Intel 80287, 80286 manual Additional Software to Meet the Standard

IMPLEMENTING THE IEEE P754 STANDARD

1.The Standard requires that a Normalizing Mode be provided, in which any nonnormal operands to functions are automatically normalized before the function is performed. The NPX provides a "Denormal operand" exception for this case, allowing the exception handler the opportunity to perform the normalization specified by the Standard. The Denormal operand exception handler provided by EH287.LIB implements the Standard's Normalizing Mode completely for Single- and Double-precision arguments. Normalizing mode for Double Extended operands is implemented in EH287.LIB with one non-Standard feature, discussed in the next section.

2.The Standard specifies that in comparing two operands whose relationship is "unordered," the equality test yield an answer of FALSE, with no errors or exceptions. The 80287 FCOM and FTST instructions themselves issue an Invalid Operation exception in this case. The error handler EH287.LIB filters out this Invalid Operation error using the following convention: Whenever an FCOM or FTST instruction is followed by a MOV AX,AX instruction (8BCO Hex), and neither argument is a trapping NaN, the error handler will assume that a Standard equality comparison was intended, and return the correct answer with the Invalid Operation exception flag erased. Note that the Invalid Operation exception must be unmasked for this action to occur.

3.The Standard requires that two kinds of NaN's be provided: trapping and nontrapping. Nontrap- ping NaNs will not cause further Invalid Operation errors when they occur as operands to calcu- lations. The NPX hardware directly supports only trapping NaN's; the EH287.LIB software implements nontrapping NaNs by returning the correct answer with the Invalid Operation excep- tion flag erased. Note that the Invalid Operation exception must be unmasked for this action to occur.

4.The Standard requires that all functions that convert real numbers to integer formats automati- cally normalize the inputs if necessary. The integer conversion functions contained in CEL287.LIB fully meet the Standard in this respect; the 80287 FIST instruction alone does not perform this normalization.

5.The Standard specifies the remainder function which is provided by mqerRMD in CEL287.LIB. The 80287 FPREM instruction returns answers within a different range.

ADDITIONAL SOFTWARE TO MEET THE STANDARD

There are two cases in which additional software is required in conjunction with the 80287 Support Library in order to meet the standard. The 80287 Support Library does not provide this software in the interest of saving space and because the vast majority of applications will never encounter these cases.

1.When the Invalid Operation exception is masked, Nontrapping NaNs are not implemented fully. Likewise, the Standard's equality test for "unordered" operands is not implemented when the Invalid Operation exception is masked. Programmers can simulate the Standard notion of a masked Invalid Operation exception by unmasking the 80287 Invalid Operation exception, and providing an Invalid Operation exception handler that supports nontrapping NaNs and the equality test, but otherwise acts just as ii {he invaiid Opt::raiiull cA0~pi.l0iJ. Vv-~lC li-..a:;kcd.Th~ 802B7 S:;.ppc~t L!,br~!"y

Reference Manual contains examples for programming this handler in both ASM286 and PL/M-286.

2.In Normalizing Mode, Denormal operands in the TEMP_REAL format are converted to 0 by EH287.LIB, giving sharp Underflow to O. The Standard specifies that the operation be performed on the real numbers represented by the denormals, giving gradual underflow. To correctly perform such arithmetic while in Normalizing Mode, programmers would have to normalize the operands into a format identical to TEMP_REAL except for two extra exponent bits, then perform the operation on those numbers. Thus, software must be written to handle the 17-bit exponent explicitly.

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