diff --git a/LICENSE b/LICENSE new file mode 100644 --- /dev/null +++ b/LICENSE @@ -0,0 +1,674 @@ + GNU GENERAL PUBLIC LICENSE + Version 3, 29 June 2007 + + Copyright (C) 2007 Free Software Foundation, Inc. + Everyone is permitted to copy and distribute verbatim copies + of this license document, but changing it is not allowed. + + Preamble + + The GNU General Public License is a free, copyleft license for +software and other kinds of works. + + The licenses for most software and other practical works are designed +to take away your freedom to share and change the works. By contrast, +the GNU General Public License is intended to guarantee your freedom to +share and change all versions of a program--to make sure it remains free +software for all its users. We, the Free Software Foundation, use the +GNU General Public License for most of our software; it applies also to +any other work released this way by its authors. You can apply it to +your programs, too. + + When we speak of free software, we are referring to freedom, not +price. Our General Public Licenses are designed to make sure that you +have the freedom to distribute copies of free software (and charge for +them if you wish), that you receive source code or can get it if you +want it, that you can change the software or use pieces of it in new +free programs, and that you know you can do these things. + + To protect your rights, we need to prevent others from denying you +these rights or asking you to surrender the rights. Therefore, you have +certain responsibilities if you distribute copies of the software, or if +you modify it: responsibilities to respect the freedom of others. + + For example, if you distribute copies of such a program, whether +gratis or for a fee, you must pass on to the recipients the same +freedoms that you received. You must make sure that they, too, receive +or can get the source code. And you must show them these terms so they +know their rights. + + Developers that use the GNU GPL protect your rights with two steps: +(1) assert copyright on the software, and (2) offer you this License +giving you legal permission to copy, distribute and/or modify it. + + For the developers' and authors' protection, the GPL clearly explains +that there is no warranty for this free software. For both users' and +authors' sake, the GPL requires that modified versions be marked as +changed, so that their problems will not be attributed erroneously to +authors of previous versions. + + Some devices are designed to deny users access to install or run +modified versions of the software inside them, although the manufacturer +can do so. This is fundamentally incompatible with the aim of +protecting users' freedom to change the software. The systematic +pattern of such abuse occurs in the area of products for individuals to +use, which is precisely where it is most unacceptable. Therefore, we +have designed this version of the GPL to prohibit the practice for those +products. If such problems arise substantially in other domains, we +stand ready to extend this provision to those domains in future versions +of the GPL, as needed to protect the freedom of users. + + Finally, every program is threatened constantly by software patents. +States should not allow patents to restrict development and use of +software on general-purpose computers, but in those that do, we wish to +avoid the special danger that patents applied to a free program could +make it effectively proprietary. To prevent this, the GPL assures that +patents cannot be used to render the program non-free. + + The precise terms and conditions for copying, distribution and +modification follow. + + TERMS AND CONDITIONS + + 0. Definitions. + + "This License" refers to version 3 of the GNU General Public License. + + "Copyright" also means copyright-like laws that apply to other kinds of +works, such as semiconductor masks. + + "The Program" refers to any copyrightable work licensed under this +License. Each licensee is addressed as "you". "Licensees" and +"recipients" may be individuals or organizations. + + To "modify" a work means to copy from or adapt all or part of the work +in a fashion requiring copyright permission, other than the making of an +exact copy. The resulting work is called a "modified version" of the +earlier work or a work "based on" the earlier work. + + A "covered work" means either the unmodified Program or a work based +on the Program. + + To "propagate" a work means to do anything with it that, without +permission, would make you directly or secondarily liable for +infringement under applicable copyright law, except executing it on a +computer or modifying a private copy. Propagation includes copying, +distribution (with or without modification), making available to the +public, and in some countries other activities as well. + + To "convey" a work means any kind of propagation that enables other +parties to make or receive copies. Mere interaction with a user through +a computer network, with no transfer of a copy, is not conveying. + + An interactive user interface displays "Appropriate Legal Notices" +to the extent that it includes a convenient and prominently visible +feature that (1) displays an appropriate copyright notice, and (2) +tells the user that there is no warranty for the work (except to the +extent that warranties are provided), that licensees may convey the +work under this License, and how to view a copy of this License. If +the interface presents a list of user commands or options, such as a +menu, a prominent item in the list meets this criterion. + + 1. Source Code. + + The "source code" for a work means the preferred form of the work +for making modifications to it. "Object code" means any non-source +form of a work. + + A "Standard Interface" means an interface that either is an official +standard defined by a recognized standards body, or, in the case of +interfaces specified for a particular programming language, one that +is widely used among developers working in that language. + + The "System Libraries" of an executable work include anything, other +than the work as a whole, that (a) is included in the normal form of +packaging a Major Component, but which is not part of that Major +Component, and (b) serves only to enable use of the work with that +Major Component, or to implement a Standard Interface for which an +implementation is available to the public in source code form. A +"Major Component", in this context, means a major essential component +(kernel, window system, and so on) of the specific operating system +(if any) on which the executable work runs, or a compiler used to +produce the work, or an object code interpreter used to run it. + + The "Corresponding Source" for a work in object code form means all +the source code needed to generate, install, and (for an executable +work) run the object code and to modify the work, including scripts to +control those activities. However, it does not include the work's +System Libraries, or general-purpose tools or generally available free +programs which are used unmodified in performing those activities but +which are not part of the work. For example, Corresponding Source +includes interface definition files associated with source files for +the work, and the source code for shared libraries and dynamically +linked subprograms that the work is specifically designed to require, +such as by intimate data communication or control flow between those +subprograms and other parts of the work. + + The Corresponding Source need not include anything that users +can regenerate automatically from other parts of the Corresponding +Source. + + The Corresponding Source for a work in source code form is that +same work. + + 2. Basic Permissions. + + All rights granted under this License are granted for the term of +copyright on the Program, and are irrevocable provided the stated +conditions are met. This License explicitly affirms your unlimited +permission to run the unmodified Program. The output from running a +covered work is covered by this License only if the output, given its +content, constitutes a covered work. This License acknowledges your +rights of fair use or other equivalent, as provided by copyright law. + + You may make, run and propagate covered works that you do not +convey, without conditions so long as your license otherwise remains +in force. You may convey covered works to others for the sole purpose +of having them make modifications exclusively for you, or provide you +with facilities for running those works, provided that you comply with +the terms of this License in conveying all material for which you do +not control copyright. Those thus making or running the covered works +for you must do so exclusively on your behalf, under your direction +and control, on terms that prohibit them from making any copies of +your copyrighted material outside their relationship with you. + + Conveying under any other circumstances is permitted solely under +the conditions stated below. Sublicensing is not allowed; section 10 +makes it unnecessary. + + 3. Protecting Users' Legal Rights From Anti-Circumvention Law. + + No covered work shall be deemed part of an effective technological +measure under any applicable law fulfilling obligations under article +11 of the WIPO copyright treaty adopted on 20 December 1996, or +similar laws prohibiting or restricting circumvention of such +measures. + + When you convey a covered work, you waive any legal power to forbid +circumvention of technological measures to the extent such circumvention +is effected by exercising rights under this License with respect to +the covered work, and you disclaim any intention to limit operation or +modification of the work as a means of enforcing, against the work's +users, your or third parties' legal rights to forbid circumvention of +technological measures. + + 4. Conveying Verbatim Copies. + + You may convey verbatim copies of the Program's source code as you +receive it, in any medium, provided that you conspicuously and +appropriately publish on each copy an appropriate copyright notice; +keep intact all notices stating that this License and any +non-permissive terms added in accord with section 7 apply to the code; +keep intact all notices of the absence of any warranty; and give all +recipients a copy of this License along with the Program. + + You may charge any price or no price for each copy that you convey, +and you may offer support or warranty protection for a fee. + + 5. Conveying Modified Source Versions. + + You may convey a work based on the Program, or the modifications to +produce it from the Program, in the form of source code under the +terms of section 4, provided that you also meet all of these conditions: + + a) The work must carry prominent notices stating that you modified + it, and giving a relevant date. + + b) The work must carry prominent notices stating that it is + released under this License and any conditions added under section + 7. This requirement modifies the requirement in section 4 to + "keep intact all notices". + + c) You must license the entire work, as a whole, under this + License to anyone who comes into possession of a copy. This + License will therefore apply, along with any applicable section 7 + additional terms, to the whole of the work, and all its parts, + regardless of how they are packaged. This License gives no + permission to license the work in any other way, but it does not + invalidate such permission if you have separately received it. + + d) If the work has interactive user interfaces, each must display + Appropriate Legal Notices; however, if the Program has interactive + interfaces that do not display Appropriate Legal Notices, your + work need not make them do so. + + A compilation of a covered work with other separate and independent +works, which are not by their nature extensions of the covered work, +and which are not combined with it such as to form a larger program, +in or on a volume of a storage or distribution medium, is called an +"aggregate" if the compilation and its resulting copyright are not +used to limit the access or legal rights of the compilation's users +beyond what the individual works permit. Inclusion of a covered work +in an aggregate does not cause this License to apply to the other +parts of the aggregate. + + 6. Conveying Non-Source Forms. + + You may convey a covered work in object code form under the terms +of sections 4 and 5, provided that you also convey the +machine-readable Corresponding Source under the terms of this License, +in one of these ways: + + a) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by the + Corresponding Source fixed on a durable physical medium + customarily used for software interchange. + + b) Convey the object code in, or embodied in, a physical product + (including a physical distribution medium), accompanied by a + written offer, valid for at least three years and valid for as + long as you offer spare parts or customer support for that product + model, to give anyone who possesses the object code either (1) a + copy of the Corresponding Source for all the software in the + product that is covered by this License, on a durable physical + medium customarily used for software interchange, for a price no + more than your reasonable cost of physically performing this + conveying of source, or (2) access to copy the + Corresponding Source from a network server at no charge. + + c) Convey individual copies of the object code with a copy of the + written offer to provide the Corresponding Source. This + alternative is allowed only occasionally and noncommercially, and + only if you received the object code with such an offer, in accord + with subsection 6b. + + d) Convey the object code by offering access from a designated + place (gratis or for a charge), and offer equivalent access to the + Corresponding Source in the same way through the same place at no + further charge. You need not require recipients to copy the + Corresponding Source along with the object code. If the place to + copy the object code is a network server, the Corresponding Source + may be on a different server (operated by you or a third party) + that supports equivalent copying facilities, provided you maintain + clear directions next to the object code saying where to find the + Corresponding Source. Regardless of what server hosts the + Corresponding Source, you remain obligated to ensure that it is + available for as long as needed to satisfy these requirements. + + e) Convey the object code using peer-to-peer transmission, provided + you inform other peers where the object code and Corresponding + Source of the work are being offered to the general public at no + charge under subsection 6d. + + A separable portion of the object code, whose source code is excluded +from the Corresponding Source as a System Library, need not be +included in conveying the object code work. + + A "User Product" is either (1) a "consumer product", which means any +tangible personal property which is normally used for personal, family, +or household purposes, or (2) anything designed or sold for incorporation +into a dwelling. In determining whether a product is a consumer product, +doubtful cases shall be resolved in favor of coverage. For a particular +product received by a particular user, "normally used" refers to a +typical or common use of that class of product, regardless of the status +of the particular user or of the way in which the particular user +actually uses, or expects or is expected to use, the product. A product +is a consumer product regardless of whether the product has substantial +commercial, industrial or non-consumer uses, unless such uses represent +the only significant mode of use of the product. + + "Installation Information" for a User Product means any methods, +procedures, authorization keys, or other information required to install +and execute modified versions of a covered work in that User Product from +a modified version of its Corresponding Source. The information must +suffice to ensure that the continued functioning of the modified object +code is in no case prevented or interfered with solely because +modification has been made. + + If you convey an object code work under this section in, or with, or +specifically for use in, a User Product, and the conveying occurs as +part of a transaction in which the right of possession and use of the +User Product is transferred to the recipient in perpetuity or for a +fixed term (regardless of how the transaction is characterized), the +Corresponding Source conveyed under this section must be accompanied +by the Installation Information. But this requirement does not apply +if neither you nor any third party retains the ability to install +modified object code on the User Product (for example, the work has +been installed in ROM). + + The requirement to provide Installation Information does not include a +requirement to continue to provide support service, warranty, or updates +for a work that has been modified or installed by the recipient, or for +the User Product in which it has been modified or installed. Access to a +network may be denied when the modification itself materially and +adversely affects the operation of the network or violates the rules and +protocols for communication across the network. + + Corresponding Source conveyed, and Installation Information provided, +in accord with this section must be in a format that is publicly +documented (and with an implementation available to the public in +source code form), and must require no special password or key for +unpacking, reading or copying. + + 7. Additional Terms. + + "Additional permissions" are terms that supplement the terms of this +License by making exceptions from one or more of its conditions. +Additional permissions that are applicable to the entire Program shall +be treated as though they were included in this License, to the extent +that they are valid under applicable law. If additional permissions +apply only to part of the Program, that part may be used