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test_dse.py
1591 lines (1334 loc) · 62.1 KB
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test_dse.py
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from sympy import Add, cos, sin, sqrt # noqa
import numpy as np
import pytest
from cached_property import cached_property
from conftest import skipif, EVAL # noqa
from devito import (NODE, Eq, Inc, Constant, Function, TimeFunction, SparseTimeFunction, # noqa
Dimension, SubDimension, Grid, Operator, norm, grad, div, dimensions,
switchconfig, configuration, centered, first_derivative, transpose)
from devito.exceptions import InvalidOperator
from devito.finite_differences.differentiable import diffify
from devito.ir import DummyEq, Expression, FindNodes, FindSymbols, retrieve_iteration_tree
from devito.passes.clusters.aliases import collect
from devito.passes.clusters.cse import _cse
from devito.symbolics import estimate_cost, pow_to_mul, indexify
from devito.tools import generator
from devito.types import Scalar, Array
from examples.seismic.acoustic import AcousticWaveSolver
from examples.seismic import demo_model, AcquisitionGeometry
from examples.seismic.tti import AnisotropicWaveSolver
def test_scheduling_after_rewrite():
"""Tests loop scheduling after expression hoisting."""
grid = Grid((10, 10))
u1 = TimeFunction(name="u1", grid=grid, save=10, time_order=2)
u2 = TimeFunction(name="u2", grid=grid, time_order=2)
sf1 = SparseTimeFunction(name='sf1', grid=grid, npoint=1, nt=10)
const = Function(name="const", grid=grid, space_order=2)
# Deliberately inject into u1, rather than u1.forward, to create a WAR
eqn1 = Eq(u1.forward, u1 + sin(const))
eqn2 = sf1.inject(u1.forward, expr=sf1)
eqn3 = Eq(u2.forward, u2 - u1.dt2 + sin(const))
op = Operator([eqn1] + eqn2 + [eqn3])
trees = retrieve_iteration_tree(op)
# Check loop nest structure
assert all(i.dim is j for i, j in zip(trees[0], grid.dimensions)) # time invariant
assert trees[1].root.dim is grid.time_dim
assert all(trees[1].root.dim is tree.root.dim for tree in trees[1:])
@pytest.mark.parametrize('exprs,expected', [
# Simple cases
(['Eq(tu, 2/(t0 + t1))', 'Eq(ti0, t0 + t1)', 'Eq(ti1, t0 + t1)'],
['t0 + t1', '2/r0', 'r0', 'r0']),
(['Eq(tu, 2/(t0 + t1))', 'Eq(ti0, 2/(t0 + t1) + 1)', 'Eq(ti1, 2/(t0 + t1) + 1)'],
['1/(t0 + t1)', '2*r5', 'r3 + 1', 'r3', 'r2', 'r2']),
(['Eq(tu, (tv + tw + 5.)*(ti0 + ti1) + (t0 + t1)*(ti0 + ti1))'],
['ti0[x, y, z] + ti1[x, y, z]',
'r0*(t0 + t1) + r0*(tv[t, x, y, z] + tw[t, x, y, z] + 5.0)']),
(['Eq(tu, t0/t1)', 'Eq(ti0, 2 + t0/t1)', 'Eq(ti1, 2 + t0/t1)'],
['t0/t1', 'r2 + 2', 'r2', 'r1', 'r1']),
# Across expressions
(['Eq(tu, tv*4 + tw*5 + tw*5*t0)', 'Eq(tv, tw*5)'],
['5*tw[t, x, y, z]', 'r0 + 5*t0*tw[t, x, y, z] + 4*tv[t, x, y, z]', 'r0']),
# Intersecting
pytest.param(['Eq(tu, ti0*ti1 + ti0*ti1*t0 + ti0*ti1*t0*t1)'],
['ti0*ti1', 'r0', 'r0*t0', 'r0*t0*t1'],
marks=pytest.mark.xfail),
# Divisions (== powers with negative exponenet) are always captured
(['Eq(tu, tv**-1*(tw*5 + tw*5*t0))', 'Eq(ti0, tv**-1*t0)'],
['1/tv[t, x, y, z]', 'r0*(5*t0*tw[t, x, y, z] + 5*tw[t, x, y, z])', 'r0*t0']),
# `compact_temporaries` must detect chains of isolated temporaries
(['Eq(t0, tv)', 'Eq(t1, t0)', 'Eq(t2, t1)', 'Eq(tu, t2)'],
['tv[t, x, y, z]']),
# Dimension-independent data dependences should be a stopper for CSE
(['Eq(tu.forward, tu.dx + 1)', 'Eq(tv.forward, tv.dx + 1)',
'Eq(tw.forward, tv.dt + 1)', 'Eq(tz.forward, tv.dt + 2)'],
['1/h_x', '1/dt', '-r1*tv[t, x, y, z]',
