dissenting.
With all due deference, I cannot agree that the presently claimed invention falls within any class of judicially established exceptions to § 101.1
General
The court is unanimous in holding erroneous the board’s rejection, described in the board’s brief opinion as based on the sole ground that the claimed process “falls within the purview” of Benson because “it can only be performed by the computer,” and because the claims “pre-empt whatever is carried out by the computer, be it characterized as algorithm, formula, machine process or program or the like,” and because the board knew “no way of operating a digital computer” except “by some form of programming.”
In the interest of judicial economy, the court has elected not to remand the case to the board so that it might cure its inexplicable failure to conduct or supply an analysis of the claims.
The advent of a wholly new technology confronts the Patent and Trademark Office (PTO) with administrative problems in performing its vital service to the public interest in encouraging true progress of the useful arts. The solution to administrative problems does not lie, however, in so interpreting the law as to reduce an administrative burden. Avoiding a petition to Congress for increased funds or legislative relief, using § 101 to exclude new technology, presenting to the Supreme Court patentability issues not considered in the PTO or in this court, and employing phrases from the Court’s opinions as rejection rubrics under § 101 in subsequent cases, is an approach long overdue for abandonment. Sadly, the exclusionary approach is extant in the board’s treatment of the present appeal.
The Board
The board decision is predicated on the notion that no process performed by use of a computer can be statutory. That approach is repeated in the solicitor’s brief:
While others may have doubted that the broad proscription in the concluding paragraphs of Benson is applicable, without exception[,] to computer programming cases, no room for doubt can exist any longer in view of the decision in Flook [Parker v. Flook, 437 U.S. 584, 98 S.Ct. 2522, 57 L.Ed.2d 451, 198 USPQ 193 (1978)]. * * * [T]he mandate of the court is that it will not “extend patent *43rights into areas wholly unforeseen by Congress,” and that claims directed to computer programming fall within this proscription.
A process invention cannot, however, be declared nonstatutory on the sole basis of the means employed in carrying out the process.
This court has patiently explained the impropriety of reading Benson so broadly as to exclude all processes performed with a computer. See, e. g., In re Freeman, 573 F.2d 1237, 1244-45, 197 USPQ 464, 470 (Cust. & Pat.App.1978); In re de Castelet, 562 F.2d 1236, 1240-43, 195 USPQ 439, 443-45 (Cust. & Pat.App.1977); In re Chatfield, 545 F.2d 152, 155-57, 191 USPQ 730, 733-34 (Cust. & Pat.App.1976), cert. denied, 434 U.S. 875, 98 S.Ct. 226, 54 L.Ed.2d 155, 195 USPQ 465 (1977).
Indeed, the Supreme Court attempted, in unequivocal language, to forestall such broad reading of its opinion in Benson, inserting an express caveat: “It is said that the decision precludes a patent for any program servicing a computer. We do not so hold.” 409 U.S. at 71, 93 S.Ct. at 257, 175 USPQ at 676.
In Flook, the Court again declined to declare all process inventions involving “computer programs” nonstatutory per se. It characterized its holding in Benson : “In Gottschalk v. Benson, 409 U.S. 63, 93 S.Ct. 253, 34 L.Ed.2d 273, we held that the discovery of a novel and useful mathematical formula may not be patented,” 437 U.S. at 585, 98 S.Ct. at 2523, 198 USPQ at 195 (emphasis added). It stated, “[w]e use the word ‘algorithm’ in this case, as we did in Gottschalk v. Benson, 409 U.S. 63, 65, 93 S.Ct. 253, 34 L.Ed.2d 273, to mean ‘[a] procedure for solving a given type of mathematical problem * * ” 437 U.S. at 585 n.1, 98 S.Ct. at 2523 n.1, 198 USPQ at 195 n.1 (emphasis added). It summarized its holding as, “Very simply, our holding today is that a claim for an improved method of calculation, even when tied to a specific end use, is unpatentable subject matter under § 101.” 437 U.S. at 595 n.18, 98 S.Ct. at 2529 n.18, 198 USPQ at 199 n.18 (emphasis added). It added:
Neither the dearth of precedent, nor this decision, should therefore be interpreted as reflecting a judgment that patent protection of certain novel and useful computer programs will not promote the progress of science and the useful arts, or that such protection is undesirable as a matter of policy. Difficult questions of policy concerning the kinds of programs that may be appropriate for patent protection and the form and duration of such protection can be answered by Congress on the basis of current empirical data not equally available to this tribunal.
