pystencils/datahandling/vtk.py → src/pystencils/datahandling/vtk.py

-from pyevtk.vtk import VtkFile, VtkImageData
 from pyevtk.hl import _addDataToFile, _appendDataToFile
+from pyevtk.vtk import VtkFile, VtkImageData
 
 
 def image_to_vtk(path, cell_data, origin=(0.0, 0.0, 0.0), spacing=(1.0, 1.0, 1.0)):

pystencils/display_utils.py → src/pystencils/display_utils.py

+from typing import Any, Dict, Optional, Union
+
 import sympy as sp
-from typing import Any, Dict, Optional
+
 from pystencils.astnodes import KernelFunction
+from pystencils.enums import Backend
+from pystencils.kernel_wrapper import KernelWrapper
 
 
 def to_dot(expr: sp.Expr, graph_style: Optional[Dict[str, Any]] = None, short=True):
     """Show a sympy or pystencils AST as dot graph"""
     from pystencils.astnodes import Node
-    import graphviz
+    try:
+        import graphviz
+    except ImportError:
+        print("graphviz is not installed. Visualizing the AST is not available")
+        return
+
     graph_style = {} if graph_style is None else graph_style
 
     if isinstance(expr, Node):
@@ -27,29 +36,69 @@ def highlight_cpp(code: str):
     from pygments.lexers import CppLexer
 
     css = HtmlFormatter().get_style_defs('.highlight')
-    css_tag = "<style>{css}</style>".format(css=css)
+    css_tag = f"<style>{css}</style>"
     display(HTML(css_tag))
     return HTML(highlight(code, CppLexer(), HtmlFormatter()))
 
 
-def show_code(ast: KernelFunction):
+def get_code_obj(ast: Union[KernelFunction, KernelWrapper], custom_backend=None):
     """Returns an object to display generated code (C/C++ or CUDA)
 
-    Can either  be displayed as HTML in Jupyter notebooks or printed as normal string.
+    Can either be displayed as HTML in Jupyter notebooks or printed as normal string.
     """
     from pystencils.backends.cbackend import generate_c
-    dialect = 'cuda' if ast.backend == 'gpucuda' else 'c'
+
+    if isinstance(ast, KernelWrapper):
+        ast = ast.ast
+
+    if ast.backend not in {Backend.C, Backend.CUDA}:
+        raise NotImplementedError(f'get_code_obj is not implemented for backend {ast.backend}')
+    dialect = ast.backend
 
     class CodeDisplay:
         def __init__(self, ast_input):
             self.ast = ast_input
 
         def _repr_html_(self):
-            return highlight_cpp(generate_c(self.ast, dialect=dialect)).__html__()
+            return highlight_cpp(generate_c(self.ast, dialect=dialect, custom_backend=custom_backend)).__html__()
 
         def __str__(self):
-            return generate_c(self.ast, dialect=dialect)
+            return generate_c(self.ast, dialect=dialect, custom_backend=custom_backend)
 
         def __repr__(self):
-            return generate_c(self.ast, dialect=dialect)
+            return generate_c(self.ast, dialect=dialect, custom_backend=custom_backend)
     return CodeDisplay(ast)
+
+
+def get_code_str(ast, custom_backend=None):
+    return str(get_code_obj(ast, custom_backend))
+
+
+def _isnotebook():
+    try:
+        shell = get_ipython().__class__.__name__
+        if shell == 'ZMQInteractiveShell':
+            return True   # Jupyter notebook or qtconsole
+        elif shell == 'TerminalInteractiveShell':
+            return False  # Terminal running IPython
+        else:
+            return False  # Other type (?)
+    except NameError:
+        return False
+
+
+def show_code(ast: Union[KernelFunction, KernelWrapper], custom_backend=None):
+    code = get_code_obj(ast, custom_backend)
+
+    if _isnotebook():
+        from IPython.display import display
+        display(code)
+    else:
+        try:
+            import rich.syntax
+            import rich.console
+            syntax = rich.syntax.Syntax(str(code), "c++", theme="monokai", line_numbers=True)
+            console = rich.console.Console()
+            console.print(syntax)
+        except ImportError:
+            print(code)

src/pystencils/enums.py

+from enum import Enum, auto
+
+
+class Target(Enum):
+    """
+    The Target enumeration represents all possible targets that can be used for the code generation.
+    """
+    CPU = auto()
+    """
+    Target CPU architecture.
+    """
+    GPU = auto()
+    """
+    Target GPU architecture.
+    """
+
+
+class Backend(Enum):
+    """
+    The Backend enumeration represents all possible backends that can be used for the code generation.
+    Backends and targets must be combined with care. For example CPU as a target and CUDA as a backend makes no sense.
+    """
+    C = auto()
+    """
+    Use the C Backend of pystencils.
+    """
+    CUDA = auto()
+    """
+    Use the CUDA backend to generate code for NVIDIA GPUs.
+    """

pystencils/fast_approximation.py → src/pystencils/fast_approximation.py

-import sympy as sp
 from typing import List, Union
 
+import sympy as sp
+
 from pystencils.astnodes import Node
 from pystencils.simp import AssignmentCollection
+from pystencils.assignment import Assignment
 
 
 # noinspection PyPep8Naming
 class fast_division(sp.Function):
+    """
+    Produces special float instructions for CUDA kernels
+    """
     nargs = (2,)
 
 
 # noinspection PyPep8Naming
 class fast_sqrt(sp.Function):
+    """
+    Produces special float instructions for CUDA kernels
+    """
     nargs = (1, )
 
 
 # noinspection PyPep8Naming
 class fast_inv_sqrt(sp.Function):
+    """
+    Produces special float instructions for CUDA kernels
+    """
     nargs = (1, )
 
 
@@ -31,7 +42,7 @@ def _run(term, visitor):
         return visitor(term)
 
 
-def insert_fast_sqrts(term: Union[sp.Expr, List[sp.Expr], AssignmentCollection]):
+def insert_fast_sqrts(term: Union[sp.Expr, List[sp.Expr], AssignmentCollection, Assignment]):
     def visit(expr):
         if isinstance(expr, Node):
             return expr
@@ -47,7 +58,7 @@ def insert_fast_sqrts(term: Union[sp.Expr, List[sp.Expr], AssignmentCollection])
     return _run(term, visit)
 
 
-def insert_fast_divisions(term: Union[sp.Expr, List[sp.Expr], AssignmentCollection]):
+def insert_fast_divisions(term: Union[sp.Expr, List[sp.Expr], AssignmentCollection, Assignment]):
 
     def visit(expr):
         if isinstance(expr, Node):

pystencils/fd/__init__.py → src/pystencils/fd/__init__.py

-from .derivative import Diff, DiffOperator, \
-    diff_terms, collect_diffs, zero_diffs, evaluate_diffs, normalize_diff_order, \
-    expand_diff_full, expand_diff_linear, expand_diff_products, combine_diff_products, \
-    functional_derivative, diff
-from .finitedifferences import advection, diffusion, transient, Discretization2ndOrder
+from .derivative import (
+    Diff, DiffOperator, collect_diffs, combine_diff_products, diff, diff_terms, evaluate_diffs,
+    expand_diff_full, expand_diff_linear, expand_diff_products, functional_derivative,
+    normalize_diff_order, zero_diffs)
+from .finitedifferences import Discretization2ndOrder, advection, diffusion, transient
+from .finitevolumes import FVM1stOrder, VOF
 from .spatial import discretize_spatial, discretize_spatial_staggered
 
 __all__ = ['Diff', 'diff', 'DiffOperator', 'diff_terms', 'collect_diffs',
            'zero_diffs', 'evaluate_diffs', 'normalize_diff_order', 'expand_diff_full', 'expand_diff_linear',
            'expand_diff_products', 'combine_diff_products', 'functional_derivative',
            'advection', 'diffusion', 'transient', 'Discretization2ndOrder', 'discretize_spatial',
-           'discretize_spatial_staggered']
+           'discretize_spatial_staggered', 'FVM1stOrder', 'VOF']

pystencils/fd/derivation.py → src/pystencils/fd/derivation.py

-import sympy as sp
+import itertools
 from collections import defaultdict
+
+import numpy as np
+import sympy as sp
+
 from pystencils.field import Field
-from pystencils.sympyextensions import prod, multidimensional_sum
-from pystencils.utils import fully_contains, LinearEquationSystem
+from pystencils.stencil import direction_string_to_offset
+from pystencils.sympyextensions import multidimensional_sum, prod
+from pystencils.utils import LinearEquationSystem, fully_contains
 
 
 class FiniteDifferenceStencilDerivation:
@@ -102,7 +107,7 @@ class FiniteDifferenceStencilDerivation:
     @staticmethod
     def symbolic_weight(*args):
         str_args = [str(e) for e in args]
-        return sp.Symbol("w_({})".format(",".join(str_args)))
+        return sp.Symbol(f"w_({','.join(str_args)})")
 
     def error_term_dict(self, order):
         error_terms = defaultdict(lambda: 0)
@@ -121,7 +126,6 @@ class FiniteDifferenceStencilDerivation:
 
     def isotropy_equations(self, order):
         def cycle_int_sequence(sequence, modulus):
-            import numpy as np
             result = []
             arr = np.array(sequence, dtype=int)
             while True:
@@ -159,22 +163,175 @@ class FiniteDifferenceStencilDerivation:
             self.is_isotropic = is_isotropic
 
         def visualize(self):
-            from pystencils.stencils import visualize_stencil
-            visualize_stencil(self.stencil, data=self.weights)
+            from pystencils.stencil import plot
+            plot(self.stencil, data=self.weights)
 
         def apply(self, field_access: Field.Access):
             f = field_access
             return sum(f.get_shifted(*offset) * weight for offset, weight in zip(self.stencil, self.weights))
 
-        def as_matrix(self):
+        def __array__(self):
+            return np.array(self.as_array().tolist())
+
+        def as_array(self):
             dim = len(self.stencil[0])
-            assert dim == 2
+            assert (dim == 2 or dim == 3), "Only 2D or 3D matrix representations are available"
             max_offset = max(max(abs(e) for e in direction) for direction in self.stencil)
-            result = sp.Matrix(2 * max_offset + 1, 2 * max_offset + 1, lambda i, j: 0)
-            for direction, weight in zip(self.stencil, self.weights):
-                result[max_offset - direction[1], max_offset + direction[0]] = weight
+            shape_list = []
+            for i in range(dim):
+                shape_list.append(2 * max_offset + 1)
+
+            number_of_elements = np.prod(shape_list)
+            shape = tuple(shape_list)
+            result = sp.MutableDenseNDimArray([0] * number_of_elements, shape)
+
+            if dim == 2:
+                for direction, weight in zip(self.stencil, self.weights):
+                    result[max_offset - direction[1], max_offset + direction[0]] = weight
+            if dim == 3:
+                for direction, weight in zip(self.stencil, self.weights):
+                    result[max_offset - direction[1], max_offset + direction[0], max_offset + direction[2]] = weight
+
             return result
 
+        def rotate_weights_and_apply(self, field_access: Field.Access, axes):
+            """derive gradient weights of other direction with already calculated weights of one direction
+               via rotation and apply them to a field."""
+            dim = len(self.stencil[0])
+            assert (dim == 2 or dim == 3), "This function is only for 2D or 3D stencils available"
+            rotated_weights = np.rot90(np.array(self.__array__()), 1, axes)
+
+            result = []
+            max_offset = max(max(abs(e) for e in direction) for direction in self.stencil)
+            if dim == 2:
+                for direction in self.stencil:
+                    result.append(rotated_weights[max_offset - direction[1],
+                                                  max_offset + direction[0]])
+            if dim == 3:
+                for direction in self.stencil:
+                    result.append(rotated_weights[max_offset - direction[1],
+                                                  max_offset + direction[0],
+                                                  max_offset + direction[2]])
+
+            f = field_access
+            return sum(f.get_shifted(*offset) * weight for offset, weight in zip(self.stencil, result))
+
         def __repr__(self):
             return "Finite difference stencil of accuracy {}, isotropic error: {}".format(self.accuracy,
                                                                                           self.is_isotropic)
+
+
+class FiniteDifferenceStaggeredStencilDerivation:
+    """Derives a finite difference stencil for application at a staggered position
+
+    Args:
+        neighbor: the neighbor direction string or vector at whose staggered position to calculate the derivative
+        dim: how many dimensions (2 or 3)
+        derivative: a tuple of directions over which to perform derivatives
+        free_weights_prefix: a string to prefix to free weight symbols. If None, do not return free weights
+    """
+
+    def __init__(self, neighbor, dim, derivative=tuple(), free_weights_prefix=None):
+        if type(neighbor) is str:
+            neighbor = direction_string_to_offset(neighbor)
+        if dim == 2:
+            assert neighbor[dim:] == 0
+        assert derivative is tuple() or max(derivative) < dim
+        neighbor = sp.Matrix(neighbor[:dim])
+        pos = neighbor / 2
+
+        def unitvec(i):
+            """return the `i`-th unit vector in three dimensions"""
+            a = np.zeros(dim, dtype=int)
+            a[i] = 1
+            return a
+
+        def flipped(a, i):
+            """return `a` with its `i`-th element's sign flipped"""
+            a = a.copy()
+            a[i] *= -1
+            return a
+
+        # determine the points to use, coordinates are relative to position
+        points = []
+        if np.linalg.norm(neighbor, 1) == 1:
+            main_points = [neighbor / 2, neighbor / -2]
+        elif np.linalg.norm(neighbor, 1) == 2:
+            nonzero_indices = [i for i, v in enumerate(neighbor) if v != 0 and i < dim]
+            main_points = [neighbor / 2, neighbor / -2, flipped(neighbor / 2, nonzero_indices[0]),
+                           flipped(neighbor / -2, nonzero_indices[0])]
+        else:
+            main_points = [sp.Matrix(np.multiply(neighbor, sp.Matrix(c) / 2))
+                           for c in itertools.product([-1, 1], repeat=3)]
+        points += main_points
+        zero_indices = [i for i, v in enumerate(neighbor) if v == 0 and i < dim]
+        for i in zero_indices:
+            points += [point + sp.Matrix(unitvec(i)) for point in main_points]
+            points += [point - sp.Matrix(unitvec(i)) for point in main_points]
+        points_tuple = tuple([tuple(p) for p in points])
+        self._stencil = points_tuple
+
+        # determine the stencil weights
+        if len(derivative) == 0:
+            weights = None
+        else:
+            derivation = FiniteDifferenceStencilDerivation(derivative, points_tuple).get_stencil()
+            if not derivation.accuracy:
+                raise Exception('the requested derivative cannot be performed with the available neighbors')
+            weights = derivation.weights
+
+            # if the weights are underdefined, we can choose the free symbols to find the sparsest stencil
+            free_weights = set(itertools.chain(*[w.free_symbols for w in weights]))
+            if free_weights_prefix is not None:
+                weights = [w.subs({fw: sp.Symbol(f"{free_weights_prefix}_{i}") for i, fw in enumerate(free_weights)})
+                           for w in weights]
+            elif len(free_weights) > 0:
+                zero_counts = defaultdict(list)
+                for values in itertools.product([-1, -sp.Rational(1, 2), 0, 1, sp.Rational(1, 2)],
+                                                repeat=len(free_weights)):
+                    subs = {free_weight: value for free_weight, value in zip(free_weights, values)}
+                    weights = [w.subs(subs) for w in derivation.weights]
+                    if not all(a == 0 for a in weights):
+                        zero_count = sum([1 for w in weights if w == 0])
+                        zero_counts[zero_count].append(weights)
+                best = zero_counts[max(zero_counts.keys())]
+                if len(best) > 1:  # if there are multiple, pick the one that contains a nonzero center weight
+                    center = [tuple(p + pos) for p in points].index((0, 0, 0)[:dim])
+                    best = [b for b in best if b[center] != 0]
+                if len(best) > 1:  # if there are still multiple, they are equivalent, so we average
+                    weights = [sum([b[i] for b in best]) / len(best) for i in range(len(weights))]
+                else:
+                    weights = best[0]
+                assert weights
+
+        points_tuple = tuple([tuple(p + pos) for p in points])
+        self._points = points_tuple
+        self._weights = weights
+
+    @property
+    def points(self):
+        """return the points of the stencil"""
+        return self._points
+
+    @property
+    def stencil(self):
+        """return the points of the stencil relative to the staggered position specified by neighbor"""
+        return self._stencil
+
+    @property
+    def weights(self):
+        """return the weights of the stencil"""
+        assert self._weights is not None
+        return self._weights
+
+    def visualize(self):
+        if self._weights is None:
+            ws = None
+        else:
+            ws = np.array([w for w in self.weights if w != 0], dtype=float)
+        pts = np.array([p for i, p in enumerate(self.points) if self.weights[i] != 0], dtype=int)
+        from pystencils.stencil import plot
+        plot(pts, data=ws)
+
+    def apply(self, access: Field.Access):
+        return sum([access.get_shifted(*point) * weight for point, weight in zip(self.points, self.weights)])

pystencils/fd/derivative.py → src/pystencils/fd/derivative.py

+from collections import defaultdict, namedtuple
+
 import sympy as sp
-from collections import namedtuple, defaultdict
 
-from pystencils import Field
+from pystencils.field import Field
 from pystencils.sympyextensions import normalize_product, prod
 
 
@@ -108,7 +109,17 @@ class Diff(sp.Expr):
         return result
 
     def __str__(self):
-        return "D(%s)" % self.arg
+        return f"D({self.arg})"
+
+    def interpolated_access(self, offset, **kwargs):
+        """Represents an interpolated access on a spatially differentiated field
+
+        Args:
+            offset (Tuple[sympy.Expr]): Absolute position to determine the value of the spatial derivative
+        """
+        from pystencils.interpolation_astnodes import DiffInterpolatorAccess
+        assert isinstance(self.arg.field, Field), "Must be field to enable interpolated accesses"
+        return DiffInterpolatorAccess(self.arg.field.interpolated_access(offset, **kwargs).symbol, self.target, *offset)
 
 
 class DiffOperator(sp.Expr):
@@ -214,6 +225,13 @@ def diff_terms(expr):
 
     This function yields different results than 'expr.atoms(Diff)' when nested derivatives are in the expression,
     since this function only returns the outer derivatives
+
+    Example:
+        >>> x, y = sp.symbols("x, y")
+        >>> diff_terms( diff(x, 0, 0) )
+        {Diff(Diff(x, 0, -1), 0, -1)}
+        >>> diff_terms( diff(x, 0, 0) + y )
+        {Diff(Diff(x, 0, -1), 0, -1)}
     """
     result = set()
 
@@ -300,7 +318,8 @@ def expand_diff_full(expr, functions=None, constants=None):
             functions.difference_update(constants)
 
     def visit(e):
-        e = e.expand()
+        if not isinstance(e, sp.Tuple):
+            e = e.expand()
 
         if e.func == Diff:
             result = 0
@@ -325,6 +344,9 @@ def expand_diff_full(expr, functions=None, constants=None):
             return result
         elif isinstance(e, sp.Piecewise):
             return sp.Piecewise(*((expand_diff_full(a, functions, constants), b) for a, b in e.args))
+        elif isinstance(expr, sp.Tuple):
+            new_args = [visit(arg) for arg in e.args]
+            return sp.Tuple(*new_args)
         else:
             new_args = [visit(arg) for arg in e.args]
             return e.func(*new_args) if new_args else e
@@ -364,6 +386,9 @@ def expand_diff_linear(expr, functions=None, constants=None):
                 return diff.split_linear(functions)
     elif isinstance(expr, sp.Piecewise):
         return sp.Piecewise(*((expand_diff_linear(a, functions, constants), b) for a, b in expr.args))
+    elif isinstance(expr, sp.Tuple):
+        new_args = [expand_diff_linear(e, functions) for e in expr.args]
+        return sp.Tuple(*new_args)
     else:
         new_args = [expand_diff_linear(e, functions) for e in expr.args]
         result = sp.expand(expr.func(*new_args) if new_args else expr)

pystencils/fd/finitedifferences.py → src/pystencils/fd/finitedifferences.py

+from typing import Optional, Union
+
 import numpy as np
 import sympy as sp
-from typing import Union, Optional
 
-from pystencils import Field, AssignmentCollection
 from pystencils.fd import Diff
 from pystencils.fd.derivative import diff_args
 from pystencils.fd.spatial import fd_stencils_standard
+from pystencils.field import Field
+from pystencils.simp.assignment_collection import AssignmentCollection
 from pystencils.sympyextensions import fast_subs
 
-
 FieldOrFieldAccess = Union[Field, Field.Access]
 
 
@@ -20,10 +21,13 @@ def diffusion(scalar, diffusion_coeff, idx=None):
 
