ECET 264 C Programming Language
with Applications
Lecture 17
C Standard Library Functions
Paul I. Lin
Professor of Electrical & Computer
Engineering Technology
http://www.etcs.ipfw.edu/~lin
http://www.etcs.ipfw.edu/~lin
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
1
Lecture 17- C Standard Library Functions
„
„
C Standard Library
Standard Math library <math.h>
• Standard Math Function Prototype
• Examples Using math.h
„
Example 1717-1: Using Trigonometry Functions: sin(),
cos(),
cos(), and tan()
•
•
Ceiling and Floor Functions
Trigonometry and Inverse Trigonometric
Functions
• Hyperbolic Functions
• Logarithm Functions
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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1
Lecture 17 - C Standard Library Functions
(continue)
„
Power and Square Functions
• Example 1717-2: Testing Math Functions
• Example 1717-3: Testing More Math Functions and
Program Documentation
„
Standard Utility Library <sdtlib.h>
• Random Number Generation Functions
„
Examples Using stdlib.h
• Example 1717-4: Using Random Number Generation
Function
• Example 1717-5: A Program for Rolling Two Dices
„
Summary
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
3
The C Standard Library
„
„
„
„
„
Standard C functions, types, and macros of the
standard library are declared in standard header
files.
Headers files can be accessed by use # include
<header>
Headers must be included outside of any external
declaration before the use of any C functions.
The standard headers are: <assert.h
>, <ctype.h
>,
<assert.h>,
<ctype.h>,
<errno.h>,
>,
<float.h
float.h>,
>,
<limit.h
limit.h>,
>,
<local.h
local.h>,
>,
<math.h>,
errno.h <
<
<
<setjmp.h>,
>, <stdarg.h
>, <stddef.h
>,
setjmp.h>, <signal.h
<signal.h>,
<stdarg.h>,
<stddef.h>,
<stdio.h>,
>, <string.h
>, and <time.h
>
stdio.h>, <stdlib.h
<stdlib.h>,
<string.h>,
<time.h>
Dscuss only <stdio.h
>, <math.h
>, <stdlib.h
>,
<stdio.h>,
<math.h>,
<stdlib.h>,
<.limit.h
>, and <float.h
>
<.limit.h>,
<float.h>
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2
Standard Math Function Prototype
„
„
„
<math.h> - the header file of mathematical
functions that declare mathematical functions
and macros
The C standard mathematics functions,
<math.h>, must be included in the C program
when using math functions
All functions in <math.h> allow the
programmer to perform certain common
mathematical calculations.
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Lecture 17&18 - Prof. Paul I. Lin
Standard Math Function Prototype
„
„
„
„
(cont.)
All the input arguments and return value from a
math function are defined as double floatingfloatingpoint number data type by default
The argument for trigonometric functions should
be in the units of radians.
Conversion formula:
Angle_radian = angle_degree * (PI/180),
where PI is 3.1416159.
Math function prototype and definition
Return value type
Argument type
double sin(double x);
Function name
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Lecture 17&18 - Prof. Paul I. Lin
Parameter name
6
3
Standard Math Functions Prototype
„
(cont.)
Standard math functions available for use through
header file inclusion #include <math.h
> are:
<math.h>
sin(x)
sine of x
cos(x)
)
cosine of x
cos(x
tan(x)
tangent of x
pow(x,
pow(x, y) x goes to power of y, x^y
sqrt(x)
square root of x
sqrt(x)
exp(x)
exponential function ex
log(x)
natural logarithm of x (base e)
ceil(x)
round x to the smallest number not less than x
floor(x)
round x to the largest number not greater than x
And more.
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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Example 17-1: Using Trigonometry Functions:
sin(), cos(), and tan()
Problem Statement:
Write a simple C program to explain how to use
trigonometry functions sin(), cos(),
cos(), and tan() functions.
