1

OperationsOperations

Chapter 4Chapter 4&&

Section 5.2Section 5.2

2

ExpressionsExpressions

As we've seen, in a C++ program, any finite As we've seen, in a C++ program, any finite sequence of sequence of objectsobjects and and operationsoperations that that combine to produce a value is called an combine to produce a value is called an expressionexpression..

A temperature conversion example:A temperature conversion example: fahrenheit = 1.8 * celsius + 32;

We now consider C++ We now consider C++ operationsoperations..Why not

fahrenheit = 9/5 * celsius + 32; ?

Numeric ExpressionsNumeric Expressions

C++ provides four familiar arithmetic operators:

+ for performing addition

- for performing subtraction

* for performing multiplication

/ for performing division

Each can be applied to either real (double) or integer (integer (int) [or character () [or character (char)] )] operandsoperands. 3

C++ provides more than 50operations (See Appendix C)

4

DivisionDivisionHowever, / behaves differently for However, / behaves differently for int than for than for double operands: operands:

Type of Operands Kind of Division Performed

intdouble

__________________________

Integer division calculates the quotient, but it also calculates the remainder. To find it we can use the modulus operator %; for example, 9 % 5 = ____.

56 / 10 =

56 % 10 =

1 / 2 =

1 % 2 =

2 / 3 =

2 % 3 =

5

456 / 100 =

456 % 100 =

More examples:

Keep in mind for Project 3

What about mixed-mode (i.e., mixed-type) expressions?

Automatic Type Conversion (p. 73): Promotion: "Narrower" types (fewer storage bits) "widened" e.g., int double; 9/3.0 9.0/3.0;

Explicit Type Conversion (p. 73-4): Type Casting

Use type name to convert an expression:

double(intVal) or (double)intValFunctional Notation Cast Notation

Numeric FunctionsNumeric Functions

The library <cmath> contains a variety The library <cmath> contains a variety of mathematical functions, including:of mathematical functions, including:

sin(x) asin(x)cos(x) acos(x)tan(x) atan(x)sqrt(x) abs(x)exp(x) pow(x, y)log(x) floor(x)log10(x) ceil(x)

6

Hyperbolic functions: cosh(x), sinh(x), tanh(x)

See Appendix Dfor other mathfunctions andother libraries.

Using <cmath> functionsUsing <cmath> functions

7

#include <iostream>

________________________

using namespace std;

int main()

{

cout << "\nEnter base and exponent: ";

double base, exponent;

cin >> base >> exponent;

double result = ________________________;

cout << base << " raised to the power "

<< exponent << " is " << result << endl;

}

C++ libraries whose namesstart with 'c' are C libraries.Their C-names do not havethe 'c' but have .h appended;

e.g., <math.h>

Essentiallysame as '\n'

PrecedencePrecedence

Issue: Is the value of the expressionIssue: Is the value of the expression

2 + 3 * 4

(2 + 3) * 4 (2 + 3) * 4 24 or 2 + (3 * 4) 24 or 2 + (3 * 4) 14 ? 14 ?

Operator __________________Operator __________________ governs governs evaluation order.evaluation order.

* has * has higher precedencehigher precedence than +, so it is than +, so it is applied first, making the answer ______.applied first, making the answer ______.

8

AssociativityAssociativity

Does the expressionDoes the expression

8 - 4 - 28 - 4 - 2

evaluate (8 - 4) - 2 evaluate (8 - 4) - 2 2 or 8 - (4 - 2) 2 or 8 - (4 - 2) 6 ? 6 ?

Precedence doesnPrecedence doesn’’t help us.t help us.

AssociativityAssociativity does. Since - is does. Since - is ______________________________________, the left - is evaluated , the left - is evaluated first.first.

Most C++ operators that we use associate left.Most C++ operators that we use associate left.

See Appendix C for a complete list.See Appendix C for a complete list.9

AssignmentAssignment

Assignment is one operator that is right-Assignment is one operator that is right-associative, which allows expressions like:associative, which allows expressions like:

int w, x, y, z;

____________________________

10

The rightmost = is applied first, assigning z zero, then y is assigned the value of z (0),

w = (x = (y = (z = 0)));

then x is assigned the value of y (0), and finally w is assigned the value of x (0).

Assignment operatorreturns the valuebeing assigned.

Mixed-mode assignments convert the value to type of variable and assign it.

