Signed Integer Arithmetic On The HPC AN 0603

User Manual: AN-0603

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National Semiconductor
Application Note 603
Raj Gopalan
July 1989

This report describes the implementation of signed integer
arithmetic operations on the HPC. HPC hardware support
for unsigned arithmetic operation. In order to support signed
integer arithmetic operations on the HPC, the user can represent negative numbers in two’s complement form and
perform the signed arithmetic operations explicitly through
software.
The following signed integer arithmetic routines are implemented in the package:
Multiplication:
16 by 16 yielding 16-bit result
32 by 32 yielding 32-bit result
Division:
16 by 8 yielding 16-bit quotient and 16-bit remainder
32 by 16 yielding 16-bit quotient and 16-bit remainder
32 by 32 yielding 16-bit quotient and 16-bit remainder
Addition:
16 by 16 yielding 16-bit

Subtraction:
16 by 16 yielding 16-bit
Comparison:
16 by 16 for greater to, less than or equal to.

.title
SIMUSL
.sect
code,rom8,byte,rel
;Signed multiply (16 by 16)
;
B
Multiplicand
;
A
Multiplier
;
X;A
return
;
.public signed mult 16
.local
signed mult 16:
st
a,0.w
mult
a,b
sc
ifbit
7,(1).b
subc
x,b
sc
ifbit
7,(B a 1).b
subc
x,0.w
$exit:
ret

REPRESENTATION OF NEGATIVE NUMBERS:
For binary numbers, negative numbers are represented in
two’s complement form. In this system, a number is positive
if the MSB is 0, negative if it is 1.
The decimal equivalent of two’s complement number is
computed the same as for an unsigned number, except that
weight of the MSB is b2**n b 1 instead of a 2**n b 1.
The range of representable numbers is b(2**n b 1)
through a (2**n b 1 b 1).
The two’s complement of a binary number is obtained by
complementing its individual bits and adding one to it.
The advantage of representing a negative number in two’s
complement form is that addition and subtraction can be
done directly using unsigned hardware.

Signed Integer Arithmetic on the HPC

Signed Integer Arithmetic
on the HPC TM

;do unsigned multiplication.
;if multiplier is negative

;if multiplicand is negative

.endsect

AN-603

HPCTM is a trademark of National Semiconductor Corporation.
C1995 National Semiconductor Corporation

TL/DD10395

RRD-B30M75/Printed in U. S. A.

The algorithm is as follows:

MULTIPLICATION

Step 1. Result e op1 * op2

Method 1:
Signed multiplication can be achieved by taking care of the
signs and magnitudes of the multiplicand and multiplier separately.
Perform the multiplication on the magnitudes alone.
The sign of the result can be set based on the signs of the
multiplier and the multiplicand.

Step 2. If op1 k 0 then subtract op2 from upper half of the
result.
Step 3. If op2 k 0 then subtract op1 from upper half of the
result.
Now the Result will yield the correct value of the multiplication on two’s complement numbers.
Method 3:
By sign extending the multiplier and multiplicand to the size
of the result one can always obtain the correct result of
signed multiplication using unsigned multiplication.

Method 2:
This method does not require finding the magnitude of the
operands. Multiplication can be done using unsigned hardware on the two’s complement numbers. The result will be
signed based on the signs of the operands.
.title
SIMULL
.sect
code,rom8,byte,rel
;Multiply (Signed or Unsigned are the same)
;32 bit
;
K:A
Multiplicand
;
14:6[SP]
Multiplier
;
K:A
return
;
.public multiply 32
.local
multiply 32:
push
x
st
a,0.w
ld
a,k
mult
a,18[sp].w
x
a,0.w
push
a
mult
a18[sp].w
add
0.w,a
pop
a
mult
a,18[sp].w
add
x,0.w
ld
k,x
pop
x
ret

;(Argument now at 16:8[SP])
;Multiply hi reg* lo stack
;hold, retrieve lo reg
;(argument now at 18:10[SP])
;Multiply lo reg* hi stack
;add into hi partial
;(Argument now at 16:8[SP])
;Multiply lo reg* lo stack
;add in hi partial
;Position
;Restore

.endsect

2

DIVISION
Similar to multiplication method 1, one can perform the division on the magnitudes of the dividend and divisor.
The sign of the quotient can be set based on the signs of the dividend and the divisor.
The sign of the remainder will be same as the dividend.

