Vivante Corporation

Patent Trials and Appeals Board

May 18, 2021

2020001452 (P.T.A.B. May. 18, 2021)

UNITED STATES PATENT AND TRADEMARK OFFICE
UNITED STATES DEPARTMENT OF COMMERCE
United States Patent and Trademark Office
Address: COMMISSIONER FOR PATENTS
P.O. Box 1450
Alexandria, Virginia 22313-1450
www.uspto.gov
APPLICATION NO. FILING DATE FIRST NAMED INVENTOR ATTORNEY DOCKET NO. CONFIRMATION NO.
15/422,862 02/02/2017 Lefan Zhong GQLA-03600 7564
34051 7590 05/18/2021
Stevens Law Group
1754 Technology Dr. Ste 226
San Jose, CA 95110
EXAMINER
LAROCQUE, EMILY E
ART UNIT PAPER NUMBER
2182
NOTIFICATION DATE DELIVERY MODE
05/18/2021 ELECTRONIC
Please find below and/or attached an Office communication concerning this application or proceeding.
The time period for reply, if any, is set in the attached communication.
Notice of the Office communication was sent electronically on above-indicated "Notification Date" to the
following e-mail address(es):
uspto@stevenslawgroup.com
PTOL-90A (Rev. 04/07)
UNITED STATES PATENT AND TRADEMARK OFFICE
____________

BEFORE THE PATENT TRIAL AND APPEAL BOARD
____________

Ex parte LEFAN ZHONG and ZHIWEI CAO
____________

Appeal 2020-001452
Application 15/422,862
Technology Center 2100
____________

Before ANTON W. FETTING, DEBRA K. STEPHENS, and
JAMES P. CALVE, Administrative Patent Judges.

FETTING, Administrative Patent Judge.

DECISION ON APPEAL
STATEMENT OF THE CASE1
Lefan Zhong and Zhiwei Cao (Appellant2) seeks review under
35 U.S.C. § 134(a) of a final rejection of claims 1–20, the only claims
pending in the application on appeal. We have jurisdiction over the appeal
pursuant to 35 U.S.C. § 6(b).

1 Our decision will make reference to the Appellant’s Appeal Brief (“Appeal
Br.,” filed July 9, 2019) and Reply Brief (“Reply Br.,” filed December 16,
2019), and the Examiner’s Answer (“Ans.,” mailed October 23, 2019), and
Final Action (“Final Act.,” mailed January 11, 2019).
2 We use the word “Appellant” to refer to “applicant” as defined in
37 C.F.R. § 1.42. Appellant identifies the real party in interest as Vivante
Corporation (Appeal Br. 3).

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The Appellant invented computational functions for graphics
processor chips. Specification para. 2.
An understanding of the invention can be derived from a reading of
exemplary claim 1, which is reproduced below (bracketed matter and some
paragraphing added).
1. A method for calculating X^Y comprising3:
(i) calculating, by an electronic device, a first transcendental
function taking as an input a function of X, the transcendental
function outputting M1H, M1L and M2, wherein M2 has a first
precision and a first sum of M1H and M1L has a second
precision greater than the first precision;
(ii) calculating, by the electronic device, a second sum of a
product of M1H and M2 and a product of M1L and M2,
wherein KH is a function of a high significance portion of the
second sum and KL is a function of a low significance portion
of the second sum;
(iii) calculating, by the electronic device, a product of (a) a
function of Y and (b) both KH and KL to obtain a high
significance output TH and low significance output TL;
(iv) calculating, by the electronic device, a second
transcendental function according to a function of TH and TL to
obtain an output that is an estimation of X^Y.

Claims 1–20 stand rejected under 35 U.S.C. § 101 as directed to a
judicial exception without significantly more.

