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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 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);
}
function int sign(int x) {
if (x > 0) {
return 1;
} else {
if (x < 0) {
return -1;
} else {
return 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.
* 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 res, shiftedX, i;
let shiftedX = x;
let i = 0;
let res = 0;
//while ((~(twoToThe[i] > y)) & (i < 16)) {
while (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.
* 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 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;
}
}
}
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