chapter 7 simple date types dr. jiung-yao huang dept. comm. eng. nat. chung cheng univ. e-mail :...

Chapter 7Simple Date Types

Dr. Jiung-yao HuangDept. Comm. Eng.Nat. Chung Cheng Univ.E-mail : [email protected]: 鄭筱親陳昱豪

3-2中正大學通訊工程系潘仁義老師 Advanced Network Technology Lab

本章重點

Enumerated typeDeclaring a function parameterBisection method


outline

7.1 REPRESENTATION AND CONVERSION OF NUMERIC TYPES

7.2 REPRESENTATION AND CONVERSION OF TYPE CHAR

7.3 ENUMERATED TYPES7.4 ITERATIVE APPROXIMATIONS

CASE STUDY: BISECTION METHOD FOR FINDING ROOTS

7.5 COMMON PROGRAMMING ERRORS


7.1 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


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: integerreal number: mantissa x 2exponent


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


7.1 (cont) Integer Types in C

Type Range in Typical Microprocessor Implementation

short -32767 ~ 32767

unsigned short 0 ~ 65535

int -32767 ~ 32767

unsigned 0 ~ 65535

long -2147483647 ~ 2147483647

unsigned long 0 ~ 4294967295


7.1 (cont) Floating-Point Types in C

Type Approximate Range*

Significant

Digits*

float 10-37 ~1038 6

double 10-307 ~10308 15

long double 10-4931 ~104932 19


7.1 (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


7.1 (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


7.1 (cont) Automatic Conversion of Data Types

variable initialized int k = 5, m = 4, n; double x = 1.5, y = 2.1, z;


7.1 (cont) Automatic Conversion of Data Types

Context of Conversion Example Explanation

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


7.1 (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


7.2 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’) …


7.2 (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’


7.2 (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


Figure 7.3 Program to Print Part of the Collating Sequence


7.3 Enumerated Types

Enumerated type A data type whose list of values is specified by

the programmer in a type declarationEnumeration 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.


Figure 7.4 Enumerated Type for Budget Expenses


Figure 7.4 Enumerated Type for Budget Expenses (cont’d)


7.3 (cont) Enumerated Type Definition

Syntax ： typedef enum

{identifier_list}

enum_type;

Example ：typedef enum

{sunday, monday, tuesday, wednesday, thursday, friday, saturday}

day_t;


7.3 (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.


Figure 7.5 Accumulating Weekday Hours Worked


7.4 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.


Figure 7.6 Six Roots for the Equation f(x) = 0


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.


7.4 (cont) Calls to Function evaluate and the Output Produced

Call to evaluate Output Produced

evaluate(sqrt, 0.25, 25.0, 100.0)

f(0.25000)=0.50000

f(25.00000)=5.00000

f(100.00000)=10.00000

evaluate(sin, 0.0, 3.14156, 0.5*3.14156)

f(0.00000)=0.00000

f(3.14159)=0.00000

f(1.57079)=1.00000


7.4 (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

xmid =xleft + xright

2.0



Analysis Problem Inputs

double x_leftdouble x_rightdouble epsilondouble f(double farg)

Problem Outputsdouble rootint *errp


Figure 7.8 Change of Sign Implies an Odd Number of Roots


Figure 7.9 Three PossibilitiesThat Arise When the Interval [xleft, xright] Is Bisected



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 flag5.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



Design Program variables

int root_founddouble x_middouble f_left, f_mid, f_right

Refinement1.1 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



Design Refinement

5.1 while x_right – x_left > epsilon and !root_found8.1 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)


Figure 7.10 Finding a Function Root Using the Bisection Method


Figure 7.10 Finding a Function Root Using the Bisection Method (cont’d)


Figure 7.11 Sample Run of Bisection Program with Trace Code Included


7.5 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


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.


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.

chapter 7 simple date types dr. jiung-yao huang dept. comm. eng. nat. chung cheng univ. e-mail :...

Documents