content: {-# OPTIONS_GHC -fno-warn-orphans #-}
  
  module Futhark.IR.Mem.IxFunTests
    ( tests,
    )
  where
  
  import Data.Bifunctor
  import Data.Function ((&))
  import Data.List qualified as L
  import Data.Map qualified as M
  import Data.Text qualified as T
  import Futhark.Analysis.PrimExp.Convert
  import Futhark.IR.Mem.IxFun.Alg qualified as IxFunAlg
  import Futhark.IR.Mem.IxFunWrapper
  import Futhark.IR.Mem.IxFunWrapper qualified as IxFunWrap
  import Futhark.IR.Mem.LMAD qualified as IxFunLMAD
  import Futhark.IR.Prop
  import Futhark.IR.Syntax
  import Futhark.IR.Syntax.Core ()
  import Futhark.Util.IntegralExp qualified as IE
  import Futhark.Util.Pretty
  import Test.Tasty
  import Test.Tasty.HUnit
  import Prelude hiding (span)
  import Prelude qualified as P
  
  instance IE.IntegralExp Int where
    quot = P.quot
    rem = P.rem
    div = P.div
    mod = P.mod
    pow = (P.^)
    sgn = Just . P.signum
  
  allPoints :: [Int] -> [[Int]]
  allPoints dims =
    let total = product dims
        strides = drop 1 $ L.reverse $ scanl (*) 1 $ L.reverse dims
     in map (unflatInd strides) [0 .. total - 1]
    where
      unflatInd :: [Int] -> Int -> [Int]
      unflatInd strides x =
        fst $
          foldl
            ( \(res, acc) span ->
                (res ++ [acc `P.div` span], acc `P.mod` span)
            )
            ([], x)
            strides
  
  compareIxFuns :: Maybe (IxFunLMAD.LMAD Int) -> IxFunAlg.IxFun Int -> Assertion
  compareIxFuns (Just ixfunLMAD) ixfunAlg =
    let lmadShape = IxFunLMAD.shape ixfunLMAD
        algShape = IxFunAlg.shape ixfunAlg
        points = allPoints lmadShape
        resLMAD = map (IxFunLMAD.index ixfunLMAD) points
        resAlg = map (IxFunAlg.index ixfunAlg) points
        errorMessage =
          T.unpack . docText $
            "lmad ixfun:  "
              <> pretty ixfunLMAD
                </> "alg ixfun:   "
              <> pretty ixfunAlg
                </> "lmad shape:  "
              <> pretty lmadShape
                </> "alg shape:   "
              <> pretty algShape
                </> "lmad points length: "
              <> pretty (length resLMAD)
                </> "alg points length:  "
              <> pretty (length resAlg)
                </> "lmad points: "
              <> pretty resLMAD
                </> "alg points:  "
              <> pretty resAlg
     in (lmadShape == algShape && resLMAD == resAlg) @? errorMessage
  compareIxFuns Nothing ixfunAlg =
    assertFailure $
      unlines
        [ "lmad ixfun: Nothing",
          "alg ixfun:  " <> prettyString ixfunAlg
        ]
  
  compareOps :: IxFunWrap.IxFun Int -> Assertion
  compareOps (ixfunLMAD, ixfunAlg) = compareIxFuns ixfunLMAD ixfunAlg
  
  compareOpsFailure :: IxFunWrap.IxFun Int -> Assertion
  compareOpsFailure (Nothing, _) = pure ()
  compareOpsFailure (Just ixfunLMAD, ixfunAlg) =
    assertFailure . T.unpack . docText $
      "Not supposed to be representable as LMAD."
        </> "lmad ixfun: "
        <> pretty ixfunLMAD
          </> "alg ixfun:  "
        <> pretty ixfunAlg
  
  -- XXX: Clean this up.
  n :: Int
  n = 19
  
  slice3 :: Slice Int
  slice3 =
    Slice
      [ DimSlice 2 (n `P.div` 3) 3,
        DimFix (n `P.div` 2),
        DimSlice 1 (n `P.div` 2) 2
      ]
  