     Examples:
         >>> f = Field.create_generic('f', spatial_dimensions=2)
-        >>> diffusion_term = diffusion(scalar=f, diffusion_coeff=sp.Symbol("d"))
+        >>> d = sp.Symbol("d")
+        >>> dx = sp.Symbol("dx")
+        >>> diffusion_term = diffusion(scalar=f, diffusion_coeff=d)
         >>> discretization = Discretization2ndOrder()
-        >>> discretization(diffusion_term)
-        (f_W*d + f_S*d - 4*f_C*d + f_N*d + f_E*d)/dx**2
+        >>> expected_output = ((f[-1, 0] + f[0, -1] - 4 * f[0, 0] + f[0, 1] + f[1, 0]) * d) / dx**2
+        >>> sp.simplify(discretization(diffusion_term) - expected_output)
+        0
     """
     if isinstance(scalar, Field):
         first_arg = scalar.center
@@ -75,13 +79,6 @@ class Discretization2ndOrder:
         self.dt = dt
         self.spatial_stencil = discretization_stencil_func
 
-    @staticmethod
-    def _diff_order(e):
-        if not isinstance(e, Diff):
-            return 0
-        else:
-            return 1 + Discretization2ndOrder._diff_order(e.args[0])
-
     def _discretize_diffusion(self, e):
         result = 0
         for c in range(e.dim):
@@ -108,6 +105,7 @@ class Discretization2ndOrder:
             return self._discretize_advection(e)
         elif isinstance(e, Diff):
             arg, *indices = diff_args(e)
+
             if not isinstance(arg, Field.Access):
                 raise ValueError("Only derivatives with field or field accesses as arguments can be discretized")
             return self.spatial_stencil(indices, self.dx, arg)
@@ -115,29 +113,6 @@ class Discretization2ndOrder:
             new_args = [self._discretize_spatial(a) for a in e.args]
             return e.func(*new_args) if new_args else e
 
-    def _discretize_diff(self, e):
-        order = self._diff_order(e)
-        if order == 1:
-            fa = e.args[0]
-            index = e.target
-            return (fa.neighbor(index, 1) - fa.neighbor(index, -1)) / (2 * self.dx)
-        elif order == 2:
-            indices = sorted([e.target, e.args[0].target])
-            fa = e.args[0].args[0]
-            if indices[0] == indices[1] and all(i >= 0 for i in indices):
-                result = (-2 * fa + fa.neighbor(indices[0], -1) + fa.neighbor(indices[0], +1))
-            elif indices[0] == indices[1]:
-                result = 0
-                for d in range(fa.field.spatial_dimensions):
-                    result += (-2 * fa + fa.neighbor(d, -1) + fa.neighbor(d, +1))
-            else:
-                assert all(i >= 0 for i in indices)
-                offsets = [(1, 1), [-1, 1], [1, -1], [-1, -1]]
-                result = sum(o1 * o2 * fa.neighbor(indices[0], o1).neighbor(indices[1], o2) for o1, o2 in offsets) / 4
-            return result / (self.dx ** 2)
-        else:
-            raise NotImplementedError("Term contains derivatives of order > 2")
-
     def __call__(self, expr):
         if isinstance(expr, list):
             return [self(e) for e in expr]
@@ -187,7 +162,7 @@ class Advection(sp.Function):
         return self.scalar.spatial_dimensions
 
     def _latex(self, printer):
-        name_suffix = "_%s" % self.scalar_index if self.scalar_index is not None else ""
+        name_suffix = f"_{self.scalar_index}" if self.scalar_index is not None else ""
         if isinstance(self.vector, Field):
             return r"\nabla \cdot(%s %s)" % (printer.doprint(sp.Symbol(self.vector.name)),
                                              printer.doprint(sp.Symbol(self.scalar.name + name_suffix)))
@@ -234,7 +209,7 @@ class Diffusion(sp.Function):
         return self.scalar.spatial_dimensions
 
     def _latex(self, printer):
-        name_suffix = "_%s" % self.scalar_index if self.scalar_index is not None else ""
+        name_suffix = f"_{self.scalar_index}" if self.scalar_index is not None else ""
         coeff = self.diffusion_coeff
         diff_coeff = sp.Symbol(coeff.name) if isinstance(coeff, Field) else coeff
         return r"div(%s \nabla %s)" % (printer.doprint(diff_coeff),
@@ -267,7 +242,7 @@ class Transient(sp.Function):
         return None if len(self.args) <= 1 else int(self.args[1])
 
     def _latex(self, printer):
-        name_suffix = "_%s" % self.scalar_index if self.scalar_index is not None else ""
+        name_suffix = f"_{self.scalar_index}" if self.scalar_index is not None else ""
         return r"\partial_t %s" % (printer.doprint(sp.Symbol(self.scalar.name + name_suffix)),)
 
 
@@ -310,8 +285,9 @@ def discretize_center(term, symbols_to_field_dict, dx, dim=3):
       >>> term
       x*x^Delta^0
       >>> f = Field.create_generic('f', spatial_dimensions=3)
-      >>> discretize_center(term, { x: f }, dx=1, dim=3)
-      f_C*(-f_W/2 + f_E/2)
+      >>> expected_output = f[0, 0, 0] * (-f[-1, 0, 0]/2 + f[1, 0, 0]/2)
+      >>> sp.simplify(discretize_center(term, { x: f }, dx=1, dim=3) - expected_output)
+      0
     """
     substitutions = {}
     for symbols, field in symbols_to_field_dict.items():
@@ -322,7 +298,7 @@ def discretize_center(term, symbols_to_field_dict, dx, dim=3):
         for d in range(dim):
             up, down = __up_down_offsets(d, dim)
             substitutions.update({g[d][i]: (field[up](i) - field[down](i)) / dx / 2 for i in range(len(symbols))})
-    return term.subs(substitutions)
+    return fast_subs(term, substitutions)
 
 
 def discretize_staggered(term, symbols_to_field_dict, coordinate, coordinate_offset, dx, dim=3):
@@ -361,7 +337,7 @@ def discretize_staggered(term, symbols_to_field_dict, coordinate, coordinate_off
 
         offset = [0] * dim
         offset[coordinate] = coordinate_offset
-        offset = np.array(offset, dtype=np.int)
+        offset = np.array(offset, dtype=int)
 
         gradient = grad(symbols)[coordinate]
         substitutions.update({s: (field[offset](i) + field(i)) / 2 for i, s in enumerate(symbols)})
@@ -393,8 +369,10 @@ def discretize_divergence(vector_term, symbols_to_field_dict, dx):
         >>> x, dx = sp.symbols("x dx")
         >>> grad_x = grad(x, dim=3)
         >>> f = Field.create_generic('f', spatial_dimensions=3)
-        >>> sp.simplify(discretize_divergence(grad_x, {x : f}, dx))
-        (f_W + f_S + f_B - 6*f_C + f_T + f_N + f_E)/dx**2
+        >>> expected_output = (f[-1, 0, 0] + f[0, -1, 0] + f[0, 0, -1] -
+        ... 6*f[0, 0, 0] + f[0, 0, 1] + f[0, 1, 0] + f[1, 0, 0])/dx**2
+        >>> sp.simplify(discretize_divergence(grad_x, {x : f}, dx) - expected_output)
+        0
     """
     dim = len(vector_term)
     result = 0
@@ -407,7 +385,7 @@ def discretize_divergence(vector_term, symbols_to_field_dict, dx):
 def __up_down_offsets(d, dim):
     coord = [0] * dim
     coord[d] = 1
-    up = np.array(coord, dtype=np.int)
+    up = np.array(coord, dtype=int)
     coord[d] = -1
-    down = np.array(coord, dtype=np.int)
+    down = np.array(coord, dtype=int)
     return up, down

src/pystencils/fd/finitevolumes.py

+import pystencils as ps
+import sympy as sp
+from pystencils.fd.derivation import FiniteDifferenceStaggeredStencilDerivation as FDS, \
+    FiniteDifferenceStencilDerivation as FD
+import itertools
+from collections import defaultdict
+from collections.abc import Iterable
+
+
+def get_access_and_direction(term):
+    direction1 = term.args[1]
+    if isinstance(term.args[0], ps.Field.Access):  # first derivative
+        access = term.args[0]
+        direction = (direction1,)
+    elif isinstance(term.args[0], ps.fd.Diff):  # nested derivative
+        if isinstance(term.args[0].args[0], ps.fd.Diff):  # third or higher derivative
+            raise ValueError("can only handle first and second derivatives")
+        elif not isinstance(term.args[0].args[0], ps.Field.Access):
+            raise ValueError("can only handle derivatives of field accesses")
+
+        access, direction2 = term.args[0].args[:2]
+        direction = (direction1, direction2)
+    else:
+        raise NotImplementedError(f"can only deal with derivatives of field accesses, "
+                                  f"but not {type(term.args[0])}; expansion of derivatives probably failed")
+    return access, direction
+
+
+class FVM1stOrder:
+    """Finite-volume discretization
+
+    Args:
+        field: the field with the quantity to calculate, e.g. a concentration
+        flux: a list of sympy expressions that specify the flux, one for each cartesian direction
+        source: a list of sympy expressions that specify the source
+    """
+    def __init__(self, field: ps.field.Field, flux=0, source=0):
+        def normalize(f, shape):
+            shape = tuple(s for s in shape if s != 1)
+            if not shape:
+                shape = None
+
+            if isinstance(f, sp.Array) or isinstance(f, Iterable) or isinstance(f, sp.Matrix):
+                return sp.Array(f, shape)
+            else:
+                return sp.Array([f] * (sp.Mul(*shape) if shape else 1))
+
+        self.c = field
+        self.dim = self.c.spatial_dimensions
+        self.j = normalize(flux, (self.dim, ) + self.c.index_shape)
+        self.q = normalize(source, self.c.index_shape)
+
+    def discrete_flux(self, flux_field: ps.field.Field):
+        """Return a list of assignments for the discrete fluxes
+
+        Args:
+            flux_field: a staggered field to which the fluxes should be assigned
+        """
+
+        assert ps.FieldType.is_staggered(flux_field)
+
+        num = 0
+
+        def discretize(term, neighbor):
+            nonlocal num
+            if isinstance(term, sp.Matrix):
+                nw = term.applyfunc(lambda t: discretize(t, neighbor))
+                return nw
+            elif isinstance(term, ps.field.Field.Access):
+                avg = (term.get_shifted(*neighbor) + term) * sp.Rational(1, 2)
+                return avg
+            elif isinstance(term, ps.fd.Diff):
+                access, direction = get_access_and_direction(term)
+
+                fds = FDS(neighbor, access.field.spatial_dimensions, direction,
+                          free_weights_prefix=f'fvm_free_{num}' if sp.Matrix(neighbor).dot(neighbor) > 2 else None)
+                num += 1
+                return fds.apply(access)
+
+            if term.args:
+                new_args = [discretize(a, neighbor) for a in term.args]
+                return term.func(*new_args)
+            else:
+                return term
+
+        fluxes = self.j.applyfunc(ps.fd.derivative.expand_diff_full)
+        fluxes = [sp.Matrix(fluxes.tolist()[i]) if flux_field.index_dimensions > 1 else fluxes.tolist()[i] 
+                  for i in range(self.dim)]
+
+        A0 = sum([sp.Matrix(ps.stencil.direction_string_to_offset(d)).norm()
+                  for d in flux_field.staggered_stencil]) / self.dim
+
+        discrete_fluxes = []
+        for neighbor in flux_field.staggered_stencil:
+            neighbor = ps.stencil.direction_string_to_offset(neighbor)
+            directional_flux = fluxes[0] * int(neighbor[0])
+            for i in range(1, self.dim):
+                directional_flux += fluxes[i] * int(neighbor[i])
+            discrete_flux = sp.simplify(discretize(directional_flux, neighbor))
+            free_weights = [s for s in discrete_flux.atoms(sp.Symbol) if s.name.startswith('fvm_free_')]
+
+            if len(free_weights) > 0:
+                discrete_flux = discrete_flux.collect(discrete_flux.atoms(ps.field.Field.Access))
+                access_counts = defaultdict(list)
+                for values in itertools.product([-1, 0, 1],
+                                                repeat=len(free_weights)):
+                    subs = {free_weight: value for free_weight, value in zip(free_weights, values)}
+                    simp = discrete_flux.subs(subs)
+                    access_count = len(simp.atoms(ps.field.Field.Access))
+                    access_counts[access_count].append(simp)
+                best_count = min(access_counts.keys())
+                discrete_flux = sum(access_counts[best_count]) / len(access_counts[best_count])
+            discrete_fluxes.append(discrete_flux / sp.Matrix(neighbor).norm())
+
+        if flux_field.index_dimensions > 1:
+            return [ps.Assignment(lhs, rhs / A0)
+                    for i, d in enumerate(flux_field.staggered_stencil) if discrete_fluxes[i]
+                    for lhs, rhs in zip(flux_field.staggered_vector_access(d), sp.simplify(discrete_fluxes[i]))]
+        else:
+            return [ps.Assignment(flux_field.staggered_access(d), sp.simplify(discrete_fluxes[i]) / A0)
+                    for i, d in enumerate(flux_field.staggered_stencil)]
+
+    def discrete_source(self):
+        """Return a list of assignments for the discrete source term"""
+
+        def discretize(term):
+            if isinstance(term, ps.fd.Diff):
+                access, direction = get_access_and_direction(term)
+
+                if self.dim == 2:
+                    stencil = ["".join(a).replace(" ", "") for a in itertools.product("NS ", "EW ")
+                               if "".join(a).strip()]
+                else:
+                    stencil = ["".join(a).replace(" ", "") for a in itertools.product("NS ", "EW ", "TB ")
+                               if "".join(a).strip()]
+                weights = None
+                for stencil in [["N", "S", "E", "W", "T", "B"][:2 * self.dim], stencil]:
+                    stencil = [tuple(ps.stencil.direction_string_to_offset(d, self.dim)) for d in stencil]
+
+                    derivation = FD(direction, stencil).get_stencil()
+                    if not derivation.accuracy:
+                        continue
+                    weights = derivation.weights
+
+                    # if the weights are underdefined, we can choose the free symbols to find the sparsest stencil
+                    free_weights = set(itertools.chain(*[w.free_symbols for w in weights]))
+                    if len(free_weights) > 0:
+                        zero_counts = defaultdict(list)
+                        for values in itertools.product([-1, -sp.Rational(1, 2), 0, 1, sp.Rational(1, 2)],
+                                                        repeat=len(free_weights)):
+                            subs = {free_weight: value for free_weight, value in zip(free_weights, values)}
+                            weights = [w.subs(subs) for w in derivation.weights]
+                            if not all(a == 0 for a in weights):
+                                zero_count = sum([1 for w in weights if w == 0])
+                                zero_counts[zero_count].append(weights)
+                        best = zero_counts[max(zero_counts.keys())]
+                        if len(best) > 1:
+                            raise NotImplementedError("more than one suitable set of weights found, "
+                                                      "don't know how to proceed")
+                        weights = best[0]
+                    break
+                if not weights:
+                    raise Exception('the requested derivative cannot be performed with the available neighbors')
+                assert weights
+
+                if access._field.index_dimensions == 0:
+                    return sum([access._field.__getitem__(point) * weight for point, weight in zip(stencil, weights)])
+                else:
+                    total = access.get_shifted(*stencil[0]).at_index(*access.index) * weights[0]
+                    for point, weight in zip(stencil[1:], weights[1:]):
+                        addl = access.get_shifted(*point).at_index(*access.index) * weight
+                        total += addl
+                    return total
+
+            if term.args:
+                new_args = [discretize(a) for a in term.args]
+                return term.func(*new_args)
+            else:
+                return term
+
+        source = self.q.applyfunc(ps.fd.derivative.expand_diff_full)
+        source = source.applyfunc(discretize)
+
+        return [ps.Assignment(lhs, rhs) for lhs, rhs in zip(self.c.center_vector, sp.flatten(source)) if rhs]
+
+    def discrete_continuity(self, flux_field: ps.field.Field):
+        """Return a list of assignments for the continuity equation, which includes the source term
+
+        Args:
+            flux_field: a staggered field from which the fluxes are taken
+        """
+
+        assert ps.FieldType.is_staggered(flux_field)
+
+        neighbors = flux_field.staggered_stencil + [ps.stencil.inverse_direction_string(d)
+                                                    for d in flux_field.staggered_stencil]
+        divergence = flux_field.staggered_vector_access(neighbors[0])
+        for d in neighbors[1:]:
+            divergence += flux_field.staggered_vector_access(d)
+
+        source = self.discrete_source()
+        source = {s.lhs: s.rhs for s in source}
+
+        return [ps.Assignment(lhs, (lhs - rhs + source[lhs]) if lhs in source else (lhs - rhs))
+                for lhs, rhs in zip(self.c.center_vector, divergence)]
+
+
+def VOF(j: ps.field.Field, v: ps.field.Field, ρ: ps.field.Field):
+    """Volume-of-fluid discretization of advection
+
+    Args:
+        j: the staggered field to write the fluxes to. Should have a D2Q9/D3Q27 stencil. Other stencils work too, but
+           incur a small error (D2Q5/D3Q7: v^2, D3Q19: v^3).
+        v: the flow velocity field
+        ρ: the quantity to advect
+    """
+    assert ps.FieldType.is_staggered(j)
+
+    fluxes = [[] for i in range(j.index_shape[0])]
+
+    v0 = v.center_vector
+    for d, neighbor in enumerate(j.staggered_stencil):
+        c = ps.stencil.direction_string_to_offset(neighbor)
+        v1 = v.neighbor_vector(c)
+
+        # going out
+        cond = sp.And(*[sp.Or(c[i] * v0[i] > 0, c[i] == 0) for i in range(len(v0))])
+        overlap1 = [1 - sp.Abs(v0[i]) for i in range(len(v0))]
+        overlap2 = [c[i] * v0[i] for i in range(len(v0))]
+        overlap = sp.Mul(*[(overlap1[i] if c[i] == 0 else overlap2[i]) for i in range(len(v0))])
+        fluxes[d].append(ρ.center_vector * overlap * sp.Piecewise((1, cond), (0, True)))
+
+        # coming in
+        cond = sp.And(*[sp.Or(c[i] * v1[i] < 0, c[i] == 0) for i in range(len(v1))])
+        overlap1 = [1 - sp.Abs(v1[i]) for i in range(len(v1))]
+        overlap2 = [v1[i] for i in range(len(v1))]
+        overlap = sp.Mul(*[(overlap1[i] if c[i] == 0 else overlap2[i]) for i in range(len(v1))])
+        sign = (c == 1).sum() % 2 * 2 - 1
+        fluxes[d].append(sign * ρ.neighbor_vector(c) * overlap * sp.Piecewise((1, cond), (0, True)))
+
+    for i, ff in enumerate(fluxes):
+        fluxes[i] = ff[0]
+        for f in ff[1:]:
+            fluxes[i] += f
+
+    assignments = []
+    for i, d in enumerate(j.staggered_stencil):
+        for lhs, rhs in zip(j.staggered_vector_access(d).values(), fluxes[i].values()):
+            assignments.append(ps.Assignment(lhs, rhs))
+    return assignments

pystencils/fd/spatial.py → src/pystencils/fd/spatial.py

+from functools import lru_cache
 from typing import Tuple
+
 import sympy as sp
+
 from pystencils.astnodes import LoopOverCoordinate
-from pystencils.cache import memorycache
-from pystencils import Field
 from pystencils.fd import Diff
+from pystencils.field import Field
 from pystencils.transformations import generic_visit
-from .derivative import diff_args
+
 from .derivation import FiniteDifferenceStencilDerivation
+from .derivative import diff_args
 
 
 def fd_stencils_standard(indices, dx, fa):
     order = len(indices)
+    assert all(i >= 0 for i in indices), "Can only discretize objects with (integer) subscripts"
     if order == 1:
         idx = indices[0]
         return (fa.neighbor(idx, 1) - fa.neighbor(idx, -1)) / (2 * dx)
@@ -68,43 +72,12 @@ def fd_stencils_forth_order_isotropic(indices, dx, fa):
     return stencils[dim].apply(fa) / dx
 
