Floating-point unit

A floating-point unit (FPU), numeric processing unit (NPU), colloquially math coprocessor, is a part of a computer system specially designed to carry out operations on floating-point numbers. Typical operations are addition, subtraction, multiplication, division, and square root. Modern designs generally include a fused multiply-add instruction, which was found to be very common in real-world code. Some FPUs can also perform various transcendental functions such as exponential or trigonometric calculations, but the accuracy can be low, so some systems prefer to compute these functions in software.

Floating-point operations were originally handled in software in early computers. Over time, manufacturers began to provide standardized floating-point libraries as part of their software collections. Some machines, those dedicated to scientific processing, would include specialized hardware to perform some of these tasks with much greater speed. The introduction of microcode in the 1960s allowed these instructions to be included in the system's instruction set architecture (ISA). Normally these would be decoded by the microcode into a series of instructions that were similar to the libraries, but on those machines with an FPU, they would instead be routed to that unit, which would perform them much faster. This allowed floating-point instructions to become universal while the floating-point hardware remained optional; for instance, on the PDP-11 one could add the floating-point processor unit at any time using plug-in expansion cards.

The introduction of the microprocessor in the 1970s led to a similar evolution as the earlier mainframes and minicomputers. Early microcomputer systems performed floating point in software, typically in a vendor-specific library included in ROM. Dedicated single-chip FPUs began to appear late in the decade, but they remained rare in real-world systems until the mid-1980s, and using them required software to be re-written to call them. As they became more common, the software libraries were modified to work like the microcode of earlier machines, performing the instructions on the main CPU if needed, but offloading them to the FPU if one was present. By the late 1980s, semiconductor manufacturing had improved to the point where it became possible to include an FPU with the main CPU, resulting in designs like the i486 and 68040. These designs were known as an "integrated FPU"s, and from the mid-1990s, FPUs were a standard feature of most CPU designs except those designed as low-cost as embedded processors.

In modern designs, a single CPU will typically include several arithmetic logic units (ALUs) and several FPUs, reading many instructions at the same time and routing them to the various units for parallel execution. By the 2000s, even embedded processors generally included an FPU as well.

In 1954, the IBM 704 had floating-point arithmetic as a standard feature, one of its major improvements over its predecessor the IBM 701. This was carried forward to its successors the 709, 7090, and 7094.

In 1963, Digital announced the PDP-6, which had floating point as a standard feature.

In 1963, the GE-235 featured an "Auxiliary Arithmetic Unit" for floating point and double-precision calculations.

Historically, some systems implemented floating point with a coprocessor rather than as an integrated unit (but now in addition to the CPU, e.g. GPUs – that are coprocessors not always built into the CPU – have FPUs as a rule, while first generations of GPUs did not). This could be a single integrated circuit, an entire circuit board or a cabinet. Where floating-point calculation hardware has not been provided, floating-point calculations are done in software, which takes more processor time, but avoids the cost of the extra hardware. For a particular computer architecture, the floating-point unit instructions may be emulated by a library of software functions; this may permit the same object code to run on systems with or without floating-point hardware. Emulation can be implemented on any of several levels: in the CPU as microcode, as an operating system function, or in user-space code. When only integer functionality is available, the CORDIC methods are most commonly used for transcendental function evaluation.^{[citation needed]}