A Crash Course in C

copyright 1995 by Anand Mehta

Notes



Table of Contents



Introduction

Reasons to use C:

References: Three steps are necessary to use C: Different systems have different procedures to use C. See the manual or help files for details.


Chapter 1: Fundamentals


Example programs

The following are simple examples to get things started. They do not do anything useful, but they illustrate some key characteristics of C.

/* this is a comment */
main()				/* function definition */
{				/* start of block */
  printf("Hello world\n");	/* output; statement ends with a semicolon */
				/* use '\n' in printf to get a linefeed */
}				/* end of block */

Things to note in example programs:

main()
{
	variable declarations
	statements
}

main()
{
  int x;			/* declaration and definition */
  x=5;				/* assignment */
  printf("%d\n", x);		/* output x as an integer */
}

main()
{
  int x=17, y=12, z;				/* declaration, definition, and initialization */
  z = x + y;					/* arithmetic expression */
  printf("z = %d + %d = %d\n", x, y, z);	/* each %d prints one integer */
  printf("%d * %d = %d\n", x, y, x*y);
}


main()
{
  int x;
  scanf("%d", &x);           /*  values input from the keyboard using scanf():  */
  printf("x = %d\n", x);     /*    and a pointer to x  */
}

A common error when using scanf() is not giving pointers as the arguments; to input a variable, use

int x;
scanf("%d", &x); /* correct */
NOT
int x;
scanf("%d", x); /* incorrect */


Variables

All variables must be declared and defined before they can be used. Variable names can be composed of characters, digits, and the underscore character ( _), and can usually be up to 32 characters long. Variable names should not begin with an underscore---these names are used by the compiler and the libraries.

Variables have specific types and usage; basic data types:

The specific size of each type depends on the implementation; see <limits.h> for details. On Unix systems, <limits.h> is usually the file /usr/include/limits.h.

The derived data types are

All variables must be declared and defined; they can also be initialized and assigned a value.

/***  definition of constants  ***/
main()
{
  char c = 'x';
  char c1 = '0';    /* the character 'zero', with the integer value for ASCII(0) */
  char c2 = '\0';   /* has the "integer" value zero */

  int n = 10;
  int n_oct = 065;  /* octal */
  int n_hex = 0x3d; /* hexadecimal */

  long m = 10L;
  unsigned int k = 304U;
  unsigned long l = 3040UL;

  float x1 = 143.0;
  float x2 = 24.6e-3;
  double y = 34.1L;

} 


Input / Output

Basic input/output is obtained using the standard library. The syntax is given below.

printf("control string",  variable1,  variable2, ...);
scanf("control string", &pointer1, &pointer2, ...);

The control string has place holders for the variables being used (see tables on page 16 - click here) there can also be characters in the control string. For scanf(), the pointers to the variables being inputed must be used. Special characters are listed on table 5 on page 16 (click here).

 /**  using printf() and scanf()  **/
main()
{
  int x=10;
  float y;

  printf("(1)  %d\n", x);
  printf("(2)  %d\n", x*5);

  printf("(3)  x = ");
  printf("%d", x);
  printf("\n");                                      /**  same as (4)  **/

  printf("(4)  x = %d\n", x);                        /**  same as (3)  **/

  printf("input x: ");  scanf("%d", &x);       /**  prompts for input  **/
  printf("(5)  x = %d\n", x);
  
/**  can input several values of different types with one scanf command  **/ 
  printf("input x, y: ");  scanf("%d %f", &x, &y);
  printf("(6)  x = %d, y = %f\n", x, y);
}

Output:
(1)  10
(2)  50
(3)  x = 10
(4)  x = 10
input x: 40
(5)  x = 40
input x, y: 20 34.5
(6)  x = 20, y = 34.500000


Keywords and Operators: The C Language

C has a small set of keywords; all are used to either declare data types or control the flow of the program. See table 1 below for a list of the keywords. The C operators are listed in Table 2 at the end of the chapter.

Table 1: Keywords (K & R, p. 192)
Data Type Declarations Control Flow Statements
autofloatlongstatic unsignedbreakdoif
charenumregisterstruct voidcaseelsereturn
constexternshorttypedef volatilecontinueforswitch
doubleintsignedunion
defaultgotowhile

Basic Operators

Some basic operators are

Examples of Conditional Operators
main()
{
  int x=0, y=10, w=20, z, T=1, F=0;

  z = (x == 0);            /***  logical operator; result --> 0 or 1  ***/
  z = (x = 0);             /***  assignment operator; result -->   ***/
  z = (x == 1);
  z = (x = 15);
  z = (x != 2);
  z = (x < 10);
  z = (x <= 50);
  z = ((x=y) < 10);   /***  performs assignment, compares  with 10  ***/
  z = (x==5 && y<15);
  z = (x==5 && y>5 && w==10);
  z = (x==5 || y>5 && w==10);

  z = (T && T && F && x && x);  /***  ==> F; ***/
  z = (F || T || x || x);       /***  ==> T; ***/
  /***  for && and !!, order is specified, stops when result is known,  ***/
  /***  value of x doesn't matter  ***/
}

Examples of the Increment and Decrement Operators
/**  examples of the increment and decrement operators  **/
main()
{
  int x,y;

  x=5;
  y = ++x;                             /**  prefix increment  **/
  printf("++x:  x=%d, y=%d\n", x, y);

  x=5;
  y = x++;                             /**  postfix increment  **/
  printf("x++:  x=%d, y=%d\n", x, y);

  x=5;
  y = --x;                             /**  prefix decrement  **/
  printf("--x:  x=%d, y=%d\n", x, y);

  x=5;
  y = x--;                             /**  postfix decrement  **/
  printf("x--:  x=%d, y=%d\n", x, y);
}

Output:
++x:  x=6, y=6
x++:  x=6, y=5
--x:  x=4, y=4
x--:  x=4, y=5

More Operator Examples
main()
{
  int x, y, z;

  x = 128;
  y = x / 10;            /**  y = 12, the remainder is dropped  **/
  y = x % 10;            /**  y = 8, which is remainder  **/

  x = 10;
  y = !x;                /**  y = 0  **/
  y = !(!x);             /**  y = 1  **/

  x = 0;
  y = !x;                /**  y = 1  **/

  x = 10;
  x += 2;                /**  x = 12  **/
  x += 2;                /**  x = 14  **/

  x = 10;
  x -= 4;                /**  x = 6  **/

  x = 10;
  x *= 5;                /**  x = 50  **/

  x = 10;
  x /= 2;                /**  x = 5  **/
  x /= 2;                /**  x = 2  **/

  x = 2
  y = (x < 5) ? 5 : 10;              /**  y=5  **/

  x = 8
  y = (x < 5) ? 5 : 10;              /**  y=10  **/

  if (x < 5)          /**  same as the conditional   y = (x < 5) ? 5 : 10;  **/
    y = 5;
  else
    y = 10;
}

Order of Evaluation

Operands of most operators will be evaluated in an unspecified order; do not assume a particular order and be careful about side effects of evaluations. Also, the order in which function arguments are evaluated is not specified. There are four operators, however, that do have a specified order of operand evaluation: && || , ?:

/**  test of order of operations  **/
main()
{
  int x=5, y, i=4;

  y = x * ++x;
  printf("x = %d, y = %d\n", x, y);

  printf("i = %d, ++i = %d\n", i, ++i);
}

Depending on the order of evaluation of the function arguments, the output can be

x = 6, y = 30
I = 4, ++I = 5
or

x = 6, y = 36
I = 5, ++I = 5

These types of expressions should be avoided.

Type Conversion

C does some automatic type conversion if the expression types are mixed. If there are no unsigned values, the rules for conversion for two operands are:

If there are unsigned expressions, the conversion rules are in K&R, p. 198.

Any explicit type conversions can be made by casting an expression to another type, using (double), (float), etc., before the expression to be cast.

Truncation Problem wth Integer Divide
/***  truncation problem with integer divide  ***/
main()
{
  int x=8, y=10;
  float z1, z2;

  z1 = x/y;
  z2 = (float) x / (float) y;
  printf("z1 = %6.2f, z2 = %6.2f\n", z1, z2);
}

Output:
z1 =   0.00, z2 =   0.80


Expressions and Statements

Expressions include variable names, function names, array names, constants, function calls, array references, and structure references. Applying an operator to an expression is still an expression, and an expression enclosed within parentheses is also an expression. An lvalue is an expression which may be assigned a value, such as variables.
i++ x+y z = x+y

A statement is


Control Flow

Basic control flow is governed by the if..else, while,do...while, and for statements.

