User's Manual

OVERVIEW OF NUMERIC PROCESSING
(3) Severe underflows in storing to short or long real may generate zeros.
(4) Small values ( Ixl < 1) stored into integers may round to zero.
(5) Sign is determined by round mode:
* = + for nearest, up, or chop
* = - for down
(6) t = sign of X.
(7) Very small values of X and Y may yield zeros, after rounding of true result. NPX signals underflow to
warn that zero has been yielded by nonzero operands.
(8) Very small X and very large Y may yield zero, after rounding of true result. NPX signals underflow to
warn that zero has been
yielded from nonzero operands.
(9) When Y divides into X exactly.
NaNs could also be used to speed up debugging. In its early testing phase, a program often contains
multiple errors. An exception handler could be written to save diagnostic information in memory
whenever it
was invoked. After storing the diagnostic data, it could supply a NaN as the result of the
erroneous instruction, and that
NaN could point to its associated diagnostic area in memory. The
program would then continue, creating a different
NaN for each error. When the program ended, the
NaN results could be used to access the diagnostic data saved at the time the errors occurred. Many
errors could thus be diagnosed and corrected in one test run.
Table 1-11. Masked Overflow Response with Directed Rounding
True Result
Rounding
Normalization
Sign
Mode
Normal
+
Up
Normal
+
Down
Normal
-
Up
Normal
-
Down
Unnormal
+
Up
Unnormal
-
Down
Unnormal
+
Up
Un normal
-
Down
NOTES:
I') The largest valid representable reals are encoded:
exponent: 11...108
significand:
(1 ),:l11 ... 1 08
Result Delivered
+co
Largest finite positive number
l
')
Largest finite negative number
l
')
-co
+co
Largest exponent, result's significand
(2
)
Largest exponent, result's significand
(2
)
-co
(2) The significand retains its identity as an un normal; the true result is rounded as usual (effectively chopped
toward
0 in this case). The exponent is encoded 11 ... 108.
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