University of Washington Computer Programming I Lecture 4 Arithmetic Expressions 2000 UW CSE D 1 Overview Arithmetic expressions Integer and floating point double types Unary and binary operators Precedence Associativity Conversions and casts Symbolic constants Reading Text sec 2 5 D 2 Why Study Expressions We need precise rules that define exactly what an expression means What is the value of 4 4 4 4 Arithmetic on a computer may differ from everyday arithmetic or math 1 0 9 0 9 0 could be 0 99999998213 2 3 is zero in C not 667 D 3 Assignment Statement Review double area radius area 3 14 radius radius assignment statement expression Execution of an assignment statement Evaluate the expression on the right hand side Store the value of the expression into the variable named on the left hand side D 4 Expressions Expressions are things that have values A variable by itself is an expression radius A constant by itself is an expression 3 14 Often expressions are combinations of variables constants and operators area 3 14 radius radius D 5 Expression Evaluation Some terminology Data or operand means the integer or floatingpoint constants and or variables in the expression Operators are things like addition multiplication etc The value of an expression will depend on the data types and values and on the operators used Additionally the final result of an assignment statement will depend on the type of the assignment variable D 6 Arithmetic Types Review C provides two different kinds of numeric values Integers 0 12 17 142 Type int Values are exact Constants have no decimal point or exponent Floating point numbers 3 14 6 023e23 Type double Values are approximate 12 14 digits precision typical Constants must have decimal point and or D 7 exponent Operator Jargon Binary operates on two operands 3 0 b zebra giraffe Unary operates on one operand 23 4 C operators are unary or binary Puzzle what about expressions like a b c D 8 Answer this is two binary ops in sequence Expressions with doubles Constants of type double 0 0 3 14 2 1 5 0 6 02e23 1 0e 3 not 0 or 17 Operators on doubles unary binary Note no exponentiation operator in C D 9 Example Expressions with doubles Declarations double height base radius x c1 c2 Sample expressions not statements 0 5 height base 4 0 3 0 3 14 radius radius radius 3 0 c1 x c2 x x D 10 Expressions with ints Constants of type int 0 1 17 42 not 0 0 or 1e3 Operators on ints unary binary D 11 int Division and Remainder Integer operators include integer division and integer remainder symbols and Caution division looks like an old friend but there is a new wrinkle 2 rem 99 1 100 299 200 99 D 12 int Division and Remainder is integer division no remainder no rounding 299 100 2 6 4 1 5 6 0 is mod or remainder 299 100 99 6 4 2 5 6 5 D 13 Expressions with ints Time Example Given total minutes 359 Find hours 5 minutes 59 Solution in C hours total minutes 60 minutes total minutes 60 D 14 A Cautionary Example int radius double volume double pi 3 141596 volume 4 3 pi radius radius radius D 15 Why Use ints Why Not doubles Always Sometimes only ints make sense the 15th spreadsheet cell not the 14 997th cell Doubles may be inaccurate representing ints In mathematics 3 15 1 3 15 But 3 0 15 0 1 0 3 0 might be 14 9999997 Last and least operations with doubles is slower on some computers doubles often require more memory D 16 Order of Evaluation Precedence determines the order of evaluation of operators Is a b a b equal to a b a b or a b a b And does it matter Try this 4 3 2 1 4 3 2 1 7 4 3 2 1 9 D 17 Operator Precedence Rules Precedence rules 1 do s first starting with innermost 2 then do unary minus negation 3 then do multiplicative ops 4 lastly do additive ops binary D 18 Precedence Isn t Enough Precedence doesn t help if all the operators have the same precedence Is a b c equal to a b c or a b c Associativity determines the order among consecutive operators of equal precedence Does it matter Try this 15 4 2 D 19 Associativity Matters Associativity determines the order among consecutive operators of equal precedence Does it matter Try this 15 4 2 15 4 2 3 2 6 15 4 2 15 8 1 D 20 Associativity Rules Most C arithmetic operators are left associative within the same precedence level a b c equals a b c a b c d equals a b c d C also has a few operators that are right associative D 21 The Full Story C has about 50 operators 18 precedence levels A Precedence Table shows all the operators their precedence and associativity Look on inside front cover of our textbook Look in any C reference manual When in doubt check the table When faced with an unknown operator check the table D 22 Precedence and Associativity Example Mathematical formula b b2 4 a c 2a C formula b sqrt b b 4 0 a c 2 0 a D 23 Depicting Expressions b b 4 0 a c 2 5 1 0 2 5 6 25 4 0 15 2 60 8 D 24 67 05 Mixed Type Expressions What is 2 3 14 Compiler will implicitly automatically convert int to double when they occur together int double double double likewise 2 3 3 14 2 3 3 14 6 3 14 6 0 3 14 18 84 2 3 3 14 2 3 3 14 0 3 14 0 0 3 14 0 0 We strongly recommend you avoid mixed types D 25 e g use 2 0 3 0 3 14 instead Conversions in Assignments int total count value double avg total 97 count 10 avg total count avg is 9 0 value total 2 2 implicit conversion to double bad news implicit conversion D 26 to int drops fraction with no warning Explicit Conversions Use a cast to explicitly convert the result of an expression to a different type Format type expression Examples double myage int balance deposit This does not change the rules for evaluating the expression itself types etc Good style because it shows the reader that the conversion was intentional not an accident D 27 Using Casts int total count double avg total 97 count 10 explicit conversion to double right way avg double total double count avg is 9 7 explicit conversion to double wrong way avg double total count avg is 9 0 D 28 define Symbolic Constants Named constants define PI 3 14159265 define HEIGHT 50 define WIDTH 80 define AREA HEIGHT WIDTH circle area PI radius radius volume length AREA Note and are not used for define can be used in define D 29 Why define Centralize changes No magic numbers unexplained …
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