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(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.)
Variable length arithmetic represents numbers as a string of digits of a variable's length limited only by the memory available. Variable-length arithmetic operations are considerably slower than fixed-length format floating-point instructions.
Round-to-nearest: () is set to the nearest floating-point number to . When there is a tie, the floating-point number whose last stored digit is even (also, the last digit, in binary form, is equal to 0) is used.
Exception handling in the IEEE 754 floating-point standard refers in general to exceptional conditions and defines an exception as "an event that occurs when an operation on some particular operands has no outcome suitable for every reasonable application. That operation might signal one or more exceptions by invoking the default or, if ...
The IEEE Standard for Floating-Point Arithmetic (IEEE 754) is a technical standard for floating-point arithmetic originally established in 1985 by the Institute of Electrical and Electronics Engineers (IEEE). The standard addressed many problems found in the diverse floating-point implementations that made them difficult to use reliably and ...
Some operations of floating-point arithmetic are invalid, such as taking the square root of a negative number. The act of reaching an invalid result is called a floating-point exception. An exceptional result is represented by a special code called a NaN, for "Not a Number". All NaNs in IEEE 754-1985 have this format: sign = either 0 or 1.
Floating-point operations other than ordered comparisons normally propagate a quiet NaN (qNaN). Most floating-point operations on a signaling NaN (sNaN) signal the invalid-operation exception; the default exception action is then the same as for qNaN operands and they produce a qNaN if producing a floating-point result.
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).