[{"data":1,"prerenderedAt":2289},["ShallowReactive",2],{"yWytRNFHoK":3,"VyF3Mmj32r":702,"N9m89Rcq0G":930},{"title":4,"description":5,"body":6,"_type":701,"_id":4},"VK_EXT_frame_boundary.proposal","VK_EXT_frame_boundary is a device extension that helps tools (such as\ndebuggers) to group queue submissions per frames in non-trivial scenarios,\ntypically when vkQueuePresentKHR is not a relevant frame boundary delimiter.",{"type":7,"children":8,"toc":675},"root",[9,40,53,60,93,114,126,133,145,151,162,168,180,200,210,222,228,238,243,249,255,276,303,308,316,343,356,405,413,418,444,449,474,480,485,490,495,503,509,515,520,528,534,539,547,553,558,566,572,578,583,610,616,621,626,638,651,657,662],{"type":10,"tag":11,"props":12,"children":13},"element","p",{},[14,22,24,30,32,38],{"type":10,"tag":15,"props":16,"children":18},"code",{"className":17},[],[19],{"type":20,"value":21},"text","VK_EXT_frame_boundary",{"type":20,"value":23}," is a device extension that helps ",{"type":10,"tag":25,"props":26,"children":27},"em",{},[28],{"type":20,"value":29},"tools",{"type":20,"value":31}," (such as\ndebuggers) to group queue submissions per frames in non-trivial scenarios,\ntypically when ",{"type":10,"tag":15,"props":33,"children":35},{"className":34},[],[36],{"type":20,"value":37},"vkQueuePresentKHR",{"type":20,"value":39}," is not a relevant frame boundary delimiter.",{"type":10,"tag":11,"props":41,"children":42},{},[43,45],{"type":20,"value":44},"See also the discussion in ",{"type":10,"tag":46,"props":47,"children":51},"a",{"href":48,"rel":49},"https://gitlab.khronos.org/vulkan/vulkan/-/issues/2436",[50],"nofollow",[52],{"type":20,"value":48},{"type":10,"tag":54,"props":55,"children":57},"h2",{"id":56},"_problem_statement",[58],{"type":20,"value":59},"Problem Statement",{"type":10,"tag":11,"props":61,"children":62},{},[63,65,70,72,77,79,84,86,91],{"type":20,"value":64},"Various Vulkan tools (e.g. debuggers) use a layer to monitor all Vulkan\ncommands, and need to know where a frame starts and ends. In general,\n",{"type":10,"tag":15,"props":66,"children":68},{"className":67},[],[69],{"type":20,"value":37},{"type":20,"value":71}," is a natural frame boundary delimiter: a frame is made by\nall commands between two ",{"type":10,"tag":15,"props":73,"children":75},{"className":74},[],[76],{"type":20,"value":37},{"type":20,"value":78},". However, there are scenarios where\n",{"type":10,"tag":15,"props":80,"children":82},{"className":81},[],[83],{"type":20,"value":37},{"type":20,"value":85}," is not a suitable frame boundary delimiter. The\n",{"type":10,"tag":15,"props":87,"children":89},{"className":88},[],[90],{"type":20,"value":21},{"type":20,"value":92}," device extension lets application developers indicate to\ntools where the frames start and end.",{"type":10,"tag":11,"props":94,"children":95},{},[96,98,104,106,112],{"type":20,"value":97},"Note: here, ",{"type":10,"tag":15,"props":99,"children":101},{"className":100},[],[102],{"type":20,"value":103},"frame",{"type":20,"value":105}," is understood as ",{"type":10,"tag":15,"props":107,"children":109},{"className":108},[],[110],{"type":20,"value":111},"a unit of workload that spans one or more queue submissions",{"type":20,"value":113},". The notion of frame is application-dependent. In graphical\napplications, a frame is typically the work needed to render into the image that\nis eventually presented. In a compute-only application, a frame could be a set\nof compute kernels dispatches that treat one unit of work.",{"type":10,"tag":11,"props":115,"children":116},{},[117,119,124],{"type":20,"value":118},"There are a number of cases where ",{"type":10,"tag":15,"props":120,"children":122},{"className":121},[],[123],{"type":20,"value":37},{"type":20,"value":125}," is not a suitable frame\nboundary delimiter.",{"type":10,"tag":127,"props":128,"children":130},"h3",{"id":129},"_graphics_applications_bypassing_the_khronos_swapchain",[131],{"type":20,"value":132},"Graphics applications bypassing the Khronos