Analysis and Requirements:
„
„
„
Two symbolic constants are defined using the identity:
360°
360° = 2π
2π radians
define variable as double floatingfloating-point number type
examine the program output by print them using the
%1f format specifier for double type.
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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4
Example 17-1: Using Trigonometry
Functions: sin(), cos(), and tan() (cont.)
/* trigomath.c */
#include <math.h>
#include <stdio.h
>
<stdio.h>
#define PI
3.14159
#define Deg_to_Rad
PI/180.0
#define Rad_to_Deg
180.0/PI
void main(void)
{
double theta = 45.0;
double ysin,
ysin, ycos,
ycos, ytan;
ytan;
ysin = sin(theta * Deg_to_Rad);
Deg_to_Rad);
//theta * Deg_to_Rad = 45.0 * PI/180.0 =
// 45.0 * 3.14159/180.0 = 0.785397
// ysin = sin(theta * Deg_to_Rad)
Deg_to_Rad) = sin(0.7853975);
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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Example 17-1: Using Trigonometry
Functions: sin(), cos(), and tan() (cont.)
ycos = cos(theta * Deg_to_Rad);
Deg_to_Rad);
ytan = tan(theta * Deg_to_Rad);
Deg_to_Rad);
printf("sin(%lf Degree) = %lf\
%lf\n", theta, ysin);
ysin);
printf("cos(%lf Degree) = %lf\
%lf\n", theta, ycos);
ycos);
printf("tan(%lf Degree) = %lf\
%lf\n", theta, ytan);
ytan);
printf("tan(%lf Degree) = %e\
%e\n", theta, ytan);
ytan);
}
March 21, 2009
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5
Example 17-1
(cont.)
Program Output:
sin(45.000000 Degree) = 0.707106
cos(45.000000 Degree) = 0.707107
tan(45.000000 Degree) = 0.999999
tan(45.000000 Degree) = 9.999987e9.999987e-001
March 21, 2009
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11
Ceiling and Floor Functions
double ceil(double x)
• Calculate the ceiling of a value
• returns a smallest integer that is greater than or
equal to x.
• It round up the digits after the decimal points
• Use ceil(xceil(x-0.5) to increase accuracy
double floor(double x)
• returns a largest integer that is less than or equal to
x.
• It round off the digits after the decimal points
• Use floor(x +0.5) to increase accuracy
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6
Trigonometric and Inverse Trigonometric
Functions
double cos(double x)
• Cosine function takes the x in radians
• The result is a value in the range –1.0 to 1.0
double sin(double x)
• Sine function takes x in radians
• The result is a value in the range –1.0 to 1.0
double tan(double x)
• Tangent function takes x in radians
• The result is a value in the range –1.0 to 1.0
March 21, 2009
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Trigonometric and Inverse Trigonometric
Functions (cont.)
double acos(double x)
• Arc cosine function accepts x in the range –1 to 1
• The result is an angle with value between 0 to π
double asin(double x)
• Arc sine function accepts x in the range –1 to 1
• The result is an angle with value between -π/2 to π/2
double atan(double x)
•
•
•
Arc tangent function accepts x in the range –1 to 1
The result is an angle with value between -π/2 to π/2
If x is 0, atan()
atan() returns 0
double atan2(double y, double x)
• The function accepts the argument in the form of y/x.