Decision Making

Use the if...else for conditional decisions. (exp is any valid expression, statement is any valid statement)
Syntax:
if (exp)
 	statement
 
if (exp)
 	statement
else
 	statement
 
if (exp1)
   statement
else if (exp2)
 	statement
 	.
	.
	.
else
 	statement

 main()        /*** check if a number is odd or even ***/
{
  int i;
  scanf("%d", &i);
  if (i%2 == 0)                /** OR   if (!(i%2))  **/
    printf("i is even\n");
  else 
    printf("i is odd\n");
}

Examples of the 'if' Statement
main()
{
  int x=5;

  if (x > 0)
    printf("x = %d\n", x);

  if (x < 10)
    {
      printf("x = %d\n", x);
      x += 10;
    }
  else
    x -= 10;

  if (x==1)
    printf("one\n");
  else if (x==2)
    printf("two\n");
  else if (x==4)
    {
      printf("four\n");
      x /= 2;
    }
  else if (x==5)
    printf("five\n");
  else
    {
      printf("x = %d\n", x);
      x %= 10;
    }

  /**  'else' matches up with last unmatched 'if' in same block level  **/

  if (x > 0)
    if (x % 2)
      printf("odd\n");
    else
      printf("even\n");
  else
    printf("negative\n");

  if (!(x % 2))
    {
      if (!(x % 5))
	x /= 10;
    }
  else
    printf("odd\n");
}

Looping

Syntax:
while (exp)
	{
 		statement
 	}
do
 	{
 	 	statement
 	} while (exp);
 
for (exp1-opt ;  exp2-opt ;  exp3-opt)
	{
 		statement
	}
Here exp-opt is an optional expression.

main()        /*** print the numbers from 1 to 10 ***/
{
  int i;

  i=1;
  while (i<=10)
    {
      printf("%d\n", i);
      i++;
    }
}

main()        /*** print the numbers from 1 to 10 ***/
{
  int i;

  i=1;
  do
    {
      printf("%d\n", i++);
    } while (i<=10);
}

main()        /*** print the numbers from 1 to 10 ***/
{
  int i;
  for (i=1 ; i<=10; i++)
    printf("%d\n", i);
}

Other Control Flow

Other program control flow is governed by the switch statement, which allows comparison to a series of constant values, and the goto, continue, break, and return statements.

Syntax:
switch(exp)
 {
  	case (const-exp):
   		statement-opt
   	 	break;
  	case (const-exp):
   	 	statement-opt
   	 	statement-opt
   		break;
  	.
	.
	.
  	default:
   	 	statement-opt
   		break;
 }
Here const-exp is a constant expression, and statement-opt is an optional statement. The break; after the default: case is optional.

Syntax:
 label:  statement
 	goto  label;
 
 	continue;
 
 	break;
 
 	return (exp-opt);
}
Here label is a statement label.

The break; statement is used inside the while, do...while, for, and switch statements to automatically drop out of the current loop. The continue statement is used inside the loops (not switch) to jump to the end of the loop. With while and do...while, this jumps to the next test; with for, it jumps to the increment step, and then the test.

/**  Example with 'do...while' and 'switch': waiting for a yes/no answer  **/
main()
{
  char ans, c;
  int answer;

  do
    {
      printf("enter y/n: ");    scanf("%c", &ans);
      switch (ans)
	{
	case 'y': case 'Y':     answer =  1;      break;
	case 'n': case 'N':     answer =  0;      break;
	default:                answer = -1;      break;
	}
    } while (answer == -1);
  printf("answer = %d\n", answer);
}


The C Preprocessor

Two essential preprocessor commands are #define and #include. Constants and macros are defined with #define. The program can be split into separate files and combined with #include, and header files can also be inserted. (See sections 2.6 and 2.7)

#include <stdio.h>
#include <math.h>
#include "functions.c"

#define MAX 10
#define TRUE 1
#define FALSE 0

After inserting the math.h header file, math subroutines can be used properly. To compile using the math library on Unix, use

% cc -o .c -lm

 /**  program to calculate x using the quadratic formula **/
#include 
main()
{
  float a, b, c, d, x, x1, x2;
  printf("input a, b, c:  ");
  scanf("%f %f %f", &a, &b, &c);
  d = b*b - 4.0*a*c;
  if (d >= 0)               /**  check if solution will be real or complex  **/
    {         
      x1 = (-b+sqrt(d)) / (2.0*a);        /** sqrt() from the math library  **/
      x2 = (-b-sqrt(d)) / (2.0*a);
                      /**  need parentheses for proper order of operations  **/
      printf("x = %f, %f\n",x1,x2);
    }
  else
    printf("x is complex");
}

/**  an example of formated output  **/
#include 
main()
{
  int n=10, i, x;
                          
  for (i=0, x=1; i

Output:
log(    1) =    0.000
log(    2) =    0.693
log(    4) =    1.386
log(    8) =    2.079
log(   16) =    2.773
log(   32) =    3.466
log(   64) =    4.159
log(  128) =    4.852
log(  256) =    5.545
log(  512) =    6.238

The #if...#endif preprocessor command can be used to comment out a section of code which may have comments within it.

/** using #if for nested comments  **/
#define   TRUE    1
#define   FALSE   0

main()
{
  int x=5;

  printf("x = %d\n", x);

#if FALSE        /**  everything until the matching #endif is commented  **/
  x = 304;
#endif

  printf("x = %d\n", x);
}

Output:
x = 5
x = 5


Problems

  1. Run example programs to become familiar with using C
  2. Write a rogram to print all Fahrenheit and Celsius temperatures using the conversion
    C = (F-32)*5/9
    for 20 degree increments from 32 to 212. (See K&R,p. 9 if you are stuck.)
  3. Input a number in print all its factors
  4. Input a number and decide if it is prime
  5. Change the quadradic formula program so that it also prints the complex solutions
  6. Input an integer and print the value of each digit in English: 932 => nine three two
  7. Count the number of characters and lines in a file (use '\n' to find lines)


Table 2: Summary of C operators (K&R, p. 53)
OperatorDescriptionAssociativity
()Function callleft to right
[]Array element reference
->Pointer to structure member reference
.Structure member reference
-Unary minusright to left
+Unary plus
++Increment
--Decrement
!Logical negation
~Ones complement
*Pointer reference (indirection)
&Address
sizeofSize of an object
(type)Type cast (conversion)
*Multiplicationleft to right
/Division
%Modulus
+Addition
-Subtraction
<<Left shift
>>Right shift
<Less than
<=Less than or equal to
>Greater than
>=Greater than or equal to
==Equality
!=Inequality
&Bitwise AND
^Bitwise XOR
|Bitwise OR
&&Logical AND *
||Logical OR *
?:Conditional *right to left
=*=/=Assignment operators
%=+=-=
^=&=|=
<<=>>=
,Comma operator *left to right
* order of operand evaluation is specified


Table 3: Basic printfConversions (K&R, p.244)
CharacterArgument Type; Printed As
d, Iint; decimal number
oint; unsigned octal number (without a leading zero)
x, Xint; unsigned hexadecimal number (without a leading Ox or OX, using abcdef or ABCDEF for 10,...,15)
uint; unsigned decimal number
cint; single character
schar; print characters from the string until a '\0' or the number of charachters given by the precision
fdouble; [-]m.dddddd, where the number of d's is given by the precision (default is 6)
e, Edouble; [-]m.dddddde ± xx or [-]m.ddddddE ± xx where the number of d's is given by the precision (default is 6)
g, Gdouble; use %e or %E if the exponent is less than -4 or greater than or equal to the precision; otherwise use %f; trailing zeros and a trailing decimal point are not printed
pvoid *; pointer (implementation-dependent representation)
%no argument is converted; print a %


Table 4: Basic scanf Conversions (K&R, p.246)
CharacterInput Data; Argument Type
ddecimal integer; int *
Iinteger; int * ; the integer may be in octal (leading 0) or hexadecimal (leading 0x or 0X)
ooctal intger (with or without leading zero); int *
uunsigned decimal integer; unsigned int *
xhexadecimal number (with or without a leading 0x or 0X); int *
ccharacters; char *. The next input characters (default 1) are placed at the indicated spot. The normal skip over white space is suppressed; to read the next non-white space character, use %1s
scharacter string (not quoted); char * ; pointing to an array of characters large enough for the string and a terminating `\0' that will be added
e, f, gfloating-point number with optional sign, optional decimal point, and optional exponent; float *
%literal %; no assignment is made


Table 5: Escape Sequences (K&R, p.193)
\abell
\thorizontal tab
\'single quote
\nnewline
\rcarriage return
\bbackspace
\vvertical tab
\"double quote
\?question mark


\fformfeed
\\backslash
\ooooctal number
\xhhhexadecimal number



Table 6: ASCII Character Set (hexadecimal value, 0xNM, base 16)
Row
(M)
Column (N)
0x20x30x40x50x6 0x7
0x0SPC0@P`p
0x1!1AQaq
0x2"2BRbr
0x3#3CScs
0x4$4DTdt
0x5%5EUef
0x6&6FVfv
0x7'7GWgw
0x8(8HXhx
0x9)9IYiy
0xA*:JZjz
0xB+;K[k{
0xC,<L\l|
0xD-=M]m}
0xE.>N^n~
0xF/?O_oDEL


Chapter 2: Functions

Reasons for Using Functions


Basic Structure

The syntax for declaring a function is
return-type function-name (argument declarations)
{
local variable declarations
statements
}
The function prototype is a declaration and is needed if the function is defined after its use in the program. The syntax is
return-type function-name (argument declarations);

where the argument declarations must include the types of the arguments, but the argument names are optional. If the function is defined before its use, then a prototype is not necessary, since the definition also serves as a declaration.

If the return-type is omitted, int is assumed. If there are no argument declarations, use void, not empty parentheses.

Here are four examples of how functions can be used:


Return Statement

A function can return a value of any type, using the return statement,
Syntax:
return exp;
return (exp);
return;

The return statement can occur anywhere in the function, and will immediately end that function and return control to the function which called it. If there is no return statement, the function will continue execution until the closing of the function definition, and return with an undefined value.

The type of the expression returned should match the type of the function; C will automatically try to convert exp to the return-type.


