TweetFollow Us on Twitter

MPW Calculator
Volume Number:9
Issue Number:1
Column Tag:Jörg's Folder

MPW Calculator Tool in C++

An MPW tool written in bare bones C++ - not with MacApp.

By Jörg Langowski, MacTech Magazine Regular Contributing Author

Note: Source code files accompanying this article are located on MacTech CD-ROM or source code disks.

After a long break, you’ll find another C++ example in my column. Not with MacApp - we’re going back to the basics here and show a simple ‘bare C++’ program that executes as an MPW tool, or in the Simple Input/Output Window environment (SIOW) provided by Apple.

I came across this example reading a book on C++, “Programming in C++”, by Stephen Dewhurst and Kathy Stark (1989, Prentice Hall). I very much recommend this book for those of you who want to get the basic notions of C++ and an idea of its ‘programming flavor’. It may be not as comprehensive as the “C++ programming language” by Stroustrup (Addison-Wesley), or as the manuals that come with Apple’s C++ compiler; but it contains a lot of examples and exercises.

One classic exercise in computer science is to write a parser for algebraic expressions, that is, a program that takes an input string like

(3 + 5) * (-4 + (2 - 9))

and calculates the result of this expression. In fact, what you do to compute that expression is to convert it into an internal representation, and then evaluate that representation.

You can represent the expression given above by a linked list:

where each node of the list either contains an operator or a number. Once the arithmetic expression is given in list form, evaluating it is easy and can be done in a straightforward, object oriented way. Suppose you define a class node (also in listing):

class node {
 protected:
 
 node() {}
 public:
 virtual ~node() {}
 virtual int set (int)
 { cout << "Error: node::set(int) undefined" << eoln;
  return 0;} 
 virtual int eval() 
 { cout << "Error: node::eval() undefined" << eoln; 
 return 0;} 
};

where the constructor and destructor do nothing at the moment; they will have to be overridden by the derived node classes. There are two more virtual methods: eval(), which returns the value of the node, and set(), which can ‘set something’ in the node if defined in a subclass. For the base class, the methods just print error messages and return zero. These methods will be overridden, and they are virtual because we want their behavior to be determined at run time. That is, if we define a pointer mynode *node and assign it an object of a subclass of node, the actual eval() or set() methods used will be the ones corresponding to the subclass of the object that the pointer contains.

We now define two types of subclasses of node: dyadic operators and other stuff. All dyadic operators will be derived from the subclass :

class dyad : public node {
 protected:
 node *left, *right;
 dyad(node *l, node *r) {left=l; right=r;}
 ~dyad() {delete left; delete right;}
};

dyad only defines the two nodes that the operator connects: the constructor assigns these two nodes to two instance variables, and the destructor deletes them again. The classes derived from dyad define the four arithmetic operations, and the assignment (see listing). For example, addition is defined as:

class plus : public dyad {
 public:
 plus(node *l, node *r) : dyad(l,r) {}
 int eval() { return left->eval() + right->eval();} 
};

where the constructor just calls the superclass constructor, and

eval() returns the value of the sum of the values of the left and right hand side of the plus operation.

For the ‘expression tree’ shown above, you need one more class: numbers, which are ‘end nodes’ of the list. Thus, they do not contain pointers to other nodes, but an integer value in an instance variable. Their constructor assigns the value, and their eval() method simply returns it:

class inumber : public node {
 int value;
 public:
 inumber(int v) {value = v;}
 int eval() {return value;}
};

Finally, the unary minus operator (uminus in the listing) will return the negative value of the node that it points to.

The listing contains two more node classes: variables (id) and the assignment operator (equals), Variables contain a pointer to the head of a symbol table, and a pointer to the entry of this variable into the symbol table. The symbol table is a linked list of entries, and the pointer to its head is a static class variable. This means that, unlike instance variables, the pointer is not created again for every object of the class, but only one copy exists. Thus, all objects of this class reference the same symbol table, which is just what you want.

