コード例 #1
0
ファイル: test_fortran.py プロジェクト: spillai/loopy
def test_fuse_kernels(ctx_factory):
    fortran_template = """
        subroutine {name}(nelements, ndofs, result, d, q)
          implicit none
          integer e, i, j, k
          integer nelements, ndofs
          real*8 result(nelements, ndofs, ndofs)
          real*8 q(nelements, ndofs, ndofs)
          real*8 d(ndofs, ndofs)
          real*8 prev

          do e = 1,nelements
            do i = 1,ndofs
              do j = 1,ndofs
                do k = 1,ndofs
                  {inner}
                end do
              end do
            end do
          end do
        end subroutine
        """

    xd_line = """
        prev = result(e,i,j)
        result(e,i,j) = prev + d(i,k)*q(e,i,k)
        """
    yd_line = """
        prev = result(e,i,j)
        result(e,i,j) = prev + d(i,k)*q(e,k,j)
        """

    xderiv, = lp.parse_fortran(
        fortran_template.format(inner=xd_line, name="xderiv"))
    yderiv, = lp.parse_fortran(
        fortran_template.format(inner=yd_line, name="yderiv"))
    xyderiv, = lp.parse_fortran(
        fortran_template.format(inner=(xd_line + "\n" + yd_line),
                                name="xyderiv"))

    knl = lp.fuse_kernels((xderiv, yderiv))
    knl = lp.prioritize_loops(knl, "e,i,j,k")

    assert len(knl.temporary_variables) == 2

    # This is needed for correctness, otherwise ordering could foul things up.
    knl = lp.assignment_to_subst(knl, "prev")
    knl = lp.assignment_to_subst(knl, "prev_0")

    ctx = ctx_factory()
    lp.auto_test_vs_ref(xyderiv,
                        ctx,
                        knl,
                        parameters=dict(nelements=20, ndofs=4))
コード例 #2
0
ファイル: test_fortran.py プロジェクト: cmsquared/loopy
def test_fuse_kernels(ctx_factory):
    fortran_template = """
        subroutine {name}(nelements, ndofs, result, d, q)
          implicit none
          integer e, i, j, k
          integer nelements, ndofs
          real*8 result(nelements, ndofs, ndofs)
          real*8 q(nelements, ndofs, ndofs)
          real*8 d(ndofs, ndofs)
          real*8 prev

          do e = 1,nelements
            do i = 1,ndofs
              do j = 1,ndofs
                do k = 1,ndofs
                  {inner}
                end do
              end do
            end do
          end do
        end subroutine
        """

    xd_line = """
        prev = result(e,i,j)
        result(e,i,j) = prev + d(i,k)*q(e,i,k)
        """
    yd_line = """
        prev = result(e,i,j)
        result(e,i,j) = prev + d(i,k)*q(e,k,j)
        """

    xderiv, = lp.parse_fortran(
            fortran_template.format(inner=xd_line, name="xderiv"))
    yderiv, = lp.parse_fortran(
            fortran_template.format(inner=yd_line, name="yderiv"))
    xyderiv, = lp.parse_fortran(
            fortran_template.format(
                inner=(xd_line + "\n" + yd_line), name="xyderiv"))

    knl = lp.fuse_kernels((xderiv, yderiv))
    knl = lp.set_loop_priority(knl, "e,i,j,k")

    assert len(knl.temporary_variables) == 2

    # This is needed for correctness, otherwise ordering could foul things up.
    knl = lp.assignment_to_subst(knl, "prev")
    knl = lp.assignment_to_subst(knl, "prev_0")

    ctx = ctx_factory()
    lp.auto_test_vs_ref(xyderiv, ctx, knl, parameters=dict(nelements=20, ndofs=4))
コード例 #3
0
ファイル: test_fortran.py プロジェクト: sv2518/loopy
def test_if(ctx_factory):
    fortran_src = """
        subroutine fill(out, out2, inp, n)
          implicit none