 
-def fd_stencils_isotropic_high_density_code(indices, dx, fa):
-    dim = fa.field.spatial_dimensions
-    if dim == 1:
-        return fd_stencils_standard(indices, dx, fa)
-    elif dim == 2:
-        order = len(indices)
-
-        if order == 1:
-            idx = indices[0]
-            assert 0 <= idx < 2
-            other_idx = 1 if indices[0] == 0 else 0
-            weights = {-1: sp.Rational(1, 12) / dx,
-                       0: sp.Rational(1, 3) / dx,
-                       1: sp.Rational(1, 12) / dx}
-            upper_terms = sum(fa.neighbor(idx, +1).neighbor(other_idx, off) * w for off, w in weights.items())
-            lower_terms = sum(fa.neighbor(idx, -1).neighbor(other_idx, off) * w for off, w in weights.items())
-            return upper_terms - lower_terms
-        elif order == 2:
-            if indices[0] == indices[1]:
-                idx = indices[0]
-                diagonals = sp.Rational(1, 8) * sum(fa.neighbor(0, i).neighbor(1, j) for i in (-1, 1) for j in (-1, 1))
-                div_direction = sp.Rational(1, 2) * sum(fa.neighbor(idx, i) for i in (-1, 1))
-                center = - sp.Rational(3, 2) * fa
-                return (diagonals + div_direction + center) / (dx ** 2)
-            else:
-                return fd_stencils_standard(indices, dx, fa)
-    raise NotImplementedError("Supports only derivatives up to order 2 for 1D and 2D setups")
-
-
 def discretize_spatial(expr, dx, stencil=fd_stencils_standard):
     if isinstance(stencil, str):
         if stencil == 'standard':
             stencil = fd_stencils_standard
         elif stencil == 'isotropic':
             stencil = fd_stencils_isotropic
-        elif stencil == 'isotropic_hd':
-            stencil = fd_stencils_isotropic_high_density_code
         else:
             raise ValueError("Unknown stencil. Supported 'standard' and 'isotropic'")
 
@@ -122,7 +95,6 @@ def discretize_spatial(expr, dx, stencil=fd_stencils_standard):
 
 
 def discretize_spatial_staggered(expr, dx, stencil=fd_stencils_standard):
-
     def staggered_visitor(e, coordinate, sign):
         if isinstance(e, Diff):
             arg, *indices = diff_args(e)
@@ -164,9 +136,7 @@ def discretize_spatial_staggered(expr, dx, stencil=fd_stencils_standard):
 
 
 # -------------------------------------- special stencils --------------------------------------------------------------
-
-
-@memorycache(maxsize=1)
+@lru_cache(maxsize=1)
 def forth_order_2d_derivation() -> Tuple[FiniteDifferenceStencilDerivation.Result, ...]:
     # Symmetry, isotropy and 4th order conditions are not enough to fully specify the stencil
     # one weight has to be specifically set to a somewhat arbitrary value

pystencils/field.py → src/pystencils/field.py

+import functools
+import hashlib
+import operator
+import pickle
+import re
 from enum import Enum
 from itertools import chain
-from typing import Tuple, Sequence, Optional, List, Set
+from typing import List, Optional, Sequence, Set, Tuple, Union
+
 import numpy as np
 import sympy as sp
-import re
 from sympy.core.cache import cacheit
+
+import pystencils
 from pystencils.alignedarray import aligned_empty
-from pystencils.data_types import create_type, StructType
-from pystencils.kernelparameters import FieldShapeSymbol, FieldStrideSymbol
-from pystencils.stencils import offset_to_direction_string, direction_string_to_offset
+from pystencils.typing import StructType, TypedSymbol, BasicType, create_type
+from pystencils.typing.typed_sympy import FieldShapeSymbol, FieldStrideSymbol
+from pystencils.stencil import (
+    direction_string_to_offset, inverse_direction, offset_to_direction_string)
 from pystencils.sympyextensions import is_integer_sequence
-import pickle
-import hashlib
-
-__all__ = ['Field', 'fields', 'FieldType']
-
-
-def fields(description=None, index_dimensions=0, layout=None, **kwargs):
-    """Creates pystencils fields from a string description.
-
-    Examples:
-        Create a 2D scalar and vector field:
-            >>> s, v = fields("s, v(2): double[2D]")
-            >>> assert s.spatial_dimensions == 2 and s.index_dimensions == 0
-            >>> assert (v.spatial_dimensions, v.index_dimensions, v.index_shape) == (2, 1, (2,))
-
-        Create an integer field of shape (10, 20):
-            >>> f = fields("f : int32[10, 20]")
-            >>> f.has_fixed_shape, f.shape
-            (True, (10, 20))
-
-        Numpy arrays can be used as template for shape and data type of field:
-            >>> arr_s, arr_v = np.zeros([20, 20]), np.zeros([20, 20, 2])
-            >>> s, v = fields("s, v(2)", s=arr_s, v=arr_v)
-            >>> assert s.index_dimensions == 0 and s.dtype.numpy_dtype == arr_s.dtype
-            >>> assert v.index_shape == (2,)
-
-
-        Format string can be left out, field names are taken from keyword arguments.
-            >>> fields(f1=arr_s, f2=arr_s)
-            [f1, f2]
-
-        The keyword names ``index_dimension`` and ``layout`` have special meaning, don't use them for field names
-            >>> f = fields(f=arr_v, index_dimensions=1)
-            >>> assert f.index_dimensions == 1
-            >>> f = fields("pdfs(19) : float32[3D]", layout='fzyx')
-            >>> f.layout
-            (2, 1, 0)
-    """
-    result = []
-    if description:
-        field_descriptions, dtype, shape = _parse_description(description)
-        layout = 'numpy' if layout is None else layout
-        for field_name, idx_shape in field_descriptions:
-            if field_name in kwargs:
-                arr = kwargs[field_name]
-                idx_shape_of_arr = () if not len(idx_shape) else arr.shape[-len(idx_shape):]
-                assert idx_shape_of_arr == idx_shape
-                f = Field.create_from_numpy_array(field_name, kwargs[field_name], index_dimensions=len(idx_shape))
-            elif isinstance(shape, tuple):
-                f = Field.create_fixed_size(field_name, shape + idx_shape, dtype=dtype,
-                                            index_dimensions=len(idx_shape), layout=layout)
-            elif isinstance(shape, int):
-                f = Field.create_generic(field_name, spatial_dimensions=shape, dtype=dtype,
-                                         index_shape=idx_shape, layout=layout)
-            elif shape is None:
-                f = Field.create_generic(field_name, spatial_dimensions=2, dtype=dtype,
-                                         index_shape=idx_shape, layout=layout)
-            else:
-                assert False
-            result.append(f)
-    else:
-        assert layout is None, "Layout can not be specified when creating Field from numpy array"
-        for field_name, arr in kwargs.items():
-            result.append(Field.create_from_numpy_array(field_name, arr, index_dimensions=index_dimensions))
 
-    if len(result) == 0:
-        return None
-    elif len(result) == 1:
-        return result[0]
-    else:
-        return result
+__all__ = ['Field', 'fields', 'FieldType', 'Field']
 
 
 class FieldType(Enum):
@@ -94,6 +33,10 @@ class FieldType(Enum):
     # unsafe fields may be accessed in an absolute fashion - the index depends on the data
     # and thus may lead to out-of-bounds accesses
     CUSTOM = 3
+    # staggered field
+    STAGGERED = 4
+    # staggered field that reverses sign when accessed via opposite direction
+    STAGGERED_FLUX = 5
 
     @staticmethod
     def is_generic(field):
@@ -115,6 +58,16 @@ class FieldType(Enum):
         assert isinstance(field, Field)
         return field.field_type == FieldType.CUSTOM
 
+    @staticmethod
+    def is_staggered(field):
+        assert isinstance(field, Field)
+        return field.field_type == FieldType.STAGGERED or field.field_type == FieldType.STAGGERED_FLUX
+
+    @staticmethod
+    def is_staggered_flux(field):
+        assert isinstance(field, Field)
+        return field.field_type == FieldType.STAGGERED_FLUX
+
 
 class Field:
     """
@@ -148,6 +101,14 @@ class Field:
         First specify the spatial offsets in [], then in case index_dimension>0 the indices in ()
         e.g. ``f[-1,0,0](7)``
 
+    Staggered Fields:
+        Staggered fields are used to store a value on a second grid shifted by half a cell with respect to the usual
+        grid.
+
+        The first index dimension is used to specify the position on the staggered grid (e.g. 0 means half-way to the
+        eastern neighbor, 1 is half-way to the northern neighbor, etc.), while additional indices can be used to store
+        multiple values at each position.
+
     Example using no index dimensions:
         >>> a = np.zeros([10, 10])
         >>> f = Field.create_from_numpy_array("f", a, index_dimensions=0)
@@ -177,8 +138,9 @@ class Field:
             index_shape: optional shape of the index dimensions i.e. maximum values allowed for each index dimension,
                         has to be a list or tuple
             field_type: besides the normal GENERIC fields, there are INDEXED fields that store indices of the domain
-                        that should be iterated over, and BUFFER fields that are used to generate
-                        communication packing/unpacking kernels
+                        that should be iterated over, BUFFER fields that are used to generate communication
+                        packing/unpacking kernels, and STAGGERED fields, which store values half-way to the next
+                        cell
         """
         if index_shape is not None:
             assert index_dimensions == 0 or index_dimensions == len(index_shape)
@@ -200,11 +162,14 @@ class Field:
                 raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
             shape += (1,)
             strides += (1,)
+        if field_type == FieldType.STAGGERED and index_dimensions == 0:
+            raise ValueError("A staggered field needs at least one index dimension")
 
         return Field(field_name, field_type, dtype, layout, shape, strides)
 
     @staticmethod
-    def create_from_numpy_array(field_name: str, array: np.ndarray, index_dimensions: int = 0) -> 'Field':
+    def create_from_numpy_array(field_name: str, array: np.ndarray, index_dimensions: int = 0,
+                                field_type=FieldType.GENERIC) -> 'Field':
         """Creates a field based on the layout, data type, and shape of a given numpy array.
 
         Kernels created for these kind of fields can only be called with arrays of the same layout, shape and type.
@@ -213,6 +178,7 @@ class Field:
             field_name: symbolic name for the field
             array: numpy array
             index_dimensions: see documentation of Field
+            field_type: kind of field
         """
         spatial_dimensions = len(array.shape) - index_dimensions
         if spatial_dimensions < 1:
@@ -231,12 +197,15 @@ class Field:
                 raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
             shape += (1,)
             strides += (1,)
+        if field_type == FieldType.STAGGERED and index_dimensions == 0:
+            raise ValueError("A staggered field needs at least one index dimension")
 
-        return Field(field_name, FieldType.GENERIC, array.dtype, spatial_layout, shape, strides)
+        return Field(field_name, field_type, array.dtype, spatial_layout, shape, strides)
 
     @staticmethod
     def create_fixed_size(field_name: str, shape: Tuple[int, ...], index_dimensions: int = 0,
-                          dtype=np.float64, layout: str = 'numpy', strides: Optional[Sequence[int]] = None) -> 'Field':
+                          dtype=np.float64, layout: str = 'numpy', strides: Optional[Sequence[int]] = None,
+                          field_type=FieldType.GENERIC) -> 'Field':
         """
         Creates a field with fixed sizes i.e. can be called only with arrays of the same size and layout
 
@@ -247,6 +216,7 @@ class Field:
             dtype: numpy data type of the array the kernel is called with later
             layout: full layout of array, not only spatial dimensions
             strides: strides in bytes or None to automatically compute them from shape (assuming no padding)
+            field_type: kind of field
         """
         spatial_dimensions = len(shape) - index_dimensions
         assert spatial_dimensions >= 1
@@ -267,11 +237,13 @@ class Field:
                 raise ValueError("Structured arrays/fields are not allowed to have an index dimension")
             shape += (1,)
             strides += (1,)
+        if field_type == FieldType.STAGGERED and index_dimensions == 0:
+            raise ValueError("A staggered field needs at least one index dimension")
 
         spatial_layout = list(layout)
         for i in range(spatial_dimensions, len(layout)):
             spatial_layout.remove(i)
-        return Field(field_name, FieldType.GENERIC, dtype, tuple(spatial_layout), shape, strides)
+        return Field(field_name, field_type, dtype, tuple(spatial_layout), shape, strides)
 
     def __init__(self, field_name, field_type, dtype, layout, shape, strides):
         """Do not use directly. Use static create* methods"""
@@ -283,10 +255,17 @@ class Field:
         self._layout = normalize_layout(layout)
         self.shape = shape
         self.strides = strides
-        self.latex_name = None  # type: Optional[str]
+        self.latex_name: Optional[str] = None
+        self.coordinate_origin = sp.Matrix([0] * self.spatial_dimensions)
+        self.coordinate_transform = sp.eye(self.spatial_dimensions)
+        if field_type == FieldType.STAGGERED:
+            assert self.staggered_stencil
 
     def new_field_with_different_name(self, new_name):
-        return Field(new_name, self.field_type, self._dtype, self._layout, self.shape, self.strides)
+        if self.has_fixed_shape:
+            return Field(new_name, self.field_type, self._dtype, self._layout, self.shape, self.strides)
+        else:
+            return Field(new_name, self.field_type, self.dtype, self.layout, self.shape, self.strides)
 
     @property
     def spatial_dimensions(self) -> int:
@@ -296,6 +275,13 @@ class Field:
     def index_dimensions(self) -> int:
         return len(self.shape) - len(self._layout)
 
+    @property
+    def ndim(self) -> int:
+        return len(self.shape)
+
+    def values_per_cell(self) -> int:
+        return functools.reduce(operator.mul, self.index_shape, 1)
+
     @property
     def layout(self):
         return self._layout
@@ -332,8 +318,24 @@ class Field:
     def dtype(self):
         return self._dtype
 
+    @property
+    def itemsize(self):
+        return self.dtype.numpy_dtype.itemsize
+
     def __repr__(self):
-        return self._field_name
+        if any(isinstance(s, sp.Symbol) for s in self.spatial_shape):
+            spatial_shape_str = f'{self.spatial_dimensions}d'
+        else:
+            spatial_shape_str = ','.join(str(i) for i in self.spatial_shape)
+        index_shape_str = ','.join(str(i) for i in self.index_shape)
+
+        if self.index_shape:
+            return f'{self._field_name}({index_shape_str}): {self.dtype}[{spatial_shape_str}]'
+        else:
+            return f'{self._field_name}: {self.dtype}[{spatial_shape_str}]'
+
+    def __str__(self):
+        return self.name
 
     def neighbor(self, coord_id, offset):
         offset_list = [0] * self.spatial_dimensions
@@ -348,19 +350,37 @@ class Field:
         index_shape = self.index_shape
         if len(index_shape) == 0:
             return sp.Matrix([self.center])
-        if len(index_shape) == 1:
+        elif len(index_shape) == 1:
             return sp.Matrix([self(i) for i in range(index_shape[0])])
         elif len(index_shape) == 2:
-            def cb(*args):
-                r = self.__call__(*args)
-                return r
-            return sp.Matrix(*index_shape, cb)
+            return sp.Matrix([[self(i, j) for j in range(index_shape[1])] for i in range(index_shape[0])])
+        elif len(index_shape) == 3:
+            return sp.Array([[[self(i, j, k) for k in range(index_shape[2])]
+                              for j in range(index_shape[1])] for i in range(index_shape[0])])
+        else:
+            raise NotImplementedError("center_vector is not implemented for more than 3 index dimensions")
 
     @property
     def center(self):
         center = tuple([0] * self.spatial_dimensions)
         return Field.Access(self, center)
 
+    def neighbor_vector(self, offset):
+        """Like neighbor, but returns the entire vector/tensor stored at offset."""
+        if self.spatial_dimensions == 2 and len(offset) == 3:
+            assert offset[2] == 0
+            offset = offset[:2]
+
+        if self.index_dimensions == 0:
+            return sp.Matrix([self.__getitem__(offset)])
+        elif self.index_dimensions == 1:
+            return sp.Matrix([self.__getitem__(offset)(i) for i in range(self.index_shape[0])])
+        elif self.index_dimensions == 2:
+            return sp.Matrix([[self.__getitem__(offset)(i, k) for k in range(self.index_shape[1])]
+                              for i in range(self.index_shape[0])])
+        else:
+            raise NotImplementedError("neighbor_vector is not implemented for more than 2 index dimensions")
+
     def __getitem__(self, offset):
         if type(offset) is np.ndarray:
             offset = tuple(offset)
@@ -369,21 +389,115 @@ class Field:
         if type(offset) is not tuple:
             offset = (offset,)
         if len(offset) != self.spatial_dimensions:
-            raise ValueError("Wrong number of spatial indices: "
-                             "Got %d, expected %d" % (len(offset), self.spatial_dimensions))
+            raise ValueError(f"Wrong number of spatial indices: Got {len(offset)}, expected {self.spatial_dimensions}")
         return Field.Access(self, offset)
 
     def absolute_access(self, offset, index):
         assert FieldType.is_custom(self)
         return Field.Access(self, offset, index, is_absolute_access=True)
 
+    def staggered_access(self, offset, index=None):
+        """If this field is a staggered field, it can be accessed using half-integer offsets.
+        For example, an offset of ``(0, sp.Rational(1,2))`` or ``"E"`` corresponds to the staggered point to the east
+        of the cell center, i.e. half-way to the eastern-next cell.
+        If the field stores more than one value per staggered point (e.g. a vector or a tensor), the index (integer or
+        tuple of integers) refers to which of these values to access.
+        """
+        assert FieldType.is_staggered(self)
+
+        offset_orig = offset
+        if type(offset) is np.ndarray:
+            offset = tuple(offset)
+        if type(offset) is str:
+            offset = tuple(direction_string_to_offset(offset, self.spatial_dimensions))
+            offset = tuple([o * sp.Rational(1, 2) for o in offset])
+        if len(offset) != self.spatial_dimensions:
+            raise ValueError(f"Wrong number of spatial indices: Got {len(offset)}, expected {self.spatial_dimensions}")
+
+        prefactor = 1
+        neighbor_vec = [0] * len(offset)
+        for i in range(self.spatial_dimensions):
+            if (offset[i] + sp.Rational(1, 2)).is_Integer:
+                neighbor_vec[i] = sp.sign(offset[i])
+        neighbor = offset_to_direction_string(neighbor_vec)
+        if neighbor not in self.staggered_stencil:
+            neighbor_vec = inverse_direction(neighbor_vec)
+            neighbor = offset_to_direction_string(neighbor_vec)
+            if FieldType.is_staggered_flux(self):
+                prefactor = -1
+        if neighbor not in self.staggered_stencil:
+            raise ValueError(f"{offset_orig} is not a valid neighbor for the {self.staggered_stencil_name} stencil")
+
+        offset = tuple(sp.Matrix(offset) - sp.Rational(1, 2) * sp.Matrix(neighbor_vec))
+
+        idx = self.staggered_stencil.index(neighbor)
+
+        if self.index_dimensions == 1:  # this field stores a scalar value at each staggered position
+            if index is not None:
+                raise ValueError("Cannot specify an index for a scalar staggered field")
+            return prefactor * Field.Access(self, offset, (idx,))
+        else:  # this field stores a vector or tensor at each staggered position
+            if index is None:
+                raise ValueError(f"Wrong number of indices: Got 0, expected {self.index_dimensions - 1}")
+            if type(index) is np.ndarray:
+                index = tuple(index)
+            if type(index) is not tuple:
+                index = (index,)
+            if self.index_dimensions != len(index) + 1:
+                raise ValueError(f"Wrong number of indices: Got {len(index)}, expected {self.index_dimensions - 1}")
+
+            return prefactor * Field.Access(self, offset, (idx, *index))
+
+    def staggered_vector_access(self, offset):
+        """Like staggered_access, but returns the entire vector/tensor stored at offset."""
+        assert FieldType.is_staggered(self)
+
+        if self.index_dimensions == 1:
+            return sp.Matrix([self.staggered_access(offset)])
+        elif self.index_dimensions == 2:
+            return sp.Matrix([self.staggered_access(offset, i) for i in range(self.index_shape[1])])
+        elif self.index_dimensions == 3:
+            return sp.Matrix([[self.staggered_access(offset, (i, k)) for k in range(self.index_shape[2])]
+                              for i in range(self.index_shape[1])])
+        else:
+            raise NotImplementedError("staggered_vector_access is not implemented for more than 3 index dimensions")
+
+    @property
+    def staggered_stencil(self):
+        assert FieldType.is_staggered(self)
+        stencils = {
+            2: {
+                2: ["W", "S"],  # D2Q5
+                4: ["W", "S", "SW", "NW"]  # D2Q9
+            },
+            3: {
+                3: ["W", "S", "B"],  # D3Q7
+                7: ["W", "S", "B", "BSW", "TSW", "BNW", "TNW"],  # D3Q15
+                9: ["W", "S", "B", "SW", "NW", "BW", "TW", "BS", "TS"],  # D3Q19
+                13: ["W", "S", "B", "SW", "NW", "BW", "TW", "BS", "TS", "BSW", "TSW", "BNW", "TNW"]  # D3Q27
+            }
+        }
+        if not self.index_shape[0] in stencils[self.spatial_dimensions]:
+            raise ValueError(f"No known stencil has {self.index_shape[0]} staggered points")
+        return stencils[self.spatial_dimensions][self.index_shape[0]]
+
+    @property
+    def staggered_stencil_name(self):
+        assert FieldType.is_staggered(self)
+        return f"D{self.spatial_dimensions}Q{self.index_shape[0] * 2 + 1}"
+
     def __call__(self, *args, **kwargs):
         center = tuple([0] * self.spatial_dimensions)
         return Field.Access(self, center)(*args, **kwargs)
 
     def hashable_contents(self):
-        dth = hash(self._dtype)
-        return self._layout, self.shape, self.strides, dth, self.field_type, self._field_name, self.latex_name
+        return (self._layout,
+                self.shape,
+                self.strides,
+                self.field_type,
+                self._field_name,
+                self.latex_name,
+                self._dtype)
 
     def __hash__(self):
         return hash(self.hashable_contents())
@@ -393,8 +507,48 @@ class Field:
             return False
         return self.hashable_contents() == other.hashable_contents()
 