3 “^” is a generic programming language exponentiation operator. See
Specification 8 referring to EXP or exponentiation. Thus X^Y is another
way of expressing XY.
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ISSUES
The issues of eligible subject matter turn primarily on whether the
claims recite more than abstract conceptual advice of results desired.4
ANALYSIS
Initially, as a matter of claim construction, we note that representative
claim 1 recites various variables, X, Y, M1H, M1L, M2, KH, KL, TH, and
TL. None of these is lexicographically defined in the Specification.
The preamble recites a function X^Y. Step i recites input X and
outputting M1H, M1L and M2, wherein M2 has a first precision and a first
sum of M1H and M1L has a second precision greater than the first precision.
Step ii recites computing a sum of a product of M1H and M2 and a product
of M1L and M2, wherein KH is a function of a high significance portion of
the second sum and KL is a function of a low significance portion of the
second sum. Step iii recites computing a product of a function of Y and both
KH and KL to obtain a high significance output TH and low significance
output TL. Step iv recites computing transcendental function according to a
function of TH and TL to obtain an output that is an estimate of X^Y.
Thus, X and Y are input parameters, and the remaining variables are
mathematical results derived from X and Y. The steps do not recite a
relationship between the values of M1H, M1L, and M2, only that they are all
derived from X and that the sum of M1H and M1L, whatever they are, has a
precision greater than that of M2. The steps further recite that KH and KL
are each some unrecited function of some high and low significance portion
of a sum derived from the products of M1H and M2 and M1L and M2. The

4 A rejection under 35 U.S.C. 112(b) (Final Action 5) was withdrawn.
Advisory Act. mailed April 26, 2019.
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steps additionally recite that TH and TL are high and low significance
outputs respectively derived from a product of some unrecited function of Y,
along with KH and KL. No relationship between TH and TL is recited other
than that they are both being derived from such a computation. Claim 1
recites that the output is that of a transcendental function having TH and TL
as inputs.
The only variables recited as being a high and a low significance
portion of the same value are KH and KL. Even here, the steps only recite
being of high and low significance, not having any particular data
representation or being derived from some data representation. KH and KL
are both recited as being mathematically rather than technologically derived.
Claim 1 does not recite bits, digits, or other computer representations of
values. All of the steps recite mathematical functions and none recite
computer data parsing or splitting operations. Therefore, none of the
variables are construed as being some particular set of bits in computer
representations of those variables. The variables, other than inputs X and Y,
are thus construed as being some intermediate results of the recited steps,
each derived by the mathematical functions recited in the steps.
STEP 15
Claim 1, as a method claim, nominally recites one of the enumerated
categories of eligible subject matter in 35 U.S.C. § 101. The issue before us
is whether it is directed to a judicial exception without significantly more.

5 For continuity of analysis, we adopt the steps nomenclature from 2019
Revised Patent Subject Matter Eligibility Guidance, 84 Fed. Reg. 50 (Jan. 7,
2019) (“Revised Guidance”).
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STEP 2

The Supreme Court
set forth a framework for distinguishing patents that claim laws
of nature, natural phenomena, and abstract ideas from those that
claim patent-eligible applications of those concepts. First, . . .
determine whether the claims at issue are directed to one of those
patent-ineligible concepts. If so, we then ask, “[w]hat else is
there in the claims before us? To answer that question, . . .
consider the elements of each claim both individually and “as an
ordered combination” to determine whether the additional
elements “transform the nature of the claim” into a patent-
eligible application. [The Court] described step two of this
analysis as a search for an “‘inventive concept’”—i.e., an
element or combination of elements that is “sufficient to ensure
that the patent in practice amounts to significantly more than a
patent upon the [ineligible concept] itself.”
Alice Corp. v. CLS Bank Int’l, 573 U.S. 208, 217–18 (2014) (citations
omitted) (citing Mayo Collaborative Servs. v. Prometheus Labs, Inc.,
566 U.S. 66 (2012)). To perform this test, we must first determine what the
claims are directed to. This begins by determining whether the claims recite
one of the judicial exceptions (a law of nature, a natural phenomenon, or an
abstract idea). Then, if the claims recite a judicial exception, determining
whether the claims at issue are directed to the recited judicial exception, or
whether the recited judicial exception is integrated into a practical
application of that exception, i.e., that the claims “apply, rely on, or use the
judicial exception in a manner that imposes a meaningful limit on the
judicial exception, such that the claim is more than a drafting effort designed
to monopolize the judicial exception.” Revised Guidance, 84 Fed. Reg. at
54. If the claims are directed to a judicial exception, then finally
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determining whether the claims provide an inventive concept because the
additional elements recited in the claims provide significantly more than the
recited judicial exception.
STEP 2A Prong 1
At a high level, and for our preliminary analysis, we note that method
claim 1 recites calculating a transcendental function, a sum and product, and
another product and transcendental function. Calculating transcendental
functions, products and sums are mathematical analysis. Thus, claim 1
recites analyzing data. None of the limitations recites technological
implementation details for any of these steps, but instead recite only results
desired by any and all possible means.
From this we see that claim 1 does not recite the judicial exceptions of
either natural phenomena or laws of nature.
Under Supreme Court precedent, claims directed purely to an abstract
idea are patent in-eligible. As set forth in the Revised Guidance, which
extracts and synthesizes key concepts identified by the courts, abstract ideas
include (1) mathematical concepts6, (2) certain methods of organizing