Assume we create a new node for a variable with its name given by the *char pointer nm. The constructor then first looks up the name in the symbol table (see listing, method look); if it is already there, it will put a pointer to the symbol table entry in the instance variable ent of the node. Otherwise, it will add a new entry to the symbol table, put its pointer into ent, make the new entry the head of the list, and change the (static) pointer so that it references the new head. All other variable objects will now have an updated reference to the symbol table.

A variable is assigned a value by the assignment operation equals. When an equals node is created, its right and left hand sides are set just as for the arithmetic operations; when its eval() method is called, the variable on the left hand side is set to the result of the right hand side. No check is done whether the left hand side is really a node of class id; but only those nodes contain a set method. The assignment operation also returns a value (just as in C), the right hand side of the statement.

So now we have defined a syntax tree for simple arithmetic expressions with assignment of variables. If, lets say, root is the pointer to the root of this tree (the times symbol in the drawing), and we call root->eval(), the result returned should be the value of the expression, in our case (3 + 5) * (-4 + (2 - 9)) = -88. With the class definitions given so far, this should work. But how do we set up the syntax tree in the first place? We need a routine, an expression parser, that takes the string expression and constructs the tree from it.

In order to write the parser, we first need to formalize the syntax of our simple arithmetic expressions. Such a formal description would for instance look like this:

<expression> :== <term> { [+|-] <term> }
<term>   :== <factor> { [*|/] <factor> }
<factor> :== <identifier> | <inumber> |
 (<expression >) | -<factor> |
 <identifier> = <expression>

We then define three parser routines that return an object of class node: e(), t(), and f(), returning, respectively, a pointer to an expression, a term, and a factor. Each of these routines makes repeated calls to another routine scan(), which gets the next token from the input stream. A token is a separate syntactic element, such as an open or close bracket, an arithmetic operator, a number or an identifier. scan() returns a character value, either the ascii value of a symbol if the token consists of one symbol, or a special value > 127. For the special values ID and INT, additional information can be found in a static char variable; this string will be used for the value of a number or the name of a variable. Other possible values are BAD (the scanner found something it couldn’t interpret), or EOLN (end of line found).

The first of the three parser routines, e(), is called from the main program (see listing for main()). On entry, one token has been read from the input stream; then e() tries to parse the input into a valid arithmetic expression and assign a pointer to its syntax tree to root. It does so by calling t() (see listing), which makes a term out of one or several factors by calling f(), just like e() makes the expression out of one or several term. When e() encounters a plus or minus sign after a term, is makes a new plus resp. minus node which connects the first term with the next one. Same for t(); here eventually a times or divide node is made, which connects two factors. f(), finally, will look for a number or identifier token and return a pointer to the corresponding node; or it might find an open bracket or a minus sign, after which a new expression or a factor have to follow. When all these recursive calls have been evaluated and no syntax errors have been found, the top-level e() returns the expression’s syntax tree.

In order to get the value of the expression, all we have to do then is call root->eval(), and the syntax tree will be evaluated as described above.

As long as no syntax errors are found, the main program loops continuously and asks for new expressions; the names and values of identifiers are remembered from one evaluation to the next, so you can play around with stored values a little.

As you may imagine, it is not too difficult to add on to this extremely simple calculator program e.g. to implement exponentiation or to include functions like exp(), log() etc. The constructed syntax tree could also serve in a bigger program as an internal representation of a function that the user has typed in and that has to be evaluated a lot of times (and computed fast). One could even imagine to generate real machine code out of the syntax tree, which makes this program some kind of a rudimentary compiler. We’ll add to the example during the next columns.

