def test_laplacian(ctx_factory):
1/0 # not adapted to new language
dtype = np.float32
ctx = ctx_factory()
order = "C"
n = 8
from pymbolic import var
K_sym = var("K")
field_shape = (K_sym, n, n, n)
# load: 1+6 fields + 1/N D entry
# store: 1 fields
# perform: N*2*6 + 3*5 flops
# ratio: (12*N+15)/8 flops per 4 bytes on bus
# ~ 14 FLOPS per 4 bytes at N=8
# ~ 525 GFLOPS max on a 150GB/s device at N=8 if done perfectly
# K - run-time symbolic
knl = lp.make_kernel(ctx.devices[0],
"[K] -> {[i,j,k,e,m,o1,o2,o3,gi]: 0<=i,j,k,m,o1,o2,o3<%d and 0<=e<K and 0<=gi<6}" % n,
[
"CSE: ur(i,j,k) = sum_float32(o1, D[i,o1]*cse(u[e,o1,j,k], urf))",
"CSE: us(i,j,k) = sum_float32(o2, D[j,o2]*cse(u[e,i,o2,k], usf))",
"CSE: ut(i,j,k) = sum_float32(o3, D[k,o3]*cse(u[e,i,j,o3], utf))",
# define function
"CSE: Gu(i,j,k) = G[0,e,i,j,k]*ur(i,j,k) + G[1,e,i,j,k]*us(i,j,k) + G[2,e,i,j,k]*ut(i,j,k)",
"CSE: Gv(i,j,k) = G[1,e,i,j,k]*ur(i,j,k) + G[3,e,i,j,k]*us(i,j,k) + G[4,e,i,j,k]*ut(i,j,k)",
"CSE: Gw(i,j,k) = G[2,e,i,j,k]*ur(i,j,k) + G[4,e,i,j,k]*us(i,j,k) + G[5,e,i,j,k]*ut(i,j,k)",
"lap[e,i,j,k] = "
" sum_float32(m, D[m,i]*Gu(m,j,k))"
"+ sum_float32(m, D[m,j]*Gv(i,m,k))"
"+ sum_float32(m, D[m,k]*Gw(i,j,m))"
],
[
lp.GlobalArg("u", dtype, shape=field_shape, order=order),
lp.GlobalArg("lap", dtype, shape=field_shape, order=order),
lp.GlobalArg("G", dtype, shape=(6,)+field_shape, order=order),
lp.GlobalArg("D", dtype, shape=(n, n), order=order),
lp.ValueArg("K", np.int32, approximately=1000),
],
name="semlap", assumptions="K>=1")
#print lp.preprocess_kernel(knl, cse_ok=True)
#1/0
#
#print knl
#1/0
knl = lp.realize_cse(knl, "urf", np.float32, ["o1"])
knl = lp.realize_cse(knl, "usf", np.float32, ["o2"])
knl = lp.realize_cse(knl, "utf", np.float32, ["o3"])
knl = lp.realize_cse(knl, "Gu", np.float32, ["m", "j", "k"])
knl = lp.realize_cse(knl, "Gv", np.float32, ["i", "m", "k"])
knl = lp.realize_cse(knl, "Gw", np.float32, ["i", "j", "m"])
knl = lp.realize_cse(knl, "ur", np.float32, ["k", "j", "m"])
knl = lp.realize_cse(knl, "us", np.float32, ["i", "m", "k"])
knl = lp.realize_cse(knl, "ut", np.float32, ["i", "j", "m"])
if 0:
pass
#seq_knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"], "G[gi,e,m,j,k]")
#seq_knl = lp.add_prefetch(seq_knl, "D", ["m", "j"])
#seq_knl = lp.add_prefetch(seq_knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
else:
seq_knl = knl
knl = lp.split_iname(knl, "e", 16, outer_tag="g.0")#, slabs=(0, 1))
knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"], "G[gi,e,m,j,k]")
knl = lp.add_prefetch(knl, "D", ["m", "j"])
#knl = lp.add_prefetch(knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
#knl = lp.split_iname(knl, "e_inner", 4, inner_tag="ilp")
#print seq_knl