437 U.S. at 595, 98 S.Ct. at 2528, 198 USPQ at 199 — 20 (emphasis added and footnotes omitted). Thus, until Congress decides that some kinds of programs are not statutory, it remains the duty of the PTO and the courts to carefully analyze the claimed inventions presented, and to determine whether each falls within or without the judicially established exceptions to § 101.
The solicitor quotes the Court’s reference in Flook to “areas wholly unforeseen by Congress.” That reference, however, must be read in the light of the facts then before the Court.2 In both Benson and Flook, the Court was dealing with claims it viewed as drawn to mathematical formulae. In Benson it referred to the necessity for Congress to speak if “these” programs are to be statutory. In Flook it spoke of the need for Congress to determine what “kinds” of programs may be patented. The Court no*44where described the invention in Flook as a “program,” but merely responded to importunings of amici who sought a judicial pronouncement that “computer programs” were per se statutory or nonstatutory. It is just such pronouncement the Court refused to make.3 Hence it is improper to interpret Flook as holding nonstatutory all claims describable in the solicitor’s (not the Court’s) words as, “directed to computer programming.” In all events, the words of the Court in Benson and Flook cannot be interpreted as condemning all claims to process inventions which are merely carried out by use of a computer. Congress and the courts having refrained from so directing, it should be manifest to all that “no basis exists for a moratorium on protection of inventions embodying or using computer programs.” In re de Castelet, supra, 562 F.2d at 1240, 195 USPQ at 443 (emphasis added).
The board’s inexplicably superficial consideration of the claims on appeal led it to find them preempting “whatever is carried out by the computer,” and because computers are operated by “programs,” the board held the invention nonstatutory on that ground alone. We explained our view of the error of that approach in a statement in In re Freeman, supra, reflecting the law applicable here:
Though the board gave no clear reasons for so concluding, its approach would appear to be that every implementation with a programmed computer equals “algorithm” in the Benson sense. If that rubric be law, every claimed method that can be so implemented would equal non-statutory subject matter under 35 U.S.C. § 101. That reasoning sweeps too wide and is without basis in law. * * *
As a bare minimum, application of Benson in a particular case requires a careful analysis of the claims, to determine whether, as in Benson, they recite a “procedure for solving a given type of mathematical problem.” [Gottschalk v. Benson,] 409 U.S. at 65, 93 S.Ct. 253, 175 USPQ at 674 (emphasis added).
573 F.2d at 1245, 197 USPQ at 470.
Mathematical Relationship
This is the first computer-related case in which this court has affirmed a rejection of claims not drawn in essence to a mathematical relationship.
In clarifying the distinction between statutory and nonstatutory subject matter in these types of cases, this court has recognized that “[t]he mathematical expression of scientific truth or principle is itself not patentable,” and has pointed out that the Supreme Court “viewed Benson’s claims as effectively claiming the ‘effect,’ principle, or law or force of nature (the algorithm) itself.” In re de Castelet, supra at 1243, 195 USPQ at 445. In Flook, supra, 437 U.S. at 589, 98 S.Ct. at 2525, 198 USPQ at 197, the Court said, “Reasoning that an algorithm, or mathematical formula, is like a law of nature, Benson applied the established rule that a law of nature cannot be the subject of a patent.” The import of that statement is that the meaning of “algorithm” is limited by its association with the “mathematical formula = law of nature” concept. Neither “algorithm” nor “mathematics” may alone serve as a label substitute for “nonstatutory.”
Nor, as above indicated, is the term “program” an acceptable substitute for “non-statutory.” Confusion may be avoided if it be realized that what is at issue is not the “program,” i. e., the software, but the process steps which the software directs the computer to perform.
