Modular%20Programming

1
Modular Programming

• Advantages of using functions (to make a modular
  program) are
• Changing the program into separate pieces
• Code reusing
• Easier modification and maintenance of the
• program
• More understandable program
• Functions can be called from anywhere in the main
  program with different input data
• Functions enable the programmers to generate
  their own libraries of the functions.
• How is the information exchanging between the
  main function and function subprograms?

2
Functions with input arguments

• The arguments of the functions are used to carry
  information between the function subprogram and
  the main function
• Input arguments carry information into the
  function subprogram
• Output arguments are the return results of the
  functions
• Examples
• c factorial(n) / (factorial(r)factorial(n-r))
• print_rboxed(135.68)

actual parameters
3

• Calling print_rboxed(135.68)
• /
• Displays a real number in a box.
• /
• void
• print_rboxed(double rnum)
• printf("\n")
• printf(" \n")
• printf(" 7.2f \n", rnum)
• printf(" \n")
• printf("\n")
• 135.68
  Formal Parameter

4

• /
• Computes n! for n greater than or equal to
  zero
• /
• int indicates function result
  is an integer number
• factorial(int n)
• int i, / local variables /
• product 1
• / Computes the product n x (n-1) x (n-2) x
  ... x 2 x 1 /
• for (i n i gt 1 --i)
• product i
• / Returns function result /
• return (product)

5
Functions with input arguments

• The local and formal parameters of a function
  cannot be referenced by name in other functions
• Functions can not reference the variables defined
  in the main by the name
• Functions can use the constant names (define ..)
  if they are in the same file. Also functions
  should have been defined after the constant names
  definition

6

• Syntax of function definition
• function interface comment
• return-type function-name(formal parameter
  declaration list)
• local variable declarations
• executable statements
• Example
• / Finds the larger of two numbers /
• double
• bigger(double n1, double n2)
• double larger
• if (n1 gt n2) largern1
• else largern2
• return(larger)

7
A function can be called with different actual
parameters. for example for finding the number
of combinations of selecting 2 items from 6 items
without regards to order main program calls
factorial 3 times c factorial(6) / (factorial
(2) factorial(6-2)

• Calling factorial with n6 in the main program
• int
• factorial(int n) value of 6 copies into n
• int i, / local variables /
• product 1
• / Computes the product n x (n-1) x (n-2)
  x ... x 2 x 1 /
• for (i n i gt 1 --i)
• product i
• / Returns function result /
• return (product) Returns the result
  value of 720

8
Logical FunctionsThe type
int result by a function can be interpret as a
logical value

• Function That Checks Whether a Value Is Even
• /
• Indicates whether or not num is even
  (divisible by 2)
• returns 1 if it is, 0 if not
• /
• int
• even(int num)
• int ans
• ans ((num 2) 0)
• return (ans)

9
Function with Multiple Arguments

• /
• Multiplies its first argument by the power of
  10 specified
• by its second argument.
• /
• double
• scale(double x, int n)
• double scale_factor / local variable
  /
• scale_factor pow(10, n)
• return (x scale_factor)
• A function can be tested by a program (driver
  program) included main function and a call to
  that function

10

• Testing Function scale
• /
• Tests function scale.
• /
• include ltmath.hgt
• / Function prototype /
• double scale(double x, int n)
• int
• main(void)
• double num 1
• int num 2
• / Get values for num 1 and num 2 /
• printf("Enter a real numbergt ")
• scanf("lf", num 1)
• printf("Enter an integergt ")
• scanf("d", num 2)
• / Call scale and display result. /
• printf("Result of call to function scale is
  .3f\n",

11

• double
• scale(double x, int n)
• double scale_factor / local variable -
  10 to power n /
• scale_factor pow(10, n)
• return (x scale_factor)
• ----------------
• Output
• Enter a real numbergt 2.5
• Enter an integergt -2
• Result of call to function scale is 0.025
• ------------------- After calling function
  scale in the main
• Function main data area Function scale data
  area
• num_1 2.5 x2.5
• num_2 -2 n-2
• 
  scale_factor?