Difference between ANSI-C and "Traditional C"

If the function return type is not int, it must be specified by the function prototype declaration. This is done differently in ANSI C and "Traditional C." For a function returning the maximum of two numbers, the ANSI-C function would be

float max(float x, float y);
    /*  OR: float max(float, float); */
              /**  variable names {x,y} are not necessary, only the types  **/
              /**    are, but using the names makes the code more readable  **/
main()
{
  float x,y,z;
  ...
  z = max(x,y);
  ...
}

float max(float x, float y)     /**  argument types are in the definition  **/
{
  if (x < y)
    return y;
  else
    return x;
}

The "Traditional C" declarations would be

float max();       /**  argument types are not included in the declaration  **/

main()
{
  float x,y,z;
  ...
  z = max(x,y);    /**  the function call is the same  **/
  ...
}

float max(x,y)
     float x,y;    /**  argument types listed after the definition  **/
{
  if (x < y)
    return y;
  else
    return x;
}


Object Storage Classes and Scope

Functions, as with any compound statement designated by braces {}, have their own scope, and can therefore define any variables without affecting the values of variables with the same name in other functions. To be able to affect the variables, they can be made "global" by defining them externally

Available storage classes for variables are

The scope of an object can be local to a function or block, local to a file, or completely global.

Again, it is important to distinguish between a declaration and a definition.

There can only be one definition of a variable within a given scope.

main()
{
  int x;
  int x;     /***  illegal: cannot define x twice  ***/
  x=6;
}

Also, external variables can only be defined once, although they can be declared as often as necessary. If an external variable is initialized during the declaration, then that also serves as a definition of the variable.

int x;			/***  definition of global variable  ***/
extern int x;		/***  declaration so other files can use it  ***/
extern int y;		/***  declaration, must be defined elsewhere  ***/
extern int z=0;		/***  declaration, definition, and initialization  ***/
           			/***    can be used by other files  ***/

main()
{
  printf("%d", z);
}

/**  An example with limited variable scope within a file  **/

main()
{
  int m=2, n=5;
  float x=10.0, y=14.1;
  int count;

  int print_pair_i(int x, int y);
  int print_pair_f(float x, float y);
  int print_pair_d(double x, double y);
  void reset_count(void);

  count = print_pair_f(x, y);    printf("%d\n", count);

  print_pair_i(m, n);
  count = print_pair_i(m, n);    printf("%d\n", count);

  reset_count();
  count = print_pair_f(x, y);    printf("%d\n", count);

  print_pair_d(15.0, 28.0);
  count = print_pair_d(20.0, 30.0);    printf("%d\n", count);
}

int count=0;             /**  all functions following this declaration **/
                         /**    can use this variable **/

int print_pair_i(int x, int y)
{
  printf("(%d, %d)\n", x, y);
  return ++count;
}

int print_pair_f(float x, float y)
{
  printf("(%f, %f)\n", x, y);
  return ++count;
}

void reset_count(void)        /**  resets the counter that print_pair_i  **/
{
  count=0;                    /**  and print_pair_f use    **/
}

int print_pair_d(double x, double y)
{
  static int count=0;      /** a private copy, supersedes previous variable **/
  printf("(%lf, %lf)\n", x, y);
  return ++count;
}

Output:
(10.000000,14.100000)
1
(2,5)
(2,5)
3
(10.000000,14.100000)
1
(15.000000,28.000000)
(20.000000,30.000000)
2


Larger Programs

A program can also be made of pieces, with a header file. This uses the #include preprocessor command. One way is to compile all the files separately. This can most easily be done with make (see Appendix A).

/* FILE: large_prog.c */
#include "large.h"

int max_val;       /***  the ONLY definition of max_val  ***/

main()
{
  int n=1;
  float x=5.0;

  printf("%f, %f, %f\n", A(x), B(), C(n));
  printf("%f, %f, %f\n", A(x), C(n*2), B());
}

float A(float x)
{
  return (x*x*x);
}

/*
**	to compile:
**	  % cc -o large large_prog.c large_sub.c
**
**	if large_sub.c will not been changed, can use
**	  % cc -c large_sub.c
**	once, followed by 
**	  % cc -o large large_prog.c large_sub.o
**	whenever large_prog.c is changed
*/

/* FILE: large.h */
#include 

#define  TRUE   1
#define  FALSE  0

extern int max_val;

extern float A(float x);
extern float B(void);
extern float C(int n);


/* FILE: large_sub.c */
#include "large.h"

int num;     /***  only functions in this file can access num  ***/

float B(void)
{
  return ((float) num);
}

float C(int n)
{
  num=n;
  return (n*4.0);
}

This has the following output, which shows a dependence on the argument evaluation order in printf().

Output:

125.000000, 0.000000, 4.000000
125.000000, 8.000000, 2.000000

Alternatively, the files can be put together by the preprocessor. This is simpler, but it compiles all the files, not just the unchanged ones.

/* FILE: large-2.h */
#include 

#define  TRUE   1
#define  FALSE  0

int max_val;                  /*** global variable ***/

/* FILE: large_sub.c */
#include "large.h"

int num;     /***  only functions in this file can access num  ***/

float B(void)
{
  return ((float) num);
}

float C(int n)
{
  num=n;
  return (n*4.0);
}

/* FILE: large-2_prog.c */
#include "large-2.h"
#include "large-2_sub.c"

float A(float x);

main()
{
  int n=1;
  float x=5.0;

  printf("%f, %f, %f\n", A(x), B(), C(n));
  printf("%f, %f, %f\n", A(x), C(n*2), B());
}

float A(float x)
{
  return (x*x*x);
}

/***

to compile:
  % cc -o large large-2_prog.c
 ***/


Macros

Small procedures like swap() and max() can also be written as macros using #define

#define MAX(x,y)  ((x) > (y) ? (x) : (y))           /**  macro for maximum  **/

float max(float x, float y)                      /**  function for maximum  **/
{
  return (x>y ? x : y);
}

There are advantages to each. Since #define causes a macro substitution, code is replaced before compilation. It will run faster, since it won't make a function call, but it will evaluate either x or y twice, which may have side effects or take extra computational effort. MAX will work on any arithmetic type, while max() will only work on floats. The functions dmax() and imax() are needed for double and integer values.

Macro substitutions do not happen within quoted strings or as parts of other identifiers: `#define NO 0' does not replace `NO' in `x = NOTHING;' or `printf("NO!");.' Also, parentheses are very important:

#define RECIPROCAL_1(x)     1/(x)
#define RECIPROCAL_2(x)     1/x

main()
{
  float x=8.0, y;
  y = RECIPROCAL_1(x+10.0);
  printf("1/%3.1f = %8.5f\n", x, y);
  y = RECIPROCAL_2(x+10.0);
  printf("1/%3.1f = %8.5f\n", x, y);
}

Output:
1/8.0 =  0.05556
1/8.0 = 10.12500

To continue a macro definition onto the next line, use a '\' at the end of the current line.


Problems

  1. Write a function to raise a number to an integer power, x_to_int_n(x,n)
  2. Write a function to calculate factorial (n)
  3. Try to write the factorial function recursively
  4. Write a program to input a positive number and print all the prime number less than or equal to that number, using functions like is_prime() and get_positive_int()


Table 7: Summary of Storage Classes (Kochan, p. 416)
If storage class isAnd variable is declaredThen it can be referencedAnd can be initialized withComments
staticOutside a functionAnywhere within the fileConstant expressions onlyVariables are initialized only once at the start of program execution; values are retained through function calls; default initial value is 0
Inside a function/ blockWithin the function/ block
externOutside a functionAnywhere within the file Constant expressions onlyVariable must be declared in at least one place without the extern keyword or in exactly one place with an initial value
Inside a function/ blockWithin the function/ block
autoInside a function/ blockWithin the function/ block Any valid expression; arrays, structs, unions to constant expressions only if {...} list is usedVariable is initialized each time the function/ block is entered; no default value
registerInside a function/ block Within the function/ blockAny valid expressionAssignment to a register not guaranteed; varying restrictions on types of variables that can be declared; cannot take the address of a register variable; initialized each time function/ block is entered; no default value
omittedOutside a functionAnywhere within the file or by other files that contain appropriate declarations Constant expressions onlyThis declaration can appear in only one place; variable is initialized at the start of program execution; default value is 0
Inside a function/ block(See auto)(See auto) Defaults to auto



Chapter 3: Pointers

Pointer Definition and Use

A pointer is a variable whose value is the address of some other object. This object can have any valid type: int, float, struct, etc. The pointer declaration syntax is
type *ptr-name;
A pointer to an integer is declared as
int *p;
where `p' is of type `int *', pointer to an integer, and `*p' is of type integer. The type of object the pointer references must be specified before a value can be obtained. The operators used with pointers are the pointer reference/indirection (*) and address (&) operators:

main()
{
  int x, *px;               /*  defines the pointer px  */
  px = &x;                  /*  &x ==> address of x  */
  *px = x;                  /*  *px ==> value px points to  */
}
where the value of px is the address of x, and *px is equivalent to x.



