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A floating-point unit (FPU), numeric processing unit (NPU), [1] colloquially math coprocessor, is a part of a computer system specially designed to carry out operations on floating-point numbers. [2] Typical operations are addition , subtraction , multiplication , division , and square root .
Conversely to floating-point arithmetic, in a logarithmic number system multiplication, division and exponentiation are simple to implement, but addition and subtraction are complex. The ( symmetric ) level-index arithmetic (LI and SLI) of Charles Clenshaw, Frank Olver and Peter Turner is a scheme based on a generalized logarithm representation.
A floating-point number system is normalized if the leading digit is always nonzero unless the number is zero. [3] Since the significand is d 0 . d 1 d 2 … d p − 1 {\displaystyle d_{0}.d_{1}d_{2}\ldots d_{p-1}} , the significand of a nonzero number in a normalized system satisfies 1 ≤ significand < β p {\displaystyle 1\leq {\text ...
For example, floating-point addition is not associative since the rounding errors introduced can depend on the order of the additions. This means that the result of (+) + is sometimes different from the result of + (+). [121] The most common technical standard used for floating-point arithmetic is called IEEE 754.
An LNS can be considered as a floating-point number with the significand being always equal to 1 and a non-integer exponent. This formulation simplifies the operations of multiplication, division, powers and roots, since they are reduced down to addition, subtraction, multiplication, and division, respectively.
x87 is a floating-point-related subset of the x86 architecture instruction set. It originated as an extension of the 8086 instruction set in the form of optional floating-point coprocessors that work in tandem with corresponding x86 CPUs. These microchips have names ending in "87".