Distance Learning Center

1
Distance Learning Center

• Lecture 10
• C Programming Language with Applications
• Melissa Lin, IT Consultant
• HenEm, Inc. Parkville, Missouri
• linm_at_ipfw.edu
• http//www.etcs.ipfw.edu/linm

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Lecture 10 - C Standard Library Functions

• C Standard Library
• Standard Math library ltmath.hgt
• Standard Math Function Prototype
• Examples Using math.h
• Example 10-1 Using Trigonometry Functions
  sin(), cos(), and tan()
• Ceiling and Floor Functions
• Trigonometry and Inverse Trigonometric Functions
• Hyperbolic Functions
• Logarithm Functions

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Lecture 10 - C Standard Library Functions
(continue)

• Power and Square Functions
• Example 10-2 Testing Math Functions 1
• Example 10-3 Testing More Math Functions and
  Program Documentation
• Standard Utility Library ltsdtlib.hgt
• Random Number Generation Functions
• Examples Using stdlib.h
• Example 10-4 Using Random Number Generation
  Function
• Example 10-5 A Program for Rolling Two Dices
• Summary

4
The C Standard Library

• Standard C functions, types, and macros of the
  standard library are declared in standard header
  files.
• Headers can be accessed by include ltheadergt
• Headers must be included outside of any external
  declaration before the use of any C functions.
• The standard headers are ltassert.hgt, ltctype.hgt,
  lterrno.hgt, ltfloat.hgt, ltlimit.hgt, ltlocal.hgt,
  ltmath.hgt, ltsetjmp.hgt, ltsignal.hgt, ltstdarg.hgt,
  ltstddef.hgt, ltstdio.hgt, ltstdlib.hgt, ltstring.hgt,
  and lttime.hgt
• Will discuss only ltstdio.hgt, ltmath.hgt,
  ltstdlib.hgt, lt.limit.hgt, and ltfloat.hgt

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Standard Math Function Prototype

• ltmath.hgt - the header file of mathematical
  functions that declare mathematical functions and
  macros
• The C standard mathematics functions, ltmath.hgt,
  must be included in the C program when using math
  functions
• All functions in ltmath.hgt allow the programmer to
  perform certain common mathematical calculations.

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Standard Math Function Prototype (continue)

• All the input arguments and return value from a
  math function are defined as double
  floating-point 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

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Standard Math Functions Prototype (continue)

• Standard math functions available for use through
  header file inclusion include ltmath.hgt are
• sin(x) sine of x
• cos(x) cosine of x
• tan(x) tangent of x
• pow(x, y) x goes to power of y, xy
• sqrt(x) square root of 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.

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Example 10-1 Using Trigonometry Functions
sin(), cos(), and tan()

• Problem Statement
• Write a simple C program to explain how to use
  trigonometry functions sin(), cos(), and tan()
  functions.
• Analysis and Requirements
• Two symbolic constants are defined using the
  identity 360? 2? radians
• define variable as double floating-point number
  type
• examine the program output by print them using
  the 1f format specifier for double type.

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Example 10-1 Using Trigonometry Functions
sin(), cos(), and tan() (continue)

• / trigomath.c /
• include ltmath.hgt
• include ltstdio.hgt
• 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, ycos, ytan
• ysin sin(theta 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)
  sin(0.7853975)

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Example 10-1 Using Trigonometry Functions
sin(), cos(), and tan() (continue)

• ycos cos(theta Deg_to_Rad)
• ytan tan(theta Deg_to_Rad)
• printf("sin(lf Degree) lf\n", theta, ysin)
• printf("cos(lf Degree) lf\n", theta, ycos)
• printf("tan(lf Degree) lf\n", theta, ytan)
• printf("tan(lf Degree) e\n", theta, ytan)

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Example 10-1 (continue)

• Program Output
• sin(45.000000 Degree) 0.707106
• cos(45.000000 Degree) 0.707107
• tan(45.000000 Degree) 0.999999
• tan(45.000000 Degree) 9.999987e-001

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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(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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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

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Trigonometric and Inverse Trigonometric Functions
(continue)

• 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 ?
• double asin(double x)
• Arc sine function accepts x in the range 1 to 1
• The result is an angle with value between -?/2 to
  ?/2
• double atan(double x)
• Arc tangent function accepts x in the range 1 to
  1
• The result is an angle with value between -?/2 to
  ?/2
• If x is 0, 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 -? to ?

