diff options
| -rw-r--r-- | projects/12/Math.jack | 98 | ||||
| -rw-r--r-- | projects/12/MathTest/Main.vm | 162 | ||||
| -rw-r--r-- | projects/12/MathTest/Math.jack | 146 | ||||
| -rw-r--r-- | projects/12/MathTest/Math.vm | 446 | ||||
| -rw-r--r-- | projects/12/MathTest/MathTest.out | 2 |
5 files changed, 854 insertions, 0 deletions
diff --git a/projects/12/Math.jack b/projects/12/Math.jack index a57f023..61e09fc 100644 --- a/projects/12/Math.jack +++ b/projects/12/Math.jack @@ -8,13 +8,33 @@ * 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);
}
/** 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.
@@ -23,6 +43,18 @@ class Math { * the Jack expressions x*y and multiply(x,y) return the same value.
*/
function int multiply(int x, int y) {
+ var int z, res, shiftedX, i;
+ let shiftedX = x;
+ let i = 0;
+ let res = 0;
+ while ((twoToThe[i] > x) & (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.
@@ -31,17 +63,83 @@ class Math { * 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;
+ }
}
}
diff --git a/projects/12/MathTest/Main.vm b/projects/12/MathTest/Main.vm new file mode 100644 index 0000000..025f20c --- /dev/null +++ b/projects/12/MathTest/Main.vm @@ -0,0 +1,162 @@ +function Main.main 1 +push constant 8000 +pop local 0 +push constant 0 +push local 0 +add +push constant 2 +push constant 3 +call Math.multiply 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 1 +push local 0 +add +push constant 0 +push local 0 +add +pop pointer 1 +push that 0 +push constant 30 +neg +call Math.multiply 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 2 +push local 0 +add +push constant 1 +push local 0 +add +pop pointer 1 +push that 0 +push constant 100 +call Math.multiply 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 3 +push local 0 +add +push constant 1 +push constant 2 +push local 0 +add +pop pointer 1 +push that 0 +call Math.multiply 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 4 +push local 0 +add +push constant 3 +push local 0 +add +pop pointer 1 +push that 0 +push constant 0 +call Math.multiply 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 5 +push local 0 +add +push constant 9 +push constant 3 +call Math.divide 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 6 +push local 0 +add +push constant 18000 +neg +push constant 6 +call Math.divide 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 7 +push local 0 +add +push constant 32766 +push constant 32767 +neg +call Math.divide 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 8 +push local 0 +add +push constant 9 +call Math.sqrt 1 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 9 +push local 0 +add +push constant 32767 +call Math.sqrt 1 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 10 +push local 0 +add +push constant 345 +push constant 123 +call Math.min 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 11 +push local 0 +add +push constant 123 +push constant 345 +neg +call Math.max 2 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 12 +push local 0 +add +push constant 27 +call Math.abs 1 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 13 +push local 0 +add +push constant 32767 +neg +call Math.abs 1 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push constant 0 +return diff --git a/projects/12/MathTest/Math.jack b/projects/12/MathTest/Math.jack new file mode 100644 index 0000000..6bac42e --- /dev/null +++ b/projects/12/MathTest/Math.jack @@ -0,0 +1,146 @@ +// 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);
+ }
+
+ /** 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;
+ }
+ }
+}
diff --git a/projects/12/MathTest/Math.vm b/projects/12/MathTest/Math.vm new file mode 100644 index 0000000..dad8ff5 --- /dev/null +++ b/projects/12/MathTest/Math.vm @@ -0,0 +1,446 @@ +function Math.init 2 +push constant 1 +pop local 1 +push constant 0 +pop local 0 +push constant 16 +call Array.new 1 +pop static 0 +label WHILE_EXP0 +push local 0 +push constant 16 +lt +not +if-goto WHILE_END0 +push local 0 +push static 0 +add +push local 1 +pop temp 0 +pop pointer 1 +push temp 0 +pop that 0 +push local 1 +push local 1 +add +pop local 1 +push local 0 +push constant 1 +add +pop local 0 +goto WHILE_EXP0 +label WHILE_END0 +push constant 0 +return +function Math.bit 0 +push argument 0 +push argument 1 +push static 0 +add +pop pointer 1 +push that 0 +and +push constant 0 +eq +not +return +function Math.abs 0 +push argument 0 +push constant 0 +gt +if-goto IF_TRUE0 +goto IF_FALSE0 +label IF_TRUE0 +push argument 0 +return +goto IF_END0 +label IF_FALSE0 +push argument 0 +neg +return +label IF_END0 +function Math.multiply 3 +push argument 0 +pop local 1 +push constant 0 +pop local 2 +push constant 0 +pop local 0 +label WHILE_EXP0 +push local 2 +push constant 16 +lt +not +if-goto WHILE_END0 +push argument 1 +push local 2 +call Math.bit 2 +if-goto IF_TRUE0 +goto IF_FALSE0 +label IF_TRUE0 +push local 0 +push local 1 +add +pop local 0 +label IF_FALSE0 +push local 1 +push local 1 +add +pop local 1 +push local 2 +push constant 1 +add +pop local 2 +goto WHILE_EXP0 +label WHILE_END0 +push local 0 +return +function Math.divide 2 +push argument 0 +push constant 0 +gt +if-goto IF_TRUE0 +goto IF_FALSE0 +label IF_TRUE0 +push argument 1 +push constant 0 +gt +if-goto IF_TRUE1 +goto IF_FALSE1 +label IF_TRUE1 +push argument 0 +push argument 1 +call Math.divide1 2 +return +goto IF_END1 +label IF_FALSE1 +push argument 0 +push argument 1 +neg +call