def make_knl():
target = NumbaTarget()
# build individual kernels
osc = model.Kuramoto()
osc.dt = 1.0
osc.const['omega'] = 10.0 * 2.0 * np.pi / 1e3
osc_knl = osc.kernel(target)
cfun = coupling.Kuramoto(osc)
cfun.param['a'] = pm.parse('a')
net = network.Network(osc, cfun)
net_knl = net.kernel(target)
scm = scheme.EulerStep(osc.dt)
scm_knl = scm.kernel(target)
scm_knl = lp.fix_parameters(scm_knl, nsvar=len(osc.state_sym))
# fuse kernels
knls = osc_knl, net_knl, scm_knl
data_flow = [('input', 1, 0), ('diffs', 0, 2), ('drift', 0, 2),
('state', 2, 0)]
knl = lp.fuse_kernels(knls, data_flow=data_flow)
# and time step
knl = lp.to_batched(knl, 'nstep', [], 'i_step', sequential=True)
knl = lp.fix_parameters(knl,
i_time=pm.parse('(i_step + i_step_0) % ntime'))
knl.args.append(lp.ValueArg('i_step_0', np.uintc))
knl = lp.add_dtypes(knl, {'i_step_0': np.uintc})
return knl, osc
def network_time_step(
model: model.BaseKernel,
coupling: coupling.BaseCoupling,
scheme: scheme.TimeStepScheme,
target: lp.target.TargetBase=None,
):
target = target or utils.default_target()
# fuse kernels
kernels = [
model.kernel(target),
network.Network(model, coupling).kernel(target),
lp.fix_parameters(scheme.kernel(target), nsvar=len(model.state_sym)),
]
data_flow = [
('input', 1, 0),
('diffs', 0, 2),
('drift', 0, 2),
('state', 2, 0)
]
knl = lp.fuse_kernels(kernels, data_flow=data_flow)
# time step
knl = lp.to_batched(knl, 'nstep', [], 'i_step', sequential=True)
new_i_time = pm.parse('(i_step + i_step_0) % ntime')
knl = lp.fix_parameters(knl, i_time=new_i_time)
knl.args.append(lp.ValueArg('i_step_0', np.uintc))
knl = lp.add_dtypes(knl, {'i_step_0': np.uintc})
return knl
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))
def test_fusion():
exp_kernel = lp.make_kernel(''' { [i]: 0<=i<n } ''',
''' exp[i] = pow(E, z[i])''',
assumptions="n>0")
sum_kernel = lp.make_kernel('{ [j]: 0<=j<n }',
'out2 = sum(j, exp[j])',
assumptions='n>0')
knl = lp.fuse_kernels([exp_kernel, sum_kernel])
print(knl)
def test_fusion():
exp_kernel = lp.make_kernel(""" { [i]: 0<=i<n } """,
""" exp[i] = pow(E, z[i])""",
assumptions="n>0")
sum_kernel = lp.make_kernel("{ [j]: 0<=j<n }",
"out2 = sum(j, exp[j])",
assumptions="n>0")
knl = lp.fuse_kernels([exp_kernel, sum_kernel])
print(knl)
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["xderiv"], yderiv["yderiv"]),
data_flow=[("result", 0, 1)])
knl = knl.with_kernel(
lp.prioritize_loops(knl["xderiv_and_yderiv"], "e,i,j,k"))
assert len(knl["xderiv_and_yderiv"].temporary_variables) == 2
ctx = ctx_factory()
lp.auto_test_vs_ref(xyderiv,
ctx,
knl,
parameters=dict(nelements=20, ndofs=4))
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))
def test_fusion():
exp_kernel = lp.make_kernel(
''' { [i]: 0<=i<n } ''',
''' exp[i] = pow(E, z[i])''',
assumptions="n>0")
sum_kernel = lp.make_kernel(
'{ [j]: 0<=j<n }',
'out2 = sum(j, exp[j])',
assumptions='n>0')
knl = lp.fuse_kernels([exp_kernel, sum_kernel])
print(knl)
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)
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)
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), data_flow=[("result", 0, 1)])
knl = lp.prioritize_loops(knl, "e,i,j,k")
assert len(knl.temporary_variables) == 2
ctx = ctx_factory()
lp.auto_test_vs_ref(xyderiv, ctx, knl, parameters=dict(nelements=20, ndofs=4))
def test_two_kernel_fusion(ctx_factory):
"""
A simple fusion test of two sets of instructions.