On the source code disk, I have compiled two versions of the program, one as an MPW tool, and the other one using the Simple Input/Output Window mechanism. Actually, the only thing that has to be changed is the linking. The MPW sequence to create the two versions of the program look like the following:

cplus calc.cp
Link -w -c 'MPS ' -t MPST 
 calc.cp.o 
 "{CLibraries}"StdCLib.o 
 "{Libraries}"ToolLibs.o 
 "{Libraries}"Runtime.o 
 "{Libraries}"Interface.o 
 "{CLibraries}"CPlusLib.o 
 -o calc

Rez -a "{MPW}"Interfaces:Rincludes:SIOW.r -o calcAppl
Link -w -c 'JLMT' -t 'APPL' 
 calc.cp.o 
 "{CLibraries}"StdClib.o 
 "{MPW}"Libraries:Libraries:SIOW.o 
 "{Libraries}"Runtime.o 
 "{Libraries}"Interface.o 
 "{CLibraries}"CPlusLib.o 
 -o calcAppl

So the second version can be run also by those of you who don’t have MPW.

FORTHcoming

I’m still waiting for those MacForth contributions coming in we’d really like to see more of that in MacTutor. I’m sure there are quite a few of you satisfied MacForth users who have something interesting to write about. Please contact me: I promise that you get your space in this column. My network address has changed in the meantime, since our institute is going from the Bitnet to the Internet world; so in the future, please send messages to either of those three addresses (in order of preference):

 jl@macjl.embl-grenoble.fr
 langowski.j@applelink.apple.com
 langowsk@titan.embl-grenoble.fr 

(note the missing last letter in the name)

Meanwhile, we do have news from the Forth world. I don’t have to tell you that the NEON successor, Yerk, keeps being updated faster than I can write about it; you know that you can get the current version by ftp from oddjob.uchicago.edu. Mops, the NEON lookalike with real 680x0 machine code, can also be found there.

But here is something very interesting for those of you who used and liked Mach2, the Forth in which I did most of my examples here: Two users of Mach2, John Fleming who works at Motorola, and Steven Wiley, a molecular biologist at the University of Utah, got together and made all those modifications to Mach2 that the implementers should have done two years ago; now it is System7 and 32-bit compatible. It may also be soon in the public domain (non-commercial) like Yerk is, with the full source code available. You’ll hear more about it in one of the next columns. Until then.

Listing: The MPW calculator tool
// 
// calc.cp
//
// a simple calculator program
// based on an example from Dewhurst/Stark
// "Programming in C++"
//
// J. Langowski November 1992
//

#include <Ctype.h>
#include <StdIO.h>
#include <String.h>
#include <Stream.h>
#include <StdLib.h>

#define NIL 0

// basic syntax tree structure
//
class node {
 protected:
 node() {}
 public:
 virtual ~node() {}
 virtual int set (int)
 { cout << "Error: node::set(int) undefined" << eoln;
  return 0;} 
 virtual int eval() 
 { cout << "Error: node::eval() undefined" << eoln; 
 return 0;} 
};

class dyad : public node {
 protected:
 node *left, *right;
 dyad(node *l, node *r) {left=l; right=r;}
 ~dyad() {delete left; delete right;}
};
// operators
//
class plus : public dyad {
 public:
 plus(node *l, node *r) : dyad(l,r) {}
 int eval() { return left->eval() + right->eval();} 
};

class minus : public dyad {
 public:
 minus(node *l, node *r) : dyad(l,r) {}
 int eval() { return left->eval() - right->eval();}
};

class times : public dyad {
 public:
 times(node *l, node *r) : dyad(l,r) {}
 int eval() { return left->eval() * right->eval();}
};

class divide : public dyad {
 public:
 divide(node *l, node *r) : dyad(l,r) {}
 int eval() { return left->eval() / right->eval();}
};

class uminus : public node {
 node *operand;
 public:
 uminus(node *o) {operand = o;}
 ~uminus() {delete operand;}
 int eval() {return -operand->eval();}
};

class inumber : public node {
 int value;
 public:
 inumber(int v) {value = v;}
 int eval() {return value;}
};