;Division
;16,8 bit
;
;
;
;

.title
.sect

SIDVSS
code,rom8,byte,rel

& Remainder
(signed only,
A
14[SP]
A

unsigned uses inline code)
Dividend
Divisor
return

.public signed divide 8,signed remainder 8
.public signed divide 16,signed remainder 16
.local
signed divide 8:
jsr
$shared 8
ret
;
signed remainder 8:
jsr
$shared 8
ld
a,k
ret
;
$shared 8:
ifgt
a,#0x7f
or
a,#0xff00
st
a,k
ld
a,16[sp].w
ifgt
a,#0x7f
or
a,#0xff00
jp
$shared
;
signed divide 16:
jsr
$shared 16
ret
;
signed remainder 16:
jsr
$shared 16
ld
a,k
ret
;
$share 16:
st
a,k
ld
a,16[sp].w
$shared
ifeq
a,#0
ret
push
x
ifgt
a,#0x7fff
jp
$unknown negative
x
a,k
ifgt
a,#0x7fff
jp
$negative positive
div
a,k
jp
$positive positive

3

;Uses shared routine

;Uses shared routine
;Return remainder

;Get arguments

;Uses shared routine

;Uses shared routine
;Return remainder

;Get arguments

;division by zero

;unknown/negative

;negative/positive
;Positive/positive is plus,plus

$unknown negative:
comp
inc
x
ifgt
jp
div
comp
inc
$positive positive:
ld
jp
$negative positive:
comp
inc
div
comp
inc
jp
$negative negative:
comp
inc
div
$negate remainder:
x
comp
inc
st
ld
$exit:
pop
ret

;Unknown/negative
a
a
a,k
a,#0x7fff
$negative negative
a,k
a
a

; negative/negative
;Positive/negative is minus,plus

k,x
$exit
;Negative/positive is minus,minus
a
a
a,k
a
a
$negate remainder
;Negative/negative is plus,minus
a
a
a,k
a,x
a
a
a,k
a,x
x

.endsect

4

.title
.sect

SIDVLS
code,rom8,byte,rel

;Division & Remainder
;Signed 32 by 16 divide
;
X;A
Dividend
;
K
Divisor
;
X,A
return (remainder and quotient)
;
.public signed div 32
.local
signed div 32:
sc
ifeq
k,#0
ret
;Divide by zero, set carry and return
$shared signed:
ifbit
7,x01.b
jp
$negative dividend
jsr
$process divisor
;Skipping return
ret
;0/040,0
$negate quotient:
comp
a
inc
a
ret
;0/14 1,0
$negative dividend;
comp
a
add
a,#01
x
a,x
comp
a
adc
a,#0
x
a,x
jsr
$process divisor
;skipping return
jsr
$negate quotient
;1/041,1
;1/140,1
$negate remainder:
x
a,x
comp
a
inc
a
x
a,x
ret
$process divisor:
ifbit
7,k01.b
jp
$negative divisor
divd
a,k
;?/0
ret
$negative divisor:
x
a,k
comp
a
inc
a
x
a,k
divd
a,k
;?/1
retsk
.endsect

5

.title
.sect

SUDVLL
code,rom8,byte,rel

;Division & Remainder
;Signed 32 by 32 Divide
;
K:A
Dividend
;
14:6[SP]
Divisor
;
K:A
return
;
;Stack frame as built and used consists of
;top:
;
0, initial subtrahend hi /dividend shifts into subtrahend
;
0, initial subtrahend lo /becomes remainder
;
k, dividend hi /dividend shifts into subtrahend, and
;
a, dividend lo /quotient shifts into dividend
;
b preserved
;
x preserved
;
return address
;
sp-4–12, divisor hi
;
sp-6–12, divisor lo
;Sign flag (0 4 negative, 1 4 positive, for test sense at exit)
;bit 0, divisor sign (1 4 negative)
;bit 1, dividend sign (1 4 positive)
;Inc of flag causes bit 1 4 (bit 1 xor bit 0) by carry/nocarry out of bit 0
;so that two positives (010) or two negatives (001) indicate a positive
;quotient (011 or 010) in bit 1. Bit 1 always indicates sign if remainder.
;Operation is indicated by bit 3 of the flag, 1 4 remainder.
;
.public signed divide 32, signed remainder 32
.public unsigned divide 32, unsigned remainder 32
.local
signed divide 32:
ld
1.b,#0x02
jp
$shared signed
;
signed remainder 32:
ld
1.b,#0x0a
$shared signed:
ifbit
7,k01.b
;Check dividend
jsr
$negate
;Negate dividend and note sign
ifbit
7,1603[sp].b
;Check divisor
jp
$negate divisor
jmp
$shared
;
$negate divisor:
x
comp
add
x
x
comp
adc
x
sbit
jp
;
unsigned divide 32:
ld
jp
;
unsigned remainder 32:
ld