+    @property
+    def physical_coordinates(self):
+        if hasattr(self.coordinate_transform, '__call__'):
+            return self.coordinate_transform(self.coordinate_origin + pystencils.x_vector(self.spatial_dimensions))
+        else:
+            return self.coordinate_transform @ (self.coordinate_origin + pystencils.x_vector(self.spatial_dimensions))
+
+    @property
+    def physical_coordinates_staggered(self):
+        return self.coordinate_transform @ \
+            (self.coordinate_origin + pystencils.x_staggered_vector(self.spatial_dimensions))
+
+    def index_to_physical(self, index_coordinates: sp.Matrix, staggered=False):
+        if staggered:
+            index_coordinates = sp.Matrix([0.5] * len(self.coordinate_origin)) + index_coordinates
+        if hasattr(self.coordinate_transform, '__call__'):
+            return self.coordinate_transform(self.coordinate_origin + index_coordinates)
+        else:
+            return self.coordinate_transform @ (self.coordinate_origin + index_coordinates)
+
+    def physical_to_index(self, physical_coordinates: sp.Matrix, staggered=False):
+        if hasattr(self.coordinate_transform, '__call__'):
+            if hasattr(self.coordinate_transform, 'inv'):
+                return self.coordinate_transform.inv()(physical_coordinates) - self.coordinate_origin
+            else:
+                idx = sp.Matrix(sp.symbols(f'index_coordinates:{self.ndim}', real=True))
+                rtn = sp.solve(self.index_to_physical(idx) - physical_coordinates, idx)
+                assert rtn, f'Could not find inverese of coordinate_transform: {self.index_to_physical(idx)}'
+                return rtn
+
+        else:
+            rtn = self.coordinate_transform.inv() @ physical_coordinates - self.coordinate_origin
+        if staggered:
+            rtn = sp.Matrix([i - 0.5 for i in rtn])
+
+        return rtn
+
+    def set_coordinate_origin_to_field_center(self):
+        self.coordinate_origin = -sp.Matrix([i / 2 for i in self.spatial_shape])
+
     # noinspection PyAttributeOutsideInit,PyUnresolvedReferences
-    class Access(sp.Symbol):
+    class Access(TypedSymbol):
         """Class representing a relative access into a `Field`.
 
         This class behaves like a normal sympy Symbol, it is actually derived from it. One can built up
@@ -413,11 +567,13 @@ class Field:
             >>> central_y_component.at_index(0)  # change component
             v_C^0
         """
+        _iterable = False  # see https://i10git.cs.fau.de/pycodegen/pystencils/-/merge_requests/166#note_10680
+
         def __new__(cls, name, *args, **kwargs):
             obj = Field.Access.__xnew_cached_(cls, name, *args, **kwargs)
             return obj
 
-        def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None, is_absolute_access=False):
+        def __new_stage2__(self, field, offsets=(0, 0, 0), idx=None, is_absolute_access=False, dtype=None):
             field_name = field.name
             offsets_and_index = (*offsets, *idx) if idx is not None else offsets
             constant_offsets = not any([isinstance(o, sp.Basic) and not o.is_Integer for o in offsets_and_index])
@@ -442,11 +598,15 @@ class Field:
                 offset_name = hashlib.md5(pickle.dumps(offsets_and_index)).hexdigest()[:12]
                 superscript = None
 
-            symbol_name = "%s_%s" % (field_name, offset_name)
+            symbol_name = f"{field_name}_{offset_name}"
             if superscript is not None:
                 symbol_name += "^" + superscript
 
-            obj = super(Field.Access, self).__xnew__(self, symbol_name)
+            if dtype:
+                obj = super(Field.Access, self).__xnew__(self, symbol_name, dtype)
+            else:
+                obj = super(Field.Access, self).__xnew__(self, symbol_name, field.dtype)
+
             obj._field = field
             obj._offsets = []
             for o in offsets:
@@ -454,7 +614,7 @@ class Field:
                     obj._offsets.append(o)
                 else:
                     obj._offsets.append(int(o))
-            obj._offsets = tuple(obj._offsets)
+            obj._offsets = tuple(sp.sympify(obj._offsets))
             obj._offsetName = offset_name
             obj._superscript = superscript
             obj._index = idx
@@ -468,7 +628,10 @@ class Field:
             return obj
 
         def __getnewargs__(self):
-            return self.field, self.offsets, self.index, self.is_absolute_access
+            return self.field, self.offsets, self.index, self.is_absolute_access, self.dtype
+
+        def __getnewargs_ex__(self):
+            return (self.field, self.offsets, self.index, self.is_absolute_access, self.dtype), {}
 
         # noinspection SpellCheckingInspection
         __xnew__ = staticmethod(__new_stage2__)
@@ -485,18 +648,18 @@ class Field:
                 idx = ()
 
             if len(idx) != self.field.index_dimensions:
-                raise ValueError("Wrong number of indices: "
-                                 "Got %d, expected %d" % (len(idx), self.field.index_dimensions))
-            return Field.Access(self.field, self._offsets, idx)
+                raise ValueError(f"Wrong number of indices: Got {len(idx)}, expected {self.field.index_dimensions}")
+            if len(idx) == 1 and isinstance(idx[0], str):
+                dtype = BasicType(self.field.dtype.numpy_dtype[idx[0]])
+                return Field.Access(self.field, self._offsets, idx,
+                                    is_absolute_access=self.is_absolute_access, dtype=dtype)
+            else:
+                return Field.Access(self.field, self._offsets, idx,
+                                    is_absolute_access=self.is_absolute_access, dtype=self.dtype)
 
         def __getitem__(self, *idx):
             return self.__call__(*idx)
 
-        def __iter__(self):
-            """This is necessary to work with parts of sympy that test if an object is iterable (e.g. simplify).
-            The __getitem__ would make it iterable"""
-            raise TypeError("Field access is not iterable")
-
         @property
         def field(self) -> 'Field':
             """Field that the Access points to"""
@@ -546,7 +709,8 @@ class Field:
             """
             offset_list = list(self.offsets)
             offset_list[coord_id] += offset
-            return Field.Access(self.field, tuple(offset_list), self.index)
+            return Field.Access(self.field, tuple(offset_list), self.index,
+                                is_absolute_access=self.is_absolute_access, dtype=self.dtype)
 
         def get_shifted(self, *shift) -> 'Field.Access':
             """Returns a new Access with changed spatial coordinates
@@ -556,7 +720,11 @@ class Field:
                 >>> f[0,0].get_shifted(1, 1)
                 f_NE
             """
-            return Field.Access(self.field, tuple(a + b for a, b in zip(shift, self.offsets)), self.index)
+            return Field.Access(self.field,
+                                tuple(a + b for a, b in zip(shift, self.offsets)),
+                                self.index,
+                                is_absolute_access=self.is_absolute_access,
+                                dtype=self.dtype)
 
         def at_index(self, *idx_tuple) -> 'Field.Access':
             """Returns new Access with changed index.
@@ -566,7 +734,15 @@ class Field:
                 >>> f(0).at_index(8)
                 f_C^8
             """
-            return Field.Access(self.field, self.offsets, idx_tuple)
+            return Field.Access(self.field, self.offsets, idx_tuple,
+                                is_absolute_access=self.is_absolute_access, dtype=self.dtype)
+
+        def _eval_subs(self, old, new):
+            return Field.Access(self.field,
+                                tuple(sp.sympify(a).subs(old, new) for a in self.offsets),
+                                tuple(sp.sympify(a).subs(old, new) for a in self.index),
+                                is_absolute_access=self.is_absolute_access,
+                                dtype=self.dtype)
 
         @property
         def is_absolute_access(self) -> bool:
@@ -583,30 +759,125 @@ class Field:
 
         def _hashable_content(self):
             super_class_contents = super(Field.Access, self)._hashable_content()
-            return (super_class_contents, self._field.hashable_contents(), *self._index, *self._offsets)
+            return (super_class_contents, self._field.hashable_contents(), *self._index,
+                    *self._offsets, self._is_absolute_access)
+
+        def _staggered_offset(self, offsets, index):
+            assert FieldType.is_staggered(self._field)
+            neighbor = self._field.staggered_stencil[index]
+            neighbor = direction_string_to_offset(neighbor, self._field.spatial_dimensions)
+            return [(o + sp.Rational(int(neighbor[i]), 2)) for i, o in enumerate(offsets)]
 
         def _latex(self, _):
             n = self._field.latex_name if self._field.latex_name else self._field.name
             offset_str = ",".join([sp.latex(o) for o in self.offsets])
+            if FieldType.is_staggered(self._field):
+                offset_str = ",".join([sp.latex(self._staggered_offset(self.offsets, self.index[0])[i])
+                                       for i in range(len(self.offsets))])
             if self.is_absolute_access:
-                offset_str = "\\mathbf{}".format(offset_str)
+                offset_str = f"\\mathbf{offset_str}"
             elif self.field.spatial_dimensions > 1:
-                offset_str = "({})".format(offset_str)
+                offset_str = f"({offset_str})"
 
-            if self.index and self.index != (0,):
-                return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
+            if FieldType.is_staggered(self._field):
+                if self.index and self.field.index_dimensions > 1:
+                    return f"{{{n}}}_{{{offset_str}}}^{{{self.index[1:] if len(self.index) > 2 else self.index[1]}}}"
+                else:
+                    return f"{{{n}}}_{{{offset_str}}}"
             else:
-                return "{{%s}_{%s}}" % (n, offset_str)
+                if self.index and self.field.index_dimensions > 0:
+                    return f"{{{n}}}_{{{offset_str}}}^{{{self.index if len(self.index) > 1 else self.index[0]}}}"
+                else:
+                    return f"{{{n}}}_{{{offset_str}}}"
 
         def __str__(self):
             n = self._field.latex_name if self._field.latex_name else self._field.name
             offset_str = ",".join([sp.latex(o) for o in self.offsets])
+            if FieldType.is_staggered(self._field):
+                offset_str = ",".join([sp.latex(self._staggered_offset(self.offsets, self.index[0])[i])
+                                       for i in range(len(self.offsets))])
             if self.is_absolute_access:
-                offset_str = "[abs]{}".format(offset_str)
-            if self.index and self.index != (0,):
-                return "%s[%s](%s)" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
+                offset_str = f"[abs]{offset_str}"
+
+            if FieldType.is_staggered(self._field):
+                if self.index and self.field.index_dimensions > 1:
+                    return f"{n}[{offset_str}]({self.index[1:] if len(self.index) > 2 else self.index[1]})"
+                else:
+                    return f"{n}[{offset_str}]"
+            else:
+                if self.index and self.field.index_dimensions > 0:
+                    return f"{n}[{offset_str}]({self.index if len(self.index) > 1 else self.index[0]})"
+                else:
+                    return f"{n}[{offset_str}]"
+
+
+def fields(description=None, index_dimensions=0, layout=None,
+           field_type=FieldType.GENERIC, **kwargs) -> Union[Field, List[Field]]:
+    """Creates pystencils fields from a string description.
+
+    Examples:
+        Create a 2D scalar and vector field:
+            >>> s, v = fields("s, v(2): double[2D]")
+            >>> assert s.spatial_dimensions == 2 and s.index_dimensions == 0
+            >>> assert (v.spatial_dimensions, v.index_dimensions, v.index_shape) == (2, 1, (2,))
+
+        Create an integer field of shape (10, 20):
+            >>> f = fields("f : int32[10, 20]")
+            >>> f.has_fixed_shape, f.shape
+            (True, (10, 20))
+
+        Numpy arrays can be used as template for shape and data type of field:
+            >>> arr_s, arr_v = np.zeros([20, 20]), np.zeros([20, 20, 2])
+            >>> s, v = fields("s, v(2)", s=arr_s, v=arr_v)
+            >>> assert s.index_dimensions == 0 and s.dtype.numpy_dtype == arr_s.dtype
+            >>> assert v.index_shape == (2,)
+
+        Format string can be left out, field names are taken from keyword arguments.
+            >>> fields(f1=arr_s, f2=arr_s)
+            [f1: double[20,20], f2: double[20,20]]
+
+        The keyword names ``index_dimension`` and ``layout`` have special meaning, don't use them for field names
+            >>> f = fields(f=arr_v, index_dimensions=1)
+            >>> assert f.index_dimensions == 1
+            >>> f = fields("pdfs(19) : float32[3D]", layout='fzyx')
+            >>> f.layout
+            (2, 1, 0)
+    """
+    result = []
+    if description:
+        field_descriptions, dtype, shape = _parse_description(description)
+        layout = 'numpy' if layout is None else layout
+        for field_name, idx_shape in field_descriptions:
+            if field_name in kwargs:
+                arr = kwargs[field_name]
+                idx_shape_of_arr = () if not len(idx_shape) else arr.shape[-len(idx_shape):]
+                assert idx_shape_of_arr == idx_shape
+                f = Field.create_from_numpy_array(field_name, kwargs[field_name], index_dimensions=len(idx_shape),
+                                                  field_type=field_type)
+            elif isinstance(shape, tuple):
+                f = Field.create_fixed_size(field_name, shape + idx_shape, dtype=dtype,
+                                            index_dimensions=len(idx_shape), layout=layout, field_type=field_type)
+            elif isinstance(shape, int):
+                f = Field.create_generic(field_name, spatial_dimensions=shape, dtype=dtype,
+                                         index_shape=idx_shape, layout=layout, field_type=field_type)
+            elif shape is None:
+                f = Field.create_generic(field_name, spatial_dimensions=2, dtype=dtype,
+                                         index_shape=idx_shape, layout=layout, field_type=field_type)
             else:
-                return "%s[%s]" % (n, offset_str)
+                assert False
+            result.append(f)
+    else:
+        assert layout is None, "Layout can not be specified when creating Field from numpy array"
+        for field_name, arr in kwargs.items():
+            result.append(Field.create_from_numpy_array(field_name, arr, index_dimensions=index_dimensions,
+                                                        field_type=field_type))
+
+    if len(result) == 0:
+        raise ValueError("Could not parse field description")
+    elif len(result) == 1:
+        return result[0]
+    else:
+        return result
 
 
 def get_layout_from_strides(strides: Sequence[int], index_dimension_ids: Optional[List[int]] = None):
@@ -669,8 +940,6 @@ def create_numpy_array_with_layout(shape, layout, alignment=False, byte_offset=0
     if not alignment:
         res = np.empty(shape, order='c', **kwargs)
     else:
-        if alignment is True:
-            alignment = 8 * 4
         res = aligned_empty(shape, alignment, byte_offset=byte_offset, **kwargs)
 
     for a, b in reversed(swaps):
@@ -679,24 +948,35 @@ def create_numpy_array_with_layout(shape, layout, alignment=False, byte_offset=0
 
 
 def spatial_layout_string_to_tuple(layout_str: str, dim: int) -> Tuple[int, ...]:
-    if layout_str in ('fzyx', 'zyxf'):
-        assert dim <= 3
-        return tuple(reversed(range(dim)))
+    if dim <= 0:
+        raise ValueError("Dimensionality must be positive")
+    
+    layout_str = layout_str.lower()
 
-    if layout_str in ('fzyx', 'f', 'reverse_numpy', 'SoA'):
+    if layout_str in ('fzyx', 'zyxf', 'soa', 'aos'):
+        if dim > 3:
+            raise ValueError(f"Invalid spatial dimensionality for layout descriptor {layout_str}: May be at most 3.")
+        return tuple(reversed(range(dim)))
+    
+    if layout_str in ('f', 'reverse_numpy'):
         return tuple(reversed(range(dim)))
-    elif layout_str in ('c', 'numpy', 'AoS'):
+    elif layout_str in ('c', 'numpy'):
         return tuple(range(dim))
     raise ValueError("Unknown layout descriptor " + layout_str)
 
 
 def layout_string_to_tuple(layout_str, dim):
+    if dim <= 0:
+        raise ValueError("Dimensionality must be positive")
+    
     layout_str = layout_str.lower()
     if layout_str == 'fzyx' or layout_str == 'soa':
-        assert dim <= 4
+        if dim > 4:
+            raise ValueError(f"Invalid total dimensionality for layout descriptor {layout_str}: May be at most 4.")
         return tuple(reversed(range(dim)))
     elif layout_str == 'zyxf' or layout_str == 'aos':
-        assert dim <= 4
+        if dim > 4:
+            raise ValueError(f"Invalid total dimensionality for layout descriptor {layout_str}: May be at most 4.")
         return tuple(reversed(range(dim - 1))) + (dim - 1,)
     elif layout_str == 'f' or layout_str == 'reverse_numpy':
         return tuple(reversed(range(dim)))
@@ -759,16 +1039,17 @@ type_description_regex = re.compile(r"""
 """, re.VERBOSE | re.IGNORECASE)
 
 
-def _parse_description(description):
-    def parse_part1(d):
+def _parse_part1(d):
+    result = field_description_regex.match(d)
+    while result:
+        name, index_str = result.group(1), result.group(2)
+        index = tuple(int(e) for e in index_str.split(",")) if index_str else ()
+        yield name, index
+        d = d[result.end():]
         result = field_description_regex.match(d)
-        while result:
-            name, index_str = result.group(1), result.group(2)
-            index = tuple(int(e) for e in index_str.split(",")) if index_str else ()
-            yield name, index
-            d = d[result.end():]
-            result = field_description_regex.match(d)
 
+
+def _parse_description(description):
     def parse_part2(d):
         result = type_description_regex.match(d)
         if result:
@@ -792,7 +1073,7 @@ def _parse_description(description):
     else:
         field_description, field_info = description, 'float64[2D]'
 