6 See, e.g., Gottschalk v. Benson, 409 U.S. 63, 71–72 (1972); Bilski v.
Kappos, 561 U.S. 593, 611 (2010); Mackay Radio & Telegraph Co. v. Radio
Corp. of Am., 306 U.S. 86, 94 (1939); SAP America, Inc. v. InvestPic, LLC,
898 F.3d 1161, 1163 (Fed. Cir. 2018).
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human activity7, and (3) mental processes8. Among those certain methods
of organizing human activity listed in the Revised Guidance are
mathematical concepts. Like those concepts, claim 1 recites the concept of
mathematically computing an estimate. Specifically, claim 1 recites
operations that would ordinarily take place in advising one to compute an
estimate of exponentiation from transcendental function, sum, and product
mathematical calculations. The advice to compute an estimate of
exponentiation from transcendental function, sum, and product mathematical
calculations involves calculating a transcendental function, which is a
mathematical algorithm, and calculating a sum of a product, which is an act
ordinarily performed in a mathematical algorithm. For example, claim 1
recites “calculating . . . a first transcendental function,” which is an activity
that would take place whenever one is using transcendental functions in a
mathematical algorithm. Similarly, claim 1 recites “calculating . . . a second
sum of a product,” which is also characteristic of mathematical algorithms.
The Examiner determines the claims to be directed to calculating a
value of X raised to the power of Y. Final Act. 6. The preamble to claim 1
recites that it is a method for calculating X^Y (the exponentiation function).
The steps in claim 1 result in mathematically computing an estimate by
computing an estimate of exponentiation from transcendental function, sum,

