1. 1 Operations 4 & Section 5.2 Chapter 4 & Section 5.2

2. Expressions As we've seen, in a C++ program, any finite sequence of objects and operations that combine to produce a value is called an expression. A temperature conversion example: fahrenheit = 1.8 * celsius + 32; We now consider C++ operations. 2 Why not fahrenheit = 9/5 * celsius + 32; ?

3. Numeric 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 ( int ) [or character ( char )] operands. 3 C++ provides more than 50 operations (See Appendix C) mult. symbols: <<. ++, words ((sizeof)

4. Division However, / behaves differently for int than for double operands: 1 1.8 4 9.0 / 5  9 / 5.0  Type of Operands Kind of Division Performed int integer real 9.0 / 5.0  9 / 5  double Integer division calculates the quotient, but it also calculates the remainder. To find it we can use the modulus operator % ; for example, 9 % 5 =. 4 “guzinta” b = aq + r

5. 2 % 3 = 456 / 100 = 456 % 100 = 1 / 2 = 56 / 10 = 56 % 10 = 1 % 2 = 2 / 3 = More examples: 5 1 4 56 0 0 2 5 6 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 ; 9.0/5  9.0/5.0 Explicit Type Conversion (p. 73-4): Type Casting Use type name to convert an expression: double(intVal) or (double)intVal Functional Notation Cast Notation b = aq + r Assign 3 – chang maker double(a) / double(b)

6. Numeric Functions The library contains a variety 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 D for other math functions and other libraries. sqrt(<0) nan -1.#IND pow(x, 1/3) efficiency –Asgn 2: quadratic

7. Using functions int main() { cout << "\nEnter base and exponent: "; double base, exponent; cin >> base >> exponent; double result = pow(base, exponent); cout << base << " raised to the power " << exponent << " is " << result << endl; } 7 #include using namespace std; C++ libraries whose names start with 'c' are C libraries. Their C-names do not have the 'c' but have.h appended; e.g., Essentially same as '\n'

8. Precedence ( or priority) Issue: Is the value of the expression 2 + 3 * 4 (2 + 3) * 4  24 or 2 + (3 * 4)  14 ? Operator precedence governs evaluation order. * has higher precedence than +, so it is applied first, making the answer 14. 8 See Slide #32 int a = 8, b = 4, c = 2 pow(a, 2) + b * c -> 72 a/b+c -> 4 a/(b+c_ -> 1

9. Associativity Does the expression 8 - 4 - 2 evaluate (8 - 4) - 2  2 or 8 - (4 - 2)  6 ? Precedence doesn’t help us. Associativity does. Since - is left-associative, the left - is evaluated first. 9 Most of the C++ operators that we use associate left. See Appendix C for a complete list. int a = 8, b = 4, c = 2 a – b + c a / b*c See App. D

10. Assignment The rightmost = is applied first, assigning z zero, then y is assigned the value of z (0), 10 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 is one operator that is right- associative, which allows expressions like: int w, x, y, z; w = x = y = z = 0; Mixed-mode assignments convert the value to type of variable and assign it. Assignment operator returns the value being assigned. ( ) double pi = 3.1416; int w = pi; 3 ; pi = w 3.0 y = 2*(x = a + b) + c

11. Assignment Shortcuts Certain assignments are very common: var = var + x; // add x to var var = var - y; // sub y from var C++ provides shortcuts for them: // add x to var // sub y from var var += x; var -= y; 11 Watch out! x += 2; x =+2; Don’t use?

12. In General Most arithmetic expressions of the form: var = var  value; can be written in the "shortcut" form: var  = value; Examples: double x, y; cin >> x >> y; // double x’s value // decrease y by half x *= 2.0; y /= 2.0; 12

13. Increment and Decrement 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: // add 1 to var // sub 1 from var var++; ++var; var--; --var; 13 Integer variables only!

14. Prefix 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  1 1

15. However, ++ and -- can be used within other expressions; then 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. 15 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 16 

17. I/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 operators >> and << : input_stream >> variable output_stream << expression. printf, scanf

18. 18 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. But these are side effects. Because >> and << are operators, these i/o expessions must also produce a value. cin >> variable returns ____ as its value; cout << expression returns _____ as its value. cin cout Use at end of course

19. 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??? left skim

20. 20 Example: cout << "Width =" << width << " ft.\n"; (cout << "Width =") << width << " ft.\n"; ____ << width << " ft.\n"; (cout << width) << " ft.\n"; ____ << " ft.\n"; ____ cout cout; Width = 8.5 ft. skim

21. Relational Operations x == y x != y x = y x > y x <= y 21 C++ provides six operators for comparisons. Each has two operands and produces a bool value (true or false): Warning: 1 < x < 2 boolean expressions Chap. 5: prep. for control list on board §5.2

22. 22 C, the parent language of C++, has no bool type. Instead, it uses 0 to represent false and nonzero values to represent true. For upward compatibility, C++ also does this: 0 is interpreted as false nonzero is interpreted as true For input and output, 0 is used for false, 1 for true (see program on Slide #29) unless boolalpha 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). dec, oct, hex

