{
  "domain": "com.microsoft",
  "name": "SkipGroupNorm",
  "sinceVersion": 1,
  "inputs": {
    "X": { "dtype": "T", "rank": 4 },
    "gamma": { "dtype": "M", "rank": 1 },
    "beta": { "dtype": "M", "rank": 1 },
    "skip": { "dtype": "T" },
    "bias": { "dtype": "T", "rank": 1, "optional": true }
  },
  "outputs": {
    "Y": { "dtype": "T", "rank": 4, "shape": "shapes.X" },
    "S": { "dtype": "T", "rank": 4, "optional": true, "shape": "shapes.X" }
  },
  "attributes": { "activation": {}, "groups": {}, "channels_last": { "default": 1 }, "epsilon": { "default": 0.00001 } },
  "attributeConstraints": { "activation": { "required": true, "values": [0, 1] }, "groups": { "required": true } },
  "typeConstraints": { "T": ["float32", "float16"], "M": ["float32", "float16"] },
  "tunables": {
    "WORKGROUP_SIZE": { "default": 256 },
    "MAX_SPLITS": { "default": 256 },
    "VALUES_PER_SPLIT": { "default": 4096 },
    "SPLIT_MIN_ELEMENTS": { "default": 262144 },
    "APPLY_SLAB_ELEMENTS": { "default": 8192 },
    "FUSED_MIN_ROWS": { "default": 64 },
    "FUSED_MAX_GROUP_BYTES": { "default": 131072 }
  },
  "derive": {
    "attrsPresent": "has(attrs, \"groups\") and has(attrs, \"activation\")",
    "numGroups": "attrs.groups if attrsPresent else 0",
    "activationKind": "attrs.activation if attrsPresent else 0",
    "channelsLast": "attrs.channels_last != 0",
    "rankOk": "ranks.X == 4 and ranks.Y == 4 and ranks.gamma == 1 and ranks.beta == 1",
    "dimN": "dim(shapes.X, 0) if rankOk else 0",
    "dimC": "(dim(shapes.X, 3) if channelsLast else dim(shapes.X, 1)) if rankOk else 0",
    "dimHW": "(dim(shapes.X, 1) * dim(shapes.X, 2) if channelsLast else dim(shapes.X, 2) * dim(shapes.X, 3)) if rankOk else 0",
    "groupsOk": "numGroups >= 1 and dimC >= 1 and dimC % numGroups == 0",
    "channelsPerGroup": "dimC / numGroups if groupsOk else 0",
    "planeCount": "dimN * dimC",
    "groupSize": "channelsPerGroup * dimHW",
    "normRows": "dimN * numGroups",
    "elementCount": "numel(shapes.X) if rankOk else 0",
    "shapeOk": "rankOk and groupsOk and dimN > 0 and dimHW > 0 and groupSize > 0 and sameShape(shapes.Y, shapes.X) and dim(shapes.gamma, 0) == dimC and dim(shapes.beta, 0) == dimC",
    "deviceWorkgroupCap": "min(device.limits.maxComputeInvocationsPerWorkgroup, device.limits.maxComputeWorkgroupSizeX)",
    "storageBufferLimit": "min(device.limits.maxStorageBufferBindingSize, device.limits.maxBufferSize)",
    "foldedDispatchCapacity": "min(device.limits.maxComputeWorkgroupsPerDimension, 65535) * min(device.limits.maxComputeWorkgroupsPerDimension, 65535)",
    "statsVec4Ok": "(channelsPerGroup % 4 == 0 and dimC % 4 == 0) if channelsLast else (dimHW % 4 == 0)",
    "applyVec4Ok": "(dimC % 4 == 0) if channelsLast else (dimHW % 4 == 0)",
    "fusedVecWidth": "4 if statsVec4Ok else 1",
    "statsVecWidth": "4 if statsVec4Ok else (2 if channelsLast and channelsPerGroup % 2 == 0 else 1)",
    "applyVecWidth": "4 if applyVec4Ok else 1",
    "workgroupCap": "max(1, floor(pow2ceil(min(tunables.WORKGROUP_SIZE, deviceWorkgroupCap) + 1) / 2))",
    "statsChunks": "max(1, floor(dimC / statsVecWidth))",
    "fusedRowChunks": "max(1, floor(dimC / fusedVecWidth))",
    "statsSegment": "max(1, floor(channelsPerGroup / statsVecWidth))",