The terms “mathematics” and “mathematical exercises”4 are so broad as to be *45applicable to any process in which numbers are involved. Not every process, however, in which the doer works with numbers should be declared nonstatutory on that ground alone. When the numbers involved satisfy a mathematical relationship, like the relationship defined in an equation, a formula, or a mathematical algorithm, and the invention is the mere plugging of numbers into that equation, formula, or algorithm, i. e., a solution technique or method of calculation, that invention has been judicially declared nonstatutory. When the numbers involved satisfy no mathematical relationship, and the invention merely employs numbers in the place of physical elements, that invention may, in my view, be statutory.
In In re Richman, 563 F.2d 1026, 1029, 195 USPQ 340, 343 (Cust. & Pat.App.1977), the nonstatutory process at issue was carefully described as “method of calculation] (utilizing mathematical formulae)” (emphasis added). Some, perhaps most, computer software merely directs the performance of nonstatutory mathematical exercises, as those in Riehman, Benson, and Flook were found to be. Other software, however, may be a means for directing the performance of clearly statutory process.5 Simply stated, the labeling approach risks freezing from the patent system disclosures of processes the claims to which, as here, are not in essence analogous to claims to mathematical formulae or laws of nature.
Efforts to follow precedent in “computer program” type cases require repeated wrestling with the interpretation and effect of such terms as “program,” “mathematical formula,” “algorithm,” “solution,” “equation,” and “calculation.” See, e. g., In re Toma, 575 F.2d 872, 197 USPQ 852 (Cust. & Pat.App.1978); In re Freeman, supra; In re Chatfield, supra. In Benson, some of those terms were used interchangeably. “Algorithm” was defined as “[a] procedure for solving a given type of mathematical problem.” 409 U.S. at 65, 93 S.Ct. at 254, 175 USPQ at 674 (emphasis added). The claimed process was variously described as “a method of programming a general purpose digital computer,” 409 U.S. at 65, 93 S.Ct. at 254, 175 USPQ at 674; “a generalized formulation for programs to solve mathematical problems of converting one form of numerical representation to another,” 409 U.S. at 65, 93 S.Ct. at 254, 175 USPQ at 674; and a “formula for converting BCD numerals to pure binary numerals,” 409 U.S. at 71, 93 S.Ct. at 257, 175 USPQ at 676. It was said that a patent containing Benson’s claims “would wholly pre-empt the mathematical formula and in practical effect would be a patent on the algorithm itself,” 409 U.S. at 72, 93 S.Ct. at 257, 175 USPQ at 676.
In Flook, Benson’s invention was characterized as “a novel and useful mathematical formula,” 437 U.S. at 585, 98 S.Ct. at 2523, 198 USPQ at 195, and the definition of “algorithm” in Benson was employed in identifying steps (2) and (3) of Flook’s claim 1 as an “algorithm” or “formula.” Id. The claimed invention in Flook was described as a “method for calculating alarm limit values,” 437 U.S. at 594, 98 S.Ct. at 2528, 198 USPQ at 199. In re Richman, supra, was quoted in the course of holding the invention in Flook nonstatutory, even if its formula’s “solution is for a specific purpose,” 437 U.S. at 595, 98 S.Ct. at 2528, 198 USPQ at 199.
In Benson, the claimed process presumed a fixed relationship between BCD numbers and pure binary numbers and included a series of manipulatory steps that, when practiced on the digits in a BCD number, converted that number to its pure binary equivalent. In In re de Castelet, supra, the *46claims recited a process for solving a set of mathematical equations to transform discrete coordinate points into a smooth curve. In In re Waldbaum, 559 F.2d 611, 194 USPQ 465 (Cust. & Pat.App.1977), the claimed process was a series of counting steps for determining the number of l’s in a binary data word. In In re Richman, supra, In re Christensen, 478 F.2d 1392, 178 USPQ 35 (Cust. & Pat.App.1973), In re Sarkar, supra note 2, and Flook, the claims were found to be directed essentially to the solution of mathematical equations and were not rendered statutory by the inclusion of data-gathering and post-solution steps dictated by the equations. In referring to the rule that the discovery of a law of nature cannot be patented, the Court in Flook said, “The underlying notion is that a scientific principle, such as that expressed in respondents’ algorithm, reveals a relationship that has always existed.” Parker v. Flook, supra, 437 U.S. at 593 n.15, 98 S.Ct. at 2527, n.15, 198 USPQ at 198 n.15.