a,16[sp].w
a
a,#1
a,16[sp].w
a,14[sp].w
a
a,#0
a,14[sp].w
0,1.b
$shared

;Negate divisor and note sign

1.b,#0x02
$shared

1.b,#0x0a

6

$shared:
push
push
ld
push
push
ld
clr
push
push
ld
add
ld
or
ifeq
jmp
ld

x
b
b,sp
a
k
x,sp
a
a
a
k,#118
k,sp
a,[k].w
a,2[k].w
a,#0
$zero
0.b,#32

;Preserve registers

a,[b].w
a
a,[b0].w

;Shift Dividend:Quotient

;Place dividend, becomes quotient

;Set subtrahend, becomes remainder

;Access divisor argument

;division by zero
;Set counter

$loop:
ld
shl
xs
nop
ld
rlc
xs
nop
ld
rlc
x
ld
rlc
x
ifc
jp
sc
ld
subc
ld
subc
ifnc
jp
$subtract:
ld
subc
x
ld
subc
x
sbit
$count:
decsz
jmp
$zero:
pop
pop
pop
pop
ifbit
jp
ld
ld
inc

a,[b].w
a
a,[b1].w
a,[x].w
a
a,[x0].w
a,[x].w
a
a,[x1].w
;Carry out 1 dividend divisor
;Check for dividend divisor

$subtract
a,[x0].w
a,[k].w
a,[x1].w
a,2[k].w
$count

;dividend divisor

a,[x].w
a,[k].w
a,[x0].w
a,[x].w
a,2[k].w
a,[x1].w
0,[b].b

;Subtract out divisor (c is set)

0.b
$loop

;Count 32 shifts

k
a
x
b
3,1.b
$exit
a,b
k,x
1.b

;Get Remainder and/or Quotient
;and clear working off stack

;Set quotient bit

;want remainder, have it
;Want Quotient
;Divisor’s sign Xors Dividend’s

7

$exit:
pop
pop
ifbit
ret

b
x
1,1.b

comp
add
x
comp
adc
x
rbit
ret

a
a,#1
a,k
a
a,#0
a,k
1,1.b

;Restore registers

;positive result

$negate:
;Negate K:A

;Note sign (for entrance)

.endsect

8

ADDITION
Two’s complement numbers can be added by ordinary binary addition, ignoring any carries beyond the MSB. The result will
always be the correct sum as long as the result doesn’t exceed the range.
If the result is the same as for the subtrahend, then overflow has occurred.
.title
SIADD
.sect
code,rom8,byte,rel
;Signed add (16 by 16)
;
A
Operand1
;
B
Operand2
;
Carry
Return
.public sign add
.local
sign add:
ld
0.b,#00
ifbit 7,(A01).b
inc
0.b
ifbit 7,(B01).b
inc
0.b
;if bit 0 of 0.b 4 1 then op1 and op2 have different sign
;if bit 0 of 0.b 4 0 then op1 and op2 sign are same
;then if bit 1 of 0.b 4 0 both operands are positive
;else both operands are negative.
add
a,b
rc
ifbit 0,0.b
ret
ifbit 1,0.b
jp $negatives
$positives:
ifbit 7,(A01).b

;Perform unsigned addition
;both operands are different sign
;both op1 and op2 are negative
;both op1 and op2 are positive
;if result sign is negative then
set overflow bit
;overflow

sc
ret
$negatives:
ifbit 7,(A01).b

;if sign bit of result is
negative, then no overflow

ret
sc

;overflow

$exit:
ret
.endsect

9

SUBTRACTION
Subtraction can be achieved by negating the subtrahend and perform the addition operation.
Overflow can be detected as mentioned before by checking the signs of minuhend and the negation of the subtrahend and that
of the sum.
.title
.sect