    "statsGroupsPerBlock": "max(1, min(numGroups, floor(workgroupCap / statsSegment))) if channelsLast and statsChunks > deviceWorkgroupCap and statsSegment <= workgroupCap else max(1, numGroups)",
    "statsGroupBlocks": "ceilDiv(max(1, numGroups), statsGroupsPerBlock)",
    "statsTileChunks": "statsGroupsPerBlock * statsSegment if statsGroupBlocks > 1 else statsChunks",
    "applyChunks": "max(1, floor(dimC / applyVecWidth))",
    "statsRowsPerStep": "max(1, floor(workgroupCap / statsTileChunks))",
    "applyRowsPerStep": "max(1, floor(workgroupCap / applyChunks))",
    "planeVecs": "max(1, floor(dimHW / statsVecWidth))",
    "slabCount": "ceilDiv(dimHW, ceilDiv(dimHW, max(1, min(tunables.MAX_SPLITS, dimHW, ceilDiv(dimHW * dimC, tunables.VALUES_PER_SPLIT)))))",
    "planeSplits": "max(1, min(tunables.MAX_SPLITS, planeVecs, ceilDiv(dimHW, tunables.VALUES_PER_SPLIT)))",
    "splitCount": "slabCount if channelsLast else planeSplits",
    "partialsPerRow": "slabCount if channelsLast else max(1, channelsPerGroup) * planeSplits",
    "partialElements": "max(1, normRows * partialsPerRow)",
    "statsElements": "max(1, normRows)",
    "statsWorkgroup": "(statsTileChunks * statsRowsPerStep) if channelsLast else min(workgroupCap, max(32, pow2ceil(ceilDiv(planeVecs, planeSplits))))",
    "applyWorkgroup": "(applyChunks * applyRowsPerStep) if channelsLast else statsWorkgroup",
    "applySlabCount": "ceilDiv(dimHW, ceilDiv(dimHW, max(1, min(dimHW, min(device.limits.maxComputeWorkgroupsPerDimension, 65535), ceilDiv(elementCount, tunables.APPLY_SLAB_ELEMENTS)))))",
    "applySplit": "applySlabCount if channelsLast else planeSplits",
    "applyUnits": "(dimN * applySlabCount) if channelsLast else (planeCount * planeSplits)",
    "workUnits": "(dimN * slabCount * statsGroupBlocks) if channelsLast else (planeCount * planeSplits)",
    "splitFits": "statsWorkgroup <= deviceWorkgroupCap and applyWorkgroup <= deviceWorkgroupCap and statsWorkgroup * 8 <= device.limits.maxComputeWorkgroupStorageSize and partialElements * 8 <= storageBufferLimit and workUnits > 0 and workUnits <= foldedDispatchCapacity and applyUnits <= foldedDispatchCapacity",
    "fusedChunks": "max(1, floor(channelsPerGroup / fusedVecWidth)) if channelsLast else 1",
    "fusedWorkgroup": "(fusedChunks * max(1, floor(workgroupCap / fusedChunks))) if channelsLast else min(workgroupCap, max(32, pow2ceil(max(1, floor(groupSize / fusedVecWidth)))))",
    "fusedLanes": "pow2ceil(fusedWorkgroup)",
    "fusedFits": "fusedWorkgroup <= deviceWorkgroupCap and fusedLanes * 8 <= device.limits.maxComputeWorkgroupStorageSize and normRows <= min(device.limits.maxComputeWorkgroupsPerDimension, 65535) * min(device.limits.maxComputeWorkgroupsPerDimension, 65535)",
    "combineWorkgroup": "min(workgroupCap, 64)",
    "statsElement": "(\"vec\" ~ statsVecWidth ~ \"<\" ~ dtypes.T ~ \">\") if statsVecWidth > 1 else dtypes.T",
    "fusedElement": "(\"vec4<\" ~ dtypes.T ~ \">\") if statsVec4Ok else dtypes.T",
    "applyElement": "(\"vec4<\" ~ dtypes.T ~ \">\") if applyVec4Ok else dtypes.T",
    "mScalar": "dtypes.M",
    "tScalar": "dtypes.T",
    "skipExact": "rankOk and ranks.skip == 4 and sameShape(shapes.skip, shapes.X)",
    "skipBroadcast2": "rankOk and ranks.skip == 2 and dim(shapes.skip, 0) == dimN and dim(shapes.skip, 1) == dimC",
    "skipBroadcast4": "rankOk and ranks.skip == 4 and dim(shapes.skip, 0) == dimN and dim(shapes.skip, 1) == 1 and dim(shapes.skip, 2) == 1 and dim(shapes.skip, 3) == dimC",
