SAS/C Compiler Changes in Release 7.50

Floating-Point Changes for SAS/C Release 7.50

The SAS/C compiler and library's floating-point support has been extensively changed and improved for Release 7.50. The changes are concentrated in three distinct, but overlapping areas:

In recent years, the 390 Architecture has been augmented by the addition of support for IEEE standard floating-point. Programs can now be written in SAS/C to exploit this support. Traditional mainframe floating-point continues to be supported. See IEEE Floating-Point Support for more information.
The same architectural extensions that introduced IEEE floating-point support also introduced enhancements that can significantly improve the performance of traditional floating-point applications. For instance, the number of floating-point registers has increased. SAS/C now provides a compiler option to generate code targeting the extended floating-point architecture. See SAS/C IEEE Support and SAS/C and Mainframe Floating-Point Extensions for more information.
The ANSI/ISO C99 standard mandates a great deal of floating-point support beyond that required by the 1989 C Standard, including new math functions and new pragmas. SAS/C now supports many of these C99 features, for both IEEE and traditional mainframe floating-point. See SAS/C C99 Support for more information.

IEEE Floating-Point Support

The ISO standards document IEC 60559 defines a portable standard for floating-point computation known informally as IEEE floating-point. This standard is implemented by almost all computer systems presently in use. Until recently, the major exception to this statement was the IBM mainframe, which offered a different floating-point implementation defined by IBM in the 1960's. In the last decade, IBM has remedied this situation by offering an implementation of IEEE floating-point parallel to traditional IBM floating-point. Depending on their requirements, mainframe programs can choose to use traditional IBM floating-point, the more portable IEEE floating-point, or, for very advanced applications, both floating-point implementations.

There are advantages and limitations to the use of IEEE floating-point by applications, and the choice between traditional mainframe floating-point and IEEE floating-point is not always obvious.

Advantages of IEEE Floating-Point

The following list contains a few of the reasons that you might prefer to use IEEE floating-point:

IEEE floating-point is far more portable. If an application needs to produce exactly the same answers for the same inputs on all platforms, it should use IEEE floating-point.
A number of the IEEE features make it more flexible for dealing with errors and inaccuracies than IBM traditional floating-point. Examples of such features include not-a-numbers (NaNs), infinities, rounding modes, and the use of status flags rather than trapping for error handling.
IEEE double precision enables a wider range of exponents than traditional mainframe floating-point. The range of positive IEEE double precision values is approximately from 5E-324 to 2E308. The corresponding range for traditional mainframe floating-point is about 5E-79 to 7E75.
IEEE floating-point is more uniform in its handling of inaccuracy because it uses base 2 instead of base 16.

Advantages of the Traditional Mainframe Floating-Point

The following list contains a few of the reasons that you might prefer to use traditional mainframe floating-point:

On present mainframe models, the traditional floating-point hardware runs significantly faster than the IEEE hardware to perform the same computation. This could change in future hardware.
For a single double-precision computation, traditional mainframe floating-point is never less accurate than the corresponding IEEE computation (assuming the result is within the range of both), and can be up to 3 bits more accurate. It is not possible to generalize this statement to more complex calculations due to the effects of accumulated rounding.
Traditional floating-point uses a simpler conceptual model than does IEEE floating-point. This can make analysis of the characteristics of a particular algorithm more manageable.

IBM's traditional floating-point format uses a base-16 representation, that is, the exponent represents a power of sixteen. IEEE floating-point uses a binary representation, with the exponent representing a power of two. For this reason, IBM calls its traditional floating-point format HFP (hexadecimal floating-point), and its IEEE format BFP (binary floating point). HFP and BFP are used as synonyms for traditional mainframe floating-point and IEEE floating-point in the rest of this document.

SAS/C IEEE Support

When you compile a SAS/C program, you can specify the BFP or NOBFP option to specify whether the default floating-point format is BFP or HFP. HFP is the default.