Figure 1: Memory diagram with pointers. The memory address are given by (n)


/* example program */
main()
{
  int x=5, y=6, *p;
  p = &x;                         /**  pointer needs to point to something  **/
  printf("1.  x=%d, y=%d, *p=%d\n", x, y, *p);
  x = 7;
  printf("2.  x=%d, y=%d, *p=%d\n", x, y, *p);
  *p = 8;
  printf("3.  x=%d, y=%d, *p=%d\n", x, y, *p);
  p = &y;
  printf("4.  x=%d, y=%d, *p=%d\n", x, y, *p);
  *p += 10 * (x * *p);
  printf("5.  x=%d, y=%d, *p=%d\n", x, y, *p);
}

Output:
1.  x=5, y=6, *p=5
2.  x=7, y=6, *p=7
3.  x=8, y=6, *p=8
4.  x=8, y=6, *p=6
5.  x=8, y=486, *p=486



Figure 2: Memory diagram with pointers - the example program


Valid pointer operations:

/**  Valid Pointer Operations  **/
#define   NULL  0

main()
{
  int x, y;
  int *px=(&x);              /**  can initialize an automatic pointer  **/
  int *py;
  void *pv;

  py = px;                   /**  assign to pointer of same type  **/
  px = (int *) pv;           /**  recast a (void *) pointer  **/
  pv = (void *) px;          /**  recast to type (void *)  **/
  py = px+2;                 /**  for use with arrays  **/
  px++;                      /**  for use with arrays  **/
  if (px == NULL)            /**  compare to null pointer  **/
    py=NULL;                 /**  assign to null pointer  **/
}

Invalid pointer operations:

/**  Illegal Pointer Operations  **/
main()
{
  int x, y;
  int *px, *py, *p;
  float *pf;

  px = &x;              /**  legal assignment  **/
  py = &y;              /**  legal assignment  **/
  p = px + py;          /**  addition is illegal  **/
  p = px * py;          /**  multiplication is illegal  **/
  p = px + 10.0;        /**  addition of float is illegal  **/
  pf = px;              /**  assignment of different types is illegal  **/
}


Pointers as Function Arguments: "Call by Value"

When a function is called, it gets a copy of the arguments ("call by value"). The function cannot affect the value that was passed to it, only its own copy. If it is necessary to change the original values, the addresses of the arguments can be passed. The function gets a copy of the addresses, but this still gives it access to the value itself. For example, to swap two numbers,

main()
{
  float x=5.0, y=6.0;
  void swap_A(float *x, float *y), swap_V(float x, float y);

  printf("x = %6.2f, y = %6.2f\n", x, y);
  swap_V(x, y);
  printf("x = %6.2f, y = %6.2f\n", x, y);
  swap_A(&x, &y);
  printf("x = %6.2f, y = %6.2f\n", x, y);
}

void swap_A(float *x, float *y)      /**  passes addresses of x and y  **/
{
  float tmp = *x;
  *x = *y;
  *y = tmp;
}

void swap_V(float x, float y)        /**  passes values of x and y  **/
{
  float tmp = x;
  x = y;
  y = tmp;
}

Output:
x =   5.00, y =   6.00
x =   5.00, y =   6.00
x =   6.00, y =   5.00
Here, swap_V() does not work, but swap_A() does.


Arrays

An array is a contiguous space in memory which holds a certain number of objects of one type. The syntax for array declarations is
type array-name[const-size];
static type array-name[const-size] = initialization-list;
static type array-name[] = initialization-list;

An array of 10 integers is declared as

int x[10];
with index values from 0 to 9.

A static array can be initialized:

static int x[5] = 7,23,0,45,9;
static int x[] = 7,23,0,45,9;

static int x[10] = 7,23,0,45,9,0,0,0,0,0;
static int x[10] = 7,23,0,45,9;

where the remaining five elements of x[10] will automatically be 0. Part of the array can be passed as an argument by taking the address of the first element of the required subarray (using &), so &x[6] is an array with 4 elements.



Figure 3: Box-and-pointer diagram of arrays: static int[5]: = {7, 23, 0, 45, 9};



Figure 4: Memory diagram of arrays


#define   MAX   10
static int b[MAX] = {1, 5, 645, 43, 4, 65, 5408};

main()
{
  int i;
  int *p, *p_max;
  static int a[] = {1, 5, 645, 43, 4, 65, 5408, 4, 7, 90};
  
  printf("array elements:  ");
  for (i=0; i *p_max)
      {
	p_max = p;
	printf("new maximum value: %d\n", *p);
      }
    else
      printf("\"distance\" from maximum element: %d\n", (p-p_max));
}

Output:
array elements:  1  5  645  43  4  65  5408  4  7  90  
"distance" from maximum element: 0
new maximum value: 5
new maximum value: 645
"distance" from maximum element: 1
"distance" from maximum element: 2
"distance" from maximum element: 3
new maximum value: 5408
"distance" from maximum element: 1
"distance" from maximum element: 2
"distance" from maximum element: 3

The array and pointer are closely related, in that x[i] and *(x+i) both get the i+1 element in the array, and &x[i] and (x+i) are both pointers to the i+1 element.

There are differences between them, however. An array name is a constant, while a pointer is a variable, so

int x[10], *px;
px = x; px++; /** valid **/
x = px; x++; /** invalid, cannot assign a new value **/

Also, defining the pointer only allocates memory space for the address, not for any array elements, and the pointer does not point to anything. Defining an array (x[10]) gives a pointer to a specific place in memory and allocates enough space to hold the array elements. To allocate space for an array declared as a pointer, use *malloc() or *calloc(), which are declared in stdlib.h, and then free() to deallocate the space after it is used.

/***  memory_allocation for arrays  ***/
#include 

main()
{
  int n;
  float *a, *b;

  a = (float *) malloc(n * sizeof(float));   /***  not initialized  ***/
  b = (float *) calloc(n, sizeof(float));    /***  initialized to 0  ***/

  if ((a == NULL) || (b == NULL))
    printf("unable to allocate space");

  free(a);
  free(b);
}


Functions Returning Pointers

In addition to passing pointers to functions, a pointer can be returned by a function. Three pointers must be of the same type (or be recast appropriately): The pointer should not point to an automatic local variable within the function, since the variable will not be defined after the function is exited so the pointer value will be invalid.

/***  returns a pointer to the maximum value in an array  ***/

int maximum_val1(int A[], int n);
int maximum_val2(int *a, int n);
int *maximum_ptr1(int *a, int n);
int *maximum_ptr2(int *a, int n);

main()
{
  int i,n;
  int A[100], *max;

  printf("number of elements: "); scanf("%d",&n);

  printf("input %d values:\n", n);
  for (i=0; i<n; i++)
    scanf("%d", A+i);

  printf("maximum value = %d\n", maximum_val1(A,n));
  printf("maximum value = %d\n", maximum_val2(A,n));

  max = maximum_ptr1(A,n);
  printf("maximum value = %d\n", *max);
}

int maximum_val1(int A[], int n)
{
  int max, i;
  for (i=0, max=0; i max)
      max = A[i];
  return max;
}

int maximum_val2(int *a, int n)
{
  int max=0;
  for ( ; n>0 ; n--, a++)
    if (*a > max)
      max = *a;
  return max;
}

int *maximum_ptr1(int *a, int n)   /***  will work  ***/
{
  int *max = a;
  for ( ; n>0; n--, a++)
    if (*a > *max)
      max = a;
  return max;         /***  max points to an element of the array  ***/
}

int *maximum_ptr2(int *a, int n)   /***  won't work  ***/
{
  int max = *a;
  for ( ; n>0; n--, a++)
    if (*a > max)
      max = *a;
  return &max;     /***  max will not exist after function ends  ***/
}

Output:
number of elements: 10
input 10 values:
3
4
5
3
6
5
4
7
5
6
maximum value = 7
maximum value = 7
maximum value = 7


Multidimensional Arrays

A multidimensional array can be defined and initialized with the following syntax:
type array-name[const-num-rows][const-num-cols];
static type array-name[const-num-rows][const-num-cols] = init-list;
static type array-name[][const-num-cols] = initialization-list;

static int x[][3] = {{3, 6, 9}, {4, 8, 12}};   /* static--can be initialized */
static int y[2][3] = {{3},{4}};                /* OR {{3,0,0},{4,0,0}}  */

main()
{
  int z[2][3];
  printf("%d\n", x[1][2]);                     /**  output: 12  **/
}

To get a pointer to the ith row of the array, use x[i-1].

Alternatively, a pointer to a pointer can be used instead of a multidimensional array, declared as int **y. Then y points to a one-dimensional array whose elements are pointers, *y points to the first row, and **y is the first value.

When passing a two-dimensional array to a function, it can be be referenced in four ways:

Here COL and ROW must be constants.


