Assignment Statements and Arithmetic Expressions

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

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

Arithmetic Expressions

Arithmetic expressions are constructions of:

• operators• operands• parentheses• function calls

Arithmetic Expressions

The operators can be

• unary• binary• ternary

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

Arithmetic Expressions: Precedence

FORTRANhighest: ** (exponentiation)

*, / (multiplication, division)all +, - (unary and binary addition and

subtraction)lowest:

Arithmetic Expressions: Precedence

Pascalhighest: *, /,div, mod

all +, - lowest:

Arithmetic Expressions: Precedence

Chighest: postfix ++, --

prefix ++, --unary +, -*, /, %binary +, -

lowest:

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)

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

Tree Structure Representation

• prefix (Polish prefix) notation

• infix

• postfix or reverse Polish notation (RPN)

Tree Structure RepresentationSyntactic 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

Tree Structure RepresentationSyntactic 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

Syntactic Representation Options

• postfix or reverse Polish notation (RPN) the operands are written first, followed by the operator

- advantages and disadvantages similar to prefix

Tree Structure Representation

(a + b) x (c - a)

x

+ -

cba a

Tree Structure Representation

(a + b) x (c - a)

x

+ -

cba a

Prefix?

Infix?

Postfix?

Tree Structure Representation

Evaluations of Expressions

Postfix evaluation: (evaluate using an execution stack)

1. Scan expression left to right2. 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.

• Find the postfix representation

• Evaluate the postfix expression using an execution stack.

(a + b) x (c - a), let a=3, b=4, c=5

-b + b - 4ac let a=2, b=-7, c=3

2a

2

Evaluations of Expressions

Prefix evaluation: (evaluate using an execution stack)

1. Scan expression left to right2. If OPERATOR, push onto stack. Set argument count to n, number of arguments req’d by operator3. 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.

Evaluations of Expressions

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.

Arithmetic Expressions:

Conditional expression: C and C++:

expression1 ? expression2 : expression3

avg = (count == 0) ? 0 : sum / count;

if (count == 0) avg = 0;else avg = sum / count;

Arithmetic Expressions:

Overloaded Operators

Arithmetic operators are often used for more than one purpose examples:

+ for integer and floating point addition, string catenation

& for addressing and bitwise and operation in C

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

Arithmetic Expressions:

Type Coercion

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.

Arithmetic Expressions:

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

Boolean and Relational Expressions:

Relational Expressions

A relational operator compares the values of its two operands

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)

Boolean and Relational Expressions:

Relational Operators

Pascal FORTRAN C = .EQ. == <> .NE. != <= .LE. <= < .LT. < >= .GE. >= > .GT. !>

Boolean and Relational Expressions:

Boolean Expressions consist of

boolean variablesboolean constantsrelational expressions

and boolean operators

Boolean and Relational Expressions:

Boolean Operators

Pascal FORTRAN C not .NOT. ! and .AND. && or .OR. ||

Boolean and Relational Expressions:

The precedence of boolean operators is normally

not - highestand or - lowest

but the precedence of relational operators and arithmetic operators as compared to boolean operators, differs according to each language.

Boolean and Relational Expressions:

FORTRAN 77:Highest **

*, /+, -// (string catenation).EQ., .NE., .GT., .GE., .LT., .LE..NOT..AND..OR.

Lowest .EQV., .NEQV. (logical compare)

Boolean and Relational Expressions:

Pascal:

Highest not*, /, div, mod, and+, -, or

Lowest =, <>, <, <=, >, >=, in

Boolean and Relational Expressions:

C: !, ~, ++, ---, sizeof(), (type), +,-(unary), *(indirection), &(address)

Highest *, /, %+, ->>, <<<, <=, >, >===, !=&^|&&

Lowest ||