Introduction to Arithmetic Expressions and Assignment Statements

1. Chapter 7 Expressions and Assignment Statements

2. Introduction Arithmetic Expressions Overloaded Operators Type Conversions Relational and Boolean Expressions Short-Circuit Evaluation Assignment Statements Mixed-Mode Assignment

3. - Expressions are the fundamental means of specifying computations in a programming language - To understand expression evaluation, we need to be familiar with the orders of operator and operand evaluation - The essence of imperative languages is the dominant role of assignment statements

4. Introduction • Issues • Order of evaluation • Type mismatch and coercions • Short circuit evaluation • Assignment statement • Used in imperative languages to change the value of a variable • Contains an expression to be evaluated and a target location for the answer.

5. Arithmetic Expressions • Most of the characteristics of arithmetic expressions in programming languages were inherited from conventions that had evolved in mathematics. • The purpose of an arithmetic expression is to specify an arithmetic computation. The two actions of this are: • fetching the operands, usually from memory, • executing the arithmetic operations on those operands • In programming languages, arithmetic expressions consist of operators, operands, parentheses, and function calls. • The operators can be unary, meaning they have a single operand, or binary, meaning they have two operands. • C, C++, and Java include a ternary operator, which has three operands.

6. Arithmetic Expressions (continued) • Design issues for arithmetic expressions • What are the operator precedence (priority) rules? • What are the operator associativity rules? • What is the order of operand evaluation? • Are there restrictions on operand evaluation side effects? • Does the language allow user-defined operator overloading? • What mode mixing is allowed in expressions?

7. Arithmetic Expressions (continued) • Number of operands for an operator • A unary operator has one operand • A binary operator has two operands • A ternary operator has three operands • The operator precedence rules for expression evaluation define the order in which “adjacent” operators of different precedence levels are evaluated. • Typical precedence levels • parentheses • unary operators • ** (if the language supports it) • *, /, % • +, -

8. Arithmetic Expressions (continued) • The order of an expression depends on the order of evaluation of the operators • The operator precedence rules for expression evaluation define the order in which operators of different precedence levels are evaluated. These rules are based on the hierarchy of operator priorities. • Unary addition is called identity operator because it usually has no associated operation and thus has no effect on its operand.

9. Arithmetic Expressions (continued) • The operator associativity rules for expression evaluation, define the order in which adjacent operators with the same precedence level are evaluated • Typical associativity rules: • Left to right, except **, which is right to left • Sometimes unary operators associate right to left (e.g., FORTRAN) • APL is different; all operators have equal precedence and all operators associate right to left • Precedence and associativity rules can be overriden with parentheses • Operand evaluation order The process: • Variables: just fetch the value • Constants: sometimes a fetch from memory; sometimes the constant is in the machine language instruction • Parenthesized expressions: evaluate all operands and operators first • Function references: The case of most interest! • Order of evaluation is crucial

10. Arithmetic Expressions (continued) • Functional side effects - when a function changes a two-way parameter or a nonlocal variable • The problem with functional side effects: • When a function referenced in an expression alters another operand of the expression e.g., for a parameter change: a = 10; b = a + fun(&a); /* Assume that fun changes its parameter */ • Same problem with global variables

11. Arithmetic Expressions (continued) • Two Possible Solutions to the Problem: • Write the language definition to disallow functional side effects • No two-way parameters in functions • No nonlocal references in functions • Advantage: it works! • Disadvantage: Programmers want the flexibility of two-way parameters (what about Java?) and nonlocal references • Write the language definition to demand that operand evaluation order be fixed • Disadvantage: limits some compiler optimizations • Conditional Expressions • C, C++, and Java (?:) e.g. average = (count == 0)? 0 : sum / count;

12. Overloaded Operators • Operator overloading is the multiple use of operators. • Example, the “+” is used for addition and for string concatenation in Java. • The “&’’ in C is a problem and overloading the – and + operator is also a problem. • Loss of compiler • Loss of readability • Can be avoided by introducing new symbols • C++ and Ada allow user-defined overloaded operators • Potential problem if user defines ”nonsense” operators like using + to mean multiply

