test_gpu_common.py

import cloudpickle as pickle

import pytest
import numpy as np
import sympy
import scipy.sparse

from conftest import assert_structure
from devito import (Constant, Eq, Inc, Grid, Function, ConditionalDimension,
                    Dimension, MatrixSparseTimeFunction, SparseTimeFunction,
                    SubDimension, SubDomain, SubDomainSet, TimeFunction, exp,
                    Operator, configuration, switchconfig, TensorTimeFunction,
                    Buffer, assign)
from devito.arch import get_gpu_info, get_cpu_info, Device, Cpu64
from devito.exceptions import InvalidArgument
from devito.ir import (Conditional, Expression, Section, FindNodes, FindSymbols,
                       retrieve_iteration_tree)
from devito.passes.iet.languages.openmp import OmpIteration
from devito.types import DeviceID, DeviceRM, Lock, NPThreads, PThreadArray, Symbol

from conftest import skipif

pytestmark = skipif(['nodevice'], whole_module=True)


class TestGPUInfo:

    def test_get_gpu_info(self):
        info = get_gpu_info()
        known = ['nvidia', 'tesla', 'geforce', 'quadro', 'amd', 'unspecified']
        try:
            assert info['architecture'].lower() in known
        except KeyError:
            # There might be than one GPUs, but for now we don't care
            # as we're not really exploiting this info yet...
            pytest.xfail("Unsupported platform for get_gpu_info")

    def custom_compiler(self):
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)

        eqn = Eq(u.forward, u + 1)

        with switchconfig(compiler='custom'):
            op = Operator(eqn)()
            # Check jit-compilation and correct execution
            op.apply(time_M=10)
            assert np.all(u.data[1] == 11)

    def test_host_threads(self):
        plat = configuration['platform']

        assert isinstance(plat, Device)

        nth = plat.cores_physical
        assert nth == get_cpu_info()['physical']
        assert nth == Cpu64("test").cores_physical


class TestCodeGeneration:

    def test_maxpar_option(self):
        """
        Make sure the `cire-maxpar` option is set to True by default.
        """
        grid = Grid(shape=(10, 10, 10))

        u = TimeFunction(name='u', grid=grid, space_order=4)

        eq = Eq(u.forward, u.dy.dy)

        op = Operator(eq)

        trees = retrieve_iteration_tree(op)
        assert len(trees) == 2
        assert trees[0][0] is trees[1][0]
        assert trees[0][1] is not trees[1][1]

    @pytest.mark.parametrize('dtype', [np.complex64, np.complex128])
    def test_complex(self, dtype):
        grid = Grid((5, 5))
        x, y = grid.dimensions

        c = Constant(name='c', dtype=dtype)
        u = Function(name="u", grid=grid, dtype=dtype)

        eq = Eq(u, x + sympy.I*y + exp(sympy.I + x.spacing) * c)
        op = Operator(eq)
        op(c=1.0 + 2.0j)

        # Check against numpy
        dx = grid.spacing_map[x.spacing]
        xx, yy = np.meshgrid(np.linspace(0, 4, 5), np.linspace(0, 4, 5))
        npres = xx + 1j*yy + np.exp(1j + dx) * (1.0 + 2.0j)

        assert np.allclose(u.data, npres.T, rtol=5e-7, atol=0)


class TestPassesOptional:

    def test_linearize(self):
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)

        eqn = Eq(u.forward, u + 1)

        op = Operator(eqn, opt=('advanced', {'linearize': True}))

        # Check generated code
        assert 'uL0' in str(op)

        # Check jit-compilation and correct execution
        op.apply(time_M=10)
        assert np.all(u.data[1] == 11)


class TestPassesEdgeCases:

    def test_fission(self):
        nt = 20
        grid = Grid(shape=(10, 10))
        time = grid.time_dim

        usave = TimeFunction(name='usave', grid=grid, save=nt, time_order=2)
        vsave = TimeFunction(name='vsave', grid=grid, save=nt, time_order=2)

        ctime0 = ConditionalDimension(name='ctime', parent=time, condition=time > 4)
        ctime1 = ConditionalDimension(name='ctime', parent=time, condition=time <= 4)

        eqns = [Eq(usave, time + 0.2, implicit_dims=[ctime0]),
                Eq(vsave, time + 0.2, implicit_dims=[ctime1])]

        op = Operator(eqns)

        # Check generated code
        trees = retrieve_iteration_tree(op, mode='superset')
        assert len(trees) == 2
        assert trees[0].root is trees[1].root
        assert trees[0][1] is not trees[1][1]
        assert trees[0].root.dim is time
        assert not trees[0].root.pragmas
        assert trees[0][1].pragmas
        assert trees[1][1].pragmas

        op.apply()

        expected = np.full(shape=(20, 10, 10), fill_value=0.2, dtype=np.float32)
        for i in range(nt):
            expected[i] += i

        assert np.all(usave.data[5:] == expected[5:])
        assert np.all(vsave.data[:5] == expected[:5])

    def test_incr_perfect_outer(self):
        grid = Grid((5, 5))
        d = Dimension(name="d")

        u = Function(name="u", dimensions=(*grid.dimensions, d),
                     grid=grid, shape=(*grid.shape, 5), )
        v = Function(name="v", dimensions=(*grid.dimensions, d),
                     grid=grid, shape=(*grid.shape, 5))
        w = Function(name="w", grid=grid)

        u.data.fill(1)
        v.data.fill(2)

        summation = Inc(w, u*v)

        op = Operator([summation])

        assert 'reduction' not in str(op)
        assert 'collapse(2)' in str(op)
        assert 'parallel' in str(op)

        op()
        assert np.all(w.data == 10)

    def test_reduction_many_dims(self):
        grid = Grid(shape=(25, 25, 25))

        u = TimeFunction(name='u', grid=grid, time_order=1, save=Buffer(1))
        s = Symbol(name='s', dtype=np.float32)

        eqns = [Eq(s, 0),
                Inc(s, 2*u + 1)]

        op0 = Operator(eqns)
        op1 = Operator(eqns, opt=('advanced', {'mapify-reduce': True}))

        tree, = retrieve_iteration_tree(op0)
        assert 'collapse(3) reduction(+:s)' in str(tree[1].pragmas[0])

        tree, = retrieve_iteration_tree(op1)
        assert 'collapse(3) reduction(+:s)' in str(tree[1].pragmas[0])


class Bundle(SubDomain):
    """
    We use this SubDomain to enforce Eqs to end up in different loops.
    """

    name = 'bundle'

    def define(self, dimensions):
        x, y, z = dimensions
        return {x: ('middle', 0, 0), y: ('middle', 0, 0), z: ('middle', 0, 0)}


class TestStreaming:

    @pytest.mark.parametrize('opt', [
        ('tasking', 'orchestrate'),
        ('tasking', 'orchestrate', {'linearize': True}),
    ])
    def test_tasking_in_isolation(self, opt):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(10, 10, 10), subdomains=bundle0)

        tmp = Function(name='tmp', grid=grid)
        u = TimeFunction(name='u', grid=grid, save=nt)
        v = TimeFunction(name='v', grid=grid)

        eqns = [Eq(tmp, v),
                Eq(v.forward, v + 1),
                Eq(u.forward, tmp, subdomain=bundle0)]

        op = Operator(eqns, opt=opt)

