1 files changed, 98 insertions, 0 deletions
diff --git a/projects/12/Math.jack b/projects/12/Math.jack
index a57f023..61e09fc 100644
--- a/projects/12/Math.jack
+++ b/projects/12/Math.jack
@@ -8,13 +8,33 @@
  * Note: Jack compilers implement multiplication and division using OS method calls.
  */
 class Math {
+    static Array twoToThe;
 
     /** Initializes the library. */
     function void init() {
+        var int i, x;
+        let x = 1;
+        let i = 0;
+        let twoToThe = Array.new(16);
+        while (i < 16){
+            let twoToThe[i] = x;
+            let x = x + x;
+            let i = i + 1;
+        }
+        return;
+    }
+
+    function boolean bit(int x, int i) {
+        return ~(x & twoToThe[i] = 0);
     }
 
     /** Returns the absolute value of x. */
     function int abs(int x) {
+        if (x > 0){
+            return x;
+        } else {
+            return -x;
+        }
     }
 
     /** Returns the product of x and y. 
@@ -23,6 +43,18 @@ class Math {
      *  the Jack expressions x*y and multiply(x,y) return the same value.
      */
     function int multiply(int x, int y) {
+        var int z, res, shiftedX, i;
+        let shiftedX = x;
+        let i = 0;
+        let res = 0;
+        while ((twoToThe[i] > x) & (i < 16)) {
+            if (Math.bit(y, i)){
+                let res = res + shiftedX;
+            }
+            let shiftedX = shiftedX + shiftedX;
+            let i = i + 1;
+        }
+        return res;
     }
 
     /** Returns the integer part of x/y.
@@ -31,17 +63,83 @@ class Math {
      *  the Jack expressions x/y and divide(x,y) return the same value.
      */
     function int divide(int x, int y) {
+        var int ax, ay;
+        if (x > 0) {
+            if (y > 0) {
+                return Math.divide1(x, y);
+            } else {
+                return -Math.divide1(x, -y);
+            }
+        } else {
+            if (y > 0) {
+                return -Math.divide1(-x, y);
+            } else {
+                return Math.divide1(-x, -y);
+            }
+        }
+    }
+
+    function int divide1(int x, int y) {
+        var int q;
+        if (y = 0) {
+            do Output.printString("Error: division by zero.");
+            do Sys.error(0);
+        }
+        if ((y > x) | (y < 0)) {
+            return 0;
+        }
+        let q = Math.divide1(x, y * 2);
+        if (x - (2 * q * y) < y) {
+            return 2 * q;
+        } else {
+            return 2 * q + 1;
+        }
+    }
+
+    function int length(int x){
+        var int n;
+        let n = 14;
+        while (twoToThe[n] > x){
+            let n = n - 1;
+        }
+        return n;
     }
 
     /** Returns the integer part of the square root of x. */
     function int sqrt(int x) {
+        var int y, k, z, w;
+        if (x < 0) {
+            do Output.printString("Error: square rooting a negative number.");
+            do Sys.error(0);
+        }
+        let k = Math.length(x) / 2;
+        let y = 0;
+        while (~(k < 0)) {
+            let z = y + twoToThe[k];
+            let w = z * z;
+            if ((w < x) & (w > 0)) {
+                let y = z;
+            }
+            let k = k - 1;
+        }
+        return y;
     }
 
     /** Returns the greater number. */
     function int max(int a, int b) {
+        if (a > b) {
+            return a;
+        } else {
+            return b;
+        }
     }
 
     /** Returns the smaller number. */
     function int min(int a, int b) {
+        if (a < b) {
+            return a;
+        } else {
+            return b;
+        }
     }
 }