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all r-values are l-values. An example of an rvalue that is not an lvalue is a literal.
Thus, you can write <TT>x = 5;</TT>, but you cannot write <TT>5 = x;</TT>.
<HR>
</DL>
<H4 ALIGN="CENTER"><A NAME="Heading11"></A><FONT COLOR="#000077">Mathematical Operators</FONT></H4>
<P>There are five mathematical operators: addition (<TT>+</TT>), subtraction (<TT>-</TT>),
multiplication (<TT>*</TT>), division (<TT>/</TT>), and modulus (<TT>%</TT>).</P>
<P>Addition and subtraction work as you would expect, although subtraction with <TT>unsigned</TT>
integers can lead to surprising results, if the result is a negative number. You
saw something much like this yesterday, when variable overflow was described. Listing
4.2 shows what happens when you subtract a large <TT>unsigned</TT> number from a
small <TT>unsigned</TT> number.</P>
<P><A NAME="Heading12"></A><FONT SIZE="4" COLOR="#000077"><B>Listing 4.2. A demonstration
of subtraction and integer overflow</B></FONT><FONT SIZE="2" COLOR="#000077"><B>.</B></FONT><FONT
COLOR="#0066FF"></FONT>
<PRE><FONT COLOR="#0066FF">1: // Listing 4.2 - demonstrates subtraction and
2: // integer overflow
3: #include <iostream.h>
4:
5: int main()
6: {
7: unsigned int difference;
8: unsigned int bigNumber = 100;
9: unsigned int smallNumber = 50;
10: difference = bigNumber - smallNumber;
11: cout << "Difference is: " << difference;
12: difference = smallNumber - bigNumber;
13: cout << "\nNow difference is: " << difference <<endl;
14: return 0;
<TT>15: }</TT>
Output: Difference is: 50
Now difference is: 4294967246
</FONT></PRE>
<P><FONT COLOR="#000077"><B>Analysis:</B></FONT><B> </B>The subtraction operator
is invoked on line 10, and the result is printed on line 11, much as we might expect.
The subtraction operator is called again on line 12, but this time a large <TT>unsigned</TT>
number is subtracted from a small <TT>unsigned</TT> number. The result would be negative,
but because it is evaluated (and printed) as an <TT>unsigned</TT> number, the result
is an overflow, as described yesterday. This topic is reviewed in detail in Appendix
A, "Operator Precedence."
<H4 ALIGN="CENTER"><A NAME="Heading14"></A><FONT COLOR="#000077">Integer Division
and Modulus</FONT></H4>
<P>Integer division is somewhat different from everyday division. When you divide
21 by 4, the result is a real number (a number with a fraction). Integers don't have
fractions, and so the "remainder" is lopped off. The answer is therefore
5. To get the remainder, you take 21 modulus 4 (21 % 4) and the result is 1. The
modulus operator tells you the remainder after an integer division.</P>
<P>Finding the modulus can be very useful. For example, you might want to print a
statement on every 10th action. Any number whose value is 0 when you modulus 10 with
that number is an exact multiple of 10. Thus 1 % 10 is 1, 2 % 10 is 2, and so forth,
until 10 % 10, whose result is 0. 11 % 10 is back to 1, and this pattern continues
until the next multiple of 10, which is 20. We'll use this technique when looping
is discussed on Day 7, "More Program Flow."
<DL>
<DD>
<HR>
<FONT COLOR="#000077"><B>WARNING:</B></FONT><B> </B>Many novice C++ programmers inadvertently
put a semicolon after their <TT>if</TT> statements:
<PRE><FONT COLOR="#0066FF">if(SomeValue < 10);
SomeValue = 10;</FONT></PRE>
<DD><BR>
What was intended here was to test whether <TT>SomeValue</TT> is less than 10, and
if so, to set it to <TT>10</TT>, making <TT>10</TT> the minimum value for <TT>SomeValue</TT>.
Running this code snippet will show that <TT>SomeValue</TT> is always set to <TT>10</TT>!
Why? The <TT>if</TT> statement terminates with the semicolon (the do-nothing operator).
Remember that indentation has no meaning to the compiler. This snippet could more
accurately have been written as:
<PRE><FONT COLOR="#0066FF">if (SomeValue < 10) // test
; // do nothing
SomeValue = 10; // assign
</FONT></PRE>
<DD>Removing the semicolon will make the final line part of the <TT>if</TT> statement
and will make this code do what was intended.
