U.S. patent application number 12/148509 was filed with the patent office on 2009-03-26 for shift-add based multiplication.
Invention is credited to Charles H. Moore.
Application Number | 20090083361 12/148509 |
Document ID | / |
Family ID | 40472867 |
Filed Date | 2009-03-26 |
United States Patent
Application |
20090083361 |
Kind Code |
A1 |
Moore; Charles H. |
March 26, 2009 |
Shift-add based multiplication
Abstract
A system for multiplication of multi-bit first and second
values. A processor is provided that has first and second memories
with bit-positions that can all be zero or one and where the first
memory has a low bit (LB). The first value is arranged in the first
memory so its LSB is in the first memory LB, and the remaining
bit-positions in the first memory are set to zero. The second value
is arranged in the second memory such that its LSB is in the
bit-position of the second memory that is next higher in order than
the MSB of the first value in the first memory, and the remaining
bit-positions in the second memory are set to zero. A +* operation
is then performed a quantity of times equaling the number of
significant bits in the first value, inclusive, thus obtaining the
product of the first and second values.
Inventors: |
Moore; Charles H.; (Sierra
City, CA) |
Correspondence
Address: |
HENNEMAN & ASSOCIATES, PLC
714 W. MICHIGAN AVE.
THREE RIVERS
MI
49093
US
|
Family ID: |
40472867 |
Appl. No.: |
12/148509 |
Filed: |
April 18, 2008 |
Related U.S. Patent Documents
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Application
Number |
Filing Date |
Patent Number |
|
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60974820 |
Sep 24, 2007 |
|
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Current U.S.
Class: |
708/628 |
Current CPC
Class: |
G06F 7/582 20130101 |
Class at
Publication: |
708/628 |
International
Class: |
G06F 7/523 20060101
G06F007/523 |
Claims
1. A system for multiplication of multi-bit first and second values
each having a least significant bit (LSB) and a most significant
bit (MSB), comprising: (a) a processor having first and second
memories with bit-positions that can all be zero or one and wherein
said first memory has a low bit (LB); (b) a logic to arrange the
first value in said first memory such that the LSB of the first
value is in said LB and to set each of said bit-positions remaining
in said first memory to zero; (c) a logic to arrange the second
value in said second memory such that the LSB of the second value
is in said bit-position of said second memory which is next higher
in order than the MSB of the first value in said first memory and
to set each of said bit-positions remaining in said second memory
to zero; (d) a logic to perform a +* op-code for a quantity of
iterations equaling how many bits comprise the MSB through the LSB
of the first value, inclusive, thereby obtaining a product of the
first and second values.
2. The system of claim 1, wherein said processor includes a
plurality of registers and said first memory comprises one or more
said registers, or said second memory comprises one or more said
registers, or both.
3. A method for multiplication of multi-bit first and second values
in a processor, wherein the first and second values each have a
least significant bit (LSB) and a most significant bit (MSB), and
wherein the processor has first and second memories with
bit-positions that can all be zero or one and the first memory has
a low bit (LB), the method comprising: (a) arranging the first
value in the first memory such that the LSB of the first value is
in the LB and such that each of the bit-positions remaining in said
first memory is set to zero; (b) arranging the second value in the
second memory such that the LSB of the second value is in the
bit-position of the second memory which is next higher in order
than the MSB of the first value in the first memory and such that
each of the bit-positions remaining in said second memory is set to
zero; (c) performing a +* op-code for a quantity of iterations
equaling how many bits comprise the MSB through the LSB of the
first value, inclusive, thereby obtaining a product of the first
and second values.
4. The method of claim 3, wherein the processor includes a
plurality of registers and the first memory includes one or more
said registers, or the second memory includes one or more said
registers, or both.
Description
[0001] This application claims the benefit of U.S. Provisional
Application No. 60/974,820 entitled "Shift-Add Mechanism," filed
Sep. 24, 2007 by at least one common inventor, which is
incorporated herein by reference in its entirety.