Figure 5: Box-and-pointer & memory diagrams of 2D arrays:
static int x[2][3] = {{3, 6, 9},{4, 8, 12}};


#define  MAX  5
#define  LINEFEED   printf("\n")

int **imatrix(int n, int m);

void print_imatrix1(int A[][MAX], int n, int m);
void print_imatrix2(int *a[], int n, int m);

int sum_imatrix1(int a[][MAX], int n, int m);
int sum_imatrix2(int **a, int n, int m);

void input_imatrix(int **a, int n, int m);


main()
{
  int i, j, n = MAX;
  int **A, **b, C[MAX][MAX];

  A = imatrix(n, n);
  for (i=0; i

Output:
0      1      2      3      4
1      2      3      4      5
2      3      4      5      6
3      4      5      6      7
4      5      6      7      8

0      0      0      0      0
0      1      2      3      4
0      2      4      6      8
0      3      6      9     12
0      4      8     12     16

100
100

size of array to input: 2
3 4
7 5
    3      4
    7      5


Strings

Strings are simply character arrays, or more accurately, pointers to characters. A string literal is enclosed within quotes,"...", and is an array with those characters and `0' at the end, so "hello" <==>{'h','e','l','l','o','\0'}. The string can be defined as
static char *p = "hello"

An example illustrating the use of pointers with the string copies one string into another:
main()
{
  char *t = "hello", s[100]; 
  void strcpy(char *, char *);
  strcpy(s,t);
  printf("%s\n", s);                          /**  will print 'hello'  **/
}

/**  strcpy:  copy t to s; pointer version 2  (K&R, p 105)  **/

void strcpy(char *s,char *t)
{
  while (*s++ = *t++)         /**  OR   while ((*s++ = *t++) != '\0')  **/
    ;
}


Command Line Arguments

It is often useful to give a program arguments when it is run. This is done with command line arguments, which are arguments of main(). There are two arguments: an integer, argc, which is the number of items in the command line (including the program name), and an array of strings, *argv[], which are the actual items. The first string, argv[0], is the name of the function being executed.

If a number is needed, it has to be obtained using sscanf(), which is the same as scanf() except it takes a string as its first argument. This example prints the square root of a number.

#include 
main(int argc, char *argv[])             /**  program to find sqrt(x)  **/
{
  float x;
  if (argc == 2)
    {
      sscanf(argv[1], "%f", &x);
      printf("the square root of %f is %f\n", x, sqrt(x));
    }
  else
    {
      printf("Wrong number of arguments\n");
      printf("usage: %s x \n", *argv);
    }
}


Pointers to Functions

Functions can return pointers, or a pointer can point to a function:

int *f(); /* a function f returning a pointer to an int */
int (*f)(); /* a pointer to a f which returns an int */

Since the precedence of () is higher than *, parentheses are needed around *f to get a pointer to a function.
float square(float x);
float cube(float x);
float arith(float x, float (*func)(float));

main()
{
  float x, y, z;
  printf("Enter x: ");    scanf("%f", &x);
  y = arith(x, square);
  z = arith(x, cube);
  printf("x = %f, x^2 = %f, x^3 = %f\n", x, y, z);
}

/**  the arguments for arith() are x and func,
 **    which is a pointer to a function whose argument is one float
 **/

float arith(float x, float (*func)(float))
{
  return (*func)(x);
}

float square(float x)
{
  return x*x;
}

float cube(float x)
{
  return x*x*x;
}


Problems

  1. Write a program to input two matrices, add and multiply them, and print the resulting matrices. The matrices can be any size up to a maximum (#define MAX 5, for example). Use functions input_matrix, print_matrix, multiply_matrix.



Chapter 4: Structures

Syntax and Operations

A structure is a data type which puts a variety of pieces together into one object. The syntax is given below.
struct structure-tag-opt {
member-declarations
structure-names-opt ; }

struct structure-tag structure-name;

structure-name.member ptr-to-structure->member

struct time
{
	int hur;
	int minute;
	int second;
} now;

main()
{
	struct time later;

now.hour = 10;
now.minute = 30;
now.second = 4;

later = now;
printf("the later time is %d:%2d:%2d\n", later.hour, later.minute, later.second);
}

This declares structure tag, struct time, which keeps the members, hour, minute, second, in one piece. The variables now and later are structures of type struct time, declared the same way as integers. The members of the structure can be any type: int, float, double, char, arrays, other structures, and pointers to any of these. To access the members, there are two operators available (. and ->). To access the specified member, use the . operator.

Valid structure operations:

Invalid structure operations:


With ANSI-C, structures are initialized in the same way as arrays,
struct time noon = 12, 00, 00;

Pointers to structures are very useful, and often necessary when functions are used. For example,
     struct time now, *t;
     t = &now;	 	            /* identical to x=&y with numerical types */
     (*t).hour = 6;        		/* gets the hour */
     t->minutes = 30;      	/* gets the minutes */

The variable t is a pointer to a structure. Since the precedence of . is higher that that of *, the parentheses are needed to get the actual structure from the pointer to it. Since this is used often, the -> operator was made to do the same thing.

Structure members can be other structures. For example,

struct time
{
  int hour, minute, second;
} ;
struct date
{
  int month, day, year;
} ;
struct dt
{
  struct date d;
  struct time t;
} ;

main()
{
  struct dt start_class;
  start_class.d.month = 1;
  start_class.d.day = 5;
  start_class.d.year = 93;
}


typedef

typedef defines a new type, which can simplify the code. Here is the syntax:
typedef data-type TYPE-NAME;
typedef struct structure-tag TYPE-NAME;
typedef struct
{
	member-declarations
} TYPE-NAME ;

Using typedef also helps portability, especially with machine dependent data types and sizes. With typedef, the change can be made in one place and is fixed for the whole program. For example,

typedef int Length, Width, Height;
typedef struct time TIME;
TIME now, *t;

will specify the types Length, Width, Height and TIME, and now and t are defined above. typedef is a syntactic simplification to aid reading and modifying the program. It does not actually create new types.


Array of Structures

An array of structures can also be defined:
struct date
{
  int month, day, year;
};
typedef struct date DATE;

main()
{
  int i;
  DATE birthdays[10], *bday;
  bday = birthdays;                  /***  pointer <==> array name  ***/
  for (i=0; i<10; i++, bday++)
    scanf("%d %d %d", &bday->month, &((*bday).day), &birthdays[i].year);

  for (i=0, bday = birthdays; i<10; i++, bday++)
    printf("%2d/%02d/%2d\n", bday->month, bday->day, bday->year);
}
     /***  the %02d pads the field with 0s, not spaces  ***/

When bday is defined as a pointer of type DATE (struct date), incrementing will be done properly to get to successive structures in the array.


Use with Functions

Structures can be used with functions. Just as with other data types, either the structure or a pointer to the structure can be passed to the function. The choice should be based on three things,
1. does the structure need to be changed by the function,
2. is the structure small enough that copying it as a local argument will not affect performance,
3. does compatibility with old compilers require using pointers to the structures.

In addition, the function can return a structure or a pointer to a structure.
/***  functions to a increment the time and date  ***/

#define  PRINT_TIME(t)  printf("%2d:%2d:%2d", t.hour, t.minute, t.second)
#define  PRINT_DATE(d)  printf("%2d/%2d/%2d", d.month, d.day, d.year)
#define  LINEFEED       printf("\n")

typedef struct
  {
    int hour, minute, second;
  }  TIME;

typedef struct
  {
    int month, day, year;
  }  DATE;

void time_increment(TIME *t, DATE *d);
void date_increment(DATE *d);
DATE date_increment2(DATE d); 

main()
{
  TIME now;
  DATE today;
  
  now.hour = 12;  now.minute = 30;  now.second = 15;
  today.month = 1;  today.day = 7;  today.year = 93;

  PRINT_TIME(now);  LINEFEED;
  PRINT_DATE(today);  LINEFEED;

  time_increment(&now, &today);
  PRINT_TIME(now);  LINEFEED;
  PRINT_DATE(today);  LINEFEED;

  date_increment(&today);
  PRINT_DATE(today);  LINEFEED;

  PRINT_DATE(date_increment2(today));  LINEFEED;
    /***  calls date_increment2 three times in macro  ***/
}

/*** time_increment needs to be able to change two values  ***/
void time_increment(TIME *t, DATE *d)
{
  DATE d2;
  if (t->second != 59)      /*** count seconds  0...59  ***/
      ++t->second;
  else if (t->minute != 59)
    {
      t->second = 0;      t->minute++;
    }
  else if (t->hour != 23)
    {
      t->second = 0;      t->minute = 0;      t->hour++;
    }
  else
    {
      t->second = 0;      t->minute = 0;      t->hour = 0;
      date_increment(d);
    }
}

void date_increment(DATE *d)
{
  if (d->day != 31)      /*** assume all months have 31 days  ***/
    d->day++;
  else if (d->month != 12)      /*** count months  1...12  ***/
    {
      d->day = 1;      d->month++;
    }
  else
    {
      d->day = 1;      d->month = 1;      d->year++;
    }
}

/*** an alternative to date_increment, if it only returns one value ***/

DATE date_increment2(DATE d)         /* can also pass date one structure */
{
  if (d.day != 31)      /*** assume all months have 31 days  ***/
    ++d.day;
  else if (d.month != 12)      /*** count months  1...12  ***/
    {
      d.day = 1;
      d.month++;
    }
  else
    {
      d.month = 1;
      d.year++;
    }
  return d;
}

Output:
12:30:15
 1/ 7/93
12:30:16
 1/ 7/93
 1/ 8/93
 1/ 9/93
 1/ 8/93

For another example, see the complex variable functions.


Linked Lists

A member of a structure can also be a pointer to the same structure type. This is useful with linked lists and trees.

