User's Manual

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.
C-2