        # Check generated code
        assert len(retrieve_iteration_tree(op)) == 3
        assert len([i for i in FindSymbols().visit(op) if isinstance(i, Lock)]) == 1
        sections = FindNodes(Section).visit(op)
        assert len(sections) == 3
        assert str(sections[0].body[0].body[0].body[0].body[0]) == 'while(lock0[0] == 0);'
        body = op._func_table['release_lock0'].root.body
        assert str(body.body[0].condition) == 'Ne(lock0[0], 2)'
        assert str(body.body[1]) == 'lock0[0] = 0;'
        body = op._func_table['activate0'].root.body
        assert str(body.body[0].condition) == 'Ne(sdata0[0].flag, 1)'
        assert str(body.body[1]) == 'sdata0[0].time = time;'
        assert str(body.body[2]) == 'sdata0[0].flag = 2;'

        op.apply(time_M=nt-2)

        assert np.all(u.data[nt-1] == 8)

    def test_tasking_fused(self):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(10, 10, 10), subdomains=bundle0)

        tmp = Function(name='tmp', grid=grid)
        u = TimeFunction(name='u', grid=grid, save=nt)
        v = TimeFunction(name='v', grid=grid, save=nt)
        w = TimeFunction(name='w', grid=grid)

        eqns = [Eq(w.forward, w + 1),
                Eq(tmp, w.forward),
                Eq(u.forward, tmp, subdomain=bundle0),
                Eq(v.forward, tmp, subdomain=bundle0)]

        op = Operator(eqns, opt=('tasking', 'fuse', 'orchestrate', {'linearize': False}))

        # Check generated code
        assert len(retrieve_iteration_tree(op)) == 3
        locks = [i for i in FindSymbols().visit(op) if isinstance(i, Lock)]
        assert len(locks) == 1  # Only 1 because it's only `tmp` that needs protection
        assert len(op._func_table) == 5
        exprs = FindNodes(Expression).visit(op._func_table['copy_to_host0'].root)
        b = 17 if configuration['language'] == 'openacc' else 16  # No `qid` w/ OMP
        assert str(exprs[b]) == 'const int deviceid = sdata0->deviceid;'
        assert str(exprs[b+1]) == 'volatile int time = sdata0->time;'
        assert str(exprs[b+2]) == 'lock0[0] = 1;'
        assert exprs[b+3].write is u
        assert exprs[b+4].write is v
        assert str(exprs[b+5]) == 'lock0[0] = 2;'
        assert str(exprs[b+6]) == 'sdata0->flag = 1;'

        op.apply(time_M=nt-2)

        assert np.all(u.data[nt-1] == 9)
        assert np.all(v.data[nt-1] == 9)

    def test_tasking_unfused_two_locks(self):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(10, 10, 10), subdomains=bundle0)

        tmp0 = Function(name='tmp0', grid=grid)
        tmp1 = Function(name='tmp1', grid=grid)
        u = TimeFunction(name='u', grid=grid, save=nt)
        v = TimeFunction(name='v', grid=grid, save=nt)
        w = TimeFunction(name='w', grid=grid)

        eqns = [Eq(w.forward, w + 1),
                Eq(tmp0, w.forward),
                Eq(tmp1, w.forward),
                Eq(u.forward, tmp0, subdomain=bundle0),
                Eq(v.forward, tmp1, subdomain=bundle0)]

        op = Operator(eqns, opt=('tasking', 'fuse', 'orchestrate', {'linearize': False}))

        # Check generated code
        trees = retrieve_iteration_tree(op)
        assert len(trees) == 3
        assert len([i for i in FindSymbols().visit(op) if isinstance(i, Lock)]) == 5
        sections = FindNodes(Section).visit(op)
        assert len(sections) == 4
        assert (str(sections[1].body[0].body[0].body[0].body[0]) ==
                'while(lock0[0] == 0 || lock1[0] == 0);')  # Wait-lock
        body = sections[2].body[0].body[0]
        assert str(body.body[0]) == 'release_lock0(lock0);'
        assert str(body.body[1]) == 'activate0(time,sdata0);'
        assert len(op._func_table) == 5
        exprs = FindNodes(Expression).visit(op._func_table['copy_to_host0'].root)
        b = 18 if configuration['language'] == 'openacc' else 17  # No `qid` w/ OMP
        assert str(exprs[b]) == 'lock0[0] = 1;'

        op.apply(time_M=nt-2)

        assert np.all(u.data[nt-1] == 9)
        assert np.all(v.data[nt-1] == 9)

    def test_tasking_forcefuse(self):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(10, 10, 10), subdomains=bundle0)

        tmp0 = Function(name='tmp0', grid=grid)
        tmp1 = Function(name='tmp1', grid=grid)
        u = TimeFunction(name='u', grid=grid, save=nt)
        v = TimeFunction(name='v', grid=grid, save=nt)
        w = TimeFunction(name='w', grid=grid)

        eqns = [Eq(w.forward, w + 1),
                Eq(tmp0, w.forward),
                Eq(tmp1, w.forward),
                Eq(u.forward, tmp0, subdomain=bundle0),
                Eq(v.forward, tmp1, subdomain=bundle0)]

        op = Operator(eqns, opt=('tasking', 'fuse', 'orchestrate',
                                 {'fuse-tasks': True, 'linearize': False}))

        # Check generated code
        assert len(retrieve_iteration_tree(op)) == 3
        assert len([i for i in FindSymbols().visit(op) if isinstance(i, Lock)]) == 2
        sections = FindNodes(Section).visit(op)
        assert len(sections) == 3
        assert (str(sections[1].body[0].body[0].body[0].body[0]) ==
                'while(lock0[0] == 0 || lock1[0] == 0);')  # Wait-lock
        body = op._func_table['release_lock0'].root.body
        assert str(body.body[0].condition) == 'Ne(lock0[0], 2) | Ne(lock1[0], 2)'
        assert str(body.body[1]) == 'lock0[0] = 0;'  # Set-lock
        assert str(body.body[2]) == 'lock1[0] = 0;'  # Set-lock
        body = op._func_table['activate0'].root.body
        assert str(body.body[0].condition) == 'Ne(sdata0[0].flag, 1)'  # Wait-thread
        assert str(body.body[1]) == 'sdata0[0].time = time;'
        assert str(body.body[2]) == 'sdata0[0].flag = 2;'
        assert len(op._func_table) == 5
        exprs = FindNodes(Expression).visit(op._func_table['copy_to_host0'].root)
        b = 21 if configuration['language'] == 'openacc' else 20  # No `qid` w/ OMP
        assert str(exprs[b]) == 'lock0[0] = 1;'
        assert str(exprs[b+1]) == 'lock1[0] = 1;'
        assert exprs[b+2].write is u
        assert exprs[b+3].write is v

        op.apply(time_M=nt-2)

        assert np.all(u.data[nt-1] == 9)
        assert np.all(v.data[nt-1] == 9)

    @pytest.mark.parametrize('opt', [
        ('tasking', 'orchestrate'),
        ('tasking', 'streaming', 'orchestrate'),
    ])
    def test_attempt_tasking_but_no_temporaries(self, opt):
        grid = Grid(shape=(10, 10, 10))

        u = TimeFunction(name='u', grid=grid, save=10)

        op = Operator(Eq(u.forward, u + 1), opt=opt)

        piters = FindNodes(OmpIteration).visit(op)
        assert len(piters) == 0

        op = Operator(Eq(u.forward, u + 1), opt=(opt, {'par-disabled': False}))