<HR>
</DL>
<H3 ALIGN="CENTER"><A NAME="Heading15"></A><FONT COLOR="#000077">Combining the Assignment
and Mathematical Operators</FONT></H3>
<P>It is not uncommon to want to add a value to a variable, and then to assign the
result back into the variable. If you have a variable <TT>myAge</TT> and you want
to increase the value by two, you can write</P>
<PRE><FONT COLOR="#0066FF">int myAge = 5;
int temp;
temp = myAge + 2; // add 5 + 2 and put it in temp
myAge = temp; // put it back in myAge
</FONT></PRE>
<P>This method, however, is terribly convoluted and wasteful. In C++, you can put
the same variable on both sides of the assignment operator, and thus the preceding
becomes</P>
<PRE><FONT COLOR="#0066FF">myAge = myAge + 2;
</FONT></PRE>
<P>which is much better. In algebra this expression would be meaningless, but in
C++ it is read as "add two to the value in <TT>myAge</TT> and assign the result
to <TT>myAge</TT>."</P>
<P>Even simpler to write, but perhaps a bit harder to read is</P>
<PRE><FONT COLOR="#0066FF">myAge += 2;
</FONT></PRE>
<P>The self-assigned addition operator (<TT>+=</TT>) adds the rvalue to the lvalue
and then reassigns the result into the lvalue. This operator is pronounced "plus-equals."
The statement would be read "<TT>myAge</TT> plus-equals two." If <TT>myAge</TT>
had the value <TT>4</TT> to start, it would have <TT>6</TT> after this statement.</P>
<P>There are self-assigned subtraction (<TT>-=</TT>), division (<TT>/=</TT>), multiplication
(<TT>*=</TT>), and modulus (<TT>%=</TT>) operators as well.
<H3 ALIGN="CENTER"><A NAME="Heading16"></A><FONT COLOR="#000077">Increment and Decrement</FONT></H3>
<P>The most common value to add (or subtract) and then reassign into a variable is
<TT>1</TT>. In C++, increasing a value by 1 is called incrementing, and decreasing
by 1 is called decrementing. There are special operators to perform these actions.</P>
<P>The increment operator (<TT>++</TT>) increases the value of the variable by 1,
and the decrement operator (<TT>--</TT>) decreases it by 1. Thus, if you have a variable,
<TT>C</TT>, and you want to increment it, you would use this statement:</P>
<PRE><FONT COLOR="#0066FF">C++; // Start with C and increment it.
</FONT></PRE>
<P>This statement is equivalent to the more verbose statement</P>
<PRE><FONT COLOR="#0066FF">C = C + 1;
</FONT></PRE>
<P>which you learned is also equivalent to the moderately verbose statement</P>
<PRE><FONT COLOR="#0066FF">C += 1;
</FONT></PRE>
<H4 ALIGN="CENTER"><A NAME="Heading17"></A><FONT COLOR="#000077">Prefix and Postfix</FONT></H4>
<P>Both the increment operator (<TT>++</TT>) and the decrement operator(<TT>--</TT>)
come in two varieties: prefix and postfix. The prefix variety is written before the
variable name (<TT>++myAge</TT>); the postfix variety is written after (<TT>myAge++</TT>).</P>
<P>In a simple statement, it doesn't much matter which you use, but in a complex
statement, when you are incrementing (or decrementing) a variable and then assigning
the result to another variable, it matters very much. The prefix operator is evaluated
before the assignment, the postfix is evaluated after.</P>
<P>The semantics of prefix is this: Increment the value and then fetch it. The semantics
of postfix is different: Fetch the value and then increment the original.</P>
<P>This can be confusing at first, but if <TT>x</TT> is an integer whose value is
<TT>5</TT> and you write</P>
<PRE><FONT COLOR="#0066FF">int a = ++x;
</FONT></PRE>
<P>you have told the compiler to increment <TT>x</TT> (making it <TT>6</TT>) and
then fetch that value and assign it to <TT>a</TT>. Thus, <TT>a</TT> is now <TT>6</TT>
