Add solutions for part 1

projects/12/MathTest/Main.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/MathTest/Main.jack
+
+/** Test program for the OS Math class. */
+class Main {
+
+    /** Performs various mathematical operations, using calls to the Math class methods. */
+    function void main() {
+        var Array r;          // stores the test results;
+        
+        let r = 8000;
+    
+        let r[0] = 2 * 3;                  // 6
+        let r[1] = r[0] * (-30);           // 6 * (-30) = -180
+        let r[2] = r[1] * 100;             // (-180) * 100 = -18000
+        let r[3] = 1 * r[2];               // 1 * (-18000) = -18000
+        let r[4] = r[3] * 0;               // 0
+        
+        let r[5] = 9 / 3;                  // 3
+        let r[6] = (-18000) / 6;           // -3000
+        let r[7] = 32766 / (-32767);       // 0
+        
+        let r[8] = Math.sqrt(9);           // 3
+        let r[9] = Math.sqrt(32767);       // 181
+        
+        let r[10] = Math.min(345, 123);    // 123
+        let r[11] = Math.max(123, -345);   // 123
+        let r[12] = Math.abs(27);          // 27
+        let r[13] = Math.abs(-32767);      // 32767
+        
+        return;
+    }
+}

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 {
+
+    /** Initializes the library. */
+    function void init() {
+        return;
+    }
+
+    /** Returns the absolute value of x. */
+    function int abs(int x) {
+        if (x < 0) {
+            let x = -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;
+        var int i;
+        var int mask;
+        var int xShifted;
+
+        let sum = 0;
+        let i = 0;
+        let mask = 1;
+        let xShifted = x;
+
+        if (x = 1) {
+            return y;
+        }
+
+        if (y = 1) {
+            return x;
+        }
+
+        while (i < 16) { // 16 because we got a 16 bit architecture
+            if (y & mask) {
+                let sum = sum + xShifted;
+            }
+            let xShifted = xShifted + xShifted; // xShifted << 2;
+            let mask = mask + mask; // mask << 2;
+            let i = i + 1;
+        }
+
+        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;
+        var int sign;
+
+        let sign = 1;
+
+        if (x < 0) {
+            let x = -x;
+            let sign = -sign;
+        }
+
+        if (y < 0) {
+            let y = -y;
+            let sign = -sign;
+        }
+
+        if (y > x) {
+            return 0;
+        }
+
+        let q = x / (y + y);
+
+        if ((x - (2 * q * y)) < y) {
+            return (q + q) * sign;
+        } else {
+            return (q + q + 1) * sign;
+        }
+    }
+
+    /** Returns the integer part of the square root of x. */
+    function int sqrt(int x) {
+        var int y;
+        var int p;
+        var int s;
+        var int s2;
+
+        let y = 0;
+        let p = 128; // 2^7
+
+        while (p > 0) {
+            let s = y + p;
+            let s2 = s * s;
+            if ((s2 - 1) < x) {
+                if (s2 > 0) {
+                    let y = s;
+                }
+            }
+            let p = p / 2; // p >> 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;
+    }
+}

projects/12/MathTest/MathTest.cmp

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+|RAM[8000]|RAM[8001]|RAM[8002]|RAM[8003]|RAM[8004]|RAM[8005]|RAM[8006]|RAM[8007]|RAM[8008]|RAM[8009]|RAM[8010]|RAM[8011]|RAM[8012]|RAM[8013]|
+|       6 |    -180 |  -18000 |  -18000 |       0 |       3 |   -3000 |       0 |       3 |     181 |     123 |     123 |      27 |   32767 |

projects/12/MathTest/MathTest.tst

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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/MathTest/MathTest.tst
+
+load,
+output-file MathTest.out,
+compare-to MathTest.cmp,
+output-list RAM[8000]%D2.6.1 RAM[8001]%D2.6.1 RAM[8002]%D2.6.1 RAM[8003]%D2.6.1 RAM[8004]%D2.6.1 RAM[8005]%D2.6.1 RAM[8006]%D2.6.1 RAM[8007]%D2.6.1 RAM[8008]%D2.6.1 RAM[8009]%D2.6.1 RAM[8010]%D2.6.1 RAM[8011]%D2.6.1 RAM[8012]%D2.6.1 RAM[8013]%D2.6.1;
+
+repeat 1000000 {
+  vmstep;
+}
+
+output;