'-r2*tu[t, x, y, z] + r2*tu[t, x + 1, y, z] + 1',
'-r2*tv[t, x, y, z] + r2*tv[t, x + 1, y, z] + 1',
'r0 + r1*tv[t + 1, x, y, z] + 1',
'r0 + r1*tv[t + 1, x, y, z] + 2']),
# Fancy use case with lots of temporaries
(['Eq(tu.forward, tu.dx + 1)', 'Eq(tv.forward, tv.dx + 1)',
'Eq(tw.forward, tv.dt.dx2.dy2 + 1)', 'Eq(tz.forward, tv.dt.dy2.dx2 + 2)'],
['h_x**(-2)', 'h_y**(-2)', '1/h_x', '1/dt', '-r9*tv[t, x, y, z]',
'-r9*tv[t, x - 1, y, z] + r9*tv[t + 1, x - 1, y, z]',
'-r9*tv[t, x + 1, y, z] + r9*tv[t + 1, x + 1, y, z]',
'-r9*tv[t, x, y - 1, z] + r9*tv[t + 1, x, y - 1, z]',
'-r9*tv[t, x - 1, y - 1, z] + r9*tv[t + 1, x - 1, y - 1, z]',
'-r9*tv[t, x + 1, y - 1, z] + r9*tv[t + 1, x + 1, y - 1, z]',
'-r9*tv[t, x, y + 1, z] + r9*tv[t + 1, x, y + 1, z]',
'-r9*tv[t, x - 1, y + 1, z] + r9*tv[t + 1, x - 1, y + 1, z]',
'-r9*tv[t, x + 1, y + 1, z] + r9*tv[t + 1, x + 1, y + 1, z]',
'-r10*tu[t, x, y, z] + r10*tu[t, x + 1, y, z] + 1',
'-r10*tv[t, x, y, z] + r10*tv[t, x + 1, y, z] + 1',
'r11*(r0*r12 + r1*r12 - 2.0*r12*r2) + r11*(r12*r3 + r12*r4 - 2.0*r12*r5) - '
'2.0*r11*(r12*r6 + r12*r7 - 2.0*r12*(r8 + r9*tv[t + 1, x, y, z])) + 1',
'r12*(r0*r11 + r11*r3 - 2.0*r11*r6) + r12*(r1*r11 + r11*r4 - 2.0*r11*r7) - '
'2.0*r12*(r11*r2 + r11*r5 - 2.0*r11*(r8 + r9*tv[t + 1, x, y, z])) + 2']),
])
def test_cse(exprs, expected):
"""Test common subexpressions elimination."""
grid = Grid((3, 3, 3))
dims = grid.dimensions
tu = TimeFunction(name="tu", grid=grid, space_order=2) # noqa
tv = TimeFunction(name="tv", grid=grid, space_order=2) # noqa
tw = TimeFunction(name="tw", grid=grid, space_order=2) # noqa
tz = TimeFunction(name="tz", grid=grid, space_order=2) # noqa
ti0 = Array(name='ti0', shape=(3, 5, 7), dimensions=dims).indexify() # noqa
ti1 = Array(name='ti1', shape=(3, 5, 7), dimensions=dims).indexify() # noqa
t0 = Scalar(name='t0') # noqa
t1 = Scalar(name='t1') # noqa
t2 = Scalar(name='t2') # noqa
# List comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = DummyEq(indexify(diffify(eval(e).evaluate)))
counter = generator()
make = lambda: Scalar(name='r%d' % counter()).indexify()
processed = _cse(exprs, make)
assert len(processed) == len(expected)
assert all(str(i.rhs) == j for i, j in zip(processed, expected))
@pytest.mark.parametrize('expr,expected', [
('2*fa[x] + fb[x]', '2*fa[x] + fb[x]'),
('fa[x]**2', 'fa[x]*fa[x]'),
('fa[x]**2 + fb[x]**3', 'fa[x]*fa[x] + fb[x]*fb[x]*fb[x]'),
('3*fa[x]**4', '3*(fa[x]*fa[x]*fa[x]*fa[x])'),
('fa[x]**2', 'fa[x]*fa[x]'),
('1/(fa[x]**2)', '1/(fa[x]*fa[x])'),
('1/(fb[x]**2 + 1)', '1/(fb[x]*fb[x] + 1)'),
('1/(fa[x] + fb[x])', '1/(fa[x] + fb[x])'),
('3*sin(fa[x])**2', '3*(sin(fa[x])*sin(fa[x]))'),
('fa[x]/(fb[x]**2)', 'fa[x]/((fb[x]*fb[x]))'),
('(fa[x]**0.5)**2', 'fa[x]'),
])
def test_pow_to_mul(expr, expected):
grid = Grid((4, 5))
x, y = grid.dimensions
s = Scalar(name='s') # noqa
fa = Function(name='fa', grid=grid, dimensions=(x,), shape=(4,)) # noqa
fb = Function(name='fb', grid=grid, dimensions=(x,), shape=(4,)) # noqa
assert str(pow_to_mul(eval(expr))) == expected
@pytest.mark.parametrize('expr,expected,estimate', [
('Eq(t0, t1)', 0, False),
('Eq(t0, fa[x] + fb[x])', 1, False),
('Eq(t0, fa[x + 1] + fb[x - 1])', 1, False),
('Eq(t0, fa[fb[x+1]] + fa[x])', 1, False),
('Eq(t0, fa[fb[x+1]] + fc[x+2, y+1])', 1, False),
('Eq(t0, t1*t2)', 1, False),
('Eq(t0, 2.*t0*t1*t2)', 3, False),
('Eq(t0, cos(t1*t2))', 2, False),
('Eq(t0, (t1*t2)**0)', 0, False),
('Eq(t0, (t1*t2)**t1)', 2, False),
('Eq(t0, (t1*t2)**2)', 3, False), # SymPy distributes integer exponents in a Mul