separately +under those permissions, but the entire Program remains governed by +this License without regard to the additional permissions. + + When you convey a copy of a covered work, you may at your option +remove any additional permissions from that copy, or from any part of +it. (Additional permissions may be written to require their own +removal in certain cases when you modify the work.) You may place +additional permissions on material, added by you to a covered work, +for which you have or can give appropriate copyright permission. + + Notwithstanding any other provision of this License, for material you +add to a covered work, you may (if authorized by the copyright holders of +that material) supplement the terms of this License with terms: + + a) Disclaiming warranty or limiting liability differently from the + terms of sections 15 and 16 of this License; or + + b) Requiring preservation of specified reasonable legal notices or + author attributions in that material or in the Appropriate Legal + Notices displayed by works containing it; or + + c) Prohibiting misrepresentation of the origin of that material, or + requiring that modified versions of such material be marked in + reasonable ways as different from the original version; or + + d) Limiting the use for publicity purposes of names of licensors or + authors of the material; or + + e) Declining to grant rights under trademark law for use of some + trade names, trademarks, or service marks; or + + f) Requiring indemnification of licensors and authors of that + material by anyone who conveys the material (or modified versions of + it) with contractual assumptions of liability to the recipient, for + any liability that these contractual assumptions directly impose on + those licensors and authors. + + All other non-permissive additional terms are considered "further +restrictions" within the meaning of section 10. If the Program as you +received it, or any part of it, contains a notice stating that it is +governed by this License along with a term that is a further +restriction, you may remove that term. If a license document contains +a further restriction but permits relicensing or conveying under this +License, you may add to a covered work material governed by the terms +of that license document, provided that the further restriction does +not survive such relicensing or conveying. + + If you add terms to a covered work in accord with this section, you +must place, in the relevant source files, a statement of the +additional terms that apply to those files, or a notice indicating +where to find the applicable terms. + + Additional terms, permissive or non-permissive, may be stated in the +form of a separately written license, or stated as exceptions; +the above requirements apply either way. + + 8. Termination. + + You may not propagate or modify a covered work except as expressly +provided under this License. Any attempt otherwise to propagate or +modify it is void, and will automatically terminate your rights under +this License (including any patent licenses granted under the third +paragraph of section 11). + + However, if you cease all violation of this License, then your +license from a particular copyright holder is reinstated (a) +provisionally, unless and until the copyright holder explicitly and +finally terminates your license, and (b) permanently, if the copyright +holder fails to notify you of the violation by some reasonable means +prior to 60 days after the cessation. + + Moreover, your license from a particular copyright holder is +reinstated permanently if the copyright holder notifies you of the +violation by some reasonable means, this is the first time you have +received notice of violation of this License (for any work) from that +copyright holder, and you cure the violation prior to 30 days after +your receipt of the notice. + + Termination of your rights under this section does not terminate the +licenses of parties who have received copies or rights from you under +this License. If your rights have been terminated and not permanently +reinstated, you do not qualify to receive new licenses for the same +material under section 10. + + 9. Acceptance Not Required for Having Copies. + + You are not required to accept this License in order to receive or +run a copy of the Program. Ancillary propagation of a covered work +occurring solely as a consequence of using peer-to-peer transmission +to receive a copy likewise does not require acceptance. However, +nothing other than this License grants you permission to propagate or +modify any covered work. These actions infringe copyright if you do +not accept this License. Therefore, by modifying or propagating a +covered work, you indicate your acceptance of this License to do so. + + 10. Automatic Licensing of Downstream Recipients. + + Each time you convey a covered work, the recipient automatically +receives a license from the original licensors, to run, modify and +propagate that work, subject to this License. You are not responsible +for enforcing compliance by third parties with this License. + + An "entity transaction" is a transaction transferring control of an +organization, or substantially all assets of one, or subdividing an +organization, or merging organizations. If propagation of a covered +work results from an entity transaction, each party to that +transaction who receives a copy of the work also receives whatever +licenses to the work the party's predecessor in interest had or could +give under the previous paragraph, plus a right to possession of the +Corresponding Source of the work from the predecessor in interest, if +the predecessor has it or can get it with reasonable efforts. + + You may not impose any further restrictions on the exercise of the +rights granted or affirmed under this License. For example, you may +not impose a license fee, royalty, or other charge for exercise of +rights granted under this License, and you may not initiate litigation +(including a cross-claim or counterclaim in a lawsuit) alleging that +any patent claim is infringed by making, using, selling, offering for +sale, or importing the Program or any portion of it. + + 11. Patents. + + A "contributor" is a copyright holder who authorizes use under this +License of the Program or a work on which the Program is based. The +work thus licensed is called the contributor's "contributor version". + + A contributor's "essential patent claims" are all patent claims +owned or controlled by the contributor, whether already acquired or +hereafter acquired, that would be infringed by some manner, permitted +by this License, of making, using, or selling its contributor version, +but do not include claims that would be infringed only as a +consequence of further modification of the contributor version. For +purposes of this definition, "control" includes the right to grant +patent sublicenses in a manner consistent with the requirements of +this License. + + Each contributor grants you a non-exclusive, worldwide, royalty-free +patent license under the contributor's essential patent claims, to +make, use, sell, offer for sale, import and otherwise run, modify and +propagate the contents of its contributor version. + + In the following three paragraphs, a "patent license" is any express +agreement or commitment, however denominated, not to enforce a patent +(such as an express permission to practice a patent or covenant not to +sue for patent infringement). To "grant" such a patent license to a +party means to make such an agreement or commitment not to enforce a +patent against the party. + + If you convey a covered work, knowingly relying on a patent license, +and the Corresponding Source of the work is not available for anyone +to copy, free of charge and under the terms of this License, through a +publicly available network server or other readily accessible means, +then you must either (1) cause the Corresponding Source to be so +available, or (2) arrange to deprive yourself of the benefit of the +patent license for this particular work, or (3) arrange, in a manner +consistent with the requirements of this License, to extend the patent +license to downstream recipients. "Knowingly relying" means you have +actual knowledge that, but for the patent license, your conveying the +covered work in a country, or your recipient's use of the covered work +in a country, would infringe one or more identifiable patents in that +country that you have reason to believe are valid. + + If, pursuant to or in connection with a single transaction or +arrangement, you convey, or propagate by procuring conveyance of, a +covered work, and grant a patent license to some of the parties +receiving the covered work authorizing them to use, propagate, modify +or convey a specific copy of the covered work, then the patent license +you grant is automatically extended to all recipients of the covered +work and works based on it. + + A patent license is "discriminatory" if it does not include within +the scope of its coverage, prohibits the exercise of, or is +conditioned