12
Argument List Correspondence

• The number of actual arguments in a call to a
  function must be the same as the number of formal
  arguments listed in the function definition
• The order of actual argument must be the same as
  the order of formal arguments
• Each actual argument must be of a data type that
  can be assigned to the corresponding formal
  parameter with no unexpected loss of information

13
Case Study with Top-Down Design

• Problem Write a program that finds the smallest
  divisor of a number or determines that the number
  is a prime number.
• Analysis
• Constant NMAX 1000
• Input int n
• Output int min_div

14

• Design Algorithm
• Get the number to check whether it is prime
• 1.1 Get a value for n
• 1.2 if n lt 2
• Display an error message
• else if n lt NMAX
• Do Step 2 and 3
• else
• Display an error message
• 2. Find smallest divisor other than 1, or
  determine number is prime
• 3. Display smallest divisor or a message number
  is prime
• 3.1 if the smallest divisor is n
• Display a message that n is prime
• else
• Display the smallest divisor of n

15

• include ltstdio.hgt
• define NMAX 1000
• Int main(void)
• int n, / ckeck for prime/ min_div
  / minimum divisor /
• / Gets a number to test. /
• printf("Enter a number that you think is a
  prime numbergt ")
• scanf("d", n)
• / Checks that the number is in the range
  2...NMAX /
• if (n lt 2)
• printf("Error number too small. The
  smallest prime is 2.\n")
• else if (n lt NMAX)
• / Finds the smallest divisor (gt 1)
  of n /
• min_div find_div(n)
• / Displays the smallest divisor or a
  message that n is prime. /
• if (min_div n)
• printf("d is a prime
  number.\n", n)
• else
• printf("d is the smallest
  divisor of d.\n", min_div, n)

16
Step 2 as a sub-problem Function find_div

• Analysis
• Input (formal parameter) int n
• Output (result to return) int divisor
• Local variable int trial
• Design
• 1. if n is even, set divisor to 2, otherwise,
  set divisor to 0 and trial to 3
• 2. As long as divisor is 0, keep trying odd
  integers (trial). If a divisor is found, store it
  in divisor. If trial exceeds , store n in
  divisor.
• 3. Return divisor

17

• include ltmath.hgt
• / Finds the smallest divisor of n between 2 and
  n (n is greater than 1) /
• Int find_div(int n)
• int trial, / current candidate for
  smallest divisor of n /
• divisor / smallest divisor of n zero
  means divisor not yet found /
• / Chooses initialization of divisor and
  trial depends on n being even or odd. /
• if (even(n))
• divisor 2
• else
• divisor 0
• trial 3
• / Tests each odd integer as a divisor of n
  until a divisor is found /
• while (divisor 0)
• if (trial gt sqrt(n))
• divisor n
• else if ((n trial) 0)
• divisor trial

18
Function Output Parameters with Pointers

• So far the return part of a function ,at most
  could only return one result value.
• By using pointers functions can return multiple
  result values to the caller
• So far the input argument values could be passed
  only by the values. It means the value of actual
  parameters are copied into the value of formal
  parameters and call to the functions can not
  change value of arguments.
• By using pointers the address of the arguments
  can be passed to the functions and the value of
  these arguments can be changed by the functions.
  For example the second argument of the scanf or
  fscanf is passing by address when calling scanf
  of fscanf

19
Pointers

• A pointer is a variable whose value is the
  address of a memory cell that reserved for
  another variable
• For example int nump means nump is a pointer
  to another variable of type int
• n
  nump
• Each pointer has two parts
• 1- Direct value of a pointer, which is an
  address of a memory cell. For example nump is
  1024
• 2- Indirect value of a pointer, which is the
  value of the memory cell whose address is the
  pointers direct value.
• For example nump is 84

84
1024
20
Meaning of Symbol

• can be used for all of these purposes
• Binary operator. For example 2 3 means 2 times
  3
• For file pointer. For example FILE inp means
  inp is a pointer to file
• Definition of the pointers. For example
• char singp means signp is of type
  pointer to char. Note that signp is address of
  a memory cell.
• 4. Unary operator. for example nump gets
  84 which is the int value and can be used in the
  expressions. Also singp is a char value such
  as a or b

21
Example of a function that uses arguments of the
type of pointers

• /Separates a number into three parts a sign (,
  -, or blank), a whole number magnitude, and a
  fractional part./
• void
• separate(double num, / input - value to be
  split /
• char signp, / output - sign of
  num /
• int wholep, / output - whole number
  magnitude of num /
• double fracp) / output - fractional
  part of num /
• double magnitude / local variable -
  magnitude of num /
• / Determines sign of num /
• if (num lt 0)
• signp '-'
• else if (num 0)
• signp ' '
• else
• signp ''
• / Finds magnitude of num (its absolute
  value) and
• separates it into whole and fractional
  parts /
• magnitude fabs(num)
• wholep floor(magnitude)

22
Example of a program that calls a function with
multiple output arguments

• / Demonstrates the use of a function with input
  and output parameters./
• include ltstdio.hgt
• include ltmath.hgt
• void separate(double num, char signp, int
  wholep, double fracp)
• int
• main(void)
• 
  prototype
  of separate
• double value / input - number to
  analyze /
• char sn / output - sign of value /
• int whl / output - whole number
  magnitude of value /
• double fr / output - fractional part
  of value /
• / Gets data /
• printf("Enter a value to analyzegt ")
• scanf("lf", value)
• / Separates data value into three parts /
• separate(value, sn, whl, fr)
• / Prints results /
• printf("Parts of .4f\n sign c\n",
  value, sn)
• printf(" whole number magnitude d\n",
  whl)

