
RCPU
REFERENCE MANUAL
OPERAND CONVENTIONS
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MOTOROLA
3-21
Figure 3-22
shows a graphical representation of Z, Z1, and Z2.
Figure 3-22 Relation of Z1 and Z2
Rounding follows the four following rules:
Round to nearest — Choose the best approximation (Z1 or Z2). In case of a
tie, choose the one which is even (i.e., with least significant bit equal to zero).
Refer to
3.4.1 Execution Model for IEEE Operations
for details on how the
processor selects the best approximation.
Round toward zero — Choose the smaller in magnitude (Z1 or Z2).
Round toward +infinity — Choose Z1.
Round toward –infinity — Choose Z2.
If Z is to be rounded up and Z1 does not exist (that is, if there is no number larger
than Z that is representable in the target format), then an overflow exception occurs
if Z is positive and an underflow exception occurs if Z is negative. Similarly, if Z is
to be rounded down and Z2 does not exist, then an overflow exception occurs if Z
is negative and an underflow exception occurs if Z is positive. The results in these
cases are defined in
6.11.10 Floating-Point Assist Exception (0x00E00)
.
3.4 Floating-Point Execution Models
The following paragraphs describe the floating-point execution models for IEEE
operations, as well as that for a special multiply-add type of instruction. In addition,
the execution model for non-IEEE compliant operation, used to accelerate time-
critical operations, is described.
The IEEE-754 standard includes 32-bit and 64-bit arithmetic. The standard re-
quires that single-precision arithmetic be provided for single-precision operands.
The standard permits double-precision arithmetic instructions to have either (or
both) single-precision or double-precision operands, but states that single-preci-
sion arithmetic instructions should not accept double-precision operands.
The PowerPC architecture follows these guidelines:
Double-precision arithmetic instructions can have operands of either or both
precisions.
By incrementing LSB of Z
Infinitely precise value
By truncating after LSB
Z2
Z1
0
Z2
Z1
Z
Z
Negative values
Positive values
Z1/Z2
F
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n
.