#define  NodeMemory  (NodePtr) malloc(sizeof (struct node))

struct node
{
  int val;
  struct node *r_branch;
  struct node *l_branch;
} ;
typedef struct node * NodePtr;
 
main()
{
  NodePtr tree, branch;

  tree = (NodePtr) malloc(sizeof (struct node));
  tree->val = 10;
  tree->r_branch = NodeMemory;
  tree->l_branch = NodeMemory;

  tree->r_branch->val = 3;
  tree->l_branch->val = 40;
  printf("%d, %d, %d\n", tree->val, tree->r_branch->val, tree->l_branch->val);
}


union

With union, different types of values can be stored in the same location at different times. Space is allocated to accomodate the largest member data type. They are syntactically identical to structures, Syntax:
union union-tag-opt
{
	member-declarations
}  union-names-opt;

union-name.member
ptr-to-union->member

/**  a simple example with unions  **/

union union_ifd     /** can store either an integer, float, or double value **/
{
  int ival;
  float fval;
  double dval;
} ;

main()
{
  union union_ifd  u1;

  u1.ival = 10;
  printf("%d\n", u1.ival);
  u1.fval = 10.34;
  printf("%f\n", u1.fval);
  u1.dval = 10.03454834;
  printf("%.10lf\n", u1.dval);
}

It is the programmer's reponsibility to know which variable type is being stored at a given time. The code

u1.ival=10;
printf("fn", u1.fval);

will produce an undefined result.


enum

The type enum lets one specify a limited set of integer values a variable can have. For example, flags are very common, and they can be either true or false.
Syntax:
enum enum-tag-opt {enum-tags} enum-variable-names-opt;

enum-name variable-name

The values of the enum variable are integers, but the program can be easier to read when using enum instead of integers. Other common enumerated types are weekdays and months.

The enumerated values can be set by the compiler or set explicitly. If the compiler sets the values, it starts at 0 and continues in order. If any value is set explicitly, then subsequent values are implicitly assigned.

enum flag_o_e {EVEN, ODD};
enum flag_o_e test1;
typedef enum flag_o_e FLAGS;

FLAGS if_even(int n);

main()
{
  int x;
  FLAGS test2;

  printf("input an integer: ");  scanf("%d", &x);
  test2 = if_even(x);
  if (test2 == EVEN)
    printf("test succeeded (%d is even)\n", x);
  else
    printf("test failed (%d is odd)\n", x);
}

FLAGS if_even(int n)
{
  if (n%2)
    return ODD;
  else
    return EVEN;
}

This is a more detailed program, showing an array of unions and ways to manipulate them, as well as enum.

/***  example with unions  ***/
#define   ASSIGN_U_NONE(x)        {x.utype = NONE;}
#define   ASSIGN_U_INT(x,val)     {x.utype = INT;     x.u.i = val;}
#define   ASSIGN_U_FLOAT(x,val)   {x.utype = FLOAT;   x.u.f = val;}
#define   ASSIGN_U_DOUBLE(x,val)  {x.utype = DOUBLE;  x.u.d = val;}

typedef union
{
  int i;
  float f;
  double d;
}  Arith_U;
typedef enum {NONE, INT, FLOAT, DOUBLE} Arith_E;
typedef struct
{
  Arith_E utype;
  Arith_U u;
}  Var_Storage;

main()
{
  int i;
  Var_Storage a[10];

  a->utype = INT;  a->u.i = 10;             /**  pointer to union operation **/
  a[1].utype = FLOAT;  a[1].u.f = 11.0;
  a[2].utype = DOUBLE;  a[2].u.d = 12.0;
  ASSIGN_U_NONE(a[3]);
  ASSIGN_U_INT(a[4], 20);
  ASSIGN_U_FLOAT(a[5], 21.0);
  ASSIGN_U_DOUBLE(a[6], 22.);

  for (i=0; i<7; i++)
    {
      if (print_Var(a[i]))
	printf("\n");
    }
}

int print_Var(Var_Storage x)
{
  switch (x.utype)
    {
    case INT:        printf("%d",x.u.i);       break;
    case FLOAT:      printf("%f",x.u.f);       break;
    case DOUBLE:     printf("%.8lf",x.u.d);    break;
    default:         return (0);               break;
    }
  return (1);
}


Example: Complex Numbers

A complex number can be represented as
z = a+bi = r * e^(i*theta)
with
a = r * cos(theta)
b = r * sin(theta)
r = (a^2 + b^2)^(1/2)
theta = (tan(b/a))^(-1)

and

z = z1 + z2 = (a1 + a2) + (b1 + b2)i
z = z1 * z2 = (a1*a2 - b1*b2) + (a1*b2 + a2*b1)i
= r1*r2 * e^(theta1 + theta2)i


/***  Example using structures to represent complex numbers  ***/
#include 
#include "prog4-06.h"

main()
{
  static COMPLEX z1 = {{1.0, 2.0}, {0.0, 0.0}};
  static COMPLEX z[MAX] = { {{1.0, 1.0}, {0.0, 0.0}},
			      {{2.0, -1.0}, {0.0, 0.0}} };

  rect_to_polar(&z1);
  rect_to_polar(z);
  rect_to_polar(z+1);
  complex_print(z1, BOTH);
  complex_print(*z, BOTH);
  complex_print(*(z+1), BOTH);
  z[2] = z1;

  z[3] = complex_add(z[0], z[1]);
  complex_print(z[3], BOTH);
/**  write complex_multiply() as an exercise:  **/
/**  *(z+4) = complex_multiply(*z, *(z+1));    **/
/**  complex_print(*(z+4), BOTH);              **/
}

void complex_print(COMPLEX z, C_FLAG flag)
{
  switch (flag)
    {
    case RECT:
      printf("z = %8.3f + %8.3f i\n", (z.r.a), (z.r.b));
      break;
    case POLAR:
      printf("z = "); PRINT_POLAR(z);
      break;
    case BOTH:
      PRINT_BOTH(z);
      break;
    }
}

void rect_to_polar(COMPLEX *z)
{
  double a = (z->r.a);
  double b = (z->r.b);
  z->p.r = sqrt(a*a + b*b);
  z->p.theta = atan2(b,a);
}

COMPLEX complex_add(COMPLEX z1, COMPLEX z2)
{
  COMPLEX sum;
  sum.r.a = (z1.r.a) + (z2.r.a);
  sum.r.b = (z1.r.b) + (z2.r.b);
  rect_to_polar(&sum);
  return (sum);
}

/**  File: prog4-06.h  **/
#define MAX 10

#define  PRINT_RECT(z)  printf("%8.3f + %8.3f i", (z.r.a), (z.r.b))
#define  PRINT_POLAR(z) printf("%8.3f * exp(%8.3f i)", (z.p.r), (z.p.theta))
#define  PRINT_BOTH(z)  { \
            printf("z = "); PRINT_RECT(z); \
            printf(" = "); PRINT_POLAR(z); printf("\n"); }

struct rect
  {
    double a, b;
  };

struct polar
  {
    double r, theta;
  };

struct complex
  {
    struct rect r;
    struct polar p;
  } ;
typedef struct complex COMPLEX;

enum c_flag {RECT, POLAR, BOTH};
typedef enum c_flag C_FLAG;

/*** function prototypes for rect_to_polar, complex_add, complex_print  ***/
void rect_to_polar(COMPLEX *z);
COMPLEX complex_add(COMPLEX z1, COMPLEX z2);
void complex_print(COMPLEX z, C_FLAG flag);

/*** function prototypes for polar_to_rect, complex_multiply, complex_input,
     to be written as exercises  ***/
void polar_to_rect(COMPLEX *z);
COMPLEX complex_multiply(COMPLEX z1, COMPLEX z2);
COMPLEX complex_input(void);

Output:
z =    1.000 +    2.000 i =    2.236 * exp(   1.107 i)
z =    1.000 +    1.000 i =    1.414 * exp(   0.785 i)
z =    2.000 +   -1.000 i =    2.236 * exp(  -0.464 i)
z =    3.000 +    0.000 i =    3.000 * exp(   0.000 i)


Problems

  1. Write the functions polar_to_rect, complex_multiply, and complex_input to be used with the answer to question 11.


Chapter 5: C Libraries

The standard C libraries include functions for

Memory Allocation

To have variable array sizes, dynamic memory allocation can be used.

#include 

void *malloc(size_t size);
void *calloc(n, size_t size);
void free(void *p);

in ANSI C, size_t+ is the size of a character. The (sizeof) operator returns the size of an object in units of size_t. In addition, the type of the pointer returned by malloc and calloc has to be cast as needed. For example,

#include 

main()
{
  int i, n;
  double *A, *a;

  scanf("%d", &n);
  A = (double *) malloc(n * sizeof (double));

  for (i=0; i

Math Libraries

There are a variety of math functions available, all declared in /usr/include/math.h. Most take arguments of type double and return values of type double. For example,

#include 

main()
{
  double x,y,z,theta;
  z = sqrt(x);
  z = sin(theta);          /***  theta is in radians  ***/
  z = asin(x);
  z = atan(x);
  z = atan2(y, x);         /***  atan(y/x)  ***/
  z = exp(x);              /***  e^x  ***/
  z = log(x);              /***  ln(x) [natural log]  ***/
  z = pow(x, y);           /***  x^y  ***/
}

#include 

main()
{
  double x, y, theta;

  scanf("%lf", &x);
  printf("sqrt(%f) = %f\n", x, sqrt(x));
  printf("sin(0.6) = %f\n", sin(0.6));
  printf("atan(10) = %lf\n", atan(10.0));
  printf("atan(10/20) = %lf\n", atan2(10.0, 20.0));
  printf("exp(10) = %lf\n", exp(10.0));
  printf("log(10) = %lf\n", log(10.0));
  printf("log_10(10) = %lf\n", log10(10.0));
  printf("10^1.3 = %lf\n", pow(10.0, 1.3));
}

Output:
sqrt(10.000000) = 3.162278
sin(0.6) = 0.564642
atan(10) = 1.471128
atan(10/20) = 0.463648
exp(10) = 22026.465795
log(10) = 2.302585
log_10(10) = 1.000000
10^1.3 = 19.952623

When compiling, is must be specified that the math libraries are being used. For example, on Unix systems, use

cc -o .c -lm


Random Variables

Using random variables is system dependent. The ANSI C functions are rand() and srand().

int rand(void);
void srand(unsigned int seed);
int RAND_MAX;

The function rand() will return a value between 0 and RAND\_MAX, where RAND\_MAX is defined in and is at least 32,767. The function srand() is used to seed the random number generator. Many systems have better random number generators, and C can usually access them, although this would then not be very portable. A good practice is to write a function or macro which returns a random number, and have this call the system-specific routines.

