A floating-point unit (FPU, colloquially a 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. Some FPUs can also perform various transcendental functions such as exponential or trigonometric calculations, but the accuracy can be very low, so that some systems prefer to compute these functions in software. In general-purpose computer architectures, one or more FPUs may be integrated as execution units within the central processing unit; however, many embedded processors do not have hardware support for floating-point operations (while they increasingly have them as standard, at least 32-bit ones). When a CPU is executing a program that calls for a floating-point operation, there are three ways to carry it out: A floating-point unit emulator (a floating-point library) Add-on FPU Integrated FPU History 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 didn't). 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 (not a common practice), as an operating system function, or in user-space code. When only integer functionality is available, the CORDIC floating-point emulation methods are most commonly used. In most modern computer architectures, there is some division of floating-point operations from integer operations. This division varies significantly by architecture; some have dedicated floating-point registers, while some, like Intel x86, take it as