• If both y and x parameters are 0, the result is 0
• The result is an angle with value between -π to π
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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7
Hyperbolic Functions
A special class of exponential functions:
double cosh(double x)
• Hyperbolic cosine
• cosh x = (ex + e-x)/2
double sinh(double x)
• Hyperbolic sine
• sinh x = (ex - e-x)/2
double tanh(double x)
• Hyperbolic tangent
• tanh x = sinh x/ cos hx
March 21, 2009
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15
Logarithm Functions
double log(double x)
• logex
• Calculate natural logarithm, of a positive x; if x is
negative it returns a NaN (not a number or
infinite)
double log10(double x)
• log10x
• Compute logarithm to the base 10 of a positive x
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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8
Power and Square Root Functions
double sqrt(double x)
• Square root of a nonnegative x or x1/2
double pow(double x, double y)
• Calculate x to the y power or xy
double exp(double x)
• Raise e (2.718281828..) to the power of x or
ex
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
17
Example 17-2: Testing Math Function
/* logex.c - Write a program to test various math
functions*/
functions*/
#include <math.h>
#include <stdio.h
>
<stdio.h>
#define PI 3.14159
void main(void)
{
double y;
printf("log10(1000.0) = %lf\
%lf\n", log10(1000.0));
printf("log(1000.0) = %lf\
%lf\n", log(1000.0));
printf("exp(1)
= %lf\
%lf\n", exp(1));
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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9
Example 17-2: Testing Math Function
(cont.)
(cont.)
printf("pow(2,16) = %8.0lf\
%8.0lf\n", pow(2.0, 16.0));
printf("sqrt(9) = %lf\
%lf\n", sqrt(9.0));
printf("ceil(99.9999) = %lf\
%lf\n", ceil(99.9999));
printf("ceil(99.4) = %lf\
%lf\n", ceil(99.4));
printf("ceil(99.0001) = %lf\
%lf\n", ceil(99.0001));
printf("floor(99.9999)= %lf\
%lf\n", floor(99.9999));
printf("floor(99.4) = %lf\
%lf\n", floor(99.4));
printf("floor(99.0001) = %lf\
%lf\n", floor(99.0001));
}
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
19
Example 17-2: Testing Math Function (cont.)
(cont.)
Output:
Output:
log10(1000.0)
log(1000.0)
exp(1)
pow(2,16)
sqrt(9)
ceil(99.9999)
ceil(99.4)
ceil(99.0001)
floor(99.9999)
floor(99.4)
floor(99.0001)
March 21, 2009
=
=
=
=
=
=
=
=
=
=
=
3.000000
6.907755
2.718282
65536
3.000000
100.000000
100.000000
100.000000
99.000000
99.000000
99.000000
Lecture 17&18 - Prof. Paul I. Lin
20
10
Example 17 – 3: Testing More Math
Functions and Program Documentation
Problem Statement
„
„
March 21, 2009
As a technical staff, you are asked to test the
following math functions and report your finding
to other technical staffs in your group.
The functions that will be tested are sqrt(),
sqrt(),
exp(), log(), log10(), fabs(),
fabs(), ceil(), floor(), pow(),
pow(),
fmod(),
fmod(), sin(), cos(),
cos(), and tan()
Lecture 17&18 - Prof. Paul I. Lin
21
Example 17 – 3: Testing More Math
Functions and Program Documentation (cont.)
Analysis
We should study the problem statement in details,
and should ask at least one additional question for
clarification:
„
1. What is the testing environment? Microsoft Visual
Studio.NET running under Windows Vista, Windows
XP, Windows 2003, Windows 2000, Linux, etc
„
„
March 21, 2009
We should also have a copy of technical info that
describes function prototypes. The C
Programming Language book by Ritche should be
a good desk reference.
We need to study the functions under testing:
sqrt(),
sqrt(), exp(), log(), log10(), fabs(),
fabs(), ceil(), floor(),
pow(),
pow(), fmod(),
fmod(), sin(), cos(),
cos(), and tan()
Lecture 17&18 - Prof. Paul I. Lin
22
11
Example 17 – 3: Testing More Math
Functions and Program Documentation (cont.)
/* ex05_03.c */
/* Testing the math library functions */
#include <stdio.h
>
<stdio.h>
#include <math.h
>
<math.h>
/* function main begins program execution */
int main()
{
/* calculates and outputs the square root */
printf(
printf( "sqrt(%.1f) = %.1f\
%.1f\n", 900.0, sqrt(
sqrt( 900.0 ) );
printf(
printf( "sqrt(%.1f) = %.1f\
%.1f\n", 9.0, sqrt(
sqrt( 9.0 ) );
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
23
Example 17 – 3: Testing More Math
Functions and Program Documentation (cont.)