('Eq(t0, 2.*t0*t1*t2 + t0*fa[x+1])', 5, False),
('Eq(t0, (2.*t0*t1*t2 + t0*fa[x+1])*3. - t0)', 7, False),
('[Eq(t0, (2.*t0*t1*t2 + t0*fa[x+1])*3. - t0), Eq(t0, cos(t1*t2))]', 9, False),
('Eq(t0, cos(t1*t2))', 51, True),
('Eq(t0, t1**3)', 2, True),
('Eq(t0, t1**4)', 3, True),
('Eq(t0, t2*t1**-1)', 26, True),
('Eq(t0, t1**t2)', 50, True),
])
def test_estimate_cost(expr, expected, estimate):
# Note: integer arithmetic isn't counted
grid = Grid(shape=(4, 4))
x, y = grid.dimensions # noqa
t0 = Scalar(name='t0') # noqa
t1 = Scalar(name='t1') # noqa
t2 = Scalar(name='t2') # noqa
fa = Function(name='fa', grid=grid, shape=(4,), dimensions=(x,)) # noqa
fb = Function(name='fb', grid=grid, shape=(4,), dimensions=(x,)) # noqa
fc = Function(name='fc', grid=grid) # noqa
assert estimate_cost(eval(expr), estimate) == expected
@pytest.mark.parametrize('exprs,exp_u,exp_v', [
(['Eq(s, 0, implicit_dims=(x, y))', 'Eq(s, s + 4, implicit_dims=(x, y))',
'Eq(u, s)'], 4, 0),
(['Eq(s, 0, implicit_dims=(x, y))', 'Eq(s, s + s + 4, implicit_dims=(x, y))',
'Eq(s, s + 4, implicit_dims=(x, y))', 'Eq(u, s)'], 8, 0),
(['Eq(s, 0, implicit_dims=(x, y))', 'Inc(s, 4, implicit_dims=(x, y))',
'Eq(u, s)'], 4, 0),
(['Eq(s, 0, implicit_dims=(x, y))', 'Inc(s, 4, implicit_dims=(x, y))', 'Eq(v, s)',
'Eq(u, s)'], 4, 4),
(['Eq(s, 0, implicit_dims=(x, y))', 'Inc(s, 4, implicit_dims=(x, y))', 'Eq(v, s)',
'Eq(s, s + 4, implicit_dims=(x, y))', 'Eq(u, s)'], 8, 4),
(['Eq(s, 0, implicit_dims=(x, y))', 'Inc(s, 4, implicit_dims=(x, y))', 'Eq(v, s)',
'Inc(s, 4, implicit_dims=(x, y))', 'Eq(u, s)'], 8, 4),
(['Eq(u, 0)', 'Inc(u, 4)', 'Eq(v, u)', 'Inc(u, 4)'], 8, 4),
(['Eq(u, 1)', 'Eq(v, 4)', 'Inc(u, v)', 'Inc(v, u)'], 5, 9),
])
def test_makeit_ssa(exprs, exp_u, exp_v):
"""
A test building Operators with non-trivial sequences of input expressions
that push hard on the `makeit_ssa` utility function.
"""
grid = Grid(shape=(4, 4))
x, y = grid.dimensions # noqa
u = Function(name='u', grid=grid) # noqa
v = Function(name='v', grid=grid) # noqa
s = Scalar(name='s') # noqa
# List comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = eval(e)
op = Operator(exprs)
op.apply()
assert np.all(u.data == exp_u)
assert np.all(v.data == exp_v)
@pytest.mark.parametrize('opt', ['noop', 'advanced'])
def test_time_dependent_split(opt):
grid = Grid(shape=(10, 10))
u = TimeFunction(name='u', grid=grid, time_order=2, space_order=2, save=3)
v = TimeFunction(name='v', grid=grid, time_order=2, space_order=0, save=3)
# The second equation needs a full loop over x/y for u then
# a full one over x.y for v
eq = [Eq(u.forward, 2 + grid.time_dim),
Eq(v.forward, u.forward.dx + u.forward.dy + 1)]
op = Operator(eq, opt=opt)
trees = retrieve_iteration_tree(op)
assert len(trees) == 2
op()
assert np.allclose(u.data[2, :, :], 3.0)
assert np.allclose(v.data[1, 1:-1, 1:-1], 1.0)
@pytest.mark.parametrize('exprs,expected', [
# none (different distance)
(['Eq(y.symbolic_max, g[0, x], implicit_dims=(t, x))',
'Inc(h1[0, 0], 1, implicit_dims=(t, x, y))'],
[6., 0., 0.]),
(['Eq(y.symbolic_max, g[0, x], implicit_dims=(t, x))',
'Eq(h1[0, 0], y, implicit_dims=(t, x, y))'],
[2., 0., 0.]),
(['Eq(y.symbolic_max, g[0, x], implicit_dims=(t, x))',
'Eq(h1[0, y], y, implicit_dims=(t, x, y))'],
[0., 1., 2.]),
(['Eq(y.symbolic_min, g[0, x], implicit_dims=(t, x))',
'Eq(h1[0, y], 3 - y, implicit_dims=(t, x, y))'],
[3., 2., 1.]),
(['Eq(y.symbolic_min, g[0, x], implicit_dims=(t, x))',
'Eq(y.symbolic_max, g[0, x], implicit_dims=(t, x))',
