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

Capture One 11.0.1.40 - RAW workflow sof...
Capture One is a professional RAW converter offering you ultimate image quality with accurate colors and incredible detail from more than 400 high-end cameras -- straight out of the box. It offers... Read more
Capture One 11.0.1.40 - RAW workflow sof...
Capture One is a professional RAW converter offering you ultimate image quality with accurate colors and incredible detail from more than 400 high-end cameras -- straight out of the box. It offers... Read more
GraphicConverter 10.5.4 - $39.95
GraphicConverter is an all-purpose image-editing program that can import 200 different graphic-based formats, edit the image, and export it to any of 80 available file formats. The high-end editing... Read more
Dash 4.1.3 - Instant search and offline...
Dash is an API documentation browser and code snippet manager. Dash helps you store snippets of code, as well as instantly search and browse documentation for almost any API you might use (for a full... Read more
Microsoft OneNote 16.9 - Free digital no...
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
DEVONthink Pro 2.9.17 - Knowledge base,...
Save 10% with our exclusive coupon code: MACUPDATE10 DEVONthink Pro is your essential assistant for today's world, where almost everything is digital. From shopping receipts to important research... Read more
OmniGraffle 7.6 - Create diagrams, flow...
OmniGraffle helps you draw beautiful diagrams, family trees, flow charts, org charts, layouts, and (mathematically speaking) any other directed or non-directed graphs. We've had people use Graffle to... Read more
iFinance 4.3.7 - Comprehensively manage...
iFinance allows you to keep track of your income and spending -- from your lunchbreak coffee to your new car -- in the most convenient and fastest way. Clearly arranged transaction lists of all your... Read more
Opera 50.0.2762.58 - High-performance We...
Opera is a fast and secure browser trusted by millions of users. With the intuitive interface, Speed Dial and visual bookmarks for organizing favorite sites, news feature with fresh, relevant content... Read more
Microsoft Office 2016 16.9 - Popular pro...
Microsoft Office 2016 - Unmistakably Office, designed for Mac. The new versions of Word, Excel, PowerPoint, Outlook and OneNote provide the best of both worlds for Mac users - the familiar Office... Read more

Latest Forum Discussions

See All

Around the Empire: What have you missed...
Around this time every week we're going to have a look at the comings and goings on the other sites in Steel Media's pocket-gaming empire. We'll round up the very best content you might have missed, so you're always going to be up to date with the... | Read more »
Everything about Hero Academy 2: Part 4...
In this part of our Hero Academy 2 guide, we're going to have a look at some of the tactics you're going to need to learn if you want to rise up the ranks. We're going to start off slow, then get more advanced in the next section. [Read more] | Read more »
All the best games on sale for iPhone an...
Another week has flown by. Sometimes it feels like the only truly unstoppable thing is time. Time will make dust of us all. But before it does, we should probably play as many awesome mobile videogames as we can. Am I right, or am I right? [Read... | Read more »
The 7 best games that came out for iPhon...
Well, it's that time of the week. You know what I mean. You know exactly what I mean. It's the time of the week when we take a look at the best games that have landed on the App Store over the past seven days. And there are some real doozies here... | Read more »
Popular MMO Strategy game Lords Mobile i...
Delve into the crowded halls of the Play Store and you’ll find mobile fantasy strategy MMOs-a-plenty. One that’s kicking off the new year in style however is IGG’s Lords Mobile, which has beaten out the fierce competition to receive Google Play’s... | Read more »
Blocky Racing is a funky and fresh new k...
Blocky Racing has zoomed onto the App Store and Google Play this week, bringing with it plenty of classic kart racing shenanigans that will take you straight back to your childhood. If you’ve found yourself hooked on games like Mario Kart or Crash... | Read more »
Cytus II (Games)
Cytus II 1.0.1 Device: iOS Universal Category: Games Price: $1.99, Version: 1.0.1 (iTunes) Description: "Cytus II" is a music rhythm game created by Rayark Games. It's our fourth rhythm game title, following the footsteps of three... | Read more »
JYDGE (Games)
JYDGE 1.0.0 Device: iOS Universal Category: Games Price: $4.99, Version: 1.0.0 (iTunes) Description: Build your JYDGE. Enter Edenbyrg. Get out alive. JYDGE is a lawful but awful roguehate top-down shooter where you get to build your... | Read more »
Tako Bubble guide - Tips and Tricks to S...
Tako Bubble is a pretty simple and fun puzzler, but the game can get downright devious with its puzzle design. If you insist on not paying for the game and want to manage your lives appropriately, check out these tips so you can avoid getting... | Read more »
Everything about Hero Academy 2 - The co...
It's fair to say we've spent a good deal of time on Hero Academy 2. So much so, that we think we're probably in a really good place to give you some advice about how to get the most out of the game. And in this guide, that's exactly what you're... | Read more »