swapchain",{"type":10,"tag":11,"props":134,"children":135},{},[136,138,143],{"type":20,"value":137},"Graphics applications are not tied to use the Khronos swapchain, and they may\ninteract directly with a platform presentation engine. In this case, they will\nnot call ",{"type":10,"tag":15,"props":139,"children":141},{"className":140},[],[142],{"type":20,"value":37},{"type":20,"value":144},".",{"type":10,"tag":127,"props":146,"children":148},{"id":147},"_compute_only_applications",[149],{"type":20,"value":150},"Compute-only applications",{"type":10,"tag":11,"props":152,"children":153},{},[154,156,161],{"type":20,"value":155},"Compute-only applications typically do not interact with a presentation engine at\nall, so they would not call ",{"type":10,"tag":15,"props":157,"children":159},{"className":158},[],[160],{"type":20,"value":37},{"type":20,"value":144},{"type":10,"tag":127,"props":163,"children":165},{"id":164},"_overlapping_frames",[166],{"type":20,"value":167},"Overlapping frames",{"type":10,"tag":11,"props":169,"children":170},{},[171,173,179],{"type":20,"value":172},"A graphics application may pipeline its frame preparation such that work for\ndifferent frames is being submitted in an interleaved way, a scenario we call\nhere ",{"type":10,"tag":15,"props":174,"children":176},{"className":175},[],[177],{"type":20,"value":178},"overlapping frames",{"type":20,"value":144},{"type":10,"tag":11,"props":181,"children":182},{},[183,185,191,193,198],{"type":20,"value":184},"For instance, consider a graphics application where each frame is executed\nvia two ",{"type":10,"tag":15,"props":186,"children":188},{"className":187},[],[189],{"type":20,"value":190},"vkQueueSubmit",{"type":20,"value":192}," followed by a ",{"type":10,"tag":15,"props":194,"children":196},{"className":195},[],[197],{"type":20,"value":37},{"type":20,"value":199},", and frame\npreparation is pipelined, such that the serialized commands look like:",{"type":10,"tag":201,"props":202,"children":204},"pre",{"code":203},"vkQueueSubmit(); // 1st submit of Frame N\nvkQueueSubmit(); // 2nd submit of Frame N-1\nvkQueuePresentKHR(); // present Frame N-1\nvkQueueSubmit(); // 1st submit of Frame N+1\nvkQueueSubmit(); // 2nd submit of Frame N\nvkQueuePresentKHR(); // present Frame N\n",[205],{"type":10,"tag":15,"props":206,"children":208},{"__ignoreMap":207},"",[209],{"type":20,"value":203},{"type":10,"tag":11,"props":211,"children":212},{},[213,215,220],{"type":20,"value":214},"Here, relying on ",{"type":10,"tag":15,"props":216,"children":218},{"className":217},[],[219],{"type":20,"value":37},{"type":20,"value":221}," as a frame boundary delimiter would lead to\nthe erroneous grouping of queue submissions of different frames as the work of a\nsingle frame.",{"type":10,"tag":54,"props":223,"children":225},{"id":224},"_solution_space",[226],{"type":20,"value":227},"Solution Space",{"type":10,"tag":229,"props":230,"children":231},"ul",{},[232],{"type":10,"tag":233,"props":234,"children":235},"li",{},[236],{"type":20,"value":237},"Debug utilities: existing debug utilities let us tag Vulkan objects, could we\nuse that to identify which work belongs to which frame? We can think of\ntagging the command buffers submitted with a frame identifier. However some\ncommand buffers may be used concurrently by several frames, so that is not a\nviable approach. In the same vein, queue debug label regions are not\nsatisfactory since they cannot handle overlapping frames.",{"type":10,"tag":11,"props":239,"children":240},{},[241],{"type":20,"value":242},"What we need is a way to associate a frame identifier to the one or more queue\nsubmissions that submit the work for this frame. This is what the\nVK_EXT_frame_boundary extension does.",{"type":10,"tag":54,"props":244,"children":246},{"id":245},"_proposal",[247],{"type":20,"value":248},"Proposal",{"type":10,"tag":127,"props":250,"children":252},{"id":251},"_overview",[253],{"type":20,"value":254},"Overview",{"type":10,"tag":11,"props":256,"children":257},{},[258,260,266,268,274],{"type":20,"value":259},"We