Chapter 7 Simple Date Types Dr. Jiung-yao Huang Dept. Comm. Eng. Nat. Chung Cheng Univ. TA: 鄭筱親 陳昱豪

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-2 本章重點  Enumerated type  Declaring a function parameter  Bisection method

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-3 outline  7.1 REPRESENTATION AND CONVERSION OF NUMERIC TYPES  7.2 REPRESENTATION AND CONVERSION OF TYPE CHAR  7.3 ENUMERATED TYPES  7.4 ITERATIVE APPROXIMATIONS  CASE STUDY: BISECTION METHOD FOR FINDING ROOTS  7.5 COMMON PROGRAMMING ERRORS

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab Representation and Conversion of Numeric Types  Simple data type  A data type used to store a single value  Uses a single memory cell to store a variable  Different numeric types has different binary strings representation in memory

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-5 Figure 7.1 Internal Formats of Type int and Type double mantissa: binary fraction between 0.5~1.0 for positive numbers -0.5~-1.0 for negative numbers exponent: integer real number: mantissa x 2 exponent

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-6 Figure 7.2 Program to Print Implementation- Specific Ranges for Positive Numeric Data %e : print DBL_MIN, DBL_MAX in scientific notation p.805, limits.h, float.h

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Integer Types in C TypeRange in Typical Microprocessor Implementation short ~ unsigned short0 ~ int ~ unsigned0 ~ long ~ unsigned long0 ~

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Floating-Point Types in C TypeApproximate Range* Significant Digits* float ~ double ~ long double ~

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Numerical Inaccuracies  Representational error (round-off error)  An error due to coding a real number as a finite number of binary digits  Cancellation error  An error resulting from applying an arithmetic operation to operands of vastly different magnitudes; effect of smaller operand is lost

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Numerical Inaccuracies  Arithmetic underflow  An error in which a very small computational result is represented as zero  Arithmetic overflow  An error that is an attempt to represent a computational result that is too large

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Automatic Conversion of Data Types  variable initialized  int k = 5, m = 4, n;  double x = 1.5, y = 2.1, z;

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Automatic Conversion of Data Types Context of ConversionExampleExplanation Expression with binary operator and operands of different numeric types k + x value is 6.5 Value of int k is converted to type double Assignment statement with type double target variable and type int expression z = k / m; expression value is 1; value assigned to z is 1.0 Expression is evaluated first. The result is converted to type double Assignment statement with type int target variable and type double expression n = x * y; expression value is 3.15; value assigned to n is 3 Expression is evaluated first. The result is converted to type int

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Explicit Conversion of Data Types  cast  an explicit type conversion operation  not change what is stored in the variable  Ex.  frac = (double) n1 / (double) d1;  Average = (double) total_score / num_students (p.63) p.63 Table 2.9

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab Representation and Conversion of Type char  A single character variable or value may appear on the right-hand side of a character assignment statement.  Character values may also be compared, printed, and converted to type int. #define star ‘*’ char next_letter = ‘A’; if (next_letter < ‘Z’) …

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Three Common character codes (Appendix A)  Digit character  ASCII ‘0’ ~’9’ have code value 48~57  ‘0’ < ‘1’ < ‘2’…….< ‘9’  Uppercase letters  ASCII ‘A’~’Z’ have code values 65~90  ‘A’ < ‘B’ < ‘C’……< ‘Z’  Lowercase letters  ASCII ‘a’~’z’ have code values 97~122  ‘a’ < ‘b’ < ‘c’…….< ‘z’

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Example 7.1  collating sequence  A sequence of characters arranged by character code number  Fig. 7.3 uses explicit conversion of type int to type char to print part of C collating sequence

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-17 Figure 7.3 Program to Print Part of the Collating Sequence

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab Enumerated Types  Enumerated type  A data type whose list of values is specified by the programmer in a type declaration  Enumeration constant  An identifier that is one of the values of an enumerated type  Fig. 7.4 shows a program that scans an integer representing an expense code and calls a function that uses a switch statement to display the code meaning.

