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Logic and integer arithmetic

A look at the bytecodes of the Java virtual machine that perform logical and arithmetic operations

By Bill Venners, JavaWorld.com, 11/11/96

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Welcome to yet another installment of Under The Hood. This column aims to give Java developers a glimpse of the mysterious mechanisms clicking and whirring beneath their running Java programs. This month's article continues the discussion of the bytecode instruction set of the Java virtual machine (JVM). The article takes a look at integer arithmetic and logic in the JVM, and covers the bytecodes that perform logical and arithmetic operations on integers. Subsequent articles will discuss other members of the bytecode family.



Integer arithmetic

The Java virtual machine offers bytecodes that perform integer arithmetic operations on ints and longs. Values of type byte, short, and char are converted to int before they take part in arithmetic operations. For each bytecode that performs arithmetic on ints, there is a corresponding bytecode that performs the same operation on longs.



All integer types supported by the JVM -- bytes, shorts, ints, and longs -- are signed two's-complement numbers. The two's-complement scheme allows both positive and negative integers to be represented. The most significant bit of a two's-complement number is its sign bit. The sign bit is one for negative numbers and zero for positive numbers and for the number zero.



The number of unique values that can be represented by the two's-complement scheme is two raised to the power of the total number of bits. For example, the short type in Java is a 16-bit signed two's-complement integer. The number of unique integers that can be represented by this scheme is 216, or 65,536. Half of the short type's range of values are used to represent zero and positive numbers; the other half of the short type's range are used to represent negative numbers. The range of negative values for a 16-bit two's-complement number is -32,768 (0x8000) to -1 (0xffff). Zero is 0x0000. The range of positive values is one (0x0001) to 32,767 (0x7fff).

Positive numbers are intuitive in that they are merely the base two representation of the number. Negative numbers can be calculated by adding the negative number to two raised to the power of the total number of bits. For example, the total number of bits in a short is 16, so the two's-complement representation of a negative number in the valid range for a short (-32,768 to -1) can be calculated by adding the negative number to 216, or 65,536. The two's-complement representation for -1 is 65,536 + (-1) or 65,535 (0xffff). The two's-complement representation for -2 is 65,536 + (-2) or 65,534 (0xfffe).



Addition is performed on two's-complement signed numbers in the same way it would be performed on unsigned binary numbers. The two numbers are added, overflow is ignored, and the result is interpreted as a signed two's-complement number. This will work as long as the result is actually within the range of valid values for the type. For example, to add 4 + (-2), just add 0x0004 and 0xfffe. The result is actually 0x10002, but because there are only 16 bits in a short, the overflow is ignored and the result becomes 0x0002.

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Resources
  • Previous Under The Hood articles:
  • The lean, mean virtual machine -- Gives an introduction to the Java virtual machine. Look here to see how the garbage collected heap fits in with the other parts of the JVM.
  • The Java class file lifestyle -- Gives an overview to the Java class file, the file format into which all Java programs are compiled.
  • Java's garbage-collected heap -- Gives an overview of garbage collection in general and the garbage-collected heap of the Java virtual machine in particular.
  • Bytecode basics -- Introduces the bytecodes of the JVM, and discusses primitive types, conversion operations, and stack operations in particular.
  • Floating point arithmetic -- Discusses the Java virtual machine's floating point support and the bytecodes that perform floating point arithmetic.