want applications to be able to group queue submissions by frames. To this\naim, we let applications tag queue submissions with a ",{"type":10,"tag":15,"props":261,"children":263},{"className":262},[],[264],{"type":20,"value":265},"uint64_t",{"type":20,"value":267}," frame\nidentifier. However, this is not sufficient: given that a frame may span more\nthan one queue submissions, in order to know when a frame ends, tools also need\nto know which queue submission is the last one for a given frame. So in addition\nto the frame identifier, we also want to be able to tag queue submissions with a\n",{"type":10,"tag":15,"props":269,"children":271},{"className":270},[],[272],{"type":20,"value":273},"frame end",{"type":20,"value":275}," flag, to mark the last submission for a given frame identifier.",{"type":10,"tag":11,"props":277,"children":278},{},[279,281,286,288,294,296,301],{"type":20,"value":280},"There is one clarification left to do: the ",{"type":10,"tag":15,"props":282,"children":284},{"className":283},[],[285],{"type":20,"value":273},{"type":20,"value":287}," submission is the\n",{"type":10,"tag":15,"props":289,"children":291},{"className":290},[],[292],{"type":20,"value":293},"logical last",{"type":20,"value":295}," queue submission, but in the presence of timeline semaphores it\nmay not be the last one to be submitted. Since timeline semaphores permit queue\nsubmissions to wait on semaphores whose signal is not yet submitted, the\nsemaphore meant to be the last part of work for a given frame may not be the\nlast one to be submitted. In this context, we want to mark the ",{"type":10,"tag":15,"props":297,"children":299},{"className":298},[],[300],{"type":20,"value":273},{"type":20,"value":302},"\nsubmission as the one that is logically the last submission for the frame: if\nthis submission waits on semaphores whose signal is not yet submitted, then all\nsubsequent submissions with the same frame identifier until the submission that\nsignals these semaphores are also associated to that frame.",{"type":10,"tag":11,"props":304,"children":305},{},[306],{"type":20,"value":307},"To illustrate this on a small example, considering serialized Vulkan commands:",{"type":10,"tag":201,"props":309,"children":311},{"code":310},"// At this point, the latest signal of timeline semaphore TLS set its value to 1\n\n// Logical last submission for frame N, wait on TLS value 2\nvkQueueSubmit( frameID:N, frameEnd, wait:TLS(2) )\n\n// The actual final submission, which unblocks the previous one, is also part\n// of the work for frame N, even if in submit order it comes after the frameEnd\n// submission.\nvkQueueSubmit( frameID:N, signal:TLS(2) )\n",[312],{"type":10,"tag":15,"props":313,"children":314},{"__ignoreMap":207},[315],{"type":20,"value":310},{"type":10,"tag":11,"props":317,"children":318},{},[319,321,326,328,333,335,341],{"type":20,"value":320},"So we want a way to tag queue submissions with a ",{"type":10,"tag":15,"props":322,"children":324},{"className":323},[],[325],{"type":20,"value":265},{"type":20,"value":327}," frame identifier,\nand a frameEnd flag. To this aim, the ",{"type":10,"tag":15,"props":329,"children":331},{"className":330},[],[332],{"type":20,"value":21},{"type":20,"value":334}," device extension\ndefines the new ",{"type":10,"tag":15,"props":336,"children":338},{"className":337},[],[339],{"type":20,"value":340},"VkFrameBoundaryEXT",{"type":20,"value":342}," type that is meant to be passed in queue\nsubmission pNext chains.",{"type":10,"tag":127,"props":344,"children":346},{"id":345},"_the_vkframeboundaryext_type",[347,349,354],{"type":20,"value":348},"The ",{"type":10,"tag":15,"props":350,"children":352},{"className":351},[],[353],{"type":20,"value":340},{"type":20,"value":355}," type",{"type":10,"tag":11,"props":357,"children":358},{},[359,360,365,367,372,374,380,382,388,389,395,397,403],{"type":20,"value":348},{"type":10,"tag":15,"props":361,"children":363},{"className":362},[],[364],{"type":20,"value":21},{"type":20,"value":366}," device