'Eq(h1[0, y], y, implicit_dims=(t, x, y))'],
[0., 1., 2.]),
(['Eq(y.symbolic_min, g[0, 0], implicit_dims=(t, x))',
'Eq(y.symbolic_max, g[0, 2], implicit_dims=(t, x))',
'Eq(h1[0, y], y, implicit_dims=(t, x, y))'],
[0., 1., 2.]),
(['Eq(y.symbolic_min, g[0, x], implicit_dims=(t, x))',
'Eq(y.symbolic_max, g[0, 2], implicit_dims=(t, x))',
'Inc(h1[0, y], y, implicit_dims=(t, x, y))'],
[0., 2., 6.]),
(['Eq(y.symbolic_min, g[0, x], implicit_dims=(t, x))',
'Eq(y.symbolic_max, g[0, 2], implicit_dims=(t, x))',
'Inc(h1[0, x], y, implicit_dims=(t, x, y))'],
[3., 3., 2.]),
(['Eq(y.symbolic_min, g[0, 0], implicit_dims=(t, x))',
'Inc(h1[0, y], x, implicit_dims=(t, x, y))'],
[3., 3., 3.]),
(['Eq(y.symbolic_min, g[0, 2], implicit_dims=(t, x))',
'Inc(h1[0, x], y.symbolic_min, implicit_dims=(t, x))'],
[2., 2., 2.]),
(['Eq(y.symbolic_min, g[0, 2], implicit_dims=(t, x))',
'Inc(h1[0, x], y.symbolic_min, implicit_dims=(t, x, y))'],
[2., 2., 2.]),
(['Eq(y.symbolic_min, g[0, 2], implicit_dims=(t, x))',
'Eq(h1[0, x], y.symbolic_min, implicit_dims=(t, x))'],
[2., 2., 2.]),
(['Eq(y.symbolic_min, g[0, x], implicit_dims=(t, x))',
'Eq(y.symbolic_max, g[0, x]-1, implicit_dims=(t, x))',
'Eq(h1[0, y], y, implicit_dims=(t, x, y))'],
[0., 0., 0.])
])
def test_lifting(exprs, expected):
t, x, y = dimensions('t x y')
g = TimeFunction(name='g', shape=(1, 3), dimensions=(t, x),
time_order=0, dtype=np.int32)
g.data[0, :] = [0, 1, 2]
h1 = TimeFunction(name='h1', shape=(1, 3), dimensions=(t, y), time_order=0)
h1.data[0, :] = 0
# List comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = eval(e)
op = Operator(exprs)
op.apply()
assert np.all(h1.data == expected)
class TestAliases(object):
@pytest.mark.parametrize('exprs,expected', [
# none (different distance)
(['Eq(t0, fa[x] + fb[x])', 'Eq(t1, fa[x+1] + fb[x])'],
['fa[x] + fb[x]', 'fa[x+1] + fb[x]']),
# none (different dimension)
(['Eq(t0, fa[x] + fb[x])', 'Eq(t1, fa[x] + fb[y])'],
['fa[x] + fb[x]']),
# none (different operation)
(['Eq(t0, fa[x] + fb[x])', 'Eq(t1, fa[x] - fb[x])'],
['fa[x] + fb[x]', 'fa[x] - fb[x]']),
# simple
(['Eq(t0, fa[x] + fb[x])', 'Eq(t1, fa[x+1] + fb[x+1])',
'Eq(t2, fa[x+2] + fb[x+2])'],
['fa[x+1] + fb[x+1]']),
# 2D simple
(['Eq(t0, fc[x,y] + fd[x,y])', 'Eq(t1, fc[x+1,y+1] + fd[x+1,y+1])'],
['fc[x+1,y+1] + fd[x+1,y+1]']),
# 2D with stride
(['Eq(t0, fc[x,y] + fd[x+1,y+2])', 'Eq(t1, fc[x+1,y+1] + fd[x+2,y+3])'],
['fc[x+1,y+1] + fd[x+2,y+3]']),
# 2D with subdimensions
(['Eq(t0, fc[xi,yi] + fd[xi+1,yi+2])',
'Eq(t1, fc[xi+1,yi+1] + fd[xi+2,yi+3])'],
['fc[xi+1,yi+1] + fd[xi+2,yi+3]']),
# 2D with constant access
(['Eq(t0, fc[x,y]*fc[x,0] + fd[x,y])',
'Eq(t1, fc[x+1,y+1]*fc[x+1,0] + fd[x+1,y+1])'],
['fc[x+1,y+1]*fc[x+1,0] + fd[x+1,y+1]']),
# 2D with multiple, non-zero, constant accesses
(['Eq(t0, fc[x,y]*fc[x,0] + fd[x,y]*fc[x,1])',
'Eq(t1, fc[x+1,y+1]*fc[x+1,0] + fd[x+1,y+1]*fc[x+1,1])'],
['fc[x+1,0]*fc[x+1,y+1] + fc[x+1,1]*fd[x+1,y+1]']),
# 2D with different shapes
(['Eq(t0, fc[x,y]*fa[x] + fd[x,y])',
'Eq(t1, fc[x+1,y+1]*fa[x+1] + fd[x+1,y+1])'],
['fc[x+1,y+1]*fa[x+1] + fd[x+1,y+1]']),
# complex (two 2D aliases with stride inducing relaxation)
(['Eq(t0, fc[x,y] + fd[x+1,y+2])',
'Eq(t1, fc[x+1,y+1] + fd[x+2,y+3])',
'Eq(t2, fc[x+1,y+1]*3. + fd[x+2,y+2])',
'Eq(t3, fc[x+2,y+2]*3. + fd[x+3,y+3])'],
['fc[x+1,y+1] + fd[x+2,y+3]', '3.*fc[x+2,y+2] + fd[x+3,y+3]']),
])
def test_collection(self, exprs, expected):
"""
Unit test for the detection and collection of aliases out of a series
of input expressions.