  -- Actual tests.
  tests :: TestTree
  tests =
    testGroup "IxFunTests" $
      concat
        [ test_iota,
          test_slice_iota,
          test_slice_reshape_iota1,
          test_permute_slice_iota,
          test_reshape_iota,
          test_reshape_permute_iota,
          test_slice_reshape_iota2,
          test_reshape_slice_iota3,
          test_flatten_strided,
          test_complex1,
          test_complex2,
          test_expand1,
          test_expand2,
          test_expand3,
          test_expand4,
          test_flatSlice_iota,
          test_slice_flatSlice_iota,
          test_flatSlice_flatSlice_iota,
          test_flatSlice_slice_iota,
          test_flatSlice_transpose_slice_iota
          -- TODO: Without z3, these tests fail. Ideally, our internal simplifier
          -- should be able to handle them:
          --
          -- test_disjoint3
        ]
  
  singleton :: TestTree -> [TestTree]
  singleton = (: [])
  
  test_iota :: [TestTree]
  test_iota =
    singleton . testCase "iota" . compareOps $
      iota [n]
  
  test_slice_iota :: [TestTree]
  test_slice_iota =
    singleton . testCase "slice . iota" . compareOps $
      slice (iota [n, n, n]) slice3
  
  test_slice_reshape_iota1 :: [TestTree]
  test_slice_reshape_iota1 =
    singleton . testCase "slice . reshape . iota 1" . compareOps $
      slice (reshape (iota [n, n, n]) [n `P.div` 2, n `P.div` 3, 1]) slice3
  
  test_permute_slice_iota :: [TestTree]
  test_permute_slice_iota =
    singleton . testCase "permute . slice . iota" . compareOps $
      permute (slice (iota [n, n, n]) slice3) [1, 0]
  
  test_reshape_iota :: [TestTree]
  test_reshape_iota =
    -- This tests a pattern that occurs with ScalarSpace.
    singleton . testCase "reshape . zeroslice . iota" . compareOps $
      let s = Slice [DimSlice 0 n 0, DimSlice 0 n 1]
       in reshape (slice (iota [n, n]) s) [1, n, 1, n]
  
  test_reshape_permute_iota :: [TestTree]
  test_reshape_permute_iota =
    -- negative reshape test
    singleton . testCase "reshape . permute . iota" . compareOpsFailure $
      let newdims = [n * n, n]
       in reshape (permute (iota [n, n, n]) [1, 2, 0]) newdims
  
  test_slice_reshape_iota2 :: [TestTree]
  test_slice_reshape_iota2 =
    singleton . testCase "slice . reshape . iota 2" . compareOps $
      let newdims = [n * n, n]
          slc =
            Slice
              [ DimFix (n `P.div` 2),
                DimSlice 0 n 1
              ]
       in slice (reshape (iota [n, n, n, n]) newdims) slc
  
  test_reshape_slice_iota3 :: [TestTree]
  test_reshape_slice_iota3 =
    -- negative reshape test
    singleton . testCase "reshape . slice . iota 3" . compareOpsFailure $
      let newdims = [n * n, n]
          slc =
            Slice
              [ DimFix (n `P.div` 2),
                DimSlice 0 n 1,
                DimSlice 0 (n `P.div` 2) 1,
                DimSlice 0 n 1
              ]
       in reshape (slice (iota [n, n, n, n]) slc) newdims
  
  -- Tests flattening something that is strided - this can occur after
  -- memory expansion.
  test_flatten_strided :: [TestTree]
  test_flatten_strided =
    singleton . testCase "reshape . fix . iota 3d" . compareOps $
      let slc = Slice [DimSlice 0 n 1, DimSlice 0 2 1, DimFix 1]
       in reshape (slice (iota [n, 2, n * n]) slc) [2 * 10]
  
  test_complex1 :: [TestTree]
  test_complex1 =
    singleton . testCase "permute . slice . permute . slice . iota 1" . compareOps $
      let slice33 =
            Slice
              [ DimSlice (n - 1) (n `P.div` 3) (-1),
                DimSlice (n - 1) n (-1),
                DimSlice (n - 1) n (-1),
                DimSlice 0 n 1
              ]
          ixfun = permute (slice (iota [n, n, n, n, n]) slice33) [3, 1, 2, 0]
          m = n `P.div` 3
          slice1 =
            Slice
              [ DimSlice 0 n 1,
                DimSlice (n - 1) n (-1),
                DimSlice (n - 1) n (-1),
                DimSlice 1 (m - 2) (-1)
              ]
          ixfun' = slice ixfun slice1
       in ixfun'
  