    "broadcastSkipSpec": "(not skipExact) and (skipBroadcast2 or skipBroadcast4)",
    "skipOk": "skipExact or broadcastSkipSpec",
    "biasOk": "(not present.bias) or (ranks.bias == 1 and dim(shapes.bias, 0) == dimC)",
    "sumOk": "(not present.S) or (ranks.S == 4 and sameShape(shapes.S, shapes.X))",
    "contractOk": "shapeOk and skipOk and biasOk and sumOk and f16Ok(dtypes.T) and f16Ok(dtypes.M)",
    "skipElement": "dtypes.T if broadcastSkipSpec else statsElement"
  },
  "when": ["contractOk"],
  "bindings": {
    "xIn": { "arg": "X", "name": "X", "elementType": "$statsElement" },
    "gamma": { "elementType": "$mScalar" },
    "beta": { "elementType": "$mScalar" },
    "yOut": { "arg": "Y", "name": "Y", "elementType": "$applyElement" },
    "partialsW": { "name": "partials", "buffer": "storage", "elementType": "vec2<f32>" },
    "partialsR": { "name": "partials", "buffer": "read-only-storage", "elementType": "vec2<f32>" },
    "statsW": { "name": "stats", "buffer": "storage", "elementType": "vec2<f32>" },
    "statsR": { "name": "stats", "buffer": "read-only-storage", "elementType": "vec2<f32>" },
    "yFused": { "arg": "Y", "name": "Y", "elementType": "$statsElement" },
    "skipIn": { "arg": "skip", "name": "skip", "elementType": "$skipElement" },
    "biasIn": { "arg": "bias", "name": "bias", "elementType": "$tScalar" },
    "sumDstS": { "arg": "S", "name": "sum_dst", "elementType": "$statsElement" },
    "sumDstY": { "arg": "Y", "name": "sum_dst", "elementType": "$statsElement" },
    "srcCombineS": { "arg": "S", "name": "src", "buffer": "read-only-storage", "elementType": "$statsElement" },
    "srcCombineY": { "arg": "Y", "name": "src", "buffer": "read-only-storage", "elementType": "$statsElement" },
    "srcApplyS": { "arg": "S", "name": "src", "buffer": "read-only-storage", "elementType": "$applyElement" }
  },
  "variants": [
    {
      "id": "split_bias_sum",
      "priority": 20,
      "when": ["splitFits", "present.bias", "present.S"],
      "demoteWhen": ["elementCount < tunables.SPLIT_MIN_ELEMENTS * statsGroupBlocks", "(not channelsLast) and normRows >= tunables.FUSED_MIN_ROWS and groupSize * dtypeBytes(tensorDtypes.X) <= tunables.FUSED_MAX_GROUP_BYTES"],
      "derive": {
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "true",
        "broadcastSkip": "broadcastSkipSpec",
        "vecSpec": "statsVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "statsChunks",
        "rowsPerStepSpec": "statsRowsPerStep",
        "splitSpec": "splitCount",
        "rowsPerSlabSpec": "ceilDiv(dimHW, slabCount)",
        "planeVecsSpec": "planeVecs",
        "chunkVecsSpec": "ceilDiv(planeVecs, planeSplits)",
        "partialsPerRowSpec": "partialsPerRow",
        "wgSpec": "statsWorkgroup",
        "combineWgSpec": "combineWorkgroup",
        "vecF32": "(\"vec\" ~ statsVecWidth ~ \"<f32>\") if statsVecWidth > 1 else \"f32\"",
        "storeElement": "statsElement",
        "applySrc": "\"src\"",
        "groupUniform": "true"
      },
      "intermediates": [
        { "id": "partials", "dtype": "float32", "shape": "[partialElements, 2]" },
        { "id": "stats", "dtype": "float32", "shape": "[statsElements, 2]" }
      ],
      "passes": [
        {
          "id": "stats",
          "name": "GroupNorm.Partials",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"stats\"",
