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

Tidy Up 5.3.7 - Find duplicate files and...
Tidy Up is a full-featured duplicate finder and disk-tidiness utility. Features: Supports Lightroom: it is now possible to search and collect duplicates directly in the Lightroom library. Multiple... Read more
Pinegrow 5.97 - Mockup and design web pa...
Pinegrow (was Pinegrow Web Designer) is desktop app that lets you mockup and design webpages faster with multi-page editing, CSS and LESS styling, and smart components for Bootstrap, Foundation,... Read more
BlueStacks 4.210.0 - Run Android applica...
BlueStacks App Player lets you run your Android apps fast and fullscreen on your Mac. Feature comparison chart How to install Bluestacks on your Mac Go to MacUpdate and click the green "Download"... Read more
WhatsApp 2.2027.10 - Desktop client for...
WhatsApp is the desktop client for WhatsApp Messenger, a cross-platform mobile messaging app which allows you to exchange messages without having to pay for SMS. WhatsApp Messenger is available for... Read more
Art Text 4.0.1 - $29.99
Art Text is graphic design software specifically tuned for lettering, typography, text mockups and various artistic text effects. Supplied with a great variety of ready to use styles and materials,... Read more
Adobe Dreamweaver CC 2020 20.2 - Build w...
Dreamweaver CC 2020 is available as part of Adobe Creative Cloud for as little as $20.99/month (or $9.99/month if you're a previous Dreamweaver customer). Adobe Dreamweaver CC 2020 allows you to... Read more
Adobe Acrobat DC 20.009.20074 - Powerful...
Acrobat DC is available only as a part of Adobe Creative Cloud, and can only be installed and/or updated through Adobe's Creative Cloud app. Adobe Acrobat DC with Adobe Document Cloud services is... Read more
beaTunes 5.2.10 - Organize your music co...
beaTunes is a full-featured music player and organizational tool for music collections. How well organized is your music library? Are your artists always spelled the same way? Any R.E.M. vs REM?... Read more
DiskCatalogMaker 8.1.5 - Catalog your di...
DiskCatalogMaker is a simple disk management tool which catalogs disks. Simple, light-weight, and fast Finder-like intuitive look and feel Super-fast search algorithm Can compress catalog data for... Read more
Meteorologist 3.4.1 - Popular weather ap...
Meteorologist is a simple interface to weather provided by weather.com. It provides the ability to show the weather in the main menu bar, displaying more detail in a pop-up menu, whose contents are... Read more

Latest Forum Discussions

See All

Steam Link Spotlight - Disco Elysium
Steam Link Spotlight is a feature where we look at PC games that play exceptionally well using the Steam Link app. Our last entry was Signs of the Sojourner Read about how it plays using Steam Link over here. | Read more »
Distract Yourself With These Great Mobil...
There’s a lot going on right now, and I don’t really feel like trying to write some kind of pithy intro for it. All I’ll say is lots of people have been coming together and helping each other in small ways, and I’m choosing to focus on that as I... | Read more »
Pokemon Go's July Community Day wil...
Pokemon Go developers have announced the details concerning the upcoming Gastly Community Day. This particular event was selected by the players of the game after the Gas Pokemon came in second place after a poll that decided which Pokemon would... | Read more »
Clash Royale: The Road to Legendary Aren...
Supercell recently celebrated its 10th anniversary and their best title, Clash Royale, is as good as it's ever been. Even for lapsed players, returning to the game is as easy as can be. If you want to join us in picking the game back up, we've put... | Read more »
Detective Di is a point-and-click murder...
Detective Di is a point-and-click murder mystery set in Tang Dynasty-era China. You'll take on the role of China's best-known investigator, Di Renjie, as he solves a series of grisly murders that will ultimately lead him on a collision course with... | Read more »
Dissidia Final Fantasy Opera Omnia is se...
Dissidia Final Fantasy Opera Omnia, one of Square Enix's many popular mobile RPGs, has announced a plethora of in-game events that are set to take place over the summer. This will include several rewards, Free Multi Draws and more. [Read more] | Read more »
Sphaze is a neat-looking puzzler where y...
Sphaze is a neat-looking puzzler where you'll work to guide robots through increasingly elaborate mazes. It's set in a visually distinct world that's equal parts fantasy and sci-fi, and it's finally launched today for iOS and Android devices. [... | Read more »
Apple Arcade is in trouble
Yesterday, Bloomberg reported that Apple is disappointed in the performance of Apple Arcade and will be shifting their approach to the service by focusing on games that can retain subscribers and canceling other upcoming releases that don't fit... | Read more »
Pixel Petz, an inventive platform for de...
Pixel Petz has built up a sizeable player base thanks to its layered, easy-to-understand creative tools and friendly social experience. It revolves around designing, trading, and playing with a unique collection of pixel art pets, and it's out now... | Read more »
The King of Fighters Allstar's late...
The King of Fighters ALLSTAR, Netmarble's popular action RPG, has once again been updated with a plethora of new content. This includes battle cards, events and 21 new fighters, which increases the already sizeable roster even more. [Read more] | Read more »