#print lp.preprocess_kernel(knl)
#1/0
knl = lp.tag_inames(knl, dict(i="l.0", j="l.1"))
kernel_gen = lp.generate_loop_schedules(knl,
loop_priority=["m_fetch_G", "i_fetch_u"])
kernel_gen = lp.check_kernels(kernel_gen, dict(K=1000))
K = 1000
lp.auto_test_vs_ref(seq_knl, ctx, kernel_gen,
op_count=K*(n*n*n*n*2*3 + n*n*n*5*3 + n**4 * 2*3)/1e9,
op_label="GFlops",
parameters={"K": K}, print_seq_code=True)
def test_laplacian(ctx_factory):
1 / 0 # not adapted to new language
dtype = np.float32
ctx = ctx_factory()
order = "C"
n = 8
from pymbolic import var
K_sym = var("K")
field_shape = (K_sym, n, n, n)
# load: 1+6 fields + 1/N D entry
# store: 1 fields
# perform: N*2*6 + 3*5 flops
# ratio: (12*N+15)/8 flops per 4 bytes on bus
# ~ 14 FLOPS per 4 bytes at N=8
# ~ 525 GFLOPS max on a 150GB/s device at N=8 if done perfectly
# K - run-time symbolic
knl = lp.make_kernel(
ctx.devices[0],
"[K] -> {[i,j,k,e,m,o1,o2,o3,gi]: 0<=i,j,k,m,o1,o2,o3<%d and 0<=e<K and 0<=gi<6}"
% n,
[
"CSE: ur(i,j,k) = sum_float32(o1, D[i,o1]*cse(u[e,o1,j,k], urf))",
"CSE: us(i,j,k) = sum_float32(o2, D[j,o2]*cse(u[e,i,o2,k], usf))",
"CSE: ut(i,j,k) = sum_float32(o3, D[k,o3]*cse(u[e,i,j,o3], utf))",
# define function
"CSE: Gu(i,j,k) = G[0,e,i,j,k]*ur(i,j,k) + G[1,e,i,j,k]*us(i,j,k) + G[2,e,i,j,k]*ut(i,j,k)",
"CSE: Gv(i,j,k) = G[1,e,i,j,k]*ur(i,j,k) + G[3,e,i,j,k]*us(i,j,k) + G[4,e,i,j,k]*ut(i,j,k)",
"CSE: Gw(i,j,k) = G[2,e,i,j,k]*ur(i,j,k) + G[4,e,i,j,k]*us(i,j,k) + G[5,e,i,j,k]*ut(i,j,k)",
"lap[e,i,j,k] = "
" sum_float32(m, D[m,i]*Gu(m,j,k))"
"+ sum_float32(m, D[m,j]*Gv(i,m,k))"
"+ sum_float32(m, D[m,k]*Gw(i,j,m))"
],
[
lp.GlobalArg("u", dtype, shape=field_shape, order=order),
lp.GlobalArg("lap", dtype, shape=field_shape, order=order),
lp.GlobalArg("G", dtype, shape=(6, ) + field_shape, order=order),
lp.GlobalArg("D", dtype, shape=(n, n), order=order),
lp.ValueArg("K", np.int32, approximately=1000),
],
name="semlap",
assumptions="K>=1")
#print lp.preprocess_kernel(knl, cse_ok=True)
#1/0
#
#print knl
#1/0
knl = lp.realize_cse(knl, "urf", np.float32, ["o1"])
knl = lp.realize_cse(knl, "usf", np.float32, ["o2"])
knl = lp.realize_cse(knl, "utf", np.float32, ["o3"])
knl = lp.realize_cse(knl, "Gu", np.float32, ["m", "j", "k"])
knl = lp.realize_cse(knl, "Gv", np.float32, ["i", "m", "k"])
knl = lp.realize_cse(knl, "Gw", np.float32, ["i", "j", "m"])
knl = lp.realize_cse(knl, "ur", np.float32, ["k", "j", "m"])
knl = lp.realize_cse(knl, "us", np.float32, ["i", "m", "k"])
knl = lp.realize_cse(knl, "ut", np.float32, ["i", "j", "m"])
if 0:
pass
#seq_knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"], "G[gi,e,m,j,k]")
#seq_knl = lp.add_prefetch(seq_knl, "D", ["m", "j"])