"""
grid = Grid(shape=(4, 4))
x, y = grid.dimensions # noqa
xi, yi = grid.interior.dimensions # noqa
t0 = Scalar(name='t0') # noqa
t1 = Scalar(name='t1') # noqa
t2 = Scalar(name='t2') # noqa
t3 = Scalar(name='t3') # noqa
fa = Function(name='fa', grid=grid, shape=(4,), dimensions=(x,), space_order=4) # noqa
fb = Function(name='fb', grid=grid, shape=(4,), dimensions=(x,), space_order=4) # noqa
fc = Function(name='fc', grid=grid, space_order=4) # noqa
fd = Function(name='fd', grid=grid, space_order=4) # noqa
# List/dict comprehension would need explicit locals/globals mappings to eval
for i, e in enumerate(list(exprs)):
exprs[i] = DummyEq(indexify(eval(e).evaluate))
for i, e in enumerate(list(expected)):
expected[i] = eval(e)
aliases = collect(exprs, False, lambda i: False)
assert len(aliases) == len(expected)
assert all(i in expected for i in aliases)
def test_full_shape(self):
"""
Check the shape of the Array used to store an aliasing expression.
The shape is impacted by loop blocking, which reduces the required
write-to space.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
f = Function(name='f', grid=grid)
f.data_with_halo[:] = 1.
u = TimeFunction(name='u', grid=grid, space_order=3)
u.data_with_halo[:] = 0.5
# Leads to 3D aliases
eqn = Eq(u.forward, ((u[t, x, y, z] + u[t, x+1, y+1, z+1])*3*f +
(u[t, x+2, y+2, z+2] + u[t, x+3, y+3, z+3])*3*f + 1))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'cire-mincost-sops': 1}))
x0_blk_size = op1.parameters[2]
y0_blk_size = op1.parameters[3]
z_size = op1.parameters[4]
# Check Array shape
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 1
a = arrays[0]
assert len(a.dimensions) == 3
assert a.halo == ((1, 1), (1, 1), (1, 1))
assert Add(*a.symbolic_shape[0].args) == x0_blk_size + 2
assert Add(*a.symbolic_shape[1].args) == y0_blk_size + 2
assert Add(*a.symbolic_shape[2].args) == z_size + 2
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 0.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_contracted_shape(self):
"""
Conceptually like `test_full_shape`, but the Operator used in this
test leads to contracted Arrays (2D instead of 3D).
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
f = Function(name='f', grid=grid)
f.data_with_halo[:] = 1.
u = TimeFunction(name='u', grid=grid, space_order=3)
u.data_with_halo[:] = 0.5
# Leads to 2D aliases
eqn = Eq(u.forward, ((u[t, x, y, z] + u[t, x, y+1, z+1])*3*f +
(u[t, x, y+2, z+2] + u[t, x, y+3, z+3])*3*f + 1))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'cire-mincost-sops': 1}))
y0_blk_size = op1.parameters[2]
z_size = op1.parameters[3]
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 1
a = arrays[0]
assert len(a.dimensions) == 2
assert a.halo == ((1, 1), (1, 1))
assert Add(*a.symbolic_shape[0].args) == y0_blk_size + 2
assert Add(*a.symbolic_shape[1].args) == z_size + 2
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 0.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_uncontracted_shape(self):
"""
Like `test_contracted_shape`, but the potential contraction is
now along the innermost Dimension, which causes falling back to
3D Arrays.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
f = Function(name='f', grid=grid)
f.data_with_halo[:] = 1.
u = TimeFunction(name='u', grid=grid, space_order=3)
u.data_with_halo[:] = 0.5
# Leads to 3D aliases
eqn = Eq(u.forward, ((u[t, x, y, z] + u[t, x+1, y+1, z])*3*f +
(u[t, x+2, y+2, z] + u[t, x+3, y+3, z])*3*f + 1))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'cire-mincost-sops': 1}))
x0_blk_size = op1.parameters[2]
y0_blk_size = op1.parameters[3]
z_size = op1.parameters[4]
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 1
a = arrays[0]
assert len(a.dimensions) == 3
assert a.halo == ((1, 1), (1, 1), (0, 0))
assert Add(*a.symbolic_shape[0].args) == x0_blk_size + 2
assert Add(*a.symbolic_shape[1].args) == y0_blk_size + 2
assert a.symbolic_shape[2] == z_size
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 0.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_uncontracted_shape_invariants(self):
"""
Like `test_uncontracted_shape`, but now with some (outer-)Dimension-invariant
aliasing expressions.
"""
grid = Grid(shape=(6, 6, 6))
x, y, z = grid.dimensions # noqa
f = Function(name='f', grid=grid)
f.data_with_halo[:] =\
np.linspace(-1, 1, f.data_with_halo.size).reshape(*f.shape_with_halo)
u = TimeFunction(name='u', grid=grid, space_order=3)
u.data_with_halo[:] = 0.5
def func(f):
return sqrt(f**2 + 1.)
