project12 - complete

12/Math.jack

@@ -15,6 +15,17 @@ class Math {
 
     // Initializes the Math library.
     function void init() {
+        var int i, val;
+        let n = 16;
+        let powersOfTwo = Array.new(n);
+        let i = 0;
+        let val = 1;
+        while (i < n) {
+            let powersOfTwo[i] = val;
+            let val = val + val;
+            let i = i + 1;
+        }
+        return;
     }
 
     /** Returns the product of x and y. 
@@ -22,6 +33,24 @@ class Math {
      *  in an expression, it handles it by invoking this method. 
      *  Thus, in Jack, x * y and Math.multiply(x,y) return the same value. */
     function int multiply(int x, int y) {
+        var int sum, shiftedX, i;
+        let sum = 0;
+        let shiftedX = x;
+        let i = 0;
+        
+        while (i < n) {
+            if (Math.bit(y, i)) {
+                let sum = sum + shiftedX;
+            }
+            let shiftedX = shiftedX + shiftedX;
+            let i = i + 1;
+        }
+        return sum;
+    }
+
+    /** Returns true if the i-th bit of x is 1, false otherwise */
+    function boolean bit(int x, int i) {
+        return ~((x & powersOfTwo[i]) = 0);
     }
 
     /** Returns the integer part of x / y.
@@ -29,21 +58,78 @@ class Math {
      *  an an expression, it handles it by invoking this method.
      *  Thus, x/y and Math.divide(x,y) return the same value. */
     function int divide(int x, int y) {
+        var int q;
+        var int absX, absY;
+        var int result;
+        var boolean neg;
+        
+        let neg = (x < 0) = (y > 0); // true if signs differ
+        let absX = Math.abs(x);
+        let absY = Math.abs(y);
+
+        if (absY > absX) {
+            return 0;
+        }
+        
+        // Handle overflow for 2*y
+        if ((absY + absY) < 0) {
+            let q = 0;
+        } else {
+            let q = Math.divide(absX, absY + absY);
+        }
+
+        if ((absX - (2 * q * absY)) < absY) {
+            let result = q + q;
+        } else {
+            let result = q + q + 1;
+        }
+
+        if (neg) {
+            return -result;
+        }
+        return result;
     }
 
     /** Returns the integer part of the square root of x. */
     function int sqrt(int x) {
+        var int y, j, approx, approxSq;
+        let y = 0;
+        let j = 7; // n/2 - 1 for n=16
+        
+        while (j > -1) {
+            let approx = y + powersOfTwo[j];
+            let approxSq = approx * approx;
+            
+            // Checks if approxSq > 0 (overflow check) and approxSq <= x
+            if (((approxSq > 0) | (approxSq = 0)) & ((approxSq < x) | (approxSq = x))) {
+                let y = approx;
+            }
+            let j = j - 1;
+        }
+        return y;
     }
 
     /** Returns the greater value. */
     function int max(int a, int b) {
+        if (a > b) {
+            return a;
+        }
+        return b;
     }
 
     /** Returns the smaller value. */
     function int min(int a, int b) {
+        if (a < b) {
+            return a;
+        }
+        return b;
     }
 
     /** Returns the absolute value of x. */
     function int abs(int x) {
+        if (x < 0) {
+            return -x;
+        }
+        return x;
     }
 }