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Although Java's floating-point arithmetic is largely based on IEEE 754 (Standard for Binary Floating-Point Arithmetic), certain features are unsupported even when using the strictfp modifier, such as Exception Flags and Directed Roundings, abilities mandated by IEEE Standard 754 (see Criticism of Java, Floating point arithmetic).
For example in Java, such operations throw instances of java.lang.ArithmeticException. [25] In C , they lead to undefined behavior , but if annex F is supported, the operation yields an "invalid" floating-point exception (as required by the IEEE standard) and an unspecified value.
(The term "exception" as used in IEEE 754 is a general term meaning an exceptional condition, which is not necessarily an error, and is a different usage to that typically defined in programming languages such as a C++ or Java, in which an "exception" is an alternative flow of control, closer to what is termed a "trap" in IEEE 754 terminology.)
For example, an addition may produce an arithmetic overflow (it does not fulfill its contract of computing a good approximation to the mathematical sum); or a routine may fail to meet its postcondition. Exception: an abnormal event occurring during the execution of a routine (that routine is the "recipient" of
The register width of a processor determines the range of values that can be represented in its registers. Though the vast majority of computers can perform multiple-precision arithmetic on operands in memory, allowing numbers to be arbitrarily long and overflow to be avoided, the register width limits the sizes of numbers that can be operated on (e.g., added or subtracted) using a single ...
The first hardware exception handling was found in the UNIVAC I from 1951. Arithmetic overflow executed two instructions at address 0 which could transfer control or fix up the result. [16] Software exception handling developed in the 1960s and 1970s. Exception handling was subsequently widely adopted by many programming languages from the ...
Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions. When high performance is not a requirement, but high precision is, variable length arithmetic can prove useful, though the actual accuracy of the result may not be known.
Where necessary, the exception can be caught and recovered from—for instance, the operation could be restarted in software using arbitrary-precision arithmetic. In many cases, the task or the programmer can guarantee that the integer values in a specific application will not grow large enough to cause an overflow.