The INTEL ® 8087 numeric data

The INTEL® 8087 is a high performance general purpose numeric data processor. It is used with the INTEL® 8086, or the INTEL® 8088, microprocessors to extend their instruction sets with over 100 instructions (not counting addressing mode). The 8087 has all of the 8086 addressing modes and through a coprocessing interface is able to execute numeric instructions concurrently with the 8086 (or 8088). The high performance overlapped execution is transparent to the user who sees the 8087 simply as an extension of the 8086 (8088). Furthermore, the 8087 is the only chip that must be added to an 8086-based system to provide numerics capability with a performance enhancement over software of more than 100. In addition to high performance, great care was taken to ensure that the 8087 could be used in any application involving numbers-including commercial calculations. This required an unprecedented level of accuracy and reliability to be built into the processor. The intent was to greatly simplify the production of high performance but reliable numeric software. Mathematical software is easy for the uninitiated to write but notoriously hard for the expert. This paradox exists because the beginner is satisfied if his code usually works in his own machine while the expert attempts, against overwhelming obstacles, to produce programs that always work on a large number of computers. The problem is that while standard formulas of mathematics are fairly easy to translate into FORTRAN they often are subject to instabilities due to roundoff error. Consider, for example, the quadratic equation