          real*8 a, b, out(n), out2(n), inp(n)
          integer n, i, j

          do i = 1, n
            a = inp(i)
            if (a.ge.3) then
                b = 2*a
                do j = 1,3
                    b = 3 * b
                end do
                out(i) = 5*b
            else
                out(i) = 4*a
            endif
          end do
        end
        """

    knl, = lp.parse_fortran(fortran_src)

    ref_knl = knl

    knl = lp.assignment_to_subst(knl, "a")

    ctx = ctx_factory()
    lp.auto_test_vs_ref(ref_knl, ctx, knl, parameters=dict(n=5))
コード例 #4
0
ファイル: test_fortran.py プロジェクト: sv2518/loopy
def test_assignment_to_subst_indices(ctx_factory):
    fortran_src = """
        subroutine fill(out, out2, inp, n)
          implicit none

          real*8 a(n), out(n), out2(n), inp(n)
          integer n, i

          do i = 1, n
            a(i) = 6*inp(i)
          enddo

          do i = 1, n
            out(i) = 5*a(i)
          end do
        end
        """

    knl, = lp.parse_fortran(fortran_src)

    knl = lp.fix_parameters(knl, n=5)

    ref_knl = knl

    assert "a" in knl.temporary_variables
    knl = lp.assignment_to_subst(knl, "a")
    assert "a" not in knl.temporary_variables

    ctx = ctx_factory()
    lp.auto_test_vs_ref(ref_knl, ctx, knl)
コード例 #5
0
ファイル: test_fortran.py プロジェクト: sv2518/loopy
def test_assignment_to_subst_two_defs(ctx_factory):
    fortran_src = """
        subroutine fill(out, out2, inp, n)
          implicit none

          real*8 a, out(n), out2(n), inp(n)
          integer n, i

          do i = 1, n
            a = inp(i)
            out(i) = 5*a
            a = 3*inp(n)
            out2(i) = 6*a
          end do
        end
        """

    knl, = lp.parse_fortran(fortran_src)

    ref_knl = knl

    knl = lp.assignment_to_subst(knl, "a")

    ctx = ctx_factory()
    lp.auto_test_vs_ref(ref_knl, ctx, knl, parameters=dict(n=5))
コード例 #6
0
ファイル: test_fortran.py プロジェクト: cmsquared/loopy
def test_if(ctx_factory):
    fortran_src = """
        subroutine fill(out, out2, inp, n)
          implicit none

          real*8 a, b, out(n), out2(n), inp(n)
          integer n, i, j

          do i = 1, n
            a = inp(i)
            if (a.ge.3) then
                b = 2*a
                do j = 1,3
                    b = 3 * b
                end do
                out(i) = 5*b
            else
                out(i) = 4*a
            endif
          end do
        end
        """

    knl, = lp.parse_fortran(fortran_src)

    ref_knl = knl

    knl = lp.assignment_to_subst(knl, "a")

    ctx = ctx_factory()
    lp.auto_test_vs_ref(ref_knl, ctx, knl, parameters=dict(n=5))
コード例 #7
0
ファイル: test_fortran.py プロジェクト: cmsquared/loopy
def test_assignment_to_subst_indices(ctx_factory):
    fortran_src = """
        subroutine fill(out, out2, inp, n)
          implicit none

          real*8 a(n), out(n), out2(n), inp(n)
          integer n, i

          do i = 1, n
            a(i) = 6*inp(i)
          enddo

          do i = 1, n
            out(i) = 5*a(i)
          end do
        end
        """

    knl, = lp.parse_fortran(fortran_src)

    knl = lp.fix_parameters(knl, n=5)

    ref_knl = knl

    assert "a" in knl.temporary_variables
    knl = lp.assignment_to_subst(knl, "a")
    assert "a" not in knl.temporary_variables

