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from __future__ import division
import numpy as np
import pyopencl as cl
import loopy as lp
from pyopencl.tools import pytest_generate_tests_for_pyopencl \
as pytest_generate_tests
dtype = np.float32
ctx = ctx_factory()
order = "C"
n = 8
from pymbolic import var
K_sym = var("K")
# 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)",
" 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.ArrayArg("u", dtype, shape=field_shape, order=order),
lp.ArrayArg("lap", dtype, shape=field_shape, order=order),
lp.ArrayArg("G", dtype, shape=(6,)+field_shape, order=order),
lp.ArrayArg("D", dtype, shape=(n, n), order=order),
lp.ScalarArg("K", np.int32, approximately=1000),
#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]")
knl = lp.split_dimension(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_dimension(knl, "e_inner", 4, inner_tag="ilp")
Andreas Klöckner
committed
#print seq_knl
Andreas Klöckner
committed
#1/0
knl = lp.tag_dimensions(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_seq(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)
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def test_laplacian_lmem(ctx_factory):
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.ArrayArg("u", dtype, shape=field_shape, order=order),
lp.ArrayArg("lap", dtype, shape=field_shape, order=order),
lp.ArrayArg("G", dtype, shape=(6,)+field_shape, order=order),
lp.ArrayArg("D", dtype, shape=(n, n), order=order),
lp.ScalarArg("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_dimension(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_dimension(knl, "e_inner", 4, inner_tag="ilp")
#print seq_knl
#print lp.preprocess_kernel(knl)
#1/0
knl = lp.tag_dimensions(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_seq(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)
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def test_advect(ctx_factory):
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)
# 1. direction-by-direction similarity transform on u
# 2. invert diagonal
# 3. transform back (direction-by-direction)
# K - run-time symbolic
# A. updated for CSE: notation.
# B. fixed temp indexing and C ordering
# load: 3+9 fields + 1/N D entry
# store: 3 fields
# perform: N*2*6 + 3*5 + 3*5 flops
# ratio: (12*N+30)/15 flops per 4 bytes on bus
# ~ 8.4 FLOPS per 4 bytes at N=8
# ~ 300 GFLOPS max on a 150GB/s device at N=8 if done perfectly
knl = lp.make_kernel(ctx.devices[0],
"[K] -> {[i,j,k,m,e]: 0<=i,j,k,m<%d AND 0<=e<K}" % N,
[
# differentiate u
"CSE: ur(i,j,k) = sum_float32(@m, D[i,m]*u[e,m,j,k])",
"CSE: us(i,j,k) = sum_float32(@m, D[j,m]*u[e,i,m,k])",
"CSE: ut(i,j,k) = sum_float32(@m, D[k,m]*u[e,i,j,m])",
# differentiate v
"CSE: vr(i,j,k) = sum_float32(@m, D[i,m]*v[e,m,j,k])",
"CSE: vs(i,j,k) = sum_float32(@m, D[j,m]*v[e,i,m,k])",
"CSE: vt(i,j,k) = sum_float32(@m, D[k,m]*v[e,i,j,m])",
# differentiate w
"CSE: wr(i,j,k) = sum_float32(@m, D[i,m]*w[e,m,j,k])",
"CSE: ws(i,j,k) = sum_float32(@m, D[j,m]*w[e,i,m,k])",
"CSE: wt(i,j,k) = sum_float32(@m, D[k,m]*w[e,i,j,m])",
# find velocity in (r,s,t) coordinates
# CSE?
"CSE: Vr(i,j,k) = G[0,e,i,j,k]*u[e,i,j,k] + G[1,e,i,j,k]*v[e,i,j,k] + G[2,e,i,j,k]*w[e,i,j,k]",
"CSE: Vs(i,j,k) = G[3,e,i,j,k]*u[e,i,j,k] + G[4,e,i,j,k]*v[e,i,j,k] + G[5,e,i,j,k]*w[e,i,j,k]",
"CSE: Vt(i,j,k) = G[6,e,i,j,k]*u[e,i,j,k] + G[7,e,i,j,k]*v[e,i,j,k] + G[8,e,i,j,k]*w[e,i,j,k]",
# form nonlinear term on integration nodes
"Nu[e,i,j,k] = Vr(i,j,k)*ur(i,j,k)+Vs(i,j,k)*us(i,j,k)+Vt(i,j,k)*ut(i,j,k)",
"Nv[e,i,j,k] = Vr(i,j,k)*vr(i,j,k)+Vs(i,j,k)*vs(i,j,k)+Vt(i,j,k)*vt(i,j,k)",
"Nw[e,i,j,k] = Vr(i,j,k)*wr(i,j,k)+Vs(i,j,k)*ws(i,j,k)+Vt(i,j,k)*wt(i,j,k)",
],
[
lp.ArrayArg("u", dtype, shape=field_shape, order=order),
lp.ArrayArg("v", dtype, shape=field_shape, order=order),
lp.ArrayArg("w", dtype, shape=field_shape, order=order),
lp.ArrayArg("Nu", dtype, shape=field_shape, order=order),
lp.ArrayArg("Nv", dtype, shape=field_shape, order=order),
lp.ArrayArg("Nw", dtype, shape=field_shape, order=order),
lp.ArrayArg("G", dtype, shape=(9,)+field_shape, order=order),
lp.ArrayArg("D", dtype, shape=(N, N), order=order),
lp.ScalarArg("K", np.int32, approximately=1000),
],
name="sem_advect", assumptions="K>=1")
print knl
1/0
seq_knl = knl
knl = lp.split_dimension(knl, "e", 16, outer_tag="g.0")#, slabs=(0, 1))
knl = lp.tag_dimensions(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), kill_level_min=5)
K = 1000
lp.auto_test_vs_seq(seq_knl, ctx, kernel_gen,
op_count=0,
op_label="GFlops",
parameters={"K": K}, print_seq_code=True,)
if __name__ == "__main__":
import sys
if len(sys.argv) > 1:
exec(sys.argv[1])
else:
from py.test.cmdline import main
main([__file__])