concurring in part, dissenting in part.
I agree that claim 10 of the '616 patent is valid and infringed, and I agree that claim 1 of the '616 patent is valid. Thus I join Parts II and III-B of the court’s opinion. I also agree that, in view of changed law, remand is appropriate on the issue of willful infringement, and to that extent I join Part IV of the court’s opinion.
However, I do not share the court’s view that claims 6 and 7 of the '691 patent are invalid for indefiniteness. The district court’s finding of indefiniteness was contrary to the testimony of the experts for both sides. I respectfully dissent from the court’s decision in Part III-A.
As for the district court’s vacatur of the jury’s damages verdict and order for a retrial of damages, I do not agree that the order is immune from the appellate review requested by the district court under Rule 54(b). Thus I respectfully dissent from part V of the court’s decision.
I
Indefíniteness of Claims 6 and 7
The court affirms the invalidation of claims 6 and 7 on the ground that the Foundation does not persuasively show that the microprocessor performs a logarithmic conversion function. Maj. Op. at 1343. This position is contrary to the evidence presented by both sides; Cochlear failed to carry its burden to present clear and convincing evidence of invalidity on the ground of indefiniteness.
The court also finds the claims indefinite because the '691 patent does not state which of several known methods was used for the logarithmic conversion. The specification expressly discloses the non-linear *1349mapping steps, and the experts for both sides agreed that persons in the field of the invention know how to perform the simple conversion, which was well-known in the prior art.
The claims at issue, claims 6 and 7 of the '691 patent, are challenged only for the clause here shown in bold:
6. A cochlea stimulation system, comprising:
audio signal receiving means;
an externally wearable signal processor (WP) for receiving and processing the audio signals received by the audio signal receiving means and including means for generating data indicative of the audio signal;
means for transmitting the data to an implanted cochlear stimulator (ICS), the ICS including:
means for transmission from the WP, processor means for processing such transmissions to generate stimulation pulses and for controlling the pulse width of the stimulation pulses,
a plurality of electrically isolated capacitor-coupled cochlea stimulating electrodes for receiving the stimulation pulses,
means in the ICS responsive to data from the WP for selectively monitoring at least one of the electrodes or voltages in the ICS and for generating ICS-status-indicating signals, and
means in the ICS for transmitting such ICS-status-indicating signals to the WP; and
means in the WP for receiving and processing the ICS-status-indicating signals. ■ •
'691 Patent, cl. 6. The structure described in the specification for the “means for generating data indicative of the audio signal” is a microprocessor performing a logarithmic conversion function.
The '691 patent describes all of the claim elements in the form that is customary in computer-facilitated inventions: stating the function and how it is performed, in text, drawings, and flow-charts. The patent explains that the cochlear electrodes mimic sound by outputting stimulation signals in the cochlear electrodes with voltages' between 0 and 2600 microamps. '691 Patent, col. 6 11. 8-48. The specification includes a detailed logarithmic schedule of steps corresponding to the range of sounds. '691 Patent, "col. 4 11.43-64. Sound waves are translated into digital information in the D/A converter and then into the selected output voltage in the microprocessor by a logarithmic conversion. '691 Patent, col. 10, 11. 1-8. The patent teaches that the means for generating “data indicative of the audio signal” is a microprocessor performing a basic logarithmic conversion, for which the specification includes a look-up table. '691 Patent, col. 6 11. 8-48.
Precedent requires that the court views the technology as it would be viewed by persons of skill in the field of the invention. See Finisar Corp. v. DirecTV Grp., Inc., 523 F.3d 1323, 1340 (Fed. Cir. 2008) (“[T]he specification must permit one of ordinary skill in the art to ‘know and understand what structure corresponds to the means limitation.’”). The overarching requirement is that the particular factual situation must be viewed, and definiteness evaluated, in the same way as by persons in the field of the invention.
