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projects/12/MathTest/Math.jack

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+// This file is part of www.nand2tetris.org
+// and the book "The Elements of Computing Systems"
+// by Nisan and Schocken, MIT Press.
+// File name: projects/12/Math.jack
+
+/**
+ * A library of commonly used mathematical functions.
+ * Note: Jack compilers implement multiplication and division using OS method calls.
+ */
+class Math {
+    static Array st;
+    static int division_tmp, f;
+
+    /** Initializes the library. */
+    function void init() {
+        var int a;
+        let st = Array.new(16);
+        let st[0] = 1;
+        while (a < 15){
+            let a = a + 1;
+            let st[a] = st[a - 1] + st[a - 1];
+        }
+        return;
+    }
+
+    /** Returns the absolute value of x. */
+    function int abs(int x) {
+        if (x > 0){
+            return x;
+            }
+        return -x;
+    }
+
+    /** Returns the product of x and y. 
+     *  When a Jack compiler detects the multiplication operator '*' in the 
+     *  program's code, it handles it by invoking this method. In other words,
+     *  the Jack expressions x*y and multiply(x,y) return the same value.
+     */
+    function int multiply(int x, int y) {
+        var int sum, temp, y_comp, i, neg;
+        let neg = ((x < 0) & (y > 0)) | ((x > 0) & (y < 0)); 
+        let x = Math.abs(x);
+        let y = Math.abs(y);
+        if (x < y){
+            let temp = x;
+            let x = y;
+            let y = temp;
+        }
+        if (y = 1){
+            if(neg){
+                return -x;
+            }
+            return x;
+        }
+        while((y_comp - 1) < (y - 1)){
+            if ((st[i] & y) > 0) {
+                let sum = sum + x;
+                let y_comp = y_comp + st[i];
+            }
+            let x = x + x;
+            let i = i + 1;
+        }
+        if(neg){
+            let sum = -sum;
+        }
+        return sum;
+    }
+
+    /** Returns the integer part of x/y.
+     *  When a Jack compiler detects the multiplication operator '/' in the 
+     *  program's code, it handles it by invoking this method. In other words,
+     *  the Jack expressions x/y and divide(x,y) return the same value.
+     */
+    function int divide(int x, int y) {
+        var int q, neg;
+        if (f = 0){
+            let division_tmp = 0;
+            let neg = ((x < 0) & (y > 0)) | ((x > 0) & (y < 0)); 
+            let x = Math.abs(x);  
+            let y = Math.abs(y); 
+            if (y = 0){
+                do Sys.error(3);
+            }
+            let f = 1;
+        }
+        if ((y > x) | (y < 0)){
+            return 0;
+        }
+        let q = divide(x, y + y);
+        let f = 0;
+        let q = Math.abs(q);
+        if ((q & 1) = 1){
+            let division_tmp = division_tmp + y + y;
+        }
+        if (x - division_tmp < y){
+            if (neg){
+                return -(q + q);
+            }
+            return q + q;
+        }
+        else{
+            if (neg){
+                return -(q + q + 1);
+            }
+            return q + q + 1;
+        }
+    }
+    
+    /** Returns the integer part of the square root of x. */
+    function int sqrt(int x) {
+        var int j, b, d, y;
+        
+        if (x < 0){
+            do Sys.error(4);
+            }
+        let j = 7;
+        while (j > -1){
+            let d = y + st[j];
+            let b = d * d;
+            if ((~(b > x)) & (b > 0)){
+                let y = d;
+            }
+            let j = j - 1;
+        }
+        return y;
+    }
+
+    /** Returns the greater number. */
+    function int max(int a, int b) {
+        if (a > b){
+            return a;
+            }
+        return b;
+    }
+
+    /** Returns the smaller number. */
+    function int min(int a, int b) {
+        if (a < b){
+            return a;
+            }
+        return b;
+    }
+}