            "unitsSpec": "workUnits",
            "statsBlockedSpec": "channelsLast and statsGroupBlocks > 1",
            "statsGroupsPerBlockSpec": "statsGroupsPerBlock",
            "statsGroupBlocksSpec": "statsGroupBlocks",
            "statsTileChunksSpec": "statsTileChunks"
          },
          "bindings": ["xIn", "skipIn", "biasIn", "sumDstS", "partialsW"],
          "dispatch": { "x": "min(workUnits, 65535)", "y": "ceilDiv(workUnits, 65535)", "z": 1 }
        },
        {
          "id": "combine",
          "name": "GroupNorm.Combine",
          "shader": "group-norm-combine.wgsl.jinja",
          "bindings": ["srcCombineS", "partialsR", "statsW"],
          "dispatch": {
            "x": "min(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "y": "ceilDiv(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "z": 1
          }
        },
        {
          "id": "apply",
          "name": "GroupNorm.Apply",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"apply\"",
            "vecSpec": "applyVecWidth",
            "chunksSpec": "applyChunks",
            "rowsPerStepSpec": "applyRowsPerStep",
            "wgSpec": "applyWorkgroup",
            "splitSpec": "applySplit",
            "rowsPerSlabSpec": "ceilDiv(dimHW, applySlabCount)",
            "groupUniform": "(channelsPerGroup % applyVecWidth == 0) if channelsLast else true",
            "storeElement": "applyElement",
            "vecF32": "\"vec4<f32>\" if applyVec4Ok else \"f32\"",
            "unitsSpec": "applyUnits",
            "applySrc": "\"src\""
          },
          "bindings": ["srcApplyS", "gamma", "beta", "statsR", "yOut"],
          "dispatch": { "x": "min(applyUnits, 65535)", "y": "ceilDiv(applyUnits, 65535)", "z": 1 }
        }
      ]
    },
    {
      "id": "fused_bias_sum",
      "priority": 10,
      "when": ["fusedFits", "present.bias", "present.S"],
      "derive": {
        "statsElement": "fusedElement",
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "true",
        "broadcastSkip": "broadcastSkipSpec",
        "useVec4": "statsVec4Ok",
        "vecSpec": "fusedVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "fusedRowChunks",
        "fusedChunksSpec": "fusedChunks",
        "fusedRowsSpec": "max(1, floor(fusedWorkgroup / fusedChunks))",
        "spanVecsSpec": "max(1, floor(groupSize / fusedVecWidth))",
        "wgSpec": "fusedWorkgroup",
        "ldsSpec": "fusedLanes",
        "vecF32": "\"vec4<f32>\" if statsVec4Ok else \"f32\"",
        "storeElement": "fusedElement",
        "fusedSrc": "\"sum_dst\"",
        "planeVecsSpec": "planeVecs",
        "skipElement": "tScalar if broadcastSkipSpec else fusedElement"
      },
      "passes": [
        {
          "id": "main",
          "name": "GroupNorm.Fused",
          "shader": "group-norm-fused.wgsl.jinja",
          "bindings": ["xIn", "skipIn", "biasIn", "gamma", "beta", "sumDstS", "yFused"],
          "dispatch": { "x": "min(normRows, 65535)", "y": "ceilDiv(normRows, 65535)", "z": 1 }
        }
      ]
    },
    {
      "id": "split_bias_plain",
      "priority": 20,
      "when": ["splitFits", "present.bias", "not present.S"],
      "demoteWhen": ["elementCount < tunables.SPLIT_MIN_ELEMENTS * statsGroupBlocks", "(not channelsLast) and normRows >= tunables.FUSED_MIN_ROWS and groupSize * dtypeBytes(tensorDtypes.X) <= tunables.FUSED_MAX_GROUP_BYTES"],