-    fields_info = [e for e in parse_part1(field_description)]
+    fields_info = [e for e in _parse_part1(field_description)]
     if not field_info:
         raise ValueError("Could not parse field description")
 

src/pystencils/functions.py

+import sympy as sp
+from pystencils.typing import PointerType
+
+
+class DivFunc(sp.Function):
+    """
+    DivFunc represents a division operation, since sympy represents divisions with ^-1
+    """
+    is_Atom = True
+    is_real = True
+
+    def __new__(cls, *args, **kwargs):
+        if len(args) != 2:
+            raise ValueError(f'{cls} takes only 2 arguments, instead {len(args)} received!')
+        divisor, dividend, *other_args = args
+
+        return sp.Function.__new__(cls, divisor, dividend, *other_args, **kwargs)
+
+    def _eval_evalf(self, *args, **kwargs):
+        return self.divisor.evalf() / self.dividend.evalf()
+
+    @property
+    def divisor(self):
+        return self.args[0]
+
+    @property
+    def dividend(self):
+        return self.args[1]
+
+
+class AddressOf(sp.Function):
+    """
+    AddressOf is the '&' operation in C. It gets the address of a lvalue.
+    """
+    is_Atom = True
+
+    def __new__(cls, arg):
+        obj = sp.Function.__new__(cls, arg)
+        return obj
+
+    @property
+    def canonical(self):
+        if hasattr(self.args[0], 'canonical'):
+            return self.args[0].canonical
+        else:
+            raise NotImplementedError()
+
+    @property
+    def is_commutative(self):
+        return self.args[0].is_commutative
+
+    @property
+    def dtype(self):
+        if hasattr(self.args[0], 'dtype'):
+            return PointerType(self.args[0].dtype, restrict=True)
+        else:
+            raise ValueError(f'pystencils supports only non void pointers. Current address_of type: {self.args[0]}')

pystencils/gpucuda/__init__.py → src/pystencils/gpu/__init__.py

-from pystencils.gpucuda.kernelcreation import create_cuda_kernel, created_indexed_cuda_kernel
-from pystencils.gpucuda.cudajit import make_python_function
+from pystencils.gpu.gpu_array_handler import GPUArrayHandler, GPUNotAvailableHandler
+from pystencils.gpu.gpujit import make_python_function
+from pystencils.gpu.kernelcreation import create_cuda_kernel, created_indexed_cuda_kernel
+
 from .indexing import AbstractIndexing, BlockIndexing, LineIndexing
-__all__ = ['create_cuda_kernel', 'created_indexed_cuda_kernel', 'make_python_function',
+
+__all__ = ['GPUArrayHandler', 'GPUNotAvailableHandler',
+           'create_cuda_kernel', 'created_indexed_cuda_kernel', 'make_python_function',
            'AbstractIndexing', 'BlockIndexing', 'LineIndexing']

src/pystencils/gpu/gpu_array_handler.py

+try:
+    import cupy as cp
+    import cupyx as cpx
+except ImportError:
+    cp = None
+    cpx = None
+
+import numpy as np
+
+
+class GPUArrayHandler:
+    def __init__(self, device_number):
+        self._device_number = device_number
+
+    def zeros(self, shape, dtype=np.float64, order='C'):
+        with cp.cuda.Device(self._device_number):
+            return cp.zeros(shape=shape, dtype=dtype, order=order)
+
+    def ones(self, shape, dtype=np.float64, order='C'):
+        with cp.cuda.Device(self._device_number):
+            return cp.ones(shape=shape, dtype=dtype, order=order)
+
+    def empty(self, shape, dtype=np.float64, order='C'):
+        with cp.cuda.Device(self._device_number):
+            return cp.empty(shape=shape, dtype=dtype, order=order)
+
+    def to_gpu(self, numpy_array):
+        swaps = _get_index_swaps(numpy_array)
+        if numpy_array.base is not None and isinstance(numpy_array.base, np.ndarray):
+            with cp.cuda.Device(self._device_number):
+                gpu_array = cp.asarray(numpy_array.base)
+            for a, b in reversed(swaps):
+                gpu_array = gpu_array.swapaxes(a, b)
+            return gpu_array
+        else:
+            return cp.asarray(numpy_array)
+
+    def upload(self, array, numpy_array):
+        assert self._device_number == array.device.id
+        if numpy_array.base is not None and isinstance(numpy_array.base, np.ndarray):
+            with cp.cuda.Device(self._device_number):
+                array.base.set(numpy_array.base)
+        else:
+            with cp.cuda.Device(self._device_number):
+                array.set(numpy_array)
+
+    def download(self, array, numpy_array):
+        assert self._device_number == array.device.id
+        if numpy_array.base is not None and isinstance(numpy_array.base, np.ndarray):
+            with cp.cuda.Device(self._device_number):
+                numpy_array.base[:] = array.base.get()
+        else:
+            with cp.cuda.Device(self._device_number):
+                numpy_array[:] = array.get()
+
+    def randn(self, shape, dtype=np.float64):
+        with cp.cuda.Device(self._device_number):
+            return cp.random.randn(*shape, dtype=dtype)
+
+    @staticmethod
+    def pinned_numpy_array(layout, shape, dtype):
+        assert set(layout) == set(range(len(shape))), "Wrong layout descriptor"
+        cur_layout = list(range(len(shape)))
+        swaps = []
+        for i in range(len(layout)):
+            if cur_layout[i] != layout[i]:
+                index_to_swap_with = cur_layout.index(layout[i])
+                swaps.append((i, index_to_swap_with))
+                cur_layout[i], cur_layout[index_to_swap_with] = cur_layout[index_to_swap_with], cur_layout[i]
+        assert tuple(cur_layout) == tuple(layout)
+
+        shape = list(shape)
+        for a, b in swaps:
+            shape[a], shape[b] = shape[b], shape[a]
+
+        res = cpx.empty_pinned(tuple(shape), order='c', dtype=dtype)
+
+        for a, b in reversed(swaps):
+            res = res.swapaxes(a, b)
+        return res
+
+    from_numpy = to_gpu
+
+
+class GPUNotAvailableHandler:
+    def __getattribute__(self, name):
+        raise NotImplementedError("Unable to utilise cupy! Please make sure cupy works correctly in your setup!")
+
+
+def _get_index_swaps(array):
+    swaps = []
+    if array.base is not None and isinstance(array.base, np.ndarray):
+        for stride in array.base.strides:
+            index_base = array.base.strides.index(stride)
+            index_view = array.strides.index(stride)
+            if index_base != index_view and (index_view, index_base) not in swaps:
+                swaps.append((index_base, index_view))
+    return swaps

pystencils/gpucuda/cudajit.py → src/pystencils/gpu/gpujit.py

 import numpy as np
-from pystencils.backends.cbackend import generate_c, get_headers
-from pystencils.kernelparameters import FieldPointerSymbol
-from pystencils.data_types import StructType
+
+from pystencils.backends.cbackend import get_headers
+from pystencils.backends.cuda_backend import generate_cuda
+from pystencils.typing import StructType
 from pystencils.field import FieldType
 from pystencils.include import get_pystencils_include_path
-
+from pystencils.kernel_wrapper import KernelWrapper
+from pystencils.typing import BasicType, FieldPointerSymbol
 
 USE_FAST_MATH = True
 
 
-def make_python_function(kernel_function_node, argument_dict=None):
+def get_cubic_interpolation_include_paths():
+    from os.path import join, dirname
+
+    return [join(dirname(__file__), "CubicInterpolationCUDA", "code"),
+            join(dirname(__file__), "CubicInterpolationCUDA", "code", "internal")]
+
+
+def make_python_function(kernel_function_node, argument_dict=None, custom_backend=None):
     """
     Creates a kernel function from an abstract syntax tree which
-    was created e.g. by :func:`pystencils.gpucuda.create_cuda_kernel`
-    or :func:`pystencils.gpucuda.created_indexed_cuda_kernel`
+    was created e.g. by :func:`pystencils.gpu.create_cuda_kernel`
+    or :func:`pystencils.gpu.created_indexed_cuda_kernel`
 
     Args:
         kernel_function_node: the abstract syntax tree
         argument_dict: parameters passed here are already fixed. Remaining parameters have to be passed to the
                        returned kernel functor.
+        custom_backend: use own custom printer for code generation
 
     Returns:
         compiled kernel as Python function
     """
-    import pycuda.autoinit  # NOQA
-    from pycuda.compiler import SourceModule
+    import cupy as cp
 
     if argument_dict is None:
         argument_dict = {}
 
-    header_list = ['<stdint.h>'] + list(get_headers(kernel_function_node))
-    includes = "\n".join(["#include %s" % (include_file,) for include_file in header_list])
+    headers = get_headers(kernel_function_node)
+    if cp.cuda.runtime.is_hip:
+        headers.add('"gpu_defines.h"')
+        for field in kernel_function_node.fields_accessed:
+            if isinstance(field.dtype, BasicType) and field.dtype.is_half():
+                headers.add('<hip/hip_fp16.h>')
+    else:
+        headers.update({'"gpu_defines.h"', '<cstdint>'})
+        for field in kernel_function_node.fields_accessed:
+            if isinstance(field.dtype, BasicType) and field.dtype.is_half():
+                headers.add('<cuda_fp16.h>')
+
+    header_list = sorted(headers)
+    includes = "\n".join([f"#include {include_file}" for include_file in header_list])
 
     code = includes + "\n"
     code += "#define FUNC_PREFIX __global__\n"
     code += "#define RESTRICT __restrict__\n\n"
-    code += str(generate_c(kernel_function_node, dialect='cuda'))
-    options = options = ["-w", "-std=c++11", "-Wno-deprecated-gpu-targets", "-use_fast_math"]
+    code += 'extern "C" {\n%s\n}\n' % str(generate_cuda(kernel_function_node, custom_backend=custom_backend))
+
+    options = ["-w", "-std=c++11"]
     if USE_FAST_MATH:
         options.append("-use_fast_math")
-    mod = SourceModule(code, options=options, include_dirs=[get_pystencils_include_path()])
-    func = mod.get_function(kernel_function_node.function_name)
+    options.append("-I" + get_pystencils_include_path())
 
+    func = cp.RawKernel(code, kernel_function_node.function_name, options=tuple(options), backend="nvrtc", jitify=True)
     parameters = kernel_function_node.get_parameters()
 
     cache = {}
@@ -52,7 +74,10 @@ def make_python_function(kernel_function_node, argument_dict=None):
                          for k, v in kwargs.items()))
         try:
             args, block_and_thread_numbers = cache[key]
-            func(*args, **block_and_thread_numbers)
+            device = set(a.device.id for a in args if type(a) is cp.ndarray)
+            assert len(device) == 1, "All arrays used by a kernel need to be allocated on the same device"
+            with cp.cuda.Device(device.pop()):
+                func(block_and_thread_numbers['grid'], block_and_thread_numbers['block'], args)
         except KeyError:
             full_arguments = argument_dict.copy()
             full_arguments.update(kwargs)
@@ -63,14 +88,20 @@ def make_python_function(kernel_function_node, argument_dict=None):
             block_and_thread_numbers['block'] = tuple(int(i) for i in block_and_thread_numbers['block'])
             block_and_thread_numbers['grid'] = tuple(int(i) for i in block_and_thread_numbers['grid'])
 
-            args = _build_numpy_argument_list(parameters, full_arguments)
+            args = tuple(_build_numpy_argument_list(parameters, full_arguments))
             cache[key] = (args, block_and_thread_numbers)
             cache_values.append(kwargs)  # keep objects alive such that ids remain unique
-            func(*args, **block_and_thread_numbers)
-        # import pycuda.driver as cuda
+            device = set(a.device.id for a in args if type(a) is cp.ndarray)
+            assert len(device) == 1, "All arrays used by a kernel need to be allocated on the same device"
+            with cp.cuda.Device(device.pop()):
+                func(block_and_thread_numbers['grid'], block_and_thread_numbers['block'], args)
+                # useful for debugging:
+                # cp.cuda.runtime.deviceSynchronize()
+
         # cuda.Context.synchronize() # useful for debugging, to get errors right after kernel was called
-    wrapper.ast = kernel_function_node
-    wrapper.parameters = kernel_function_node.get_parameters()
+    ast = kernel_function_node
+    parameters = kernel_function_node.get_parameters()
+    wrapper = KernelWrapper(wrapper, parameters, ast)
     wrapper.num_regs = func.num_regs
     return wrapper
 
@@ -85,8 +116,8 @@ def _build_numpy_argument_list(parameters, argument_dict):
             actual_type = array.dtype
             expected_type = param.fields[0].dtype.numpy_dtype
             if expected_type != actual_type:
-                raise ValueError("Data type mismatch for field '%s'. Expected '%s' got '%s'." %
-                                 (param.field_name, expected_type, actual_type))
+                raise ValueError(f"Data type mismatch for field {param.field_name}. "
+                                 f"Expected {expected_type} got {actual_type}.")
             result.append(array)
         elif param.is_field_stride:
             cast_to_dtype = param.symbol.dtype.numpy_dtype.type
@@ -121,22 +152,22 @@ def _check_arguments(parameter_specification, argument_dict):
             try:
                 field_arr = argument_dict[symbolic_field.name]
             except KeyError:
-                raise KeyError("Missing field parameter for kernel call " + str(symbolic_field))
+                raise KeyError(f"Missing field parameter for kernel call {str(symbolic_field)}")
 
             if symbolic_field.has_fixed_shape:
                 symbolic_field_shape = tuple(int(i) for i in symbolic_field.shape)
                 if isinstance(symbolic_field.dtype, StructType):
                     symbolic_field_shape = symbolic_field_shape[:-1]
                 if symbolic_field_shape != field_arr.shape:
-                    raise ValueError("Passed array '%s' has shape %s which does not match expected shape %s" %
-                                     (symbolic_field.name, str(field_arr.shape), str(symbolic_field.shape)))
+                    raise ValueError(f"Passed array {symbolic_field.name} has shape {str(field_arr.shape)} "
+                                     f"which does not match expected shape {str(symbolic_field.shape)}")
             if symbolic_field.has_fixed_shape:
                 symbolic_field_strides = tuple(int(i) * field_arr.dtype.itemsize for i in symbolic_field.strides)
                 if isinstance(symbolic_field.dtype, StructType):
                     symbolic_field_strides = symbolic_field_strides[:-1]
                 if symbolic_field_strides != field_arr.strides:
-                    raise ValueError("Passed array '%s' has strides %s which does not match expected strides %s" %
-                                     (symbolic_field.name, str(field_arr.strides), str(symbolic_field_strides)))
+                    raise ValueError(f"Passed array {symbolic_field.name} has strides {str(field_arr.strides)} "
+                                     f"which does not match expected strides {str(symbolic_field_strides)}")
 
             if FieldType.is_indexed(symbolic_field):
                 index_arr_shapes.add(field_arr.shape[:symbolic_field.spatial_dimensions])
@@ -144,9 +175,9 @@ def _check_arguments(parameter_specification, argument_dict):
                 array_shapes.add(field_arr.shape[:symbolic_field.spatial_dimensions])
 
     if len(array_shapes) > 1:
-        raise ValueError("All passed arrays have to have the same size " + str(array_shapes))
+        raise ValueError(f"All passed arrays have to have the same size {str(array_shapes)}")
     if len(index_arr_shapes) > 1:
-        raise ValueError("All passed index arrays have to have the same size " + str(array_shapes))
+        raise ValueError(f"All passed index arrays have to have the same size {str(array_shapes)}")
 
     if len(index_arr_shapes) > 0:
         return list(index_arr_shapes)[0]