        # Degenerates to host execution with no data movement, since `u` is
        # a host Function
        piters = FindNodes(OmpIteration).visit(op)
        assert len(piters) == 1
        assert type(piters.pop()) == OmpIteration

    def test_tasking_multi_output(self):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(10, 10, 10), subdomains=bundle0)
        t = grid.stepping_dim
        x, y, z = grid.dimensions

        u = TimeFunction(name='u', grid=grid, time_order=2)
        u1 = TimeFunction(name='u', grid=grid, time_order=2)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        usave1 = TimeFunction(name='usave', grid=grid, save=nt)

        eqns = [Eq(u.forward, u + 1),
                Eq(usave, u.forward + u + u.backward + u[t, x-1, y, z],
                   subdomain=bundle0)]

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': usave}))
        op1 = Operator(eqns, opt=('tasking', 'orchestrate', {'linearize': False}))

        # Check generated code
        assert len(retrieve_iteration_tree(op1)) == 2
        assert len([i for i in FindSymbols().visit(op1) if isinstance(i, Lock)]) == 1
        sections = FindNodes(Section).visit(op1)
        assert len(sections) == 2
        assert str(sections[0].body[0].body[0].body[0].body[0]) ==\
            'while(lock0[t2] == 0);'
        body = op1._func_table['release_lock0'].root.body
        for i in range(3):
            assert 'lock0[t' in str(body.body[1 + i])  # Set-lock
        body = op1._func_table['activate0'].root.body
        assert str(body.body[-1]) == 'sdata0[wi0].flag = 2;'
        assert len(op1._func_table) == 5
        exprs = FindNodes(Expression).visit(op1._func_table['copy_to_host0'].root)
        b = 21 if configuration['language'] == 'openacc' else 20  # No `qid` w/ OMP
        for i in range(3):
            assert 'lock0[t' in str(exprs[b + i])
        assert exprs[b+3].write is usave

        op0.apply(time_M=nt-2)
        op1.apply(time_M=nt-2, u=u1, usave=usave1)

        assert np.all(u.data[:] == u1.data[:])
        assert np.all(usave.data[:] == usave1.data[:])

    def test_tasking_lock_placement(self):
        grid = Grid(shape=(10, 10, 10))

        f = Function(name='f', grid=grid, space_order=2)
        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=10)

        eqns = [Eq(f, u + 1),
                Eq(u.forward, f.dx + u + 1),
                Eq(usave, u)]

        op = Operator(eqns, opt=('tasking', 'orchestrate'))

        # Check generated code -- the wait-lock is expected in section1
        assert len(retrieve_iteration_tree(op)) == 3
        assert len([i for i in FindSymbols().visit(op) if isinstance(i, Lock)]) == 1
        sections = FindNodes(Section).visit(op)
        assert len(sections) == 3
        assert sections[0].body[0].body[0].body[0].is_Iteration
        assert str(sections[1].body[0].body[0].body[0].body[0]) ==\
            'while(lock0[t1] == 0);'

    @pytest.mark.parametrize('opt,ntmps', [
        (('buffering', 'streaming', 'orchestrate'), 2),
        (('buffering', 'streaming', 'orchestrate', {'linearize': True}), 2),
    ])
    def test_streaming_basic(self, opt, ntmps):
        nt = 10
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)

        for i in range(nt):
            usave.data[i, :] = i

        eqn = Eq(u.forward, u + usave)

        op = Operator(eqn, opt=opt)

        # Check generated code
        if configuration['language'] == 'openacc':
            assert len(op._func_table) == 9
        else:
            assert len(op._func_table) == 8
        assert len([i for i in FindSymbols().visit(op) if i.is_Array]) == ntmps

        op.apply(time_M=nt-2)

        assert np.all(u.data[0] == 28)
        assert np.all(u.data[1] == 36)

    @pytest.mark.parametrize('opt,ntmps', [
        (('buffering', 'streaming', 'orchestrate'), 13),
        (('buffering', 'streaming', 'fuse', 'orchestrate', {'fuse-tasks': True}), 7),
    ])
    def test_streaming_two_buffers(self, opt, ntmps):
        nt = 10
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        vsave = TimeFunction(name='vsave', grid=grid, save=nt)

        for i in range(nt):
            usave.data[i, :] = i
            vsave.data[i, :] = i

        eqn = Eq(u.forward, u + usave + vsave)

        op = Operator(eqn, opt=opt)

        # Check generated code
        arrays = [i for i in FindSymbols().visit(op) if i.is_Array]
        if configuration['language'] == 'openacc':
            assert len(op._func_table) == 9
            assert len(arrays) == ntmps
        else:
            assert len(op._func_table) == 8
            assert len(arrays) == ntmps - 1

        op.apply(time_M=nt-2)

        assert np.all(u.data[0] == 56)
        assert np.all(u.data[1] == 72)

    def test_streaming_fused(self):
        nt = 10
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)
        v = TimeFunction(name='v', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        vsave = TimeFunction(name='vsave', grid=grid, save=nt)

        for i in range(nt):
            usave.data[i, :] = i
            vsave.data[i, :] = i

        eqns = [Eq(u.forward, u + usave + vsave),
                Eq(v.forward, v + usave + vsave)]

        op = Operator(eqns, opt=('buffering', 'streaming', 'fuse', 'orchestrate'))

        # Check generated code
        trees = retrieve_iteration_tree(op)
        assert len(trees) == 2
        assert trees[0][-1].nodes[0].body[0].write is u
        assert trees[0][-1].nodes[0].body[1].write is v

        op.apply(time_M=nt-2)

        assert np.all(u.data[0] == 56)
        assert np.all(v.data[0] == 56)
        assert np.all(u.data[1] == 72)
        assert np.all(v.data[1] == 72)

    @pytest.mark.parametrize('opt', [
        ('buffering', 'streaming', 'orchestrate'),
    ])
    def test_streaming_conddim_forward(self, opt):
        nt = 10
        grid = Grid(shape=(4, 4))
        time_dim = grid.time_dim

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, time_order=0,
                             save=(int(nt//factor.data)), time_dim=time_sub)

        for i in range(usave.save):
            usave.data[i, :] = i

        eqn = Eq(u.forward, u.forward + u + usave)

        op = Operator(eqn, opt=opt)

        # TODO: we are *not* using the last entry of usave, so we gotta ensure
        # it is *not* streamed on to the device (thus avoiding dangerous leaks).
        # But how can we explicitly check this?
        time_M = 6

        op.apply(time_M=time_M)

        # We entered the eq four times (at time=0,2,4,6)
        # Since factor=2, we *only* write to u.data[(time+1)%2]=u.data[1]
        assert np.all(u.data[0] == 0)
        # 1st time u[1] = u[0]+u[1]+usave[0] = 0+0+0 = 0
        # 2nd time u[1] = u[0]+u[1]+usave[1] = 0+0+1 = 1
        # 3rd time u[1] = u[0]+u[1]+usave[2] = 0+1+2 = 3
        # 4th time u[1] = u[0]+u[1]+usave[3] = 0+3+3 = 6
        assert np.all(u.data[1] == 6)

    @pytest.mark.parametrize('opt', [
        ('buffering', 'streaming', 'orchestrate'),
    ])
    def test_streaming_conddim_backward(self, opt):
        nt = 10
        grid = Grid(shape=(4, 4))
        time_dim = grid.time_dim

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, time_order=0,
                             save=(int(nt//factor.data)), time_dim=time_sub)

        for i in range(usave.save):
            usave.data[i, :] = i

        eqn = Eq(u.backward, u.backward + u + usave)

        op = Operator(eqn, opt=opt)