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-19 Figure 7.4 Enumerated Type for Budget Expenses

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-20 Figure 7.4 Enumerated Type for Budget Expenses (cont’d)

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-21 Figure 7.4 Enumerated Type for Budget Expenses (cont’d)

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Enumerated Type Definition  Syntax ： typedef enum {identifier_list} enum_type;  Example ： typedef enum {sunday, monday, tuesday, wednesday, thursday, friday, saturday} day_t;

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Example 7.3  The for loop in Fig. 7.5 scans the hours worked each weekday for an employee and accumulates the sum of these hours in week_hours.

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-24 Figure 7.5 Accumulating Weekday Hours Worked

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab Iterative Approximations  root (zero of a function)  A function argument value that causes the function result to be zero  Bisection method  Repeatedly generates approximate roots until a true root is discovered.

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-26 Figure 7.6 Six Roots for the Equation f(x) = 0

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-27 Figure 7.7 Using a Function Parameter  Declaring a function parameter is accomplished by simply including a prototype of the function in the parameter list.

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Calls to Function evaluate and the Output Produced Call to evaluateOutput Produced evaluate(sqrt, 0.25, 25.0, 100.0) f( )= f( )= f( )= evaluate(sin, 0.0, , 0.5* ) f( )= f( )= f( )=

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) 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 x mid = x left + x right 2.0

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Case Study: Bisection Method for Finding Roots  Analysis  Problem Inputs  double x_left  double x_right  double epsilon  double f(double farg)  Problem Outputs  double root  int *errp

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-31 Figure 7.8 Change of Sign Implies an Odd Number of Roots

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-32 Figure 7.9 Three Possibilities That Arise When the Interval [xleft, xright] Is Bisected

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Case Study: Bisection Method for Finding Roots  Design  Initial Algorithm 1.if the interval contains an even number of roots 2.Set error flag 3.Display error message else 4.Clear error flag 5.repeat as long as interval size is greater than epsilon and root is not found 6.Compute the function value at the midpoint of the interval 7.if the function value is zero, the midpoint is a root else 8.Choose the left or right half of the interval in which to continue the search 9.Return the midpoint of the final interval as the root

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Case Study: Bisection Method for Finding Roots  Design  Program variables  int root_found  double x_mid  double f_left, f_mid, f_right  Refinement  1.1 f_left = f(x_left)  1.2 f_right = f(x_right)  1.3 if signs of f_left and f_right are the same

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab (cont) Case Study: Bisection Method for Finding Roots  Design  Refinement  5.1 while x_right – x_left > epsilon and !root_found  8.1 if root is in left half of interval (f_left*f_mid<0.0) 8.2 Change right end to midpoint else 8.3 Change left end to midpoint  Implementation (Figure 7.10)

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-36 Figure 7.10 Finding a Function Root Using the Bisection Method

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-37 Figure 7.10 Finding a Function Root Using the Bisection Method (cont’d)

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-38 Figure 7.10 Finding a Function Root Using the Bisection Method (cont’d)

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-39 Figure 7.11 Sample Run of Bisection Program with Trace Code Included

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab Common Programming Errors  Arithmetic underflow and overflow resulting from a poor choice of variable type are causes of erroneous results.  Programs that approximate solutions to numerical problems by repeated calculations often magnify small errors.  Not reuse the enumerated identifiers in another type or as a variable name  C does not verify the value validity in enum variables

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-41 Chapter Review(1)  Type int and double have different internal representations.  Arithmetic with floating-point data may not be precise, because not all real numbers can be represented exactly.  Type char data are represented by storing a binary code value for each symbol.  Defining an enumerated type requires listing the identifier that are the values of the type.

中正大學通訊工程系 潘仁義老師 Advanced Network Technology Lab 3-42 Chapter Review(2)  A variable or expression can be explicitly converted to another type by writing the new type’s name in parentheses before the value to convert.  A function can take another function as a parameter.  The bisection method is a technique for iterative approximation of a root of a function.