Assignment ShortcutsAssignment Shortcuts

Certain assignments are very common:Certain assignments are very common:var = var + x; // add x to var

var = var - y; // sub y from var

C++ provides shortcuts for them:C++ provides shortcuts for them:

______________________________; // add x to var

______________________________; // sub y from var

11

In GeneralIn General

Most arithmetic expressions of the form:Most arithmetic expressions of the form:var = var value;

can be written in the "shortcut" form:can be written in the "shortcut" form:var = value;

Examples:Examples:double x, y;

cin >> x >> y;

________________________; // double x’s value

________________________; // decrease y by half12

Increment and DecrementIncrement and Decrement

Other common assignments include:Other common assignments include:var = var + 1; // add 1 to var

var = var - 1; // sub 1 from var

so C++ provides shortcuts for them, too:so C++ provides shortcuts for them, too:

________________________; // add 1 to var

_____________;

________________________; // sub 1 from var

________________________;13

Integer variables

only!

Prefix vs. PostfixPrefix vs. Postfix

As long as the increment (or decrement) operator is used as a separate statement:

int y = 0, x = 0;

. . .

++x; // x becomes ____

y++; // y becomes ____

it makes no difference which version is used.

14

15

If the increment operator is used within another expression, it does make a difference whether it is prefix or postfix.

The prefix form of increment produces the final (incremented) value as its result:

int x, y = 0;

x = 2 * (++y);

cout << x << " " << y; //

The prefix decrement behaves similarly.

2 1 is displayed

16

The postfix form of increment produces the original (unincremented) value as its result:

int x, y = 0;

x = 2 * (y++);

cout << x << " " << y; //

The prefix decrement behaves similarly.

0 1 is displayed

I/OI/O

•17

In most programming languages, input and output are performed by functions with names like read() and print(). In C++, however, (but not C) they are performed by ____________ >> and <<:•input_stream >> variable

•output_stream << expression.

18

But these are _____________. Because >> and <<

are operators, these i/o expessions must alsoproduce a ___________.cin >> variable returns ______ as its value;

cout << expression returns _______ as its value.

We know that:

cin >> variable reads a value from the keyboard and assigns it to variable

cout << expression outputs the value of expression to the screen.

19

Arithmetic operators can be chained together in expressions like a + b + c and a - b - c.

Input and output operators can also be chained; for example:

cout << "Width =" << width << " ft.\n";

and

cin >> length >> width;

These work because of the values returned by >> and << and both are ________-associative.

Why???

20

Example:

cout << "Width =" << width << " ft.\n";

_cout << "Width ="_ << width << " ft.\n";

______ << width << " ft.\n";

_cout << width_ << " ft.\n";

______ << " ft.\n";

______; Width = 8.5 ft.

Relational OperationsRelational Operations

C++ provides six operators for comparisons. C++ provides six operators for comparisons.

Each has two operands and produces a Each has two operands and produces a

______________ value ( value (______________________________________):):

x == y x != y

x < y x >= y

x > y x <= y

21Warning: 1 < x < 2

22

C, the parent language of C++, has no bool type. Instead, it uses _____ to represent false

and ______________ values to represent true.

For upward compatibility, C++ also does this:• 0 is interpreted as false• nonzero is interpreted as trueFor input and output, 0 is used for false, 1 for true (see program on Slide #29)unless_____________ is inserted in an I/O statement (see modification of program on Slide #29). It remains in effect for rest of program (unless noboolalpha is used in an I/O statement).

Also, it can be dangerous to compare reals

with _____ and _____ when one or both of the reals may have roundoff error.

See the program on Slide #25.

One of the easiest mistakes to make

in C++ is using __________________

in place of ________________

See the program on Slide #24.

23

#include <iostream>using namespace std;

int main(){ int x; cout << "Enter an integer: "; cin >> x;

if (x = 99) cout << "Yes\n"; else cout << "No\n";}}

24

Executions:

Enter an integer: 99Yes

Enter an integer: -99Yes

Enter an integer: 0Yes

With change:

if (x if (x == 99) 99)

Enter an integer: 99

Yes

Enter an integer: -99

No

Enter an integer: 0

No

//-- Effect of roundoff error//-- Effect of roundoff error#include <iostream>#include <iostream>#include <cmath>#include <cmath>using namespace std;using namespace std;

int main()int main(){{ for (float x = 0; for (float x = 0; x != 50.0; x = x + 0.1); x = x + 0.1) {{ float y = x * sqrt(1 + sin(x));float y = x * sqrt(1 + sin(x)); cout << x << " " << y << endl;;cout << x << " " << y << endl;; }}} }

25

Execution:

0 0

0.1 0.104873

0.2 0.218968

. . .