"""
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
knla = lp.make_kernel("{[i]: 0<=i<10}", """
out[i] = i
""")
knlb = lp.make_kernel("{[j]: 0<=j<10}", """
out[j] = j+100
""")
knl = lp.fuse_kernels([knla, knlb], data_flow=[("out", 0, 1)])
evt, (out, ) = knl(queue)
np.testing.assert_allclose(out.get(), np.arange(100, 110))
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)
def test_write_block_matrix_fusion(ctx_factory):
"""
A slightly more complicated fusion test, where all
sub-kernels write into the same global matrix, but
in well-defined separate blocks. This tests makes sure
data flow specification is preserved during fusion for
matrix-assembly-like programs.
"""
ctx = ctx_factory()
queue = cl.CommandQueue(ctx)
def init_global_mat_prg():
return lp.make_kernel(
["{[idof]: 0 <= idof < n}", "{[jdof]: 0 <= jdof < m}"],
"""
result[idof, jdof] = 0 {id=init}
""",
[
lp.GlobalArg("result", None, shape="n, m", offset=lp.auto),
lp.ValueArg("n, m", np.int32),
"...",
],
options=lp.Options(return_dict=True),
default_offset=lp.auto,
name="init_a_global_matrix",
)
def write_into_mat_prg():
return lp.make_kernel(
["{[idof]: 0 <= idof < ndofs}", "{[jdof]: 0 <= jdof < mdofs}"],
"""
result[offset_i + idof, offset_j + jdof] = mat[idof, jdof]
""",
[
lp.GlobalArg("result", None, shape="n, m", offset=lp.auto),
lp.ValueArg("n, m", np.int32),
lp.GlobalArg("mat", None, shape="ndofs, mdofs",
offset=lp.auto),
lp.ValueArg("offset_i", np.int32),
lp.ValueArg("offset_j", np.int32),
"...",
],
options=lp.Options(return_dict=True),
default_offset=lp.auto,
name="write_into_global_matrix",
)
# Construct a 2x2 diagonal matrix with
# random 5x5 blocks on the block-diagonal,
# and zeros elsewhere
n = 10
block_n = 5
mat1 = np.random.randn(block_n, block_n)
mat2 = np.random.randn(block_n, block_n)
answer = np.block([[mat1, np.zeros((block_n, block_n))],
[np.zeros((block_n, block_n)), mat2]])
kwargs = {"n": n, "m": n}
# Do some renaming of individual programs before fusion
kernels = [init_global_mat_prg()]
for idx, (offset, mat) in enumerate([(0, mat1), (block_n, mat2)]):
knl = lp.rename_argument(write_into_mat_prg(), "mat", f"mat_{idx}")
kwargs[f"mat_{idx}"] = mat
for iname in knl.default_entrypoint.all_inames():
knl = lp.rename_iname(knl, iname, f"{iname}_{idx}")
knl = lp.rename_argument(knl, "ndofs", f"ndofs_{idx}")
knl = lp.rename_argument(knl, "mdofs", f"mdofs_{idx}")
kwargs[f"ndofs_{idx}"] = block_n
kwargs[f"mdofs_{idx}"] = block_n
knl = lp.rename_argument(knl, "offset_i", f"offset_i_{idx}")
knl = lp.rename_argument(knl, "offset_j", f"offset_j_{idx}")
kwargs[f"offset_i_{idx}"] = offset
kwargs[f"offset_j_{idx}"] = offset
kernels.append(knl)
fused_knl = lp.fuse_kernels(
kernels,
data_flow=[("result", 0, 1), ("result", 1, 2)],
)
fused_knl = lp.add_nosync(fused_knl,
"global",
"writes:result",
"writes:result",
bidirectional=True,
force=True)
evt, result = fused_knl(queue, **kwargs)
result = result["result"]
np.testing.assert_allclose(result, answer)
''' exp[i] = E ** z[i]''',
assumptions="n>0")
sum_kernel = lp.make_kernel(
'{ [j]: 0<=j<n }',
'total = sum(j, exp[j])',
assumptions='n>0')
softmax_kernel = lp.make_kernel(
'{ [k]: 0<=k<n }',
'out3[k] = exp[k] / total',
[
lp.GlobalArg("total", None, shape=()),
"..."