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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

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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

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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

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Example 10-2 Testing Math Function 1

• / logex.c - Write a program to test various
  math functions/
• include ltmath.hgt
• include ltstdio.hgt
• define PI 3.14159
• void main(void)
• double y
• printf("log10(1000.0) lf\n", log10(1000.0))
• printf("log(1000.0) lf\n", log(1000.0))
• printf("exp(1) lf\n", exp(1))

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Example 10-2 Testing Math Function 1 (continue)

• printf("pow(2,16) 8.0lf\n", pow(2.0, 16.0))
• printf("sqrt(9) lf\n", sqrt(9.0))
• printf("ceil(99.9999) lf\n",
  ceil(99.9999))
• printf("ceil(99.4) lf\n", ceil(99.4))
• printf("ceil(99.0001) lf\n", ceil(99.0001))
• printf("floor(99.9999) lf\n",
  floor(99.9999))
• printf("floor(99.4) lf\n", floor(99.4))
• printf("floor(99.0001) lf\n",
  floor(99.0001))

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Example 10-2 Testing Math Function 1 (continue)

• Output
• log10(1000.0) 3.000000
• log(1000.0) 6.907755
• exp(1) 2.718282
• pow(2,16) 65536
• sqrt(9) 3.000000
• ceil(99.9999) 100.000000
• ceil(99.4) 100.000000
• ceil(99.0001) 100.000000
• floor(99.9999) 99.000000
• floor(99.4) 99.000000
• floor(99.0001) 99.000000

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Example 10 3 Testing More Math Functions and
Program Documentation

• Problem Statement
• As a technical staff, you are asked to test the
  following math functions and report your finding
  to other technical staff in your group.
• The functions that will be tested are sqrt(),
  exp(), log(), log10(), fabs(), ceil(), floor(),
  pow(), fmod(), sin(), cos(), and tan()

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Example 10 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
• What is the testing environment? Microsoft Visual
  Studio.NET running under Windows XP, Windows
  2003, Windows 2000, Linux, etc
• 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(), exp(), log(), log10(), fabs(), ceil(),
  floor(), pow(), fmod(), sin(), cos(), and tan()

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Example 10 3 Testing More Math Functions and
Program Documentation (cont.)

• / ex05_03.c /
• / Testing the math library functions /
• include ltstdio.hgt
• include ltmath.hgt
• / function main begins program execution /
• int main()
• / calculates and outputs the square root /
• printf( "sqrt(.1f) .1f\n", 900.0, sqrt(
  900.0 ) )
• printf( "sqrt(.1f) .1f\n", 9.0, sqrt( 9.0
  ) )
• / calculates and outputs the exponential
  function e to the x /
• printf( "exp(.1f) f\n", 1.0, exp( 1.0 ) )
• printf( "exp(.1f) f\n", 2.0, exp( 2.0 ) )

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Example 10 3 Testing More Math Functions and
Program Documentation (cont.)

• / calculates and outputs the logarithm (base
  e) /
• printf( "log(f) .1f\n", 2.718282, log(
  2.718282 ) )
• printf( "log(f) .1f\n", 7.389056, log(
  7.389056 ) )
• / calculates and outputs the logarithm (base
  10) /
• printf( "log10(.1f) .1f\n", 1.0, log10(
  1.0 ) )
• printf( "log10(.1f) .1f\n", 10.0, log10(
  10.0 ) )
• printf( "log10(.1f) .1f\n", 100.0, log10(
  100.0 ) )
• / calculates and outputs the absolute value
  /
• printf( "fabs(.1f) .1f\n", 13.5, fabs(
  13.5 ) )
• printf( "fabs(.1f) .1f\n", 0.0, fabs( 0.0
  ) )
• printf( "fabs(.1f) .1f\n", -13.5, fabs(
  -13.5 ) )

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Example 10 3 Testing More Math Functions and
Program Documentation (cont.)

• / calculates and outputs ceil( x ) /
• printf( "ceil(.1f) .1f\n", 9.2, ceil( 9.2
  ) )
• printf( "ceil(.1f) .1f\n", -9.8, ceil(
  -9.8 ) )
• / calculates and outputs floor( x ) /
• printf( "floor(.1f) .1f\n", 9.2, floor(
  9.2 ) )
• printf( "floor(.1f) .1f\n", -9.8, floor(
  -9.8 ) )
• / calculates and outputs pow( x, y ) /
• printf( "pow(.1f, .1f) .1f\n", 2.0, 7.0,
  pow( 2.0, 7.0 ) )
• printf( "pow(.1f, .1f) .1f\n", 9.0, 0.5,
  pow( 9.0, 0.5 ) )
• / calculates and outputs fmod( x, y ) /
• printf( "fmod(.3f/.3f) .3f\n", 13.675,
  2.333,
• fmod( 13.675, 2.333 ) )

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Example 10 3 Testing More Math Functions and
Program Documentation (cont.)