BACKGROUND OF THE INVENTION
[0002] 1. Technical Field
[0003] The present invention relates generally to electrical
computers and digital processing systems having processing
architectures and performing instruction processing, and more
particularly to processes for multiplication that can be
implemented in such.
[0004] 2. Background Art
[0005] Powerful and efficient operational codes (op-codes) are
critical for modern computer processors to perform many tasks. For
example, some such tasks are multiplication and producing sequences
of pseudorandom numbers.
BRIEF SUMMARY OF THE INVENTION
[0006] Accordingly, it is an object of the present invention to
provide a shift-add based multiplication process that is useful for
various operations in a processor.
[0007] Briefly, a preferred embodiment of the present invention is
a system for multiplication of multi-bit first and second values
that each has a least significant bit (LSB) and a most significant
bit (MSB). A processor is provided that has first and second
memories with bit-positions that can all be zero or one, and where
the first memory has a low bit (LB). A logic arranges the first
value in the first memory such that its LSB is in the LB, and sets
each of the bit-positions remaining in the first memory to zero. A
logic arranges the second value in the second memory such that its
LSB is in the bit-position of the second memory that is next higher
in order than the MSB of the first value in the first memory, and
sets each of the bit-positions remaining in the second memory to
zero. A logic then performs a +* op-code a quantity of iterations
equaling how many bits comprise the MSB through the LSB of the
first value, inclusive, thus obtaining a product of the first and
second values.
[0008] These and other objects and advantages of the present
invention will become clear to those skilled in the art in view of
the description of the best presently known mode of carrying out
the invention and the industrial applicability of the preferred
embodiment as described herein and as illustrated in the figures of
the drawings.
BRIEF DESCRIPTION OF THE SEVERAL VIEWS OF THE DRAWING(S)
[0009] The purposes and advantages of the present invention will be
apparent from the following detailed description in conjunction
with the appended tables and figures of drawings in which:
[0010] TBLS. 1-4 represent the values in the T-register and the
S-register in a SEAforth.TM. 24a device in a set of hypothetical +*
(shift-add mechanism) examples.
[0011] TBLS. 5-10 represent the values in the T-register and the
S-register in a SEAforth.TM. 24a device in a set of hypothetical +*
(shift-add mechanism) multiplication examples.
[0012] FIG. 1 (background art) is a table of the thirty two
operational codes (op-codes) in the Venture Forth.TM. programming
language.
[0013] FIG. 2 (background art) is a block diagram showing the
general architecture of each of the cores in a SEAforth.TM. 24a
device.
[0014] FIGS. 3a-b (background art) are schematic block diagrams
depicting how the 18 bit wide registers in the SEAforth.TM. 24a can
be represented, wherein FIG. 3a shows the actual bit arrangement
and FIG. 3b shows a conceptual bit arrangement.
[0015] FIGS. 4a-b (background art) are schematic block diagrams
depicting register content, wherein FIG. 4a shows the slots filled
with four .cndot. (nop) op-codes and FIG. 4b shows the register
filled with the number 236775 (as unsigned binary).
[0016] FIGS. 5a-b (background art) are block diagrams respectively
and stylistically showing the return and the data stack elements in
SEAforth.TM. 24a cores, wherein FIG. 5a depicts elements in the
return stack region and FIG. 5b depicts elements in the data stack
region.
[0017] FIG. 6 is a flow chart of a shift-add mechanism, as used by
the present invention, that shows all of the possible actions
associated with a single execution of the +* op-code.
[0018] FIG. 7 is a table showing bit relationships in accord with
FIG. 6.
[0019] FIG. 8 is a flow chart of a shift-add based multiplication
process in accord with the present invention.
[0020] In the various figures of the drawings, like references are
used to denote like or similar elements or steps.
DETAILED DESCRIPTION OF THE INVENTION
[0021] A preferred embodiment of the present invention is a
shift-add based multiplication process. As illustrated in the
various drawings herein, and particularly in the view of FIG. 8,
preferred embodiments of the invention are depicted by the general
reference character 200.