extension defines a new\n",{"type":10,"tag":15,"props":368,"children":370},{"className":369},[],[371],{"type":20,"value":340},{"type":20,"value":373}," type that is meant to be added to pNext chains of queue\nsubmissions, such as ",{"type":10,"tag":15,"props":375,"children":377},{"className":376},[],[378],{"type":20,"value":379},"VkSubmitInfo",{"type":20,"value":381},", ",{"type":10,"tag":15,"props":383,"children":385},{"className":384},[],[386],{"type":20,"value":387},"VkSubmitInfo2",{"type":20,"value":381},{"type":10,"tag":15,"props":390,"children":392},{"className":391},[],[393],{"type":20,"value":394},"VkBindSparseInfo",{"type":20,"value":396},"\nor ",{"type":10,"tag":15,"props":398,"children":400},{"className":399},[],[401],{"type":20,"value":402},"VkPresentInfoKHR",{"type":20,"value":404},". This type looks like:",{"type":10,"tag":201,"props":406,"children":408},{"code":407},"// Flags\ntypedef enum VkFrameBoundaryFlagBitsEXT {\n VK_FRAME_BOUNDARY_FRAME_END_BIT_EXT = 0x00000001,\n} VkFrameBoundaryFlagBitsEXT;\ntypedef VkFlags VkFrameBoundaryFlagsEXT;\n\n// VkFrameBoundaryEXT can be passed in any queue submission's pNext chain\ntypedef struct VkFrameBoundaryEXT {\n VkStructureType sType;\n const void* pNext;\n\n // Necessary members:\n // flags is necessary to mark the last submission of a frame\n VkFrameBoundaryFlagsEXT flags;\n // frameID is necessary to disambiguate overlapping frames\n uint64_t frameID;\n\n // Extra members: provide a list of objects which No need to pass the layout as\n // trace-replay tools will track the layout anyway.\n uint32_t imageCount;\n const VkImage* pImages;\n uint32_t bufferCount;\n const VkBuffer* pBuffers;\n\n // Extra info can be passed with an arbitrary tag payload, typically\n // a tool-specific struct.\n uint64_t tagName;\n size_t tagSize;\n const void* pTag;\n} VkFrameBoundaryEXT;\n",[409],{"type":10,"tag":15,"props":410,"children":411},{"__ignoreMap":207},[412],{"type":20,"value":407},{"type":10,"tag":11,"props":414,"children":415},{},[416],{"type":20,"value":417},"Where:",{"type":10,"tag":419,"props":420,"children":421},"ol",{},[422,433],{"type":10,"tag":233,"props":423,"children":424},{},[425,431],{"type":10,"tag":15,"props":426,"children":428},{"className":427},[],[429],{"type":20,"value":430},"flags",{"type":20,"value":432}," provides a way to tag submissions with a frameEnd flag.",{"type":10,"tag":233,"props":434,"children":435},{},[436,442],{"type":10,"tag":15,"props":437,"children":439},{"className":438},[],[440],{"type":20,"value":441},"frameID",{"type":20,"value":443}," provides a way to tag submissions with a frame identifier.",{"type":10,"tag":11,"props":445,"children":446},{},[447],{"type":20,"value":448},"In addition to these two necessary members, we have a few extras:",{"type":10,"tag":419,"props":450,"children":451},{},[452,464,469],{"type":10,"tag":233,"props":453,"children":454},{},[455,457,462],{"type":20,"value":456},"a list of VkImage: this makes this extension as expressive as\n",{"type":10,"tag":15,"props":458,"children":460},{"className":459},[],[461],{"type":20,"value":37},{"type":20,"value":463},", the classic frame boundary delimiter. For the classic\nframe-oriented graphics workloads, it is convenient to have a list of images\nstoring the final frame renderings. We do not need the image layout as the\ntrace-replay tools would have to track image layout already anyway.",{"type":10,"tag":233,"props":465,"children":466},{},[467],{"type":20,"value":468},"a list of VkBuffer: which allows applications that do not produce their\nfinal result as an image (eg. compute applications) to provide the final\nresult of the frame.",{"type":10,"tag":233,"props":470,"children":471},{},[472],{"type":20,"value":473},"a way to attach a binary payload: this can be used to pass tool-specific\nextra information.",{"type":10,"tag":127,"props":475,"children":477},{"id":476},"_validation",[478],{"type":20,"value":479},"Validation",{"type":10,"tag":11,"props":481,"children":482},{},[483],{"type":20,"value":484},"Since