some new things, mostly not working or finished

fib/fib.py

@@ -0,0 +1,41 @@
+# tiny class to hold a 2x2 matrix
+class Matrix2x2:
+    def __init__(self, m00, m01, m10, m11):
+        self.m00 = m00
+        self.m01 = m01
+        self.m10 = m10
+        self.m11 = m11
+
+# multiply two 2x2 matrices
+def multiply(a, b):
+    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
+def matrix_pow(base, n):
+    result = Matrix2x2(1, 0, 0, 1)  # start with identity matrix
+    while n > 0:
+        if n % 2 == 1:  # if n is odd, multiply once
+            result = multiply(result, base)
+        base = multiply(base, base)  # square the base
+        n //= 2  # integer division
+    return result
+
+# get nth fibonacci number using matrix exponentiation
+def fibonacci_matrix(n):
+    if n == 0:
+        return 0  # edge case
+    base = Matrix2x2(1, 1, 1, 0)  # Fibonacci Q-matrix
+    result = matrix_pow(base, n - 1)
+    return result.m00  # top-left is F(n)
+
+# print first n fibonacci numbers
+if __name__ == "__main__":
+    n = 50
+    for i in range(n):
+        print(fibonacci_matrix(i), end=" ")
+    print()