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

Smultron 9.4.2 - Easy-to-use, powerful t...
Smultron 9 is an elegant and powerful text editor that is easy to use. Use it to create or edit any text document. Everything from a web page, a note or a script to any single piece of text or code.... Read more
Xcode 9.0 - Integrated development envir...
Xcode includes everything developers need to create great applications for Mac, iPhone, iPad, and Apple Watch. Xcode provides developers a unified workflow for user interface design, coding, testing... Read more
iShowU Instant 1.2.0 - Full-featured scr...
iShowU Instant gives you real-time screen recording like you've never seen before! It is the fastest, most feature-filled real-time screen capture tool from shinywhitebox yet. All of the features you... Read more
Apple Safari 11.0 - Apple's Web bro...
Note: The direct download link is currently unavailable. It is available in the OS X 10.12.6 release, as well as in the Apple Security Updates. Apple Safari is Apple's web browser that comes with... Read more
Typinator 7.3 - Speedy and reliable text...
Typinator turbo-charges your typing productivity. Type a little. Typinator does the rest. We've all faced projects that require repetitive typing tasks. With Typinator, you can store commonly used... Read more
ExpanDrive 6.0.16 - Access cloud storage...
ExpanDrive builds cloud storage in every application, acts just like a USB drive plugged into your Mac. With ExpanDrive, you can securely access any remote file server directly from the Finder or... Read more
coconutBattery 3.6.4 - Displays info abo...
With coconutBattery you're always aware of your current battery health. It shows you live information about your battery such as how often it was charged and how is the current maximum capacity in... Read more
NTFS 15.0.911 - $19.95
NTFS breaks down the barriers between Windows and macOS. Paragon NTFS effectively solves the communication problems between the Mac system and NTFS. Write, edit, copy, move, delete files on NTFS... Read more
Apple iOS 11 - The latest version of App...
iOS 11 sets a new standard for what is already the world’s most advanced mobile operating system. It makes iPhone better than before. It makes iPad more capable than ever. And now it opens up both to... Read more
BetterTouchTool 2.302 - Customize Multi-...
BetterTouchTool adds many new, fully customizable gestures to the Magic Mouse, Multi-Touch MacBook trackpad, and Magic Trackpad. These gestures are customizable: Magic Mouse: Pinch in / out (zoom... Read more

The best games to play while you wait fo...
SteamWorld Dig 2 is out this week on PC and Switch, and people are understandably excited. This clever series by Image and Form combines our favorite metroidvania mechanics with an esquisite universe, excellent storytelling, and true wit. While... | Read more »
Drag'n'Boom beginner's gu...
Have you ever wanted to burn and pillage a village as a bloodthirsty dragon? If you answered yes to that question, Drag'n'Boom offers you the perfect chance to do so, casting you as an adorable little dragon that wants to set humankind aflame. It... | Read more »
Thimbleweed Park (Games)
Thimbleweed Park 1.0.0 Device: iOS Universal Category: Games Price: $9.99, Version: 1.0.0 (iTunes) Description: A brand new adventure game from Ron Gilbert and Gary Winnick, creators of the classics Monkey Island and Maniac Mansion!... | Read more »
The best simulation games on mobile
There's nothing like a good sim -- from the seemingly ridiculous to the incredibly mundane, you can be there's a simulation game out there for your every whim. [Read more] | Read more »
INKS guide - how to create works of pinb...
INKS puts a clever new spin on everyone's favorite classic arcade game, pinball. The core mechanics are the same -- keep a little ball pinging around the board for as long as possible without letting it fall into the precarious holes in the board.... | Read more »
Warbands: Bushido (Games)
Warbands: Bushido 1.0 Device: iOS Universal Category: Games Price: $3.99, Version: 1.0 (iTunes) Description: Warbands:Bushido is a miniatures board game with cards, miniatures, dice and beautiful terrains to fight on, with both... | Read more »
The best mobile games like Divinity: Ori...
Divinity: Original Sin 2 launched this week to the excitement of RPG fans everywhere. The game, which derives a lot of of its story and mechanics from old-school isometric RPGs and Dungeons & Dragons, has unseated PlayerUnknown's... | Read more »
Iron Marines guide - beginner tips and t...
Iron Marines is a brilliant RTS title that feels a bit like Starcraft. It's got a sci-fi setting and some of the most spectacular strategy mechanics we've seen in mobile games to date. With that said, the RTS genre can be a bit tricky to break... | Read more »
The best new games we played this week -...
The work week can be tough, but on the bright side, it's almost overandthere are bunches of brand new games to try out this weekend. This week definitely makes up for last week's sleepiness ten-fold. We've got one of the finest RTS game on mobile... | Read more »
Through the Ages (Games)
Through the Ages 1.0.60 Device: iOS Universal Category: Games Price: $9.99, Version: 1.0.60 (iTunes) Description: The offical adaptation of Vlaada Chvátil’s strategy classic, the second best board game ever by Board Game Geek website... | Read more »

