Inside Macintosh: PowerPC Numerics / Part 1 - The PowerPC Numerics Environment

Chapter 1 - IEEE Standard Arithmetic

About the FPCE Technical Report

Even though many computers now conform to the IEEE standard, the standard has suffered from a lack of high-level portability. The reason is that the standard does not define bindings to high-level languages; it only defines a programming environment. For instance, the standard defines data formats that should be supported but does not tell how these data formats should map to variable types in high-level languages. It also specifies that the user must be able to control rounding direction but falls short of defining how the user is able to do so.

However, the definition of a binding is in progress for the C programming language. The Floating-Point C Extensions (FPCE) branch of the Numerical C Extensions Group (NCEG), or ANSI X3J11.1, has proposed a general floating-point specification for the C programming language, called the FPCE technical report, that contains additional specifications for implementations that comply with IEEE floating-point standards 754 and 854.

The FPCE technical report not only specifies how to implement the requirements of the IEEE standards, but also requires some additional functions, called transcendental functions (sometimes called elementary functions). These functions are consistent with
the IEEE standard and can be used as building blocks in numerical functions. The transcendental functions include the usual logarithmic and exponential functions, as well as $ln(1+x)$ and $ex+-1$ ; financial functions for compound interest and annuity calculations; trigonometric functions; error and gamma functions; and a random number generator. The PowerPC Numerics library, contained in the file MathLib, implements the transcendental functions.

Part 2 of this book describes how PowerPC Numerics complies with the recommendations in the FPCE technical report.