src/pystencils/gpu/indexing.py

+import abc
+from functools import partial
+import math
+from typing import List, Tuple
+
+import sympy as sp
+from sympy.core.cache import cacheit
+
+from pystencils.astnodes import Block, Conditional, SympyAssignment
+from pystencils.typing import TypedSymbol, create_type
+from pystencils.integer_functions import div_ceil, div_floor
+from pystencils.sympyextensions import is_integer_sequence, prod
+
+
+class ThreadIndexingSymbol(TypedSymbol):
+    def __new__(cls, *args, **kwds):
+        obj = ThreadIndexingSymbol.__xnew_cached_(cls, *args, **kwds)
+        return obj
+
+    def __new_stage2__(cls, name, dtype, *args, **kwargs):
+        obj = super(ThreadIndexingSymbol, cls).__xnew__(cls, name, dtype, *args, **kwargs)
+        return obj
+
+    __xnew__ = staticmethod(__new_stage2__)
+    __xnew_cached_ = staticmethod(cacheit(__new_stage2__))
+
+
+BLOCK_IDX = [ThreadIndexingSymbol("blockIdx." + coord, create_type("int32")) for coord in ('x', 'y', 'z')]
+THREAD_IDX = [ThreadIndexingSymbol("threadIdx." + coord, create_type("int32")) for coord in ('x', 'y', 'z')]
+BLOCK_DIM = [ThreadIndexingSymbol("blockDim." + coord, create_type("int32")) for coord in ('x', 'y', 'z')]
+GRID_DIM = [ThreadIndexingSymbol("gridDim." + coord, create_type("int32")) for coord in ('x', 'y', 'z')]
+
+
+class AbstractIndexing(abc.ABC):
+    """
+    Abstract base class for all Indexing classes. An Indexing class defines how an iteration space is mapped
+    to GPU's block and grid system. It calculates indices based on GPU's thread and block indices
+    and computes the number of blocks and threads a kernel is started with.
+    The Indexing class is created with an iteration space that is given as list of slices to determine start, stop
+    and the step size for each coordinate. Further the data_layout is given as tuple to determine the fast and slow
+    coordinates. This is important to get an optimal mapping of coordinates to GPU threads.
+    """
+
+    def __init__(self, iteration_space: Tuple[slice], data_layout: Tuple):
+        for iter_space in iteration_space:
+            assert isinstance(iter_space, slice), f"iteration_space must be of type Tuple[slice], " \
+                                                  f"not tuple of type {type(iter_space)}"
+        self._iteration_space = iteration_space
+        self._data_layout = data_layout
+        self._dim = len(iteration_space)
+
+    @property
+    def iteration_space(self):
+        """Iteration space to loop over"""
+        return self._iteration_space
+
+    @property
+    def data_layout(self):
+        """Data layout of the kernels arrays"""
+        return self._data_layout
+
+    @property
+    def dim(self):
+        """Number of spatial dimensions"""
+        return self._dim
+
+    @property
+    @abc.abstractmethod
+    def coordinates(self):
+        """Returns a sequence of coordinate expressions for (x,y,z) depending on symbolic GPU block and thread indices.
+        These symbolic indices can be obtained with the method `index_variables` """
+
+    @property
+    def index_variables(self):
+        """Sympy symbols for GPU's block and thread indices, and block and grid dimensions. """
+        return BLOCK_IDX + THREAD_IDX + BLOCK_DIM + GRID_DIM
+
+    @abc.abstractmethod
+    def get_loop_ctr_assignments(self, loop_counter_symbols) -> List[SympyAssignment]:
+        """Adds assignments for the loop counter symbols depending on the gpu threads.
+
+        Args:
+            loop_counter_symbols: typed symbols representing the loop counters
+        Returns:
+            assignments for the loop counters
+        """
+
+    @abc.abstractmethod
+    def call_parameters(self, arr_shape):
+        """Determine grid and block size for kernel call.
+
+        Args:
+            arr_shape: the numeric (not symbolic) shape of the array
+        Returns:
+            dict with keys 'blocks' and 'threads' with tuple values for number of (x,y,z) threads and blocks
+            the kernel should be started with
+        """
+
+    @abc.abstractmethod
+    def guard(self, kernel_content, arr_shape):
+        """In some indexing schemes not all threads of a block execute the kernel content.
+
+        This function can return a Conditional ast node, defining this execution guard.
+
+        Args:
+            kernel_content: the actual kernel contents which can e.g. be put into the Conditional node as true block
+            arr_shape: the numeric or symbolic shape of the field
+
+        Returns:
+            ast node, which is put inside the kernel function
+        """
+
+    @abc.abstractmethod
+    def max_threads_per_block(self):
+        """Return maximal number of threads per block for launch bounds. If this cannot be determined without
+        knowing the array shape return None for unknown """
+
+    @abc.abstractmethod
+    def symbolic_parameters(self):
+        """Set of symbols required in call_parameters code"""
+
+
+# -------------------------------------------- Implementations ---------------------------------------------------------
+
+
+class BlockIndexing(AbstractIndexing):
+    """Generic indexing scheme that maps sub-blocks of an array to GPU blocks.
+
+    Args:
+        iteration_space: list of slices to determine start, stop and the step size for each coordinate
+        data_layout: tuple specifying loop order with innermost loop last.
+                     This is the same format as returned by `Field.layout`.
+        permute_block_size_dependent_on_layout: if True the block_size is permuted such that the fastest coordinate
+                                                gets the largest amount of threads
+        compile_time_block_size: compile in concrete block size, otherwise the gpu variable 'blockDim' is used
+        maximum_block_size: maximum block size that is possible for the GPU. Set to 'auto' to let cupy define the
+                            maximum block size from the device properties
+        device_number: device number of the used GPU. By default, the zeroth device is used.
+    """
+
+    def __init__(self, iteration_space: Tuple[slice], data_layout: Tuple[int],
+                 block_size=(128, 2, 1), permute_block_size_dependent_on_layout=True, compile_time_block_size=False,
+                 maximum_block_size=(1024, 1024, 64), device_number=None):
+        super(BlockIndexing, self).__init__(iteration_space, data_layout)
+
+        if self._dim > 4:
+            raise NotImplementedError("This indexing scheme supports at most 4 spatial dimensions")
+
+        if permute_block_size_dependent_on_layout and self._dim < 4:
+            block_size = self.permute_block_size_according_to_layout(block_size, data_layout)
+
+        self._block_size = block_size
+        if maximum_block_size == 'auto':
+            assert device_number is not None, 'If "maximum_block_size" is set to "auto" a device number must be stated'
+            # Get device limits
+            import cupy as cp
+            # See https://github.com/cupy/cupy/issues/7676
+            if cp.cuda.runtime.is_hip:
+                maximum_block_size = tuple(cp.cuda.runtime.deviceGetAttribute(i, device_number) for i in range(26, 29))
+            else:
+                da = cp.cuda.Device(device_number).attributes
+                maximum_block_size = tuple(da[f"MaxBlockDim{c}"] for c in ["X", "Y", "Z"])
+
+        self._maximum_block_size = maximum_block_size
+        self._compile_time_block_size = compile_time_block_size
+        self._device_number = device_number
+
+    @property
+    def cuda_indices(self):
+        block_size = self._block_size if self._compile_time_block_size else BLOCK_DIM
+        indices = [block_index * bs + thread_idx
+                   for block_index, bs, thread_idx in zip(BLOCK_IDX, block_size, THREAD_IDX)]
+
+        return indices[:self._dim]
+
+    @property
+    def coordinates(self):
+        if self._dim < 4:
+            coordinates = [c + iter_slice.start for c, iter_slice in zip(self.cuda_indices, self._iteration_space)]
+            return coordinates[:self._dim]
+        else:
+            coordinates = list()
+            width = self._iteration_space[1].stop - self.iteration_space[1].start
+            coordinates.append(div_floor(self.cuda_indices[0], width))
+            coordinates.append(sp.Mod(self.cuda_indices[0], width))
+            coordinates.append(self.cuda_indices[1] + self.iteration_space[2].start)
+            coordinates.append(self.cuda_indices[2] + self.iteration_space[3].start)
+            return coordinates
+
+    def get_loop_ctr_assignments(self, loop_counter_symbols):
+        return _loop_ctr_assignments(loop_counter_symbols, self.coordinates, self._iteration_space)
+
+    def call_parameters(self, arr_shape):
+        numeric_iteration_slice = _get_numeric_iteration_slice(self._iteration_space, arr_shape)
+        widths = _get_widths(numeric_iteration_slice)
+
+        if len(widths) > 3:
+            widths = [widths[0] * widths[1], widths[2], widths[3]]
+
+        extend_bs = (1,) * (3 - len(self._block_size))
+        block_size = self._block_size + extend_bs
+        if not self._compile_time_block_size:
+            assert len(block_size) == 3
+            adapted_block_size = []
+            for i in range(len(widths)):
+                factor = div_floor(prod(block_size[:i]), prod(adapted_block_size))
+                adapted_block_size.append(sp.Min(block_size[i] * factor, widths[i]))
+            extend_adapted_bs = (1,) * (3 - len(adapted_block_size))
+            block_size = tuple(adapted_block_size) + extend_adapted_bs
+
+        block_size = tuple(sp.Min(bs, max_bs) for bs, max_bs in zip(block_size, self._maximum_block_size))
+        grid = tuple(div_ceil(length, block_size) for length, block_size in zip(widths, block_size))
+        extend_gr = (1,) * (3 - len(grid))
+
+        return {'block': block_size,
+                'grid': grid + extend_gr}
+
+    def guard(self, kernel_content, arr_shape):
+        arr_shape = arr_shape[:self._dim]
+        if len(self._iteration_space) - 1 == len(arr_shape):
+            numeric_iteration_slice = _get_numeric_iteration_slice(self._iteration_space[1:], arr_shape)
+            numeric_iteration_slice = [self.iteration_space[0]] + numeric_iteration_slice
+        else:
+            assert len(self._iteration_space) == len(arr_shape), "Iteration space must be equal to the array shape"
+            numeric_iteration_slice = _get_numeric_iteration_slice(self._iteration_space, arr_shape)
+        end = [s.stop if s.stop != 0 else 1 for s in numeric_iteration_slice]
+        for i, s in enumerate(numeric_iteration_slice):
+            if s.step and s.step != 1:
+                end[i] = div_ceil(s.stop - s.start, s.step) + s.start
+
+        if self._dim < 4:
+            conditions = [c < e for c, e in zip(self.coordinates, end)]
+        else:
+            end = [end[0] * end[1], end[2], end[3]]
+            coordinates = [c + iter_slice.start for c, iter_slice in zip(self.cuda_indices, self._iteration_space[1:])]
+            conditions = [c < e for c, e in zip(coordinates, end)]
+        condition = conditions[0]
+        for c in conditions[1:]:
+            condition = sp.And(condition, c)
+        return Block([Conditional(condition, kernel_content)])
+
+    def numeric_iteration_space(self, arr_shape):
+        return _get_numeric_iteration_slice(self._iteration_space, arr_shape)
+
+    def limit_block_size_by_register_restriction(self, block_size, required_registers_per_thread):
+        """Shrinks the block_size if there are too many registers used per block.
+        This is not done automatically, since the required_registers_per_thread are not known before compilation.
+        They can be obtained by ``func.num_regs`` from a cupy function.
+        Args:
+            block_size: used block size that is target for limiting
+            required_registers_per_thread: needed registers per thread
+        returns: smaller block_size if too many registers are used.
+        """
+        import cupy as cp
+
+        # See https://github.com/cupy/cupy/issues/7676
+        if cp.cuda.runtime.is_hip:
+            max_registers_per_block = cp.cuda.runtime.deviceGetAttribute(71, self._device_number)
+        else:
+            device = cp.cuda.Device(self._device_number)
+            da = device.attributes
+            max_registers_per_block = da.get("MaxRegistersPerBlock")
+
+        result = list(block_size)
+        while True:
+            required_registers = math.prod(result) * required_registers_per_thread
+            if required_registers <= max_registers_per_block:
+                return result
+            else:
+                largest_list_entry_idx = max(range(len(result)), key=lambda e: result[e])
+                assert result[largest_list_entry_idx] >= 2
+                result[largest_list_entry_idx] //= 2
+
+    @staticmethod
+    def permute_block_size_according_to_layout(block_size, layout):
+        """Returns modified block_size such that the fastest coordinate gets the biggest block dimension"""
+        if not is_integer_sequence(block_size):
+            return block_size
+        sorted_block_size = list(sorted(block_size, reverse=True))
+        while len(sorted_block_size) > len(layout):
+            sorted_block_size[0] *= sorted_block_size[-1]
+            sorted_block_size = sorted_block_size[:-1]
+
+        result = list(block_size)
+        for l, bs in zip(reversed(layout), sorted_block_size):
+            result[l] = bs
+        return tuple(result[:len(layout)])
+
+    def max_threads_per_block(self):
+        if is_integer_sequence(self._block_size):
+            return prod(self._block_size)
+        else:
+            return None
+
+    def symbolic_parameters(self):
+        return set(b for b in self._block_size if isinstance(b, sp.Symbol))
+
+
+class LineIndexing(AbstractIndexing):
+    """
+    Indexing scheme that assigns the innermost 'line' i.e. the elements which are adjacent in memory to a 1D GPU block.
+    The fastest coordinate is indexed with thread_idx.x, the remaining coordinates are mapped to block_idx.{x,y,z}
+    This indexing scheme supports up to 4 spatial dimensions, where the innermost dimensions is not larger than the
+    maximum amount of threads allowed in a GPU block (which depends on device).
+
+    Args:
+        iteration_space: list of slices to determine start, stop and the step size for each coordinate
+        data_layout: tuple to determine the fast and slow coordinates.
+    """
+
+    def __init__(self, iteration_space: Tuple[slice], data_layout: Tuple):
+        super(LineIndexing, self).__init__(iteration_space, data_layout)
+
+        if len(iteration_space) > 4:
+            raise NotImplementedError("This indexing scheme supports at most 4 spatial dimensions")
+
+    @property
+    def cuda_indices(self):
+        available_indices = [THREAD_IDX[0]] + BLOCK_IDX
+        coordinates = available_indices[:self.dim]
+
+        fastest_coordinate = self.data_layout[-1]
+        coordinates[0], coordinates[fastest_coordinate] = coordinates[fastest_coordinate], coordinates[0]
+
+        return coordinates
+
+    @property
+    def coordinates(self):
+        return [i + o.start for i, o in zip(self.cuda_indices, self._iteration_space)]
+
+    def get_loop_ctr_assignments(self, loop_counter_symbols):
+        return _loop_ctr_assignments(loop_counter_symbols, self.coordinates, self._iteration_space)
+
+    def call_parameters(self, arr_shape):
+        numeric_iteration_slice = _get_numeric_iteration_slice(self._iteration_space, arr_shape)
+        widths = _get_widths(numeric_iteration_slice)
+
+        def get_shape_of_cuda_idx(cuda_idx):
+            if cuda_idx not in self.cuda_indices:
+                return 1
+            else:
+                idx = self.cuda_indices.index(cuda_idx)
+                return widths[idx]
+
+        return {'block': tuple([get_shape_of_cuda_idx(idx) for idx in THREAD_IDX]),
+                'grid': tuple([get_shape_of_cuda_idx(idx) for idx in BLOCK_IDX])}
+
+    def guard(self, kernel_content, arr_shape):
+        return kernel_content
+
+    def max_threads_per_block(self):
+        return None
+
+    def symbolic_parameters(self):
+        return set()
+
+    def numeric_iteration_space(self, arr_shape):
+        return _get_numeric_iteration_slice(self._iteration_space, arr_shape)
+
+
+# -------------------------------------- Helper functions --------------------------------------------------------------
+
+def _get_numeric_iteration_slice(iteration_slice, arr_shape):
+    res = []
+    for slice_component, shape in zip(iteration_slice, arr_shape):
+        result_slice = slice_component
+        if not isinstance(result_slice.start, int):
+            start = result_slice.start
+            assert len(start.free_symbols) == 1
+            start = start.subs({symbol: shape for symbol in start.free_symbols})
+            result_slice = slice(start, result_slice.stop, result_slice.step)
+        if not isinstance(result_slice.stop, int):
+            stop = result_slice.stop
+            assert len(stop.free_symbols) == 1
+            stop = stop.subs({symbol: shape for symbol in stop.free_symbols})
+            result_slice = slice(result_slice.start, stop, result_slice.step)
+        assert isinstance(result_slice.step, int)
+        res.append(result_slice)
+    return res
+
+
+def _get_widths(iteration_slice):
+    widths = []
+    for iter_slice in iteration_slice:
+        step = iter_slice.step
+        assert isinstance(step, int), f"Step can only be of type int not of type {type(step)}"
+        start = iter_slice.start
+        stop = iter_slice.stop
+        if step == 1:
+            if stop - start == 0:
+                widths.append(1)
+            else:
+                widths.append(stop - start)
+        else:
+            width = (stop - start) / step
+            if isinstance(width, int):
+                widths.append(width)
+            elif isinstance(width, float):
+                widths.append(math.ceil(width))
+            else:
+                widths.append(div_ceil(stop - start, step))
+    return widths
+
+
+def _loop_ctr_assignments(loop_counter_symbols, coordinates, iteration_space):
+    loop_ctr_assignments = []
+    for loop_counter, coordinate, iter_slice in zip(loop_counter_symbols, coordinates, iteration_space):
+        if isinstance(iter_slice, slice) and iter_slice.step > 1:
+            offset = (iter_slice.step * iter_slice.start) - iter_slice.start
+            loop_ctr_assignments.append(SympyAssignment(loop_counter, coordinate * iter_slice.step - offset))
+        elif iter_slice.start == iter_slice.stop:
+            loop_ctr_assignments.append(SympyAssignment(loop_counter, 0))
+        else:
+            loop_ctr_assignments.append(SympyAssignment(loop_counter, coordinate))
+
+    return loop_ctr_assignments
+
+
+def indexing_creator_from_params(gpu_indexing, gpu_indexing_params):
+    if isinstance(gpu_indexing, str):
+        if gpu_indexing == 'block':
+            indexing_creator = BlockIndexing
+        elif gpu_indexing == 'line':
+            indexing_creator = LineIndexing
+        else:
+            raise ValueError(f"Unknown GPU indexing {gpu_indexing}. Valid values are 'block' and 'line'")
+        if gpu_indexing_params:
+            indexing_creator = partial(indexing_creator, **gpu_indexing_params)
+        return indexing_creator
+    else:
+        return gpu_indexing

pystencils/gpucuda/kernelcreation.py → src/pystencils/gpu/kernelcreation.py

-from functools import partial
+import sympy as sp
 
-from pystencils.gpucuda.indexing import BlockIndexing
-from pystencils.transformations import resolve_field_accesses, add_types, parse_base_pointer_info, \
-    get_common_shape, resolve_buffer_accesses, unify_shape_symbols, get_base_buffer_index
-from pystencils.astnodes import Block, KernelFunction, SympyAssignment, LoopOverCoordinate
-from pystencils.data_types import TypedSymbol, BasicType, StructType
-from pystencils import Field, FieldType
-from pystencils.gpucuda.cudajit import make_python_function
+from pystencils.astnodes import Block, KernelFunction, LoopOverCoordinate, SympyAssignment
+from pystencils.config import CreateKernelConfig
+from pystencils.typing import StructType, TypedSymbol
+from pystencils.typing.transformations import add_types
+from pystencils.field import Field, FieldType
+from pystencils.enums import Target, Backend
+from pystencils.gpu.gpujit import make_python_function
+from pystencils.node_collection import NodeCollection
+from pystencils.gpu.indexing import indexing_creator_from_params
+from pystencils.slicing import normalize_slice
+from pystencils.transformations import (
+    get_base_buffer_index, get_common_field, get_common_indexed_element, parse_base_pointer_info,
+    resolve_buffer_accesses, resolve_field_accesses, unify_shape_symbols)
 
 
-def create_cuda_kernel(assignments, function_name="kernel", type_info=None, indexing_creator=BlockIndexing,
-                       iteration_slice=None, ghost_layers=None, skip_independence_check=False):
-    fields_read, fields_written, assignments = add_types(assignments, type_info, not skip_independence_check)
+def create_cuda_kernel(assignments: NodeCollection, config: CreateKernelConfig):
+
+    function_name = config.function_name
+    indexing_creator = indexing_creator_from_params(config.gpu_indexing, config.gpu_indexing_params)
+    iteration_slice = config.iteration_slice
+    ghost_layers = config.ghost_layers
+
+    fields_written = assignments.bound_fields
+    fields_read = assignments.rhs_fields
+    assignments = assignments.all_assignments
+
+    assignments = add_types(assignments, config)
+
     all_fields = fields_read.union(fields_written)
     read_only_fields = set([f.name for f in fields_read - fields_written])
 
@@ -20,11 +36,16 @@ def create_cuda_kernel(assignments, function_name="kernel", type_info=None, inde
 
     field_accesses = set()
     num_buffer_accesses = 0
+    indexed_elements = set()
     for eq in assignments:
+        indexed_elements.update(eq.atoms(sp.Indexed))
         field_accesses.update(eq.atoms(Field.Access))
+        field_accesses = {e for e in field_accesses if not e.is_absolute_access}
         num_buffer_accesses += sum(1 for access in eq.atoms(Field.Access) if FieldType.is_buffer(access.field))
 
-    common_shape = get_common_shape(fields_without_buffers)
+    # common shape and field to from the iteration space
+    common_field = get_common_field(fields_without_buffers)
+    common_shape = common_field.spatial_shape
 
     if iteration_slice is None:
         # determine iteration slice from ghost layers
@@ -42,33 +63,51 @@ def create_cuda_kernel(assignments, function_name="kernel", type_info=None, inde
                 iteration_slice.append(slice(ghost_layers[i][0],
                                              -ghost_layers[i][1] if ghost_layers[i][1] > 0 else None))
 
-    indexing = indexing_creator(field=list(fields_without_buffers)[0], iteration_slice=iteration_slice)
-    coord_mapping = indexing.coordinates
-
-    cell_idx_assignments = [SympyAssignment(LoopOverCoordinate.get_loop_counter_symbol(i), value)
-                            for i, value in enumerate(coord_mapping)]
-    cell_idx_symbols = [LoopOverCoordinate.get_loop_counter_symbol(i) for i, _ in enumerate(coord_mapping)]
-    assignments = cell_idx_assignments + assignments
+        iteration_space = normalize_slice(iteration_slice, common_shape)
+    else:
+        iteration_space = normalize_slice(iteration_slice, common_shape)
+    
+    iteration_space = tuple([s if isinstance(s, slice) else slice(s, s + 1, 1) for s in iteration_space])
+
+    loop_counter_symbols = [LoopOverCoordinate.get_loop_counter_symbol(i) for i in range(len(iteration_space))]
+
+    if len(indexed_elements) > 0:
+        common_indexed_element = get_common_indexed_element(indexed_elements)
+        index = common_indexed_element.indices[0].atoms(TypedSymbol)
+        assert len(index) == 1, "index expressions must only contain one symbol representing the index"
+        indexing = indexing_creator(iteration_space=(slice(0, common_indexed_element.shape[0], 1), *iteration_space),
+                                    data_layout=common_field.layout)
+        extended_ctrs = [index.pop(), *loop_counter_symbols]
+        loop_counter_assignments = indexing.get_loop_ctr_assignments(extended_ctrs)
+    else:
+        indexing = indexing_creator(iteration_space=iteration_space, data_layout=common_field.layout)
+        loop_counter_assignments = indexing.get_loop_ctr_assignments(loop_counter_symbols)
+    assignments = loop_counter_assignments + assignments
+    block = indexing.guard(Block(assignments), common_shape)
 
-    block = Block(assignments)
-
-    block = indexing.guard(block, common_shape)
     unify_shape_symbols(block, common_shape=common_shape, fields=fields_without_buffers)
 
-    ast = KernelFunction(block, function_name=function_name, ghost_layers=ghost_layers, backend='gpucuda')
+    ast = KernelFunction(block,
+                         Target.GPU,
+                         Backend.CUDA,
+                         make_python_function,
+                         ghost_layers,
+                         function_name,
+                         assignments=assignments)
     ast.global_variables.update(indexing.index_variables)
 
-    base_pointer_spec = [['spatialInner0']]
+    base_pointer_spec = config.base_pointer_specification
+    if base_pointer_spec is None:
+        base_pointer_spec = []
     base_pointer_info = {f.name: parse_base_pointer_info(base_pointer_spec, [2, 1, 0],
                                                          f.spatial_dimensions, f.index_dimensions)
                          for f in all_fields}
 
-    coord_mapping = {f.name: cell_idx_symbols for f in all_fields}
-
-    loop_strides = list(fields_without_buffers)[0].shape
+    coord_mapping = {f.name: loop_counter_symbols for f in all_fields}
 
     if any(FieldType.is_buffer(f) for f in all_fields):
-        resolve_buffer_accesses(ast, get_base_buffer_index(ast, indexing.coordinates, loop_strides), read_only_fields)
+        base_buffer_index = get_base_buffer_index(ast, loop_counter_symbols, iteration_space)
+        resolve_buffer_accesses(ast, base_buffer_index, read_only_fields)
 
     resolve_field_accesses(ast, read_only_fields, field_to_base_pointer_info=base_pointer_info,
                            field_to_fixed_coordinates=coord_mapping)
@@ -84,47 +123,63 @@ def create_cuda_kernel(assignments, function_name="kernel", type_info=None, inde
         ast.body.insert_front(SympyAssignment(loop_counter, indexing.coordinates[i]))
 
     ast.indexing = indexing
-    ast.compile = partial(make_python_function, ast)
     return ast
 
 
-def created_indexed_cuda_kernel(assignments, index_fields, function_name="kernel", type_info=None,
-                                coordinate_names=('x', 'y', 'z'), indexing_creator=BlockIndexing):
-    fields_read, fields_written, assignments = add_types(assignments, type_info, check_independence_condition=False)
+def created_indexed_cuda_kernel(assignments: NodeCollection, config: CreateKernelConfig):
+
+    index_fields = config.index_fields
+    function_name = config.function_name
+    coordinate_names = config.coordinate_names
+    indexing_creator = indexing_creator_from_params(config.gpu_indexing, config.gpu_indexing_params)
+    fields_written = assignments.bound_fields
+    fields_read = assignments.rhs_fields
+
     all_fields = fields_read.union(fields_written)
     read_only_fields = set([f.name for f in fields_read - fields_written])
+    # extract the index fields based on the name. The original index field might have been modified
+    index_fields = [idx_field for idx_field in index_fields if idx_field.name in [f.name for f in all_fields]]
+    non_index_fields = [f for f in all_fields if f not in index_fields]
+    spatial_coordinates = {f.spatial_dimensions for f in non_index_fields}
+    assert len(spatial_coordinates) == 1, f"Non-index fields do not have the same number of spatial coordinates " \
+                                          f"Non index fields are {non_index_fields}, spatial coordinates are " \
+                                          f"{spatial_coordinates}"
+    spatial_coordinates = list(spatial_coordinates)[0]
+
+    assignments = assignments.all_assignments
+    assignments = add_types(assignments, config)
 
     for index_field in index_fields:
         index_field.field_type = FieldType.INDEXED
         assert FieldType.is_indexed(index_field)
         assert index_field.spatial_dimensions == 1, "Index fields have to be 1D"
 