    ctx = ctx_factory()
    lp.auto_test_vs_ref(ref_knl, ctx, knl)
コード例 #8
0
ファイル: test_fortran.py プロジェクト: cmsquared/loopy
def test_assignment_to_subst_two_defs(ctx_factory):
    fortran_src = """
        subroutine fill(out, out2, inp, n)
          implicit none

          real*8 a, out(n), out2(n), inp(n)
          integer n, i

          do i = 1, n
            a = inp(i)
            out(i) = 5*a
            a = 3*inp(n)
            out2(i) = 6*a
          end do
        end
        """

    knl, = lp.parse_fortran(fortran_src)

    ref_knl = knl

    knl = lp.assignment_to_subst(knl, "a")

    ctx = ctx_factory()
    lp.auto_test_vs_ref(ref_knl, ctx, knl, parameters=dict(n=5))
コード例 #9
0
ファイル: test_loopy.py プロジェクト: dokempf/loopy
def test_finite_difference_expr_subst(ctx_factory):
    ctx = ctx_factory()
    queue = cl.CommandQueue(ctx)

    grid = np.linspace(0, 2*np.pi, 2048, endpoint=False)
    h = grid[1] - grid[0]
    u = cl.clmath.sin(cl.array.to_device(queue, grid))

    fin_diff_knl = lp.make_kernel(
        "{[i]: 1<=i<=n}",
        "out[i] = -(f[i+1] - f[i-1])/h",
        [lp.GlobalArg("out", shape="n+2"), "..."])

    flux_knl = lp.make_kernel(
        "{[j]: 1<=j<=n}",
        "f[j] = u[j]**2/2",
        [
            lp.GlobalArg("f", shape="n+2"),
            lp.GlobalArg("u", shape="n+2"),
            ])

    fused_knl = lp.fuse_kernels([fin_diff_knl, flux_knl],
            data_flow=[
                ("f", 1, 0)
                ])

    fused_knl = lp.set_options(fused_knl, write_cl=True)
    evt, _ = fused_knl(queue, u=u, h=np.float32(1e-1))

    fused_knl = lp.assignment_to_subst(fused_knl, "f")

    fused_knl = lp.set_options(fused_knl, write_cl=True)

    # This is the real test here: The automatically generated
    # shape expressions are '2+n' and the ones above are 'n+2'.
    # Is loopy smart enough to understand that these are equal?
    evt, _ = fused_knl(queue, u=u, h=np.float32(1e-1))

    fused0_knl = lp.affine_map_inames(fused_knl, "i", "inew", "inew+1=i")

    gpu_knl = lp.split_iname(
            fused0_knl, "inew", 128, outer_tag="g.0", inner_tag="l.0")

    precomp_knl = lp.precompute(
            gpu_knl, "f_subst", "inew_inner", fetch_bounding_box=True)

    precomp_knl = lp.tag_inames(precomp_knl, {"j_0_outer": "unr"})
    precomp_knl = lp.set_options(precomp_knl, return_dict=True)
    evt, _ = precomp_knl(queue, u=u, h=h)
コード例 #10
0
ファイル: test_loopy.py プロジェクト: dokempf/loopy
def test_finite_difference_expr_subst(ctx_factory):
    ctx = ctx_factory()
    queue = cl.CommandQueue(ctx)

    grid = np.linspace(0, 2 * np.pi, 2048, endpoint=False)
    h = grid[1] - grid[0]
    u = cl.clmath.sin(cl.array.to_device(queue, grid))

    fin_diff_knl = lp.make_kernel("{[i]: 1<=i<=n}",
                                  "out[i] = -(f[i+1] - f[i-1])/h",
                                  [lp.GlobalArg("out", shape="n+2"), "..."])

