1.5 Casting and Range of Variables

1. Exam Points

• Range of the int type: [Integer.MIN_VALUE , Integer.MAX_VALUE]
• Integer overflow(int): if a value is outside of the allowed range, an integer overflow occurs.
• Round-off error(double) - if a value is more precise than can be stored in the allotted memory, a round-off error occurs. (Ex. 2.3 is stored as 2.29999)
• Casting operators (int) and (double) can be used to convert from a double value to an int value (or vice versa).
  • (int)0.3*11 is 0
  • (int)(0.3*11) is 3
• Casting a double value to an int value causes the digits to the right of the decimal point to be truncated. (Ex. 10.9 -> 10)
• int to double conversion is done automatically. (Ex. double b = 10, b is 10.0)

2. Knowledge Points

(1) Range of Variables

• An int variable is stored using 4 bytes.
• Range of int variables: [Integer.MIN_VALUE , Integer.MAX_VALUE]
• Integer overflow: if a value is outside of the allowed range, an integer overflow(溢出错误) occurs.
• 如果尝试在int变量中存储超出其范围的值，发生溢出错误。
• Example:

     int x = 100; 
     x = Integer.MAX_VALUE;
     
     // y is out of the range of int, leading to overflow error
     int y = x * 100 ; 
  

• A double variable is stored using 8 bytes.
• Round-off error(舍入误差): If a value is more precise than can be stored in the allotted amount of memory, a round-off error occurs. The result will be rounded to the representable value. (对于double变量，有的值无法准确表示，会得到一个四舍五入的值，这种Java能表示的值和实际值之间的误差叫做舍入误差)
• Example:
  3.1433 is 28.26, but is represented as 28.259999999999998 in Java.

(2) Type Casting (类型转换)

• Casting(转换) means converting from one type to another.
• Casting from a small range to a large range:
  
  • Example: int to double

  int x = 100 ;
  double y = 20.9 ;
  y = x;  // int -> double , casted automatically
  

• Casting from a large range to a small range:
  
  • Example: double to int

  double y = 20.9 ;
  
  // convert from double to int, 
  // must be done manually by adding (int) before y
  int x =(int) y ;  
  

• Casting a double value to an int value causes the digits to the right of the decimal point to be truncated.
  • int a = (int) 20.9
  • result is 20
• Double values can be rounded to the nearest integer by:
  • (int) (x + 0.5) for non-negative numbers
  • (int)(x - 0.5) for negative numbers
  • Example:\
• Precedence(优先级) : casting has a higher precedence over arithmetic operations.
  • Example: (int)0.3*11 will evaluate (int)0.3 first, and then *
    

3. Exercises

• Practice
• Solution