7 See, e.g., Bilski, 561 U.S. at 628; Alice, 573 U.S. at 219–20; Ultramercial,
Inc. v. Hulu, LLC, 772 F.3d 709, 715 (Fed Cir. 2014); Smart Sys.
Innovations, LLC v. Chicago Transit Auth., 873 F.3d 1364, 1383 (Fed. Cir.
2017); In re Marco Guldenaar Holding B.V., 911 F.3d 1157, 1160–61 (Fed.
Cir. 2018).
8 See, e.g., Benson, 409 U.S. at 67; CyberSource Corp. v. Retail Decisions,
Inc., 654 F.3d 1366, 1371–72 (Fed. Cir. 2011); Intellectual Ventures I LLC
v. Symantec Corp., 838 F.3d 1307, 1318 (Fed. Cir. 2016).
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and product mathematical calculations absent any technological mechanism
other than a conventional computer for doing so.
As to the specific limitations, limitations i–iv recite computing
mathematical functions, which advise one to apply generic functions to get
to these results. The limitations thus recite advice for computing an estimate
of exponentiation from transcendental function, sum, and product
mathematical calculations. To advocate computing an estimate of
exponentiation from transcendental function, sum, and product mathematical
calculations is conceptual advice for results desired and not technological
operations.
The Specification at paragraph 2 describes the invention as relating to
computational functions for graphics processor chips. Thus, all this intrinsic
evidence shows that claim 1 recites mathematically computing an estimate.
This is consistent with the Examiner’s determination.
This in turn is an example of mathematical algorithms as a
mathematical concept because mathematical algorithms are expressions of
mathematical concepts. The concept of mathematically computing an
estimate by computing an estimate of exponentiation from transcendental
function, sum, and product mathematical calculations is one idea for such an
algorithm. The steps recited in claim 1 are part of how this might
conceptually be premised.
Our reviewing court has found claims to be directed to abstract ideas
when they recited similar subject matter. See Benson, above.
Alternatively, this is an example of concepts performed in the human
mind as mental processes because the steps of analyzing data mimic human
thought processes of observation, evaluation, judgment, and opinion,
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perhaps with paper and pencil, where the data interpretation is perceptible
only in the human mind. See In re TLI Commc’ns LLC Patent Litig., 823
F.3d 607, 611 (Fed. Cir. 2016); FairWarning IP, LLC v. Iatric Sys., Inc., 839
F.3d 1089, 1093–94 (Fed. Cir. 2016). Claim 1, unlike the claims found non-
abstract in prior cases, uses generic computer technology to perform data
analysis and does not recite an improvement to a particular computer
technology. See, e.g., McRO, Inc. v. Bandai Namco Games Am. Inc., 837
F.3d 1299, 1314–15 (Fed. Cir. 2016) (finding claims not abstract because
they “focused on a specific asserted improvement in computer animation”).
As such, claim 1 recites analyzing data, and not a technological
implementation or application of that idea.
From this we conclude that, at least to this degree, claim 1 recites
mathematically computing an estimate by computing an estimate of
exponentiation from transcendental function, sum, and product mathematical
calculations, which is a mathematical algorithm, one of the mathematical
concepts identified in the Revised Guidance, and, thus, recites an abstract
idea.
STEP 2A Prong 2
The next issue is whether claim 1 not only recites, but is more
precisely directed to this concept itself or whether it is instead directed to
some technological implementation or application of, or improvement to,
this concept i.e. integrated into a practical application.9
At the same time, we tread carefully in construing this
exclusionary principle lest it swallow all of patent law. At some
level, “all inventions ... embody, use, reflect, rest upon, or apply

9 See, e.g., Alice, 573 U.S. at 223, discussing Diamond v. Diehr, 450 U.S.
175 (1981).
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laws of nature, natural phenomena, or abstract ideas.” Thus, an
invention is not rendered ineligible for patent simply because it
involves an abstract concept. “[A]pplication[s]” of such
concepts “ ‘to a new and useful end,’ ” we have said, remain
eligible for patent protection. Accordingly, in applying the § 101
exception, we must distinguish between patents that claim the “
‘buildin[g] block[s]’ ” of human ingenuity and those that
integrate the building blocks into something more.
Alice, 573 U.S. at 217 (citations omitted).
Taking the claim elements separately, the operation performed by the
computer at each step of the process is expressed purely in terms of results,
devoid of implementation details. Steps i–iv are pure mathematical
algorithms. Limitations describing the nature of the data do not alter this.
These steps recite generic computer processing expressed in terms of results
desired by any and all possible means and so present no more than
conceptual advice. All purported inventive aspects reside in how the data is
interpreted and the results desired, and not in how the process physically
enforces such a data interpretation or in how the processing technologically
achieves those results.
Viewed as a whole, Appellant’s claim 1 simply recites the concept of
mathematically computing an estimate by computing an estimate of
exponentiation from transcendental function, sum, and product mathematical
calculations as performed by a generic computer. This is no more than
conceptual advice on the parameters for this concept and the generic
computer processes necessary to process those parameters, and do not recite
any particular implementation.
Claim 1 does not, for example, purport to improve the functioning of
the computer itself. Nor does it effect an improvement in any other
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technology or technical field. The 19+ pages of Specification do not bulge
with disclosure, but only spell out different generic equipment10 and
parameters that might be applied using this concept and the particular steps
such conventional processing would entail based on the concept of
mathematically computing an estimate by computing an estimate of
exponentiation from transcendental function, sum, and product mathematical
calculations under different scenarios. They do not describe any particular
improvement in the manner a computer functions. Instead, claim 1 at issue
amounts to nothing significantly more than an instruction to apply
mathematically computing an estimate by computing an estimate of
exponentiation from transcendental function, sum, and product mathematical
calculations using some unspecified, generic computer. Under our
precedents, that is not enough to transform an abstract idea into a patent-
eligible invention. See Alice, 573 U.S. at 225–26.
Although, as construed above, some of the variables have differing
levels of precision, we determined above that none of the claims recite that
these levels of precision are based on digital representations or numbers of
bits in such representations. The variables are all expressed as the results of
mathematical operations, and not of technological operations. Thus, none of
the steps recite doing something technological to overcome digital
representation limitations. While we recognize that Specification paragraphs