    flux_knl = lp.make_kernel("{[j]: 1<=j<=n}", "f[j] = u[j]**2/2", [
        lp.GlobalArg("f", shape="n+2"),
        lp.GlobalArg("u", shape="n+2"),
    ])

    fused_knl = lp.fuse_kernels([fin_diff_knl, flux_knl],
                                data_flow=[("f", 1, 0)])

    fused_knl = lp.set_options(fused_knl, write_cl=True)
    evt, _ = fused_knl(queue, u=u, h=np.float32(1e-1))

    fused_knl = lp.assignment_to_subst(fused_knl, "f")

    fused_knl = lp.set_options(fused_knl, write_cl=True)

    # This is the real test here: The automatically generated
    # shape expressions are '2+n' and the ones above are 'n+2'.
    # Is loopy smart enough to understand that these are equal?
    evt, _ = fused_knl(queue, u=u, h=np.float32(1e-1))

    fused0_knl = lp.affine_map_inames(fused_knl, "i", "inew", "inew+1=i")

    gpu_knl = lp.split_iname(fused0_knl,
                             "inew",
                             128,
                             outer_tag="g.0",
                             inner_tag="l.0")

    precomp_knl = lp.precompute(gpu_knl,
                                "f_subst",
                                "inew_inner",
                                fetch_bounding_box=True)

    precomp_knl = lp.tag_inames(precomp_knl, {"j_0_outer": "unr"})
    precomp_knl = lp.set_options(precomp_knl, return_dict=True)
    evt, _ = precomp_knl(queue, u=u, h=h)
コード例 #11
0
ファイル: test_transform.py プロジェクト: connorjward/loopy
def test_precompute_does_not_lead_to_dep_cycle(ctx_factory):
    # See https://github.com/inducer/loopy/issues/498
    ctx = ctx_factory()

    knl = lp.make_kernel(
        "{[i]: 0<=i<10}", """
        <> tmp0[i] = 2 * i
        <> tmp1[i] = 2 * tmp0[i]
        <> tmp2[i] = 3 * tmp1[i]
        out[i] = 2*tmp1[i] + 3*tmp2[i]
        """)
    ref_knl = knl

    knl = lp.assignment_to_subst(knl, "tmp1")
    knl = lp.precompute(knl, "tmp1_subst")

    lp.auto_test_vs_ref(knl, ctx, ref_knl)
コード例 #12
0
def test_gnuma_horiz_kernel(ctx_factory, ilp_multiple, Nq, opt_level):
    ctx = ctx_factory()

    filename = "strongVolumeKernels.f90"
    with open(filename, "r") as sourcef:
        source = sourcef.read()

    source = source.replace("datafloat", "real*4")

    hsv_r, hsv_s = [
        knl
        for knl in lp.parse_fortran(source, filename, auto_dependencies=False)
        if "KernelR" in knl.name or "KernelS" in knl.name
    ]
    hsv_r = lp.tag_instructions(hsv_r, "rknl")
    hsv_s = lp.tag_instructions(hsv_s, "sknl")
    hsv = lp.fuse_kernels([hsv_r, hsv_s], ["_r", "_s"])
    #hsv = hsv_s

    from gnuma_loopy_transforms import (fix_euler_parameters,
                                        set_q_storage_format,
                                        set_D_storage_format)

    hsv = lp.fix_parameters(hsv, Nq=Nq)
    hsv = lp.set_loop_priority(hsv, "e,k,j,i")
    hsv = lp.tag_inames(hsv, dict(e="g.0", j="l.1", i="l.0"))
    hsv = lp.assume(hsv, "elements >= 1")

    hsv = fix_euler_parameters(hsv, p_p0=1, p_Gamma=1.4, p_R=1)
    for name in ["Q", "rhsQ"]:
        hsv = set_q_storage_format(hsv, name)

    hsv = set_D_storage_format(hsv)
    #hsv = lp.add_prefetch(hsv, "volumeGeometricFactors")

    ref_hsv = hsv

    if opt_level == 0:
        tap_hsv = hsv

    hsv = lp.add_prefetch(hsv, "D[:,:]")

    if opt_level == 1:
        tap_hsv = hsv

    # turn the first reads into subst rules
    local_prep_var_names = set()
    for insn in lp.find_instructions(hsv, "tag:local_prep"):
        assignee, = insn.assignee_var_names()
        local_prep_var_names.add(assignee)
        hsv = lp.assignment_to_subst(hsv, assignee)