# Leads to 3D aliases despite the potential contraction along x and y
eqn = Eq(u.forward, u*(func(f) + func(f[x, y, z-1])))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True}))
x_size = op1.parameters[2]
y_size = op1.parameters[3]
z_size = op1.parameters[4]
arrays = [i for i in FindSymbols().visit(op1) if i.is_Array]
assert len(arrays) == 1
a = arrays[0]
assert len(a.dimensions) == 3
assert a.halo == ((0, 0), (0, 0), (1, 0))
assert a.symbolic_shape[0] == x_size
assert a.symbolic_shape[1] == y_size
assert Add(*a.symbolic_shape[2].args) == z_size + 1
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 0.5
op1(time_M=1)
assert np.allclose(u.data, exp, rtol=10e-7)
def test_full_shape_w_subdims(self):
"""
Like `test_full_shape`, but SubDomains (and therefore SubDimensions) are used.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
f = Function(name='f', grid=grid)
f.data_with_halo[:] = 1.
u = TimeFunction(name='u', grid=grid, space_order=3)
u.data_with_halo[:] = 0.5
# Leads to 3D aliases
eqn = Eq(u.forward, ((u[t, x, y, z] + u[t, x+1, y+1, z+1])*3*f +
(u[t, x+2, y+2, z+2] + u[t, x+3, y+3, z+3])*3*f + 1),
subdomain=grid.interior)
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'cire-mincost-sops': 1}))
i0x0_blk_size = op1.parameters[1]
i0y0_blk_size = op1.parameters[2]
z_size = op1.parameters[4]
# Check Array shape
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 1
a = arrays[0]
assert len(a.dimensions) == 3
assert a.halo == ((1, 1), (1, 1), (1, 1))
assert Add(*a.symbolic_shape[0].args) == i0x0_blk_size + 2
assert Add(*a.symbolic_shape[1].args) == i0y0_blk_size + 2
assert Add(*a.symbolic_shape[2].args) == z_size + 2
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 0.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_mixed_shapes(self):
"""
Test that if running with ``opt=(..., {'min-storage': True})``, then,
when possible, aliasing expressions are assigned to (n-k)D Arrays (k>0)
rather than nD Arrays.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
d = Dimension(name='d')
c = Function(name='c', grid=grid, shape=(2, 3), dimensions=(d, z))
f = Function(name='f', grid=grid)
u = TimeFunction(name='u', grid=grid, space_order=3)
c.data_with_halo[:] = 1.
f.data_with_halo[:] = 1.
u.data_with_halo[:] = 1.5
# Leads to 2D and 3D aliases
eqn = Eq(u.forward,
((c[0, z]*u[t, x+1, y+1, z] + c[1, z+1]*u[t, x+1, y+1, z+1])*f +
(c[0, z]*u[t, x+2, y+2, z] + c[1, z+1]*u[t, x+2, y+2, z+1])*f +
(u[t, x, y+1, z+1] + u[t, x+1, y+1, z+1])*3*f +
(u[t, x, y+3, z+1] + u[t, x+1, y+3, z+1])*3*f))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'min-storage': True,
'cire-mincost-sops': 1}))
x0_blk_size = op1.parameters[3]
y0_blk_size = op1.parameters[4]
z_size = op1.parameters[5]
# Expected one single loop nest
assert len(op1._func_table) == 1
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 2
assert len(arrays[0].dimensions) == 2
assert arrays[0].halo == ((1, 1), (0, 0))
assert Add(*arrays[0].symbolic_shape[0].args) == y0_blk_size + 2
assert arrays[0].symbolic_shape[1] == z_size
assert len(arrays[1].dimensions) == 3
assert arrays[1].halo == ((1, 0), (1, 0), (0, 0))
assert Add(*arrays[1].symbolic_shape[0].args) == x0_blk_size + 1
assert Add(*arrays[1].symbolic_shape[1].args) == y0_blk_size + 1
assert arrays[1].symbolic_shape[2] == z_size
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 1.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_min_storage_in_isolation(self):
"""
Test that if running with ``opt=(..., opt=('cire-sops', {'min-storage': True})``,
then, when possible, aliasing expressions are assigned to (n-k)D Arrays (k>0)
rather than nD Arrays.
"""
grid = Grid(shape=(8, 8, 8))
x, y, z = grid.dimensions
u = TimeFunction(name='u', grid=grid, space_order=2)
u1 = TimeFunction(name="u1", grid=grid, space_order=2)
u2 = TimeFunction(name="u1", grid=grid, space_order=2)
u.data_with_halo[:] = 1.42
u1.data_with_halo[:] = 1.42
u2.data_with_halo[:] = 1.42
eqn = Eq(u.forward, u.dy.dy + u.dx.dx)
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('cire-sops', {'openmp': True, 'min-storage': True}))
op2 = Operator(eqn, opt=('advanced-fsg', {'openmp': True}))
# `min-storage` leads to one 2D and one 3D Arrays
arrays = [i for i in FindSymbols().visit(op1) if i.is_Array]
assert len(arrays) == 2
assert len([i for i in arrays if i._mem_shared]) == 1
assert len([i for i in arrays if i._mem_local]) == 1
assert len(arrays[0].dimensions) == 2
assert arrays[0].halo == ((1, 0), (0, 0))
assert Add(*arrays[0].symbolic_shape[0].args) == y.symbolic_size + 1
assert arrays[0].symbolic_shape[1] == z.symbolic_size
assert len(arrays[1].dimensions) == 3
assert arrays[1].halo == ((1, 0), (0, 0), (0, 0))
assert Add(*arrays[1].symbolic_shape[0].args) == x.symbolic_size + 1
assert arrays[1].symbolic_shape[1] == y.symbolic_size
assert arrays[1].symbolic_shape[2] == z.symbolic_size
try:
Operator(eqn, opt=('advanced-fsg', {'openmp': True, 'min-storage': True}))
except InvalidOperator:
# Incompatible `advanced-fsg` + `min-storage`
assert True
except:
assert False
u1.data_with_halo[:] = 1.42
op0(time_M=1)
op1(time_M=1, u=u1)
op2(time_M=1, u=u2)
expected = norm(u)
assert np.isclose(expected, norm(u1), rtol=1e-5)
assert np.isclose(expected, norm(u2), rtol=1e-5)
def test_mixed_shapes_v2_w_subdims(self):
"""
Analogous `test_mixed_shapes`, but with different sets of aliasing expressions.