      "derive": {
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "true",
        "broadcastSkip": "broadcastSkipSpec",
        "vecSpec": "statsVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "statsChunks",
        "rowsPerStepSpec": "statsRowsPerStep",
        "splitSpec": "splitCount",
        "rowsPerSlabSpec": "ceilDiv(dimHW, slabCount)",
        "planeVecsSpec": "planeVecs",
        "chunkVecsSpec": "ceilDiv(planeVecs, planeSplits)",
        "partialsPerRowSpec": "partialsPerRow",
        "wgSpec": "statsWorkgroup",
        "combineWgSpec": "combineWorkgroup",
        "vecF32": "(\"vec\" ~ statsVecWidth ~ \"<f32>\") if statsVecWidth > 1 else \"f32\"",
        "storeElement": "statsElement",
        "applySrc": "\"Y\"",
        "groupUniform": "true"
      },
      "intermediates": [
        { "id": "partials", "dtype": "float32", "shape": "[partialElements, 2]" },
        { "id": "stats", "dtype": "float32", "shape": "[statsElements, 2]" }
      ],
      "passes": [
        {
          "id": "stats",
          "name": "GroupNorm.Partials",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"stats\"",
            "unitsSpec": "workUnits",
            "statsBlockedSpec": "channelsLast and statsGroupBlocks > 1",
            "statsGroupsPerBlockSpec": "statsGroupsPerBlock",
            "statsGroupBlocksSpec": "statsGroupBlocks",
            "statsTileChunksSpec": "statsTileChunks"
          },
          "bindings": ["xIn", "skipIn", "biasIn", "sumDstY", "partialsW"],
          "dispatch": { "x": "min(workUnits, 65535)", "y": "ceilDiv(workUnits, 65535)", "z": 1 }
        },
        {
          "id": "combine",
          "name": "GroupNorm.Combine",
          "shader": "group-norm-combine.wgsl.jinja",
          "bindings": ["srcCombineY", "partialsR", "statsW"],
          "dispatch": {
            "x": "min(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "y": "ceilDiv(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "z": 1
          }
        },
        {
          "id": "apply",
          "name": "GroupNorm.Apply",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"apply\"",
            "vecSpec": "applyVecWidth",
            "chunksSpec": "applyChunks",
            "rowsPerStepSpec": "applyRowsPerStep",
            "wgSpec": "applyWorkgroup",
            "splitSpec": "applySplit",
            "rowsPerSlabSpec": "ceilDiv(dimHW, applySlabCount)",
            "groupUniform": "(channelsPerGroup % applyVecWidth == 0) if channelsLast else true",
            "storeElement": "applyElement",
            "vecF32": "\"vec4<f32>\" if applyVec4Ok else \"f32\"",
            "unitsSpec": "applyUnits",
            "applySrc": "\"Y\""
          },
          "bindings": ["gamma", "beta", "statsR", "yOut"],
          "dispatch": { "x": "min(applyUnits, 65535)", "y": "ceilDiv(applyUnits, 65535)", "z": 1 }
        }
      ]
    },
    {
      "id": "fused_bias_plain",
      "priority": 10,
      "when": ["fusedFits", "present.bias", "not present.S"],
      "derive": {
        "statsElement": "fusedElement",
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "true",
        "broadcastSkip": "broadcastSkipSpec",
        "useVec4": "statsVec4Ok",
        "vecSpec": "fusedVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "fusedRowChunks",
        "fusedChunksSpec": "fusedChunks",
