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; 
 }
 }
}

 
AAPL
$95.60
Apple Inc.
-2.55
MSFT
$43.16
Microsoft Corpora
-0.42
GOOG
$571.60
Google Inc.
-15.82

MacTech Search:
Community Search:

Software Updates via MacUpdate

OneNote 15.2 - Free digital notebook fro...
OneNote is your very own digital notebook. With OneNote, you can capture that flash of genius, that moment of inspiration, or that list of errands that’s too important to forget. Whether you’re at... Read more
iStat Menus 4.22 - Monitor your system r...
iStat Menus lets you monitor your system right from the menubar. Included are 8 menu extras that let you monitor every aspect of your system. Some features: CPU -- Monitor cpu usage. 7 display... Read more
Ember 1.8 - Versatile digital scrapbook....
Ember (formerly LittleSnapper) is your digital scrapbook of things that inspire you: websites, photos, apps or other things. Just drag in images that you want to keep, organize them into relevant... Read more
OmniPlan 2.3.6 - Robust project manageme...
With OmniPlan, you can create logical, manageable project plans with Gantt charts, schedules, summaries, milestones, and critical paths. Break down the tasks needed to make your project a success,... Read more
Command-C 1.1.1 - Clipboard sharing tool...
Command-C is a revolutionary app which makes easy to share your clipboard between iOS and OS X using your local WiFi network, even if the app is not currently opened. Copy anything (text, pictures,... Read more
Knock 1.1.7 - Unlock your Mac by knockin...
Knock is a faster, safer way to sign in. You keep your iPhone with you all the time. Now you can use it as a password. You never have to open the app -- just knock on your phone twice, even when it's... Read more
Mellel 3.3.6 - Powerful word processor w...
Mellel is the leading word processor for OS X and has been widely considered the industry standard since its inception. Mellel focuses on writers and scholars for technical writing and multilingual... Read more
LibreOffice 4.3.0.4 - Free Open Source o...
LibreOffice is an office suite (word processor, spreadsheet, presentations, drawing tool) compatible with other major office suites. The Document Foundation is coordinating development and... Read more
Freeway Pro 7.0 - Drag-and-drop Web desi...
Freeway Pro lets you build websites with speed and precision... without writing a line of code! With it's user-oriented drag-and-drop interface, Freeway Pro helps you piece together the website of... Read more
Drive Genius 3.2.4 - Powerful system uti...
Drive Genius is an OS X utility designed to provide unsurpassed storage management. Featuring an easy-to-use interface, Drive Genius is packed with powerful tools such as a drive optimizer, a... Read more

Latest Forum Discussions

See All

Dawn of the Immortals Review
Dawn of the Immortals Review By Jennifer Allen on July 31st, 2014 Our Rating: :: RESPECTABLE EXPLORATIONUniversal App - Designed for iPhone and iPad Dawn of the Immortals might not re-invent the wheel, but it does tweak it a little... | Read more »
80 Days Review
80 Days Review By Jennifer Allen on July 31st, 2014 Our Rating: :: EPIC ADVENTUREUniversal App - Designed for iPhone and iPad A fantastic and fascinating re-envisioning of the classic novel by Jules Verne, 80 Days is a delightful... | Read more »
Battleheart Legacy Guide
The world of Battleheart Legacy is fun and deep; full of wizards, warriors, and witches. Here are some tips and tactics to help you get the most enjoyment out of this great game. | Read more »
Puzzle Roo Review
Puzzle Roo Review By Jennifer Allen on July 31st, 2014 Our Rating: :: PUZZLE-BASED TWISTUniversal App - Designed for iPhone and iPad A different take on the usual block dropping puzzle game, Puzzle Roo is quite pleasant.   | Read more »
Super Crossfire Re-Release Super Crossfi...
Super Crossfire Re-Release Super Crossfighter Coming Soon, Other Radiangames Titles Go 50% Off Posted by Ellis Spice on July 31st, 2014 [ | Read more »
Hexiled Review
Hexiled Review By Rob Thomas on July 31st, 2014 Our Rating: :: HEX SELLSUniversal App - Designed for iPhone and iPad In space, no one can hear you… spell? Hexiled is a neat concept for a word scramble puzzle, but it doesn’t go too... | Read more »
Summoners War: Sky Arena Passes 10 Milli...
Summoners War: Sky Arena Passes 10 Million Installs! Posted by Jessica Fisher on July 31st, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »
Deep Loot Review
Deep Loot Review By Jennifer Allen on July 31st, 2014 Our Rating: :: DIVE DEEPUniversal App - Designed for iPhone and iPad Dive deep in this fun explore-em-up that’s a little grind heavy but ultimately quite entertaining.   | Read more »
Despicable Me: Minion Rush is One Year O...
Despicable Me: Minion Rush is One Year Old, Gets its Biggest Update Yet Posted by Jennifer Allen on July 31st, 2014 [ permalink ] Universal App - Designed for iPhone and iPad | Read more »
Fish & Shark Review
Fish & Shark Review By Jordan Minor on July 31st, 2014 Our Rating: :: FLAPPY FISHUniversal App - Designed for iPhone and iPad Fish & Shark’s beauty is only scale deep.   | Read more »