Enter a value to analyzegt 35.817 Parts of
35.8170 sign whole number magnitude 35
fractional part 0.8170
23
Side effect of function call separate(value, sn,
whl,fr)

• Function main
  Function separate
• Data Area Data
  Area

value
value
35.817
35.817
sign
sn
7421
Address of sn sn
?
whl
wholep
7422
?
fracp
fr
7423
?
magnitude
?
24
More on Functions

• When a pointer is passed to a function it can be
  used as output or input/output parameter.
• Scope of the name refers to the region of a
  program where the name is visible
• For example scope of the formal and local
• variables, is from their declaration to the
  closing brace of a function in which they are
  declared
• The scope of predefine constants is the whole
• program (they are global)
• If the same name is repeated to declare the
  variable one of them may shadow another one. For
  example in the following example fun-two can be
  called by one, main and itself but function one
  can only ba called by main and itself not fun-two
  

25

• define MAX 950
• define LIMIT 200
• void one(int anarg, double second) /
  prototype 1 /
• int fun_two(int one, char anarg) /
  prototype 2 /
• int
• main(void)
• int localvar both of two functions
  one and fun_two can be called here
• . . .
• / end main /
• void
• one(int anarg, double second) / header
  1 /
• int onelocal / local
  1 / function fun-two can be called here
• . . .
• / end one /
• int
• fun_two(int one, char anarg) / header
  2 /

26

• Using formal parameters as actual parameters
• void scan_fraction(int nump, / output -
  numerator /
• int denomp) / output -
  denominator /
• char slash / local - character between
  numerator denominator /
• int status / status code returned by
  scanf indicating number
• of valid values obtained
  /
• int error / flag indicating whether or
  not an error has been
• detected in current input
  /
• char discard / unprocessed character from
  input line /
• do
• / No errors detected yet /
• error 0
• / Get a fraction from the user /
• status scanf("dcd", nump,
  slash,denomp )
• while (error)

27
Recursive Functions

• A function that calls itself is said to be
  recursive
• Also if f1 calls f2 and f2 calls f1, f1 is
  considered as a recursive function
• A recursive algorithm has the following form
• if this is a simple case
• solve it
• else
• redefine the problem using recursion
• For the simple case of the problem a
  straightforward, non-recursive solution is known

28
Recursive Functions

• For example to calculate the multiplication of 6
  by 3 when only we allowed to use the addition
  operation
• The simple case is multiplication of 6 by 1
• And the recursive algorithm is
• 1. Multiply 6 by 2.
• 1.1 Multiply 6 by 1 simple case
• 1.2 Add 6 to the result
• 2. Add 6 to the result of problem 1

29
Recursive Functions

• /
• Performs integer multiplication using
  operator.
• Assumes n gt 0
• /
• int
• multiply(int m, int n)
• int ans
• if (n 1)
• ans m / simple case /
• else
• ans m multiply(m, n - 1) /
  recursive step /
• return (ans)

30
18

multiply (6,3)
Tracing a recursive function
m is 6 n is 3 3 1 is false ans is 6
multiply(6, 2) return ans
Each activation frame corresponding to each
function call
m is 6 n is 2 2 1 is false ans is 6
multiply(6, 1) return ans
12
m is 6 n is 1 1 1 is true ans is 6 return ans
6
31
Local Variable and Parameter Stack of
multiply(6,3)
n
m
ans
?
6
3
1
6
2
?
2
6
3
?
6
1
?
n
m
ans
6
2
?
3
?
6
3
7
6
3
?
return from the third call
6
1
6
n
m
ans
6
2
?
4
18
6
3
8
6
3
?
6
2
?
return from the first call
5
6
3
?
6
2
12
return from the second call
6
6
3
?
32
Tracing a Recursive Function

• int
• multiply(int m, int n)
• int ans
• printf("Entering multiply with m d, n
  d\n", m, n)
• if (n 1)
• ans m / simple case /
• else
• ans m multiply(m, n - 1) /
  recursive step /
• printf("multiply(d, d) returning d\n", m, n,
  ans)
• return (ans)
• Entering multiply with m 8, n 3
• Entering multiply with m 8, n 2
• Entering multiply with m 8, n 1
• multiply(8, 1) returning 8
• multiply(8, 2) returning 16

printf is used to make a self-trace recursive
function
33
Case Study Bisection Method for Finding Roots

• Problem Develop a function bisect that
  approximates a root of a function f on an
  interval that contains an odd number of roots
• Analysis
• Input double x_l, x_r / endpoints of interval
  /
• double epsilon / error tolerance /
• Output double root / approximate root of f /
• Variable double x_mid /interval midpoint /