],
assumptions='n>0')
big_honkin_knl = lp.fuse_kernels([exp_kernel, sum_kernel, softmax_kernel])
#big_honkin_knl = lp.fuse_kernels([exp_kernel, sum_kernel])
print softmax_kernel.arg_dict["total"].shape
#big_honkin_knl = lp.tag_inames(big_honkin_knl, dict(i="l.0"))
big_honkin_knl = lp.set_options(big_honkin_knl, write_cl=True)
a = np.random.randn(20)
big_honkin_knl = big_honkin_knl(queue, z=a, E=np.float64(5))
#Raw coupling
couplingknl = lp.make_kernel("{ [i_node, j_node]: 0<=i_node, j_node<n_node}",
coupling_raw,
target=target)
couplingknl = lp.add_dtypes(
couplingknl, {
"lengths": np.float32,
"state": np.float32,
"weights": np.float32,
"theta_i": np.float32,
"rec_speed_dt": np.float32
})
couplingknl = lp.split_iname(couplingknl, "j_node", 1, outer_tag='l.0')
#Raw model
modelknl = lp.make_kernel("{ [i_node]: 0<=i_node<n_node}",
model_raw,
target=target)
modelknl = lp.add_dtypes(modelknl, {
"state": np.float32,
"theta_i": np.float32,
"tavg": np.float32
})
# Fuse
knls = couplingknl, modelknl
data_flow = [('state', 0, 1)]
knl = lp.fuse_kernels(knls, data_flow=data_flow)
print(knl)
print("****")
knl = lp.split_iname(knl, "i_node", 128, outer_tag='g.0')
print(lp.generate_code_v2(knl).all_code())
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)
def __call__(self, ary):
from meshmode.dof_array import DOFArray
if not isinstance(ary, DOFArray):
raise TypeError("non-array passed to discretization connection")
actx = ary.array_context
@memoize_in(actx, (
DirectDiscretizationConnection,
"resample_by_mat_knl",
self.is_surjective,
))
def mat_knl():
if self.is_surjective:
domains = [
"""
{[iel, idof, j]:
0<=iel<nelements and
0<=idof<n_to_nodes and
0<=j<n_from_nodes}
""",
]
instructions = """
result[to_element_indices[iel], idof] \
= sum(j, resample_mat[idof, j] \
* ary[from_element_indices[iel], j])
"""
else:
domains = [
"""
{[iel_init, idof_init]:
0<=iel_init<nelements_result and
0<=idof_init<n_to_nodes}
""",
"""
{[iel, idof, j]:
0<=iel<nelements and
0<=idof<n_to_nodes and
0<=j<n_from_nodes}
""",
]
instructions = """
result[iel_init, idof_init] = 0 {id=init}
... gbarrier {id=barrier, dep=init}
result[to_element_indices[iel], idof] \
= sum(j, resample_mat[idof, j] \
* ary[from_element_indices[iel], j]) {dep=barrier}
"""
knl = make_loopy_program(
domains,
instructions, [
lp.GlobalArg("result",
None,
shape="nelements_result, n_to_nodes",
offset=lp.auto),
lp.GlobalArg("ary",
None,
shape="nelements_vec, n_from_nodes",
offset=lp.auto),
lp.ValueArg("nelements_result", np.int32),
lp.ValueArg("nelements_vec", np.int32),
lp.ValueArg("n_from_nodes", np.int32),
"...",
],
name="resample_by_mat")
return knl
@memoize_in(actx, (DirectDiscretizationConnection,
"resample_by_picking_knl", self.is_surjective))
def pick_knl():
if self.is_surjective:
domains = [
"""{[iel, idof]:
0<=iel<nelements and
0<=idof<n_to_nodes}"""