[0022] The present inventive shift-add based multiplication process
200 (FIG. 8) is an application of a shift-add mechanism by the
present inventor. In view of this, that shift-add mechanism is
discussed first, below.
The +* Op-Code On The SEAforth.TM. 24a Device
[0023] The shift-add mechanism 100 (FIG. 6) can be used for a
variety of tasks including, without limitation, multiplication and
pseudorandom number generation. In the Venture Forth.TM.
programming language, the shift-add mechanism 100 exists as a "+*"
op-code. Before presenting more detailed examples, it is useful to
consider a simple example in the context of a SEAforth.TM. 24a
device by IntellaSys.TM. Corporation of Cupertino, Calif., a member
of The TPL Group.TM. of companies.
[0024] As general background, the SEAforth.TM. 24a has 24 stack
based microprocessor cores that all use the Venture Forth.TM.
programming language. FIG. 1 (background art) is a table of the
thirty two operational codes (op-codes) in this language, in hex,
mnemonic, and binary representations. These op-codes are divided
into two main categories, memory instructions and arithmetic logic
unit (ALU) instructions, with sixteen op-codes in each division.
The memory instructions are shown in the left half of the table in
FIG. 1, and the ALU instructions are shown in the right half of the
table in FIG. 1. It can be appreciated that one clear distinction
between the divisions of op-codes is that the memory instructions
contain a zero (0) in the left-most bit whereas the ALU
instructions contain a one (1) in the left-most bit. Furthermore,
this is the case regardless of whether the op-codes are viewed in
their hex or binary representations. The +* op-code of present
interest is shown upper-most in the right-hand column.
[0025] FIG. 2 (background art) is a block diagram showing the
general architecture of each of the cores in the SEAforth.TM. 24a
device. All of the registers in the SEAforth.TM. 24a are 18 bits
wide, except for the B- and PC-registers, which are not relevant
here.
[0026] There are two distinct approaches that can be taken when a
programmer is selecting the bits that will make up the 18 bit wide
register space in a SEAforth.TM. 24a (with limited exceptions for
some op-codes that use the A-register). The first of these is to
divide this space into four equal slots that can be called: slot 0,
slot 1, slot 2, and slot 3. The bit lengths of these slots are not
all equal, however, because division of 18 by 4 results in a
remainder. The first three slots, slot 0, slot 1, and slot 2;
therefore can each hold 5 bits while slot 3 holds only three
bits.
[0027] FIGS. 3a-b (background art) are schematic block diagrams
depicting how the 18 bit wide registers in the SEAforth.TM. 24a
device can be represented, wherein FIG. 3a shows the actual
arrangement of the bits as bits 0 through 17, and FIG. 3b shows a
conceptual arrangement of the bits as bits -2 through 17. In FIG.
3a it can be seen that bits 13-17 inclusive make up slot 0, bits
8-12 inclusive make up slot 1, bits 3-7 inclusive make up slot 2,
and bits 0-2 make up slot 3. The designers of the SEAforth.TM. 24a
device often point out the fact that the 18-bit wide registers can
each contain three and three/five instructions, and this prompts
the question whether slot 3 is significant, since none of the
op-codes in FIG. 1 would appear to fit in slot 3. FIG. 3b shows how
the designers of the SEAforth.TM. 24a device have handled this.
They allow only certain op-codes to fit into slot 3 by treating the
two least significant bits, called bit -1 and bit -2 here, as being
hard wired to ground or zero. Of course, since slot 3 effectively
has only three bits rather than five bits of space, the number of
op-codes that fit into slot 3 is limited to only eight of the 32
possible op-codes. Specifically, these op codes are:
TABLE-US-00001 $00 00000b ;(return) $04 00100b unext $08 01000b @p+
$0C 01100b !p+ $10 10000b +* $14 10100b + $18 11000b dup $1C 11100b
.cndot.(nop).