        "fusedRowsSpec": "max(1, floor(fusedWorkgroup / fusedChunks))",
        "spanVecsSpec": "max(1, floor(groupSize / fusedVecWidth))",
        "wgSpec": "fusedWorkgroup",
        "ldsSpec": "fusedLanes",
        "vecF32": "\"vec4<f32>\" if statsVec4Ok else \"f32\"",
        "storeElement": "fusedElement",
        "fusedSrc": "\"Y\"",
        "planeVecsSpec": "planeVecs",
        "skipElement": "tScalar if broadcastSkipSpec else fusedElement"
      },
      "passes": [
        {
          "id": "main",
          "name": "GroupNorm.Fused",
          "shader": "group-norm-fused.wgsl.jinja",
          "bindings": ["xIn", "skipIn", "biasIn", "gamma", "beta", "yFused"],
          "dispatch": { "x": "min(normRows, 65535)", "y": "ceilDiv(normRows, 65535)", "z": 1 }
        }
      ]
    },
    {
      "id": "split_sum",
      "priority": 20,
      "when": ["splitFits", "not present.bias", "present.S"],
      "demoteWhen": ["elementCount < tunables.SPLIT_MIN_ELEMENTS * statsGroupBlocks", "(not channelsLast) and normRows >= tunables.FUSED_MIN_ROWS and groupSize * dtypeBytes(tensorDtypes.X) <= tunables.FUSED_MAX_GROUP_BYTES"],
      "derive": {
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "false",
        "broadcastSkip": "broadcastSkipSpec",
        "vecSpec": "statsVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "statsChunks",
        "rowsPerStepSpec": "statsRowsPerStep",
        "splitSpec": "splitCount",
        "rowsPerSlabSpec": "ceilDiv(dimHW, slabCount)",
        "planeVecsSpec": "planeVecs",
        "chunkVecsSpec": "ceilDiv(planeVecs, planeSplits)",
        "partialsPerRowSpec": "partialsPerRow",
        "wgSpec": "statsWorkgroup",
        "combineWgSpec": "combineWorkgroup",
        "vecF32": "(\"vec\" ~ statsVecWidth ~ \"<f32>\") if statsVecWidth > 1 else \"f32\"",
        "storeElement": "statsElement",
        "applySrc": "\"src\"",
        "groupUniform": "true"
      },
      "intermediates": [
        { "id": "partials", "dtype": "float32", "shape": "[partialElements, 2]" },
        { "id": "stats", "dtype": "float32", "shape": "[statsElements, 2]" }
      ],
      "passes": [
        {
          "id": "stats",
          "name": "GroupNorm.Partials",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"stats\"",
            "unitsSpec": "workUnits",
            "statsBlockedSpec": "channelsLast and statsGroupBlocks > 1",
            "statsGroupsPerBlockSpec": "statsGroupsPerBlock",
            "statsGroupBlocksSpec": "statsGroupBlocks",
            "statsTileChunksSpec": "statsTileChunks"
          },
          "bindings": ["xIn", "skipIn", "sumDstS", "partialsW"],
          "dispatch": { "x": "min(workUnits, 65535)", "y": "ceilDiv(workUnits, 65535)", "z": 1 }
        },
        {
          "id": "combine",
          "name": "GroupNorm.Combine",
          "shader": "group-norm-combine.wgsl.jinja",
          "bindings": ["srcCombineS", "partialsR", "statsW"],
          "dispatch": {
            "x": "min(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "y": "ceilDiv(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "z": 1
          }
        },
        {
          "id": "apply",
          "name": "GroupNorm.Apply",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"apply\"",
            "vecSpec": "applyVecWidth",
            "chunksSpec": "applyChunks",
            "rowsPerStepSpec": "applyRowsPerStep",