]
instructions = """
result[to_element_indices[iel], idof] \
= ary[from_element_indices[iel], pick_list[idof]]
"""
else:
domains = [
"""
{[iel_init, idof_init]:
0<=iel_init<nelements_result and
0<=idof_init<n_to_nodes}
""", """
{[iel, idof]:
0<=iel<nelements and
0<=idof<n_to_nodes}
"""
]
instructions = """
result[iel_init, idof_init] = 0 {id=init}
... gbarrier {id=barrier, dep=init}
result[to_element_indices[iel], idof] \
= ary[from_element_indices[iel], pick_list[idof]] {dep=barrier}
"""
knl = make_loopy_program(
domains,
instructions, [
lp.GlobalArg("result",
None,
shape="nelements_result, n_to_nodes",
offset=lp.auto),
lp.GlobalArg("ary",
None,
shape="nelements_vec, n_from_nodes",
offset=lp.auto),
lp.ValueArg("nelements_result", np.int32),
lp.ValueArg("nelements_vec", np.int32),
lp.ValueArg("n_from_nodes", np.int32),
"...",
],
name="resample_by_picking")
return knl
if ary.shape != (len(self.from_discr.groups), ):
raise ValueError("invalid shape of incoming resampling data")
group_idx_to_result = []
for i_tgrp, (tgrp,
cgrp) in enumerate(zip(self.to_discr.groups,
self.groups)):
kernels = [] # get kernels for each batch; to be fused eventually
kwargs = {} # kwargs to the fused kernel
for i_batch, batch in enumerate(cgrp.batches):
if batch.from_element_indices.size == 0:
continue
point_pick_indices = self._resample_point_pick_indices(
actx, i_tgrp, i_batch)
if point_pick_indices is None:
knl = mat_knl()
knl = lp.rename_argument(knl, "resample_mat",
f"resample_mat_{i_batch}")
kwargs[f"resample_mat_{i_batch}"] = (self._resample_matrix(
actx, i_tgrp, i_batch))
else:
knl = pick_knl()
knl = lp.rename_argument(knl, "pick_list",
f"pick_list_{i_batch}")
kwargs[f"pick_list_{i_batch}"] = point_pick_indices
# {{{ enforce different namespaces for the kernels
for iname in knl.all_inames():
knl = lp.rename_iname(knl, iname, f"{iname}_{i_batch}")
knl = lp.rename_argument(knl, "ary", f"ary_{i_batch}")
knl = lp.rename_argument(knl, "from_element_indices",
f"from_element_indices_{i_batch}")
knl = lp.rename_argument(knl, "to_element_indices",
f"to_element_indices_{i_batch}")
knl = lp.rename_argument(knl, "nelements",
f"nelements_{i_batch}")
# }}}
kwargs[f"ary_{i_batch}"] = ary[batch.from_group_index]
kwargs[f"from_element_indices_{i_batch}"] = (
batch.from_element_indices)
kwargs[f"to_element_indices_{i_batch}"] = (
batch.to_element_indices)
kernels.append(knl)
fused_knl = lp.fuse_kernels(kernels)
# order of operations doesn't matter
fused_knl = lp.add_nosync(fused_knl,
"global",
"writes:result",
"writes:result",
bidirectional=True,
force=True)
result_dict = actx.call_loopy(fused_knl,
nelements_result=tgrp.nelements,
n_to_nodes=tgrp.nunit_dofs,
**kwargs)
group_idx_to_result.append(result_dict["result"])
from meshmode.dof_array import DOFArray
return DOFArray.from_list(actx, group_idx_to_result)