        # TODO: we are *not* using the first two entries of usave, so we gotta ensure
        # they are *not* streamed on to the device (thus avoiding dangerous leaks).
        # But how can we explicitly check this?
        time_m = 4

        op.apply(time_m=time_m, time_M=nt-2)

        # We entered the eq three times (at time=8,6,4)
        # Since factor=2, we *only* write to u.data[(time-1)%2]=u.data[1]
        assert np.all(u.data[0] == 0)
        # 1st time u[1] = u[0]+u[1]+usave[4] = 0+0+4 = 4
        # 2nd time u[1] = u[0]+u[1]+usave[3] = 0+4+3 = 7
        # 3rd time u[1] = u[0]+u[1]+usave[2] = 0+7+2 = 9
        assert np.all(u.data[1] == 9)

    @pytest.mark.parametrize('opt,ntmps', [
        (('buffering', 'streaming', 'orchestrate'), 2),
    ])
    def test_streaming_multi_input(self, opt, ntmps):
        nt = 100
        grid = Grid(shape=(10, 10))

        u = TimeFunction(name='u', grid=grid, save=nt, time_order=2, space_order=2)
        v = TimeFunction(name='v', grid=grid, save=None, time_order=2, space_order=2)
        grad = Function(name='grad', grid=grid)
        grad1 = Function(name='grad', grid=grid)

        v.data[:] = 0.02
        for i in range(nt):
            u.data[i, :] = i + 0.1

        eqn = Eq(grad, grad - u.dt2 * v)

        op0 = Operator(eqn, opt=('noop', {'gpu-fit': u}))
        op1 = Operator(eqn, opt=opt)

        # Check generated code
        if configuration['language'] == 'openacc':
            assert len(op1._func_table) == 9
        else:
            assert len(op1._func_table) == 8
        assert len([i for i in FindSymbols().visit(op1) if i.is_Array]) == ntmps

        op0.apply(time_M=nt-2, dt=0.1)
        op1.apply(time_M=nt-2, dt=0.1, grad=grad1)

        assert np.all(grad.data == grad1.data)

    def test_streaming_multi_input_conddim_foward(self):
        nt = 10
        grid = Grid(shape=(4, 4))
        time_dim = grid.time_dim
        x, y = grid.dimensions

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        u = TimeFunction(name='u', grid=grid, time_order=2, save=nt, time_dim=time_sub)
        v = TimeFunction(name='v', grid=grid)
        v1 = TimeFunction(name='v', grid=grid)

        for i in range(u.save):
            u.data[i, :] = i

        expr = u.dt2 + 3.*u.dt(x0=time_sub - time_sub.spacing)

        eqns = [Eq(v.forward, v + expr + 1.)]

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': u}))
        op1 = Operator(eqns, opt=('buffering', 'streaming', 'orchestrate'))

        op0.apply(time_M=nt, dt=.01)
        op1.apply(time_M=nt, dt=.01, v=v1)

        assert np.all(v.data == v1.data)

    def test_streaming_multi_input_conddim_backward(self):
        nt = 10
        grid = Grid(shape=(4, 4))
        time_dim = grid.time_dim
        x, y = grid.dimensions

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        u = TimeFunction(name='u', grid=grid, time_order=2, save=nt, time_dim=time_sub)
        v = TimeFunction(name='v', grid=grid)
        v1 = TimeFunction(name='v', grid=grid)

        for i in range(u.save):
            u.data[i, :] = i

        expr = u.dt2 + 3.*u.dt(x0=time_sub - time_sub.spacing)

        eqns = [Eq(v.backward, v + expr + 1.)]

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': u}))
        op1 = Operator(eqns, opt=('buffering', 'streaming', 'orchestrate'))

        op0.apply(time_M=nt, dt=.01)
        op1.apply(time_M=nt, dt=.01, v=v1)

        assert np.all(v.data == v1.data)

    @pytest.mark.parametrize('opt,ntmps', [
        (('buffering', 'streaming', 'orchestrate'), 2),
    ])
    def test_streaming_postponed_deletion(self, opt, ntmps):
        nt = 10
        grid = Grid(shape=(10, 10, 10))

        u = TimeFunction(name='u', grid=grid)
        v = TimeFunction(name='v', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        u1 = TimeFunction(name='u', grid=grid)
        v1 = TimeFunction(name='v', grid=grid)

        for i in range(nt):
            usave.data[i, :] = i

        eqns = [Eq(u.forward, u + usave),
                Eq(v.forward, v + u.forward.dx + usave)]

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': usave}))
        op1 = Operator(eqns, opt=opt)

        # Check generated code
        if configuration['language'] == 'openacc':
            assert len(op1._func_table) == 9
        else:
            assert len(op1._func_table) == 8
        assert len([i for i in FindSymbols().visit(op1) if i.is_Array]) == ntmps

        op0.apply(time_M=nt-1)
        op1.apply(time_M=nt-1, u=u1, v=v1)

        assert np.all(u.data == u1.data)
        assert np.all(v.data == v1.data)

    def test_composite_buffering_tasking(self):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(4, 4, 4), subdomains=bundle0)

        u = TimeFunction(name='u', grid=grid, time_order=2)
        u1 = TimeFunction(name='u', grid=grid, time_order=2)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        usave1 = TimeFunction(name='usave', grid=grid, save=nt)

        eqns = [Eq(u.forward, u*1.1 + 1),
                Eq(usave, u.dt2, subdomain=bundle0)]

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': usave}))
        op1 = Operator(eqns, opt=('buffering', 'tasking', 'orchestrate'))

        # Check generated code -- thanks to buffering only expect 1 lock!
        assert len(retrieve_iteration_tree(op0)) == 2
        assert len(retrieve_iteration_tree(op1)) == 3
        symbols = FindSymbols().visit(op1)
        assert len([i for i in symbols if isinstance(i, Lock)]) == 1
        threads = [i for i in symbols if isinstance(i, PThreadArray)]
        assert len(threads) == 1
        assert threads[0].size == 1

        op0.apply(time_M=nt-1, dt=0.1)
        op1.apply(time_M=nt-1, dt=0.1, u=u1, usave=usave1)

        assert np.all(u.data == u1.data)
        assert np.all(usave.data == usave1.data)

    def test_composite_buffering_tasking_multi_output(self):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(4, 4, 4), subdomains=bundle0)

        u = TimeFunction(name='u', grid=grid, time_order=2)
        v = TimeFunction(name='v', grid=grid, time_order=2)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        vsave = TimeFunction(name='vsave', grid=grid, save=nt)

        eqns = [Eq(u.forward, u + 1),
                Eq(v.forward, v + 1),
                Eq(usave, u, subdomain=bundle0),
                Eq(vsave, v, subdomain=bundle0)]

        async_degree = 3

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': (usave, vsave)}))
        op1 = Operator(eqns, opt=('buffering', 'tasking', 'topofuse', 'orchestrate',
                                  {'buf-async-degree': async_degree}))
        op2 = Operator(eqns, opt=('buffering', 'tasking', 'topofuse', 'orchestrate',
                                  {'buf-async-degree': async_degree,
                                   'fuse-tasks': True}))

        # Check generated code -- thanks to buffering only expect 1 lock!
        assert len(retrieve_iteration_tree(op0)) == 2
        assert len(retrieve_iteration_tree(op1)) == 4
        assert len(retrieve_iteration_tree(op2)) == 3
        symbols = FindSymbols().visit(op1)
        assert len([i for i in symbols if isinstance(i, Lock)]) == 5
        threads = [i for i in symbols if isinstance(i, PThreadArray)]
        assert len(threads) == 2
        assert threads[0].size.size == async_degree
        assert threads[1].size.size == async_degree
        symbols = FindSymbols().visit(op2)
        assert len([i for i in symbols if isinstance(i, Lock)]) == 1 + 1
        threads = [i for i in symbols if isinstance(i, PThreadArray)]
        assert len(threads) == 1
        assert threads[0].size.size == async_degree

