ARCHIVED: What are math coprocessors?

The following information comes from the Usenet:

  Article 18096 of comp.sys.ibm.pc.hardware:
  Xref: usenet.ucs.indiana.edu comp.sys.intel:1907
  comp.sys.ibm.pc.hardware:18096
  Path:
  usenet.ucs.indiana.edu!sol.ctr.columbia.edu!ira.uka.de!uka!uka!news
  From: S_JUFFA@IRAV1.ira.uka.de (|S| Norbert Juffa)
  Newsgroups: comp.sys.intel,comp.sys.ibm.pc.hardware
  Date: 13 Jan 1993 19:31:19 GMT
  Organization: University of Karlsruhe, FRG

A math coprocessor in the traditional sense is a chip or part of a chip that specializes in doing math, extending the capabilities of a CPU in a transparent manner. It is a piece of hardware that attaches to the motherboard or is part of the CPU.

The 80x87 family of math coprocessors (also known as MCPs [Math CoProcessors], NDPs [Numerical Data Processors], NPXs [Numerical Processor eXtensions], or FPUs [Floating-Point Units], or "math chips") are typical examples of such coprocessors. The 80x86 CPUs, with the exception of the 80486 (which has a built-in FPU) can only handle 8, 16, or 32 bit integers as their basic data types. However, many PC-based applications require the use of not only integers, but floating-point numbers. The use of floating-point numbers enables a binary representation of not only integers, but also fractional values over a wide range. A common application of floating-point numbers is in scientific applications, where very small (e.g., Planck's constant) and very large numbers (e.g., speed of light) must be accurately expressed. But floating-point numbers are also useful for business applications such as computing interest, and in the geometric calculations inherent in CAD/CAM processing.

Because the instruction sets of all 80x86 CPUs directly support only integers and calculations upon integers, floating-point numbers and operations on them must be programmed indirectly by using series of CPU integer instructions. This means that computations when floating-point numbers are used are far slower than normal, integer calculations. And this is where the 80x87 coprocessors come in: adding an 80x87 to an 80x86-based system augments the CPU architecture with eight floating-point registers, five additional data types and over 70 additional instructions, all designed to deal directly with floating-point numbers as a basic data type. This removes the 'penalty' for floating-point computations, and greatly increases overall system performance for applications which depend heavily on these calculations.

In addition to being able to quickly execute load/store operations on floating-point numbers, the 80x87 coprocessors can directly perform all the basic arithmetic operations on them. Besides "knowing" how to add, subtract, multiply and divide floating-point numbers, they can also operate on them to perform comparisons, square roots, transcendental functions (such as logarithms and sine/cosine/tangent), and compute their absolute value and remainder.

Floating-point arithmetic has been standardized. The relevant standard is the "IEEE-754 Standard for Binary Floating-Point Arithmetic" [10,11]. The standard specifies numeric formats, value sets and how the basic arithmetic (+,-,*,/,sqrt, remainder) has to work.