[0028] The second approach that a programmer can use when selecting
the bits that will make up the 18-bit wide register space in the
SEAforth.TM. 24a is to simply not divide the 18-bit wide register
into slots, and to instead consider the register as containing a
single 18-bit binary value. This may appear at first to be a
completely different approach than the slot-based approach, but
both representations are actually equivalent. FIGS. 4a-b
(background art) are schematic block diagrams depicting an example
illustrating this. FIG. 4a shows the slots filled with four .cndot.
(nop) op-codes, and FIG. 4b shows the register filled with the
number 236775 (as unsigned binary). With reference to FIG. 1, it
can be appreciated that the binary bit values in FIGS. 4a-b are the
very same. This means that it is been left up to the programmer to
differentiate whether a register will contain a number or contain
four op-codes.
[0029] FIGS. 5a-b (background art) are block diagrams stylistically
showing the return and the data stack elements, respectively, that
exist in each core of a SEAforth.TM. 24a device. FIG. 5a depicts
how the return stack region includes a top register that is
referred to as "R" (or as the R-register) and an eight-register
circular buffer. FIG. 5b depicts how the data stack region includes
a top register that is referred to as "T" (or as the T-register), a
(second) register below T that is referred to as "S" (or as the
S-register), and also an eight-register circular buffer. In total,
the return stack thus contains nine registers and the data stack
contains ten registers. Only the data stack region needs to be
considered in the following example.
[0030] TBLS. 1-4 represent the values in the T-register and the
S-register in a set of hypothetical +* examples. For simplicity,
only 4-bit field widths are shown. It is important to note in the
following that the value in the T-register (T) is changed while the
value in the S-register (S) remains unchanged during execution of
the +* op-code. [N.b., to avoid confusion between the bits making
up values and the locations in memory that may hold such, we herein
refer to bits in values and to bit-positions in memory. It then
follows that a value has a most significant bit (MSB) and a least
significant bit (LSB), and that a location in memory has a high bit
(HB) position and a low bit (LB) position.]
[0031] TBL. 1 shows the value one (1) initially placed in the
T-register and the value three (3) placed in the S-register.
Because the low bit (LB) position of T here is a 1, during
execution of the +* op-code: [0032] (1) S and T are added together
and the result is put in T (TBL. 2 shows the result of this); and
[0033] (2) the contents of T are shifted to the right and a 0 is
placed in bit 4 (TBL. 3 shows the result of this).
[0034] The reason for bit 4 being filled with a 0 is saved for
later discussion.
[0035] The contents of T an S in TBL. 3 are now used for a second
example. Because the LB position of T is now a 0, during another
execution of the +* op-code: [0036] (1) the contents of T are
simply shifted to the right and a 0 is placed in bit 4 (TBL. 4
shows the result of this).
[0037] Again, the reason for bit 4 being filled with a 0 is saved
for later discussion. Additionally, it should be noted that the
shift to the right of all of the bits in T is not associated in any
way with the fact that a 1 or 0 filled the LB position of T prior
to the execution of the +* op-code. Instead, and more importantly,
the shift of all the bits to the right in T is associated with the
+* op-code itself.
[0038] These two examples demonstrate nearly all of the actions
associated with the +* op-code. What was not fully described was
why 0 is used to fill bit 4. The following covers this.
The General Case of The +* Op-Code
[0039] A general explanation of the +* op-code is that it executes
a conditional add followed by a bit shift of all bits in T in the
direction of the low order bits when either a 1 or a 0 fills the
high bit (HB) position of T after the shift.
[0040] FIG. 6 is a block diagram of the inventive shift-add
mechanism 100 that shows all of the possible actions associated
with a single execution of the +* op-code. The +* op-code has two
major sub-processes, a shift sub-process 102 and a conditional add
sub-process 104. The shift-add mechanism 100 is embodied as a +*
op-code that starts in a step 106 and where the content of the LB
position of T is examined in a step 108.