23. 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 == (equality). See the program on Slide #24. 23 = (assignment)

24. #include 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: 99 Yes Enter an integer: -99 Yes Enter an integer: 0 Yes With change: if (x 99) if (x == 99) Enter an integer: 99 Yes Enter an integer: -99 No Enter an integer: 0 No

25. //-- Effect of roundoff error #include using namespace std; int main() { for (float x = 0; x != 50.0; x = x + 0.1) { float y = x * sqrt(1 + sin(x)); cout << x << " " << y << endl;; } 25 Execution: 0 0.1 0.104873 0.2 0.218968... 49.9998 42.937 50.0998 45.7826 50.1998 48.5246... 100.099 76.3241... With change: for (float x = 0; x < 50.0; x = x + 0.1) Execution: 0 0.1 0.104873 0.2 0.218968... 49.7998 36.9654 49.8998 39.9954 49.9998 42.937 or abs(x - 50) >= 1E-10

26. Preconditions Sometimes values must satisfy certain requirements for a program to process them (e.g., they must be positive). if statement later Such requirements are called preconditions or assertions. They are boolean expressions that must be true in order for the program to work correctly. A convenient way to check preconditions is to use C++’s assert() mechanism. e.g., Project 2.3 26 Proj. 2 b^2 > 4ac Proj. 3: payment > purchase

27. Assertions #include using namespace std; int main() { cout > month; assert(month >= 1); assert(month <= 12); 27 #include //... } assert() will halt the program if month 12 and display a message. assert1

28. NOTE Logical Operators More complex boolean expressions can be 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: cin >> month; 28 assert(1 <= month && month <= 12); NOT: assert(1 <= month <= 12); assert1

29. #include using namespace std; int main() { bool input1, input2, output; cout << "Enter inputs: "; cin >> input1 >> input2; output = (input1 || input2) && !(input1 && input2); cout << "Output for inputs " << input1 << " and " << input2 << " is " << output << '\n'; } 29 Executions: Enter inputs: 0 1 Output for inputs 0 and 1 is 1 Enter inputs: 1 1 Output for inputs 1 and 1 is 0 With change: cout << "Output for inputs " << boolalpha << input1 << " and " << input2 << " is " << output << '\n'; Enter inputs: 0 1 Output 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: (Programming Problems) XOR circuit

30. Character Functions The library contains an assortment 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: toupper(ch) tolower(ch) 30 See App. D

31. 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'); or or assert(isupper(ch)); Examples: use later - menu

32. Operator Precedence ( ) HIGHER + (positive), - (negative), ! (NOT) *, /, % + (addition), - (subtraction), >= > ==, != && || = LOWER See Appendix C for a complete list. 54 operators 18 precedence levels 32 When in doubt, use parentheses!

33. 33 OperatorAssociativityOverloadableArityDescription :: rightnounaryglobal scope :: leftnobinaryclass scope.leftnobinarydirect member selection - leftyesbinaryindirect member selection [] leftyesbinarysubscript (array index) () leftyesn/afunction call () leftyesn/atype construction sizeof rightn/aunarysize (in bytes) of an object or type ++ rightyesunaryincrement -- rightyesunarydecrement ~ rightyesunarybitwise NOT ! rightyesunarylogical NOT + rightyesunaryplus (sign) - rightyesunaryminus (sign) * rightyesunarypointer dereferencing & rightyesunaryget address of an object new rightyesunarymemory allocation delete rightyesunarymemory deallocation () rightyesbinarytype conversion (cast). leftnobinarydirect member pointer selection -> leftyesbinaryindirect member pointer selection * leftyesbinarymultiplication / leftyesbinarydivision % leftyesbinarymodulus (remainder) + leftyesbinaryaddition - leftyesbinarysubtraction << leftyesbinarybit-shift left >> leftyesbinarybit-shift right < leftyesbinaryless-than <= leftyesbinaryless-than-or-equal > leftyesbinarygreater-than >= leftyesbinarygreater-than-or-equal == leftyesbinaryequality != leftyesbinaryinequality & leftyesbinarybitwise AND ^ leftyesbinarybitwise XOR | leftyesbinarybitwise OR && leftyesbinarylogical AND || leftyesbinarylogical OR ? : leftnoternaryconditional expression = rightyesbinaryassignment += rightyesbinaryaddition-assignment shortcut -= rightyesbinarysubtraction-assignment shortcut *= rightyesbinarymultiplication-assignment shortcut /= rightyesbinarydivision-assignment shortcut %= rightyesbinarymodulus-assignment shortcut &= rightyesbinarybitwise-AND-assignment shortcut |= rightyesbinarybitwise-OR-assignment shortcut ^= rightyesbinarybitwise-XOR-assignment shortcut <<= rightyesbinarybitshift-left-assignment shortcut >>= rightyesbinarybitshift-right-assignment shortcut throw rightyesunarythrow an exception, leftyesbinaryexpression separation