chapter 7 simple date types instructor: kun-mao chao ( 台大資工趙坤茂 )

Chapter 7Simple Date Types

Instructor:Kun-Mao Chao(台大資工趙坤茂 )

Copyright ©2004 Pearson Addison-Wesley. All rights reserved. 7-2

Representation and Conversion of Numeric Types• Simple data typeSimple data type is the data type used to store a

single value.– e.g., int, double, and char.

• Operations involving integer are faster than those involving double.

• Operations with integer are always precise, whereas loss of accuracy may occur when dealing with double.


Internal Formats of Type int and Type double• IntegersIntegers are represented by standard binary

numbers.– e.g., 7 = 01101.

• DoublesDoubles are represented by two sections: mantissamantissa and exponentexponent.– real number = mantissa * 2exponont

– 4.0 = 0010 * 20001 = 2 * 21


Integer Types in C

Type Range

short -32767 .. 32767

unsigned short 0 .. 65535

int -32767 .. 32767

unsgined 0 .. 65535

long -2147483647 .. 2147483647

unsgined long 0 .. 4294967295


Floating-Point Types in C

Type Range

float 10-37 .. 1038

double 10-307 .. 10308

long double 10-4931 .. 104932


An Example to Print Ranges for Positive Numeric DataYou can determine the maximal or minimal int and double values of your C environment by the following program.

%e is the format in scientific notation


Numerical Inaccuracies

• The representation errorrepresentation error (or round-off round-off errorerror) is an error due to coding a real number by a finite number of digits.– e.g., the faction of 1/3 is 0.3333…

– It is impossible to code the precise value of 1/3.

• The representation error depends on the number of digits used in the mantissamantissa.– The more bits, the smaller the error.


An Example of the Representation Error• for (trial = 0.0;

trial != 10.0; trial = trial + 1) {

…}

• The result of adding 0.1 for one hundred times is not exactly 10.0.– The above loop may fail to terminatefail to terminate on some

computers.


Other Problems When Manipulating Numbers• Cancellation errorCancellation error is an error resulting from

applying an operation to a large number and a small number, and the effect of the smaller number is lost.– e.g., 1000.0 + 0.0000001234 is equal to 1000.0.

• Arithmetic underflowArithmetic underflow is an error in which a very small computational result is represented as zero.– e.g., 0.00000001 * 10-1000000 is equal to 0.


Other Problems When Manipulating Numbers• Arithmetic overflowArithmetic overflow is an error in which the

result is too large to be represented.– The error may be detected in compiling time or run

time.– Some machine may let the arithmetic overflow occur

and the computational result is unexpected.– e.g., 999999999 * 109999999 may become a negative

value in some machine.


Automatic Conversion of Data Types (1/2)• The data of one numeric type may be automatically

converted to another numeric type.

e.g.,int k = 5, m = 4, n;double x = 1.5, y = 2.1, z;

Context Example Explanation

Expression with binary operator and operands of different types

k + xvalue is 6.5.

Value of k is converted to double before the operation.


Automatic Conversion of Data Types (2/2)

Context Example Explanation

Assignment with type double target variable and type int expression

z = k / m;expression value is 6.5; z is 1.0.

Expression is evaluated first. Then the result is converted to double.

Assignment with type int target variable and type double expression

n = x * y;expression value is 3.15; n is 3.

Expression is evaluated first. Then the result is converted to int.


Explicit Conversion of Data Types

• C also provides an explicit type conversion operation called castcast.

• For example, frac = n1 / d1;if n1 = 2 and d1 = 4, frac would be 0.

• CastCast: place the name of the desired type in parentheses immediately before the value to be converted.– e.g., frac = (double)n1 / (double)d1;– frac is evaluated to 0.5.


Representation and Conversion of Type char (1/2)• Character values can be compared by the

equality operatorsequality operators == and !=, or by the relational operatorsrelational operators <, <=, >, and >=.

e.g., letter = ‘A’; if (letter < ‘Z’) …

• Character values may also be compared, scanned, printed, and converted to type int.


Representation and Conversion of Type char (2/2)• Each character has its own unique numeric code.• A widely used standard is called American American

Standard Code for Information Interchange Standard Code for Information Interchange (ASCII)(ASCII). (See Appendix A in the textbook)– The printable charactersprintable characters have codes from 32 to

126, and others are the control characterscontrol characters.– For example, the digit characters from ‘0’ to ‘9’ have

code values from 48 to 57 in ASCII.

• The comparison of characters (e.g., ‘a’<‘c’) depends on the the corresponding code values in ASCII.


An Example of the Conversion between char and intC permits conversion of type char to type int and vice versa.

Convert char to int

Convert int to char


Enumerated Types (1/2)

• Enumerated typeEnumerated type is a data type whose list of values is specified by the programmer.

• Syntax: typedef enum {identifier_list} enum_type;

• e.g., typedef enum{entertainment, rent, food, clothing}expense_t;


Enumerated Types (2/2)• In the above example, a new data type expense_t is

created, and we can declare a variable with this type:

e.g., expense_t expense_kind;

• The variable expense_kind can be manipulated as any other integer.

e.g., switch(expense_kind){ case entertainment:

printf(“entertainment”);break;

case rent: case food: …


Function Parameters (1/2)

• When invoking a function call, we can include function function parametersparameters in the parameter list.

• Declaring a function parameterfunction parameter is accomplished by simply including the prototype of the functionprototype of the function in the parameter list.

A function parameter


Function Parameters (2/2)

• Suppose there are two existed functions: double sqrt(double)double sqrt(double) , and double sin(double)double sin(double).

• evaluateevaluate is a function that includes a function parameter as shown in the previous slide.

• We can invoke evaluateevaluate as follows.evaluateevaluate(sqrtsqrt, 0.25, 25.0, 100.0);evaluateevaluate(sinsin, 0.0, 3.14159, 0.5*3.14159);

chapter 7 simple date types instructor: kun-mao chao ( 台大資工 趙坤茂 )

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chapter 7 simple date types instructor: kun-mao chao ( 台大資工趙坤茂 )