/* calculates and outputs the exponential function e to
the x */
printf(
printf( "exp(%.1f) = %f
%f\n", 1.0, exp( 1.0 ) );
printf(
(
"exp(%.1f)
=
%f
printf
%f\n", 2.0, exp( 2.0 ) );
/* calculates and outputs the logarithm (base e) */
printf(
printf( "log(%f
"log(%f)) = %.1f\
%.1f\n", 2.718282, log( 2.718282 ) );
printf(
printf( "log(%f
"log(%f)) = %.1f\
%.1f\n", 7.389056, log( 7.389056 ) );
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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12
Example 17 – 3: Testing More Math
Functions and Program Documentation (cont.)
/* calculates and outputs the logarithm (base 10) */
printf(
printf( "log10(%.1f) = %.1f\
%.1f\n", 1.0, log10( 1.0 ) );
printf(
printf( "log10(%.1f) = %.1f\
%.1f\n", 10.0, log10( 10.0 ) );
printf(
printf( "log10(%.1f) = %.1f\
%.1f\n", 100.0, log10( 100.0 ) );
/* calculates and outputs the absolute value */
printf(
printf( "fabs(%.1f) = %.1f\
%.1f\n", 13.5, fabs(
fabs( 13.5 ) );
printf(
printf( "fabs(%.1f) = %.1f\
%.1f\n", 0.0, fabs(
fabs( 0.0 ) );
printf(
printf( "fabs(%.1f) = %.1f\
%.1f\n", -13.5, fabs(
fabs( -13.5 ) );
/* calculates and outputs ceil( x ) */
printf(
printf( "ceil(%.1f) = %.1f\
%.1f\n", 9.2, ceil( 9.2 ) );
printf(
printf( "ceil(%.1f) = %.1f\
%.1f\n", -9.8, ceil( -9.8 ) );
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
25
Example 17 – 3: Testing More Math
Functions and Program Documentation (cont.)
/* calculates and outputs floor( x ) */
printf(
printf( "floor(%.1f) = %.1f\
%.1f\n", 9.2, floor( 9.2 ) );
printf(
printf( "floor(%.1f) = %.1f\
%.1f\n", -9.8, floor( -9.8 ) );
/* calculates and outputs pow(
pow( x, y ) */
printf(
printf( "pow(%.1f, %.1f) = %.1f\
%.1f\n", 2.0, 7.0, pow(
pow( 2.0, 7.0 ) );
printf(
printf( "pow(%.1f, %.1f) = %.1f\
%.1f\n", 9.0, 0.5, pow(
pow( 9.0, 0.5 ) );
/* calculates and outputs fmod(
fmod( x, y ) */
printf(
printf( "fmod(%.3f/%.3f) = %.3f\
%.3f\n", 13.675, 2.333,
fmod(
fmod( 13.675, 2.333 ) );
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
26
13
Example 17 – 3: Testing More Math
Functions and Program Documentation
(cont.)
/* calculates and outputs sin( x ) */
printf(
printf( "sin(%.1f) = %.1f\
%.1f\n", 0.0, sin( 0.0 ) );
/* calculates and outputs cos(
cos( x ) */
printf(
printf( "cos(%.1f) = %.1f\
%.1f\n", 0.0, cos(
cos( 0.0 ) );
/* calculates and outputs tan( x ) */
printf(
printf( "tan(%.1f) = %.1f\
%.1f\n", 0.0, tan( 0.0 ) );
return 0; /* indicates successful termination */
} /* end main */
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
27
Example 17 – 3: Testing More Math
Functions and Program Documentation
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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14
Example 17-3: Program Documentation
/************************************************************************/
/************************************************************************/
/* Program Name: ex5*/
ex5-03.c
/* Programmer: Paul Lin
*/
/* Date: March 20, 2009
*/
/* Version: 1.0
*/
/* Description:
*/
/* This program tests the following math functions sqrt(),
sqrt(), exp(), */
/* log(), log10(), fabs(),
fabs(), ceil(), floor(), pow(),
pow(), fmod(),
fmod(), sin(), cos(),
cos(), */
/* and tan(). The Windows Visual Studio.NET running under */
/* Windows XP was used to prepare testing source code, and */
/* ran testing cases
*/
/*
*/
/* Testing Results:
*/
/* COPY YOUR TESTING RESULT HERE
*/
/************************************************************************/
/************************************************************************/
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
29
Utility Function Prototypes
„
„
<stdlib.h> - the standard library header file
which declares utility functions for number
conversion, storage allocation, random number
generation, absolute value, etc.