  test_complex2 :: [TestTree]
  test_complex2 =
    singleton . testCase "permute . slice . permute . slice . iota 2" . compareOps $
      let slc2 =
            Slice
              [ DimFix (n `P.div` 2),
                DimSlice (n - 1) (n `P.div` 3) (-1),
                DimSlice (n - 1) n (-1),
                DimSlice (n - 1) n (-1),
                DimSlice 0 n 1
              ]
          ixfun = permute (slice (iota [n, n, n, n, n]) slc2) [3, 1, 2, 0]
          m = n `P.div` 3
          slice1 =
            Slice
              [ DimSlice 0 n 1,
                DimSlice (n - 1) n (-1),
                DimSlice (n - 1) n (-1),
                DimSlice 1 (m - 2) (-1)
              ]
          ixfun' = slice ixfun slice1
       in ixfun'
  
  -- Imitates a case from memory expansion.
  test_expand1 :: [TestTree]
  test_expand1 =
    [ testCase "expand . iota1d" . compareOps $
        expand t nt (iota [n])
    ]
    where
      t = 3
      nt = 7
  
  -- Imitates another case from memory expansion.
  test_expand2 :: [TestTree]
  test_expand2 =
    [ testCase "expand . iota2d" . compareOps $
        expand t nt (iota [n, n])
    ]
    where
      t = 3
      nt = 7
  
  test_expand3 :: [TestTree]
  test_expand3 =
    [ testCase "expand . permute . iota2d" . compareOps $
        expand t nt (permute (iota [n, n `div` 2]) [1, 0])
    ]
    where
      t = 3
      nt = 7
  
  test_expand4 :: [TestTree]
  test_expand4 =
    [ testCase "expand . slice . iota1d" . compareOps $
        expand t nt (slice (iota [n]) (Slice [DimSlice (n `div` 2) (n `div` 2) 1]))
    ]
    where
      t = 3
      nt = 7
  
  test_flatSlice_iota :: [TestTree]
  test_flatSlice_iota =
    singleton . testCase "flatSlice . iota" . compareOps $
      flatSlice (iota [n * n * n * n]) $
        FlatSlice 2 [FlatDimIndex (n * 2) 4, FlatDimIndex n 3, FlatDimIndex 1 2]
  
  test_slice_flatSlice_iota :: [TestTree]
  test_slice_flatSlice_iota =
    singleton . testCase "slice . flatSlice . iota " . compareOps $
      slice (flatSlice (iota [2 + n * n * n]) flat_slice) $
        Slice [DimFix 2, DimSlice 0 n 1, DimFix 0]
    where
      flat_slice = FlatSlice 2 [FlatDimIndex (n * n) 1, FlatDimIndex n 1, FlatDimIndex 1 1]
  
  test_flatSlice_flatSlice_iota :: [TestTree]
  test_flatSlice_flatSlice_iota =
    singleton . testCase "flatSlice . flatSlice . iota " . compareOps $
      flatSlice (flatSlice (iota [10 * 10]) flat_slice_1) flat_slice_2
    where
      flat_slice_1 = FlatSlice 17 [FlatDimIndex 3 27, FlatDimIndex 3 10, FlatDimIndex 3 1]
      flat_slice_2 = FlatSlice 2 [FlatDimIndex 2 (-2)]
  
  test_flatSlice_slice_iota :: [TestTree]
  test_flatSlice_slice_iota =
    singleton . testCase "flatSlice . slice . iota " . compareOps $
      flatSlice (slice (iota [210, 100]) $ Slice [DimSlice 10 100 2, DimFix 10]) flat_slice_1
    where
      flat_slice_1 = FlatSlice 17 [FlatDimIndex 3 27, FlatDimIndex 3 10, FlatDimIndex 3 1]
  
  test_flatSlice_transpose_slice_iota :: [TestTree]
  test_flatSlice_transpose_slice_iota =
    singleton . testCase "flatSlice . transpose . slice . iota " . compareOps $
      flatSlice (permute (slice (iota [20, 20]) $ Slice [DimSlice 1 5 2, DimSlice 0 5 2]) [1, 0]) flat_slice_1
    where
      flat_slice_1 = FlatSlice 1 [FlatDimIndex 2 2]
  
  -- test_disjoint2 :: [TestTree]
  -- test_disjoint2 =
  --   let add_nw64 = (+)
  
  --       mul_nw64 = (*)
  
  --       sub64 = (-)
  