Price Scanner via MacPrices.net

Save up to $130 on an iPad mini with Apple re...
The Apple Store has Certified Refurbished 2nd generation iPad minis with Retina Displays available for up to $130 off the cost of new models, starting at $339. Apple’s one-year warranty is included... Read more
iPad Cannibalization Threat “Overblown”
Seeking Alpha’s Kevin Greenhalgh observes that while many commentators think Apple’s forthcoming 5.5-inch panel iPhone 6 will cannibalize iPad sales, in his estimation, these concerns are being... Read more
Primate Labs Releases July 2014 MacBook Pro P...
Primate Labs’ John Poole has posted Geekbench 3 results for most of the new MacBook Pro models that Apple released on Tuesday. Poole observes that overall performance improvements for the new MacBook... Read more
Apple Re-Releases Bugfixed MacBook Air EFI Fi...
Apple has posted a bugfixed version EFI Firmware Update 2.9 a for MacBook Air (Mid 2011) models. The update addresses an issue where systems may take longer to wake from sleep than expected, and... Read more
Save $50 on the 2.5GHz Mac mini, plus free sh...
B&H Photo has the 2.5GHz Mac mini on sale for $549.99 including free shipping. That’s $50 off MSRP, and B&H will also include a free copy of Parallels Desktop software. NY sales tax only. Read more
Save up to $140 on an iPad Air with Apple ref...
Apple is offering Certified Refurbished iPad Airs for up to $140 off MSRP. Apple’s one-year warranty is included with each model, and shipping is free. Stock tends to come and go with some of these... Read more
$250 price drop on leftover 15-inch Retina Ma...
B&H Photo has dropped prices on 2013 15″ Retina MacBook Pros by $250 off original MSRP. Shipping is free, and B&H charges NY sales tax only: - 15″ 2.3GHz Retina MacBook Pro: $2249, $250 off... Read more
More iPad Upgrade Musings – The ‘Book Mystiqu...
Much discussed recently, what with Apple reporting iPad sales shrinkage over two consecutive quarters, is that it had apparently been widely assumed that tablet users would follow a two-year hardware... Read more
13-inch 2.5GHz MacBook Pro on sale for $999,...
Best Buy has the 13″ 2.5GHz MacBook Pro available for $999.99 on their online store. Choose free shipping or free instant local store pickup (if available). Their price is $100 off MSRP. Price is... Read more
Save up to $300 on an iMac with Apple refurbi...
The Apple Store has Apple Certified Refurbished iMacs available for up to $300 off the cost of new models. Apple’s one-year warranty is standard, and shipping is free. These are the best prices on... Read more

Jobs Board

*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. Product Leader, *Apple* Store Apps - 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
Sr Software Lead Engineer, *Apple* Online S...
Sr Software Lead Engineer, Apple Online Store Publishing Systems Keywords: Company: Apple Job Code: E3PCAK8MgYYkw Location (City or ZIP): Santa Clara Status: Full Read more
Sr Software Lead Engineer, *Apple* Online S...
Sr Software Lead Engineer, Apple Online Store Publishing Systems Keywords: Company: Apple Job Code: E3PCAK8MgYYkw Location (City or ZIP): Santa Clara Status: Full Read more
*Apple* Solutions Consultant (ASC) - Apple (...
**Job Summary** The ASC is an Apple employee who serves as an Apple brand ambassador and influencer in a Reseller's store. The ASC's role is to grow Apple Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.