SISUB
code,rom8,byte,rel

;Signed subtract (16 by 16)
;
;
;

B
Operand1
A
Operand2
Carry,A
Return
.public sign sub
.local

sign sub:
ld
ifbit
inc 0.b

0.b,#00
7,(B01).b

;initialize sign flags

$negate A:
comp A
inc A
$ngative comp A:
ifbit 7,(A01).b
inc
0.b
;if bit 0 of 0.b 4 1 then op1 and op2 have different sign
;if bit 0 of 0.b 4 0 then op1 and op2 sign are same
;then if bit 1 of 0.b 4 0 both operands are positive
;else both operands are negative.
add A,B
;Perform unsigned addition
rc
ifbit 0,0.b
;both operands are different sign
ret
ifbit 1,0.b
;both op1 and op2 are negative
jp $negatives
$positives:
;both op1 and op2 are positive
if bit 7, (A01).b
;if result sign is negative then
set overflow bit
sc
;bit 0 of byte 0.b is set to
indicate overflow
ret
$negatives:
ifbit 7, (A01).b
;if sign bit of result is
negative, then no overflow
ret
sc
;sign bit of result is positive,
hence overflow.
$exit:ret
.endsect

10

.title
.sect

NSISUB
code,rom8,byte,rel

;Signed sub (16 by 16)
;
;
;

A
Operand1
B
Operand2
Carry
Return
.public sign sub
.local

sign sub:
ld
0.b,#00
ifbit 7,(A01).b
inc
0.b
ifbit 7,(B01).b
inc
0.b
;if bit 0 of 0.b 4 1 then op1 and op2 have different sign
;if bit 0 of 0.b 4 0 then op1 and op2 sign are same
;then if bit 1 of 0.b 4 0 both operands are positive
;else both operands are negative.
sc
subc
a,b
;Perform unsigned addition
rc
ifbit 0,0.b
;both operands are different sign
jp
$chkovf
ret
;both operands are same sign,
can’t produce overflow
$chkovf:
ifbit
jp

7,(B01).b
$negminu

ifbit
sc
ret

7,(A01).b

ifbit
sc
ret

7,(A01).b

$posminu:

$negminu:

.endsect

11

Signed Integer Arithmetic on the HPC

COMPARISON
To do signed comparison on n bit two’s complement numbers first add 2**(n b 1) to the numbers. This will basically shift
the numbers from b(2**n b 1) to a (2**n b 1 b 1) range to 0 to 2**n b 1.
Now comparison operations on the numbers will produce the correct result.
.title
.sect

SICMP
code,rom8,byte,rel

;Signed compare (16 by 16)
;
A
;
B
;
0.b
;
;
signed compare:
push
push
add
add
ifgt
jp
ifeq
jp
$less:
ld
pop
pop
ret
$great:
ld
pop
pop
ret
$equ:
ld
pop
pop
ret

Operand1
Operand2
Return400
02
01

if a 4 b
if a l b
if a k b

a
b
a,#08000
b,#08000
a,b
$great
a,b
$equ
0.b,#01
b
a

0.b,#02
b
a

0.b,#00
b
a

.endsect

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DEVICES OR SYSTEMS WITHOUT THE EXPRESS WRITTEN APPROVAL OF THE PRESIDENT OF NATIONAL
SEMICONDUCTOR CORPORATION. As used herein:

AN-603

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systems which, (a) are intended for surgical implant
into the body, or (b) support or sustain life, and whose
failure to perform, when properly used in accordance
with instructions for use provided in the labeling, can
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---

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File Type                       : PDF
File Type Extension             : pdf
MIME Type                       : application/pdf
PDF Version                     : 1.3
Linearized                      : Yes
Create Date                     : 1995:07:03 18:28:17
Producer                        : Acrobat Distiller 2.0 for Windows
Title                           : Signed Integer Arithmetic on the HPC
Subject                         : AN-603
Author                          : 
Keywords                        : Application, Notes
Modify Date                     : 2001:11:23 11:46:02+05:30
Page Count                      : 12

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