With" respect to software-implemented systems, this court has explained that:
Claim definiteness ... depends on the skill .level of a person of ordinaiy skill in the art. In software cases, therefore, algorithms in the specification need only disclose adequate defining structure to render the bounds of the claim understandable to one of ordinary skill in the art. ■ .
AllVoice Computing PLC v. Nuance Commc’ns, Inc., 504 F.3d 1236, 1245 (Fed. *1350Cir. 2007) (citations omitted). In Typhoon Touch Technologies, Inc. v. Dell, Inc., 659 F.3d 1376, 1386 (Fed. Cir. 2011), the court observed that “known computer-implement[ed] operations ... are readily implemented by persons of skill in computer programming.”
Logarithmic conversion has been known for centuries. The experts for both sides agreed that logarithmic conversion is well-known, and that persons of skill in the field of the invention would understand the description of the logarithmic conversion in the claimed system. Alfred E. Mann Found. for Sci. Res. v. Cochlear Corp., No. 07-8108 FMO (SHx) (Testimony of The Foundation Expert Dr. Young) (Dkt. 454) (‘Your output relationship is well defined. I can’t change the log value. It’s a fixed function.”); Trial Tr. at 75, 11. 1-11, Alfred E. Mann Found. for Sci. Res. v. Cochlear Corp., No. 07-8108 (C.D. Cal. Jan. 22, 2014) (Dkt. 456) (Testimony of Cochlear Expert Dr. Stevenson) (testifying that a logarithmic conversion is used because “at the other end you want this exponential”); The Foundation Expert Dr. Young Deck at ¶ 17, Mann. Found, No. 07-8108 (Dkt. 406) (“That [logarithmic] algorithm is implemented with a simple logarithmic lookup table.”). The '691 patent includes a lookup table containing the results of the calculations. '691 Patent, col. 4 11.43-64.
No witness for either side testified that a person of skill in the field would have difficulty performing the logarithmic conversion. No testimony on examination or cross-examination placed this aspect in dispute. It was not disputed that the conversion of sound into “data indicative of the audio signal” is conventional and was known and used in the operation of prior art cochlear implants. No contrary evidence was presented, and no contrary argument is offered. Nonetheless, my colleagues find the claims indefinite on the ground that there are “multiple logarithmic algorithms[ ] none of which the specification describes.” Maj. Op. at 1343. Precedent does not require that well-known formulas must be stated in the specification, when they are known in the relevant art.
A known procedure is not rendered indefinite when there is more than one known way of carrying it out. As stated in Ibormeith IP, LLC v. Mercedes-Benz USA, LLC, 732 F.3d 1376, 1379 (Fed. Cir. 2013): “For a claim to be definite, a recited algorithm, or other type of structure for a section 112(f) claim limitation, need not be so particularized as to eliminate the need for any implementation choices by a skilled artisan.” Here, there was no dispute that persons “skilled in the particular art” would “understand what structure(s) the specification discloses.” Atmel Corp. v. Information Storage Devices, Inc., 198 F.3d 1374, 1382 (Fed. Cir. 1999).
Both parties’ experts and the district court agreed that the invention necessarily employs a logarithmic conversion. See Mann Found., 96 F.Supp. at 1051 (“While it may be necessary for the wearable processor (WP) ... to perform a logarithmic conversion, because the implantable cochlear system includes an exponential D/A converter, it has not been established that the logarithmic conversion must take place in the microprocessor.”). It was not disputed that logarithmic conversion was known for audio data, and had been used in prior art cochlear implants.
My colleagues’ holding that it was necessary to state which of the two or three known logarithmic conversion routines was used, on pain of invalidity, is unsupported by mathematics, reason, or precedent. See S3 Inc. v. NVIDIA Corp., 259 F.3d 1364, 1371 (Fed. Cir. 2001) (“[PJatent documents need not include subject matter that is known in the field of the invention and is in the prior art, for patents are written for *1351persons experienced in the field of the invention.”); Intel Corp. v. VIA Techs., Inc., 319 F.3d 1357, 1366-67 (Fed. Cir. 2003) (implementation choices of “known algorithms” are “properly left to the knowledge of those skilled in the art, and need not be specified in the patent”).