In short, the foregoing cases dealt with process claims that, upon careful analysis, were determined to be directed to nothing more than a mathematical relationship between quantities, i. e., processes wherein input quantities are acted upon by a series of relationship-defining steps, expressed in mathematical symbols or in prose, to produce output quantities bearing the defined mathematical relationship to the input quantities.
Each so-called “computer program” case, like all cases turning on the nature of an invention, must be decided not on a rubric but on its own facts.6 In reviewing a rejection under § 101, the controlling facts must be developed from careful and detailed analysis of the invention as described and claimed. The Supreme Court and this court have made just such analyses in the “computer program” cases thus far presented.7 It is just such analysis that the PTO must make in each such case. That analysis includes a determination of the meaning of computer-world terms, and the role and effect of the elements or steps for which they stand, in the context of the invention as a whole. Justice requires that employment of labels, rubrics, and talismans, be eschewed.
It would ease the decisional burden, for example, to merely note that one step of the present process involves a transcendental equation, to cry “algorithm,” “mathematics,” or “method of calculation,” and to affirm the rejection on that talismanic basis. But, analysis discloses that the present process as a whole is fundamentally different from processes found nonstatutory in prior “computer program” cases.
The Present Invention 8
Rejections under §§ 102, 103 were overcome because, in Gelnovatch and Arell’s (Gelnovatch’s) process, a different subset of parameters is perturbed in each exploratory search. In prior processes, all parameters were perturbed in each exploratory search. Gelnovatch’s process decreases the error faster, thus requiring less computer time to execute. The pertinent reference of record is Murray-Lasso & Kozemchak, Microwave Circuit Design By Digital Computer, IEEE Transactions on Microwave Theory and Techniques, vol. MTT-17, No. 8, August 1969, at 514. The examiner withdrew re*47jections under §§ 102, 103, and 112. The examiner also withdrew a “mental process” rejection when “computer” and “automatically” were inserted in the claims, viewing those words as limiting the process to performance by computer. The board chose not to exercise its authority under PTO Rule 196(b) (37 CFR 1.196(b)) to reinstate the §§ 102, 103, 112 rejections, electing to treat performance by computer, the limitation that overcame those rejections, as the sole basis for its rejections.9
The determinative question under § 101 is, “What did Gelnovatch invent?” If the claimed process be the input of quantities bearing a mathematical relationship to output quantities, it falls within the judicially declared class of nonstatutory inventions. The process of Gelnovatch is not such.
In Gelnovatch’s process, a transcendental equation expresses a relationship between the output data produced and the desired microwave circuit response, but the claimed process is not directed to that relationship. Thus the present process is not one in which desired circuit response data (“input quantity”) is substituted for variables in a transcendental equation (“a series of relationship-defining steps expressed in mathematical symbols”), and the equation then solved for parameter values capable of producing the desired response (“output quantity”). To so characterize the present process would not only be inaccurate, but would attribute to the process a capability for the impossible, namely, the exact solution of a transcendental equation.
Gelnovatch’s claimed process is not directed to a relationship between quantities, there being no relationship whatsoever, even in theory, between his input data (arbitrarily estimated parameter values) and his output data (parameter values approaching a desired circuit response). The present process invention is best characterized as a systematic, exploratory, trial-and-error series of particular steps to produce parameter values capable of approximating a desired microwave circuit response.
The values produced by the present process are related to the desired microwave circuit response through the medium of a particular “law of nature,” i. e., a transcendental equation, but Gelnovatch is not claiming the equation itself. Nor is he claiming a formula, or mathematical algorithm, or calculation. Nor is he claiming anything describable as a law of nature. There being no preexisting relationship or natural law that correlates the input data and the output data, Gelnovatch’s process is the antithesis of a mathematical relationship or law of nature. It is more akin to the “bread-board” experimental method employed in the development of physical products.
Indeed, the present process is technically identical with a process in which large supplies of circuit elements were one-by-one physically connected into a circuit, additional elements were substituted and resubstituted, within specific and different element groups, until a circuit was created having the desired circuit response. Such a purely physical process might or might not be patentable; it would clearly be statutory. That Gelnovatch has replaced each physical circuit element with its numerical representation, and substituted numerical representations instead of substituting the physical elements themselves, does not change the fundamental nature of the process in this case, and does not in my view render it nonstatutory.