            "wgSpec": "applyWorkgroup",
            "splitSpec": "applySplit",
            "rowsPerSlabSpec": "ceilDiv(dimHW, applySlabCount)",
            "groupUniform": "(channelsPerGroup % applyVecWidth == 0) if channelsLast else true",
            "storeElement": "applyElement",
            "vecF32": "\"vec4<f32>\" if applyVec4Ok else \"f32\"",
            "unitsSpec": "applyUnits",
            "applySrc": "\"src\""
          },
          "bindings": ["srcApplyS", "gamma", "beta", "statsR", "yOut"],
          "dispatch": { "x": "min(applyUnits, 65535)", "y": "ceilDiv(applyUnits, 65535)", "z": 1 }
        }
      ]
    },
    {
      "id": "fused_sum",
      "priority": 10,
      "when": ["fusedFits", "not present.bias", "present.S"],
      "derive": {
        "statsElement": "fusedElement",
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "false",
        "broadcastSkip": "broadcastSkipSpec",
        "useVec4": "statsVec4Ok",
        "vecSpec": "fusedVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "fusedRowChunks",
        "fusedChunksSpec": "fusedChunks",
        "fusedRowsSpec": "max(1, floor(fusedWorkgroup / fusedChunks))",
        "spanVecsSpec": "max(1, floor(groupSize / fusedVecWidth))",
        "wgSpec": "fusedWorkgroup",
        "ldsSpec": "fusedLanes",
        "vecF32": "\"vec4<f32>\" if statsVec4Ok else \"f32\"",
        "storeElement": "fusedElement",
        "fusedSrc": "\"sum_dst\"",
        "planeVecsSpec": "planeVecs",
        "skipElement": "tScalar if broadcastSkipSpec else fusedElement"
      },
      "passes": [
        {
          "id": "main",
          "name": "GroupNorm.Fused",
          "shader": "group-norm-fused.wgsl.jinja",
          "bindings": ["xIn", "skipIn", "gamma", "beta", "sumDstS", "yFused"],
          "dispatch": { "x": "min(normRows, 65535)", "y": "ceilDiv(normRows, 65535)", "z": 1 }
        }
      ]
    },
    {
      "id": "split_plain",
      "priority": 20,
      "when": ["splitFits", "not present.bias", "not present.S"],
      "demoteWhen": ["elementCount < tunables.SPLIT_MIN_ELEMENTS * statsGroupBlocks", "(not channelsLast) and normRows >= tunables.FUSED_MIN_ROWS and groupSize * dtypeBytes(tensorDtypes.X) <= tunables.FUSED_MAX_GROUP_BYTES"],
      "derive": {
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "false",
        "broadcastSkip": "broadcastSkipSpec",
        "vecSpec": "statsVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "statsChunks",
        "rowsPerStepSpec": "statsRowsPerStep",
        "splitSpec": "splitCount",
        "rowsPerSlabSpec": "ceilDiv(dimHW, slabCount)",
        "planeVecsSpec": "planeVecs",
        "chunkVecsSpec": "ceilDiv(planeVecs, planeSplits)",
        "partialsPerRowSpec": "partialsPerRow",
        "wgSpec": "statsWorkgroup",
        "combineWgSpec": "combineWorkgroup",
        "vecF32": "(\"vec\" ~ statsVecWidth ~ \"<f32>\") if statsVecWidth > 1 else \"f32\"",
        "storeElement": "statsElement",
        "applySrc": "\"Y\"",
        "groupUniform": "true"
      },
      "intermediates": [
        { "id": "partials", "dtype": "float32", "shape": "[partialElements, 2]" },
        { "id": "stats", "dtype": "float32", "shape": "[statsElements, 2]" }
      ],
      "passes": [
        {
          "id": "stats",
          "name": "GroupNorm.Partials",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"stats\"",