Price Scanner via MacPrices.net

Deals on clearance 15″ Apple MacBook Pros wit...
B&H Photo has clearance 2016 15″ MacBook Pros available for up to $800 off original MSRP. Shipping is free, and B&H charges NY & NJ sales tax only: – 15″ 2.7GHz Touch Bar MacBook Pro... Read more
Apple restocked Certified Refurbished 13″ Mac...
Apple has restocked a full line of Certified Refurbished 2017 13″ MacBook Airs starting at $849. An Apple one-year warranty is included with each MacBook, and shipping is free: – 13″ 1.8GHz/8GB/128GB... Read more
How to find the lowest prices on 2017 Apple M...
Apple has Certified Refurbished 13″ and 15″ 2017 MacBook Pros available for $200 to $420 off the cost of new models. Apple’s refurbished prices are the lowest available for each model from any... Read more
The lowest prices anywhere on Apple 12″ MacBo...
Apple has Certified Refurbished 2017 12″ Retina MacBooks available for $200-$240 off the cost of new models. Apple will include a standard one-year warranty with each MacBook, and shipping is free.... Read more
Apple now offering a full line of Certified R...
Apple is now offering Certified Refurbished 2017 10″ and 12″ iPad Pros for $100-$190 off MSRP, depending on the model. An Apple one-year warranty is included with each model, and shipping is free: –... Read more
27″ iMacs on sale for $100-$130 off MSRP, pay...
B&H Photo has 27″ iMacs on sale for $100-$130 off MSRP. Shipping is free, and B&H charges sales tax for NY & NJ residents only: – 27″ 3.8GHz iMac (MNED2LL/A): $2199 $100 off MSRP – 27″ 3.... Read more
2.8GHz Mac mini on sale for $899, $100 off MS...
B&H Photo has the 2.8GHz Mac mini (model number MGEQ2LL/A) on sale for $899 including free shipping plus NY & NJ sales tax only. Their price is $100 off MSRP. Read more
Apple offers Certified Refurbished iPad minis...
Apple has Certified Refurbished 128GB iPad minis available today for $339 including free shipping. Apple’s standard one-year warranty is included. Their price is $60 off MSRP. Read more
Amazon offers 13″ 256GB MacBook Air for $1049...
Amazon has the 13″ 1.8GHz/256B #Apple #MacBook Air on sale today for $150 off MSRP including free shipping: – 13″ 1.8GHz/256GB MacBook Air (MQD42LL/A): $1049.99, $150 off MSRP Read more
9.7-inch 2017 WiFi iPads on sale starting at...
B&H Photo has 9.7″ 2017 WiFi #Apple #iPads on sale for $30 off MSRP for a limited time. Shipping is free, and pay sales tax in NY & NJ only: – 32GB iPad WiFi: $299, $30 off – 128GB iPad WiFi... Read more

Jobs Board

*Apple* Retail - Multiple Positions - Apple,...
Job Description:SalesSpecialist - Retail Customer Service and SalesTransform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
*Apple* Data Center Site Selection and Strat...
# Apple Data Center Site Selection and Strategy Research Analyst Job Number: 83708609 Santa Clara Valley, California, United States Posted: 18-Jan-2018 Weekly Hours: Read more
Security Engineering Coordinator, *Apple* R...
# Security Engineering Coordinator, Apple Retail Job Number: 113237456 Santa Clara Valley, California, United States Posted: 18-Jan-2018 Weekly Hours: 40.00 **Job Read more
Firmware Engineer - *Apple* Accessories - A...
# Firmware Engineer - Apple Accessories Job Number: 113422485 Santa Clara Valley, California, United States Posted: 18-Jan-2018 Weekly Hours: 40.00 **Job Summary** Read more
*Apple* Retail - Multiple Positions - Apple,...
Job Description: Sales Specialist - Retail Customer Service and Sales Transform Apple Store visitors into loyal Apple customers. When customers enter the store, Read more
All contents are Copyright 1984-2011 by Xplain Corporation. All rights reserved. Theme designed by Icreon.