[0041] Turning first to the shift sub-process 102, when the LB of T
is 0, in a step 110 the content of the HB position of T is
examined. When the HB position of T is 0, in a step 112 the
contents of T are shifted right, in a step 114 the HB position of T
is filled with a 0, and in a step 116 T contains its new value.
Alternately, when the HB position of T is 1, in a step 118 the
contents of T are shifted right, in a step 120 the HB position of T
is filled with a 1, and step 116 now follows where T now contains
its new value.
[0042] Turning now to the conditional add sub-process 104, when the
LB position of T is 1, in a step 122 the contents of T and S are
added and in a step 124 whether this produces a carry is
determined. If there was no carry, the shift sub-process 102 is
entered at step 110, as shown. Alternately, if there was a carry
(the carry bit is 1), the shift sub-process 102 is entered at step
118, as shown. Then the +* op-code process (the shift-add mechanism
100) continues with the shift sub-process 102 through step 116,
where T will now contain a new value.
[0043] While the actions associated with the +* op-code are easy to
define, FIG. 6 reveals that the execution of the +* op-code is not
conceptually simple. FIG. 7 is a table showing the relationships
between the LB position and the HB position of T prior to an
execution, here called old T, an intermediate carry when the values
in S and T are added (if this action occurs), and finally the HB
and the penultimate bit (HB -1) of T which is produced after
execution, here called new T.
A +* Pseudo-Code Algorithm
[0044] The most general case of a +* op-code is now described using
a pseudo-code algorithm. For this description it is assumed that
the +* op-code is executed on an n-bit machine wherein an
n.sub.t-bit width number t is initially placed in T and an
n.sub.s-bit width number s is initially placed in S. Furthermore,
it is assumed that only one additional bit is available to
represent a carry, even if the +* op-code produces a carry that is
theoretically more than one bit can represent. There is no
restriction on the lengths of n.sub.t and n.sub.s, only that their
individual bit lengths should be less than or equal to the bit
width of n. The pseudo-code is as follows: [0045] 1. If the LB
position of T is a 1: [0046] 1a. Add the value t in T to the value
s in S where the sum of t+s, call this t', replaces the present t
in T and S is left unchanged. [0047] 1a1. If the HB position of T
is a 1: [0048] 1a1a. If the addition of t and s resulted in a
carry: 1a1a1. Shift all bits in T to the right one bit. Bit 0 of t'
after the shift contains the contents of bit 1 before the shift.
Bit 1 of t' after the shift contains the contents of bit 2 before
the shift. In the same way, the rest of t' is filled where bit m,
m<n, being filled after the shift contains the contents of bit
m+1 before the shift. This process leaves bit n devoid while
effectively destroying bit 0 of t' before the shift. Bit n of t'
after the shift will be filled with a 1. [0049] 1a1b. If the
addition of t and s did not result in a carry: 1a1b1. Shift all
bits in T to the right one bit. Bit 0 of t' after the shift
contains the contents of bit 1 before the shift. Bit 1 of t' after
the shift contains the contents of bit 2 before the shift. In the
same way, the rest of t' is filled where bit m, m<n, being
filled after the shift contains the contents of bit m+1 before the
shift. This process leaves bit n devoid while effectively
destroying bit 0 of t' before the shift. Bit n of t' after the
shift will be filled with a 1. [0050] 1a2. If the HB position of T
is a 0: [0051] 1a2a. If the addition of t and s resulted in a
carry: 1a2a1. Shift all bits in T to the right one bit. Bit 0 of t'
after the shift contains the contents of bit 1 before the shift.