    # precompute fluxes
    hsv = lp.assignment_to_subst(hsv, "JinvD_r")
    hsv = lp.assignment_to_subst(hsv, "JinvD_s")

    r_fluxes = lp.find_instructions(hsv, "tag:compute_fluxes and tag:rknl")
    s_fluxes = lp.find_instructions(hsv, "tag:compute_fluxes and tag:sknl")

    if ilp_multiple > 1:
        hsv = lp.split_iname(hsv, "k", 2, inner_tag="ilp")
        ilp_inames = ("k_inner", )
        flux_ilp_inames = ("kk", )
    else:
        ilp_inames = ()
        flux_ilp_inames = ()

    rtmps = []
    stmps = []

    flux_store_idx = 0

    for rflux_insn, sflux_insn in zip(r_fluxes, s_fluxes):
        for knl_tag, insn, flux_inames, tmps, flux_precomp_inames in [
            ("rknl", rflux_insn, (
                "j",
                "n",
            ), rtmps, (
                "jj",
                "ii",
            )),
            ("sknl", sflux_insn, (
                "i",
                "n",
            ), stmps, (
                "ii",
                "jj",
            )),
        ]:
            flux_var, = insn.assignee_var_names()
            print(insn)

            reader, = lp.find_instructions(
                hsv,
                "tag:{knl_tag} and reads:{flux_var}".format(knl_tag=knl_tag,
                                                            flux_var=flux_var))

            hsv = lp.assignment_to_subst(hsv, flux_var)

            flux_store_name = "flux_store_%d" % flux_store_idx
            flux_store_idx += 1
            tmps.append(flux_store_name)

            hsv = lp.precompute(hsv,
                                flux_var + "_subst",
                                flux_inames + ilp_inames,
                                temporary_name=flux_store_name,
                                precompute_inames=flux_precomp_inames +
                                flux_ilp_inames,
                                default_tag=None)
            if flux_var.endswith("_s"):
                hsv = lp.tag_array_axes(hsv, flux_store_name, "N0,N1,N2?")
            else:
                hsv = lp.tag_array_axes(hsv, flux_store_name, "N1,N0,N2?")

            n_iname = "n_" + flux_var.replace("_r", "").replace("_s", "")
            if n_iname.endswith("_0"):
                n_iname = n_iname[:-2]
            hsv = lp.rename_iname(hsv,
                                  "n",
                                  n_iname,
                                  within="id:" + reader.id,
                                  existing_ok=True)

    hsv = lp.tag_inames(hsv, dict(ii="l.0", jj="l.1"))
    for iname in flux_ilp_inames:
        hsv = lp.tag_inames(hsv, {iname: "ilp"})

    hsv = lp.alias_temporaries(hsv, rtmps)
    hsv = lp.alias_temporaries(hsv, stmps)

    if opt_level == 2:
        tap_hsv = hsv

    for prep_var_name in local_prep_var_names:
        if prep_var_name.startswith("Jinv") or "_s" in prep_var_name:
            continue
        hsv = lp.precompute(
            hsv, lp.find_one_rule_matching(hsv, prep_var_name + "_*subst*"))

    if opt_level == 3:
        tap_hsv = hsv

    hsv = lp.add_prefetch(hsv, "Q[ii,jj,k,:,:,e]", sweep_inames=ilp_inames)

    if opt_level == 4:
        tap_hsv = hsv
        tap_hsv = lp.tag_inames(
            tap_hsv, dict(Q_dim_field_inner="unr", Q_dim_field_outer="unr"))

    hsv = lp.buffer_array(hsv,
                          "rhsQ",
                          ilp_inames,
                          fetch_bounding_box=True,
                          default_tag="for",
                          init_expression="0",
                          store_expression="base + buffer")

    if opt_level == 5:
        tap_hsv = hsv
        tap_hsv = lp.tag_inames(
            tap_hsv,
            dict(rhsQ_init_field_inner="unr",
                 rhsQ_store_field_inner="unr",
                 rhsQ_init_field_outer="unr",
                 rhsQ_store_field_outer="unr",
                 Q_dim_field_inner="unr",
                 Q_dim_field_outer="unr"))