10 The Specification describes using processors or controllers that execute
instructions. Spec. para. 20. The Specification also describes using a
hardware pipeline (Specification paragraph 28 et al), but this in an
exemplary embodiment. Computer pipelines, having been used for over 40–
50 years, are generic and conventional. No hardware implementations for
such pipelines are described. None of the claims recite using pipelines.
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37–47 describe a more detailed process for performing the claimed
estimation function, Appellant has chosen not to incorporate those additional
details in claim 1. We do not import the Specification into the claim
limitations. “Ericsson misstates the role of the specification, which ‘cannot
be used to import details from the specification if those details are not
claimed.’ Rather, ‘any reliance on the specification in the § 101 analysis
must always yield to the claim language.’” Ericsson Inc. v. TCL Commc’n
Tech. Holdings Ltd., 955 F.3d 1317, 1328–29 (Fed. Cir. 2020)(citations
omitted).
None of the limitations reflects an improvement in the functioning of
a computer, or an improvement to other technology or technical field,
applies or uses a judicial exception to effect a particular treatment or
prophylaxis for a disease or medical condition, implements a judicial
exception with, or uses a judicial exception in conjunction with, a particular
machine or manufacture that is integral to the claim, effects a transformation
or reduction of a particular article to a different state or thing, or applies or
uses the judicial exception in some other meaningful way beyond generally
linking the use of the judicial exception to a particular technological
environment, such that the claim as a whole is more than a drafting effort
designed to monopolize the exception.
We conclude that claim 1 is directed to achieving the result of
mathematically computing an estimate by advising one to compute an
estimate of exponentiation from transcendental function, sum, and product
mathematical calculations, as distinguished from a technological
improvement for achieving or applying that result. This amounts to a
mathematical algorithm, which falls within mathematical concepts that
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constitute abstract ideas. The claim does not integrate the judicial exception
into a practical application.
STEP 2B
The next issue is whether claim 1 provides an inventive concept
because the additional elements recited in the claim provide significantly
more than the recited judicial exception.
The introduction of a computer into the claims does not generally alter
the analysis at Mayo step two.
the mere recitation of a generic computer cannot transform a
patent-ineligible abstract idea into a patent-eligible invention.
Stating an abstract idea “while adding the words ‘apply it’” is not
enough for patent eligibility. Nor is limiting the use of an
abstract idea “‘to a particular technological environment.’”
Stating an abstract idea while adding the words “apply it with a
computer” simply combines those two steps, with the same
deficient result. Thus, if a patent’s recitation of a computer
amounts to a mere instruction to “implement[t]” an abstract idea
“on . . . a computer,” that addition cannot impart patent
eligibility. This conclusion accords with the preemption concern
that undergirds our § 101 jurisprudence. Given the ubiquity of
computers, wholly generic computer implementation is not
generally the sort of “additional feature[e]” that provides any
“practical assurance that the process is more than a drafting effort
designed to monopolize the [abstract idea] itself.”
Alice, 573 U.S. at 223–24 (citations omitted).
“[T]he relevant question is whether the claims here do more than
simply instruct the practitioner to implement the abstract idea . . . on a
generic computer.” Alice, 573 U.S. at 225. They do not.
Taking the claim elements separately, the function performed by the
computer at each step of the process is purely conventional. Using a
computer for analyzing data amounts to electronic data query and retrieval—
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one of the most basic functions of a computer. All of these computer
functions are generic, routine, conventional computer activities that are
performed only for their conventional uses. See Elec. Power Grp. LLC v.
Alstom S.A., 830 F.3d 1350, 1353 (Fed. Cir. 2016). See also In re Katz
Interactive Call Processing Patent Litig., 639 F.3d 1303, 1316 (Fed. Cir.
