Assignment Statements and Arithmetic Expressions

1. Assignment Statements and Arithmetic Expressions

2. Assignment Statements • Change the value of a variable • Cause a value to be copied from one memory cell to another • Specify an expression to be evaluated and stored into a target location

3. Arithmetic Expressions The purpose of an arithmetic expressions is to specify an arithmetic computation. • The implementation of the computation involves: • fetching the operands • executing the arithmetic operations

4. Arithmetic Expressions • Arithmetic expressions are constructions of: • operators • operands • parentheses • function calls

5. Arithmetic Expressions • The operators can be • unary • binary • ternary

6. Arithmetic Expressions: • Operator evaluation order • Precedence - defines the order in which operators of different precedence are evaluated • Associativity - defines the order in which operators of equal precedence are evaluated • Parentheses - default evaluation order can be overridden with use of parentheses

7. Arithmetic Expressions: Precedence FORTRAN highest: ** (exponentiation) *, / (multiplication, division) all +, - (unary and binary addition and subtraction) lowest:

8. Arithmetic Expressions: Precedence Pascal highest: *, /,div, mod all +, - lowest:

9. Arithmetic Expressions: Precedence C highest: postfix ++, -- prefix ++, -- unary +, - *, /, % binary +, - lowest:

10. Arithmetic Expressions: associativity Left associativity- leftmost operator is evaluated first A / B * C (FORTRAN) Right associativity- rightmost operator is evaluated first A ** B ** C (FORTRAN) Non-associativity- operators of equal precedence must be parenthesized A ** (B ** C) (ADA for exponentiation)

11. Sequence Control for Arithmetic Expressions • Tree Structure Representation • clarifies control structure of an expression • syntactic representation options • Execution-time Representation • machine code • evaluation of tree structures • prefix or postfix form

12. Tree Structure Representation • prefix (Polish prefix) notation • infix • postfix or reverse Polish notation (RPN)

13. Tree Structure Representation • Syntactic Representation Options • prefix (Polish prefix) notation • the operator comes first, followed by the operands • - same notation as function calls f(x, y, z) • - no parenthesis needed • - relatively simple translation process • - unique operators needed for operations with • variable number of operands • - lack of structuring cues (reduces readability) • - number of operands must be known

14. Tree Structure Representation Syntactic Representation Options • infix • for binary operations, the operator is written • between the two operands • - gives natural representation (readability) • - best suited for binary operations • - requires complex translation process

15. Tree Structure Representation Syntactic Representation Options • postfix or reverse Polish notation (RPN) • the operands are written first, followed by the • operator • - advantages and disadvantages similar to prefix

16. Tree Structure Representation (a + b) x (c - a) x + - a b c a

17. Tree Structure Representation (a + b) x (c - a) Prefix? x Infix? Postfix? + - a b c a

18. Evaluations of Expressions Postfix evaluation: (evaluate using an execution stack) 1. Scan expression left to right 2. If OPERAND, push onto stack. 3. If OPERATOR, pop the corresponding number of arguments off the stack, apply the operator to the operands. 4. Push result onto stack as next operand.

19. 2 -b + b - 4ac let a=2, b=-7, c=3 2a Evaluations of Expressions (a + b) x (c - a), let a=3, b=4, c=5 • Find the postfix representation • Evaluate the postfix expression using an execution stack.

20. Evaluations of Expressions Prefix evaluation: (evaluate using an execution stack) 1. Scan expression left to right 2. If OPERATOR, push onto stack. Set argument count to n, number of arguments req’d by operator 3. If OPERAND, push onto stack. 4. If top n entries are operands, pop the top n entries, pop the operator and apply the operator to those operands. 5. Push result onto stack as next operand.

21. Arithmetic Expressions: Operand evaluation order: side effects A := 10; NEW := A + fun(A); Suppose function fun returns the value of its argument divided by two. And suppose as a side effect, it changes the value of its argument to 20.

