
MOTOROLA
3-22
OPERAND CONVENTIONS
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RCPU
REFERENCE MANUAL
Single-precision arithmetic instructions require all operands to be single-pre-
cision.
Double-precision arithmetic instructions produce double-precision values.
Single-precision arithmetic instructions produce single-precision values.
For arithmetic instructions, conversions from double- to single-precision must be
done explicitly by software, while conversions from single- to double-precision are
done implicitly.
Although the double-precision format specifies an 11-bit exponent, exponent arith-
metic uses two additional bit positions to avoid potential transient overflow condi-
tions. An extra bit is required when denormalized double-precision numbers are
prenormalized. A second bit is required to permit computation of the adjusted ex-
ponent value in the following cases when the corresponding exception enable bit
is one:
Underflow during multiplication using a denormalized factor.
Overflow during division using a denormalized divisor.
3.4.1 Execution Model for IEEE Operations
The following description uses 64-bit arithmetic as an example. Thirty-two-bit arith-
metic is similar except that the fraction field is a 23-bit field and the single-precision
guard, round, and sticky bits (described in this section) are logically adjacent to the
23-bit FRACTION (or mantissa) field.
The bits and fields for the IEEE 64-bit execution model are defined as follows:
The S bit is the sign bit.
The C bit is the carry bit that captures the carry out of the significand.
The L bit is the leading unit bit of the significand which receives the implicit bit
from the operands.
The FRACTION is a 52-bit field that accepts the fraction (mantissa) of the op-
erands.
The guard (G), round (R), and sticky (X) bits are extensions to the low-order
bits of the accumulator. The G and R bits are required for post normalization
of the result. The G, R, and X bits are required during rounding to determine
if the intermediate result is equally near the two nearest representable values.
The X bit serves as an extension to the G and R bits by representing the log-
ical OR of all bits that may appear to the low-order side of the R bit, either due
to shifting the accumulator right or other generation of low-order result bits.
The G and R bits participate in the left shifts with zeros being shifted into the
R bit.
Table 3-8
shows the relationship among the G, R, and X bits, the inter-
mediate result (IR), the next lower in magnitude representable number (NL),
and the next higher in magnitude representable number (NH).
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