Price Scanner via MacPrices.net

Apple Refurbished 3TB Time Capsule for $279,...
Apple has Certified Refurbished 3TB Time Capsules available for $279 including free shipping plus Apple’s standard one-year warranty. Their price is $120 off MSRP. Read more
19% off Smart Battery Cases for iPhone 7
Amazon has both Black and White Smart Battery Cases for iPhone 7s available for $80.41 including free shipping. Their price is $18.59, or 19%, off MSRP. Read more
Back on sale: 10.5-inch 64GB iPad Pros for $5...
MacMall has 10.5″ 64GB Apple iPad Pros on sale again for $599 including free shipping. That’s $50 off MSRP and the lowest price available for this model from any reseller. Read more
Verizon offers Certified Preowned 16GB iPhone...
Verizon has the 16GB iPhone 6, Certified Preowned, available for $259.99 or $10.83 per month for 24 months. Service plan required. According to Verizon, “All CPO devices have been reconditioned to... Read more
Preorder new iPhone 8 at US Cellular, and tak...
Preorder the new iPhone 8 or iPhone 8 Plus at US Cellular, and take $50 off the prepaid price: – 64GB iPhone 8: $649.99 – 128GB iPhone 8: $799.99 – 64GB iPhone 8 Plus: $749.99 – 128GB iPhone 8 Plus... Read more
12-inch and 9-inch Apple iPad Pros, Certified...
Apple has Certified Refurbished 2016 12″ WiFi iPad Pros available starting at $589. An Apple one-year warranty is included with each model, and shipping is free: – 32GB 12″ iPad Pro WiFi: $589... Read more
QuickerTek Announces Solar PV Chargers for US...
Wichita, Kansas based QuickerTek has announced its new 30 Watt and 60 Watt USB Type-C Solar Juicz Chargers. These solar panels are the only products of their kind, featuring the USB 3.1 adapter cable... Read more
Apple refurbished 128GB iPhone 6s and 6s Plus...
Apple has Certified Refurbished 128GB iPhone 6s and 6s Plus’ available for up to $100 off the price of new models. Space Gray, Silver, Gold, and Rose Gold models are available. Each phone comes... Read more
13-inch 2.3GHz Silver MacBook Pros on sale fo...
B&H Photo has 2017 13″ 2.3GHz Silver MacBook Pros in stock today and on sale for $100 off MSRP, each including free shipping plus NY & NJ sales tax only: – 13-inch 2.3GHz/128GB Silver... Read more
12-inch 64GB iPad Pros available for $749, $5...
MacMall has 12″ 64GB iPad Pros on sale for $749 including free shipping. Their price is $50 off MSRP. Read more

Jobs Board

Development Operations and Site Reliability E...
Development Operations and Site Reliability Engineer, Apple Payment Gateway Job Number: 57572631 Santa Clara Valley, California, United States Posted: Jul. 27, 2017 Read more
*Apple* Solutions Consultant - Apple Inc. (U...
…about helping others on a team while also delighting customers? As an Apple Solutions Consultant (ASC), you will discover customers needs and help connect them Read more
Software/Data Engineer, *Apple* Media Produ...
Job Summary Apple Media Products is the team behind the App Store, Apple Music, iTunes, and many other high profile products on iPhone, Mac and AppleTV. Our Data Read more
SW Engineer , *Apple* Media - Apple Inc. (U...
Job Summary Our team is responsible for exposing Apple Media content and services to the world, and building the infrastructure for next generation internal and Read more
*Apple* Data Center Site Selection and Strat...
Job Summary As Apple 's products and services scale the globe, the Data Center Affairs team works behind the scenes to secure infrastructure for Apple 's data Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.