// identifier table
//
class id;

class entry {
 char *name;
 int value;
 entry *next;
 entry (char *nm, entry *n) {
 name = strcpy (new char[strlen(nm) + 1], nm);
 value = 0;
 next = n;
 }
 friend id;
};

class id : public node {
 static entry *symtab;
 entry *ent;
 entry *look(char *);
 public:
 id(char *nm) {ent = look(nm);}
 int set(int i) {return ent->value = i;}
 int eval() {return ent->value;}
};

entry *id::look(char *nm) {
 for(entry *p = symtab; p; p = p->next)
 if(strcmp(p->name,nm) == 0) return p;


 return symtab = new entry(nm,symtab);
}

entry *id::symtab = NIL;

// assignment
//
class equals : public dyad {
 public:
 equals(node *t,node *e) : dyad(t,e) {}
 int eval()
 { return left->set(right->eval()); }
};


// parsing + evaluation
//

static char token;   // current token 
static char line[81];   // for reading identifiers + numbers
enum {ID = char(128), INT, EOLN, BAD}; // special tokens

node *e(), *t(), *f();    // parser routines 
 // for expression, term, factor

// input stream scanner, returns next token
//
char scan() {
 char c;
 while (1)
 switch (c = cin.get()) {
 case '+': case '-': case '*': case '/':
 case '(': case ')': case '=':
 return c;
 case ' ': case '\t':
 continue;
 case '\n': case '\r':
 return EOLN;
 default:
 if (isdigit(c)) {
 char *s = line;
 do*s++ = c;
 while(isdigit(c = cin.get()));
 *s = '\0'; 
 // terminate string just read
 cin.putback(c); 
 // had read one too much
 return INT;
 }
 
 if (isalpha(c)) {
 char *s = line;
 do*s++ = c;
 while(isalnum(c = cin.get()));
 *s = '\0'; 
 // terminate string just read
 cin.putback(c); 
 // had read one too much
 return ID;
 }
 
 return BAD; 
 // if nothing fits, syntax error
 }
}

// simple error routine
//
void error() { cout << "Syntax error." << endl; exit(255); }

// parser routines for expression, term, factor
//

// expression = term (+ -) term
node *e() {
 node *root = t();
 while (1)
 switch (token) {
 case '+':
 token = scan();
 root = new plus(root, t()); 
 break;
 case '-':
 token = scan();
 root = new minus(root, t());
 break;
 default:
 return root;
 }
}

// term = factor (* /) factor
node *t() {
 node *root = f();
 while (1)
 switch (token) {
 case '*':
 token = scan();
 root = new times(root, t()); 
 break;
 case '/':
 token = scan();
 root = new divide(root, t()); 
 break;
 default:
 return root;
 }
}

// factor = identifier | number | expression | -factor
node *f() {
 node *root = NIL;
 switch (token) {
 case ID:
 root = new id(line);
 token = scan();
 if (token == '=') {
 token = scan();
 root = new equals(root, e());
 }
 return root;
 case INT:
 root = new inumber(atoi(line));
 token = scan();
 return root;
 case '(':
 token = scan();
 root = e();
 if (token != ')' ) error();
 token = scan();
 return root;
 case '-':
 token = scan();
 return new uminus(f());
 default:
 error();
 }
}

// main program
//

void main() {
 node *root = NIL;
 while (1) {
 cout << "Enter expression: " << endl;
 token = scan();
 root = e();

 if (token == BAD) error();
 
 if (root != NIL)
 { 
     cout << "Result = " << root->eval() << endl;
     delete root; 
 }
 }
}

 

Community Search:
MacTech Search:

Software Updates via MacUpdate

Parallels Desktop 10.2.0 - Run Windows a...
Parallels Desktop is simply the world's bestselling, top-rated, and most trusted solution for running Windows applications on your Mac. With Parallels Desktop for Mac, you can seamlessly run both... Read more
LaunchBar 6.2 - Powerful file/URL/email...
LaunchBar is an award-winning productivity utility that offers an amazingly intuitive and efficient way to search and access any kind of information stored on your computer or on the Web. It provides... Read more
Firefox 37.0 - Fast, safe Web browser. (...
Firefox offers a fast, safe Web browsing experience. Browse quickly, securely, and effortlessly. With its industry-leading features, Firefox is the choice of Web development professionals and casual... Read more
Arq 4.11 - Online backup to Google Drive...
Arq is super-easy online backup for the Mac. Back up to your own Google Drive storage (15GB free storage), your own Amazon Glacier ($.01/GB per month storage) or S3, or any SFTP server. Arq backs up... Read more
MacFamilyTree 7.3.4 - Create and explore...
MacFamilyTree gives genealogy a facelift: it's modern, interactive, incredibly fast, and easy to use. We're convinced that generations of chroniclers would have loved to trade in their genealogy... Read more
Yummy FTP 1.10.2 - FTP/SFTP/FTPS client...
Yummy FTP is an FTP + SFTP + FTPS file transfer client which focuses on speed, reliability and productivity. Whether you need to transfer a few files or a few thousand, schedule automatic backups, or... Read more
VueScan 9.5.08 - Scanner software with a...
VueScan is a scanning program that works with most high-quality flatbed and film scanners to produce scans that have excellent color fidelity and color balance. VueScan is easy to use, and has... Read more
Iridient Developer 3.0.1 - Powerful imag...
Iridient Developer (was RAW Developer) is a powerful image conversion application designed specifically for OS X. Iridient Developer gives advanced photographers total control over every aspect of... Read more
Monodraw 0.8.4.1 - Powerful ASCII art ed...
Monodraw allows you to easily create text-based art (like diagrams, layouts, flow charts) and visually represent algorithms, data structures, binary formats and more. Because it's all just text, it... Read more
Air Video Server HD 2.1.0 - Stream video...
Air Video Server HD streams videos instantly from your computer on your iPhone, iPad, iPod touch or Apple TV. No need to worry about converting or transferring files. We took everything that was... Read more

Marvel Mighty Heroes, the Ultimate Marve...
DeNA and Marvel Entertainment have brought us a new action-packed brawler: Marvel Mighty Heroes. You can play with up to four of your friends as you favorite marvel heroes like Iron Man, Thor, Spider-Man, Captain America, Star-Lord, Hulk, and... | Read more »
Take Note - The Jot Script 2 Evernote Ed...
Adonit's Jot Script 2 sylus has an all-new edition that's meant to be Evernote's BFF. The sylus has been redesigned to work better with iPads and give you faster stroke tracking, smoother line rendering, and better tip-to-line accuracy. | Read more »
INFINIT Lets Mobile Users Send Files of...
Infinit  is a file sharing app that ignores file size limits. It maintains the original quality of your photos and videos so you can be sure they look awesome after sending. You can move entire albums of photos or full HD films from your iPhone to... | Read more »
Serious Sam Double D Developer is Making...
There's nothing like the thrill of watching a horse race, especially when the horses are drunk.  | Read more »
2K Announces WWE 2K, Mobile's First...
It seems like this month has been pretty big for wrestling. First Wrestlemania, then 2K has announces that they're releasing  WWE 2K for iOS. It's a simulation-based WWE game where you'll get to play with several WWE superstars such as John Cena, ... | Read more »
How the Apple Watch Could Change the Fac...
The Apple Watch is still a ways out, but my previous musings on the wearable’s various features got me thinking: what might it be like a year after launch? Two years? Five years? What if it becomes a symbiotic part of the iOS framework to the point... | Read more »
You Can Start Challenging Your Friends t...
Last year we reported that Sebastian Gosztyla's new game, Dual, was theorized to be released sometime during the summer of 2014. Sadly that did not become a reality, but the good news it there is now an official release date. | Read more »
Forgotten Memories : Alternate Realities...
Forgotten Memories : Alternate Realities, from Psychoz Interactive, is planned for release on April 23. The Resident Evil, Silent Hill, and Alone in the Dark inspired horror game puts you in the shoes of Rose Hawkins as she searches for a missing... | Read more »
Pie In The Sky: A Pizza Odyssey (Games)
Pie In The Sky: A Pizza Odyssey 1.0 Device: iOS Universal Category: Games Price: $2.99, Version: 1.0 (iTunes) Description: A game about delivering pizza. In space. | Read more »
Chosen Gives Hopeful Singers, Songwriter...
If YouTube videos and reality TV shows like The Voice have taught us one thing, it’s that there are a lot of people out there who are anxious to show the world their talents. And if they’ve taught us a second thing, it’s that there’s an almost... | Read more »