    # buffer axes need to be vectorized in order for this to work
    hsv = lp.tag_array_axes(hsv, "rhsQ_buf", "c?,vec,c")
    hsv = lp.tag_array_axes(hsv, "Q_fetch", "c?,vec,c")
    hsv = lp.tag_array_axes(hsv, "D_fetch", "f,f")
    hsv = lp.tag_inames(hsv, {
        "Q_dim_k": "unr",
        "rhsQ_init_k": "unr",
        "rhsQ_store_k": "unr"
    },
                        ignore_nonexistent=True)

    if opt_level == 6:
        tap_hsv = hsv
        tap_hsv = lp.tag_inames(
            tap_hsv,
            dict(rhsQ_init_field_inner="unr",
                 rhsQ_store_field_inner="unr",
                 rhsQ_init_field_outer="unr",
                 rhsQ_store_field_outer="unr",
                 Q_dim_field_inner="unr",
                 Q_dim_field_outer="unr"))

    hsv = lp.tag_inames(
        hsv,
        dict(rhsQ_init_field_inner="vec",
             rhsQ_store_field_inner="vec",
             rhsQ_init_field_outer="unr",
             rhsQ_store_field_outer="unr",
             Q_dim_field_inner="vec",
             Q_dim_field_outer="unr"))

    if opt_level == 7:
        tap_hsv = hsv

    hsv = lp.collect_common_factors_on_increment(
        hsv, "rhsQ_buf", vary_by_axes=(0, ) if ilp_multiple > 1 else ())

    if opt_level >= 8:
        tap_hsv = hsv

    hsv = tap_hsv

    if 1:
        print("OPS")
        op_poly = lp.get_op_poly(hsv)
        print(lp.stringify_stats_mapping(op_poly))

        print("MEM")
        gmem_poly = lp.sum_mem_access_to_bytes(lp.get_gmem_access_poly(hsv))
        print(lp.stringify_stats_mapping(gmem_poly))

    hsv = lp.set_options(hsv,
                         cl_build_options=[
                             "-cl-denorms-are-zero",
                             "-cl-fast-relaxed-math",
                             "-cl-finite-math-only",
                             "-cl-mad-enable",
                             "-cl-no-signed-zeros",
                         ])

    hsv = hsv.copy(name="horizontalStrongVolumeKernel")

    results = lp.auto_test_vs_ref(ref_hsv,
                                  ctx,
                                  hsv,
                                  parameters=dict(elements=300),
                                  quiet=True)

    elapsed = results["elapsed_wall"]

    print("elapsed", elapsed)
コード例 #13
0
ファイル: test_numa_diff.py プロジェクト: cmsquared/loopy
def test_gnuma_horiz_kernel(ctx_factory, ilp_multiple, Nq, opt_level):
    ctx = ctx_factory()

    filename = "strongVolumeKernels.f90"
    with open(filename, "r") as sourcef:
        source = sourcef.read()

    source = source.replace("datafloat", "real*4")

    hsv_r, hsv_s = [
           knl for knl in lp.parse_fortran(source, filename, auto_dependencies=False)
           if "KernelR" in knl.name or "KernelS" in knl.name
           ]
    hsv_r = lp.tag_instructions(hsv_r, "rknl")
    hsv_s = lp.tag_instructions(hsv_s, "sknl")
    hsv = lp.fuse_kernels([hsv_r, hsv_s], ["_r", "_s"])
    #hsv = hsv_s