        # It is true that the usave and vsave eqns are separated in two different
        # loop nests, but they eventually get mapped to the same pair of efuncs,
        # since devito attempts to maximize code reuse
        if configuration['language'] == 'openacc':
            assert len(op1._func_table) == 8
        else:
            assert len(op1._func_table) == 7

        # Check output
        op0.apply(time_M=nt-1)
        for op in [op1, op2]:
            u1 = TimeFunction(name='u', grid=grid, time_order=2)
            v1 = TimeFunction(name='v', grid=grid, time_order=2)
            usave1 = TimeFunction(name='usave', grid=grid, save=nt)
            vsave1 = TimeFunction(name='vsave', grid=grid, save=nt)

            op.apply(time_M=nt-1, u=u1, v=v1, usave=usave1, vsave=vsave1)

            assert np.all(u.data == u1.data)
            assert np.all(v.data == v1.data)
            assert np.all(usave.data == usave1.data)
            assert np.all(vsave.data == vsave1.data)

    def test_composite_full_0(self):
        nt = 10
        grid = Grid(shape=(10, 10, 10))

        u = TimeFunction(name='u', grid=grid)
        u1 = TimeFunction(name='u', grid=grid)
        fsave = TimeFunction(name='fsave', grid=grid, save=nt)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        usave1 = TimeFunction(name='usave', grid=grid, save=nt)

        for i in range(nt):
            fsave.data[i, :] = i

        eqns = [Eq(u.forward, u + fsave + 1),
                Eq(usave, u)]

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': (fsave, usave)}))
        op1 = Operator(eqns, opt=('buffering', 'tasking', 'streaming', 'orchestrate'))

        # Check generated code
        assert len(retrieve_iteration_tree(op0)) == 1
        assert len(retrieve_iteration_tree(op1)) == 3
        symbols = FindSymbols().visit(op1)
        assert len([i for i in symbols if isinstance(i, Lock)]) == 3
        threads = [i for i in symbols if isinstance(i, PThreadArray)]
        assert len(threads) == 2
        assert all(i.size == 1 for i in threads)

        op0.apply(time_M=nt-1)
        op1.apply(time_M=nt-1, u=u1, usave=usave1)

        assert np.all(u.data == u1.data)
        assert np.all(usave.data == usave1.data)

    @pytest.mark.parametrize('opt', [
        ('buffering', 'tasking', 'streaming', 'orchestrate'),
        ('buffering', 'tasking', 'streaming', 'orchestrate', {'linearize': True}),
    ])
    def test_composite_full_1(self, opt):
        nt = 10
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid, save=nt)
        v = TimeFunction(name='v', grid=grid, save=nt)
        u1 = TimeFunction(name='u', grid=grid, save=nt)
        v1 = TimeFunction(name='v', grid=grid, save=nt)

        for i in range(nt):
            u.data[i, :] = i
            u1.data[i, :] = i

        eqns = [Eq(u.forward, u + v + 1),
                Eq(v.forward, u + v + v.backward)]

        op0 = Operator(eqns, opt=('noop', {'gpu-fit': (u, v)}))
        op1 = Operator(eqns, opt=opt)

        # Check generated code
        assert len(retrieve_iteration_tree(op1)) == 3
        assert len([i for i in FindSymbols().visit(op1) if isinstance(i, Lock)]) == 2

        op0.apply(time_M=nt-2)
        op1.apply(time_M=nt-2, u=u1, v=v1)

        assert np.all(u.data == u1.data)
        assert np.all(v.data == v1.data)

    def test_tasking_over_compiler_generated(self):
        nt = 10
        bundle0 = Bundle()
        grid = Grid(shape=(4, 4, 4), subdomains=bundle0)

        u = TimeFunction(name='u', grid=grid, space_order=4)
        u1 = TimeFunction(name='u', grid=grid, space_order=4)
        usave = TimeFunction(name='usave', grid=grid, save=nt)
        usave1 = TimeFunction(name='usave', grid=grid, save=nt)

        eqns = [Eq(u.forward, u.dx.dx*0.042 + 1),
                Eq(usave, u, subdomain=bundle0)]

        op0 = Operator(eqns, opt=('cire-sops', {'gpu-fit': usave}))
        op1 = Operator(eqns, opt=('cire-sops', 'tasking', 'orchestrate'))
        op2 = Operator(eqns, opt=('tasking', 'cire-sops', 'orchestrate'))

        # Check generated code
        for op in [op1, op2]:
            assert len(retrieve_iteration_tree(op)) == 3
            assert len([i for i in FindSymbols().visit(op) if isinstance(i, Lock)]) == 1
            sections = FindNodes(Section).visit(op)
            assert len(sections) == 4
            assert 'while(lock0[t1] == 0)' in str(sections[2].body[0].body[0].body[0])

        op0.apply(time_M=nt-1)
        op1.apply(time_M=nt-1, u=u1, usave=usave1)

        assert np.all(u.data == u1.data)
        assert np.all(usave.data == usave1.data)

    @pytest.mark.parametrize('opt,gpu_fit,async_degree,linearize', [
        (('tasking', 'orchestrate'), True, None, False),
        (('buffering', 'tasking', 'orchestrate'), True, None, False),
        (('buffering', 'tasking', 'orchestrate'), False, None, False),
        (('buffering', 'tasking', 'orchestrate'), False, 3, False),
        (('buffering', 'tasking', 'orchestrate'), False, 3, True),
    ])
    def test_save(self, opt, gpu_fit, async_degree, linearize):
        nt = 10
        grid = Grid(shape=(300, 300, 300))
        time_dim = grid.time_dim

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, time_order=0,
                             save=int(nt//factor.data), time_dim=time_sub)
        # For the given `nt` and grid shape, `usave` is roughly 4*5*300**3=~ .5GB of data

        op = Operator([Eq(u.forward, u + 1), Eq(usave, u.forward)],
                      opt=(opt, {'gpu-fit': usave if gpu_fit else None,
                                 'buf-async-degree': async_degree,
                                 'linearize': linearize}))

        op.apply(time_M=nt-1)

        assert all(np.all(usave.data[i] == 2*i + 1) for i in range(usave.save))

    def test_save_multi_output(self):
        nt = 10
        grid = Grid(shape=(150, 150, 150))
        time_dim = grid.time_dim

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, time_order=0,
                             save=int(nt//factor.data), time_dim=time_sub)
        vsave = TimeFunction(name='vsave', grid=grid, time_order=0,
                             save=int(nt//factor.data), time_dim=time_sub)

        eqns = [Eq(u.forward, u + 1),
                Eq(usave, u.forward),
                Eq(vsave, u.forward)]

        op = Operator(eqns, opt=('buffering', 'tasking', 'topofuse', 'orchestrate'))

        # Check generated code
        # The `usave` and `vsave` eqns are in separate tasks, but the tasks
        # are identical, so they get mapped to the same efuncs (init + copy)
        # There also are two extra functions to allocate and free arrays
        if configuration['language'] == 'openacc':
            assert len(op._func_table) == 8
        else:
            assert len(op._func_table) == 7

        op.apply(time_M=nt-1)

        assert all(np.all(usave.data[i] == 2*i + 1) for i in range(usave.save))
        assert all(np.all(vsave.data[i] == 2*i + 1) for i in range(vsave.save))