-    non_index_fields = [f for f in all_fields if f not in index_fields]
-    spatial_coordinates = {f.spatial_dimensions for f in non_index_fields}
-    assert len(spatial_coordinates) == 1, "Non-index fields do not have the same number of spatial coordinates"
-    spatial_coordinates = list(spatial_coordinates)[0]
-
     def get_coordinate_symbol_assignment(name):
         for ind_f in index_fields:
             assert isinstance(ind_f.dtype, StructType), "Index fields have to have a struct data type"
             data_type = ind_f.dtype
             if data_type.has_element(name):
                 rhs = ind_f[0](name)
-                lhs = TypedSymbol(name, BasicType(data_type.get_element_type(name)))
+                lhs = TypedSymbol(name, data_type.get_element_type(name))
                 return SympyAssignment(lhs, rhs)
-        raise ValueError("Index %s not found in any of the passed index fields" % (name,))
+        raise ValueError(f"Index {name} not found in any of the passed index fields")
 
     coordinate_symbol_assignments = [get_coordinate_symbol_assignment(n)
                                      for n in coordinate_names[:spatial_coordinates]]
     coordinate_typed_symbols = [eq.lhs for eq in coordinate_symbol_assignments]
 
     idx_field = list(index_fields)[0]
-    indexing = indexing_creator(field=idx_field,
-                                iteration_slice=[slice(None, None, None)] * len(idx_field.spatial_shape))
+
+    iteration_space = normalize_slice(tuple([slice(None, None, None)]) * len(idx_field.spatial_shape),
+                                      idx_field.spatial_shape)
+
+    indexing = indexing_creator(iteration_space=iteration_space,
+                                data_layout=idx_field.layout)
 
     function_body = Block(coordinate_symbol_assignments + assignments)
-    function_body = indexing.guard(function_body, get_common_shape(index_fields))
-    ast = KernelFunction(function_body, function_name=function_name, backend='gpucuda')
+    function_body = indexing.guard(function_body, get_common_field(index_fields).spatial_shape)
+    ast = KernelFunction(function_body, Target.GPU, Backend.CUDA, make_python_function,
+                         None, function_name, assignments=assignments)
     ast.global_variables.update(indexing.index_variables)
 
     coord_mapping = indexing.coordinates
@@ -141,5 +196,4 @@ def created_indexed_cuda_kernel(assignments, index_fields, function_name="kernel
     # add the function which determines #blocks and #threads as additional member to KernelFunction node
     # this is used by the jit
     ast.indexing = indexing
-    ast.compile = partial(make_python_function, ast)
     return ast

pystencils/gpucuda/periodicity.py → src/pystencils/gpu/periodicity.py

 import numpy as np
-from pystencils import Field, Assignment
-from pystencils.slicing import normalize_slice, get_periodic_boundary_src_dst_slices
-from pystencils.gpucuda import make_python_function
-from pystencils.gpucuda.kernelcreation import create_cuda_kernel
+from itertools import product
+
+from pystencils import CreateKernelConfig, create_kernel
+from pystencils.gpu import make_python_function
+from pystencils import Assignment, Field
+from pystencils.enums import Target
+from pystencils.slicing import get_periodic_boundary_src_dst_slices, normalize_slice
 
 
 def create_copy_kernel(domain_size, from_slice, to_slice, index_dimensions=0, index_dim_shape=1, dtype=np.float64):
     """Copies a rectangular part of an array to another non-overlapping part"""
-    if index_dimensions not in (0, 1):
-        raise NotImplementedError("Works only for one or zero index coordinates")
 
     f = Field.create_generic("pdfs", len(domain_size), index_dimensions=index_dimensions, dtype=dtype)
     normalized_from_slice = normalize_slice(from_slice, f.spatial_shape)
@@ -19,21 +20,27 @@ def create_copy_kernel(domain_size, from_slice, to_slice, index_dimensions=0, in
         "Slices have to have same size"
 
     update_eqs = []
-    for i in range(index_dim_shape):
-        eq = Assignment(f(i), f[tuple(offset)](i))
+    if index_dimensions < 2:
+        index_dim_shape = [index_dim_shape]
+    for i in product(*[range(d) for d in index_dim_shape]):
+        eq = Assignment(f(*i), f[tuple(offset)](*i))
         update_eqs.append(eq)
 
-    ast = create_cuda_kernel(update_eqs, iteration_slice=to_slice, skip_independence_check=True)
-    return make_python_function(ast)
+    config = CreateKernelConfig(target=Target.GPU, iteration_slice=to_slice, skip_independence_check=True)
+
+    ast = create_kernel(update_eqs, config=config)
+    return ast
 
 
 def get_periodic_boundary_functor(stencil, domain_size, index_dimensions=0, index_dim_shape=1, ghost_layers=1,
-                                  thickness=None, dtype=float):
+                                  thickness=None, dtype=np.float64, target=Target.GPU):
+    assert target in {Target.GPU}
     src_dst_slice_tuples = get_periodic_boundary_src_dst_slices(stencil, ghost_layers, thickness)
     kernels = []
-    index_dimensions = index_dimensions
+
     for src_slice, dst_slice in src_dst_slice_tuples:
-        kernels.append(create_copy_kernel(domain_size, src_slice, dst_slice, index_dimensions, index_dim_shape, dtype))
+        ast = create_copy_kernel(domain_size, src_slice, dst_slice, index_dimensions, index_dim_shape, dtype)
+        kernels.append(make_python_function(ast))
 
     def functor(pdfs, **_):
         for kernel in kernels:

pystencils/include/__init__.py → src/pystencils/include/__init__.py

-import os
+from os.path import dirname, realpath
 
 
 def get_pystencils_include_path():
-    return os.path.dirname(os.path.realpath(__file__))
+    return dirname(realpath(__file__))

