• The Principle:
  • "Each data operation must involve a single data type."
  • "Any operation involving values of more than one data type" ... "is considered to be a type mismtach." (Shackelford)
• The Rationale:
  • "Disciplined thinking"

• Recall:
  • All numbers are represented in binary
  • Different types use different number of bits
• Implication:
  • Type mismtaches aren't always a problem

• Types:
  • byte (1 byte)
  • short (2 bytes)
  • int (4 bytes)
  • long (8 bytes)
• Conversions:
  • byte to short: pad with one byte of 0s
  • short to int: pad with two bytes of 0s
  • int to long: pad with four bytes of 0s
• These are called widenings

• An example byte (19 base 10):

  • 00010011

• Conversion to short:

  • 00000000

    00010011

• An example byte (-19 base 10):

  • 11101101

• Conversion to short:

  • 11111111

    11101101

• -128 base 10 (byte):

  • 10000000

• 128 base 10 (short):

  • 00000000

    10000000

• -128 base 10 (short):

  • 11111111

    10000000

• float:
  • 1 bit for the sign
  • 8 bits for the exponent
  • 23 bits for the mantissa
• double:
  • 1 bit for the sign
  • 11 bits for the exponent
  • 52 bits for the mantissa

• float to double Conversions:
  • Pad the exponent and mantissa with 0s
• long to float Conversions:
  • The largest long is 9,223,372,036,854,775,807
  • This becomes the float 9,223,372,036,854,776,000
  • This is a loss of precision but not magnitude
  • The IEEE 754 round-to-nearest rule is applied

int   small;
long  large;

.
.
.
large = small;

• Definition:
  • Widening that occurs within the context of a numeric operator
• Why is this an Issue?
  • The conversion chosen for one operand may depend in part on the type of the other operand expression
• Example:
  • large = large + small;

• Typecasting:
  • (Type)Expression
• Examples:

          int   small;
          long  large;
  
          small = (int)large;
  	

• Integer to Integer:
  • Discard the lowest order bits
• Floating Point to Integer:
  • Involves a complicated process

• Result:
  • Loss of precision
  • Possible loss of magnitude
  • Possible change of sign
• Implication:
  • Use sparingly, if at all

public class NarrowingExample
{
  public static void main(String[] args)
  {
    float fmax, fmin;

    fmax = Float.POSITIVE_INFINITY;
    fmin = Float.NEGATIVE_INFINITY;

    JMUConsole.println("long:  "+(long)fmin +".."+(long)fmax);
    JMUConsole.println("int:   "+(int)fmin  +".."+(int)fmax);
    JMUConsole.println("short: "+(short)fmin+".."+(short)fmax);
    JMUConsole.println("byte:  "+(byte)fmin +".."+(byte)fmax);
  }
}