2011) (“Absent a possible narrower construction of the terms ‘processing,’
‘receiving,’ and ‘storing,’ . . . those functions can be achieved by any
general purpose computer without special programming”). None of these
activities is used in some unconventional manner nor does any produce some
unexpected result. Appellant does not contend it invented any of these
activities. In short, each step does no more than require a generic computer
to perform generic computer functions. As to the data operated upon, “even
if a process of collecting and analyzing information is ‘limited to particular
content’ or a particular ‘source,’ that limitation does not make the collection
and analysis other than abstract.” SAP America, Inc. v. InvestPic LLC, 898
F.3d 1161, 1168 (Fed. Cir. 2018).
Considered as an ordered combination, the computer components of
Appellant’s claim 1 add nothing that is not already present when the steps
are considered separately. The sequence of data analysis is equally generic
and conventional. See Ultramercial, Inc. v. Hulu, LLC, 772 F.3d 709, 715
(Fed. Cir. 2014) (sequence of receiving, selecting, offering for exchange,
display, allowing access, and receiving payment recited an abstraction),
Inventor Holdings, LLC v. Bed Bath & Beyond, Inc., 876 F.3d 1372, 1378
(Fed. Cir. 2017) (sequence of data retrieval, analysis, modification,
generation, display, and transmission), Two-Way Media Ltd. v. Comcast
Cable Commc’ns, LLC, 874 F.3d 1329, 1339 (Fed. Cir. 2017) (sequence of
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processing, routing, controlling, and monitoring). The ordering of the steps
is therefore ordinary and conventional.
We conclude that claim 1 does not provide an inventive concept
because the additional elements recited in the claim do not provide
significantly more than the recited judicial exception.
REMAINING CLAIMS
Claim 1 is representative. The remaining method claims merely
describe process parameters. Claims 8, 9, and 17 are the only claims that
refer to bits, but only in the description of precision. We conclude that the
method claims at issue are directed to a patent-ineligible concept itself, and
not to the practical application of that concept.
As to the structural claims, they
are no different from the method claims in substance. The
method claims recite the abstract idea implemented on a generic
computer; the system claims recite a handful of generic computer
components configured to implement the same idea. This Court
has long “warn[ed] ... against” interpreting § 101“in ways that
make patent eligibility ‘depend simply on the draftsman’s art.’
Alice, 573 U.S. at 226. As a corollary, the claims are not directed to any
particular machine.
LEGAL CONCLUSION
From these determinations, we further determine that the claims do
not recite an improvement to the functioning of the computer itself or to any
other technology or technical field, a particular machine, a particular
transformation, or other meaningful limitations. From this, we conclude the
claims are directed to the judicial exception of the abstract idea of
mathematical concepts as exemplified by the mathematical algorithm of
mathematically computing an estimate by advising one to compute an
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estimate of exponentiation from transcendental function, sum, and product
mathematical calculations, without significantly more.
APPELLANT’S ARGUMENTS
As to Appellant’s Appeal Brief arguments, we adopt the Examiner’s
determinations and analysis from Final Action 5–8 and Answer 3–4 and
reach similar legal conclusions. We now turn to the Reply Brief.
We are not persuaded by Appellant’s argument that “[s]teps (i)
through (iv) recite an approach for calculating of X^Y. These steps are
performed by an electronic device and are not inherently part of the
mathematical relationship of X^Y. This mathematical relationship is not
simply calculated by reciting “apply it” to an electronic device.” Reply Br.
1. An approach is the epitome of an abstract concept. As the Supreme
Court held in Benson and Alice above, performing steps on an electronic
device is insufficient to confer eligibility. The argument as to inherency is
irrelevant as no such determination is made. Rather, the steps as recited are
themselves inherently mathematical algorithms. It is the claim that labels
the result of these steps as an estimate of exponentiation.
We are not persuaded by Appellant’s argument that
it is not inherent in X^Y that intermediate outputs are split into
high significance and low significance portions as recited in steps
