# 1.00 Lecture 4. Promotion

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1 1.00 Lecture 4 Data Types, Operators Reading for next time: Big Java: sections Promotion increasing capacity Data Type Allowed Promotions double None float double long float,double int long,float,double char int,long,float,double short int,long,float,double byte short,int,long,float,double Java performs promotions silently, from lower capacity types to higher capacity types, in operations and assignment (=) When doing binary operations, Java promotes byte or short to int In all other cases it promotes the smaller to larger capacity Don t mess around: just use int (long sometimes) and double 1

2 Casting To convert a data type to a lower capacity type, you must cast it explicitly long s= 1000*1000*1000; int q= (int) s; You are responsible for making sure the variable fits in the lower capacity representation If it doesn t, you get no warning, and there is garbage in the variable (more shortly on this topic) You can cast variables into higher capacity types, if needed In lecture 1, when computing the fraction grad students, you could have cast int students to double double s2= (double) students; Exercise Create a new project Lecture4 Write a class CastTest In the main() method: Declare ints x1=17, x2=20 and x3=12 Try to declare an int 2x= 34. What happens? Compute the average of x1, x2 and x3. Be careful. Declare a long big= L; (remember the L) Try to set int x4 = big and print x4. What happens? Cast big to an int and see what happens. If you have time: Declare a double small= ; Enter number of zeros (14) exactly Try to set int s= small. What happens? Cast small to an int. Is this ok? 2

3 Arithmetic operators Table in precedence order, highest precedence at top Operators Meaning Example Associativity ++ increment i= d++; x= ++q; Right to left -- decrement --z; y= (a--) + b; + (unary) unary + c= +d; - (unary) unary e= -f; * multiplication a= b * c * d; Left to right / division e= f / g; % modulo h= i % j; + addition k= m + n + p; Left to right - subtraction q= s t; % operator defined only for integers Arithmetic operator exercise Create a class ArithmeticTest in Lecture4 Write a main() method in class ArithmeticTest Set the number of 1.00 students to 136 Increment this by one, then decrement by one Easy come, easy go, before add or drop date Set the number of students to 20 Find total students (1.00, 1.001), but increment the students by one first, all in one line If we put students in groups of three, how many groups of three are there? How many students are left over? Use the debugger to see your answers Don t write any System.out.println statements 3

4 Precedence, associativity Operator precedence is the order in which operators are applied. Do exercises on paper: Operators in same row have equal precedence int i=5; int j= 7; int k= 9; int m=11; int n; n= i + j * k - m; // n=? Associativity determines order in which operators of equal precedence are applied int i=5; int j= 7; int k= 9; int m=11; int n; n= i + j * k / m - k; // n=? Parentheses override order of precedence int i=5; int j= 7; int k= 9; int m=11; int n; n= (i + j) * (k m)/k; // n=? Operator exercises What is the value of int n: n= / 3 * 5 % 4; // n=? n= / 3 * 7 % 4; // n=? int i= 5; int j= 7; int k= 9; n= j / 3 * --i % k--; // n=? i= 5; n= i + ++i; // n=? // Don t ever do any of these! 4

5 Integer arithmetic properties Overflows occur from: Division by zero, including 0/0 (undefined) Programmer has responsibility to check and prevent this Java will warn you (by throwing an exception) if it can t do an integer arithmetic operation Accumulating results that exceed the capacity of the integer type being used Programmer has responsibility to check and prevent, as in zero divides No warning is given by Java in this case Floating point exercise Write a program to solve the following: You have a 1 meter long bookshelf There are things that are 0.1m, 0.2m, 0.3m, 0.4m and 0.5m long Starting with the smallest thing, place each on the bookshelf until you can t place any more How many things can you put on the shelf? How much space is left over? Download BookshelfTest0, which has the skeleton of the code This exercise demonstrates the imprecision of floating point numbers Java approximates the real number line with 2 64 integers 5

6 Floating point exercise public class BookshelfTest0 { public static void main(string[] args) { double lengthleft= 1.0; // Remaining space int booksplaced= 0; // Books on shelf so far double length= 0.1; // Length of book // Your code here: try to place books of length 0.1, 0.2, // 0.3, 0.4, 0.5m on shelf. Loop while enough space } } System.out.println( Books placed: "+ booksplaced); System.out.println("Length left: "+ lengthleft); Floating point problem How do we fix this? Never use if (a == b) with floats or doubles == is ok with integer types Always use if (Math.abs(a b) < TOLERANCE) Where TOLERANCE is about 10-6 float or double Or a variation on this if the operator is not == Add TOLERANCE to one side or the other in an inequality to accommodate the representation error Correct the previous exercise 6

7 MIT OpenCourseWare / / Introduction to Computers and Engineering Problem Solving Spring 2012 For information about citing these materials or our Terms of Use, visit:

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