the concept of a frame is application dependent, there is no way to\nvalidate relevant use of frame identifier. As such there is no restrictions\nimposed on frame identifiers and is the responsibility of the application\nto use them in a relevant way.",{"type":10,"tag":11,"props":486,"children":487},{},[488],{"type":20,"value":489},"In practice it is advised that applications use a single monotonically\nincreasing counter to base their frame identifiers on and not to reuse\nidentifiers between separate frames.",{"type":10,"tag":11,"props":491,"children":492},{},[493],{"type":20,"value":494},"However, there is no way for the validation layer to detect an application\nnot adhering to these rules, since the validation layer has no idea which\nsubmissions should be grouped together, so a valid grouping like this might\nbe flagged as invalid because of the application using wait before signal:",{"type":10,"tag":201,"props":496,"children":498},{"code":497},"vkQueueSubmit( frame:0 ) // start of a frame\nvkQueueSubmit( frame:0 ) // part of the frame\nvkQueueSubmit( frame:0, frameEnd, wait:TLS(42) ) // logical end, waiting on a not-yet-signaled TLS\nvkQueueSubmit( frame:0, signal:TLS(42) ) // this is still part of the current frame, after the frameEnd marker.\n",[499],{"type":10,"tag":15,"props":500,"children":501},{"__ignoreMap":207},[502],{"type":20,"value":497},{"type":10,"tag":54,"props":504,"children":506},{"id":505},"_examples",[507],{"type":20,"value":508},"Examples",{"type":10,"tag":127,"props":510,"children":512},{"id":511},"_compute_only",[513],{"type":20,"value":514},"Compute-only",{"type":10,"tag":11,"props":516,"children":517},{},[518],{"type":20,"value":519},"Compute-only that want to split their work into frames can do so with:",{"type":10,"tag":201,"props":521,"children":523},{"code":522},"vkQueueSubmit( frame:N ) // Zero or more submits for frame N\nvkQueueSubmit( frame:N, frameEnd ) // Last submit for frame N\n\nvkQueueSubmit( frame:N+1 ) // Zero or more submits for frame N+1\nvkQueueSubmit( frame:N+1, frameEnd ) // Last submit for frame N+1\n",[524],{"type":10,"tag":15,"props":525,"children":526},{"__ignoreMap":207},[527],{"type":20,"value":522},{"type":10,"tag":127,"props":529,"children":531},{"id":530},"_graphics_sequential_frames_not_using_the_khr_swapchain",[532],{"type":20,"value":533},"Graphics, sequential frames, not using the KHR swapchain",{"type":10,"tag":11,"props":535,"children":536},{},[537],{"type":20,"value":538},"A graphics application that prepare frames in sequence (as opposed to\noverlapping frames), but makes no use of the KHR swapchain, can group\nsubmissions with:",{"type":10,"tag":201,"props":540,"children":542},{"code":541},"vkQueueSubmit( frame:N ) // Zero or more submits for frame N\nvkQueueSubmit( frame:N, frameEnd, imageCount:1, pImages:0x12345 ) // Last submit for frame N\n// here code that passes pImages to the presentation engine\n\nvkQueueSubmit( frame:N+1 ) // Zero or more submits for frame N+1\nvkQueueSubmit( frame:N+1, frameEnd, imageCount:1, pImages:0x54321 ) // Last submit for frame N+1\n// here code that passes pImages to the presentation engine\n",[543],{"type":10,"tag":15,"props":544,"children":545},{"__ignoreMap":207},[546],{"type":20,"value":541},{"type":10,"tag":127,"props":548,"children":550},{"id":549},"_overlapping_frames_with_wait_after_signal",[551],{"type":20,"value":552},"Overlapping frames with wait-after-signal",{"type":10,"tag":11,"props":554,"children":555},{},[556],{"type":20,"value":557},"A graphics application with overlapping frames and wait-after-signal (that may\nbe due to multithreading, here we look at a serialized view of Vulkan commands),\ncan group queue submissions per frame with:",{"type":10,"tag":201,"props":559,"children":561},{"code":560},"vkQueueSubmit( frame:N ); // 1st submit of frame N\n\nvkQueueSubmit( frame:N-1 ); // Some other submissions for an other frame\nvkQueueSubmit( frame:N+1 ); // Some other submissions for an other frame\n\n// 2nd submit of frame