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;
+}

fib/fib.java

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+public class recursive {
+
+	public static int fibonacci(int max) {
+
+		if (max <= 1) {
+			return max;
+		}
+
+		else {
+			return fibonacci(max - 2) + fibonacci(max - 1);
+		}
+
+	}
+
+	public static void main(String[] args) {
+
+		int max = 10;
+		for (int i = 0; i < max; i++) {
+		    System.out.print(fibonacci(i) + " ");
+		}
+	}
+}

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()

fib/sfib.c

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+#include <stdio.h>
+typedef unsigned long long U;
+
+U fib(int n) {
+    if (n < 2) return n;
+    U a = 1, b = 1, c = 1, d = 0, x = 1, y = 0, z = 0, w = 1, t;
+    while (n) {
+        if (n & 1) {
+            t = x * a + y * c; y = x * b + y * d; x = t;
+            t = z * a + w * c; w = z * b + w * d; z = t;
+        }
+        t = a * a + b * c; b = a * b + b * d; a = t;
+        t = c * a + d * c; d = c * b + d * d; c = t;
+        n >>= 1;
+    }
+    return x;
+}
+
+int main(int argc, char **argv[]) {
+    for (int i = 0;i < int(argv);i++) printf("%llu ", fib(i));
+}
+