Math.divide1 2 +neg +return +label IF_END1 +goto IF_END0 +label IF_FALSE0 +push argument 1 +push constant 0 +gt +if-goto IF_TRUE2 +goto IF_FALSE2 +label IF_TRUE2 +push argument 0 +neg +push argument 1 +call Math.divide1 2 +neg +return +goto IF_END2 +label IF_FALSE2 +push argument 0 +neg +push argument 1 +neg +call Math.divide1 2 +return +label IF_END2 +label IF_END0 +function Math.divide1 1 +push argument 1 +push constant 0 +eq +if-goto IF_TRUE0 +goto IF_FALSE0 +label IF_TRUE0 +push constant 24 +call String.new 1 +push constant 69 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 111 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 58 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 100 +call String.appendChar 2 +push constant 105 +call String.appendChar 2 +push constant 118 +call String.appendChar 2 +push constant 105 +call String.appendChar 2 +push constant 115 +call String.appendChar 2 +push constant 105 +call String.appendChar 2 +push constant 111 +call String.appendChar 2 +push constant 110 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 98 +call String.appendChar 2 +push constant 121 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 122 +call String.appendChar 2 +push constant 101 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 111 +call String.appendChar 2 +push constant 46 +call String.appendChar 2 +call Output.printString 1 +pop temp 0 +push constant 0 +call Sys.error 1 +pop temp 0 +label IF_FALSE0 +push argument 1 +push argument 0 +gt +push argument 1 +push constant 0 +lt +or +if-goto IF_TRUE1 +goto IF_FALSE1 +label IF_TRUE1 +push constant 0 +return +label IF_FALSE1 +push argument 0 +push argument 1 +push constant 2 +call Math.multiply 2 +call Math.divide1 2 +pop local 0 +push argument 0 +push constant 2 +push local 0 +call Math.multiply 2 +push argument 1 +call Math.multiply 2 +sub +push argument 1 +lt +if-goto IF_TRUE2 +goto IF_FALSE2 +label IF_TRUE2 +push constant 2 +push local 0 +call Math.multiply 2 +return +goto IF_END2 +label IF_FALSE2 +push constant 2 +push local 0 +call Math.multiply 2 +push constant 1 +add +return +label IF_END2 +function Math.length 1 +push constant 14 +pop local 0 +label WHILE_EXP0 +push local 0 +push static 0 +add +pop pointer 1 +push that 0 +push argument 0 +gt +not +if-goto WHILE_END0 +push local 0 +push constant 1 +sub +pop local 0 +goto WHILE_EXP0 +label WHILE_END0 +push local 0 +return +function Math.sqrt 4 +push argument 0 +push constant 0 +lt +if-goto IF_TRUE0 +goto IF_FALSE0 +label IF_TRUE0 +push constant 40 +call String.new 1 +push constant 69 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 111 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 58 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 115 +call String.appendChar 2 +push constant 113 +call String.appendChar 2 +push constant 117 +call String.appendChar 2 +push constant 97 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 101 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 111 +call String.appendChar 2 +push constant 111 +call String.appendChar 2 +push constant 116 +call String.appendChar 2 +push constant 105 +call String.appendChar 2 +push constant 110 +call String.appendChar 2 +push constant 103 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 97 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 110 +call String.appendChar 2 +push constant 101 +call String.appendChar 2 +push constant 103 +call String.appendChar 2 +push constant 97 +call String.appendChar 2 +push constant 116 +call String.appendChar 2 +push constant 105 +call String.appendChar 2 +push constant 118 +call String.appendChar 2 +push constant 101 +call String.appendChar 2 +push constant 32 +call String.appendChar 2 +push constant 110 +call String.appendChar 2 +push constant 117 +call String.appendChar 2 +push constant 109 +call String.appendChar 2 +push constant 98 +call String.appendChar 2 +push constant 101 +call String.appendChar 2 +push constant 114 +call String.appendChar 2 +push constant 46 +call String.appendChar 2 +call Output.printString 1 +pop temp 0 +push constant 0 +call Sys.error 1 +pop temp 0 +label IF_FALSE0 +push argument 0 +call Math.length 1 +push constant 2 +call Math.divide 2 +pop local 1 +push constant 0 +pop local 0 +label WHILE_EXP0 +push local 1 +push constant 0 +lt +not +not +if-goto WHILE_END0 +push local 0 +push local 1 +push static 0 +add +pop pointer 1 +push that 0 +add +pop local 2 +push local 2 +push local 2 +call Math.multiply 2 +pop local 3 +push local 3 +push argument 0 +gt +not +push local 3 +push constant 0 +gt +and +if-goto IF_TRUE1 +goto IF_FALSE1 +label IF_TRUE1 +push local 2 +pop local 0 +label IF_FALSE1 +push local 1 +push constant 1 +sub +pop local 1 +goto WHILE_EXP0 +label WHILE_END0 +push local 0 +return +function Math.max 0 +push argument 0 +push argument 1 +gt +if-goto IF_TRUE0 +goto IF_FALSE0 +label IF_TRUE0 +push argument 0 +return +goto IF_END0 +label IF_FALSE0 +push argument 1 +return +label IF_END0 +function Math.min 0 +push argument 0 +push argument 1 +lt +if-goto IF_TRUE0 +goto IF_FALSE0 +label IF_TRUE0 +push argument 0 +return +goto IF_END0 +label IF_FALSE0 +push argument 1 +return +label IF_END0 diff --git a/projects/12/MathTest/MathTest.out b/projects/12/MathTest/MathTest.out new file mode 100644 index 0000000..8b5a504 --- /dev/null +++ b/projects/12/MathTest/MathTest.out @@ -0,0 +1,2 @@ +|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 | |