  --       vname s i = VName (nameFromString s) i
  --    in [ let gtid_8472 = TPrimExp $ LeafExp (vname "gtid" 8472) $ IntType Int64
  
  --             gtid_8473 = TPrimExp $ LeafExp (vname "gtid" 8473) $ IntType Int64
  
  --             gtid_8474 = TPrimExp $ LeafExp (vname "gtid" 8474) $ IntType Int64
  
  --             num_blocks_8284 = TPrimExp $ LeafExp (vname "num_blocks" 8284) $ IntType Int64
  
  --             nonnegs = freeIn [gtid_8472, gtid_8473, gtid_8474, num_blocks_8284]
  
  --             j_m_i_8287 :: TPrimExp Int64 VName
  --             j_m_i_8287 = num_blocks_8284 - 1
  
  --             lessthans :: [(VName, PrimExp VName)]
  --             lessthans =
  --               [ (head $ namesToList $ freeIn gtid_8472, untyped j_m_i_8287),
  --                 (head $ namesToList $ freeIn gtid_8473, untyped j_m_i_8287),
  --                 (head $ namesToList $ freeIn gtid_8474, untyped (16 :: TPrimExp Int64 VName))
  --               ]
  
  --             lm1 :: IxFunLMAD.LMAD (TPrimExp Int64 VName)
  --             lm1 =
  --               IxFunLMAD.LMAD
  --                 256
  --                 [ IxFunLMAD.LMADDim 256 0 (sub64 (num_blocks_8284) 1) 0 ,
  --                   IxFunLMAD.LMADDim 1 0 16 1 ,
  --                   IxFunLMAD.LMADDim 16 0 16 2
  --                 ]
  --             lm2 :: IxFunLMAD.LMAD (TPrimExp Int64 VName)
  --             lm2 =
  --               IxFunLMAD.LMAD
  --                 (add_nw64 (add_nw64 (add_nw64 (add_nw64 (mul_nw64 (256) (num_blocks_8284)) (256)) (mul_nw64 (gtid_8472) (mul_nw64 (256) (num_blocks_8284)))) (mul_nw64 (gtid_8473) (256))) (mul_nw64 (gtid_8474) (16)))
  --                 [IxFunLMAD.LMADDim 1 0 16 0 ]
  --          in testCase (pretty lm1 <> " and " <> pretty lm2) $ IxFunLMAD.disjoint2 lessthans nonnegs lm1 lm2 @? "Failed"
  --       ]
  
  -- test_lessThanish :: [TestTree]
  -- test_lessThanish =
  --   [testCase "0 < 1" $ IxFunLMAD.lessThanish mempty mempty 0 1 @? "Failed"]
  
  -- test_lessThanOrEqualish :: [TestTree]
  -- test_lessThanOrEqualish =
  --   [testCase "1 <= 1" $ IxFunLMAD.lessThanOrEqualish mempty mempty 1 1 @? "Failed"]
  
  _test_disjoint3 :: [TestTree]
  _test_disjoint3 =
    let foo s = VName (nameFromString s)
        add_nw64 = (+)
        add64 = (+)
        mul_nw64 = (*)
        mul64 = (*)
        sub64 = (-)
        sdiv64 = IE.div
        sub_nw64 = (-)
        disjointTester asserts lessthans lm1 lm2 =
          let nonnegs = map (`LeafExp` IntType Int64) $ namesToList $ freeIn lm1 <> freeIn lm2
  
              scmap =
                M.fromList $
                  map (\x -> (x, Prim $ IntType Int64)) $
                    namesToList $
                      freeIn lm1 <> freeIn lm2 <> freeIn lessthans <> freeIn asserts
           in IxFunLMAD.disjoint3 scmap asserts lessthans nonnegs lm1 lm2
     in [ testCase "lm1 and lm2" $
            let lessthans =
                  [ ( i_12214,
                      sdiv64 (sub64 n_blab 1) block_size_12121
                    ),
                    (gtid_12553, add64 1 i_12214)
                  ]
                    & map (\(v, p) -> (head $ namesToList $ freeIn v, untyped p))
  
                asserts =
                  [ untyped ((2 * block_size_12121 :: TPrimExp Int64 VName) .<. n_blab :: TPrimExp Bool VName),
                    untyped ((3 :: TPrimExp Int64 VName) .<. n_blab :: TPrimExp Bool VName)
                  ]
  
