Intel 80286, 80287 manual Appendix C Implementing the Ieee P754 Standard

APPENDIX C

IMPLEMENTING THE IEEE P754 STANDARD

The 80287 NPX and standard support library software, provides an implementation of the IEEE "A Proposed Standard for Binary Floating-Point Arithmetic," Draft 10.0, Task P754, of December 2, 1982. The 80287 Support Library, described in 80287 Support Library Reference Manual, Order Number 122129, is an example of such a support library.

This appendix describes the relationship between the 80287 NPX and the IEEE Standard. Where the Standard has options, Intel's choices in implementing the 80287 are described. Where portions of the Standard are implemented through software, this appendix indicates which modules of the 80287 Support Library implement the Standard. Where special software in addition to the Support Library may be required by your application, this appendix indicates how to write this software.

This appendix contains many terms with precise technical meanings, specified in the 754 Standard. Where these terms are used, they have been capitalized to emphasize the precision of their meanings. The Glossary provides the definitions for all capitalized phrases in this appendix.

OPTIONS IMPLEMENTED IN THE 80287

The 80287 SHORT_REAL and LONG_REAL formats conform precisely to the Standard's Single and Double Floating-Point Numbers, respectively. The 80287 TEMP_REAL format is the same as the Standard's Double Extended format. The Standard allQws a choice of Bias in representing the exponent;

the 80287 uses the Bias 16383 decimal. .

For the Double Extended format, the Standard contains an option for the meaning of the minimum exponent combined with a nonzero significand. The Bias for this special case can be either 16383, as in all the other cases, or 16382, making the smallest exponent equivalent to the second-smallest exponent. The 80287 uses the Bias 16382 for this case. This allows the 80287 to distinguish between Denormal numbers (integer part is zero, fraction is nonzero, Biased exponent is 0) and Unnormal numbers of the Same value (same as the denormal except the Biased Exponent is 1).

The Standard allows flexibility in specifying which NaNs are trapping and which are nontrapping. The EH287.LIB module of the 80287 Support Library provides a software implementation of nontrapping NaNs, and defines one distinction between trapping and nontrapping NaNs: If the most significant bit of the fractional part of a NaN is 1, the NaN is nontrapping. If it is 0, the NaN is trapping.

When a masked Invalid Operation error involves two NaN inputs, the Standard allows flexibility in choosing which NaN is output. The 80287 selects the NaN whose absolute value is greatest.

AREAS OF THE STANDARD IMPLEMENTED IN SOFTWARE

There are five areas of the Standard that are not implemented directly in the 80287 hardware; these areas are instead implemented in software as part of the 80287 Support Library.

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