Integers

Objectives

1. Understand the different integer types.
2. Understand numeric overflow
3. List the basic integer operations

Notes

• This is from chapter 2.5 of the book.
• As well as from Oracle documentation.
  • This is somewhat technical, but far more complete.
• Integer literals
  • reference.
  • Literals are numbers directly entered in our program.
    • int x = 32;
    • 32 is the integer literal.
  • By default an integer literal is of type int
  • If we append a L, the type is then long.
  • long x = 32L;
  • As we have seen, we can put an underscore in an integer literal
    • int oneMillion = 1_000_000;
    • It appears to ignore these totally.
  • There are strange rules for items starting with 0
    • 010 is a number in octal.
    • 0b11001 is a number in binary
    • 0x1e3 is a number in hex
    • Just don't start an integer with 0
• As we have discussed there are four and a half integer types.
  • long - 64 bit
  • int - 32 bit
  • short - 16 bit
  • byte - 8 bit
  • char - the 1/2 type, we will discuss this later.
• All of these store integers, the difference is the size.
  • I don't expect you to remember this part
  • But numbers are stored in a format called two's complement.
  • And if we have n bits
    • Then we can represent values
    • $-2^{n-1} \le x \le 2^{n-1}-1$
    • Example: 8 bits (byte type) we can represent
    • $-2^{8-1} \le x \le 2^{8-1}-1$
    • $-2^{7} \le x \le 2^{7}-1$
    • $-128 \le x \le 127$
• Integer operations
  • +, - and * work as expected.
  • Well there is one small problem.
    • Numeric overflow occurs when the result of a mathematical operation will not fit into memory.
    • Remember the football scoreboard?
    • We can see this with addition:
    • Just for me: 2147483647 is the largest int,
      • It is $2^{32-1}-1$ from above
      • I can't show you that computation in java yet, we don't know enough.
    • But let's add one to it!
    • The result is numeric overflow.
    • This occurs when subtract 1 from the smallest number as well.
    • This occurs when we multiply too!
  • Division is integer division
    • Remember elementary school math.
    • 123 / 7

    •         17 R 4
           -------
         7 | 123
              7
             --
              53
              49 
              --
               4
                   

    • Note to self: use %% for % in printf statement.
    • Division will occasionally trip you up.
      • F = 9/5C + 32 will become F = C + 32.
      • 9/5 = 1 in integer division.
      • C = 5/9(F-32) will become C = 0
      • 5/9 = 0 in integer division.
      • We will deal with these later.
  • Some special cases
    • We do things like a = a * expression; all the time.
    • For example a = a * 3 * x + 2;
    • So there is a shortcut for this:
    • a *= 3 * x + 2;
    • +=, -=, *=, /=, %=
  • We also do this:
    • i = i + 1
    • But this time, the only value is 1.
    • We can write a shortcut for this as
      • ++i; prefix or pre-increment operator.
        • add to i, then return the value.
      • i++; postfix or post increment.
        • return the value of i, then add 1.
    • If you just use these on a line alone they are fine.
    • If you use them in an equation, you can get unexpected results.
    • By the way, --i, and i-- are also acceptable.
• Some last notes
  • If an equation has at least one long then the entire computation is carried out as a long.
  • All other values are widened or promoted to a long.
  • Otherwise all integer computations are carried out as an int, and smaller values are widened or promoted to an int.
  • We will discuss widening, promotion, narrowing, cast, and coercion later.