Also, uses SubDimensions.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
d = Dimension(name='d')
c = Function(name='c', grid=grid, shape=(2, 3), dimensions=(d, z))
f = Function(name='f', grid=grid)
u = TimeFunction(name='u', grid=grid, space_order=3)
c.data_with_halo[:] = 1.
f.data_with_halo[:] = 1.
u.data_with_halo[:] = 1.5
# Leads to 2D and 3D aliases
eqn = Eq(u.forward,
((c[0, z]*u[t, x+1, y-1, z] + c[1, z+1]*u[t, x+1, y-1, z+1])*f +
(c[0, z]*u[t, x+2, y-2, z] + c[1, z+1]*u[t, x+2, y-2, z+1])*f +
(u[t, x, y+1, z+1] + u[t, x+1, y+1, z+1])*3*f +
(u[t, x, y+3, z+2] + u[t, x+1, y+3, z+2])*3*f),
subdomain=grid.interior)
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'min-storage': True,
'cire-mincost-sops': 1}))
i0x0_blk_size = op1.parameters[2]
i0y0_blk_size = op1.parameters[3]
z_size = op1.parameters[5]
# Expected one single loop nest
assert len(op1._func_table) == 1
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 2
assert len(arrays[0].dimensions) == 2
assert arrays[0].halo == ((1, 1), (1, 0))
assert Add(*arrays[0].symbolic_shape[0].args) == i0y0_blk_size + 2
assert Add(*arrays[0].symbolic_shape[1].args) == z_size + 1
assert len(arrays[1].dimensions) == 3
assert arrays[1].halo == ((1, 0), (1, 0), (0, 0))
assert Add(*arrays[1].symbolic_shape[0].args) == i0x0_blk_size + 1
assert Add(*arrays[1].symbolic_shape[1].args) == i0y0_blk_size + 1
assert arrays[1].symbolic_shape[2] == z_size
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 1.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_in_bounds_w_shift(self):
"""
Make sure the iteration space and indexing of the aliasing expressions
are shifted such that no out-of-bounds accesses are generated.
"""
grid = Grid(shape=(5, 5, 5))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
d = Dimension(name='d')
c = Function(name='c', grid=grid, shape=(2, 5), dimensions=(d, z))
f = Function(name='f', grid=grid)
u = TimeFunction(name='u', grid=grid, space_order=4)
c.data_with_halo[:] = 1.
f.data_with_halo[:] = 1.
u.data_with_halo[:] = 1.5
# Leads to 3D aliases
eqn = Eq(u.forward,
((c[0, z]*u[t, x+1, y, z] + c[1, z+1]*u[t, x+1, y, z+1])*f +
(c[0, z]*u[t, x+2, y+2, z] + c[1, z+1]*u[t, x+2, y+2, z+1])*f +
(u[t, x, y-4, z+1] + u[t, x+1, y-4, z+1])*3*f +
(u[t, x-1, y-3, z+1] + u[t, x, y-3, z+1])*3*f))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'cire-mincost-sops': 1}))
x0_blk_size = op1.parameters[3]
y0_blk_size = op1.parameters[4]
z_size = op1.parameters[5]
# Expected one single loop nest
assert len(op1._func_table) == 1
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 2
for a in arrays:
assert len(a.dimensions) == 3
assert a.halo == ((1, 0), (1, 1), (0, 0))
assert Add(*a.symbolic_shape[0].args) == x0_blk_size + 1
assert Add(*a.symbolic_shape[1].args) == y0_blk_size + 2
assert a.symbolic_shape[2] is z_size
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 1.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_constant_symbolic_distance(self):
"""
Test the detection of aliasing expressions in the case of a
constant symbolic distance, such as `a[t, x_m+2, y, z]` when the
Dimensions are `(t, x, y, z)`; here, `x_m + 2` is a constant
symbolic access.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
x_m = x.symbolic_min
y_m = y.symbolic_min
t = grid.stepping_dim
f = Function(name='f', grid=grid)
f.data_with_halo[:] = 1.