#seq_knl = lp.add_prefetch(seq_knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
else:
seq_knl = knl
knl = lp.split_iname(knl, "e", 16, outer_tag="g.0") #, slabs=(0, 1))
knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"], "G[gi,e,m,j,k]")
knl = lp.add_prefetch(knl, "D", ["m", "j"])
#knl = lp.add_prefetch(knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
#knl = lp.split_iname(knl, "e_inner", 4, inner_tag="ilp")
#print seq_knl
#print lp.preprocess_kernel(knl)
#1/0
knl = lp.tag_inames(knl, dict(i="l.0", j="l.1"))
kernel_gen = lp.generate_loop_schedules(
knl, loop_priority=["m_fetch_G", "i_fetch_u"])
kernel_gen = lp.check_kernels(kernel_gen, dict(K=1000))
K = 1000
lp.auto_test_vs_ref(
seq_knl,
ctx,
kernel_gen,
op_count=K *
(n * n * n * n * 2 * 3 + n * n * n * 5 * 3 + n**4 * 2 * 3) / 1e9,
op_label="GFlops",
parameters={"K": K},
print_seq_code=True)
def test_laplacian_lmem(ctx_factory):
1/0 # not adapted to new language
dtype = np.float32
ctx = ctx_factory()
order = "C"
n = 8
from pymbolic import var
K_sym = var("K")
field_shape = (K_sym, n, n, n)
# K - run-time symbolic
knl = lp.make_kernel(ctx.devices[0],
"[K] -> {[i,j,k,e,m,o,gi]: 0<=i,j,k,m,o<%d and 0<=e<K and 0<=gi<6}" % n,
[
"CSE: ur(i,j,k) = sum_float32(@o, D[i,o]*u[e,o,j,k])",
"CSE: us(i,j,k) = sum_float32(@o, D[j,o]*u[e,i,o,k])",
"CSE: ut(i,j,k) = sum_float32(@o, D[k,o]*u[e,i,j,o])",
"lap[e,i,j,k] = "
" sum_float32(m, D[m,i]*(G[0,e,m,j,k]*ur(m,j,k) + G[1,e,m,j,k]*us(m,j,k) + G[2,e,m,j,k]*ut(m,j,k)))"
"+ sum_float32(m, D[m,j]*(G[1,e,i,m,k]*ur(i,m,k) + G[3,e,i,m,k]*us(i,m,k) + G[4,e,i,m,k]*ut(i,m,k)))"
"+ sum_float32(m, D[m,k]*(G[2,e,i,j,m]*ur(i,j,m) + G[4,e,i,j,m]*us(i,j,m) + G[5,e,i,j,m]*ut(i,j,m)))"
],
[
lp.GlobalArg("u", dtype, shape=field_shape, order=order),
lp.GlobalArg("lap", dtype, shape=field_shape, order=order),
lp.GlobalArg("G", dtype, shape=(6,)+field_shape, order=order),
lp.GlobalArg("D", dtype, shape=(n, n), order=order),
lp.ValueArg("K", np.int32, approximately=1000),
],
name="semlap", assumptions="K>=1")
knl = lp.realize_cse(knl, "ur", np.float32, ["k", "j", "m"])
knl = lp.realize_cse(knl, "us", np.float32, ["i", "m", "k"])
knl = lp.realize_cse(knl, "ut", np.float32, ["i", "j", "m"])
if 0:
seq_knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"], "G[gi,e,m,j,k]")
seq_knl = lp.add_prefetch(seq_knl, "D", ["m", "j"])
seq_knl = lp.add_prefetch(seq_knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
else:
seq_knl = knl
knl = lp.split_iname(knl, "e", 16, outer_tag="g.0")#, slabs=(0, 1))
knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"], "G[gi,e,m,j,k]")
knl = lp.add_prefetch(knl, "D", ["m", "j"])
knl = lp.add_prefetch(knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