and <TT>x</TT> is now <TT>6</TT>.</P>
<P>If, after doing this, you write</P>
<PRE><FONT COLOR="#0066FF">int b = x++;
</FONT></PRE>
<P>you have now told the compiler to fetch the value in <TT>x</TT> (<TT>6</TT>) and
assign it to <TT>b</TT>, and then go back and increment <TT>x</TT>. Thus, <TT>b</TT>
is now <TT>6</TT>, but <TT>x</TT> is now <TT>7</TT>. Listing 4.3 shows the use and
implications of both types.</P>
<P><A NAME="Heading18"></A><FONT SIZE="4" COLOR="#000077"><B>Listing 4.3. A demonstration
of prefix and postfix operators.</B></FONT><FONT COLOR="#0066FF"></FONT>
<PRE><FONT COLOR="#0066FF">1: // Listing 4.3 - demonstrates use of
2: // prefix and postfix increment and
3: // decrement operators
4: #include <iostream.h>
5: int main()
6: {
7: int myAge = 39; // initialize two integers
8: int yourAge = 39;
9: cout << "I am: " << myAge << " years old.\n";
10: cout << "You are: " << yourAge << " years old\n";
11: myAge++; // postfix increment
12: ++yourAge; // prefix increment
13: cout << "One year passes...\n";
14: cout << "I am: " << myAge << " years old.\n";
15: cout << "You are: " << yourAge << " years old\n";
16: cout << "Another year passes\n";
17: cout << "I am: " << myAge++ << " years old.\n";
18: cout << "You are: " << ++yourAge << " years old\n";
19: cout << "Let's print it again.\n";
20: cout << "I am: " << myAge << " years old.\n";
21: cout << "You are: " << yourAge << " years old\n";
22: return 0;
<TT>23: }</TT>
Output: I am 39 years old
You are 39 years old
One year passes
I am 40 years old
You are 40 years old
Another year passes
I am 40 years old
You are 41 years old
Let's print it again
I am 41 years old
You are 41 years old
</FONT></PRE>
<P><FONT COLOR="#000077"><B>Analysis: </B></FONT>On lines 7 and 8, two integer variables
are declared, and each is initialized with the value <TT>39</TT>. Their values are
printed on lines 9 and 10.<BR>
On line 11, <TT>myAge</TT> is incremented using the postfix increment operator, and
on line 12, <TT>yourAge</TT> is incremented using the prefix increment operator.
The results are printed on lines 14 and 15, and they are identical (both <TT>40</TT>).</P>
<P>On line 17, <TT>myAge</TT> is incremented as part of the printing statement, using
the postfix increment operator. Because it is postfix, the increment happens after
the print, and so the value <TT>40</TT> is printed again. In contrast, on line 18,
<TT>yourAge</TT> is incremented using the prefix increment operator. Thus, it is
incremented before being printed, and the value displays as <TT>41</TT>.</P>
<P>Finally, on lines 20 and 21, the values are printed again. Because the increment
statement has completed, the value in <TT>myAge</TT> is now <TT>41</TT>, as is the
value in <TT>yourAge</TT>.
<H4 ALIGN="CENTER"><A NAME="Heading20"></A><FONT COLOR="#000077">Precedence</FONT></H4>
<P>In the complex statement</P>
<PRE><FONT COLOR="#0066FF">x = 5 + 3 * 8;
</FONT></PRE>
<P>which is performed first, the addition or the multiplication? If the addition
is performed first, the answer is 8 * 8, or 64. If the multiplication is performed
first, the answer is 5 + 24, or 29.</P>
<P>Every operator has a precedence value, and the complete list is shown in Appendix
A, "Operator Precedence." Multiplication has higher precedence than addition,
and thus the value of the expression is 29.</P>
<P>When two mathematical operators have the same precedence, they are performed in
left-to-right order. Thus</P>
<PRE><FONT COLOR="#0066FF">x = 5 + 3 + 8 * 9 + 6 * 4;
</FONT></PRE>
<P>is evaluated multiplication first, left to right. Thus, 8*9 = 72, and 6*4 = 24.