(i) through (iii). This is a hardware specific innovation: it
requires and exploits a digital representation of values that can
be separated into high and low significance digits, which is not
part of the abstract mathematical definition of the function X^Y.
It is likewise not inherent in the definition of X^Y that a first
transcendental function is calculated and then its high and low
significant portions (MIH, M1L) processed as recited according
to steps (ii) through (iv) in order to calculate a second
transcendental function that gives X^Y.
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Reply Br. 2. Again, the determination is not that the steps are inherent in an
exponentiation algorithm. Rather, the steps are inherently mathematical
algorithms that when performed achieve some result. The claims label this
result as an estimate of an exponentiation algorithm result.
The arguments as to being hardware specific is also not commensurate
with the scope of the claims, which recite no particular hardware. The
arguments about reliance on digital representation are not commensurate
with the independent claims, which do not recite such reliance. As to the
dependent claims reciting precision, they refer to portions rather than digits,
and even then only refer to mathematically dividing operand values into two
portions that when added together get back to the original value. As such,
these recitations refer to additional mathematical calculations rather than
technological operations.
We are not persuaded by Appellant’s argument that “claim 1 recites a
method of computing X^Y on an electronic device that improves the
efficiency of the calculation in ways that go far beyond taking a
conventional processing device and instructing it to calculate X^Y in a
conventional manner.” Reply Br. 2. Appellant has not shown that there is
anything unconventional about computing transcendental functions, sums,
and products. Such computations have been well trodden by freshmen
science and engineering majors at least in calculus courses for decades.
Nothing “transforms” the abstract idea of encoding and decoding
into patent-eligible subject matter. Nor does the presence of a
mathematical formula dictate otherwise. Claims that are directed
to a non-abstract idea are not rendered abstract simply because
they use a mathematical formula. But the converse is also true:
A claim directed to an abstract idea does not automatically
become eligible merely by adding a mathematical formula.
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RecogniCorp, LLC v. Nintendo Co., Ltd., 855 F.3d 1322, 1328 (2017). Also
see In re Bd. of Trustees of Leland Stanford Junior Univ., 991 F.3d 1245,
1251 (Fed. Cir. 2021) (“The different use of a mathematical calculation,
even one that yields different or better results, does not render patent eligible
subject matter”).
We are not persuaded by Appellant’s argument that
claim 1 recites digital transformations that are specific to an
electronic device and are not inherent in the mathematical
relationship being calculated. This is not merely “better math.”
A mathematical relationship between numbers is independent of
how the numbers are stored or represented and claim 1 does more
than simply recite abstract mathematical operations on numbers
to obtain a result. Instead claim 1 recites both mathematical
operations such as the first and second transcendental functions
but also requires the separation of intermediate values into high
significance and low significance portions and separate
processing of these portions. This is specific to how a value is
represented and processed within the electronic device as
opposed to the mere mathematical relationship between
numbers.
Replay Br. 3. Claim 1 recites no digital transformations, only mathematical
calculations. Claim 1 also recites no manner of storage or representation and
no separation into high and low significance portions other than perhaps that
of KH and KL, but even there the claim recites two mathematical results
rather than separation of a single value.

CONCLUSIONS OF LAW
The rejection of claims 1–20 under 35 U.S.C. § 101 as directed to a
judicial exception without significantly more is proper.
Appeal 2020-001452
Application 15/422,862

19

CONCLUSION
The rejection of claims 1–20 is affirmed.
In summary:
Claims
Rejected
35 U.S.C.
§
Reference(s)/Basis Affirmed Reversed
1–20 101 Eligibility 1–20

No time period for taking any subsequent action in connection with
this appeal may be extended under 37 C.F.R. § 1.136(a). See 37 C.F.R.
§ 1.136(a)(1)(iv) (2011).

AFFIRMED