                block_size_12121 = TPrimExp $ LeafExp (foo "block_size" 12121) $ IntType Int64
                i_12214 = TPrimExp $ LeafExp (foo "i" 12214) $ IntType Int64
                n_blab = TPrimExp $ LeafExp (foo "n" 1337) $ IntType Int64
                gtid_12553 = TPrimExp $ LeafExp (foo "gtid" 12553) $ IntType Int64
  
                lm1 =
                  IxFunLMAD.LMAD
                    (add_nw64 (mul64 block_size_12121 i_12214) (mul_nw64 (add_nw64 gtid_12553 1) (sub64 (mul64 block_size_12121 n_blab) block_size_12121)))
                    [ IxFunLMAD.LMADDim (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121)) (sub_nw64 (sub_nw64 (add64 1 i_12214) gtid_12553) 1),
                      IxFunLMAD.LMADDim 1 (block_size_12121 + 1)
                    ]
  
                lm2 =
                  IxFunLMAD.LMAD
                    (block_size_12121 * i_12214)
                    [ IxFunLMAD.LMADDim (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121)) gtid_12553,
                      IxFunLMAD.LMADDim 1 (1 + block_size_12121)
                    ]
  
                lm_w =
                  IxFunLMAD.LMAD
                    (add_nw64 (add64 (add64 1 n_blab) (mul64 block_size_12121 i_12214)) (mul_nw64 gtid_12553 (sub64 (mul64 block_size_12121 n_blab) block_size_12121)))
                    [ IxFunLMAD.LMADDim n_blab block_size_12121,
                      IxFunLMAD.LMADDim 1 block_size_12121
                    ]
  
                lm_blocks =
                  IxFunLMAD.LMAD
                    (block_size_12121 * i_12214 + n_blab + 1)
                    [ IxFunLMAD.LMADDim (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121)) (i_12214 + 1),
                      IxFunLMAD.LMADDim n_blab block_size_12121,
                      IxFunLMAD.LMADDim 1 block_size_12121
                    ]
  
                lm_lower_per =
                  IxFunLMAD.LMAD
                    (block_size_12121 * i_12214)
                    [ IxFunLMAD.LMADDim (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121)) (i_12214 + 1),
                      IxFunLMAD.LMADDim 1 (block_size_12121 + 1)
                    ]
  
                res1 = disjointTester asserts lessthans lm1 lm_w
                res2 = disjointTester asserts lessthans lm2 lm_w
                res3 = disjointTester asserts lessthans lm_lower_per lm_blocks
             in res1 && res2 && res3 @? "Failed",
          testCase "nw second half" $ do
            let lessthans =
                  [ ( i_12214,
                      sdiv64 (sub64 n_blab 1) block_size_12121
                    ),
                    (gtid_12553, add64 1 i_12214)
                  ]
                    & map (\(v, p) -> (head $ namesToList $ freeIn v, untyped p))
  
                asserts =
                  [ untyped ((2 * block_size_12121 :: TPrimExp Int64 VName) .<. n_blab :: TPrimExp Bool VName),
                    untyped ((3 :: TPrimExp Int64 VName) .<. n_blab :: TPrimExp Bool VName)
                  ]
  
                block_size_12121 = TPrimExp $ LeafExp (foo "block_size" 12121) $ IntType Int64
                i_12214 = TPrimExp $ LeafExp (foo "i" 12214) $ IntType Int64
                n_blab = TPrimExp $ LeafExp (foo "n" 1337) $ IntType Int64
                gtid_12553 = TPrimExp $ LeafExp (foo "gtid" 12553) $ IntType Int64
  
                lm1 =
                  IxFunLMAD.LMAD
                    (add_nw64 (add64 n_blab (sub64 (sub64 (mul64 n_blab (add64 1 (mul64 block_size_12121 (add64 1 i_12214)))) block_size_12121) 1)) (mul_nw64 (add_nw64 gtid_12553 1) (sub64 (mul64 block_size_12121 n_blab) block_size_12121)))
                    [ IxFunLMAD.LMADDim (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121)) (sub_nw64 (sub_nw64 (sub64 (sub64 (sdiv64 (sub64 n_blab 1) block_size_12121) i_12214) 1) gtid_12553) 1),
                      IxFunLMAD.LMADDim n_blab block_size_12121
                    ]
  