    @pytest.mark.parametrize('opt', [
        ('buffering', 'tasking', 'orchestrate'),
        ('buffering', 'tasking', 'orchestrate', {'linearize': True}),
    ])
    def test_save_w_shifting(self, opt):
        factor = 4
        nt = 19
        grid = Grid(shape=(11, 11))
        time = grid.time_dim

        time_subsampled = ConditionalDimension('t_sub', parent=time, factor=factor)

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=2, time_dim=time_subsampled)

        save_shift = Constant(name='save_shift', dtype=np.int32)

        eqns = [Eq(u.forward, u + 1.),
                Eq(usave.subs(time_subsampled, time_subsampled - save_shift), u)]

        op = Operator(eqns, opt=opt)

        # Starting at time_m=10, so time_subsampled - save_shift is in range
        op.apply(time_m=10, time_M=nt-2, save_shift=3)
        assert np.all(np.allclose(u.data[0], 8))
        assert np.all([np.allclose(usave.data[i], 2+i*factor) for i in range(2)])

    def test_save_w_nonaffine_time(self):
        factor = 4
        grid = Grid(shape=(11, 11))
        x, y = grid.dimensions
        t = grid.stepping_dim
        time = grid.time_dim

        time_subsampled = ConditionalDimension('t_sub', parent=time, factor=factor)

        f = Function(name='f', grid=grid, dtype=np.int32)
        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=2, time_dim=time_subsampled)

        save_shift = Constant(name='save_shift', dtype=np.int32)

        eqns = [Eq(u.forward, u[t, f[x, x], f[y, y]] + 1.),
                Eq(usave.subs(time_subsampled, time_subsampled - save_shift), u)]

        op = Operator(eqns, opt=('buffering', 'tasking', 'orchestrate'))

        # We just check the generated code here
        assert len([i for i in FindSymbols().visit(op) if isinstance(i, Lock)]) == 1
        if configuration['language'] == 'openacc':
            assert len(op._func_table) == 8
        else:
            assert len(op._func_table) == 7

    def test_save_w_subdims(self):
        nt = 10
        grid = Grid(shape=(10, 10))
        x, y = grid.dimensions
        time_dim = grid.time_dim
        xi = SubDimension.middle(name='xi', parent=x, thickness_left=3, thickness_right=3)
        yi = SubDimension.middle(name='yi', parent=y, thickness_left=3, thickness_right=3)

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, time_order=0,
                             save=int(nt//factor.data), time_dim=time_sub)

        eqns = [Eq(u.forward, u + 1),
                Eq(usave, u.forward)]
        eqns = [e.xreplace({x: xi, y: yi}) for e in eqns]

        op = Operator(eqns, opt=('buffering', 'tasking', 'orchestrate'))

        op.apply(time_M=nt-1)

        for i in range(usave.save):
            assert np.all(usave.data[i, 3:-3, 3:-3] == 2*i + 1)
            assert np.all(usave.data[i, :3, :] == 0)
            assert np.all(usave.data[i, -3:, :] == 0)
            assert np.all(usave.data[i, :, :3] == 0)
            assert np.all(usave.data[i, :, -3:] == 0)

    @pytest.mark.parametrize('opt,ntmps', [
        (('buffering', 'streaming', 'orchestrate'), 2),
        (('buffering', 'streaming', 'orchestrate', {'linearize': True}), 2),
    ])
    def test_streaming_w_shifting(self, opt, ntmps):
        nt = 50
        grid = Grid(shape=(5, 5))
        time = grid.time_dim

        factor = Constant(name='factor', value=5, dtype=np.int32)
        t_sub = ConditionalDimension('t_sub', parent=time, factor=factor)
        save_shift = Constant(name='save_shift', dtype=np.int32)

        u = TimeFunction(name='u', grid=grid, time_order=0)
        usave = TimeFunction(name='usave', grid=grid, time_order=0,
                             save=(int(nt//factor.data)), time_dim=t_sub)

        for i in range(usave.save):
            usave.data[i, :] = i

        eqns = Eq(u.forward, u + usave.subs(t_sub, t_sub - save_shift))

        op = Operator(eqns, opt=opt)

        # Check generated code
        if configuration['language'] == 'openacc':
            assert len(op._func_table) == 9
        else:
            assert len(op._func_table) == 8
        assert len([i for i in FindSymbols().visit(op) if i.is_Array]) == ntmps

        # From time_m=15 to time_M=35 with a factor=5 -- it means that, thanks
        # to t_sub, we enter the Eq exactly (35-15)/5 + 1 = 5 times. We set
        # save_shift=1 so instead of accessing the range usave[15/5:35/5+1],
        # we rather access the range usave[15/5-1:35:5], which means accessing
        # the usave values 2, 3, 4, 5, 6.
        op.apply(time_m=15, time_M=35, save_shift=1)
        assert np.allclose(u.data, 20)

        # Again, but with a different shift
        op.apply(time_m=15, time_M=35, save_shift=-2)
        assert np.allclose(u.data, 20 + 35)

    def test_streaming_complete(self):
        nt = 50
        grid = Grid(shape=(6, 6))
        x, y = grid.dimensions
        time = grid.time_dim
        xi = SubDimension.middle(name='xi', parent=x, thickness_left=2, thickness_right=2)
        yi = SubDimension.middle(name='yi', parent=y, thickness_left=2, thickness_right=2)

        factor = Constant(name='factor', value=5, dtype=np.int32)
        t_sub = ConditionalDimension('t_sub', parent=time, factor=factor)
        save_shift = Constant(name='save_shift', dtype=np.int32)

        u = TimeFunction(name='u', grid=grid, time_order=0)
        u1 = TimeFunction(name='u', grid=grid, time_order=0)
        u2 = TimeFunction(name='u', grid=grid, time_order=0)
        u3 = TimeFunction(name='u', grid=grid, time_order=0)
        va = TimeFunction(name='va', grid=grid, time_order=0,
                          save=(int(nt//factor.data)), time_dim=t_sub)
        vb = TimeFunction(name='vb', grid=grid, time_order=0,
                          save=(int(nt//factor.data)), time_dim=t_sub)

        for i in range(va.save):
            va.data[i, :] = i
            vb.data[i, :] = i*2 - 1

        vas = va.subs(t_sub, t_sub - save_shift)
        vasb = va.subs(t_sub, t_sub - 1 - save_shift)
        vasf = va.subs(t_sub, t_sub + 1 - save_shift)

        eqns = [Eq(u.forward, u + (vasb + vas + vasf)*2. + vb)]

        eqns = [e.xreplace({x: xi, y: yi}) for e in eqns]

        op0 = Operator(eqns, opt='noop')
        op1 = Operator(eqns, opt=('buffering', 'streaming', 'orchestrate'))
        op2 = Operator(eqns, opt=('buffering', 'streaming', 'fuse', 'orchestrate'))
        op3 = Operator(eqns, opt=('buffering', 'streaming', 'fuse', 'orchestrate',
                                  {'fuse-tasks': True}))

