Microchip Technology MA330018 Data Sheet
dsPIC33FJ32MC302/304, dsPIC33FJ64MCX02/X04 AND dsPIC33FJ128MCX02/X04
DS70291G-page 32
© 2007-2012 Microchip Technology Inc.
3.8.1
MULTIPLIER
The 17-bit x 17-bit multiplier is capable of signed or
unsigned operation and can multiplex its output using a
scaler to support either 1.31 fractional (Q31) or 32-bit
integer results. Unsigned operands are zero-extended
into the 17th bit of the multiplier input value. Signed
operands are sign-extended into the 17th bit of the
multiplier input value. The output of the 17-bit x 17-bit
multiplier/scaler is a 33-bit value that is sign-extended
to 40 bits. Integer data is inherently represented as a
signed two’s complement value, where the Most
Significant bit (MSb) is defined as a sign bit. The range
of an N-bit two’s complement integer is -2
unsigned operation and can multiplex its output using a
scaler to support either 1.31 fractional (Q31) or 32-bit
integer results. Unsigned operands are zero-extended
into the 17th bit of the multiplier input value. Signed
operands are sign-extended into the 17th bit of the
multiplier input value. The output of the 17-bit x 17-bit
multiplier/scaler is a 33-bit value that is sign-extended
to 40 bits. Integer data is inherently represented as a
signed two’s complement value, where the Most
Significant bit (MSb) is defined as a sign bit. The range
of an N-bit two’s complement integer is -2
N-1
to 2
N-1
– 1.
• For a 16-bit integer, the data range is -32768
(0x8000) to 32767 (0x7FFF) including 0
• For a 32-bit integer, the data range is
-2,147,483,648 (0x8000 0000) to 2,147,483,647
(0x7FFF FFFF)
(0x7FFF FFFF)
When the multiplier is configured for fractional
multiplication, the data is represented as a two’s
complement fraction, where the MSb is defined as a
sign bit and the radix point is implied to lie just after the
sign bit (QX format). The range of an N-bit two’s
complement fraction with this implied radix point is -1.0
to (1 – 2
multiplication, the data is represented as a two’s
complement fraction, where the MSb is defined as a
sign bit and the radix point is implied to lie just after the
sign bit (QX format). The range of an N-bit two’s
complement fraction with this implied radix point is -1.0
to (1 – 2
1-N
). For a 16-bit fraction, the Q15 data range
is -1.0 (0x8000) to 0.999969482 (0x7FFF) including 0
and has a precision of 3.01518x10
and has a precision of 3.01518x10
-5
. In Fractional
mode, the 16 x 16 multiply operation generates a 1.31
product that has a precision of 4.65661 x 10
product that has a precision of 4.65661 x 10
-10
.
The same multiplier is used to support the MCU
multiply instructions, which include integer 16-bit
signed, unsigned and mixed sign multiply operations.
The MUL instruction can be directed to use byte or
word-sized operands. Byte operands direct a 16-bit
result, and word operands direct a 32-bit result to the
specified registers in the W array.
multiply instructions, which include integer 16-bit
signed, unsigned and mixed sign multiply operations.
The MUL instruction can be directed to use byte or
word-sized operands. Byte operands direct a 16-bit
result, and word operands direct a 32-bit result to the
specified registers in the W array.
3.8.2
DATA ACCUMULATORS AND
ADDER/SUBTRACTER
ADDER/SUBTRACTER
The data accumulator consists of a 40-bit adder/
subtracter with automatic sign extension logic. It can
select one of two accumulators (A or B) as its
pre-accumulation source and post-accumulation
destination. For the ADD and LAC instructions, the data
to be accumulated or loaded can be optionally scaled
using the barrel shifter prior to accumulation.
subtracter with automatic sign extension logic. It can
select one of two accumulators (A or B) as its
pre-accumulation source and post-accumulation
destination. For the ADD and LAC instructions, the data
to be accumulated or loaded can be optionally scaled
using the barrel shifter prior to accumulation.
3.8.2.1
Adder/Subtracter, Overflow and
Saturation
Saturation
The adder/subtracter is a 40-bit adder with an optional
zero input into one side, and either true or complement
data into the other input.
