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7.4 Embedded Floating-Point Results Summary
The following tables summarize the results of various
types of Embedded Floating-Point operations on various
combinations of input operands. Flag settings are
performed on appropriate element flags. For all the
tables the following annotation and general rules apply:
* denotes that this status flag is set based on the
results of the calculation.
_Calc_ denotes that the result is updated with the
results of the computation.
max denotes the maximum normalized number
with the sign set to the computation [sign(operand
A) XOR sign(operand B)].
amax denotes the maximum normalized number
with the sign set to the sign of Operand A.
bmax denotes the maximum normalized number
with the sign set to the sign of Operand B.
pmax denotes the maximum normalized positive
number. The encoding for single-precision is:
0x7F7FFFFF. The encoding for double-precision
is: 0x7FEFFFFF_FFFFFFFF.
nmax denotes the maximum normalized negative
number. The encoding for single-precision is:
0xFF7FFFFF. The encoding for double-precision
is: 0xFFEFFFFF_FFFFFFFF.
pmin denotes the minimum normalized positive
number. The encoding for single-precision is:
0x00800000. The encoding for double-precision is:
0x00100000_00000000.
nmin denotes the minimum normalized negative
number. The encoding for single-precision is:
0x80800000. The encoding for double-precision is:
0x80100000_00000000.
Calculations that overflow or underflow saturate.
Overflow for operations that have a floating-point
result force the result to max. Underflow for operations
that have a floating-point result force the
result to zero. Overflow for operations that have a
signed integer result force the result to
0x7FFFFFFF (positive) or 0x80000000 (negative).
Overflow for operations that have an unsigned
integer result force the result to 0xFFFFFFFF (positive)
or 0x00000000 (negative).
1 (superscript) denotes that the sign of the result is
positive when the sign of Operand A and the sign
of Operand B are different, for all rounding modes
except round to minus infinity, where the sign of
the result is then negative.
2 (superscript) denotes that the sign of the result is
positive when the sign of Operand A and the sign
of Operand B are the same, for all rounding modes
except round to minus infinity, where the sign of
the result is then negative.
3 (superscript) denotes that the sign for any multiply
or divide is always the result of the operation
[sign(Operand A) XOR sign(Operand B)].
4 (superscript) denotes that if an overflow is
detected, the result may be saturated.
Table 3: Embedded Floating-Point Results Summary—Add, Sub, Mul, Div
Operation Operand A Operand B Result FINV FOVF FUNF FDBZ FINX
Add
Add ∞ ∞ amax 1 0 0 0 0
Add ∞ NaN amax 1 0 0 0 0
Add ∞ denorm amax 1 0 0 0 0
Add ∞ zero amax 1 0 0 0 0
Add ∞ Norm amax 1 0 0 0 0
Add NaN ∞ amax 1 0 0 0 0
Add NaN NaN amax 1 0 0 0 0
Add NaN denorm amax 1 0 0 0 0
Add NaN zero amax 1 0 0 0 0
Add NaN norm amax 1 0 0 0 0
Add denorm ∞ bmax 1 0 0 0 0
Add denorm NaN bmax 1 0 0 0 0
Add denorm denorm zero 1 1 0 0 0 0
Add denorm zero zero 1 1 0 0 0 0
Add denorm norm operand_b 4 1 0 0 0 0
Add zero ∞ bmax 1 0 0 0 0
Add zero NaN bmax 1 0 0 0 0
Add zero denorm zero 1 1 0 0 0 0
Chapter 7. Embedded Floating-Point
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