49.9998 42.937

50.0998 45.782650.1998 48.5246 . . .100.099 76.3241 . . .

With change:

for (float x = 0; x < 50.0; x = x + 0.1)

Enter an integer: 10 0

0.1 0.104873

0.2 0.218968

. . .

49.7998 36.9654

49.8998 39.9954

49.9998 42.937

orabs(x - 50) >= 1E-10

PreconditionsPreconditions

Sometimes values must satisfy certain Sometimes values must satisfy certain requirements for a program to process them requirements for a program to process them (e.g., they must be positive) . (e.g., they must be positive) .

Such requirements are called Such requirements are called preconditionspreconditions or or ______________________________ . They are boolean . They are boolean expressions that must be true in order for expressions that must be true in order for the program to work correctly.the program to work correctly.

A convenient way to check preconditions is A convenient way to check preconditions is to use C++to use C++’’s s assert() mechanism. mechanism. if statement

later

e.g., Project 2.3

26

AssertionsAssertions#include <iostream>#include _________________using namespace std;int main(){

cout << "\nEnter the current month number: "; int month; cin >> month; _______________________________________; // ...}

assert() will halt the program if will halt the program if month < 1 or month > 12 and display a message.

27

NOTE

Logical OperatorsLogical Operators

More complex boolean expressions can be More complex boolean expressions can be built using the logical operators:built using the logical operators:

b1 && b1 // true iff b1, b2 are both true

b1 || b2 // true iff b1 or b2 is true

!b // true iff b is false

Example:Example:cin >> month;

______________________________________

28NOT: assert(1 <= month <= 12);

#include <iostream>#include <iostream>using namespace std;using namespace std;

int main()int main(){{ bool input1, input2, output;bool input1, input2, output; cout << "Enter inputs: ";cout << "Enter inputs: "; cin >> input1 >> input2;cin >> input1 >> input2;

output = (input1 || input2) && !(input1 && input2);output = (input1 || input2) && !(input1 && input2); cout << "Output for inputs " << input1 cout << "Output for inputs " << input1 << " and " << input2 << " is " << output << '\n';<< " and " << input2 << " is " << output << '\n';}}

29

Executions:

Enter inputs: 0 1Output for inputs 0 and 1 is 1

Enter inputs: 1 1Output for inputs 1 and 1 is 0

With change:

cout << "Output for inputs " << boolalpha << input1

<< " and " << input2 << " is " << output << '\n';

Enter inputs: 0 1Output for inputs false and true is true

With change: cin >> boolalpha >> input1 >> input2;

Enter inputs: false true

Output for inputs false and true is true

Binary Half-Adder: (§5.3)Full Adder: (ProgrammingProblems)

Character FunctionsCharacter FunctionsThe library <cctype> contains an assortment The library <cctype> contains an assortment of boolean character-processing functions:of boolean character-processing functions:

isalpha(ch) isalnum(ch)

isdigit(ch) iscntrl(ch)

islower(ch) isupper(ch)

isspace(ch) ispunct(ch)

isprint(ch) isgraph(ch)

and two case-conversion functions:and two case-conversion functions:toupper(ch) tolower(ch)

30

SeeApp. D

Examples:Examples:

Write an assertion that will halt the program if a char object named ch is not an uppercase letter:

31

Write an assertion that will halt the program if ch is not one of ‘A ’ through ‘G ’:

assert('A' <= ch && ch <= 'G');

assert('A' <= ch && ch <= 'Z'); oror assert(isupper(ch));

Operator PrecedenceOperator Precedence

( ) HIGHERHIGHER

+ (positive), (positive), - (negative), (negative), ! (NOT) (NOT)

*, , /, , %

+ (addition), (addition), -- (subtraction) (subtraction)

<, , <=, , >, , >=

<<, >>

==, , !=

&&

||

= LOWERLOWER

See Appendix C for a complete list.See Appendix C for a complete list.

54 operators18 precedence

levels

32

When in doubt,use parentheses!