34
Design Algorithm

• 1. if this is a simple case, solve it
• 1.1 simple case 1 if interval shorter than
  epsilon, return the midpoint
• 1.2 simple case 2 if function value at midpoint
  is zero, return midpoint
• else redefine the problem using recursion
• 1.3 bisect interval and execute a recursive
  call on the half interval that contains
  the root
• 1.3.1 if f(x_l)f(x_mid)lt0
• 1.3.2 Find the root by
  bisectingx_l,x_mid
• 1.3.3 Find the root by
  bisectingx_mid, x_r

35
Implementation

• double
• bisect(double x_l, / input - endpoints of
  interval in which /
• double x_r, / to look for a
  root /
• double epsilon) / input - error
  tolerance /
• double root, / approximate root /
• x_mid / interval midpoint /
• / Compute midpoint of interval /
• x_mid (x_l x_r) / 2.0
• if (x_r - x_l lt epsilon) /
  simple case 1 /
• root x_mid
• else if (f(x_mid) 0.0) /
  simple case 2 /
• root x_mid
• else if (f(x_l) f(x_mid) lt 0.0) / root
  in x_l, x_mid /
• root bisect(x_l, x_mid, epsilon)
• else / root
  in x_mid, x_r /
• root bisect(x_mid, x_r, epsilon)
• return (root)

36
Case Study Performing Arithmetic Operations on
Common Fractions

• Problem Write a program that will allow you to
  add, subtract, multiply, and divide common
  fractions. The program will prompt you for a
  fraction, an operator, and another fraction and
  then display the problem and the result. The
  process will be repeated until you enter an n to
  answer the question,
• Continue? (y/n)

37
Analysis

• Input int n1, d1 / numerator, denominator of
  first fraction /
• int n2, d2 / second fraction /
• char op / arithmetic operator - / /
• char again / whether to continue /
• Output int n_ans / numerator of answer /
• int d_ans / denominator of answer /

38
Design

• 1. Initialize again to y
• 2. As long as user wants to continue
• 3. Get a fraction problem
• 3.1 Get first fraction
• 3.2 Get operator
• 3.3 Get second fraction
• 4. Compute the result
• 4.1 Select a task based on operator
• 4.2 Put the result fraction in reduced form
• 5. Display problem and result
• 6. Check if user wants to continue

39
Implementation (Step 4 of the Algorithm)

• / Gets a fraction problem /
• scan_fraction(n1, d1)
• op get_operator()
• scan_fraction(n2, d2)
• / Computes the result /
• switch (op)
• case ''
• add_fractions(n1, d1, n2, d2,
  n_ans, d_ans)
• break
• case '-'
• add_fractions(n1, d1, -n2, d2,
  n_ans, d_ans)
• break
• case ''
• multiply_fractions(n1, d1, n2,
  d2, n_ans, d_ans)
• break
• case '/'
• multiply_fractions(n1, d1, d2,
  n2, n_ans, d_ans)
• reduce_fraction(n_ans, d_ans)

40
Testing

• A stub is a skeleton function that consists of a
  header, trace messages and assigned values to
  the output parameters.
• Using stubs for incomplete functions enables
  testing of the flow of control among the other
  functions before these function are completed.
• The process of testing the flow control between a
  main and subordinate functions is called top-down
  testing.

41
Stup for Function multiply_fractions

• /
• STUB
• Multiplies fractions represented by pairs of
  integers.
• Product of n1/d1 and n2/d2 is stored in
  variables pointed
• to by n_ansp and d_ansp. Result is not
  reduced.
• /
• void
• multiply_fractions(int n1, int d1, / input
  - first fraction /
• int n2, int d2, / input
  - second fraction /
• int n_ansp, /
  output - /
• int d_ansp) /
  product of two fractions /
• / Displays trace message /
• printf("\nEntering multiply fractions
  with\n")
• printf("n1 d, d1 d, n2 d, d2
  d\n", n1, d1, n2, d2)
• / Defines output arguments /
• n_ansp 1
• d_ansp 1

42
Testing

• The stub functions can be completed and test
  individually. A test of an individual function is
  referred to as unit test.
• When a module is completed and tested, it can be
  substituted for its stub in the program.
• Bottom-up testing is the process of testing
  individual functions of a program.
• Testing the entire program after replacing all
  its stubs with the pre-tested functions is
  referred to as system integration test.

43
Common Programming Errors

• The correspondence between actual parameters and
  formal parameters (number, type, order)
• Actual output arguments must be of the same
  pointer types as the corresponding formal
  parameters.
• Recursive functions should be tested to make sure
  they terminate properly
• If return is using for the expression containing
  the call to the recursive function, every path
  through a non-void function should lead to a
  return statement.