• / calculates and outputs sin( x ) /
• printf( "sin(.1f) .1f\n", 0.0, sin( 0.0 )
  )
• / calculates and outputs cos( x ) /
• printf( "cos(.1f) .1f\n", 0.0, cos( 0.0 )
  )
• / calculates and outputs tan( x ) /
• printf( "tan(.1f) .1f\n", 0.0, tan( 0.0 )
  )
• return 0 / indicates successful termination
  /
• / end main /

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Example 10 3 Testing More Math Functions and
Program Documentation
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Example 10-3 Program Documentation

• /
  /
• / Program Name ex5-03.c /
• / Programmer M Lin /
• / Date June 20, 2004
  /
• / Version 1.0
  /
• / Description
  /
• / This program tests the following math
  functions sqrt(), exp(), /
• / log(), log10(), fabs(), ceil(), floor(),
  pow(), fmod(), sin(), 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
  /
• /
  /

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Utility Function Prototypes

• ltstdlib.hgt - the standard library header file
  which declares utility functions for number
  conversion, storage allocation, random number
  generation, absolute value, etc.
• Absolute Value Calculation ltstdlib.hgt
• 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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Utility Function Prototypes (continue)

• ASCII strings to Numerical Value Conversion
  ltstdlib.hgt
• double atof(const char string)
• - Convert ASCII string to float-point number
• int atoi(const char string)
• - Convert ASCII string to integer number
• long atol(const char string)
• - Convert ASCII string to long integer

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Random Number Generator Functions

• Random Number Generator Functions - in
  ltstdlib.hgt, 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 two-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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Random Number Generator Functions (continue)

• include ltstdlib.hgt
• int 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

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Random Number Generator Functions (continue)

• include ltstdlib.hgt
• void srand(unsigned int x)
• The 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))
• where function time returns the number of
  seconds, the time function is in lttime.hgt

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Example 10 4 Using Random Number Generation
Function

• / fig05_07.c - Shifted, scaled integers
  produced by 1 rand() 6 /
• include ltstdio.hgt
• include ltstdlib.hgt
• / function main begins program execution /
• int main()
• int i / counter /
• / loop 20 times /
• for ( i 1 i lt 20 i )
• / pick random number from 1 to 6 and
  output it /
• printf( "10d", 1 ( rand() 6 ) )

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Example 10 4 Using Random Number Generation
Function

• / if counter is divisible by 5, begin new
  line of output /
• if ( i 5 0 )
• printf( "\n" )
• / end if /
• / end for /
• return 0 / indicates successful termination
  /
• / end main /

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Example 10-4 Using Random Number Generation
Function Output
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Example 10 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() which contains
  srand(), rand(), and time() for rolling two
  dices, and return the sum of the two dices
• Use enum Status(WON, LOST, CONTINUE) to define a
  new data type which is a sub-integer type WON
  0, LOST 1, and CONTINUE 2, which enhances
  the readability
• Use multiple decision making structures switch,
  case,

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Example 10 5 A Program for Rolling Two Dices
(cont.)

• include ltstdio.hgt
• include ltstdlib.hgt
• include lttime.hgt /contains prototype for
  function time/
• / enumeration constants represent game status /
• enum Status CONTINUE, WON, LOST
• int rollDice( void ) / function prototype /
• / function main begins program execution /
• int main()
• int sum / sum of rolled dice /
• int myPoint / point earned /

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Example 10 5 A Program for Rolling Two Dices
(cont.)

• / can contain CONTINUE, WON, or LOST /
• enum Status gameStatus
• /randomize random number generator using
  current time/
• srand( time( NULL ) )
• sum 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

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Example 10 5 A Program for Rolling Two Dices
(cont.)

• / remember point /
• default gameStatus CONTINUE
• myPoint sum
• printf( "Point is d\n",
  myPoint )
• break / optional /
• / end switch /
• / while game not complete /
• while ( gameStatus CONTINUE )
• sum rollDice() / roll dice again /
• / determine game status /
• if ( sum myPoint ) / win by
  making point /
• gameStatus WON / game over,
  player won /
• else

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Example 10 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( "Player wins\n" ) / did
  player win? /
• else
• printf( "Player loses\n" ) / player
  lost /
• return 0 / indicates successful termination
  /
• / end main /

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Example 10 5 A Program for Rolling Two Dices
(cont.)

• / roll dice, calculate sum and display results
  /
• int rollDice( void )
• int dice1 / first die /
• int dice2 / second die /
• int 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( "Player rolled d d d\n",
  dice1, dice2, workSum )
• return workSum / return sum of dice /
• / end function rollRice /

43
Example 10 5 A Program for Rolling Two Dices
(cont.)
44
Summary

• Standard Math.h Library
• Standard Utility Library ltstdlib.hgt
• Examples using Standard math and Utility library
• Next
• Storage classes and Scope rules
• Recursive Functions
• Standard Input/Output ltstdio.hgt
• Standard limits ltlimits.hgt
• Standard floating-point ltfloat.hgt

45
Question?

• Answers
• linm_at_ipfw.edu