    from gnuma_loopy_transforms import (
          fix_euler_parameters,
          set_q_storage_format, set_D_storage_format)

    hsv = lp.fix_parameters(hsv, Nq=Nq)
    hsv = lp.set_loop_priority(hsv, "e,k,j,i")
    hsv = lp.tag_inames(hsv, dict(e="g.0", j="l.1", i="l.0"))
    hsv = lp.assume(hsv, "elements >= 1")

    hsv = fix_euler_parameters(hsv, p_p0=1, p_Gamma=1.4, p_R=1)
    for name in ["Q", "rhsQ"]:
        hsv = set_q_storage_format(hsv, name)

    hsv = set_D_storage_format(hsv)
    #hsv = lp.add_prefetch(hsv, "volumeGeometricFactors")

    ref_hsv = hsv

    if opt_level == 0:
        tap_hsv = hsv

    hsv = lp.add_prefetch(hsv, "D[:,:]")

    if opt_level == 1:
        tap_hsv = hsv

    # turn the first reads into subst rules
    local_prep_var_names = set()
    for insn in lp.find_instructions(hsv, "tag:local_prep"):
        assignee, = insn.assignee_var_names()
        local_prep_var_names.add(assignee)
        hsv = lp.assignment_to_subst(hsv, assignee)

    # precompute fluxes
    hsv = lp.assignment_to_subst(hsv, "JinvD_r")
    hsv = lp.assignment_to_subst(hsv, "JinvD_s")

    r_fluxes = lp.find_instructions(hsv, "tag:compute_fluxes and tag:rknl")
    s_fluxes = lp.find_instructions(hsv, "tag:compute_fluxes and tag:sknl")

    if ilp_multiple > 1:
        hsv = lp.split_iname(hsv, "k", 2, inner_tag="ilp")
        ilp_inames = ("k_inner",)
        flux_ilp_inames = ("kk",)
    else:
        ilp_inames = ()
        flux_ilp_inames = ()

    rtmps = []
    stmps = []

    flux_store_idx = 0

    for rflux_insn, sflux_insn in zip(r_fluxes, s_fluxes):
        for knl_tag, insn, flux_inames, tmps, flux_precomp_inames in [
                  ("rknl", rflux_insn, ("j", "n",), rtmps, ("jj", "ii",)),
                  ("sknl", sflux_insn, ("i", "n",), stmps, ("ii", "jj",)),
                  ]:
            flux_var, = insn.assignee_var_names()
            print(insn)

            reader, = lp.find_instructions(hsv,
                  "tag:{knl_tag} and reads:{flux_var}"
                  .format(knl_tag=knl_tag, flux_var=flux_var))

            hsv = lp.assignment_to_subst(hsv, flux_var)

            flux_store_name = "flux_store_%d" % flux_store_idx
            flux_store_idx += 1
            tmps.append(flux_store_name)

            hsv = lp.precompute(hsv, flux_var+"_subst", flux_inames + ilp_inames,
                temporary_name=flux_store_name,
                precompute_inames=flux_precomp_inames + flux_ilp_inames,
                default_tag=None)
            if flux_var.endswith("_s"):
                hsv = lp.tag_data_axes(hsv, flux_store_name, "N0,N1,N2?")
            else:
                hsv = lp.tag_data_axes(hsv, flux_store_name, "N1,N0,N2?")