• In the case of addition, the Carry/Borrow input is
zero input into one side, and either true or complement
data into the other input.
• In the case of addition, the Carry/Borrow input is
active-high and the other input is true data (not
complemented)
complemented)
• In the case of subtraction, the Carry/Borrow input
is active-low and the other input is complemented
The adder/subtracter generates Overflow Status bits,
SA/SB and OA/OB, which are latched and reflected in
the STATUS register:
• Overflow from bit 39: this is a catastrophic
SA/SB and OA/OB, which are latched and reflected in
the STATUS register:
• Overflow from bit 39: this is a catastrophic
overflow in which the sign of the accumulator is
destroyed
destroyed
• Overflow into guard bits 32 through 39: this is a
recoverable overflow. This bit is set whenever all
the guard bits are not identical to each other.
the guard bits are not identical to each other.
The adder has an additional saturation block that
controls accumulator data saturation, if selected. It
uses the result of the adder, the Overflow Status bits
described previously and the SAT<A:B>
(CORCON<7:6>) and ACCSAT (CORCON<4>) mode
control bits to determine when and to what value to
saturate.
Six STATUS register bits support saturation and
overflow:
• OA: ACCA overflowed into guard bits
• OB: ACCB overflowed into guard bits
• SA: ACCA saturated (bit 31 overflow and
controls accumulator data saturation, if selected. It
uses the result of the adder, the Overflow Status bits
described previously and the SAT<A:B>
(CORCON<7:6>) and ACCSAT (CORCON<4>) mode
control bits to determine when and to what value to
saturate.
Six STATUS register bits support saturation and
overflow:
• OA: ACCA overflowed into guard bits
• OB: ACCB overflowed into guard bits
• SA: ACCA saturated (bit 31 overflow and
saturation)
or
ACCA overflowed into guard bits and saturated
(bit 39 overflow and saturation)
(bit 39 overflow and saturation)
• SB: ACCB saturated (bit 31 overflow and
saturation)
or
ACCB overflowed into guard bits and saturated
(bit 39 overflow and saturation)
(bit 39 overflow and saturation)
• OAB: Logical OR of OA and OB
• SAB: Logical OR of SA and SB
The OA and OB bits are modified each time data
passes through the adder/subtracter. When set, they
indicate that the most recent operation has overflowed
into the accumulator guard bits (bits 32 through 39).
The OA and OB bits can also optionally generate an
arithmetic warning trap when set and the
corresponding Overflow Trap Flag Enable bits (OVATE,
OVBTE) in the INTCON1 register are set (refer to
• SAB: Logical OR of SA and SB
The OA and OB bits are modified each time data
passes through the adder/subtracter. When set, they
indicate that the most recent operation has overflowed
into the accumulator guard bits (bits 32 through 39).
The OA and OB bits can also optionally generate an
arithmetic warning trap when set and the
corresponding Overflow Trap Flag Enable bits (OVATE,
OVBTE) in the INTCON1 register are set (refer to
). This allows the
user application to take immediate action, for example,
to correct system gain.
The SA and SB bits are modified each time data
passes through the adder/subtracter, but can only be
cleared by the user application. When set, they indicate
that the accumulator has overflowed its maximum
range (bit 31 for 32-bit saturation or bit 39 for 40-bit
saturation) and is saturated (if saturation is enabled).
When saturation is not enabled, SA and SB default to
bit 39 overflow and thus indicate that a catastrophic
overflow has occurred. If the COVTE bit in the
INTCON1 register is set, the SA and SB bits generate
an arithmetic warning trap when saturation is disabled.
to correct system gain.
The SA and SB bits are modified each time data
passes through the adder/subtracter, but can only be
cleared by the user application. When set, they indicate
that the accumulator has overflowed its maximum
range (bit 31 for 32-bit saturation or bit 39 for 40-bit
saturation) and is saturated (if saturation is enabled).
When saturation is not enabled, SA and SB default to
bit 39 overflow and thus indicate that a catastrophic
overflow has occurred. If the COVTE bit in the
INTCON1 register is set, the SA and SB bits generate
an arithmetic warning trap when saturation is disabled.