// 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;
    }
}