On similar facts, this court has held that claims are not invalid for indefiniteness when expert testimony “sets forth several straightforward ways that the algorithm ... could be implemented by one skilled in the art.” AllVoice, 504 F.3d at 1245. On cross examination at trial, the Foundation’s expert, Dr. Young, explained that no matter how a logarithmic conversion is implemented, the algorithm will' be the same: “your output relationship is well defined. I can’t change the log valué. It’s a fixed function.” Alfred E. Mann Found. for Sci Res. v. Cochlear Corp., No. 07-8108 FMO (SHx) (Testimony of The Foundation Expert Dr. Young) (Dkt. 454).
A finding of invalidity based on indefiniteness requires proof by clear and convincing evidence that persons skilled in the field of the invention would not be “able to perform’the recited function” based oh the description in the specification and the knowledge in the art. Intel Corp., 319 F.3d at 1366. This standard controls, along with the truism that “[p]atent documents are written for persons familiar with the relevant field ..‘. lest every patent be required to be written as á comprehensive tutorial and treatise for the generalist.” Verve, LLC v. Crane Cams, Inc., 311 F.3d 1116, 1119 (Fed. Cir. 2002).
The court errs in finding claims 6 and 7 invalid for indefiniteness, upon new and ill-defined requirements for patent specifications that are unrealistic and unnecessary, adding burdens and pitfalls with no benefit to anyone. The implementing structure “must be sufficiently defined to render the bounds of the claim—declared by section 112(f) .to cover the particular structure and its equivalents—understandable by the implementer.” Ibormeith, 732 F.3d at 1379. As computer-implemented technology continues to provide new public benefits, consistency of judicial view is essential to stability of the law and progress of the technology.
II
Jurisdiction to review the Order for a new trial
The district court vacated the jury’s damages verdict, Judgment at 2, Mann Round, No. 07-8108 (Dkt. 548), and ordered a new trial on damages on the ground that “the damages awarded by the jury were not broken down as to each claim or patent,” Order Re: Post-Trial Motions at 23, Mann Found, No. 07-8108 (Dkt. 540). My colleagues hold that this court lacks jurisdiction to review the district court’s order of vacatur and a new trial, holding that the district court abused its discretion in certifying and entering judgment under Rule 54(b), on the theory that there is not a final, decision on damages. Maj. Op. at 1346. The vacatur order is renewable under either the district court’s Rule 54(b) certification or under 28 U.S.C. § 1292(c)(2). The district court entered “judgment ... in favor of Defendants as to the vacatur of the jury’s damages award,” Judgment at 2. Thus the district court assured that its judgment of vacatur was appealable. Mann. Found, No. 07-8108 (Dkt. 547). Precedent and sound practice counsel that we attend to this appeal requested by the district court.
The Supreme Court does not view the requirement of finality as strictly “jurisdictional,” but as a matter of practical jurisprudence and comity. The Court has counseled that “the requirement of finality is to be given a practical rather than a technical construction.” Gillespie v. United States Steel Corp., 379 U.S. 148, 152, 85 S.Ct. 308, *135213 L.Ed.2d 199 (1964) (internal quotations omitted); see American Export Lines, Inc, v. Alvez, 446 U.S. 274, 279, 100 S.Ct. 1673, 64 L.Ed.2d 284 (1980) (“[N]ow that the case is before us ... the eventual costs, as all the parties recognize, will certainly be less if we now pass on the questions presented here rather than send the case back with those issues undecided.” (alterations original) (citing Gillespie, 379 U.S. at 153, 85 S.Ct. 308)). In White v. New Hampshire Department of Employment Security, the Court observed that “district courts have ample authority to deal with” the “problem” of piecemeal appeals. Here, the district court prudently exercised such authority, entering judgment as to the va-catur of the jury’s damages verdict and certifying the issue under Rule 54(b).