on the non-exercise of one or more of the rights that are +specifically granted under this License. You may not convey a covered +work if you are a party to an arrangement with a third party that is +in the business of distributing software, under which you make payment +to the third party based on the extent of your activity of conveying +the work, and under which the third party grants, to any of the +parties who would receive the covered work from you, a discriminatory +patent license (a) in connection with copies of the covered work +conveyed by you (or copies made from those copies), or (b) primarily +for and in connection with specific products or compilations that +contain the covered work, unless you entered into that arrangement, +or that patent license was granted, prior to 28 March 2007. + + Nothing in this License shall be construed as excluding or limiting +any implied license or other defenses to infringement that may +otherwise be available to you under applicable patent law. + + 12. No Surrender of Others' Freedom. + + If conditions are imposed on you (whether by court order, agreement or +otherwise) that contradict the conditions of this License, they do not +excuse you from the conditions of this License. If you cannot convey a +covered work so as to satisfy simultaneously your obligations under this +License and any other pertinent obligations, then as a consequence you may +not convey it at all. For example, if you agree to terms that obligate you +to collect a royalty for further conveying from those to whom you convey +the Program, the only way you could satisfy both those terms and this +License would be to refrain entirely from conveying the Program. + + 13. Use with the GNU Affero General Public License. + + Notwithstanding any other provision of this License, you have +permission to link or combine any covered work with a work licensed +under version 3 of the GNU Affero General Public License into a single +combined work, and to convey the resulting work. The terms of this +License will continue to apply to the part which is the covered work, +but the special requirements of the GNU Affero General Public License, +section 13, concerning interaction through a network will apply to the +combination as such. + + 14. Revised Versions of this License. + + The Free Software Foundation may publish revised and/or new versions of +the GNU General Public License from time to time. Such new versions will +be similar in spirit to the present version, but may differ in detail to +address new problems or concerns. + + Each version is given a distinguishing version number. If the +Program specifies that a certain numbered version of the GNU General +Public License "or any later version" applies to it, you have the +option of following the terms and conditions either of that numbered +version or of any later version published by the Free Software +Foundation. If the Program does not specify a version number of the +GNU General Public License, you may choose any version ever published +by the Free Software Foundation. + + If the Program specifies that a proxy can decide which future +versions of the GNU General Public License can be used, that proxy's +public statement of acceptance of a version permanently authorizes you +to choose that version for the Program. + + Later license versions may give you additional or different +permissions. However, no additional obligations are imposed on any +author or copyright holder as a result of your choosing to follow a +later version. + + 15. Disclaimer of Warranty. + + THERE IS NO WARRANTY FOR THE PROGRAM, TO THE EXTENT PERMITTED BY +APPLICABLE LAW. EXCEPT WHEN OTHERWISE STATED IN WRITING THE COPYRIGHT +HOLDERS AND/OR OTHER PARTIES PROVIDE THE PROGRAM "AS IS" WITHOUT WARRANTY +OF ANY KIND, EITHER EXPRESSED OR IMPLIED, INCLUDING, BUT NOT LIMITED TO, +THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR +PURPOSE. THE ENTIRE RISK AS TO THE QUALITY AND PERFORMANCE OF THE PROGRAM +IS WITH YOU. SHOULD THE PROGRAM PROVE DEFECTIVE, YOU ASSUME THE COST OF +ALL NECESSARY SERVICING, REPAIR OR CORRECTION. + + 16. Limitation of Liability. + + IN NO EVENT UNLESS REQUIRED BY APPLICABLE LAW OR AGREED TO IN WRITING +WILL ANY COPYRIGHT HOLDER, OR ANY OTHER PARTY WHO MODIFIES AND/OR CONVEYS +THE PROGRAM AS PERMITTED ABOVE, BE LIABLE TO YOU FOR DAMAGES, INCLUDING ANY +GENERAL, SPECIAL, INCIDENTAL OR CONSEQUENTIAL DAMAGES ARISING OUT OF THE +USE OR INABILITY TO USE THE PROGRAM (INCLUDING BUT NOT LIMITED TO LOSS OF +DATA OR DATA BEING RENDERED INACCURATE OR LOSSES SUSTAINED BY YOU OR THIRD +PARTIES OR A FAILURE OF THE PROGRAM TO OPERATE WITH ANY OTHER PROGRAMS), +EVEN IF SUCH HOLDER OR OTHER PARTY HAS BEEN ADVISED OF THE POSSIBILITY OF +SUCH DAMAGES. + + 17. Interpretation of Sections 15 and 16. + + If the disclaimer of warranty and limitation of liability provided +above cannot be given local legal effect according to their terms, +reviewing courts shall apply local law that most closely approximates +an absolute waiver of all civil liability in connection with the +Program, unless a warranty or assumption of liability accompanies a +copy of the Program in return for a fee. + + END OF TERMS AND CONDITIONS + + How to Apply These Terms to Your New Programs + + If you develop a new program, and you want it to be of the greatest +possible use to the public, the best way to achieve this is to make it +free software which everyone can redistribute and change under these terms. + + To do so, attach the following notices to the program. It is safest +to attach them to the start of each source file to most effectively +state the exclusion of warranty; and each file should have at least +the "copyright" line and a pointer to where the full notice is found. + + + Copyright (C) + + This program is free software: you can redistribute it and/or modify + it under the terms of the GNU General Public License as published by + the Free Software Foundation, either version 3 of the License, or + (at your option) any later version. + + This program is distributed in the hope that it will be useful, + but WITHOUT ANY WARRANTY; without even the implied warranty of + MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the + GNU General Public License for more details. + + You should have received a copy of the GNU General Public License + along with this program. If not, see . + +Also add information on how to contact you by electronic and paper mail. + + If the program does terminal interaction, make it output a short +notice like this when it starts in an interactive mode: + + Copyright (C) + This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. + This is free software, and you are welcome to redistribute it + under certain conditions; type `show c' for details. + +The hypothetical commands `show w' and `show c' should show the appropriate +parts of the General Public License. Of course, your program's commands +might be different; for a GUI interface, you would use an "about box". + + You should also get your employer (if you work as a programmer) or school, +if any, to sign a "copyright disclaimer" for the program, if necessary. +For more information on this, and how to apply and follow the GNU GPL, see +. + + The GNU General Public License does not permit incorporating your program +into proprietary programs. If your program is a subroutine library, you +may consider it more useful to permit linking proprietary applications with +the library. If this is what you want to do, use the GNU Lesser General +Public License instead of this License. But first, please read +. diff --git a/Setup.lhs b/Setup.lhs new file mode 100644 --- /dev/null +++ b/Setup.lhs @@ -0,0 +1,3 @@ +#! /usr/bin/env runhaskell +> import Distribution.Simple +> main = defaultMain diff --git a/src/Synthesizer/Filter/Basic.hs b/src/Synthesizer/Filter/Basic.