N, logically the last one, but waits on a TLS not yet\n// signaled for that value\nvkQueueSubmit( frame:N, frameEnd, wait:TLS(42) );\n\nvkQueueSubmit( frame:... ); // Some other submissions for other frames\n\n// 3rd submit of frame N, not the logical last one, but the last one in submit\n// order (here serialized) since it signals the TLS on which the logical last\n// submission waits\nvkQueueSubmit( frame:N, signal:TLS(42) );\n",[562],{"type":10,"tag":15,"props":563,"children":564},{"__ignoreMap":207},[565],{"type":20,"value":560},{"type":10,"tag":54,"props":567,"children":569},{"id":568},"_issues",[570],{"type":20,"value":571},"Issues",{"type":10,"tag":127,"props":573,"children":575},{"id":574},"_resolved_what_should_this_extension_be_named",[576],{"type":20,"value":577},"RESOLVED: What should this extension be named?",{"type":10,"tag":11,"props":579,"children":580},{},[581],{"type":20,"value":582},"VK_EXT_frame_boundary.",{"type":10,"tag":11,"props":584,"children":585},{},[586,592,594,600,602,608],{"type":10,"tag":15,"props":587,"children":589},{"className":588},[],[590],{"type":20,"value":591},"Frame",{"type":20,"value":593}," is still the best word to convey the meaning of ",{"type":10,"tag":15,"props":595,"children":597},{"className":596},[],[598],{"type":20,"value":599},"a unit of workload spanning one or more queue submissions",{"type":20,"value":601},". ",{"type":10,"tag":15,"props":603,"children":605},{"className":604},[],[606],{"type":20,"value":607},"Boundary",{"type":20,"value":609}," might be seen as too\nspecific since this can be seen more generally as tagging queue submissions\nwith frame identifiers, but really the goal of this tagging is precisely to\nknow when a frame starts and ends, i.e. to know its boundaries.",{"type":10,"tag":127,"props":611,"children":613},{"id":612},"_resolved_what_information_should_be_included_in_vkframeboundaryext",[614],{"type":20,"value":615},"RESOLVED: What information should be included in VkFrameBoundaryEXT?",{"type":10,"tag":11,"props":617,"children":618},{},[619],{"type":20,"value":620},"Beyond the necessary flags and frameID, we keep only a list of objects that\ncontain the end result of the frame, and a binary blob where other extra info\ncan be provided.",{"type":10,"tag":11,"props":622,"children":623},{},[624],{"type":20,"value":625},"The list of VkImage and VkBuffer objects allow the application to provide the\nend result of the frame. There is no need to provide extra information about\nthe object like the layout of these images since capture-replay tools would\ntrack the Vulkan state whilst the application is running.",{"type":10,"tag":11,"props":627,"children":628},{},[629,631,636],{"type":20,"value":630},"The list of VkImage lets this extension be as expressive as\n",{"type":10,"tag":15,"props":632,"children":634},{"className":633},[],[635],{"type":20,"value":37},{"type":20,"value":637},", which has a list of swapchain images.",{"type":10,"tag":11,"props":639,"children":640},{},[641,643,649],{"type":20,"value":642},"A binary blob (called ",{"type":10,"tag":15,"props":644,"children":646},{"className":645},[],[647],{"type":20,"value":648},"tag",{"type":20,"value":650}," to be homogeneous with\nVkDebugUtilsObjectTagInfoEXT), allows tools to define their own data containing\nany extra information that is required and update this without having to change\nthe Vulkan specification.",{"type":10,"tag":127,"props":652,"children":654},{"id":653},"_resolved_how_should_frame_identifiers_be_validated",[655],{"type":20,"value":656},"RESOLVED: How should frame identifiers be validated?",{"type":10,"tag":11,"props":658,"children":659},{},[660],{"type":20,"value":661},"Do not impose conditions on frame identifiers.",{"type":10,"tag":11,"props":663,"children":664},{},[665,667,673],{"type":20,"value":666},"Frame identifiers are just a way to indicate to tools how to group queue\nsubmissions, and that there is no ground to impose any kind of monotonic\nincrease. 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