That the claimed process may use a transcendental equation in a process step does not alone render the claimed invention as a whole nonstatutory. In re Chatfield, supra, *48545 F.2d at 158-59, 191 USPQ at 736. “Yet it is equally clear that a process is not unpatentable [nonstatutory] simply because it contains a law of nature or a mathematical algorithm.” Parker v. Flook, supra, 437 U.S. at 590, 98 S.Ct. at 2526, 198 USPQ at 197.
I would reverse the rejection.
. The majority opinion refuses to limit “method of calculation” to the plugging of inputs into a formula to produce outputs because it finds no judicial precedent for that limitation. But precedent is not required. The majority opinion elsewhere correctly recognizes that appellants’ series of steps is a process “within § 101 unless ” (emphasis the majority’s) it falls within an exception. Requiring judicial precedent for new technology would limit the patent system to the crusty molds of the past, and would frustrate disclosure of technological advances into areas unforeseen.
. The reference to “areas wholly unforeseen” cannot be read literally, or in a vacuum. The Court was quoting from its opinion in Deep-south Packing Co. v. Laitram Corp., 406 U.S. 518, 92 S.Ct. 1700, 32 L.Ed.2d 273 (1972), which dealt with infringement, and was merely refusing to revise its earlier views. The Court could not have meant that no invention in a new technology can be considered statutory until Congress says it is. Congress is not prescient. Nor can it be expected to continuously amend the statute, in a fruitless effort to stay ahead of burgeoning technology. Congress has for years broadly provided for patenting of “any process” meeting all requirements of the statute, leaving to the courts the interpretation of that phrase. See In re Sarkar, 588 F.2d 1330, 200 USPQ 132 (Cust. & Pat.App.1978).
. The Court refused the same importunings in Dann v. Johnston, 425 U.S. 219, 220, 96 S.Ct. 1393, 1394, 47 L.Ed.2d 692, 189 USPQ 257, 258 (1976), saying “We find no need to treat that question in this case, however, because we conclude that in any event respondent’s system is unpatentable on grounds of obviousness.” It is at least incongruous for the PTO to argue that the Court made a pronouncement it has consistently and explicitly refused to make.
. The mathematical exercises referred to in Sarkar, supra note 2, are those expressible as equations, formulae, and mathematical algor*45ithms. Sarkar’s invention was found to be the provision of a formula, the substitution of values therein, and the making of formula-required calculations.
. Every process may be called a “program,” i. e., a series of steps. Both the series of steps performed by a computer, and the software directing those steps, have acquired the name “computer programs.” That fact alone, as indicated in the text, supra, does not warrant the view that no computer program can on analysis be shown to represent a statutory process. Some computer-performed processes may be statutory. Some may not.
. The same is true in considering the nature of an invention in the light of § 103. To hold unpatentable, for example, all “combinations of old elements” would totally defeat the constitutional-statutory scheme for promoting progress in the useful arts. Every invention is a combination of old elements. Some combinations of old elements are not patentable, e. g., Graham v. John Deere Co., 383 U.S. 1, 86 S.Ct. 684, 15 L.Ed.2d 545, 148 USPQ 459 (1966). Some are, e. g., United States v. Adams, 383 U.S. 39, 86 S.Ct. 708, 15 L.Ed.2d 572, 148 USPQ 479 (1966).
. The analyses reached different conclusions concerning the nature of the claimed inventions in Benson and Flook, this court viewing them as a whole as processes within § 101, the Supreme Court viewing them as mathematical formulae not within § 101. The same dichotomy exists between the majority and dissenting opinions in this case.
. The real party in interest is the United States of America as represented by the Secretary of the Army.
. The sole rejection being under § 101, we are not here concerned with considerations of novelty (§ 102) or obviousness (§ 103). Nor are we at liberty, as we never are when reviewing rejections under § 101 alone, 35 U.S.C. § 144, to determine whether the claimed invention is patentable, as distinguished from whether it is statutory.