src/pystencils/include/aesni_rand.h

+/*
+Copyright 2010-2011, D. E. Shaw Research. All rights reserved.
+Copyright 2019-2023, Michael Kuron.
+
+Redistribution and use in source and binary forms, with or without
+modification, are permitted provided that the following conditions are
+met:
+
+* Redistributions of source code must retain the above copyright
+  notice, this list of conditions, and the following disclaimer.
+
+* Redistributions in binary form must reproduce the above copyright
+  notice, this list of conditions, and the following disclaimer in the
+  documentation and/or other materials provided with the distribution.
+
+* Neither the name of of the copyright holder nor the names of its
+  contributors may be used to endorse or promote products derived from
+  this software without specific prior written permission.
+
+THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
+"AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
+LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR
+A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT
+OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL,
+SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT
+LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE,
+DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY
+THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT
+(INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE
+OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.
+*/
+
+#include <emmintrin.h> // SSE2
+#include <wmmintrin.h> // AES
+#ifdef __AVX__
+#include <immintrin.h> // AVX*
+#else
+#include <smmintrin.h>  // SSE4
+#ifdef __FMA__
+#include <immintrin.h> // FMA
+#endif
+#endif
+#include <cstdint>
+#include <array>
+#include <map>
+
+#define QUALIFIERS inline
+#define TWOPOW53_INV_DOUBLE (1.1102230246251565e-16)
+#define TWOPOW32_INV_FLOAT (2.3283064e-10f)
+
+#include "myintrin.h"
+
+typedef std::uint32_t uint32;
+typedef std::uint64_t uint64;
+
+template <typename T, std::size_t Alignment>
+class AlignedAllocator
+{
+public:
+    typedef T value_type;
+
+    template <typename U>
+    struct rebind {
+        typedef AlignedAllocator<U, Alignment> other;
+    };
+
+    T * allocate(const std::size_t n) const {
+        if (n == 0) {
+            return nullptr;
+        }
+        void * const p = _mm_malloc(n*sizeof(T), Alignment);
+        if (p == nullptr) {
+            throw std::bad_alloc();
+        }
+        return static_cast<T *>(p);
+    }
+
+    void deallocate(T * const p, const std::size_t n) const {
+        _mm_free(p);
+    }
+};
+
+template <typename Key, typename T>
+using AlignedMap = std::map<Key, T, std::less<Key>, AlignedAllocator<std::pair<const Key, T>, sizeof(Key)>>;
+
+#if defined(__AES__) || defined(_MSC_VER)
+QUALIFIERS __m128i aesni_keygen_assist(__m128i temp1, __m128i temp2) {
+    __m128i temp3; 
+    temp2 = _mm_shuffle_epi32(temp2 ,0xff); 
+    temp3 = _mm_slli_si128(temp1, 0x4);
+    temp1 = _mm_xor_si128(temp1, temp3);
+    temp3 = _mm_slli_si128(temp3, 0x4);
+    temp1 = _mm_xor_si128(temp1, temp3);
+    temp3 = _mm_slli_si128(temp3, 0x4);
+    temp1 = _mm_xor_si128(temp1, temp3);
+    temp1 = _mm_xor_si128(temp1, temp2); 
+    return temp1; 
+}
+
+QUALIFIERS std::array<__m128i,11> aesni_keygen(__m128i k) {
+    std::array<__m128i,11> rk;
+    __m128i tmp;
+    
+    rk[0] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x1);
+    k = aesni_keygen_assist(k, tmp);
+    rk[1] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x2);
+    k = aesni_keygen_assist(k, tmp);
+    rk[2] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x4);
+    k = aesni_keygen_assist(k, tmp);
+    rk[3] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x8);
+    k = aesni_keygen_assist(k, tmp);
+    rk[4] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x10);
+    k = aesni_keygen_assist(k, tmp);
+    rk[5] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x20);
+    k = aesni_keygen_assist(k, tmp);
+    rk[6] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x40);
+    k = aesni_keygen_assist(k, tmp);
+    rk[7] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x80);
+    k = aesni_keygen_assist(k, tmp);
+    rk[8] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x1b);
+    k = aesni_keygen_assist(k, tmp);
+    rk[9] = k;
+    
+    tmp = _mm_aeskeygenassist_si128(k, 0x36);
+    k = aesni_keygen_assist(k, tmp);
+    rk[10] = k;
+    
+    return rk;
+}
+
+QUALIFIERS const std::array<__m128i,11> & aesni_roundkeys(const __m128i & k128) {
+    alignas(16) std::array<uint32,4> a;
+    _mm_store_si128((__m128i*) a.data(), k128);
+    
+    static AlignedMap<std::array<uint32,4>, std::array<__m128i,11>> roundkeys;
+    
+    if(roundkeys.find(a) == roundkeys.end()) {
+        auto rk = aesni_keygen(k128);
+        roundkeys[a] = rk;
+    }
+    return roundkeys[a];
+}
+
+QUALIFIERS __m128i aesni1xm128i(const __m128i & in, const __m128i & k0) {
+    auto k = aesni_roundkeys(k0);
+    __m128i x = _mm_xor_si128(k[0], in);
+    x = _mm_aesenc_si128(x, k[1]);
+    x = _mm_aesenc_si128(x, k[2]);
+    x = _mm_aesenc_si128(x, k[3]);
+    x = _mm_aesenc_si128(x, k[4]);
+    x = _mm_aesenc_si128(x, k[5]);
+    x = _mm_aesenc_si128(x, k[6]);
+    x = _mm_aesenc_si128(x, k[7]);
+    x = _mm_aesenc_si128(x, k[8]);
+    x = _mm_aesenc_si128(x, k[9]);
+    x = _mm_aesenclast_si128(x, k[10]);
+    return x;
+}
+
+
+QUALIFIERS void aesni_double2(uint32 ctr0, uint32 ctr1, uint32 ctr2, uint32 ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              double & rnd1, double & rnd2)
+{
+    // pack input and call AES
+    __m128i c128 = _mm_set_epi32(ctr3, ctr2, ctr1, ctr0);
+    __m128i k128 = _mm_set_epi32(key3, key2, key1, key0);
+    c128 = aesni1xm128i(c128, k128);
+
+    // convert 32 to 64 bit and put 0th and 2nd element into x, 1st and 3rd element into y
+    __m128i x = _mm_and_si128(c128, _mm_set_epi32(0, 0xffffffff, 0, 0xffffffff));
+    __m128i y = _mm_and_si128(c128, _mm_set_epi32(0xffffffff, 0, 0xffffffff, 0));
+    y = _mm_srli_si128(y, 4);
+
+    // calculate z = x ^ y << (53 - 32))
+    __m128i z = _mm_sll_epi64(y, _mm_set1_epi64x(53 - 32));
+    z = _mm_xor_si128(x, z);
+
+    // convert uint64 to double
+    __m128d rs = _my_cvtepu64_pd(z);
+    // calculate rs * TWOPOW53_INV_DOUBLE + (TWOPOW53_INV_DOUBLE/2.0)
+#ifdef __FMA__
+    rs = _mm_fmadd_pd(rs, _mm_set1_pd(TWOPOW53_INV_DOUBLE), _mm_set1_pd(TWOPOW53_INV_DOUBLE/2.0));
+#else
+    rs = _mm_mul_pd(rs, _mm_set1_pd(TWOPOW53_INV_DOUBLE));
+    rs = _mm_add_pd(rs, _mm_set1_pd(TWOPOW53_INV_DOUBLE/2.0));
+#endif
+
+    // store result
+    alignas(16) double rr[2];
+    _mm_store_pd(rr, rs);
+    rnd1 = rr[0];
+    rnd2 = rr[1];
+}
+
+
+QUALIFIERS void aesni_float4(uint32 ctr0, uint32 ctr1, uint32 ctr2, uint32 ctr3,
+                             uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                             float & rnd1, float & rnd2, float & rnd3, float & rnd4)
+{
+    // pack input and call AES
+    __m128i c128 = _mm_set_epi32(ctr3, ctr2, ctr1, ctr0);
+    __m128i k128 = _mm_set_epi32(key3, key2, key1, key0);
+    c128 = aesni1xm128i(c128, k128);
+
+    // convert uint32 to float
+    __m128 rs = _my_cvtepu32_ps(c128);
+    // calculate rs * TWOPOW32_INV_FLOAT + (TWOPOW32_INV_FLOAT/2.0f)
+#ifdef __FMA__
+    rs = _mm_fmadd_ps(rs, _mm_set1_ps(TWOPOW32_INV_FLOAT), _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+#else
+    rs = _mm_mul_ps(rs, _mm_set1_ps(TWOPOW32_INV_FLOAT));
+    rs = _mm_add_ps(rs, _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+#endif
+
+    // store result
+    alignas(16) float r[4];
+    _mm_store_ps(r, rs);
+    rnd1 = r[0];
+    rnd2 = r[1];
+    rnd3 = r[2];
+    rnd4 = r[3];
+}
+
+
+template<bool high>
+QUALIFIERS __m128d _uniform_double_hq(__m128i x, __m128i y)
+{
+    // convert 32 to 64 bit
+    if (high)
+    {
+        x = _mm_unpackhi_epi32(x, _mm_setzero_si128());
+        y = _mm_unpackhi_epi32(y, _mm_setzero_si128());
+    }
+    else
+    {
+        x = _mm_unpacklo_epi32(x, _mm_setzero_si128());
+        y = _mm_unpacklo_epi32(y, _mm_setzero_si128());
+    }
+
+    // calculate z = x ^ y << (53 - 32))
+    __m128i z = _mm_sll_epi64(y, _mm_set1_epi64x(53 - 32));
+    z = _mm_xor_si128(x, z);
+
+    // convert uint64 to double
+    __m128d rs = _my_cvtepu64_pd(z);
+    // calculate rs * TWOPOW53_INV_DOUBLE + (TWOPOW53_INV_DOUBLE/2.0)
+#ifdef __FMA__
+    rs = _mm_fmadd_pd(rs, _mm_set1_pd(TWOPOW53_INV_DOUBLE), _mm_set1_pd(TWOPOW53_INV_DOUBLE/2.0));
+#else
+    rs = _mm_mul_pd(rs, _mm_set1_pd(TWOPOW53_INV_DOUBLE));
+    rs = _mm_add_pd(rs, _mm_set1_pd(TWOPOW53_INV_DOUBLE/2.0));
+#endif
+
+    return rs;
+}
+
+
+QUALIFIERS void aesni_float4(__m128i ctr0, __m128i ctr1, __m128i ctr2, __m128i ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m128 & rnd1, __m128 & rnd2, __m128 & rnd3, __m128 & rnd4)
+{
+    // pack input and call AES
+    __m128i k128 = _mm_set_epi32(key3, key2, key1, key0);
+    __m128i ctr[4] = {ctr0, ctr1, ctr2, ctr3};
+    _MY_TRANSPOSE4_EPI32(ctr[0], ctr[1], ctr[2], ctr[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = aesni1xm128i(ctr[i], k128);
+    }
+    _MY_TRANSPOSE4_EPI32(ctr[0], ctr[1], ctr[2], ctr[3]);
+
+    // convert uint32 to float
+    rnd1 = _my_cvtepu32_ps(ctr[0]);
+    rnd2 = _my_cvtepu32_ps(ctr[1]);
+    rnd3 = _my_cvtepu32_ps(ctr[2]);
+    rnd4 = _my_cvtepu32_ps(ctr[3]);
+    // calculate rnd * TWOPOW32_INV_FLOAT + (TWOPOW32_INV_FLOAT/2.0f)
+#ifdef __FMA__
+    rnd1 = _mm_fmadd_ps(rnd1, _mm_set1_ps(TWOPOW32_INV_FLOAT), _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd2 = _mm_fmadd_ps(rnd2, _mm_set1_ps(TWOPOW32_INV_FLOAT), _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd3 = _mm_fmadd_ps(rnd3, _mm_set1_ps(TWOPOW32_INV_FLOAT), _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd4 = _mm_fmadd_ps(rnd4, _mm_set1_ps(TWOPOW32_INV_FLOAT), _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+#else
+    rnd1 = _mm_mul_ps(rnd1, _mm_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd1 = _mm_add_ps(rnd1, _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+    rnd2 = _mm_mul_ps(rnd2, _mm_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd2 = _mm_add_ps(rnd2, _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+    rnd3 = _mm_mul_ps(rnd3, _mm_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd3 = _mm_add_ps(rnd3, _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+    rnd4 = _mm_mul_ps(rnd4, _mm_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd4 = _mm_add_ps(rnd4, _mm_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+#endif
+}
+
+
+QUALIFIERS void aesni_double2(__m128i ctr0, __m128i ctr1, __m128i ctr2, __m128i ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m128d & rnd1lo, __m128d & rnd1hi, __m128d & rnd2lo, __m128d & rnd2hi)
+{
+    // pack input and call AES
+    __m128i k128 = _mm_set_epi32(key3, key2, key1, key0);
+    __m128i ctr[4] = {ctr0, ctr1, ctr2, ctr3};
+    _MY_TRANSPOSE4_EPI32(ctr[0], ctr[1], ctr[2], ctr[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = aesni1xm128i(ctr[i], k128);
+    }
+    _MY_TRANSPOSE4_EPI32(ctr[0], ctr[1], ctr[2], ctr[3]);
+
+    rnd1lo = _uniform_double_hq<false>(ctr[0], ctr[1]);
+    rnd1hi = _uniform_double_hq<true>(ctr[0], ctr[1]);
+    rnd2lo = _uniform_double_hq<false>(ctr[2], ctr[3]);
+    rnd2hi = _uniform_double_hq<true>(ctr[2], ctr[3]);
+}
+
+QUALIFIERS void aesni_float4(uint32 ctr0, __m128i ctr1, uint32 ctr2, uint32 ctr3,
+                             uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                             __m128 & rnd1, __m128 & rnd2, __m128 & rnd3, __m128 & rnd4)
+{
+    __m128i ctr0v = _mm_set1_epi32(ctr0);
+    __m128i ctr2v = _mm_set1_epi32(ctr2);
+    __m128i ctr3v = _mm_set1_epi32(ctr3);
+
+    aesni_float4(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1, rnd2, rnd3, rnd4);
+}
+
+QUALIFIERS void aesni_double2(uint32 ctr0, __m128i ctr1, uint32 ctr2, uint32 ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m128d & rnd1lo, __m128d & rnd1hi, __m128d & rnd2lo, __m128d & rnd2hi)
+{
+    __m128i ctr0v = _mm_set1_epi32(ctr0);
+    __m128i ctr2v = _mm_set1_epi32(ctr2);
+    __m128i ctr3v = _mm_set1_epi32(ctr3);
+
+   aesni_double2(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1lo, rnd1hi, rnd2lo, rnd2hi);
+}
+
+QUALIFIERS void aesni_double2(uint32 ctr0, __m128i ctr1, uint32 ctr2, uint32 ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m128d & rnd1, __m128d & rnd2)
+{
+    __m128i ctr0v = _mm_set1_epi32(ctr0);
+    __m128i ctr2v = _mm_set1_epi32(ctr2);
+    __m128i ctr3v = _mm_set1_epi32(ctr3);
+
+    __m128d ignore;
+   aesni_double2(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1, ignore, rnd2, ignore);
+}
+#endif
+
+
+#ifdef __AVX2__
+QUALIFIERS const std::array<__m256i,11> & aesni_roundkeys(const __m256i & k256) {
+    alignas(32) std::array<uint32,8> a;
+    _mm256_store_si256((__m256i*) a.data(), k256);
+    
+    static AlignedMap<std::array<uint32,8>, std::array<__m256i,11>> roundkeys;
+    
+    if(roundkeys.find(a) == roundkeys.end()) {
+        auto rk1 = aesni_keygen(_mm256_extractf128_si256(k256, 0));
+        auto rk2 = aesni_keygen(_mm256_extractf128_si256(k256, 1));
+        for(int i = 0; i < 11; ++i) {
+            roundkeys[a][i] = _my256_set_m128i(rk2[i], rk1[i]);
+        }
+    }
+    return roundkeys[a];
+}
+
+QUALIFIERS __m256i aesni1xm128i(const __m256i & in, const __m256i & k0) {
+#if defined(__VAES__)
+    auto k = aesni_roundkeys(k0);
+    __m256i x = _mm256_xor_si256(k[0], in);
+    x = _mm256_aesenc_epi128(x, k[1]);
+    x = _mm256_aesenc_epi128(x, k[2]);
+    x = _mm256_aesenc_epi128(x, k[3]);
+    x = _mm256_aesenc_epi128(x, k[4]);
+    x = _mm256_aesenc_epi128(x, k[5]);
+    x = _mm256_aesenc_epi128(x, k[6]);
+    x = _mm256_aesenc_epi128(x, k[7]);
+    x = _mm256_aesenc_epi128(x, k[8]);
+    x = _mm256_aesenc_epi128(x, k[9]);
+    x = _mm256_aesenclast_epi128(x, k[10]);
+#else
+    __m128i a = aesni1xm128i(_mm256_extractf128_si256(in, 0), _mm256_extractf128_si256(k0, 0));
+    __m128i b = aesni1xm128i(_mm256_extractf128_si256(in, 1), _mm256_extractf128_si256(k0, 1));
+    __m256i x = _my256_set_m128i(b, a);
+#endif
+    return x;
+}
+
+template<bool high>
+QUALIFIERS __m256d _uniform_double_hq(__m256i x, __m256i y)
+{
+    // convert 32 to 64 bit
+    if (high)
+    {
+        x = _mm256_cvtepu32_epi64(_mm256_extracti128_si256(x, 1));
+        y = _mm256_cvtepu32_epi64(_mm256_extracti128_si256(y, 1));
+    }
+    else
+    {
+        x = _mm256_cvtepu32_epi64(_mm256_extracti128_si256(x, 0));
+        y = _mm256_cvtepu32_epi64(_mm256_extracti128_si256(y, 0));
+    }
+
+    // calculate z = x ^ y << (53 - 32))
+    __m256i z = _mm256_sll_epi64(y, _mm_set1_epi64x(53 - 32));
+    z = _mm256_xor_si256(x, z);
+
+    // convert uint64 to double
+    __m256d rs = _my256_cvtepu64_pd(z);
+    // calculate rs * TWOPOW53_INV_DOUBLE + (TWOPOW53_INV_DOUBLE/2.0)
+#ifdef __FMA__
+    rs = _mm256_fmadd_pd(rs, _mm256_set1_pd(TWOPOW53_INV_DOUBLE), _mm256_set1_pd(TWOPOW53_INV_DOUBLE/2.0));
+#else
+    rs = _mm256_mul_pd(rs, _mm256_set1_pd(TWOPOW53_INV_DOUBLE));
+    rs = _mm256_add_pd(rs, _mm256_set1_pd(TWOPOW53_INV_DOUBLE/2.0));
+#endif
+
+    return rs;
+}
+
+
+QUALIFIERS void aesni_float4(__m256i ctr0, __m256i ctr1, __m256i ctr2, __m256i ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m256 & rnd1, __m256 & rnd2, __m256 & rnd3, __m256 & rnd4)
+{
+    // pack input and call AES
+    __m256i k256 = _mm256_set_epi32(key3, key2, key1, key0, key3, key2, key1, key0);
+    __m256i ctr[4] = {ctr0, ctr1, ctr2, ctr3};
+    __m128i a[4], b[4];
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm256_extractf128_si256(ctr[i], 0);
+        b[i] = _mm256_extractf128_si256(ctr[i], 1);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my256_set_m128i(b[i], a[i]);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = aesni1xm128i(ctr[i], k256);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm256_extractf128_si256(ctr[i], 0);
+        b[i] = _mm256_extractf128_si256(ctr[i], 1);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my256_set_m128i(b[i], a[i]);
+    }
+
+    // convert uint32 to float
+    rnd1 = _my256_cvtepu32_ps(ctr[0]);
+    rnd2 = _my256_cvtepu32_ps(ctr[1]);
+    rnd3 = _my256_cvtepu32_ps(ctr[2]);
+    rnd4 = _my256_cvtepu32_ps(ctr[3]);
+    // calculate rnd * TWOPOW32_INV_FLOAT + (TWOPOW32_INV_FLOAT/2.0f)
+#ifdef __FMA__
+    rnd1 = _mm256_fmadd_ps(rnd1, _mm256_set1_ps(TWOPOW32_INV_FLOAT), _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd2 = _mm256_fmadd_ps(rnd2, _mm256_set1_ps(TWOPOW32_INV_FLOAT), _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd3 = _mm256_fmadd_ps(rnd3, _mm256_set1_ps(TWOPOW32_INV_FLOAT), _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd4 = _mm256_fmadd_ps(rnd4, _mm256_set1_ps(TWOPOW32_INV_FLOAT), _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+#else
+    rnd1 = _mm256_mul_ps(rnd1, _mm256_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd1 = _mm256_add_ps(rnd1, _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+    rnd2 = _mm256_mul_ps(rnd2, _mm256_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd2 = _mm256_add_ps(rnd2, _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+    rnd3 = _mm256_mul_ps(rnd3, _mm256_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd3 = _mm256_add_ps(rnd3, _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+    rnd4 = _mm256_mul_ps(rnd4, _mm256_set1_ps(TWOPOW32_INV_FLOAT));
+    rnd4 = _mm256_add_ps(rnd4, _mm256_set1_ps(TWOPOW32_INV_FLOAT/2.0f));
+#endif
+}
+
+
+QUALIFIERS void aesni_double2(__m256i ctr0, __m256i ctr1, __m256i ctr2, __m256i ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m256d & rnd1lo, __m256d & rnd1hi, __m256d & rnd2lo, __m256d & rnd2hi)
+{
+    // pack input and call AES
+    __m256i k256 = _mm256_set_epi32(key3, key2, key1, key0, key3, key2, key1, key0);
+    __m256i ctr[4] = {ctr0, ctr1, ctr2, ctr3};
+    __m128i a[4], b[4];
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm256_extractf128_si256(ctr[i], 0);
+        b[i] = _mm256_extractf128_si256(ctr[i], 1);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my256_set_m128i(b[i], a[i]);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = aesni1xm128i(ctr[i], k256);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm256_extractf128_si256(ctr[i], 0);
+        b[i] = _mm256_extractf128_si256(ctr[i], 1);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my256_set_m128i(b[i], a[i]);
+    }
+
+    rnd1lo = _uniform_double_hq<false>(ctr[0], ctr[1]);
+    rnd1hi = _uniform_double_hq<true>(ctr[0], ctr[1]);
+    rnd2lo = _uniform_double_hq<false>(ctr[2], ctr[3]);
+    rnd2hi = _uniform_double_hq<true>(ctr[2], ctr[3]);
+}
+
+QUALIFIERS void aesni_float4(uint32 ctr0, __m256i ctr1, uint32 ctr2, uint32 ctr3,
+                             uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                             __m256 & rnd1, __m256 & rnd2, __m256 & rnd3, __m256 & rnd4)
+{
+    __m256i ctr0v = _mm256_set1_epi32(ctr0);
+    __m256i ctr2v = _mm256_set1_epi32(ctr2);
+    __m256i ctr3v = _mm256_set1_epi32(ctr3);
+
+    aesni_float4(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1, rnd2, rnd3, rnd4);
+}
+
+QUALIFIERS void aesni_double2(uint32 ctr0, __m256i ctr1, uint32 ctr2, uint32 ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m256d & rnd1lo, __m256d & rnd1hi, __m256d & rnd2lo, __m256d & rnd2hi)
+{
+    __m256i ctr0v = _mm256_set1_epi32(ctr0);
+    __m256i ctr2v = _mm256_set1_epi32(ctr2);
+    __m256i ctr3v = _mm256_set1_epi32(ctr3);
+
+    aesni_double2(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1lo, rnd1hi, rnd2lo, rnd2hi);
+}
+
+QUALIFIERS void aesni_double2(uint32 ctr0, __m256i ctr1, uint32 ctr2, uint32 ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m256d & rnd1, __m256d & rnd2)
+{
+#if 0
+    __m256i ctr0v = _mm256_set1_epi32(ctr0);
+    __m256i ctr2v = _mm256_set1_epi32(ctr2);
+    __m256i ctr3v = _mm256_set1_epi32(ctr3);
+
+    __m256d ignore;
+    aesni_double2(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1, ignore, rnd2, ignore);
+#else
+    __m128d rnd1lo, rnd1hi, rnd2lo, rnd2hi;
+    aesni_double2(ctr0, _mm256_extractf128_si256(ctr1, 0), ctr2, ctr3, key0, key1, key2, key3, rnd1lo, rnd1hi, rnd2lo, rnd2hi);
+    rnd1 = _my256_set_m128d(rnd1hi, rnd1lo);
+    rnd2 = _my256_set_m128d(rnd2hi, rnd2lo);
+#endif
+}
+#endif
+
+
+#if defined(__AVX512F__) || defined(__AVX10_512BIT__)
+QUALIFIERS const std::array<__m512i,11> & aesni_roundkeys(const __m512i & k512) {
+    alignas(64) std::array<uint32,16> a;
+    _mm512_store_si512((__m512i*) a.data(), k512);
+    
+    static AlignedMap<std::array<uint32,16>, std::array<__m512i,11>> roundkeys;
+    
+    if(roundkeys.find(a) == roundkeys.end()) {
+        auto rk1 = aesni_keygen(_mm512_extracti32x4_epi32(k512, 0));
+        auto rk2 = aesni_keygen(_mm512_extracti32x4_epi32(k512, 1));
+        auto rk3 = aesni_keygen(_mm512_extracti32x4_epi32(k512, 2));
+        auto rk4 = aesni_keygen(_mm512_extracti32x4_epi32(k512, 3));
+        for(int i = 0; i < 11; ++i) {
+            roundkeys[a][i] = _my512_set_m128i(rk4[i], rk3[i], rk2[i], rk1[i]);
+        }
+    }
+    return roundkeys[a];
+}
+
+QUALIFIERS __m512i aesni1xm128i(const __m512i & in, const __m512i & k0) {
+#ifdef __VAES__
+    auto k = aesni_roundkeys(k0);
+    __m512i x = _mm512_xor_si512(k[0], in);
+    x = _mm512_aesenc_epi128(x, k[1]);
+    x = _mm512_aesenc_epi128(x, k[2]);
+    x = _mm512_aesenc_epi128(x, k[3]);
+    x = _mm512_aesenc_epi128(x, k[4]);
+    x = _mm512_aesenc_epi128(x, k[5]);
+    x = _mm512_aesenc_epi128(x, k[6]);
+    x = _mm512_aesenc_epi128(x, k[7]);
+    x = _mm512_aesenc_epi128(x, k[8]);
+    x = _mm512_aesenc_epi128(x, k[9]);
+    x = _mm512_aesenclast_epi128(x, k[10]);
+#else
+    __m128i a = aesni1xm128i(_mm512_extracti32x4_epi32(in, 0), _mm512_extracti32x4_epi32(k0, 0));
+    __m128i b = aesni1xm128i(_mm512_extracti32x4_epi32(in, 1), _mm512_extracti32x4_epi32(k0, 1));
+    __m128i c = aesni1xm128i(_mm512_extracti32x4_epi32(in, 2), _mm512_extracti32x4_epi32(k0, 2));
+    __m128i d = aesni1xm128i(_mm512_extracti32x4_epi32(in, 3), _mm512_extracti32x4_epi32(k0, 3));
+    __m512i x = _my512_set_m128i(d, c, b, a);
+#endif
+    return x;
+}
+
+template<bool high>
+QUALIFIERS __m512d _uniform_double_hq(__m512i x, __m512i y)
+{
+    // convert 32 to 64 bit
+    if (high)
+    {
+        x = _mm512_cvtepu32_epi64(_mm512_extracti64x4_epi64(x, 1));
+        y = _mm512_cvtepu32_epi64(_mm512_extracti64x4_epi64(y, 1));
+    }
+    else
+    {
+        x = _mm512_cvtepu32_epi64(_mm512_extracti64x4_epi64(x, 0));
+        y = _mm512_cvtepu32_epi64(_mm512_extracti64x4_epi64(y, 0));
+    }
+
+    // calculate z = x ^ y << (53 - 32))
+    __m512i z = _mm512_sll_epi64(y, _mm_set1_epi64x(53 - 32));
+    z = _mm512_xor_si512(x, z);
+
+    // convert uint64 to double
+    __m512d rs = _mm512_cvtepu64_pd(z);
+    // calculate rs * TWOPOW53_INV_DOUBLE + (TWOPOW53_INV_DOUBLE/2.0)
+    rs = _mm512_fmadd_pd(rs, _mm512_set1_pd(TWOPOW53_INV_DOUBLE), _mm512_set1_pd(TWOPOW53_INV_DOUBLE/2.0));
+
+    return rs;
+}
+
+
+QUALIFIERS void aesni_float4(__m512i ctr0, __m512i ctr1, __m512i ctr2, __m512i ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m512 & rnd1, __m512 & rnd2, __m512 & rnd3, __m512 & rnd4)
+{
+    // pack input and call AES
+    __m512i k512 = _mm512_set_epi32(key3, key2, key1, key0, key3, key2, key1, key0,
+                                    key3, key2, key1, key0, key3, key2, key1, key0);
+    __m512i ctr[4] = {ctr0, ctr1, ctr2, ctr3};
+    __m128i a[4], b[4], c[4], d[4];
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm512_extracti32x4_epi32(ctr[i], 0);
+        b[i] = _mm512_extracti32x4_epi32(ctr[i], 1);
+        c[i] = _mm512_extracti32x4_epi32(ctr[i], 2);
+        d[i] = _mm512_extracti32x4_epi32(ctr[i], 3);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    _MY_TRANSPOSE4_EPI32(c[0], c[1], c[2], c[3]);
+    _MY_TRANSPOSE4_EPI32(d[0], d[1], d[2], d[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my512_set_m128i(d[i], c[i], b[i], a[i]);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = aesni1xm128i(ctr[i], k512);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm512_extracti32x4_epi32(ctr[i], 0);
+        b[i] = _mm512_extracti32x4_epi32(ctr[i], 1);
+        c[i] = _mm512_extracti32x4_epi32(ctr[i], 2);
+        d[i] = _mm512_extracti32x4_epi32(ctr[i], 3);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    _MY_TRANSPOSE4_EPI32(c[0], c[1], c[2], c[3]);
+    _MY_TRANSPOSE4_EPI32(d[0], d[1], d[2], d[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my512_set_m128i(d[i], c[i], b[i], a[i]);
+    }
+
+    // convert uint32 to float
+    rnd1 = _mm512_cvtepu32_ps(ctr[0]);
+    rnd2 = _mm512_cvtepu32_ps(ctr[1]);
+    rnd3 = _mm512_cvtepu32_ps(ctr[2]);
+    rnd4 = _mm512_cvtepu32_ps(ctr[3]);
+    // calculate rnd * TWOPOW32_INV_FLOAT + (TWOPOW32_INV_FLOAT/2.0f)
+    rnd1 = _mm512_fmadd_ps(rnd1, _mm512_set1_ps(TWOPOW32_INV_FLOAT), _mm512_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd2 = _mm512_fmadd_ps(rnd2, _mm512_set1_ps(TWOPOW32_INV_FLOAT), _mm512_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd3 = _mm512_fmadd_ps(rnd3, _mm512_set1_ps(TWOPOW32_INV_FLOAT), _mm512_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+    rnd4 = _mm512_fmadd_ps(rnd4, _mm512_set1_ps(TWOPOW32_INV_FLOAT), _mm512_set1_ps(TWOPOW32_INV_FLOAT/2.0));
+}
+
+
+QUALIFIERS void aesni_double2(__m512i ctr0, __m512i ctr1, __m512i ctr2, __m512i ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m512d & rnd1lo, __m512d & rnd1hi, __m512d & rnd2lo, __m512d & rnd2hi)
+{
+    // pack input and call AES
+    __m512i k512 = _mm512_set_epi32(key3, key2, key1, key0, key3, key2, key1, key0,
+                                    key3, key2, key1, key0, key3, key2, key1, key0);
+    __m512i ctr[4] = {ctr0, ctr1, ctr2, ctr3};
+    __m128i a[4], b[4], c[4], d[4];
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm512_extracti32x4_epi32(ctr[i], 0);
+        b[i] = _mm512_extracti32x4_epi32(ctr[i], 1);
+        c[i] = _mm512_extracti32x4_epi32(ctr[i], 2);
+        d[i] = _mm512_extracti32x4_epi32(ctr[i], 3);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    _MY_TRANSPOSE4_EPI32(c[0], c[1], c[2], c[3]);
+    _MY_TRANSPOSE4_EPI32(d[0], d[1], d[2], d[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my512_set_m128i(d[i], c[i], b[i], a[i]);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = aesni1xm128i(ctr[i], k512);
+    }
+    for (int i = 0; i < 4; ++i)
+    {
+        a[i] = _mm512_extracti32x4_epi32(ctr[i], 0);
+        b[i] = _mm512_extracti32x4_epi32(ctr[i], 1);
+        c[i] = _mm512_extracti32x4_epi32(ctr[i], 2);
+        d[i] = _mm512_extracti32x4_epi32(ctr[i], 3);
+    }
+    _MY_TRANSPOSE4_EPI32(a[0], a[1], a[2], a[3]);
+    _MY_TRANSPOSE4_EPI32(b[0], b[1], b[2], b[3]);
+    _MY_TRANSPOSE4_EPI32(c[0], c[1], c[2], c[3]);
+    _MY_TRANSPOSE4_EPI32(d[0], d[1], d[2], d[3]);
+    for (int i = 0; i < 4; ++i)
+    {
+        ctr[i] = _my512_set_m128i(d[i], c[i], b[i], a[i]);
+    }
+
+    rnd1lo = _uniform_double_hq<false>(ctr[0], ctr[1]);
+    rnd1hi = _uniform_double_hq<true>(ctr[0], ctr[1]);
+    rnd2lo = _uniform_double_hq<false>(ctr[2], ctr[3]);
+    rnd2hi = _uniform_double_hq<true>(ctr[2], ctr[3]);
+}
+
+QUALIFIERS void aesni_float4(uint32 ctr0, __m512i ctr1, uint32 ctr2, uint32 ctr3,
+                             uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                             __m512 & rnd1, __m512 & rnd2, __m512 & rnd3, __m512 & rnd4)
+{
+    __m512i ctr0v = _mm512_set1_epi32(ctr0);
+    __m512i ctr2v = _mm512_set1_epi32(ctr2);
+    __m512i ctr3v = _mm512_set1_epi32(ctr3);
+
+    aesni_float4(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1, rnd2, rnd3, rnd4);
+}
+
+QUALIFIERS void aesni_double2(uint32 ctr0, __m512i ctr1, uint32 ctr2, uint32 ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m512d & rnd1lo, __m512d & rnd1hi, __m512d & rnd2lo, __m512d & rnd2hi)
+{
+    __m512i ctr0v = _mm512_set1_epi32(ctr0);
+    __m512i ctr2v = _mm512_set1_epi32(ctr2);
+    __m512i ctr3v = _mm512_set1_epi32(ctr3);
+
+    aesni_double2(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1lo, rnd1hi, rnd2lo, rnd2hi);
+}
+
+QUALIFIERS void aesni_double2(uint32 ctr0, __m512i ctr1, uint32 ctr2, uint32 ctr3,
+                              uint32 key0, uint32 key1, uint32 key2, uint32 key3,
+                              __m512d & rnd1, __m512d & rnd2)
+{
+#if 0
+    __m512i ctr0v = _mm512_set1_epi32(ctr0);
+    __m512i ctr2v = _mm512_set1_epi32(ctr2);
+    __m512i ctr3v = _mm512_set1_epi32(ctr3);
+
+    __m512d ignore;
+    aesni_double2(ctr0v, ctr1, ctr2v, ctr3v, key0, key1, key2, key3, rnd1, ignore, rnd2, ignore);
+#else
+   __m256d rnd1lo, rnd1hi, rnd2lo, rnd2hi;
+   aesni_double2(ctr0, _mm512_extracti64x4_epi64(ctr1, 0), ctr2, ctr3, key0, key1, key2, key3, rnd1lo, rnd1hi, rnd2lo, rnd2hi);
+   rnd1 = _my512_set_m256d(rnd1hi, rnd1lo);
+   rnd2 = _my512_set_m256d(rnd2hi, rnd2lo);
+#endif
+}
+#endif
+