Absolute Value Calculation <stdlib.h>
• Int abs(int x);
// Computes absolute value of an integer value
• long labs(long x);
// Computes absolute value of a long integer value
• double fabs(double x);
// Compute absolute value of double float type value
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15
Utility Function Prototypes
„
(continue)
ASCII strings to Numerical Value Conversion
<stdlib.h>
• double atof(const char *string);
„ Convert ASCII string to floatfloat-point number
• int atoi(const char *string);
„ Convert ASCII string to integer number
• long atol(const char *string);
„ Convert ASCII string to long integer
March 21, 2009
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31
Random Number Generator Functions
Random Number Generator Functions - in
<stdlib.h>,
stdlib.h>, the standard library function
„ The range of the value of rand function is between
0 and RAND_MAX that is at least 32767, which is
the maximum value for a twotwo-byte (i.e. 16 bit)
integer.
Example:
rand() %6
Using the remainder operator (%) in conjunction
with rand function to produce integers in the range
0 to 5.
„
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16
Random Number Generator Functions
(cont.)
#include <stdlib.h
>
<stdlib.h>
int rand(void)
rand(void)
• Compute pseudo random number
• The return number in the range 0 to RAND_MAX
• Values produced by rand() can be scaled and
shifted to produce values in a specific range
• General equation for scaling and shifting a random
number is n = a + rand() % b
where a is a shifting value and b is the scaling
factor
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
Random Number Generator Functions
33
(cont.)
#include <stdlib.h
>
<stdlib.h>
void srand(unsigned int x)
• The srand()
srand() takes an unsigned integer argument and
seeds function rand() to produce a different
sequence of random numbers for each execution of
the problem
• To reinitialize the generator, use 1 as the seed
argument
• To randomize without the need for entering a seed
each time, use srand(time(NULL))
srand(time(NULL))
where function time returns the number of seconds,
the time function is in <time.h
>
<time.h>
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
34
17
Example 17 – 4: Using Random Number
Generation Function
/* fig05_07.c - Shifted, scaled integers produced by 1 +
rand() % 6 */
#include <stdio.h
>
<stdio.h>
#include <stdlib.h
>
<stdlib.h>
/* function main begins program execution */
int main()
{
int i; /* counter */
/* loop 20 times */
for ( i = 1; i <= 20; i++ )
{ /* pick random number from 1 to 6 and output it */
printf(
printf( "%10d", 1 + ( rand() % 6 ) );
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
35
Example 17 – 4: Using Random Number
Generation Function
/* if counter is divisible by 5, begin new line of output */
if ( i % 5 == 0 )
{
printf(
printf( "\
"\n" );
} /* end if */
} /* end for */
return 0; /* indicates successful termination */
} /* end main */
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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18
Example 17-4: Using Random Number
Generation Function: Output
March 21, 2009
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37
Example 17 – 5: A Program for Rolling
Two Dices
„
This program rolls two dices using rand() function,
computes sum, and determines the winning outcomes:
• 7 or 11 – WON
• 2, 3, or 12 – LOST
• Other numbers 1, 4, 5, 6, 8, 9, 10 – CONTINUE to roll again
„
This program has the following characteristics
• Use a homemade function rollDice()
rollDice() which contains srand(),
srand(),
rand(), and time() for rolling two dices, and return the sum of
the two dices
• Use enum Status(WON,
Status(WON, LOST, CONTINUE) to define a new
data type which is a subsub-integer type: WON ==0, LOST == 1,
and CONTINUE == 2, which enhances the readability
• Use multiple decision making structures: switch, case,
March 21, 2009
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19
Example 17 – 5: A Program for Rolling
Two Dices (cont.)