#include 

#define  RANDOM_NUMBER_01          ((double) rand() / RAND_MAX)
#define  SEED_RANDOM_GEN(seed)     (srand(seed))

main()
{
  int i, n, seed;
  double *x;

  printf("number of random values: ");  scanf("%d", &n);
  x = (double *) malloc(n * sizeof(double));

  printf("input seed: ");  scanf("%d", &seed);
  SEED_RANDOM_GEN(seed);

  for (i=0; i

Output:
number of random values: 5
input seed: 10
0.13864904
0.86102660
0.34318625
0.27069316
0.51536290


Input/Output

The conversions for printf() and scanf() are described in tables 3 and 4. In addition, I/O includes character output, sscanf(), and file manipulation.

#include 

int i;
char c, s[], file_name[], access_mode[];
FILE *fp;

fp = fopen(file_name, access_mode);
fflush(fp);                        /***  flush the buffers  ***/
fclose(fp);

putchar(c);                             /***  one character  ***/
putc(c, fp);
puts(s);                                /***  one line  ***/
fputs(s, fp);
printf(format, arg1, ...)               /***  formatted  ***/
fprintf(fp, format, arg1, ...)
sprintf(s, format, arg1, ...);

c=getchar();
c=getc(fp);
gets(s);
fgets(s,i,fp);           ***  first i characters or till newline  ***/
scanf(format, &arg1, ...)               /***  formatted  ***/
fscanf(fp, format, &arg1, ...);
sscanf(s, format, &arg1, ...);

/***  reads in n integers from a file,
      then prints the values to another file as type float  ***/
#include        /***  for file manipulation functions  ***/
#include       /***  for malloc()  ***/

main()
{
  int i, n, *x;
  char file_name[FILENAME_MAX];
  FILE *fp;

  printf("file name for input: "); scanf("%s", file_name);
  fp = fopen(file_name, "r");
  if (fp == NULL)
    {
      printf("error: could not open file %s\n", file_name);
      exit(-1);
    }

  fscanf(fp, "%d", &n);
  x = (int *) malloc(n * sizeof(int));
  
  for (i=0; i


Strings

A variety of string functions are available.

#include 

int i;
size_t n;
char *s, *s1, *s2, *to, *from;;
s = strcat(s1, s2);
s = strchr(s, char c);
i = strcmp(s1, s2);              /***  s1=s2 ? 0 : (s1>s2 ? 1 : -1)  ***/
s = strcpy(to, from);            /***  returns *to  ***/
n = strlen(s);
s = strstr(s1, s2);              /***  is s2 in s1?  ***/
s = strncat(s1, s2, int n);      /*** only use first n characters  ***/
i = strncmp(s1, s2, int n);
s = strncpy(to, from, int n);

#include 
#include 

main()
{
  char *s, *ct = "hello";
  s = (char *) malloc(100 * sizeof(char));

  strcpy(s, ct);
  printf("%s\n", s);

  if (strcmp(s, ct) == 0)
    printf("strings equal\n");
  else
    printf("\"%s\" and \"%s\" differ\n", s, ct);
}

#include 
#include 

main()
{
  int i, j;
  float x;
  char *s1 = "10 20 15.5", *s2;
  s2 = (char *) malloc(100 * sizeof(char));

  sscanf(s1, "%d %d %f", &i, &j, &x);
  printf("i = %d, j = %d, x = %f\n", i, j, x);

  sprintf(s2, "i = %d, j = %d, x = %f", i, j, x);
  printf("the string is \"%s\"\n", s2);
}

Output:
i = 10, j = 20, x = 15.500000
the string is "i = 10, j = 20, x = 15.500000"



Appendix A: Make Program

The make function is used to simplify the complition process. It has three main features:
  • target specifications with dependencies
  • command lines to be executed
  • assignment of strings to variables
The target is the file to be produced, either an executable file or an object file. The dependency list specifies the files on which the target depends, so if any of the dependency files has been modified since the target file was created, make will create a new target file. The command lines specify how the target is supposed to be make. Although this is primarily using the cc command, other commands can also be executed. The syntax is given below.

# comments
var = string value
$(var)		# uses variable value

target:	dependencies
TAB	command-lines

The following commands run make:

% make -k
% make -k

When calling make, the -k argutment indicates that all specified files shluld be compiled, even if there is an error compiling one file. Otherwise, make will stop when there is a compile error in any file.

# a makefile for any simple, one file program, with no dependencies

CC = /bin/cc		# specifies compiler to be used

PROGS=p		# gets file name from shell

$(PROGS) : $(PROGS).c
	    $(CC) -o $(PROGS) $(PROGS).c

Output:
% make program
/bin/cc -O program.c -o program

# a makefile for program large, Section 2

CC = /bin/cc				# specifies compiler to be used
	
OBJS = large_prog.o large_sub.o		# object files to be used

large:  $(OBJS)				# makes the executable file "large"
	$(CC) -o large $(OBJS)

$(OBJS): large.h				# makes any needed / specified object files

clean:					#cleans up - removes object files
	rm $(OBJS)

Output:
% make -k large
/bin/cc -O -c large_prog.c
/bin/cc -O -c large_sub.c
/bin/cc -o large large_prog.o large_sub.o

% make -k
/bin/cc -O -c large_prog.c
/bin/cc -O -c large_sub.c
/bin/cc -o large large_prog.o large_sub.o		

% make -k large_prog.o
/bin/cc -O -c large_prog.c

% make clean
rm large_prog.o large_sub.o


Appendix B: C Style Guide

When writing C code, especially when other people will use or modify the code, it is useful to adhere to a consistent set of coding guidelines. The following is not the only acceptable style, but rather an example of a fairly conventional style guide.


General Style

The first question is the placement of statements and braces. Consistency makes it easier to follow the flow of the program, since one can get used to looking for matching and optional braces in specific places.

/*---   avoid putting more than one statement on the same line   ---*/
  statement1; statement2;           /* BAD        */

  statement1;                       /* OK         */
  statement2;

int func(int arg)
{                           /* no indentation on the first set of braces     */
                            /*   around a procedure                          */

  statement;                /* each step of indentation is two spaces        */

  if (...)                  /* braces are indented and the matching pairs    */
    {                       /*   are lined up in the same column             */
      statement;
    }

  do                        /* 'do' braces should be lined up at the         */
    {                       /*   same column, with the 'while' on the same   */
      statement;            /*   line as the close parenthesis, to avoid     */
    } while (...);          /*   confusion with the 'while' statement        */

label:                      /* labels are lined up with the enclosing braces */
  statement;

  switch (...)
    {
    case xxx:               /* case labels are indented clearly mark the     */
      statement;            /*  places where a 'break' statement is          */
      /*fall thru*/         /*  expected but missing                         */ 
    case yyy:
      statement;
      break;
    default:
      statement;
      break;                /* should have a break statement even at the end */
    }                       /*  of the default case                          */

}                           /* all end braces line up with open braces       */

/*---   the statement following an 'if', 'while', 'for' or 'do' 
        should always be on a separate line; this is especially true for the
        null statement   ---*/

  if (...) statement;               /* BAD        */
  if (...)                          /* OK         */
    statement;

  for (...) statement;              /* BAD        */
  for (...)                         /* OK         */
    statement;

  for (...);                        /* VERY BAD   */
  for (...)                         /* OK         */
    ;

  while (...) statement;            /* BAD        */
  while (...)                       /* OK         */
    statement;

  while (...);                      /* VERY BAD   */
  while (...)                       /* OK         */
    ;

  do statement; while (...);        /* VERY BAD   */
  do                                /* OK         */
    statement;
  while (...);

/*---   arrange nested 'if...else' statements in the way that is easiest to
        read and understand   ---*/

  if (...)                       /* OK, but confusing   */
    statement;
  else
    {
      if (...)
        statement;
      else
        {
          if (...)
            statement;
        }
      }

  if (...)                       /* BETTER              */
    statement;
  else if (...)
    statement;
  else if (...)
    statement;

/*---   the above rules can be violated if the overall legibility is
        improved as a result   ---*/

  switch (...)                           /* OK        */
    {
      case xxx:
        statement;
        break;
      case yyy:
        statement;
        break;
    }

  switch (...)                           /* BETTER (by lining up the         */
    {                                    /*  statements, one can contrast    */
      case xxx: statement; break;        /*  the difference between the      */
      case yyy: statement; break;        /*  branches more easily)           */
    }


  if (...)                               /* OK        */
    {
      statement1;
      statement2;
    }
  else
    {
      statement1;
      statement2;
    }

  if (...) { statement1; statement2; }   /* BETTER (do this only for very    */
  else     { statement1; statement2; }   /*  short statements!)              */


  if (...)                               /* OK        */
    statement;
  else if (...)
    statement;
  else if (...)
    statement;

  if      (...) statement;               /* BETTER    */
  else if (...) statement;
  else if (...) statement;