u = TimeFunction(name='u', grid=grid, space_order=3)
u.data_with_halo[:] = 0.5
# Leads to 2D aliases
eqn = Eq(u.forward,
((u[t, x_m+2, y, z] + u[t, x_m+3, y+1, z+1])*3*f +
(u[t, x_m+2, y+2, z+2] + u[t, x_m+3, y+3, z+3])*3*f + 1 +
(u[t, x+2, y+2, z+2] + u[t, x+3, y+3, z+3])*3*f + # Not an alias
(u[t, x_m+1, y+2, z+2] + u[t, x_m+1, y+3, z+3])*3*f + # Not an alias
(u[t, x+2, y_m+3, z+2] + u[t, x+3, y_m+3, z+3])*3*f +
(u[t, x+1, y_m+3, z+1] + u[t, x+2, y_m+3, z+2])*3*f))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'cire-mincost-sops': 1}))
x0_blk_size = op1.parameters[2]
y0_blk_size = op1.parameters[4]
z_size = op1.parameters[6]
# Check Array shape
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 2
assert all(len(a.dimensions) == 2 for a in arrays)
assert arrays[0].halo == ((1, 0), (1, 0))
assert Add(*arrays[0].symbolic_shape[0].args) == x0_blk_size + 1
assert Add(*arrays[0].symbolic_shape[1].args) == z_size + 1
assert arrays[1].halo == ((1, 1), (1, 1))
assert Add(*arrays[1].symbolic_shape[0].args) == y0_blk_size + 2
assert Add(*arrays[1].symbolic_shape[1].args) == z_size + 2
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 0.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_outlier_with_long_diameter(self):
"""
Test that if there is a potentially aliasing expression, say A, with
excessively long diameter (that is, such that it cannot safely be
computed in a loop with other aliasing expressions), then A is ignored
and the other aliasing expressions are captured correctly.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
f = Function(name='f', grid=grid)
u = TimeFunction(name='u', grid=grid, space_order=3)
f.data_with_halo[:] = 2.
u.data_with_halo[:] = 1.5
# Leads to 3D aliases
# Note: the outlier already touches the halo extremes, so it cannot
# be computed in a loop with extra y-iterations, hence it must be ignored
# while not compromising the detection of the two aliasing sub-expressions
eqn = Eq(u.forward, ((u[t, x, y+1, z+1] + u[t, x+1, y+1, z+1])*3*f +
(u[t, x, y-3, z+1] + u[t, x+1, y+3, z+1])*3*f + # outlier
(u[t, x, y+3, z+2] + u[t, x+1, y+3, z+2])*3*f))
op0 = Operator(eqn, opt=('noop', {'openmp': True}))
op1 = Operator(eqn, opt=('advanced', {'openmp': True, 'cire-mincost-sops': 1}))
y0_blk_size = op1.parameters[2]
z_size = op1.parameters[3]
# Expected one single loop nest
assert len(op1._func_table) == 1
arrays = [i for i in FindSymbols().visit(op1._func_table['bf0'].root)
if i.is_Array and i._mem_local]
assert len(arrays) == 1
a = arrays[0]
assert len(a.dimensions) == 2
assert a.halo == ((1, 1), (1, 0))
assert Add(*a.symbolic_shape[0].args) == y0_blk_size + 2
assert Add(*a.symbolic_shape[1].args) == z_size + 1
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data_with_halo[:] = 1.5
op1(time_M=1)
assert np.all(u.data == exp)
def test_composite(self):
"""
Check that composite alias are optimized away through "smaller" aliases.
Examples
--------
Instead of the following:
t0 = a[x, y]
t1 = b[x, y]
t2 = a[x+1, y+1]*b[x, y]
out = t0 + t1 + t2 # pseudocode
We should get:
t0 = a[x, y]
t1 = b[x, y]
out = t0 + t1 + t0[x+1,y+1]*t1[x, y] # pseudocode
"""
grid = Grid(shape=(3, 3))
x, y = grid.dimensions # noqa
u = TimeFunction(name='u', grid=grid)
u.data[:] = 1.
g = Function(name='g', grid=grid)
g.data[:] = 2.
expr = (cos(g)*cos(g) +
sin(g)*sin(g) +
sin(g)*cos(g) +
sin(g[x + 1, y + 1])*cos(g[x + 1, y + 1]))*u
op0 = Operator(Eq(u.forward, expr), opt='noop')
op1 = Operator(Eq(u.forward, expr), opt=('advanced', {'cire-mincost-sops': 1}))
# We expect two temporary Arrays, one for `cos(g)` and one for `sin(g)`
arrays = [i for i in FindSymbols().visit(op1) if i.is_Array]
assert len(arrays) == 2
assert all(i._mem_heap and not i._mem_external for i in arrays)
# Check numerical output
op0(time_M=1)
exp = np.copy(u.data[:])
u.data[:] = 1.
op1(time_M=1)
assert np.allclose(u.data, exp.data, rtol=10e-7)
@pytest.mark.xfail(reason="Cannot deal with nested aliases yet")
def test_nested_invariants(self):
"""
Check that nested aliases are optimized away through "smaller" aliases.
Examples
--------
Given the expression
sqrt(cos(a[x, y]))
We should get
t0 = cos(a[x,y])
t1 = sqrt(t0)
out = t1 # pseudocode
"""
grid = Grid(shape=(3, 3))
x, y = grid.dimensions # noqa
u = TimeFunction(name='u', grid=grid)
g = Function(name='g', grid=grid)
op = Operator(Eq(u.forward, u + sin(cos(g)) + sin(cos(g[x+1, y+1]))))
# We expect two temporary Arrays: `r1 = cos(g)` and `r2 = sqrt(r1)`
arrays = [i for i in FindSymbols().visit(op) if i.is_Array and i._mem_local]
assert len(arrays) == 2
assert all(i._mem_heap and not i._mem_external for i in arrays)
def test_from_different_nests(self):
"""
Check that aliases arising from two sets of equations A and B,
characterized by a flow dependence, are scheduled within A's and B's
loop nests respectively.
"""
grid = Grid(shape=(3, 3, 3))
x, y, z = grid.dimensions # noqa
t = grid.stepping_dim
i = Dimension(name='i')
f = Function(name='f', grid=grid)
f.data_with_halo[:] = 1.
g = Function(name='g', shape=(3,), dimensions=(i,))
g.data[:] = 2.