The district court vacated the damages verdict that was fully tried on the jury instruction submitted by Cochlear, the party now complaining of the result. The verdict form, proposed and accepted by Cochlear, instructed the jury:
25. If you find that the Cochlear Defendants have infringed a valid claim of either the '616 patent or the '691 patent, what is the reasonable royalty rate that the Cochlear Defendants should pay to the Foundation?
The jury answered: 7.5%. Verdict Form, Mann Found., No. 07-8108 (Dkt. 460). The Foundation argues that the instructions were correct and Cochlear’s post-trial objection waived, and also that the verdict is well supported by the evidence.
Precedent and sound practice provide appellate jurisdiction of the vacatur order. The Ninth Circuit, whose precedent controls as to procedural matters in its district courts, has recognized that appellate review must promote judicial efficiency and sensible litigation economy. See Wabol v. Villacrusis, 958 F.2d 1450, 1455 (9th Cir. 1990) (“Though the remaining issues could eventually ascend to this court, this alone should not prevent our adjudication of important and potentially dispositive questions which have been fully briefed and argued. Such a result would disserve the cause of judicial .economy and therefore frustrate the very purpose of the final judgment rule.”). This is particularly true when, as here, -the district court invokes appellate review. Id. at n.7 (“Significantly, our exercise of jurisdiction will not interfere with the course of the trial. The trial court purported to issue a final judgment.”).
If the proposed new trial were to proceed, it would be on the basis of separating the damages assessment by patent and claim, as the district court apparently was persuaded after the verdict was rendered. However, Cochlear presented the verdict form that the district court accepted and used. The Ninth Circuit counsels reluctance to “allow litigants to play procedural brinkmanship with the jury system and take advantage of uncertainties they could well have avoided.” McCord v. Maguire, 873 F.2d 1271, 1274 (9th Cir. 1989) (holding that litigants have the responsibility to request or submit special verdict forms); see also Mitsubishi Elec. Corp. v. Ampex Corp., 190 F.3d 1300, 1304 (Fed. Cir. 1999) (party forfeited post-trial challenge on the ground that a special verdict should have been obtained, by proposing and accepting a verdict form that did not separate the potential grounds of invalidity).
Nor was the verdict form that was adopted incorrect in law. It was not disputed that the royalty base was the same as to any of the four claims, such that infringement of any claim would produce the same damages calculation. On this premise, the evidence presented by both parties did not differentiate among the four claims and two patents. See TiVo, Inc. v. EchoStar Commc’ns Corp., 516 F.3d 1290, 1312 (Fed. Cir. 2008) (“Because the damages *1353calculation at trial was not predicated on the infringement of particular claims, and because we have upheld the jury’s verdict that all of the accused devices infringe the software claims, we affirm the damages award.”); SK Hynix Inc. v. Rambus Inc., 2013 WL 1915865, at *15 (N.D. Cal. May 8, 2013) (denying new trial where “damages were awarded based upon infringement by particular products, not upon infringement of particular patent claims”).
Cochlear concedes that “[t]he evidence ... did not give the jury any way to assess a royalty rate assuming infringement of fewer claims or patents.” Cross-Appellee Resp. Br. at 28. The concession that the evidence of record provided no way to differentiate among infringement by claim or patent, distinguishes this case from the facts of DDR Holdings, LLC v. Hotels.com, L.P., 773 F.3d 1245, 1262 (Fed. Cir. 2014), where this court remanded to determine whether the invalidation of one patent might affect the damages calculation. The evidence, instructions, and damages theories presented led the jury to a single/permissible conclusion: that a reasonable royalty for the invention—back telemetry—was required to compensate the Foundation for infringement of even a single claim:
Precedent and sound practice establish the appellate obligation to review this grant of a new trial. Such review is not barred. From the court’s contrary holding, I respectfully dissent.