Now the expression is essentially</P>
<PRE><FONT COLOR="#0066FF">x = 5 + 3 + 72 + 24;
</FONT></PRE>
<P>Now the addition, left to right, is 5 + 3 = 8; 8 + 72 = 80; 80 + 24 = 104.</P>
<P>Be careful with this. Some operators, such as assignment, are evaluated in right-to-left
order! In any case, what if the precedence order doesn't meet your needs? Consider
the expression</P>
<PRE><FONT COLOR="#0066FF">TotalSeconds = NumMinutesToThink + NumMinutesToType * 60
</FONT></PRE>
<P>In this expression, you do not want to multiply the <TT>NumMinutesToType</TT>
variable by 60 and then add it to <TT>NumMinutesToThink</TT>. You want to add the
two variables to get the total number of minutes, and then you want to multiply that
number by 60 to get the total seconds.</P>
<P>In this case, you use parentheses to change the precedence order. Items in parentheses
are evaluated at a higher precedence than any of the mathematical operators. Thus</P>
<PRE><FONT COLOR="#0066FF">TotalSeconds = (NumMinutesToThink + NumMinutesToType) * 60
</FONT></PRE>
<P>will accomplish what you want.
<H3 ALIGN="CENTER"><A NAME="Heading21"></A><FONT COLOR="#000077">Nesting Parentheses</FONT></H3>
<P>For complex expressions, you might need to nest parentheses one within another.
For example, you might need to compute the total seconds and then compute the total
number of people who are involved before multiplying seconds times people:</P>
<PRE><FONT COLOR="#0066FF">TotalPersonSeconds = ( ( (NumMinutesToThink + NumMinutesToType) * 60) * Â(PeopleInTheOffice + PeopleOnVacation) )
</FONT></PRE>
<P>This complicated expression is read from the inside out. First, <TT>NumMinutesToThink</TT>
is added to <TT>NumMinutesToType</TT>, because these are in the innermost parentheses.
Then this sum is multiplied by 60. Next, <TT>PeopleInTheOffice</TT> is added to <TT>PeopleOnVacation</TT>.
Finally, the total number of people found is multiplied by the total number of seconds.</P>
<P>This example raises an important related issue. This expression is easy for a
computer to understand, but very difficult for a human to read, understand, or modify.
Here is the same expression rewritten, using some temporary integer variables:</P>
<PRE><FONT COLOR="#0066FF">TotalMinutes = NumMinutesToThink + NumMinutesToType;
TotalSeconds = TotalMinutes * 60;
TotalPeople = PeopleInTheOffice + PeopleOnVacation;
TotalPersonSeconds = TotalPeople * TotalSeconds;
</FONT></PRE>
<P>This example takes longer to write and uses more temporary variables than the
preceding example, but it is far easier to understand. Add a comment at the top to
explain what this code does, and change the <TT>60</TT> to a symbolic constant. You
then will have code that is easy to understand and maintain.
<BLOCKQUOTE>
<P>
<HR>
<B>DO</B> remember that expressions have a value.<B> DO</B> use the prefix operator
(<TT>++</TT>variable) to increment or decrement the variable before it is used in
the expression. <B>DO</B> use the postfix operator (variable<TT>++</TT>) to increment
or decrement the variable after it is used. <B>DO</B> use parentheses to change the
order of precedence. <B>DON'T</B> nest too deeply, because the expression becomes
hard to understand and maintain.
<HR>
</BLOCKQUOTE>
<H3 ALIGN="CENTER"><A NAME="Heading22"></A><FONT COLOR="#000077">The Nature of Truth</FONT></H3>
<P>In C++, zero is considered false, and all other values are considered true, although
true is usually represented by 1. Thus, if an expression is false, it is equal to
zero, and if an expression is equal to zero, it is false. If a statement is true,
all you know is that it is nonzero, and any nonzero statement is true.
<H4 ALIGN="CENTER"><A NAME="Heading23"></A><FONT COLOR="#000077">Relational Operators</FONT></H4>
<P>The relational operators are used to determine whether two numbers are equal,
or if one is greater or less than the other. Every relational statement evaluates
to either <TT>1</TT> (<TT>TRUE</TT>) or <TT>0</TT> (<TT>FALSE</TT>). The relational
operators are presented later, in Table 4.1.</P>
<P>If the integer variable <TT>myAge</TT> has the value <TT>39</TT>, and the integer
variable <TT>yourAge</TT> has the value <TT>40</TT>, you can determine whether they
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