Layout


Coding Practice

typedef struct
{
  int x, y;
} COORD;

void proc1(COORD *p)
{
  COORD c;
  ...
  c.x = p->x;                 /* OK, but verbose   */
  c.y = p->y;
  memcpy(&c, p, sizeof(c));   /* OK, but slow      */
  c = *p;                     /* BEST              */
}

void proc2(COORD *p)
{
  COORD c = *p;         /* BAD, since not all compilers support initializion */
  ...                   /*  of structures (i.e., not portable)               */
}


Naming Conventions

These are some general naming conventions:


Appendix C: Answers to Problems

/**  "A Crash Course in C", day 1, problem 2: print fahrenheit
 **  and celcius temperatures for 32-212 F in steps of 20 F **/

#define  FREEZE  32
#define  BOIL   212
#define  STEP    20

main()
{
  int f;
  for (f=FREEZE; f<=BOIL; f+=STEP)
    printf("F = %3d, C = %5.1f\n",f,(f-32.0)*5.0/9.0);
}

/**  "A Crash Course in C," problem 3:
 **    input a number and print all its factors  **/
#include 

main()
{
  int i,n;

  printf("input a number: ");  scanf("%d",&n);
  for (i=2; i<=n; i++)
    if (!(n%i))
      printf("%6d is a factor\n", i);
}

/**  "A Crash Course in C," problem 4
 **    input a number and decide if it is prime  **/
#include 
#include 
#define TRUE   1
#define FALSE  0

main()
{
  int i,n, nmax, prime_flag=TRUE;

  printf("input a number: ");  scanf("%d",&n);
  nmax = (int) sqrt((double) n);

  for (i=2; i<=nmax; i++)
    if (!(n%i))
      prime_flag=FALSE;

  if (prime_flag)
    printf("%6d is prime\n", n);
  else
    printf("%6d is not prime\n", n);
}

/**  "A Crash Course in C," problem 5
 **    program to calculate x using the quadratic formula
 **/
#include 
main()
{
  float a, b, c, d, x1, x2;
  printf("input a,b,c: ");
  scanf("%f %f %f",&a, &b, &c);
  d = b*b - 4.0*a*c;
  if (d >= 0)   /***  check if solution will be real or complex  ***/
    {
      x1 = (-b+sqrt(d)) / (2.0*a);
                     /***  need parentheses for proper order  ***/
      x2 = (-b-sqrt(d)) / (2.0*a);
                     /***  use sqrt() from the math library  ***/
      printf("x = %f, %f\n",x1,x2);
    }
  else
    {
      x1 = -b/(2.0*a);
      x2 = sqrt(-d)/(2.0*a);
      printf("x = %f + %fi, %f - %fi\n", x1, x2, x1, x2);
    }
}

/**  "A Crash Course in C," problem 6
 **    input an integer and print it in English  **/

main()
{
  int n, pow_ten;
  printf("input an integer: "); scanf("%d",&n);
  do {
    pow_ten=1;

    while (n / pow_ten)
      pow_ten *= 10;

    for (pow_ten/=10; pow_ten!=0; n%=pow_ten, pow_ten/=10)
      switch (n/pow_ten)
	{
	case 0:  printf("zero ");   break;
	case 1:  printf("one ");    break;
	case 2:  printf("two ");    break;
	case 3:  printf("three ");  break;
	case 4:  printf("four ");   break;
	case 5:  printf("five ");   break;
	case 6:  printf("six ");    break;
	case 7:  printf("seven ");  break;
	case 8:  printf("eight ");  break;
	case 9:  printf("nine ");   break;
	}
    printf("\ninput an integer: "); scanf("%d",&n);
  } while (n>0);
}

/**  "A Crash Course in C," problem 7
 **    count the number of characters and lines   **/
#include 

main()
{
  char c;
  int characters, lines;

  while ((c=getchar()) != EOF) {
    characters++;
    if (c == '\n')
      lines++;
  }
  printf("%d characters, %d lines\n",characters, lines);
}

/**  "A Crash Course in C," problem 8
 **    float x_to_int_n(float x, int n) raise a number to an integer power  **/

float x_to_int_n(float x, int n);

main()
{
  int n;
  float x;
  printf("input x, n: ");
  scanf("%f %d", &x, &n);
  printf("%f^%2d = %f\n", x, n, x_to_int_n(x,n));
}

float x_to_int_n(float x, int n)
{
  float y=1.0;
  for ( ; n>0; n--)
    y *= x;
  return y;
}

/**  "A Crash Course in C," problems 9, 10
 **    int factorial(int n);        calculate factorial(n)
 **    int factorial_r(int n);      calculate factorial(n) recursively  **/

int factorial(int n);
int factorial_r(int n);

main()
{
  int n;
  printf("input n: ");
  scanf("%d", &n);
  printf("factorial(%d) = %d\n", n, factorial(n));
  printf("factorial(%d) = %d\n", n, factorial_r(n));
}

int factorial(int n)
{
  int fact=1;
  for ( ; n>1; n--)
    fact *= n;
  return fact;
}

int factorial_r(int n)
{
  if (n>1)
    return n*factorial_r(n-1);
  else
    return 1;
}

/** "A Crash Course in C," problems 11
 **	input a number and find all primes less than it
 **/

#include 

#define TRUE 1			/**   define flag values  **/
#define FALSE 0

int is_prime(int n);		/**   function prototype declarations  **/
int get_positive_int(void);

main()
{
    int n, i;
    while (n=get_positive_int())
        for (i=2; i<=n; i++)
	if (is_prime(i))
	     printf("%d is prime\n", i);
}

int is_prime(int n)
{
    int i, max;
    max = (int) sqrt((double> n);

    for (i=2; i<=max; i++)
    if (!(n%i))
         return FALSE;
    return TRUE;
}

int get_positive_int(void)
{
    int n;
    do
         {
	printf("input a positive number, 0 to quit: ");
	scanf("%d", &n);
         }   while (n < 0);
     return n;
}

/**  "A Crash Course in C," problems 11
 **    matrix functions:
 **      input_matrix(), print_matrix, add_matrix, multiply_matrix  **/

#define MAX   5

void print_matrix(float A[][MAX], int n);
void input_matrix(float A[MAX][MAX], int n);
void add_matrix(float A[][MAX], float B[][MAX], float C[][MAX], int n)
void multiply_matrix(float A[][MAX], float B[][MAX], float C[][MAX], int n)

main()
{
  int n;
  float A[MAX][MAX], B[MAX][MAX], C[MAX][MAX];

  printf("input size of matrix: "); scanf("%d",&n);
  if (n<MAX) {
    input_matrix(A,n);
    input_matrix(B,n);
    print_matrix(A,n);
  }
  else
    printf("size of matrix is too large\n");
}

void print_matrix(float A[][MAX], int n)
{
  int i,j;
  for (i=0; i<n; i++) {
    for (j=0; j<n; j++)
      printf("%f\t",A[i][j]);
    printf("\n");
  }
}

void input_matrix(float A[MAX][MAX], int n)
{
  int i,j;
  float *a;
  for (i=0; i<n; i++) {
    for (j=0, a=A[i]; j<n; j++)
      scanf("%f",a++);
  }
}

void add_matrix(float A[][MAX], float B[][MAX], float C[][MAX], int n)
{
  int i,j;
  for (i=0; i<n; i++)
    for (j=0; j<n; j++)
      C[i][j] = A[i][j] + B[i][j];
}

void multiply_matrix(float A[][MAX], float B[][MAX], float C[][MAX], int n)
{
  int i, j, k;

  for (i=0; i<n; i++)
    for (j=0; j<n; j++)
      for (k=0, C[i][j]=0.0; k<n; k++)
	C[i][j] += A[i][k] * B[k][j];
}

/**  "A Crash Course in C," problems 13
 **    functions complex_input(), polar_to_rect(), complex_multiply()
 **/

COMPLEX complex_input(void)
{
  COMPLEX z;
  int ans;
  double x,y;
  printf("input (0,a,b) or (1,r,theta): ");
  scanf("%d %lf %lf",&ans, &x, &y);
  if (ans == 1) {
    z.p.r = x;  z.p.theta = y;
    polar_to_rect(&z);
  }
  else if (ans == 0) {
    z.r.a = x;  z.r.b = y;
    rect_to_polar(&z);
  }
  else {
    printf("invalid coordinate system\n");
    z.r.a = 0.0; z.r.b = 0.0; z.p.r = 0.0; z.p.theta = 0.0;
  }
  return z;
}

void polar_to_rect(COMPLEX *z)
{
  double r = (z->p.r);
  double theta = (z->p.theta);
  z->r.a = r * cos(theta);
  z->r.b = r * sin(theta);
}

COMPLEX complex_multiply(COMPLEX z1, COMPLEX z2)
{
  COMPLEX prod;
  prod.p.r = (z1.p.r) * (z2.p.r);
  prod.p.theta = (z1.p.theta) + (z2.p.theta);
  polar_to_rect(&prod);
  return (prod);
}