From 17c169707a1efc2d576e1b03d2956b0b4be4135d Mon Sep 17 00:00:00 2001 From: Yuchen Pei Date: Wed, 17 Jan 2018 09:02:30 +0100 Subject: finished Math.jack --- projects/12/Math.jack | 98 +++++++++ projects/12/MathTest/Main.vm | 162 ++++++++++++++ projects/12/MathTest/Math.jack | 146 +++++++++++++ projects/12/MathTest/Math.vm | 446 ++++++++++++++++++++++++++++++++++++++ projects/12/MathTest/MathTest.out | 2 + 5 files changed, 854 insertions(+) create mode 100644 projects/12/MathTest/Main.vm create mode 100644 projects/12/MathTest/Math.jack create mode 100644 projects/12/MathTest/Math.vm create mode 100644 projects/12/MathTest/MathTest.out 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 | -- cgit v1.2.3