llu ", fibonacci_matrix(i)); // print each fib number
+    }
+    printf("\n"); // newline at end
+    return 0;
+}