1. CSE115: Introduction to Computer Science I Dr. Carl Alphonce 219 Bell Hall Office hours: M-F 11:00-11:50 645-4739 alphonce@buffalo.edu

2. Agenda Today: –Primitives operator types floating point mixing types type casting and coercion wrapper classes Coming up: –More control structures

3. ‘+’ is overloaded ‘+’ is just a name ‘+’ has different interpretations –String concatenation –integer addition addition of two’s complement numbers –floating point addition addition of IEEE754 numbers

4. type of ‘+’ In the following expression, what is the type of ‘+’? 5 + 2

5. mappings an operator / function maps from a domain set to a range set: DOMAINRANGE

6. ‘+’ as int addition range is int domain is pairs of int ‘+’ has type int x int  int DOMAIN int X int RANGEint

7. int values: 0, 1, -1, 2, -2, … maximum int: 2147483647 = +2 (32-1) -1 minimum int: -2147483648 = -2 (32-1) operations: + - * / % 5+2 = 7+int X int  int 5-2 = 3-int X int  int 5*2 = 10*int X int  int 5/2 = 2 (quotient) /int X int  int 5%2 = 1 (remainder)%int X int  int

8. types of operators for type int Notice that all of these operators take two int arguments, and produce an int result. There is hardware circuitry to perform these operations.

9. double values: 0.0, 1.0, -3.5, 3141.5926535e-3 inexact representation (!) operations: + - * / 5.0 + 2.0 = 7.0+double X double  double 5.0 – 2.0 = 3.0-double X double  double 5.0 * 2.0 = 10.0*double X double  double 5.0 / 2.0 = 2.5/double X double  double

10. floating point types’ representation both double and float use the IEEE754 representation scheme size of representation differs according to type: –the representation of a float is 4 bytes wide –the representation of a double is 8 bytes wide main point: values of different types have different representations – you can’t “mix and match”!

11. Things to watch for! Representation is inexact –e.g.  has a truncated representation –0.1 does not have an exact representation representation is in terms of powers of 2: Mixing magnitudes –it is possible that x+y is the same as x! 1.0e-15 + 1.0e-15  2.0 e-15 1.0e+15 + 1.0e-15  1.0 e+15 (whoops!) Round-off errors – comparisons! double d = 0.1; double pointNine = d+d+d+d+d+d+d+d+d; pointNine is not the same as 0.9 (whoops!)

12. mixing types in expressions Operators such as +, -, * and / are overloaded: the same name has many different values + overloaded as String concatenation too! “Good” + “ ” + “morning!”  “Good morning!” What happens in an expression which mixes values of different types? 5 + 2.5 = ???? 5 is coerced to its equivalent double value, 5.0: 5.0 + 2.5 = 7.5 Type coercion happens only from “smaller” type to “larger” type (e.g. int  double, not double  int)

13. relational operators We can form expressions like: x < y which have a value of true or false (i.e. the type of this expression is boolean) relational operators: >= ==

14. Equality testing Equality testing: –of primitive values: == –of objects: equals method Consider: Foo a = new Foo();Foo c = a; Foo b = new Foo(); what is value ofwhat is value of (a==b)(a==c)