            "unitsSpec": "workUnits",
            "statsBlockedSpec": "channelsLast and statsGroupBlocks > 1",
            "statsGroupsPerBlockSpec": "statsGroupsPerBlock",
            "statsGroupBlocksSpec": "statsGroupBlocks",
            "statsTileChunksSpec": "statsTileChunks"
          },
          "bindings": ["xIn", "skipIn", "sumDstY", "partialsW"],
          "dispatch": { "x": "min(workUnits, 65535)", "y": "ceilDiv(workUnits, 65535)", "z": 1 }
        },
        {
          "id": "combine",
          "name": "GroupNorm.Combine",
          "shader": "group-norm-combine.wgsl.jinja",
          "bindings": ["srcCombineY", "partialsR", "statsW"],
          "dispatch": {
            "x": "min(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "y": "ceilDiv(ceilDiv((normRows), (combineWorkgroup)), 65535)",
            "z": 1
          }
        },
        {
          "id": "apply",
          "name": "GroupNorm.Apply",
          "shader": "group-norm-slab.wgsl.jinja",
          "derive": {
            "phase": "\"apply\"",
            "vecSpec": "applyVecWidth",
            "chunksSpec": "applyChunks",
            "rowsPerStepSpec": "applyRowsPerStep",
            "wgSpec": "applyWorkgroup",
            "splitSpec": "applySplit",
            "rowsPerSlabSpec": "ceilDiv(dimHW, applySlabCount)",
            "groupUniform": "(channelsPerGroup % applyVecWidth == 0) if channelsLast else true",
            "storeElement": "applyElement",
            "vecF32": "\"vec4<f32>\" if applyVec4Ok else \"f32\"",
            "unitsSpec": "applyUnits",
            "applySrc": "\"Y\""
          },
          "bindings": ["gamma", "beta", "statsR", "yOut"],
          "dispatch": { "x": "min(applyUnits, 65535)", "y": "ceilDiv(applyUnits, 65535)", "z": 1 }
        }
      ]
    },
    {
      "id": "fused_plain",
      "priority": 10,
      "when": ["fusedFits", "not present.bias", "not present.S"],
      "derive": {
        "statsElement": "fusedElement",
        "phaseLayout": "channelsLast",
        "hasSkip": "true",
        "hasBias": "false",
        "broadcastSkip": "broadcastSkipSpec",
        "useVec4": "statsVec4Ok",
        "vecSpec": "fusedVecWidth",
        "dimCSpec": "dimC",
        "dimHWSpec": "dimHW",
        "cpgSpec": "channelsPerGroup",
        "groupsSpec": "numGroups",
        "groupSizeSpec": "groupSize",
        "normRowsSpec": "normRows",
        "epsilonSpec": "attrs.epsilon",
        "activationSpec": "activationKind",
        "chunksSpec": "fusedRowChunks",
        "fusedChunksSpec": "fusedChunks",
        "fusedRowsSpec": "max(1, floor(fusedWorkgroup / fusedChunks))",
        "spanVecsSpec": "max(1, floor(groupSize / fusedVecWidth))",
        "wgSpec": "fusedWorkgroup",
        "ldsSpec": "fusedLanes",
        "vecF32": "\"vec4<f32>\" if statsVec4Ok else \"f32\"",
        "storeElement": "fusedElement",
        "fusedSrc": "\"Y\"",
        "planeVecsSpec": "planeVecs",
        "skipElement": "tScalar if broadcastSkipSpec else fusedElement"
      },
      "passes": [
        {
          "id": "main",
          "name": "GroupNorm.Fused",
          "shader": "group-norm-fused.wgsl.jinja",
          "bindings": ["xIn", "skipIn", "gamma", "beta", "yFused"],
          "dispatch": { "x": "min(normRows, 65535)", "y": "ceilDiv(normRows, 65535)", "z": 1 }
        }
      ]
    }
  ]
}