        # Check generated code
        diff = int(configuration['language'] == 'openmp')
        assert len(op1._func_table) == 14 - diff
        assert len([i for i in FindSymbols().visit(op1) if i.is_Array]) == 8 - diff
        assert len(op2._func_table) == 14 - diff
        assert len([i for i in FindSymbols().visit(op2) if i.is_Array]) == 8 - diff
        assert len(op3._func_table) == 10 - diff
        assert len([i for i in FindSymbols().visit(op3) if i.is_Array]) == 7 - diff

        op0.apply(time_m=15, time_M=35, save_shift=0)
        op1.apply(time_m=15, time_M=35, save_shift=0, u=u1)
        op2.apply(time_m=15, time_M=35, save_shift=0, u=u2)
        op3.apply(time_m=15, time_M=35, save_shift=0, u=u3)

        assert np.all(u.data == u1.data)
        assert np.all(u.data == u2.data)
        assert np.all(u.data == u3.data)

    def test_streaming_split_noleak(self):
        """
        Make sure the helper pthreads leak no memory in the target langauge runtime.
        """
        nt = 1000
        grid = Grid(shape=(20, 20, 20))

        u = TimeFunction(name='u', grid=grid)
        u1 = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)

        for i in range(nt):
            usave.data[i, :] = i

        eqn = Eq(u.forward, u + usave + usave.backward)

        op0 = Operator(eqn, opt='noop')
        op1 = Operator(eqn, opt=('buffering', 'streaming', 'orchestrate'))

        op0.apply(time_M=nt-2)

        # We'll call `op1` in total `X` times, which will create and destroy
        # `X` pthreads. With `X` at least O(10), this test would be enough
        # to uncover outrageous memory leaks due to leaking resources in
        # the runtime (in the past, we've seen leaks due to pthreads-local
        # pinned memory used for the data transfers)
        m = 1
        l = 20
        npairs = nt // l + (1 if nt % l > 0 else 0)
        X = [(m + i*l, min((i+1)*l, nt-2)) for i in range(npairs)]
        for m, M in X:
            op1.apply(time_m=m, time_M=M, u=u1)

        assert np.all(u.data[0] == u1.data[0])
        assert np.all(u.data[1] == u1.data[1])

    @pytest.mark.skip(reason="Unsupported MPI + .dx when streaming backwards")
    @pytest.mark.parallel(mode=4)
    @switchconfig(safe_math=True)  # Or NVC will crash
    def test_streaming_w_mpi(self, mode):
        nt = 5
        grid = Grid(shape=(16, 16))

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt, space_order=4)
        vsave = TimeFunction(name='vsave', grid=grid, save=nt, space_order=4)
        vsave1 = TimeFunction(name='vsave', grid=grid, save=nt, space_order=4)

        eqns = [Eq(u.backward, u + 1.),
                Eq(vsave, usave.dx2)]

        key = lambda f: f is not usave

        op0 = Operator(eqns, opt='noop')
        op1 = Operator(eqns, opt=('buffering', 'streaming', 'orchestrate',
                                  {'dist-drop-unwritten': key,
                                   'gpu-fit': [vsave]}))

        for i in range(nt):
            usave.data[i] = i

        op0.apply()
        op1.apply(vsave=vsave1)

        assert np.all(vsave.data, vsave1.data, rtol=1.e-5)

    @pytest.mark.parametrize('opt,opt_options,gpu_fit', [
        (('buffering', 'streaming', 'orchestrate'), {}, False),
        (('buffering', 'streaming', 'orchestrate'), {'linearize': True}, False)
    ])
    def test_xcor_from_saved(self, opt, opt_options, gpu_fit):
        nt = 10
        grid = Grid(shape=(300, 300, 300))
        time_dim = grid.time_dim

        period = 2
        factor = Constant(name='factor', value=period, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        g = Function(name='g', grid=grid)
        v = TimeFunction(name='v', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, time_order=0,
                             save=int(nt//factor.data), time_dim=time_sub)
        # For the given `nt` and grid shape, `usave` is roughly 4*5*300**3=~ .5GB of data

        for i in range(int(nt//period)):
            usave.data[i, :] = i
        v.data[:] = i*2 + 1

        opt_options = {'gpu-fit': usave if gpu_fit else None, **opt_options}

        # Assuming nt//period=5, we are computing, over 5 iterations:
        # g = 4*4  [time=8] + 3*3 [time=6] + 2*2 [time=4] + 1*1 [time=2]
        op = Operator([Eq(v.backward, v - 1), Inc(g, usave*(v/2))],
                      opt=(opt, opt_options))

        op.apply(time_M=nt-1)

        assert np.all(g.data == 30)

    @skipif('device-openmp')
    def test_gpu_create_forward(self):
        nt = 10
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)

        for i in range(nt):
            usave.data[i, :] = i

        eqn = Eq(u.forward, u + usave)

        op = Operator(eqn,
                      opt=('buffering', 'streaming', 'orchestrate', {'gpu-create': u}))

        language = configuration['language']
        if language == 'openacc':
            assert 'create(u' in str(op)
        elif language == 'openmp':
            assert 'map(alloc: u' in str(op)
        assert 'init0' in str(op)

        op.apply(time_M=nt-2)

        assert np.all(u.data[0] == 28)
        assert np.all(u.data[1] == 36)

    @skipif('device-openmp')
    def test_gpu_create_backward(self):
        nt = 10
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)

        for i in range(nt):
            usave.data[i, :] = i

        eqn = Eq(u.backward, u + usave)

        op = Operator(eqn,
                      opt=('buffering', 'streaming', 'orchestrate', {'gpu-create': u}))

        language = configuration['language']
        if language == 'openacc':
            assert 'create(u' in str(op)
        elif language == 'openmp':
            assert 'map(alloc: u' in str(op)
        assert 'init0' in op._func_table

        op.apply(time_M=nt - 2)

        assert np.all(u.data[0] == 36)
        assert np.all(u.data[1] == 35)

    def test_place_transfers(self):
        grid = Grid(shape=(4, 4))

        u = TimeFunction(name='u', grid=grid)

        eqn = Eq(u.forward, u + 1)

        op = Operator(eqn,
                      opt=('buffering', 'streaming', 'orchestrate',
                           {'place-transfers': False}))

        language = configuration['language']
        if language == 'openacc':
            assert 'copyin(u' not in str(op)
            assert 'copyout(u' not in str(op)
            assert 'delete(u' not in str(op)
        elif language == 'openmp':
            assert 'map(to: u' not in str(op)
            assert 'update from(u' not in str(op)
            assert 'map(release: u' not in str(op)

    def test_fuse_compatible_guards(self):
        nt = 10
        grid = Grid(shape=(8, 8))
        time_dim = grid.time_dim

        factor = Constant(name='factor', value=2, dtype=np.int32)
        time_sub = ConditionalDimension(name="time_sub", parent=time_dim, factor=factor)

        f = TimeFunction(name='f', grid=grid)
        fsave = TimeFunction(name='fsave', grid=grid,
                             save=int(nt//factor.data), time_dim=time_sub)
        gsave = TimeFunction(name='gsave', grid=grid,
                             save=int(nt//factor.data), time_dim=time_sub)

        eqns = [Eq(f.forward, f + 1.),
                Eq(fsave, f.forward),
                Eq(gsave, f.forward)]

        op = Operator(eqns, opt=('buffering', 'tasking', 'orchestrate',
                                 {'gpu-fit': [gsave]}))

        op.apply(time_M=nt-1)

        assert all(np.all(fsave.data[i] == 2*i + 1) for i in range(fsave.save))
        assert all(np.all(gsave.data[i] == 2*i + 1) for i in range(gsave.save))