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/Basic.hs @@ -0,0 +1,60 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE FunctionalDependencies #-} +module Synthesizer.Filter.Basic where + +import qualified Algebra.Transcendental as Trans +import qualified Algebra.Module as Module +import qualified Algebra.RealRing as RealRing +import qualified Number.Complex as Complex + +import NumericPrelude.Numeric +import NumericPrelude.Base + +{- ToDo: + - support of data before time 0 + - the problem is that all past data has to be kept, + the garbage collector can't flush it :-( + - this means we will also need functions for plain lists, + in this case we can't provide initial conditions to recursive filters + - the question of initial conditions is especially problematic + since for Graphs we have no explicit feed back + where initial conditions can be plugged in + - thus for two-way signal we must request the user + to insert initial conditions in every loop of a Graph + using the Past constructor + - all of the following filter primitives in static and modulated form: + - mask + - integer delay + - fractional delay + - shall the fractional delay constructor store the interpolation type? + (this discussion is similar to the one concerning + initial conditions for recursive filters) + - yes, because each delay may use a different interpolation type, + if no fractional delay is used, + no interpolation type needs to be specified + - no, because the interpolation is only of interest for filter + application not for the transfer function + - Is there a way to avoid the multi-parameter type class? + - Can we provide a class for lists (OneWay and TwoWay) + that help implementing filters and filter networks? + - The 'transferFunction' obviously does not depend on the signal list type. + - 'transferFunction' should not be restricted to complex numbers. + - For arguments of type 'Ratio (Polynomial Rational)' + you could compute the transfer function in terms of a rational function. +-} + +screw :: Trans.C a => a -> [Complex.T a] +screw w = iterate (Complex.cis w *) 1 + + +class Filter list filter | filter -> list where + {-| Apply a filter to a signal. -} + apply :: (RealRing.C t, Trans.C t, + Module.C a v, Module.C a (list v)) => + filter t a v -> list v -> list v + {-| Compute the complex amplification factor + that is applied to the given frequency. -} + transferFunction :: (Trans.C t, Module.C a t) => + filter t a v -> t -> Complex.T t diff --git a/src/Synthesizer/Filter/Composition.hs b/src/Synthesizer/Filter/Composition.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/Composition.hs @@ -0,0 +1,150 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE UndecidableInstances #-} +module Synthesizer.Filter.Composition where + +import qualified Synthesizer.Filter.Basic as FilterBasic +import Synthesizer.Filter.Basic (Filter, apply, ) + +import qualified Algebra.Module as Module +import qualified Algebra.Transcendental as Trans +import qualified Algebra.RealRing as RealRing +import qualified Algebra.Field as Field +import qualified Algebra.Additive as Additive +import qualified Number.Complex as Complex + +import Algebra.Additive ((+)) + +import NumericPrelude.Base +import NumericPrelude.Numeric + +{- ToDo: + - functions that build a FilterComposition for specific filters + (1st order, universal, allpass, butterworth, chebyshev) + - functions that turn physical filter parameters into + internal ones + - How can these function be combined? + A function like + [ FilterComposition v [m] ] -> FilterComposition v [[m]] + is not satisfying, since the conversion function cannot rely + that the structure of all FilterComposition v [m] is equal. + If the list is empty the structure can't even be reconstructed. +-} + +{-| + This describes a generic filter with one input and one main output + that consists of non-recursive and recursive parts. + If you use Feedback, make sure that at least + one of the filters of a circle includes a delay, + otherwise the recursion will fail. + The main output is used to glue different parts together. + Additionally the functions 'apply' and 'transferFunction' + provide the signals at every node of the network. +-} +data T filter t a v = + Prim (filter t a v) + {-^ a filter primitve -} + | Serial [T filter t a v] + {-^ serial chain of filters -} + | Parallel [T filter t a v] + {-^ filters working parallel, there output is mixed together -} + | Feedback (T filter t a v) (T filter t a v) + {-^ filter the signal in the forward direction and + feed back the output signal filtered by the second filter -} + +{-| + This is the data structure is used for the results + of 'apply' and 'transferFunction'. + Each constructor corresponds to one of 'Filter.Composition.T'. + By choosing only some of the outputs + the lazy evaluation will content + with applying the necessary filter steps, only. +-} +data Sockets s = Sockets {output :: s, socket :: SocketSpec s} + +data SocketSpec s = + Output + | Multiplier [Sockets s] + | Adder [Sockets s] + | Loop (Sockets s) (Sockets s) + +instance (Filter list filter) => + Filter (list) (T filter) where +{- + apply :: (Module.C a v) => + FilterComposition a v -> TwoWayList v -> TwoWayList v +-} + apply f x = output (applyMulti f x) +{- + transferFunction :: (Trans.C b, Module.C a (Complex.T b)) => + T filter a v -> b -> (Complex.T b) +-} + transferFunction f w = output (transferFunctionMulti f w) + + +{-| Apply a filter network to a signal and keep the output of all nodes. + Generic function that is wrapped by 'apply'. -} +applyMulti :: (RealRing.C t, Trans.C t, + Module.C a v, Module.C a (list v), Filter list filter) => + T filter t a v -> list v -> Sockets (list v) +applyMulti (Prim f) x = + Sockets (apply f x) Output +applyMulti (Serial fs) x = + let sq = scanl (\(Sockets y _) -> flip applyMulti y) (Sockets x Output) fs + in Sockets (output (last sq)) (Multiplier (tail sq)) +applyMulti (Parallel fs) x = + let socks = map (flip applyMulti x) fs + y = foldr (Additive.+) zero (map output socks) + in Sockets y (Adder socks) +{- the distinction between 'feed' and 'back' + can be dropped in a more general net structure -} +applyMulti (Feedback feed back) x = + let sockY@(Sockets y _) = applyMulti feed ((Additive.+) x z) + sockZ@(Sockets z _) = applyMulti back y + in Sockets y (Loop sockY sockZ) + + +transferFunctionMulti :: + (Trans.C t, Module.C a t, Filter list filter) => + T filter t a v -> t -> Sockets (Complex.T t) +transferFunctionMulti f w = tfAbsolutize 1 (tfRelative w f) + +{-| Compute the transitivity for each part of the filter network. + We must do this in such a relative manner to be able + to compute feedback. -} +tfRelative :: + (Trans.C t, Module.C a t, Filter list filter) => + t -> T filter t a v -> Sockets (Complex.T t) +tfRelative w (Prim f) = + Sockets (FilterBasic.transferFunction f w) Output +tfRelative w (Serial fs) = + let sq = map (tfRelative w) fs + in Sockets (product (map output sq)) (Multiplier sq) +tfRelative w (Parallel fs) = + let sq = map (tfRelative w) fs + in Sockets (sum (map output sq)) (Adder sq) +tfRelative w (Feedback feed back) = + let sockY = tfRelative w feed + sockZ = tfRelative w back + q = output sockY / (1 - output sockZ) + in Sockets q (Loop sockY sockZ) + + +{-| Make the results from 'tfRelative' absolute. -} +tfAbsolutize :: (Field.C a) => a -> Sockets a -> Sockets a +tfAbsolutize x (Sockets y spec) = Sockets (x*y) + (case spec of + (Multiplier socks) -> + let sq = scanl (\(Sockets z _) -> tfAbsolutize z) + (Sockets x Output) socks + in Multiplier (tail sq) + (Adder socks) -> + let sq = map (tfAbsolutize x) socks + in Adder sq + (Loop feed back) -> + let sockY = tfAbsolutize (x / (1 - output back)) feed + sockZ = tfAbsolutize (output sockY) back + -- it should be x*y == output sockY + in Loop sockY sockZ + Output -> spec) diff --git a/src/Synthesizer/Filter/Example.hs b/src/Synthesizer/Filter/Example.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/Example.hs @@ -0,0 +1,243 @@ +{-# LANGUAGE NoImplicitPrelude #-} +module Synthesizer.Filter.Example where + +import qualified Synthesizer.Filter.OneWay as OneWay +import qualified Synthesizer.Filter.TwoWay as TwoWay +import qualified Synthesizer.Filter.Composition as Composition +import qualified Synthesizer.Filter.Graph as Graph +import qualified Synthesizer.Plain.Interpolation as Interpolation + +import Synthesizer.Filter.Basic (apply, ) +import Synthesizer.Filter.Composition (T(..)) + +import qualified Synthesizer.Plain.Oscillator as Osci +import qualified Synthesizer.Basic.Wave as Wave +import qualified Synthesizer.Plain.Filter.Recursive.FirstOrder as Filt1 +import qualified Synthesizer.Plain.Filter.NonRecursive as FiltNR + +import qualified Algebra.Module as Module +import qualified Algebra.Transcendental as Trans +import qualified Algebra.RealField as RealField +import qualified Algebra.Field as Field +import qualified Algebra.Absolute as Absolute + +import Data.Maybe (fromMaybe) + +import NumericPrelude.Base +import NumericPrelude.Numeric + + + +{-* Reconstruction of the sound of a plucked guitar string -} + +guitarInit :: Field.C a => [a] +guitarInit = map (/128) ( + 1 : 1 : 1 : 1 : 1 : 1 : 1 : 1 : + 1 : 2 : 2 : 2 : 2 : 2 : 2 : 2 : + 2 : 2 : 2 : 2 : 2 : 2 : 2 : 2 : + 2 : 2 : 2 : 3 : 3 : 3 : 3 : 3 : + 3 : 3 : 3 : 3 : 3 : 3 : 3 : 3 : + 3 : 3 : 3 : 4 : 4 : 4 : 4 : 4 : + 4 : 4 : 4 : 4 : 4 : 4 : 4 : 4 : + 5 : 5 : 5 : 5 : 5 : 5 : 5 : 5 : + 6 : 6 : 6 : 7 : 7 : 8 : 8 : 9 : + 10 : 11 : 12 : 13 : 14 : 15 : 15 : 16 : + 17 : 17 : 17 : 18 : 18 : 18 : 18 : 18 : + 18 : 18 : 18 : 17 : 17 : 16 : 16 : 15 : + 15 : 14 : 14 : 14 : 13 : 13 : 14 : 14 : + 15 : 16 : 17 : 18 : 19 : 20 : 22 : 23 : + 25 : 27 : 30 : 32 : 35 : 37 : 39 : 41 : + 43 : 45 : 47 : 48 : 49 : 49 : 48 : 46 : + 41 : 34 : 24 : 11 : -6 : -26 : -48 : -72 : + -96 : -114 : -128 : -128 : -128 : -128 : -128 : -128 : + -128 : -125 : -110 : -93 : -75 : -57 : -41 : -27 : + -17 : -10 : -6 : -4 : -2 : -2 : -2 : -2 : + -2 : -3 : -4 : -4 : -5 : -6 : -7 : -8 : + -9 : -10 : -11 : -12 : -12 : -12 : -13 : -13 : + -13 : -13 : -13 : -13 : -12 : -12 : -11 : -10 : + -9 : -9 : -8 : -8 : -7 : -6 : -6 : -5 : + -5 : -5 : -5 : -4 : -4 : -4 : -4 : -4 : + -4 : -4 : -4 : -4 : -4 : -5 : -7 : -8 : + -8 : -9 : -10 : -11 : -12 : -13 : -13 : -14 : + -14 : -14 : -13 : -10 : -7 : -2 : 5 : 15 : + 26 : 37 : 49 : 61 : 73 : 83 : 92 : 99 : + 105 : 109 : 111 : 112 : 110 : 105 : 99 : 90 : + 80 : 71 : 63 : 57 : 52 : 49 : 47 : 47 : + 48 : 49 : 51 : 51 : 52 : 52 : 50 : 48 : + 42 : 34 : 22 : 7 : -12 : -32 : -56 : -78 : + -96 : -114 : -127 : -128 : -128 : -128 : -128 : -128 : + -128 : -118 : -102 : -83 : -67 : -50 : -37 : -26 : + -17 : -12 : -8 : -5 : -3 : -3 : -2 : -2 : + -2 : -3 : -4 : -4 : -6 : -7 : -8 : -10 : + -11 : -12 : -12 : -13 : []) + +guitarCompShort, guitarCompLong :: + Field.C a => [a] -> Composition.T TwoWay.T Double a a +guitarCompShort past = Feedback (Prim (TwoWay.Past past)) (Parallel [ + Serial [Prim (TwoWay.Delay 1), + Prim (TwoWay.Mask [0.6519177892575342, 0.2331904728998289])], + Serial [Prim (TwoWay.Delay 126), + Prim (TwoWay.Mask [0.08253506238277844, + 0.2369601607320473, 0.18367848836060044, + -0.06422525077173147, -0.31836517142623727])]]) +guitarCompLong past = Feedback (Prim (TwoWay.Past past)) ( + Serial [Prim (TwoWay.Delay 122), + Prim (TwoWay.Mask [ + -0.23742303494466988, + 0.020278040917954415, + 0.12495333789385828, + 0.16125537461091102, + 0.1993410924766678, + 0.24673057006071691, + 0.25438881375430467, + 0.1424676847770117, + 0.03848071949084291, + -0.016618282409355676, + -0.04517323927531556, + -0.0061713683480988475, + 0.11137126130878339 + ])]) + +{-| Reconstruct the guitar sound from the sampled initial wave + and the analysed feedback factors. + This sounds pretty like the sampled sound. -} +guitarRaw :: (Field.C a, Module.C a a) => [a] +guitarRaw = + let gi = guitarInit -- assert monomorphism + y = TwoWay.future + (TwoWay.delay (length gi) + (apply (guitarCompLong (reverse gi)) + (TwoWay.Signal [] []))) + in y + +{-| Reconstruct the guitar sound from the sampled initial wave + but with simple smoothing on feedback. + This sounds more statically. -} +guitarRawSimple :: (Field.C a, Module.C a a) => [a] +guitarRawSimple = + let gi = guitarInit -- assert monomorphism + y = gi ++ drop (length gi) + (FiltNR.delay 128 (Filt1.lowpass + (repeat (Filt1.Parameter (0.4 `asTypeOf` head y))) y)) + in y + +{-| Reconstruct the guitar sound with the analysed feedback factors + but with an synthetic initial wave. + The sharpness of the initial wave can be controlled. + This is used to implement various velocities. -} +guitarRawVelo :: (Absolute.C a, Trans.C a, Module.C a a) => a -> [a] +guitarRawVelo velo = + let len = 128::Int + wave = + map (Wave.power01Normed velo) + (take len (iterate (+ 2 / fromIntegral len) (-1))) + y = TwoWay.future + (TwoWay.delay len + (apply (guitarCompLong wave) + (TwoWay.Signal [] []))) + in y + + +{-| Resample the reconstructed string sound + so that notes can be played. -} +guitar :: (RealField.C a, Module.C a a) => a -> [a] +guitar freq = + let srcFreq = 128 * freq + in Interpolation.multiRelativeZeroPadLinear 0 + (repeat (srcFreq `asTypeOf` freq)) guitarRawSimple + + + +{-* Tests for FilterGraphs -} + +type CompositionDouble = + Composition.T TwoWay.T Double Double Double + +{-| a simple lowpass used to create an exponential2 -} +--expo :: (RealField.C a, Module.C a a) => TwoWay.Signal a +expo :: TwoWay.Signal Double +expo = + let _flt1 = Feedback (Serial [Prim (OneWay.Delay ([0] `asTypeOf` past))]) + (Serial [Prim (OneWay.Mask + ([0.9] `asTypeOf` past))]) + _flt2 = (Prim (TwoWay.Mask ([0.5] `asTypeOf` past))) + :: CompositionDouble + flt3 = (Feedback (Serial []) + (Prim (TwoWay.Delay 1))) + :: CompositionDouble + TwoWay.Signal past future = apply flt3 (TwoWay.Signal [] [1]) + in TwoWay.Signal past (take 10 future) + +type GraphDouble f = Graph.T f Int Double Double Double + +simpleGraph :: TwoWay.Signal Double +simpleGraph = + let out = + Graph.apply + (Graph.fromList + [(0, []), + (1, [(0, TwoWay.Delay (-1))]), + (2, [(1, TwoWay.Mask [0.95])])] :: + GraphDouble TwoWay.T) + (Graph.signalFromList + [(0, TwoWay.Signal [] [1])]) + in fromMaybe (error "requested output of non-existing socket") + (Graph.lookupSignal out (2::Int)) + +expoGraphTwoWay :: [Double] +expoGraphTwoWay = + let out = + Graph.apply + (Graph.fromList + [(0, [(2, TwoWay.Past [1])]), + (1, [(0, TwoWay.Delay 1)]), + (2, [(1, TwoWay.Mask [0.95])])] :: + GraphDouble TwoWay.T) + (Graph.signalFromList + [(0, TwoWay.Signal [] [])]) + in TwoWay.take 20 $ TwoWay.delay 10 + (fromMaybe (error "requested output of non-existing socket") + (Graph.lookupSignal out (0::Int))) + + +expoGraph :: [Double] +expoGraph = + let out = + Graph.apply + (Graph.fromList + [(0, [(1, OneWay.Delay [0])]), + (1, [(0, OneWay.Mask [0.99])])] :: + GraphDouble OneWay.T) + (Graph.signalFromList + [(0, [1])]) + in fromMaybe (error "requested output of non-existing socket") + (Graph.lookupSignal out (0::Int)) + +{-| make recursive flanger with help of the two way interpolation -} +flangedSaw :: Double -> [Double] +flangedSaw sampleRate = + let {- The flanger's principal filter frequency will vary between + flangeFreq * 2**flangeRange and flangeFreq / 2**flangeRange -} + flangeFreq = 1000 + flangeRange = 2 + sawFreq = 440 + gain = 0.6 + vol = 0.5 + + {- 'control' contains the feedback times -} + control = map (\c -> sampleRate/flangeFreq * 2**(-flangeRange*c)) + (map sin (iterate (pi/(0.5*sampleRate)+) 0)) + sawPast = Osci.freqModSaw 0 (repeat (-sawFreq/sampleRate)) + sawFuture = Osci.freqModSaw 0 (repeat ( sawFreq/sampleRate)) + --lowNoise = amplify vol noise + flt = Feedback + (Prim (TwoWay.Mask [vol])) + (Serial [Prim (TwoWay.Mask [gain]), + Prim (TwoWay.Past []), + Prim (TwoWay.ModFracDelay + Interpolation.linear + (TwoWay.Signal [] control))]) + :: CompositionDouble + + in TwoWay.future + (apply flt (TwoWay.Signal sawPast sawFuture)) diff --git a/src/Synthesizer/Filter/Fix.hs b/src/Synthesizer/Filter/Fix.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/Fix.hs @@ -0,0 +1,38 @@ +module Synthesizer.Filter.Fix where + +import qualified Synthesizer.Filter.Graph as Graph + + +{-| +A 'Graph.T' with numbered nodes is not very comfortable. +Better provide a 'Control.Monad.Fix.fix'-like function +which allows to enter a graph this way: + +> fix $ \[v,w,y] -> +> [a·(u + d·w), +> b·(v + e·y), +> c· w] + +-} + +type T filter t a v = + [Channel filter t a v] -> [[(Channel filter t a v, filter t a v)]] + +type ChannelId = Int + +data Channel filter t a v = + Channel {channelId :: ChannelId, + channelInputs :: [(ChannelId, filter t a v)]} + + +fix :: T filter t a v -> [Channel filter t a v] +fix f = + let cs = zipWith (\n inputs -> + Channel n (map (\(c,filt) -> (channelId c, filt)) inputs)) + [0 ..] (f cs) + in cs + + +toGraph :: T filter t a v -> Graph.T filter Int t a v +toGraph = + Graph.fromList . map (\(Channel n inputs) -> (n, inputs)) . fix diff --git a/src/Synthesizer/Filter/Graph.hs b/src/Synthesizer/Filter/Graph.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/Graph.hs @@ -0,0 +1,183 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleInstances #-} +{-# LANGUAGE UndecidableInstances #-} +{-# LANGUAGE FlexibleContexts #-} +module Synthesizer.Filter.Graph where + +import qualified Prelude as P +import NumericPrelude.Base +import NumericPrelude.Numeric + +import qualified Synthesizer.Filter.Basic as FilterBasic +import Synthesizer.Filter.Basic (Filter, apply, ) +import qualified Data.Map as Map +import Data.Map(Map) +import MathObj.DiscreteMap() {- Module.C instances for Map -} + +import qualified Number.Complex as Complex +import qualified Algebra.RealRing as RealRing +import qualified Algebra.Additive as Additive +import qualified Algebra.Transcendental as Trans +import qualified Algebra.Module as Module +import Algebra.Module((*>)) +import Orthogonals(Scalar,inverse,add_to_diagonal) + + +{-| +A filter network is a graph consisting +of nodes (input and output signals) +and edges (filter processes). +Output signals can be taken from every node, +inputs can be injected in some nodes +which means that the signal at this node is superposed with +the injected signal. +The same can be achieved by duplicating the network, +one duplicate per input, +and superposing the corresponding outputs. +It is also sensible to setup a graph without inputs, +e.g. a recursive filter with some initial conditions +that works independent from any input. + +In opposition to electric filter networks +digital filter networks must be directed. + +Test-case: leap-frog filters like + +> +-----------[d]-----------+ +> v | +>(u) -+-> [a] (v) -+-> [b] (w) -+-> [c] (y) -+-> +> ^ | +> +-----------[e]-----------+ + +@ +v = a·(u + d·w) +w = b·(v + e·y) +y = c· w +@ + +We model the general network by a list of nodes, +where each node is an adder that holds a list of its inputs. +Each input of a node is an output +of another node that has gone through a processor. +Additionally there may be one input from outside. +In principle a processor could be a simple filter network +as defined by the structure 'Filter'. + +The network is an applyable filter +whenever each circle contains a delay. +To compute the transfer function +we have to solve a system of linear equations +which we can construct quite straight forward +from the processors' input lists. + +The current design can be abstractly seen +as the system of linear equations: + + y = A*y + u + +where A is a matrix containing the edges hosting the filters, +y the vector of output signals, +u the vector of input signals. +In this formulation the number of inputs and outputs must match +but since you are free to ignore some of the inputs and outputs +you can use nodes for pure output, pure input or both of them. + +-} + +newtype T filter i t a v = + C (Map i + [(i, {- index of the processor whose output goes in here -} + filter t a v {- description of the filter -} + )]) + + +newtype Signal list i v = Signal (Map i (list v)) + + +fromList :: (Ord i) => [(i, [(i, filter t a v)])] -> T filter i t a v +fromList = C . Map.fromList + +toList :: T filter i t a v -> [(i, [(i, filter t a v)])] +toList (C fg) = Map.toList fg + +signalFromList :: (Ord i) => [(i, list v)] -> Signal list i v +signalFromList = Signal . Map.fromList + +signalToList :: Signal list i v -> [(i, list v)] +signalToList (Signal x) = Map.toList x + +lookupSignal :: (Ord i) => Signal list i v -> i -> Maybe (list v) +lookupSignal (Signal x) = flip Map.lookup x + + +{- + These instance may help to include FilterGraphs + in even bigger structures. +-} +instance (Ord i, Additive.C (list v), Eq (list v)) + => Additive.C (Signal list i v) where + zero = Signal Additive.zero + (+) (Signal x) (Signal y) = Signal ((Additive.