Bit 1 of t' after the shift contains the contents of bit 2 before
the shift. In the same way, the rest of t' is filled where bit m,
m<n, being filled after the shift contains the contents of bit
m+1 before the shift. This process leaves bit n devoid while
effectively destroying bit 0 of t' before the shift. Bit n of t'
after the shift will be filled with a 1. [0052] 1a2b. If the
addition of t and s did not result in a carry: 1a2b1. Shift all
bits in t to the right one bit. Bit 0 of t' after the shift
contains the contents of bit 1 before the shift. Bit 1 of t' after
the shift contains the contents of bit 2 before the shift. In the
same way, the rest of t' is filled where bit m, m<n, being
filled after the shift contains the contents of bit m+1 before the
shift. This process leaves bit n devoid while effectively
destroying bit 0 of t' before the shift. Bit n of t' after the
shift will be filled with a 0. [0053] 2. If the LB position of T is
a 0: [0054] 2a. If the HB position of T is a 1: [0055] 2a1. Shift
all bits in T to the right one bit. Bit 0 of t' after the shift
contains the contents of bit 1 before the shift. Bit 1 of t' after
the shift contains the contents of bit 2 before the shift. In the
same way, the rest of t' is filled where bit m, m<n, being
filled after the shift contains the contents of bit m+1 before the
shift. This process leaves bit n devoid while effectively
destroying bit 0 of t' before the shift. Bit n of t' after the
shift will be filled with a 1. [0056] 2b. If the HB position of T
is a 0: [0057] 2b1. Shift all bits in T to the right one bit. Bit 0
of t' after the shift contains the contents of bit 1 before the
shift. Bit 1 of t' after the shift contains the contents of bit 2
before the shift. In the same way, the rest of t' is filled where
bit m, m<n, being filled after the shift contains the contents
of bit m+1 before the shift. This process leaves bit n devoid while
effectively destroying bit 0 of t' before the shift. Bit n of t'
after the shift will be filled with a 0.
[0058] It is important to note in the preceding that the +* op-code
always involves a bit shift to the right (in the direction of the
low order bits) of all bits in T. This bit shift is not the result
of any event before, during, or after the execution of the +*
op-code. The bit shift is an always executed event associated with
the +* op-code.
Multiplication Utilizing the +* Op-Code
[0059] It has been implied herein that the shift-add mechanism 100
can be used for multiplication. An example is now presented
followed by an explanation of the general case of utilizing the +*
op-code to execute complete and correct multiplication.
[0060] Let us suppose that a person would like to multiply the
numbers nine (9) and seven (7) and that the letter T is used to
represent an 8-bit memory location where the nine is initially
placed, and S is used to represent an 8-bit memory location where
the seven is initially placed. [Nb., for simplicity we are not
using the 18-bit register width of the SEAforth.TM. 24a device
here, although the underlying concept is extendable to that or any
bit width.]
[0061] TBLS. 5-10 represent the values in the T-register and the
S-register in a set of hypothetical +* multiplication examples.
TBL. 5 shows the value nine (9) initially placed in the T-register
and the value seven (7) placed in the S-register. Next, the value
in T is right justified in the 8-bit field width such that the four
leading bits are filled with zeros. Conversely, the value in S is
left justified in the 8-bit field width so that the four trailing
bits are filled with zeroes. TBL. 6 shows the result of these
justifications.
[0062] Correct multiplication here requires the execution of four
+* op-codes in series. The first +* operation has the following
effects. The LB position of T is 1 (as shown in TBL. 6), so the
values in T and S are added and the result is placed in T (as shown
in the left portion of TBL. 7). Next, the value in T is shifted to
the right one bit in the same manner described in 1a2b1. (above).
The values after this first +* operation are shown in the right
portion of TBL. 7.
[0063] The second +* operation is quite simple, because the LB
position of T is 0. All of the bits in T are shifted right in the
manner described in 2b1. (above). The values after this second +*
operation are shown in TBL. 8.
[0064] The third +* operation is similar to the second, because the
LB position of T is again 0. All of the bits in T are again shifted
right in the manner described in 2b1. (above). The values after
this third +* operation are shown in TBL. 9.