        # Check generated code
        assert_structure(op, ['t,x,y', 't', 't,x,y', 't,x,y'],
                         't,x,y,x,y,x,y')
        nodes = FindNodes(Conditional).visit(op)
        assert len(nodes) == 2
        assert len(nodes[1].then_body) == 3
        assert len(retrieve_iteration_tree(nodes[1])) == 2


class TestAPI:

    def get_param(self, op, param):
        for i in op.parameters:
            if isinstance(i, param):
                return i
        return None

    def check_deviceid(self):
        grid = Grid(shape=(6, 6))

        u = TimeFunction(name='u', grid=grid, space_order=2, save=10)

        op = Operator(Eq(u.forward, u.dx + 1))

        deviceid = self.get_param(op, DeviceID)
        assert deviceid is not None
        assert op.arguments()[deviceid.name] == -1
        assert op.arguments(deviceid=0)[deviceid.name] == 0

    def test_deviceid(self):
        self.check_deviceid()

    @skipif('device-openmp')
    @pytest.mark.parallel(mode=1)
    def test_deviceid_w_mpi(self, mode):
        self.check_deviceid()

    def test_devicerm(self):
        grid = Grid(shape=(6, 6))

        u = TimeFunction(name='u', grid=grid, space_order=2)
        f = Function(name='f', grid=grid)

        op = Operator(Eq(u.forward, u.dx + f))

        devicerm = self.get_param(op, DeviceRM)
        assert devicerm is not None
        assert op.arguments(time_M=2)[devicerm.name] == 1  # Always evict by default
        assert op.arguments(time_M=2, devicerm=0)[devicerm.name] == 0
        assert op.arguments(time_M=2, devicerm=1)[devicerm.name] == 1
        assert op.arguments(time_M=2, devicerm=224)[devicerm.name] == 1
        assert op.arguments(time_M=2, devicerm=True)[devicerm.name] == 1
        assert op.arguments(time_M=2, devicerm=False)[devicerm.name] == 0

    def test_npthreads(self):
        nt = 10
        async_degree = 5
        grid = Grid(shape=(300, 300, 300))

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name='usave', grid=grid, save=nt)

        eqns = [Eq(u.forward, u + 1),
                Eq(usave, u.forward)]

        op = Operator(eqns, opt=('buffering', 'tasking', 'orchestrate',
                                 {'buf-async-degree': async_degree}))

        npthreads0 = self.get_param(op, NPThreads)
        assert op.arguments(time_M=2)[npthreads0.name] == 1
        assert op.arguments(time_M=2, npthreads0=4)[npthreads0.name] == 4
        # Cannot provide a value larger than the thread pool size
        with pytest.raises(InvalidArgument):
            assert op.arguments(time_M=2, npthreads0=5)

    def test_gpu_fit_w_tensor_functions(self):
        grid = Grid(shape=(10, 10))

        u = TensorTimeFunction(name='u', grid=grid)
        usave = TensorTimeFunction(name="usave", grid=grid, save=10)
        usave2 = TensorTimeFunction(name="usave2", grid=grid, save=10)

        eqns = [Eq(u.forward, u + 1),
                Eq(usave, u.forward)]

        op = Operator(eqns, opt=('noop', {'gpu-fit': usave}))
        assert set(op._options['gpu-fit']) - set(usave.values()) == set()

        eqns = [Eq(u.forward, u + 1),
                Eq(usave, u.forward),
                Eq(usave2, u.forward)]

        op = Operator(eqns, opt=('noop', {'gpu-fit': [usave, usave2]}))
        vals = set().union(usave.values(), usave2.values())
        assert set(op._options['gpu-fit']) - vals == set()


class TestMisc:

    def test_pickling(self):
        grid = Grid(shape=(10, 10))

        u = TimeFunction(name='u', grid=grid)
        usave = TimeFunction(name="usave", grid=grid, save=10)

        eqns = [Eq(u.forward, u + 1),
                Eq(usave, u.forward)]

        op = Operator(eqns)

        pkl_op = pickle.dumps(op)
        new_op = pickle.loads(pkl_op)

        assert str(op) == str(new_op)

    def test_is_transient_w_builtins(self):
        grid = Grid(shape=(4, 4))

        f = Function(name='f', grid=grid, is_transient=True)

        with pytest.raises(ValueError):
            assign(f, 4)


class TestEdgeCases:

    def test_empty_arrays(self):
        """
        MFE for issue #1641.
        """
        grid = Grid(shape=(4, 4), extent=(3.0, 3.0))

        f = TimeFunction(name='f', grid=grid, space_order=1)
        f.data[:] = 1.
        sf1 = SparseTimeFunction(name='sf1', grid=grid, npoint=0, nt=10)
        sf2 = SparseTimeFunction(name='sf2', grid=grid, npoint=0, nt=10,
                                 coordinates=sf1.coordinates,
                                 dimensions=sf1.dimensions)
        assert sf1.size == 0
        assert sf2.size == 0

        eqns = sf1.inject(field=f, expr=sf1 + sf2 + 1.)

        op = Operator(eqns)
        op.apply()
        assert np.all(f.data == 1.)

        # Again, but with a MatrixSparseTimeFunction
        mat = scipy.sparse.coo_matrix((0, 0), dtype=np.float32)
        sf = MatrixSparseTimeFunction(name="s", grid=grid, r=2, matrix=mat, nt=10)
        assert sf.size == 0

        eqns = sf.interpolate(f)

        op = Operator(eqns)

        sf.manual_scatter()
        op(time_m=0, time_M=9)
        sf.manual_gather()
        assert np.all(f.data == 1.)

    @skipif('device-openmp')
    @pytest.mark.parallel(mode=4)
    def test_degenerate_subdomainset(self, mode):
        """
        MFE for issue #1766
        """
        # There are four MPI ranks arranged in a 2x2 grid (default decomposition);
        # here we defines thicknesses for two subdomains such that (i) no subdomains
        # cross MPI-rank boundaries, (ii) the first of the two subdomains is defined
        # entirely in the top-right MPI rank, (iii) the second of the two subdomains is
        # defined entirely in the bottom-right MPI rank. This means that the left MPI
        # ranks are expected to have an empty iteration space (thus reproducing the
        # settings of issue #1766)
        shape = (10, 10)
        bounds_xm = np.array([2, 7], dtype=np.int32)
        bounds_xM = np.array([7, 2], dtype=np.int32)
        bounds_ym = np.array([5, 5], dtype=np.int32)
        bounds_yM = np.array([0, 0], dtype=np.int32)

        class MySubdomain(SubDomainSet):
            name = 'msd'

        bounds = (bounds_xm, bounds_xM, bounds_ym, bounds_yM)
        msd = MySubdomain(N=2, bounds=bounds)
        grid = Grid(shape=shape, subdomains=(msd,))

        # Expected two horizontal strips with 5 points each
        assert grid.subdomains['msd'].shape == ((1, 5), (1, 5))

        f = TimeFunction(name='f', grid=grid, time_order=0)
        f.data[:] = 0.

        eq = Eq(f, f + 1., subdomain=grid.subdomains['msd'])

        op = Operator(eq)
        op(time_m=0, time_M=8, dt=1)

        fex = Function(name='fex', grid=grid)
        fex.data[:] = np.array([[0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
                                [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
                                [0., 0., 0., 0., 0., 9., 9., 9., 9., 9.],
                                [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
                                [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
                                [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
                                [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
                                [0., 0., 0., 0., 0., 9., 9., 9., 9., 9.],
                                [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.],
                                [0., 0., 0., 0., 0., 0., 0., 0., 0., 0.]])

        assert np.all(f.data == fex.data)