22. if (count == 0) avg = 0; else avg = sum / count; Arithmetic Expressions: a ternary operator Conditional expression: C and C++: expression1 ? expression2 : expression3 avg = (count == 0) ? 0 : sum / count;

23. Arithmetic Expressions: Overloaded Operators • Arithmetic operators are often used for more than one purpose • This may adversely affect: • readabilty • same symbol is used for unrelated operations • reliability • increases the chance that a typo will compile

24. Arithmetic Expressions: Overloaded Operators Arithmetic operators are often used for more than one purpose examples: + for integer and floating point addition, string catenation in C++ & for addressing and bitwise and operation in C / for integer and floating point division in C++

25. Arithmetic Expressions: Overloaded Operators Arithmetic operators may also be overloaded by the user in C++ Properly used this may aid readabilty and writability: example: +, * overloaded for a user defined matrix data type a * b + c * d instead of MatrixAdd(MatrixMult(a,b), MatrixMult(c,d))

26. Arithmetic Expressions: Type Conversions • narrowing • widening • A narrowing conversion is one that converts an objects to a type that cannot include all of the values of the original type • A widening conversion is one in which an object is converted to a type that can include at least approximations of all the values of the original type

27. Arithmetic Expressions: Type Conversions • When arithmetic operations include operands of different types (mixed-mode expressions) implicit type conversions must be performed. • A coercion is an implicit type conversion performed by the compiler.

28. Arithmetic Expressions: Type Conversions • Explicit Type Conversion • Most languages allow for explicit type conversion. • Some provide a warning when the conversion is narrowing and significant change in value will result. ADA: AVG := FLOAT(SUM) / FLOAT(COUNT) C: avg = (float) sum / count

29. Arithmetic Expressions: Errors • operand type errors (avoided if type checking is used). • coercion • limitations of computer arithmetic • integer overflow • floating point overflow • inherent limitations of arithmetic

30. Boolean and Relational Expressions: • Relational Expressions • A relational expression has two operands and one relational operator • A relational expression has two operands and one relational operator • The value produced by a relational operator is boolean (unless boolean is not a type in the language)

31. Boolean and Relational Expressions: • Relational Operators • Pascal FORTRAN C • = .EQ. == • <> .NE. != • <= .LE. <= • < .LT. < • >= .GE. >= • > .GT. !>

32. Boolean and Relational Expressions: • Boolean Expressions consist of • boolean variables • boolean constants • relational expressions • boolean operators • used for control structures

33. Boolean and Relational Expressions: • Boolean Operators • Pascal FORTRAN C • not .NOT. ! • and .AND. && • or .OR. ||

34. Boolean and Relational Expressions: The precedence of boolean operators is normally not - highest and or - lowest but the precedence of relational operators and arithmetic operators as compared to boolean operators, differs according to each language.

35. Boolean and Relational Expressions: FORTRAN 77: Highest ** *, / +, - .EQ., .NE., .GT., .GE., .LT., .LE. .NOT. .AND. .OR. Lowest .EQV., .NEQV. (logical compare)

36. Boolean and Relational Expressions: Pascal: Highest not *, /, div, mod, and +, -, or Lowest =, <>, <, <=, >, >=, in

37. Boolean and Relational Expressions: C: Highest !, ~ *, /, % +, - <, <=, >, >= ==, != & ^ | && Lowest ||

38. Boolean and Relational Expressions: precedence Pascal: j >= 7 and k<5 Pascal: j >= 7 and k<5 <- Syntax error FORTRAN: J.GE.7 .AND. K.LT.5 FORTRAN: J.GE.7 .AND. K.LT.5 C/C++: j >= 7 && k<5 C/C++: j >= 7 && k<5

39. Boolean and Relational Expressions: type conversion Pascal: 1 <= j <= 10 <- Syntax error FORTRAN: 1 .LE. J .LE. 10 <- Syntax error C/C++: 1 <= j <= 10 <- True

40. Boolean and Relational Expressions: Short-circuit evaluation Short-circuit evaluation of an expression - result is determined without evaluating all operators Pascal:(most implementations do not use short circuit) while (count <> 0) and (sum/count > 100) do C/C++/Java:(&&, || use short circuit but &, | do not) while ((count != 0) && (sum/count > 100))

41. Assignment Statements: Options and side effects • simple assignment • multiple assignments • conditional assignment • compound assignment • unary assignment • assignment as an expression