#knl = lp.split_iname(knl, "e_inner", 4, inner_tag="ilp")
#print seq_knl
#print lp.preprocess_kernel(knl)
#1/0
knl = lp.tag_inames(knl, dict(i="l.0", j="l.1"))
kernel_gen = lp.generate_loop_schedules(knl)
kernel_gen = lp.check_kernels(kernel_gen, dict(K=1000))
K = 1000
lp.auto_test_vs_ref(seq_knl, ctx, kernel_gen,
op_count=K*(n*n*n*n*2*3 + n*n*n*5*3 + n**4 * 2*3)/1e9,
op_label="GFlops",
parameters={"K": K}, print_seq_code=True)
def test_laplacian_lmem(ctx_factory):
1 / 0 # not adapted to new language
dtype = np.float32
ctx = ctx_factory()
order = "C"
n = 8
from pymbolic import var
K_sym = var("K")
field_shape = (K_sym, n, n, n)
# K - run-time symbolic
knl = lp.make_kernel(
ctx.devices[0],
"[K] -> {[i,j,k,e,m,o,gi]: 0<=i,j,k,m,o<%d and 0<=e<K and 0<=gi<6}" %
n, [
"CSE: ur(i,j,k) = sum_float32(@o, D[i,o]*u[e,o,j,k])",
"CSE: us(i,j,k) = sum_float32(@o, D[j,o]*u[e,i,o,k])",
"CSE: ut(i,j,k) = sum_float32(@o, D[k,o]*u[e,i,j,o])",
"lap[e,i,j,k] = "
" sum_float32(m, D[m,i]*(G[0,e,m,j,k]*ur(m,j,k) + G[1,e,m,j,k]*us(m,j,k) + G[2,e,m,j,k]*ut(m,j,k)))"
"+ sum_float32(m, D[m,j]*(G[1,e,i,m,k]*ur(i,m,k) + G[3,e,i,m,k]*us(i,m,k) + G[4,e,i,m,k]*ut(i,m,k)))"
"+ sum_float32(m, D[m,k]*(G[2,e,i,j,m]*ur(i,j,m) + G[4,e,i,j,m]*us(i,j,m) + G[5,e,i,j,m]*ut(i,j,m)))"
], [
lp.GlobalArg("u", dtype, shape=field_shape, order=order),
lp.GlobalArg("lap", dtype, shape=field_shape, order=order),
lp.GlobalArg("G", dtype, shape=(6, ) + field_shape, order=order),
lp.GlobalArg("D", dtype, shape=(n, n), order=order),
lp.ValueArg("K", np.int32, approximately=1000),
],
name="semlap",
assumptions="K>=1")
knl = lp.realize_cse(knl, "ur", np.float32, ["k", "j", "m"])
knl = lp.realize_cse(knl, "us", np.float32, ["i", "m", "k"])
knl = lp.realize_cse(knl, "ut", np.float32, ["i", "j", "m"])
if 0:
seq_knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"],
"G[gi,e,m,j,k]")
seq_knl = lp.add_prefetch(seq_knl, "D", ["m", "j"])
seq_knl = lp.add_prefetch(seq_knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
else:
seq_knl = knl
knl = lp.split_iname(knl, "e", 16, outer_tag="g.0") #, slabs=(0, 1))
knl = lp.add_prefetch(knl, "G", ["gi", "m", "j", "k"], "G[gi,e,m,j,k]")
knl = lp.add_prefetch(knl, "D", ["m", "j"])
knl = lp.add_prefetch(knl, "u", ["i", "j", "k"], "u[*,i,j,k]")
#knl = lp.split_iname(knl, "e_inner", 4, inner_tag="ilp")
#print seq_knl
#print lp.preprocess_kernel(knl)
#1/0
knl = lp.tag_inames(knl, dict(i="l.0", j="l.1"))
kernel_gen = lp.generate_loop_schedules(knl)
kernel_gen = lp.check_kernels(kernel_gen, dict(K=1000))
K = 1000
lp.auto_test_vs_ref(
seq_knl,
ctx,
kernel_gen,
op_count=K *
(n * n * n * n * 2 * 3 + n * n * n * 5 * 3 + n**4 * 2 * 3) / 1e9,
op_label="GFlops",
parameters={"K": K},
print_seq_code=True)