17_9781118737637-ch11.html

Chapter 11

The Unavoidable Math Chapter

In This Chapter

Using the ++ and -- operators

Making the modulus useful

Employing various operator shortcuts

Working with various math functions

Creating random numbers

Understanding the order of precedence

One of the reasons I shunned computers in my early life was that I feared the math. Eventually, I learned that math doesn’t play a big role in programming. On one hand, you need to know some math, especially when a program involves complex calculations. On the other hand, it’s the computer that does the math — you just punch in the formula.

In the programming universe, math is necessary but painless. Most programs involve some form of simple math. Graphics programming uses a lot of math. And games wouldn’t be interesting if it weren’t for random numbers. All that stuff is math. I believe that you’ll find it more interesting than dreadful.

Math Operators from Beyond Infinity

Two things make math happen in C programming. The first are the math operators, which allow you to construct mathematical equations and formulas. These are shown in Table 11-1. The second are math functions, which implement complex calculations by using a single word. To list all those functions in a table would occupy a lot of space.

Table 11-1 C Math Operators

Operator	Function	Example
+	Addition	var=a+b
–	Subtraction	var=a-b
*	Multiplication	var=a*b
/	Division	var=a/b
%	Modulo	var=a%b
++	Increment	var++
--	Decrement	var--
+	Unary plus	+var
–	Unary minus	-var

Chapter 5 introduces the basic math operators: +, –, *, and /. The rest aren’t too heavy-duty to understand — even the malevolent modulo.

The C language comparison operators are used for making decisions. Refer to Chapter 8 for a list.

Logical operators are also covered in Chapter 8.

The single equal sign, =, is an operator, although not a mathematical operator. It’s the assignment operator, used to stuff a value into a variable.

Bitwise operators, which manipulate individual bits in a value, are covered in Chapter 17.

Appendix C lists all the C language operators.

Incrementing and decrementing

Here’s a handy trick, especially for those loops in your code: the increment and decrement operators. They’re insanely useful.

To add one to a variable's value, use ++, as in:

var++;

After this statement is executed, the value of variable var is increased (incremented) by 1. It's the same as writing this code:

var=var+1;

You'll find ++ used all over, especially in for loops; for example:

for(x=0;x<100;x++)

This looping statement repeats 100 times. It’s much cleaner than writing the alternative:

for(x=0;x<100;x=x+1)

Exercise 11-1: Code a program that displays this phrase ten times: "Get off my lawn, you kids!" Use the incrementing operator ++ in the looping statement.

Exercise 11-2: Recode your answer for Exercise 11-1 using a while loop if you used a for loop, or vice versa.

The ++ operator's opposite is the decrementing operator --, which is two minus signs. This operator decreases the value of a variable by 1; for example:

var--;

The preceding statement is the same as

var=var-1;

Exercise 11-3: Write a program that displays values from -5 through 5 and then back to -5 in increments of 1. The output should look like this:

-5 -4 -3 -2 -1 0 1 2 3 4 5 4 3 2 1 0 -1 -2 -3 -4 -5

This program can be a bit tricky, so rather than have you look up my solution on the web, I’m illustrating it in Listing 11-1. Please don’t look ahead until you’ve attempted to solve Exercise 11-3 on your own.

Listing 11-1: Counting Up and Down

#include <stdio.h>

int main()

{

int c;

for(c=-5;c<5;c++)

printf("%d ",c);

for(;c>=-5;c--)

printf("%d ",c);

putchar('\n');

return(0);

}

The crux of what I want you to see happens at Line 9 in Listing 11-1, but it also plays heavily off the first for statement at Line 7. You might suspect that a loop counting from -5 to 5 would have the value 5 as its stop condition, as in:

for(c=-5;c<=5;c++)

The problem with this construct is that the value of c is incremented to trigger the end of the loop, which means that c equals 6 when the loop is done. If c remains less than 5, as is done at Line 7, then c is automatically set to 5 when the second loop starts. Therefore, in Line 9, no initialization of the variable in the for statement is necessary.

Exercise 11-4: Construct a program that displays values from -10 to 10 and then back down to -10. Step in increments of 1, as was done in Listing 11-1, but use two while loops to display the values.

Prefixing the ++ and -- operators

The ++ operator always increments a variable's value, and the -- operator always decrements. Knowing that, consider this statement:

a=b++;

If the value of variable b is 16, you know that its value will be 17 after the ++ operation. So what's the value of variable a — 16 or 17?

Generally speaking, C language math equations are read from left to right. (Refer to the later section The Holy Order of Precedence for specifics.) Based on this rule, after the preceding statement executes, the value of variable a is 16, and the value of variable b is 17. Right?

The source code in Listing 11-2 helps answer the question of what happens to variable a when you increment variable b on the right side of the equal sign (the assignment operator).

Listing 11-2: What Comes First — the = or the ++?

#include <stdio.h>

int main()

{

int a,b;

b=16;

printf("Before, a is unassigned and b=%d\n",b);

a=b++;

printf("After, a=%d and b=%d\n",a,b);

return(0);

}

Exercise 11-5: Type the source code from Listing 11-2 into a new project. Build and run.

When you place the ++ or -- operator after a variable, it's called post-incrementing or post-decrementing, respectively. If you want to increment or decrement the variable before it's used, you place ++ or -- before the variable name; for example:

a=++b;

In the preceding line, the value of b is incremented, and then it's assigned to variable a. Exercise 11-6 demonstrates.

Exercise 11-6: Rewrite the source code from Listing 11-2 so that the equation in Line 9 increments the value of variable b before it's assigned to variable a.

And what of this monster:

a=++b++;

Never mind! The ++var++ thing is an error.

Discovering the remainder (modulus)

Of all the basic math operator symbols, % is most likely the strangest. No, it’s not the percentage operator. It’s the modulus operator. It calculates the remainder of one number divided by another, which is something easier to show than to discuss.

Listing 11-3 codes a program that lists the results of modulus 5 and a bunch of other values, ranging from 0 through 29. The value 5 is a constant, defined in Line 3 in the program. That way, you can easily change it later.

Listing 11-3: Displaying Modulus Values

#include <stdio.h>

#define VALUE 5

int main()

{

int a;

printf("Modulus %d:\n",VALUE);

for(a=0;a<30;a++)

printf("%d %% %d = %d\n",a,VALUE,a%VALUE);

return(0);

}

Line 11 displays the modulus results. The %% placeholder merely displays the % character, so don't let it throw you.

Exercise 11-7: Type the source code from Listing 11-3 into a new project. Build and run.

Now that you can see the output, I can better explain that a modulus operation displays the remainder of the first value divided by the second. So 20 % 5 is 0, but 21 % 5 is 1.

Exercise 11-8: Change the VALUE constant in Listing 11-3 to 3. Build and run.

Saving time with assignment operators

If you're a fan of the ++ and -- operators (and I certainly am), you'll enjoy the operators listed in Table 11-2. They're the math assignment operators, and like the increment and decrement operators, not only do they do something useful, but they also look really cool and confusing in your code.

Math assignment operators do nothing new, but they work in a special way. Quite often in C, you need to modify a variable’s value. For example:

alpha=alpha+10;

This statement increases the value of variable alpha by 10. In C, you can write the same statement by using an assignment operator as follows:

alpha+=10;

Both versions of this statement accomplish the same thing, but the second example is more punchy and cryptic, which seems to delight most C programmers. See Listing 11-4.

Listing 11-4: Assignment Operator Heaven

#include <stdio.h>

int main()

{

float alpha;

alpha=501;