#include <stdio.h
>
<stdio.h>
#include <stdlib.h
>
<stdlib.h>
#include <time.h
> /*contains prototype for function time*/
<time.h>
/* enumeration constants represent game status */
enum Status { CONTINUE, WON, LOST };
int rollDice(
/* function prototype */
rollDice( void );
/* function main begins program execution */
int main()
{
int sum;
/* sum of rolled dice */
int myPoint;
myPoint; /* point earned */
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
39
Example 17 – 5: A Program for Rolling
Two Dices (cont.)
/* can contain CONTINUE, WON, or LOST */
enum Status gameStatus;
gameStatus;
/*randomize random number generator using current time*/
srand(
srand( time( NULL ) );
sum = rollDice()
rollDice();; /* first roll of the dice */
/* determine game status based on sum of dice */
switch( sum )
{ /* win on first roll */
case 7:
case 11: gameStatus = WON; break;
/* lose on first roll */
case 2:
case 3:
case 12: gameStatus = LOST; break;
March 21, 2009
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20
Example 17 – 5: A Program for Rolling
Two Dices (cont.)
/* remember point */
default: gameStatus = CONTINUE;
myPoint = sum;
printf(
printf( "Point is %d
%d\n", myPoint );
break; /* optional */
} /* end switch */
/* while game not complete */
while ( gameStatus == CONTINUE )
{
sum = rollDice();
rollDice(); /* roll dice again */
/* determine game status */
if ( sum == myPoint )
/* win by making point */
gameStatus = WON; /* game over, player won */
else {
March 21, 2009
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41
Example 17 – 5: A Program for
Rolling Two Dices (cont.)
if ( sum == 7 )
/* lose by rolling 7 */
gameStatus = LOST; /* game over, player lost */
} /* end else */
} /* end while */
/* display won or lost message */
if ( gameStatus == WON )
printf(
printf( "Player wins\
wins\n" ); /* did player win? */
else
printf(
printf( "Player loses\
loses\n" ); /* player lost */
return 0; /* indicates successful termination */
} /* end main */
March 21, 2009
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42
21
Example 17– 5: A Program for
Rolling Two Dices (cont.)
/* roll dice, calculate sum and display results */
int rollDice(
rollDice( void )
{
int dice1;
/* first die */
int dice2;
/* second die */
int workSum;
workSum; /* sum of dice */
dice1 = 1 + ( rand() % 6 ); /* pick random die1 value */
dice2 = 1 + ( rand() % 6 ); /* pick random die2 value */
workSum = dice1 + dice2; /* sum die1 and die2 */
/* display results of this roll */
printf(
printf( "Player rolled %d + %d = %d
%d\n", dice1, dice2, workSum );
return workSum;
workSum; /* return sum of dice */
} /* end function rollRice */
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
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Example 17– 5: A Program for
Rolling Two Dices (cont.)
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Lecture 17&18 - Prof. Paul I. Lin
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Summary
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March 21, 2009
Standard Math.h Library
Standard Utility Library <stdlib.h>
Examples using Standard math and Utility
library
Next
• Storage classes and Scope rules
• Recursive Functions
• Standard Input/Output <stdio.h>
• Standard limits <limits.h>
• Standard floating-point <float.h>
Lecture 17&18 - Prof. Paul I. Lin
45
Question
Answer
[email protected]
March 21, 2009
Lecture 17&18 - Prof. Paul I. Lin
46
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