[0065] The fourth and final +* operation is similar to the first +*
operation. The LB position of T is 1 (as shown in TBL. 9), so the
values in T and S are added and the result is placed in T (as shown
in the left portion of TBL. 10). Next, the value in T is shifted to
the right one bit in the same manner described in 1a2b1. (above).
The values after this fourth +* operation are shown in the right
portion of TBL. 10.
[0066] The resultant T in TBL. 10 is the decimal value 63, which is
what one expects when multiplying the numbers nine and seven.
A +* Pseudo-Code Algorithm for Multiplication
[0067] The multiplication of a positive value with a positive value
will result in a correct product when the sum of the significant
bits in T and S prior to the execution of this pseudo-code is less
than or equal to 16 bits. And the multiplication of a positive
value with a negative value will result in a correct product when
the sum of the significant bits in T and S prior to the execution
of the pseudo-code is less than or equal to 17 bits. Note that S
should contain the two's complement of the desired negative value
in S prior to the execution of this pseudo code. [0068] 1. If the
desired multiplication is of a positive value with a positive
value. [0069] 1a. Right justify t in the n bit field width of T.
[0070] 1a1. Fill all leading bits in T after the MSB of t with
zeros. The number of leading bits to fill should be exactly
n-n.sub.t. [0071] 1b. Justify s in the n bit field width of S so
that the LSB of s is located one bit higher than the MSB of t in T.
[0072] 1b1. Fill all leading and trailing bits in S with zeros. The
number of bits to fill should be exactly n-n.sub.s. [0073] 1c.
Perform the multiplication. [0074] 1c1. Complete a for-loop
indexing from 1 to n.sub.t. [0075] 1c1a. Execute the +* pseudo-code
as described for the general case above. [0076] 2. If the desired
multiplication is of a positive value with a negative value. [0077]
2a. Right justify t in the n bit field width of T. [0078] 2a1. Fill
all leading bits in T after the MSB of t with zeros. The number of
leading bits to fill should be exactly n-n.sub.t. [0079] 2b.
Perform the two's complement of the value s in S. [0080] 2b1. Bit
shift the value s in S towards the HB of S by the number of
significant bits n.sub.t. [0081] 2c. Perform the multiplication.
[0082] 2c1. Complete a for-loop indexing from 1 to n.sub.t. [0083]
2c1a. Execute the +* pseudo-code as described for the general case
above. [0084] 3. If the desired multiplication is of a negative
value with a negative value. [0085] 3a. Perform the two's
complement of the value t in T. [0086] 3b. Perform the two's
complement of the value s in S. [0087] 3b. Execute 1a-1c.
[0088] Of course, the multiplication of a negative value with a
positive value is the same as 2. (above) for multiplication, as
long as the negative value is in T and the positive value in S.
FIG. 8 is a flow chart of the inventive shift-add based
multiplication process 200 in accord with the present invention. In
a step 202 the shift-add based multiplication process 200 starts or
is invoked. In a step 204 a first value is arranged in a first
memory location, i.e., in the right justified manner described in
1. (above) if T is the first memory location. In a step 206 a
second value is arranged in a second memory location, i.e., in the
left justified manner described in 2. (above) for multiplication if
S is the second memory location. [Those skilled in the programming
arts will readily appreciate that alternate programmatic control
mechanisms than the following count-compare-work-decrement approach
can be used.] In a step 208 the number of iterations of the +*
op-code is determined. Essentially, this number needs to equal the
number of significant bits in the first value (in T). In a step 210
whether all needed iterations of the +* op-code have been performed
is determined. If not, in a step 212 an iteration of the +* op-code
is performed and in a step 214 the count still needed is
decremented. Alternately, if step 210 determines that all needed
iterations of the +* op-code have been performed, in a step 216 the
product of the first and second values is now in the first memory
(i.e., in T).
[0089] While various embodiments have been described above, it
should be understood that they have been presented by way of
example only, and that the breadth and scope of the invention
should not be limited by any of the above described exemplary
embodiments, but should instead be defined only in accordance with
the following claims and their equivalents.
* * * * *