            n_iname = "n_"+flux_var.replace("_r", "").replace("_s", "")
            if n_iname.endswith("_0"):
                n_iname = n_iname[:-2]
            hsv = lp.rename_iname(hsv, "n", n_iname, within="id:"+reader.id,
                  existing_ok=True)

    hsv = lp.tag_inames(hsv, dict(ii="l.0", jj="l.1"))
    for iname in flux_ilp_inames:
        hsv = lp.tag_inames(hsv, {iname: "ilp"})

    hsv = lp.alias_temporaries(hsv, rtmps)
    hsv = lp.alias_temporaries(hsv, stmps)

    if opt_level == 2:
        tap_hsv = hsv

    for prep_var_name in local_prep_var_names:
        if prep_var_name.startswith("Jinv") or "_s" in prep_var_name:
            continue
        hsv = lp.precompute(hsv,
            lp.find_one_rule_matching(hsv, prep_var_name+"_*subst*"))

    if opt_level == 3:
        tap_hsv = hsv

    hsv = lp.add_prefetch(hsv, "Q[ii,jj,k,:,:,e]", sweep_inames=ilp_inames)

    if opt_level == 4:
        tap_hsv = hsv
        tap_hsv = lp.tag_inames(tap_hsv, dict(
              Q_dim_field_inner="unr",
              Q_dim_field_outer="unr"))

    hsv = lp.buffer_array(hsv, "rhsQ", ilp_inames,
          fetch_bounding_box=True, default_tag="for",
          init_expression="0", store_expression="base + buffer")

    if opt_level == 5:
        tap_hsv = hsv
        tap_hsv = lp.tag_inames(tap_hsv, dict(
              rhsQ_init_field_inner="unr", rhsQ_store_field_inner="unr",
              rhsQ_init_field_outer="unr", rhsQ_store_field_outer="unr",
              Q_dim_field_inner="unr",
              Q_dim_field_outer="unr"))

    # buffer axes need to be vectorized in order for this to work
    hsv = lp.tag_data_axes(hsv, "rhsQ_buf", "c?,vec,c")
    hsv = lp.tag_data_axes(hsv, "Q_fetch", "c?,vec,c")
    hsv = lp.tag_data_axes(hsv, "D_fetch", "f,f")
    hsv = lp.tag_inames(hsv,
            {"Q_dim_k": "unr", "rhsQ_init_k": "unr", "rhsQ_store_k": "unr"},
            ignore_nonexistent=True)

    if opt_level == 6:
        tap_hsv = hsv
        tap_hsv = lp.tag_inames(tap_hsv, dict(
              rhsQ_init_field_inner="unr", rhsQ_store_field_inner="unr",
              rhsQ_init_field_outer="unr", rhsQ_store_field_outer="unr",
              Q_dim_field_inner="unr",
              Q_dim_field_outer="unr"))

    hsv = lp.tag_inames(hsv, dict(
          rhsQ_init_field_inner="vec", rhsQ_store_field_inner="vec",
          rhsQ_init_field_outer="unr", rhsQ_store_field_outer="unr",
          Q_dim_field_inner="vec",
          Q_dim_field_outer="unr"))

    if opt_level == 7:
        tap_hsv = hsv

    hsv = lp.collect_common_factors_on_increment(hsv, "rhsQ_buf",
          vary_by_axes=(0,) if ilp_multiple > 1 else ())

    if opt_level >= 8:
        tap_hsv = hsv

    hsv = tap_hsv

    if 1:
        print("OPS")
        op_poly = lp.get_op_poly(hsv)
        print(lp.stringify_stats_mapping(op_poly))

        print("MEM")
        gmem_poly = lp.sum_mem_access_to_bytes(lp.get_gmem_access_poly(hsv))
        print(lp.stringify_stats_mapping(gmem_poly))

    hsv = lp.set_options(hsv, cl_build_options=[
         "-cl-denorms-are-zero",
         "-cl-fast-relaxed-math",
         "-cl-finite-math-only",
         "-cl-mad-enable",
         "-cl-no-signed-zeros",
         ])

    hsv = hsv.copy(name="horizontalStrongVolumeKernel")

    results = lp.auto_test_vs_ref(ref_hsv, ctx, hsv, parameters=dict(elements=300),
            quiet=True)

    elapsed = results["elapsed_wall"]

    print("elapsed", elapsed)