
RCPU
REFERENCE MANUAL
OPERAND CONVENTIONS
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MOTOROLA
3-17
When the sum of two operands with opposite sign, or the difference of two oper-
ands with the same sign, is exactly zero, the sign of the result is positive in all
rounding modes except round toward negative infinity (–×), in which case the sign
is negative.
The sign of the result of a multiplication or division operation is the exclusive
OR of the signs of the source operands.
The sign of the result of a round to single-precision or convert to/from integer
operation is the sign of the source operand.
For multiply-add instructions, these rules are applied first to the multiplication op-
eration and then to the addition or subtraction operation (one of the source oper-
ands to the addition or subtraction operation is the result of the multiplication
operation).
3.3.9 Normalization and Denormalization
When an arithmetic operation produces an intermediate result, consisting of a sign
bit, an exponent, and a non-zero significand with a zero leading bit, the result is not
a normalized number and must be normalized before it is stored.
A number is normalized by shifting its significand left while decrementing its expo-
nent by one for each bit shifted, until the leading significand bit becomes one. The
guard bit and the round bit participate in the shift
with zeros shifted into the round
bit; see
3.4.1 Execution Model for IEEE Operations
.
During normalization, the exponent is regarded as if its range were unlimited. If the
resulting exponent value is less than the minimum value that can be represented
in the format specified for the result, the intermediate result is said to be “tiny” and
the stored result is determined by the rules described in
6.11.10.9 Underflow Ex-
ception Condition
. The sign of the number does not change.
When an arithmetic operation produces a non-zero intermediate result whose ex-
ponent is less than the minimum value that can be represented in the format spec-
ified, the stored result may need to be denormalized. The result is determined by
the rules described in
6.11.10.9 Underflow Exception Condition
.
A number is denormalized by shifting its significand to the right while incrementing
its exponent by one for each bit shifted until the exponent equals the format's min-
imum value. If any significant bits are lost in this shifting process, a loss of accuracy
has occurred, and an underflow exception is signaled. The sign of the number does
not change.
When denormalized numbers are operands of multiply and divide operations, op-
erands are prenormalized internally before the operations are performed.
3.3.10 Data Handling and Precision
There are specific instructions for moving floating-point data between the FPRs
and memory. Data in double-precision format is not altered during the move. Sin-
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