Price Scanner via MacPrices.net

Clearance 2019 13″ 2.4GHz/256GB MacBook Pro o...
B&H Photo has dropped their price on the clearance 2019 13″ 2.4GHz/256GB Quad-Core Silver MacBook Pro by $500 off Apple’s original MSRP to a new low of only $1299. Expedited shipping is free to... Read more
$219 Apple AirPods Pro are back at Verizon, s...
Verizon has Apple AirPods Pro on sale again for a limited time for $219.99 on their online store. Their price is $30 off Apple’s MSRP, and it’s the lowest price we’ve seen for AirPods Pro. Available... Read more
Apple’s $779 13″ MacBook Air deal returns to...
Apple has clearance, Certified Refurbished, 2019 13″ MacBook Airs available again starting at $779. Each MacBook features a new outer case, comes with a standard Apple one-year warranty, and is... Read more
$200 13″ MacBook Pro discounts are back at Am...
Amazon has 2020 13″ 2.0GHz MacBook Pros on sale again today for $150-$200 off Apple’s MSRP. Shipping is free. Be sure to purchase the MacBook Pro from Amazon, rather than a third-party seller, and... Read more
Deal Alert! Apple AirPods with Wireless Charg...
Sams Club has Apple AirPods with Wireless Charging Case on sale on their online store for only $149.98 from July 6, 2020 to July 9, 2020. Their price is $50 off Apple’s MSRP, and it’s the lowest... Read more
Xfinity Mobile promo: Apple iPhone XS models...
Take $300 off the purchase of any Apple iPhone XS model at Xfinity Mobile while supplies last. Service plan required: – 64GB iPhone XS: $599.99 save $300 – 256GB iPhone XS: $749.99 save $300 – 512GB... Read more
New July 2020 promo at US Cellular: Switch an...
US Cellular has introduced a new July 2020 deal offering free 64GB Apple iPhone 11 smartphones to customers opening a new line of service. No trade-in required, and discounts are applied via monthly... Read more
Apple offers up to $400 Education discount on...
Apple has launched their Back to School promotion for 2020. They will include one free pair Apple AirPods (with charging case) with the purchase of a MacBook Air, MacBook Pro, iMac, or iMac Pro (Mac... Read more
July 4th Sale: Woot offers wide range of Macs...
Amazon-owned Woot is blowing out a wide range of Apple Macs and iPads for July 4th staring at $279 and ranging up to just over $1000. Models vary from older iPads and 11″ MacBook Airs to some newer... Read more
Apple Pro Display XDR with Nano-Texture Glass...
Abt Electronics has Apple’s new 32″ Pro Display XDR model with the nano-texture glass in stock and on sale today for up to $144 off MSRP. Shipping is free: – Pro Display XDR (nano-texture glass): $... Read more

Jobs Board

Physical Therapist Assistant - *Apple* Hill...
Physical Therapist Assistant - Apple Hill Rehab - Full Time Tracking Code 62519 Job Description General Summary: Under the direct supervision of a licensed Physical Read more
Operating Room Assistant, *Apple* Hill Surg...
Operating Room Assistant, Apple Hill Surgical Center - Full Time, Day Shift, Monday - Saturday availability required Tracking Code 62363 Job Description Operating Read more
Perioperative RN - ( *Apple* Hill Surgical C...
Perioperative RN - ( Apple Hill Surgical Center) Tracking Code 60593 Job Description Monday - Friday - Full Time Days Possible Saturdays General Summary: Under the Read more
Product Manager, *Apple* Commercial Sales -...
Product Manager, Apple Commercial Sales Austin, TX, US Requisition Number:77652 As an Apple Product Manager for the Commercial Sales team at Insight, you Read more
*Apple* Mac Product Engineer - Barclays (Uni...
Apple Mac EngineerWhippany, NJ Support the development and delivery of solutions, products, and capabilities into the Barclays environment working across technical Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.