Price Scanner via MacPrices.net

Will Microsoft’s Surface 3 Give The 12-inch M...
The more I ruminate over the new 12-inch MacBook, the more it occurs that it’s probably going to be more of a cannibalization threat to high-end iPads (including a new 12-inch ‘Pad when/if that... Read more
13-inch 2.4GHz Retina MacBook Pro available f...
MacMall has the 2013 13″ 2.4GHz/128GB Retina MacBook Pro available for $949.99 for a limited time. Shipping is free. Their price is $350 off original MSRP, and it’s the only sub-$1000 new Retina... Read more
Adobe Brings Powerful Layout-Design Capabilit...
Adobe today announced the availability of Adobe Comp CC, a free iPad app that enables rapid creation of layout concepts for mobile, Web and print projects. With Comp CC, designers can rough out and... Read more
13-inch 2.6GHz/256GB Retina MacBook Pro avail...
Best Buy has clearance 2014 13″ 2.6GHz/256GB Retina MacBook Pros available for $1199.99 including free shipping. Their price is $300 off original MSRP, and it’s the lowest price for this model.... Read more
Updated Mac Price Trackers
We’ve updated our Mac Price Trackers with the latest information on prices, bundles, and availability on systems from Apple’s authorized internet/catalog resellers: - 15″ MacBook Pros - 13″ MacBook... Read more
21-inch 1.4GHz iMac on sale for $999, save $1...
Best Buy has the 21″ 1.4GHz iMac on sale for $999.99 on their online store. Choose free shipping or free local store pick up. Price is for online orders only, in-store prices may vary. Their price is... Read more
2.6GHz Mac mini on sale for $649, save $50
Amazon has the 2.6GHz Mac mini on sale for $649.99 including free shipping. Their price is $50 off MSRP, and it’s the lowest price available for this model. Read more
Textkraft Professional 3.2 Powerful iPad Text...
Finally it’s springtime, at least theoretically in my neck of the woods, where we’re still navigating canyons between towering snowbanks with temperatures well below freezing in winter weather that... Read more
Apple offering refurbished 27-inch 5K iMacs f...
The Apple Store is offering Apple Certified Refurbished 27″ 3.5GHz 5K iMacs for $2119 including free shipping. Their price is $380 off the price of new models, and it’s the lowest price available for... Read more
16GB iPad mini on sale for $199, save $50
Walmart has 16GB iPad minis (1st generation) available for $199.99 on their online store, including free shipping. Their price is $50 off MSRP. Online orders only. Read more

Jobs Board

DevOps Software Engineer - *Apple* Pay, iOS...
**Job Summary** Imagine what you could do here. At Apple , great ideas have a way of becoming great products, services, and customer experiences very quickly. Bring Read more
*Apple* Retail - Multiple Positions (US) - A...
Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, you're also the Read more
Sr. Technical Services Consultant, *Apple*...
**Job Summary** Apple Professional Services (APS) has an opening for a senior technical position that contributes to Apple 's efforts for strategic and transactional Read more
Lead *Apple* Solutions Consultant - Retail...
**Job Summary** Job Summary The Lead ASC is an Apple employee who serves as the Apple business manager and influencer in a hyper-business critical Reseller's store Read more
*Apple* Pay - Site Reliability Engineer - Ap...
**Job Summary** Imagine what you could do here. At Apple , great ideas have a way of becoming great products, services, and customer experiences very quickly. Bring Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.