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2.8. Floating-Point Arithmetic

The Java Virtual Machine incorporates a subset of the floating-point arithmetic specified in IEEE Standard for Binary Floating-Point Arithmetic (ANSI/IEEE Std.754-1985, New York).

2.8.1. Java Virtual Machine Floating-Point Arithmetic and IEEE 754

The key differences between the floating-point arithmetic supported by the Java Virtual Machine and the IEEE 754 standard are:

  • The floating-point operations of the Java Virtual Machine do not throw exceptions, trap, or otherwise signal the IEEE 754 exceptional conditions of invalid operation, division by zero, overflow, underflow, or inexact. The Java Virtual Machine has no signaling NaN value.
  • The Java Virtual Machine does not support IEEE 754 signaling floating-point comparisons.
  • The rounding operations of the Java Virtual Machine always use IEEE 754 round to nearest mode. Inexact results are rounded to the nearest representable value, with ties going to the value with a zero least-significant bit. This is the IEEE 754 default mode. But Java Virtual Machine instructions that convert values of floating-point types to values of integral types round toward zero. The Java Virtual Machine does not give any means to change the floating-point rounding mode.
  • The Java Virtual Machine does not support either the IEEE 754 single extended or double extended format, except insofar as the double and double-extended-exponent value sets may be said to support the single extended format. The float-extended-exponent and double-extended-exponent value sets, which may optionally be supported, do not correspond to the values of the IEEE 754 extended formats: the IEEE 754 extended formats require extended precision as well as extended exponent range.

2.8.2. Floating-Point Modes

Every method has a floating-point mode, which is either FP-strict or not FP-strict. The floating-point mode of a method is determined by the setting of the ACC_STRICT flag of the access_flags item of the method_info structure (§4.6) defining the method. A method for which this flag is set is FP-strict; otherwise, the method is not FP-strict.

  • Note that this mapping of the ACC_STRICT flag implies that methods in classes compiled by a compiler in JDK release 1.1 or earlier are effectively not FP-strict.

We will refer to an operand stack as having a given floating-point mode when the method whose invocation created the frame containing the operand stack has that floating-point mode. Similarly, we will refer to a Java Virtual Machine instruction as having a given floating-point mode when the method containing that instruction has that floating-point mode.

If a float-extended-exponent value set is supported (§2.3.2), values of type float on an operand stack that is not FP-strict may range over that value set except where prohibited by value set conversion (§2.8.3). If a double-extended-exponent value set is supported (§2.3.2), values of type double on an operand stack that is not FP-strict may range over that value set except where prohibited by value set conversion.

In all other contexts, whether on the operand stack or elsewhere, and regardless of floating-point mode, floating-point values of type float and double may only range over the float value set and double value set, respectively. In particular, class and instance fields, array elements, local variables, and method parameters may only contain values drawn from the standard value sets.

2.8.3. Value Set Conversion

An implementation of the Java Virtual Machine that supports an extended floating-point value set is permitted or required, under specified circumstances, to map a value of the associated floating-point type between the extended and the standard value sets. Such a value set conversion is not a type conversion, but a mapping between the value sets associated with the same type.

Where value set conversion is indicated, an implementation is permitted to perform one of the following operations on a value:

  • If the value is of type float and is not an element of the float value set, it maps the value to the nearest element of the float value set.
  • If the value is of type double and is not an element of the double value set, it maps the value to the nearest element of the double value set.

In addition, where value set conversion is indicated, certain operations are required:

  • Suppose execution of a Java Virtual Machine instruction that is not FP-strict causes a value of type float to be pushed onto an operand stack that is FP-strict, passed as a parameter, or stored into a local variable, a field, or an element of an array. If the value is not an element of the float value set, it maps the value to the nearest element of the float value set.
  • Suppose execution of a Java Virtual Machine instruction that is not FP-strict causes a value of type double to be pushed onto an operand stack that is FP-strict, passed as a parameter, or stored into a local variable, a field, or an element of an array. If the value is not an element of the double value set, it maps the value to the nearest element of the double value set.

Such required value set conversions may occur as a result of passing a parameter of a floating-point type during method invocation, including native method invocation; returning a value of a floating-point type from a method that is not FP-strict to a method that is FP-strict; or storing a value of a floating-point type into a local variable, a field, or an array in a method that is not FP-strict.

Not all values from an extended-exponent value set can be mapped exactly to a value in the corresponding standard value set. If a value being mapped is too large to be represented exactly (its exponent is greater than that permitted by the standard value set), it is converted to a (positive or negative) infinity of the corresponding type. If a value being mapped is too small to be represented exactly (its exponent is smaller than that permitted by the standard value set), it is rounded to the nearest of a representable denormalized value or zero of the same sign.

Value set conversion preserves infinities and NaNs and cannot change the sign of the value being converted. Value set conversion has no effect on a value that is not of a floating-point type.

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