                lm2 =
                  IxFunLMAD.LMAD
                    (add_nw64 (sub64 (sub64 (mul64 n_blab (add64 1 (mul64 block_size_12121 (add64 1 i_12214)))) block_size_12121) 1) (mul_nw64 (add_nw64 gtid_12553 1) (sub64 (mul64 block_size_12121 n_blab) block_size_12121)))
                    [ IxFunLMAD.LMADDim (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121)) (sub_nw64 (sub_nw64 (sub64 (sub64 (sdiv64 (sub64 n_blab 1) block_size_12121) i_12214) 1) gtid_12553) 1),
                      IxFunLMAD.LMADDim 1 (1 + block_size_12121)
                    ]
  
                lm3 =
                  IxFunLMAD.LMAD
                    (add64 n_blab (sub64 (sub64 (mul64 n_blab (add64 1 (mul64 block_size_12121 (add64 1 i_12214)))) block_size_12121) 1))
                    [ IxFunLMAD.LMADDim (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121)) gtid_12553,
                      IxFunLMAD.LMADDim n_blab block_size_12121
                    ]
  
                lm4 =
                  IxFunLMAD.LMAD
                    (sub64 (sub64 (mul64 n_blab (add64 1 (mul64 block_size_12121 (add64 1 i_12214)))) block_size_12121) 1)
                    [ IxFunLMAD.LMADDim
                        (add_nw64 (mul_nw64 block_size_12121 n_blab) (mul_nw64 (-1) block_size_12121))
                        gtid_12553,
                      IxFunLMAD.LMADDim
                        1
                        (1 + block_size_12121)
                    ]
  
                lm_w =
                  IxFunLMAD.LMAD
                    (add_nw64 (sub64 (mul64 n_blab (add64 2 (mul64 block_size_12121 (add64 1 i_12214)))) block_size_12121) (mul_nw64 gtid_12553 (sub64 (mul64 block_size_12121 n_blab) block_size_12121)))
                    [ IxFunLMAD.LMADDim n_blab block_size_12121,
                      IxFunLMAD.LMADDim 1 block_size_12121
                    ]
  
                res1 = disjointTester asserts lessthans lm1 lm_w
                res2 = disjointTester asserts lessthans lm2 lm_w
                res3 = disjointTester asserts lessthans lm3 lm_w
                res4 = disjointTester asserts lessthans lm4 lm_w
             in res1 && res2 && res3 && res4 @? "Failed " <> show [res1, res2, res3, res4],
          testCase "lud long" $
            let lessthans =
                  [ bimap
                      (head . namesToList . freeIn)
                      untyped
                      (step, num_blocks - 1 :: TPrimExp Int64 VName)
                  ]
  
                step = TPrimExp $ LeafExp (foo "step" 1337) $ IntType Int64
  
                num_blocks = TPrimExp $ LeafExp (foo "n" 1338) $ IntType Int64
  
                lm1 =
                  IxFunLMAD.LMAD
                    (1024 * num_blocks * (1 + step) + 1024 * step)
                    [ IxFunLMAD.LMADDim (1024 * num_blocks) (num_blocks - step - 1),
                      IxFunLMAD.LMADDim 32 32,
                      IxFunLMAD.LMADDim 1 32
                    ]
  
                lm_w1 =
                  IxFunLMAD.LMAD
                    (1024 * num_blocks * step + 1024 * step)
                    [ IxFunLMAD.LMADDim 32 32,
                      IxFunLMAD.LMADDim 1 32
                    ]
  
                lm_w2 =
                  IxFunLMAD.LMAD
                    ((1 + step) * 1024 * num_blocks + (1 + step) * 1024)
                    [ IxFunLMAD.LMADDim (1024 * num_blocks) (num_blocks - step - 1),
                      IxFunLMAD.LMADDim 1024 (num_blocks - step - 1),
                      IxFunLMAD.LMADDim 1024 1,
                      IxFunLMAD.LMADDim 32 1,
                      IxFunLMAD.LMADDim 128 8,
                      IxFunLMAD.LMADDim 4 8,
                      IxFunLMAD.LMADDim 32 4,
                      IxFunLMAD.LMADDim 1 4
                    ]
  
                asserts =
                  [ untyped ((1 :: TPrimExp Int64 VName) .<. num_blocks :: TPrimExp Bool VName)
                  ]
  
                res1 = disjointTester asserts lessthans lm1 lm_w1
                res2 = disjointTester asserts lessthans lm1 lm_w2
             in res1 && res2 @? "Failed"
        ]
  