+) x y) + (-) (Signal x) (Signal y) = Signal ((Additive.-) x y) + negate (Signal x) = Signal (Additive.negate x) + +instance (Ord i, Eq a, Additive.C a, Additive.C (list v), Eq (list v), + Module.C a v, Module.C a (list v)) + => Module.C a (Signal list i v) where + s *> (Signal x) = Signal (s *> x) + + +{- + It would be interesting to make FilterGraphs + an instance of Filter. + To achieve that we had to make GraphSignals an instance of Module.C + and the transferFunction would no longer return a factor + but a function that maps input amplitudes + of a given frequency to output amplitudes. + +instance (Ord i, Show i, Filter list filter) => + Filter (Signal list i) (T filter i) where +-} + +apply :: (Ord i, Show i, Additive.C t, Trans.C t, RealRing.C t, + Module.C a v, Module.C a (list v), + Filter list filter) => + T filter i t a v -> Signal list i v -> Signal list i v +apply (C fg) (Signal inputs) = + let getInput i = Map.findWithDefault Additive.zero i inputs + getOutput i = Map.findWithDefault + (error ("Unknown processor: "++show i)) i outputs + output i edges = + foldl (Additive.+) (getInput i) (map (\(j,f) -> + FilterBasic.apply f (getOutput j)) edges) + outputs = Map.mapWithKey output fg + in Signal outputs + +{-| Compute a matrix that tells how an input frequency + is mapped to the various output nodes. + + According to the formulation given above + we have to invert the matrix (I-A). + + Currently this is done by a QR decomposition for each frequency. + It would be probably faster if we decompose + the matrix containing polynomial elements. + Then the inverted matrix would consist of some + polynomial ratios which can be evaluated for each frequency. +-} +transferFunction :: + (Ord i, Show i, Trans.C t, + P.Fractional (Complex.T t), Scalar (Complex.T t), + Module.C a t, Filter list filter) => + T filter i t a v -> t -> [[Complex.T t]] +transferFunction (C fg) w = + let keys = Map.keys fg + elts = Map.elems fg + inputsToMap procs = + Map.mapWithKey (\_ f -> FilterBasic.transferFunction f w) + (Map.fromList procs) + makeRow procs = + map (flip (Map.findWithDefault 0) (inputsToMap procs)) keys + matrix = map makeRow elts + in inverse (add_to_diagonal (-1) matrix) diff --git a/src/Synthesizer/Filter/Graphic.hs b/src/Synthesizer/Filter/Graphic.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/Graphic.hs @@ -0,0 +1,7 @@ +module Synthesizer.Filter.Graphic where + +{-| + This module should be populated with functions + that create flowchart graphics from the filter networks + of the 'Composition' module. +-} diff --git a/src/Synthesizer/Filter/MonadFix.hs b/src/Synthesizer/Filter/MonadFix.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/MonadFix.hs @@ -0,0 +1,44 @@ +module Synthesizer.Filter.MonadFix where + +import qualified Synthesizer.Filter.Graph as Graph +import qualified Synthesizer.Filter.Fix as FFix + +import Synthesizer.Filter.Fix (Channel(Channel), ChannelId) + +import Control.Monad.Trans.State (StateT, evalStateT, get, modify, ) +import Control.Monad.Trans.Writer (Writer, execWriter, tell, ) +import Control.Monad.Trans.Class (lift, ) + + +{-| +If you find 'Filter.Fix.T' still inconvenient, +and if you don't care about portability, +you can also use the following monad with the @mdo@ notation. + +> mdo +> v <- a·(u + d·w) +> w <- b·(v + e·y) +> y <- c· w + +-} + + +type T filter t a v x = StateT ChannelId (Writer [Channel filter t a v]) x + +makeChannel :: + [(ChannelId, filter t a v)] -> + T filter t a v ChannelId +makeChannel inputs = + do n <- get + modify succ + lift $ tell [Channel n inputs] + return n + + +run :: T filter t a v x -> [Channel filter t a v] +run m = execWriter (evalStateT m 0) + + +toGraph :: T filter t a v x -> Graph.T filter Int t a v +toGraph = + Graph.fromList . map (\(Channel n inputs) -> (n, inputs)) . run diff --git a/src/Synthesizer/Filter/OneWay.hs b/src/Synthesizer/Filter/OneWay.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/OneWay.hs @@ -0,0 +1,76 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleInstances #-} +module Synthesizer.Filter.OneWay where + +import Synthesizer.Filter.Basic + +import qualified Synthesizer.Plain.Interpolation as Interpolation +import qualified Synthesizer.Plain.Filter.NonRecursive as FiltNR +import Number.Complex(cis) + +import qualified Algebra.Module as Module +import qualified Algebra.Ring as Ring +import qualified Algebra.Additive as Additive + +import Algebra.Module(linearComb) +import Algebra.Additive(zero) + +import NumericPrelude.Base +import NumericPrelude.Numeric + +type Signal = [] + +{-| shift signal in time -} +delay :: (Additive.C v) => + Int -> Signal v -> Signal v +delay = FiltNR.delayPad zero + +delayOnce :: (Additive.C v) => + Signal v -> Signal v +delayOnce = (zero:) + + +{-| Unmodulated non-recursive filter -} +nonRecursiveFilter :: Module.C a v => + [a] -> [v] -> [v] +nonRecursiveFilter = FiltNR.generic + +{-| Modulated non-recursive filter. -} +nonRecursiveFilterMod :: Module.C a v => + [[a]] -> [v] -> [v] +nonRecursiveFilterMod ms x = + zipWith linearComb ms (tail (scanl (flip (:)) [] x)) + + +{-| Description of a basic filter that can be used in larger networks. -} +data T t a v = + Mask [a] + {-^ A static filter described by its mask -} + | ModMask (Signal [a]) + {-^ A modulated filter described by a list of masks -} + | FracDelay (Interpolation.T t v) t + {-^ Delay the signal by a fractional amount of samples. + This is achieved by interpolation. -} + | ModFracDelay (Interpolation.T t v) (Signal t) + {-^ Delay with varying delay times. + The delay times sequence must monotonically decrease. + (This includes constant parts!) -} + | Delay [v] + {-^ Delay the signal by prepending another one -} + +instance Filter [] T where + + apply (Mask m) = nonRecursiveFilter m + apply (ModMask m) = nonRecursiveFilterMod m + apply (FracDelay ip t) = Interpolation.multiRelativeZeroPad zero + ip (-t) (repeat 1) + apply (ModFracDelay ip ts) = Interpolation.multiRelativeZeroPad zero + ip (- head ts) (repeat 1 - FiltNR.differentiate ts) + apply (Delay x) = (x++) + + transferFunction (Mask m) w = linearComb m (screw (negate w)) + transferFunction (FracDelay _ t) w = cis (negate w * t) + transferFunction (Delay x) w = cis (negate w * fromIntegral (length x)) + transferFunction _ _ = + error "transfer function can't be computed for modulated filters" diff --git a/src/Synthesizer/Filter/TwoWay.hs b/src/Synthesizer/Filter/TwoWay.hs new file mode 100644 --- /dev/null +++ b/src/Synthesizer/Filter/TwoWay.hs @@ -0,0 +1,247 @@ +{-# LANGUAGE NoImplicitPrelude #-} +{-# LANGUAGE MultiParamTypeClasses #-} +{-# LANGUAGE FlexibleInstances #-} +module Synthesizer.Filter.TwoWay where + +import Synthesizer.Filter.Basic + +import qualified Synthesizer.Plain.Signal as Sig +import qualified Synthesizer.Plain.Interpolation as Ip +import qualified Synthesizer.Plain.Interpolation as Interpolation + +import Algebra.Module(linearComb,(*>)) + +import qualified Algebra.Module as Module +import qualified Algebra.RealRing as RealRing +import qualified Algebra.Ring as Ring +import qualified Algebra.Additive as Additive + +import Number.Complex(cis, ) +import Data.Function.HT (nest, ) +import qualified Data.List as List + +import NumericPrelude.Base hiding (take) +import NumericPrelude.Numeric + + +{-| A TwoWay.Signal stores values of the past and the future -} +data Signal v = Signal {past, future :: [v]} + deriving (Show, Eq) + +{-| Take n values starting from time zero. + If you want clips from elsewhere, + call 'take' after 'delay'. -} +take :: Int -> Signal v -> [v] +take n (Signal _ x) = List.take n x + +zipSignalWith :: (a -> b -> c) -> Signal a -> Signal b -> Signal c +zipSignalWith f (Signal xPast xFuture) (Signal yPast yFuture) = + (Signal (zipWith f xPast yPast) (zipWith f xFuture yFuture)) + +{-| Take the value at time zero. -} +origin :: Ring.C a => Signal a -> a +origin (Signal _ (x:_)) = x +origin _ = 0 + +{-| A signal that consists entirely of ones -} +ones :: Ring.C a => Signal a +ones = Signal (repeat 1) (repeat 1) + +{-| shift signal in time, + keep all values but if required pad with zeros -} +delay :: (Additive.C v) => + Int -> Signal v -> Signal v +delay = delayGen delayOnce + +delayPad :: v -> Int -> Signal v -> Signal v +delayPad z = delayGen (delayPadOnce z) + +{-| shift signal in time, + zero values at either ends will be flushed -} +delayOpt :: (Eq v, Additive.C v) => + Int -> Signal v -> Signal v +delayOpt = delayGen delayOptOnce + + +{-| Delay by one sample. -} +delayOnce :: (Additive.C v) => + Signal v -> Signal v +--delayOnce (Signal [] []) = ([],[]) +delayOnce (Signal [] ys) = Signal [] (zero:ys) +delayOnce (Signal (x:xs) ys) = Signal xs (x:ys) + +delayPadOnce :: v -> Signal v -> Signal v +--delayPadOnce _ (Signal [] []) = ([],[]) +delayPadOnce z (Signal [] ys) = Signal [] (z:ys) +delayPadOnce _ (Signal (x:xs) ys) = Signal xs (x:ys) + +delayOptOnce :: (Eq v, Additive.C v) => + Signal v -> Signal v +--delayOptOnce (Signal [] []) = Signal [] [] +delayOptOnce (Signal [] ys) = Signal [] (zero:ys) +delayOptOnce (Signal (x:xs) []) = Signal xs (if x==zero then [] else x:[]) +delayOptOnce (Signal (x:xs) ys) = Signal xs (x:ys) + + +{-| General routine that supports delaying and prefetching + using a general one-sample delaying routine. -} +delayGen :: (Signal v -> Signal v) -> + Int -> Signal v -> Signal v +{- Using this optimization applications of recursive filters + with zero initial conditions represented by an empty list will fail. + This is because in this case the value of the first item of the future list + depends on the first item of the input future list, + whereas normally the first future value depends on no input future value, + at all. +delayGen _ _ (Signal [] []) = Signal [] [] + cf. the next example -} +delayGen delOnce t = + if t < 0 + then reverseTwoWay . nest (negate t) delOnce . reverseTwoWay + else nest t delOnce + +reverseTwoWay :: Signal v -> Signal v +reverseTwoWay (Signal x y) = Signal y x + + +instance (Additive.C v) => Additive.C (Signal v) where + zero = Signal zero zero + (+) (Signal y0 y1) (Signal x0 x1) = Signal (y0 + x0) (y1 + x1) + (-) (Signal y0 y1) (Signal x0 x1) = Signal (y0 - x0) (y1 - x1) + negate (Signal x0 x1) = Signal (negate x0) (negate x1) + +instance (Module.C a v) => Module.C a (Signal v) where + (*>) s (Signal x0 x1) = Signal (s *> x0) (s *> x1) + + + + +{-| for a Signal this means a reversion of the elements -} +flipPair :: (a,b) -> (b,a) +flipPair (x,y) = (y,x) + +{- This example simulates what happens if you call + apply (Feedback (Serial []) (Prim (Delay 1)) []) ([],[1]) + depending on the implementation of delayGen it may work or + loop infinitely when yFuture is computed. + It's even before the first element of yFuture is computed. + Note, that the equivalent + apply (Feedback (Serial []) (Prim (Delay 1)) [0]) ([],[1]) + works! (i.e. set yPast = [0] -} +testDelayGen :: Signal Double +testDelayGen = + let yPast = [] + x = Signal [] [1] + y = Signal yPast yFuture + Signal _ yFuture = delayOnce (x + y) + -- Signal _ yFuture = delayOptOnce (add x y) + -- Signal _ yFuture = delayGen delayOnce 1 (add x y) + in Signal yPast (List.take 10 yFuture) + + + +{-| Unmodulated non-recursive filter -} +nonRecursiveFilter :: Module.C a v => + [a] -> Signal v -> Signal v +nonRecursiveFilter m x = + linearComb m (iterate delayOnce x) + +{-| Modulated non-recursive filter. + The number of values before time 0 (past) or + the filter mask lengths must be at most finite. -} +nonRecursiveFilterMod :: Module.C a v => + Signal [a] -> Signal v -> Signal v +nonRecursiveFilterMod (Signal mpre msuf) x = + let (pre, suf) = unzip (map (\(Signal a b) -> (a,b)) (iterate delayOnce x)) + in Signal (zipWith linearComb mpre pre) (zipWith linearComb msuf suf) + + +{-| Interpolation allowing negative frequencies, + but requires storage of all past values. -} +interpolatePaddedZero :: (Ord a, RealRing.C a) => + b -> Interpolation.T a b + -> a -> Signal a -> Signal b -> Signal b +interpolatePaddedZero z ip phase fs (Signal xPast xFuture) = + let (phInt, phFrac) = splitFraction phase + xPadded = Signal (xPast ++ repeat z) (xFuture ++ repeat z) + in interpolateCore ip phFrac fs + (delayPad z (Ip.offset ip - phInt) xPadded) + +interpolatePaddedCyclic :: (Ord a, RealRing.C a) => + Interpolation.T a b + -> a -> Signal a -> Signal b -> Signal b +interpolatePaddedCyclic ip phase fs (Signal xPast xFuture) = + let (phInt, phFrac) = splitFraction phase + xCyclic = xFuture ++ reverse xPast + in interpolateCore ip phFrac fs + -- mod is for efficiency, only + (delayPad (error "interpolate: infinite signal needs no zero padding") + (mod (Ip.offset ip - phInt) (length xCyclic)) + (Signal (cycle (reverse xCyclic)) (cycle xCyclic))) + +-- note that the extrapolation may miss some of the first and some of the last points +interpolatePaddedExtrapolation :: (Ord a, RealRing.C a) => + Interpolation.T a b + -> a -> Signal a -> Signal b -> Signal b +interpolatePaddedExtrapolation ip phase fs x = + interpolateCore ip (phase - fromIntegral (Ip.offset ip)) fs x + +interpolateCore :: (Ord a, Ring.C a) => + Interpolation.T a b -> a -> Signal a -> Signal b -> Signal b +interpolateCore ip phase (Signal freqPast freqFuture) x = + Signal (interpolateHalfWay ip (1-phase) freqPast + (delayPadOnce (error "interpolateCore: infinite signal needs no zero padding") + (reverseTwoWay x))) + (interpolateHalfWay ip phase freqFuture x) + +interpolateHalfWay :: (Ord a, Ring.C a) => + Interpolation.T a b -> a -> [a] -> Signal b -> [b] +interpolateHalfWay ip phase freqs (Signal xPast xFuture) = + if phase >= 1 && Sig.lengthAtLeast (1+Ip.number ip) xFuture + then interpolateHalfWay ip (phase-1) freqs + (Signal (head xFuture : xPast) (tail xFuture)) + else if phase < 0 && Sig.lengthAtLeast 1 xPast + then interpolateHalfWay ip (phase + 1) freqs + (Signal (tail xPast) (head xPast : xFuture)) + else Ip.func ip phase xFuture : + interpolateHalfWay ip (phase + head freqs) (tail freqs) + (Signal xPast xFuture) + + +{-| Description of a basic filter that can be used in larger networks. -} +data T t a v = + Mask [a] + {-^ A static filter described by its mask -} + | ModMask (Signal [a]) + {-^ A modulated filter described by a list of masks -} + | FracDelay (Interpolation.T t v) t + {-^ Delay the signal by a fractional amount of samples. + This is achieved by interpolation. -} + | ModFracDelay (Interpolation.T t v) (Signal t) + {-^ Delay with varying delay times. -} + | Delay Int + {-^ Delay the signal by given amount of samples. -} + | Past [v] + {-^ Replace the past by the given one. + This must be present in each recursive filter cycle + to let the magic work! -} + +instance Filter Signal T where + + apply (Mask m) = nonRecursiveFilter m + apply (ModMask m) = nonRecursiveFilterMod m + apply (FracDelay ip t) = interpolatePaddedZero zero + ip (-t) ones + apply (ModFracDelay ip ts) = interpolatePaddedZero zero + ip (- origin ts) (ts - delay (-1) ts + ones) + apply (Delay t) = delay t + apply (Past x) = Signal x . future + + {- This is in principle the same as for one way filters. + How can one merge them? -} + transferFunction (Mask m) w = linearComb m (screw (negate w)) + transferFunction (FracDelay _ t) w = cis (negate w * t) + transferFunction (Delay t) w = cis (negate w * fromIntegral t) + transferFunction (Past _) _ = 1 + transferFunction _ _ = + error "transfer function can't be computed for modulated filters" diff --git a/synthesizer-filter.cabal b/synthesizer-filter.cabal new file mode 100644 --- /dev/null +++ b/synthesizer-filter.cabal @@ -0,0 +1,49 @@ +Name: synthesizer-filter +Version: 0.4 +License: GPL +License-File: LICENSE +Author: Henning Thielemann +Maintainer: Henning Thielemann +Homepage: http://www.haskell.org/haskellwiki/Synthesizer +Category: Sound +Synopsis: Audio signal processing coded in Haskell: Filter networks +Description: + In this package we experiment with various ways + of representing filter networks. + However, none of them is mature so far. +Stability: Experimental +Tested-With: GHC==6.8.2, GHC==6.10.4 +Cabal-Version: >=1.6 +Build-Type: Simple + +Source-Repository this + Tag: 0.4 + Type: darcs + Location: http://code.haskell.org/synthesizer/filter/ + +Source-Repository head + Type: darcs + Location: http://code.haskell.org/synthesizer/filter/ + +Library + Build-Depends: + synthesizer-core >=0.4 && <0.5, + transformers >=0.2 && <0.3, + numeric-prelude >=0.2 && <0.3, + numeric-quest >= 0.1 && <0.2, + utility-ht >=0.0.5 && <0.1, + containers >=0.1 && <0.4, + base >= 3 && <5 + + GHC-Options: -Wall + Hs-source-dirs: src + Exposed-modules: + Synthesizer.Filter.Basic + Synthesizer.Filter.Composition + Synthesizer.Filter.Example + Synthesizer.Filter.Fix + Synthesizer.Filter.Graph + Synthesizer.Filter.Graphic + Synthesizer.Filter.MonadFix + Synthesizer.Filter.OneWay + Synthesizer.Filter.TwoWay