SAS/C enables programs to use both floating-point formats. This is a useful option for programs such as debuggers, and for subroutine libraries whose users want a choice of format. To support the use of both formats, SAS/C provides the _ _binfmt and _ _hexfmt type modifiers, which can be used to specify the floating-point format independently of whether the BFP option is used. Similarly, H and B suffixes can be used with floating-point constants to indicate the format.

Using Both IBM and IEEE Floating-Point Formats contains detailed rules on mixing the two formats, but the basic premise you should keep in mind is: You can use casts to convert between the two formats, but mixed-mode expressions are, in general, not supported. In other words, if you try to add a _ _binfmt double to a _ _hexfmt double, the compiler cannot determine which kind of addition operation it should perform. You therefore have to code a cast of one operand to the format of the other.

The SAS/C library of mathematical functions is completely supported for both traditional and IEEE floating-point. However, some functions (such as isinf, which tests to see if its argument is an infinite number) are not meaningful for hexadecimal floating point, and return dummy results of little utility.

SAS/C has added format modifiers to the printf and scanf series of functions to enable either format of floating-point number to be read or written. If a format specifier does not have a floating-point type, the corresponding argument is assumed to have the default floating-point format. Use of the extensions is not required for programs which use only one kind of floating-point.

SAS/C and Mainframe Floating-Point Extensions

The most recent generations of IBM mainframes have included extensions to the floating-point hardware which enable improved performance for traditional floating-point as well as for IEEE support. The SAS/C compiler option ARCHLEVEL(C) can be specified to cause the compiler to generate code that targets the newer floating-point hardware. If you specify the BFP option, ARCHLEVEL(C) is the default ARCHLEVEL setting.

The two main advantages of ARCHLEVEL(C) for traditional floating-point code are:

With the floating-point extensions, processors support sixteen floating-point registers rather than four. This feature enables much more data to be kept in registers. The global optimizer with ARCHLEVEL(C) will assign up to eight double or float register variables. Without ARCHLEVEL(C), only two register variables are supported.
The floating-point extensions offer single instructions to convert between integer types and floating-point types. Without the floating-point extensions, the compiler would have to generate a much longer and more complex sequence of instructions.

SAS/C C99 Support

SAS/C Release 7.50 supports many elements of the ISO C99 standard relating to floating-point. Some of these elements are oriented specifically to IEEE floating-point, but most apply to both formats.

The most significant SAS/C enhancements in support of C99 are:

Support for a new hexadecimal exponential format for floating-point constants.
Support for several C99 standard pragmas to enable a program to control the extent of the optimization of floating-point operations.
Augmentation of the header file, float.h, with further information about the floating-point implementation.
Support in the printf and scanf functions for a new %a format for hexadecimal input and output of floating-point data.
Addition of a new header file, fenv.h, that defines functions which enable you to test IEEE status flags, specify the rounding mode, raise IEEE exceptions, and so forth. There are dummy implementations of these functions for traditional mainframe floating point. Also, the header file fenvtrap.h (which is a SAS/C extension) defines functions which let you control IEEE exception trapping.
Addition of a number of new math functions defined by C99. Some of these are low-level IEEE functions, such as isinf (to test whether a number is infinite) and nextafter (which returns the next floating-point number in a particular direction from its argument). Others are more traditional mathematical operations like remainder and log2 (logarithm base 2). All of these functions are supported for BFP and HFP inputs. Functions specific to IEEE such as isinf will return degenerate results when called for _ _hexfmt arguments. See SAS/C Library Reference, Volume 1 for a full list of the supported math functions.
Adding versions of mathematical functions using the data type float. The C99 standard defines a set of math functions similar to the traditional set, with float arguments and return values. For example, C99 requires the exp function to have a float version named expf. While most functions, such as exp, have a differently named variant function for use with float, a few functions (for instance, the signbit function) are defined as macros that can be passed as an argument of any floating-point type.
Addition of a new header file, tgmath.h, that is defined by the C99 standard to provide generic versions of math functions. For instance, tgmath.h defines an exp macro which can accept any numeric argument, and returns a result of the correct type.

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