13. Type Conversions • A narrowingconversion is one that converts an object to a type that cannot include all of the values of the original type e.g., float to int • A wideningconversion is one in which an object is converted to a type that can include at least approximations to all of the values of the original type e.g., int to float • A mixed-mode expression is one that has operands of different types • A coercion is an implicit type conversion, either during compilation or during run time. A typical example would be an expression mixing integer and floating point numbers (like 5 + 0.1), where the integers are normally converted into the latter • The disadvantage of coercions: • They decrease the type error detection ability of the compiler • In most languages, all numeric types are coerced in expressions, using widening conversions • In Ada, there are virtually no coercions in expressions

14. Type Conversions (cont.) • Explicit Type Conversions • Often called casts e.g. • Ada: FLOAT(INDEX) -- INDEX is INTEGER type • Java: (int)speed /* speed is float type */ • Errors in Expressions • Caused by: • Inherent limitations of arithmetic e.g. division by zero • Limitations of computer arithmetic e.g. overflow • Such errors are often ignored by the run-time system

15. Relational and Boolean Expressions • Relational Expressions: • Use relational operators and operands of various types • Evaluate to some Boolean representation • Operator symbols used vary somewhat among languages (!=, /=, .NE., <>, #) • Boolean Expressions: • Operands are Boolean and the result is Boolean • Operators: FORTRAN 90 Java C Ada and & && and or | || or not ! ! not ^ xor • C has no Boolean type--it uses int type with 0 for false and nonzero for true • One odd characteristic of C’s expressions: a < b < c is a legal expression, but the result is not what you might expect

16. Relational and Boolean Expressions (continued) • The precedence of the arithmetic, relational, and Boolean operators in the C-based languages is as follows: postfix ++, -- unary +, -, prefix ++, --, ! *, /, % binary +, - <, >, <=, >= ==, != && || • C, C++, and Java have over 40 operators and least 14 different levels of precedence

17. Short Circuit Evaluation • A short-circuit evaluation of an expression is one in which the result is determined without evaluating all of the operands and/or operators. • Ex., (13 * A) * (B / 13 – 1) is independent of the value (B / 13 – 1) if a is 0. Because 0*x = 0 for any x. So if A is 0 there is no need to evaluate (B / 13 – 1). • Short-circuit evaluation of expressions exposes the problem of allowing side effects in expressions. • C, C++, and Java: use short-circuit evaluation for the usual Boolean operators (&& and ||). • Short-circuit evaluation exposes the potential problem of side effects in expressions e.g. (a > b) || (b++ / 3)

18. Assignment Statements • The operator symbol: = FORTRAN, BASIC, PL/I, C, C++, Java := ALGOLs, Pascal, Ada = Can be bad if it is overloaded for the relational operator for equality • e.g. (PL/I) A = B = C; A is set to the Boolean value for the result of B = C • In the C statement A = B = C, the value of C is assigned to B, and the value of B is assigned to A.

19. Assignment Statements (continued) • More complicated assignments: • Multiple targets (PL/I) A, B = 10 • Conditional targets (C, C++, and Java) if(flag) count1 = 0; else count2 = 0; • Compound assignment operators (C, C++, and Java) sum += next; • Unary assignment operators (C, C++, and Java) a++; • C, C++, and Java treat = as an arithmetic binary operator • e.g. a = b * (c = d * 2 + 1) + 1 • This is inherited from ALGOL 68

20. Assignment Statements (continued) • Assignment as an Expression • In C, C++, and Java, the assignment statement produces a result • So, they can be used as operands in expressions e.g. while ((ch = getchar()) != EOF) { ... } • Disadvantage • Another kind of expression side effect of changing its left operand.

21. Mixed-Mode Assignment • In FORTRAN, C, and C++, any numeric value can be assigned to any numeric scalar variable; whatever conversion is necessary is done • In Pascal, integers can be assigned to reals, but reals cannot be assigned to integers (the programmer must specify whether the conversion from real to integer is truncated or rounded) • In Java, only widening assignment coercions are done • In Ada, there is no assignment coercion

22. Summary • Expressions • Operator precedence and associativity • Operator overloading • Mixed-type expressions • Various forms of assignment