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

@@ -4,20 +4,30 @@ 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, )
 
 
@@ -32,7 +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
@@ -48,7 +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/derivation.py → src/pystencils/fd/derivation.py

@@ -126,7 +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:
@@ -200,7 +199,7 @@ class FiniteDifferenceStencilDerivation:
                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), 1, axes)
+            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)
@@ -229,9 +228,10 @@ class FiniteDifferenceStaggeredStencilDerivation:
         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()):
+    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:
@@ -261,7 +261,7 @@ class FiniteDifferenceStaggeredStencilDerivation:
             main_points = [neighbor / 2, neighbor / -2, flipped(neighbor / 2, nonzero_indices[0]),
                            flipped(neighbor / -2, nonzero_indices[0])]
         else:
-            main_points = [neighbor.multiply_elementwise(sp.Matrix(c) / 2)
+            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]
@@ -282,7 +282,10 @@ class FiniteDifferenceStaggeredStencilDerivation:
 
             # 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:
+            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)):

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

@@ -228,7 +228,9 @@ def diff_terms(expr):
 
     Example:
         >>> x, y = sp.symbols("x, y")
-        >>> diff_terms( diff(x, 0, 0)  )
+        >>> 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()

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

@@ -23,9 +23,9 @@ def diffusion(scalar, diffusion_coeff, idx=None):
         >>> f = Field.create_generic('f', spatial_dimensions=2)
         >>> d = sp.Symbol("d")
         >>> dx = sp.Symbol("dx")
-        >>> diffusion_term = diffusion(scalar=f, diffusion_coeff=sp.Symbol("d"))
+        >>> diffusion_term = diffusion(scalar=f, diffusion_coeff=d)
         >>> discretization = Discretization2ndOrder()
-        >>> expected_output = ((f[-1, 0] + f[0, -1] - 4*f[0, 0] + f[0, 1] + f[1, 0]) * 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
     """
@@ -79,13 +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):
@@ -112,38 +105,14 @@ class Discretization2ndOrder:
             return self._discretize_advection(e)
         elif isinstance(e, Diff):
             arg, *indices = diff_args(e)
-            from pystencils.interpolation_astnodes import InterpolatorAccess
 
-            if not isinstance(arg, (Field.Access, InterpolatorAccess)):
+            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)
         else:
             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]
@@ -368,7 +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)})
@@ -416,7 +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

pystencils/fd/finitevolumes.py → src/pystencils/fd/finitevolumes.py

@@ -7,6 +7,25 @@ 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
 
@@ -40,7 +59,10 @@ class FVM1stOrder:
 
         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
@@ -48,24 +70,11 @@ class FVM1stOrder:
                 avg = (term.get_shifted(*neighbor) + term) * sp.Rational(1, 2)
                 return avg
             elif isinstance(term, ps.fd.Diff):
-                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("can only deal with derivatives of field accesses, "
-                                              "but not {}; expansion of derivatives probably failed"
-                                              .format(type(term.args[0])))
+                access, direction = get_access_and_direction(term)
 
-                fds = FDS(neighbor, access.field.spatial_dimensions, direction)
+                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:
@@ -87,7 +96,20 @@ class FVM1stOrder:
             directional_flux = fluxes[0] * int(neighbor[0])
             for i in range(1, self.dim):
                 directional_flux += fluxes[i] * int(neighbor[i])
-            discrete_flux = discretize(directional_flux, neighbor)
+            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:
@@ -103,22 +125,7 @@ class FVM1stOrder:
 
         def discretize(term):
             if isinstance(term, ps.fd.Diff):
-                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("can only deal with derivatives of field accesses, "
-                                              "but not {}; expansion of derivatives probably failed"
-                                              .format(type(term.args[0])))
+                access, direction = get_access_and_direction(term)
 
                 if self.dim == 2:
                     stencil = ["".join(a).replace(" ", "") for a in itertools.product("NS ", "EW ")

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.fd import Diff
 from pystencils.field import Field
 from pystencils.transformations import generic_visit
@@ -72,43 +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'")
 
@@ -167,9 +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

@@ -5,7 +5,7 @@ import pickle
 import re
 from enum import Enum
 from itertools import chain
-from typing import List, Optional, Sequence, Set, Tuple
+from typing import List, Optional, Sequence, Set, Tuple, Union
 
 import numpy as np
 import sympy as sp
@@ -13,13 +13,13 @@ from sympy.core.cache import cacheit
 
 import pystencils
 from pystencils.alignedarray import aligned_empty
-from pystencils.data_types import StructType, TypedSymbol, create_type
-from pystencils.kernelparameters import FieldShapeSymbol, FieldStrideSymbol
+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
 
-__all__ = ['Field', 'fields', 'FieldType', 'AbstractField']
+__all__ = ['Field', 'fields', 'FieldType', 'Field']
 
 
 class FieldType(Enum):
@@ -69,81 +69,7 @@ class FieldType(Enum):
         return field.field_type == FieldType.STAGGERED_FLUX
 
 
-def fields(description=None, index_dimensions=0, layout=None, field_type=FieldType.GENERIC, **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: 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:
-                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:
-        return None
-    elif len(result) == 1:
-        return result[0]
-    else:
-        return result
-
-
-class AbstractField:
-
-    class AbstractAccess:
-        pass
-
-
-class Field(AbstractField):
+class Field:
     """
     With fields one can formulate stencil-like update rules on structured grids.
     This Field class knows about the dimension, memory layout (strides) and optionally about the size of an array.
@@ -330,9 +256,7 @@ class Field(AbstractField):
         self.shape = shape
         self.strides = strides
         self.latex_name: Optional[str] = None
-        self.coordinate_origin: tuple[float, sp.Symbol] = sp.Matrix(tuple(
-            0 for _ in range(self.spatial_dimensions)
-        ))
+        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
@@ -341,8 +265,7 @@ class Field(AbstractField):
         if self.has_fixed_shape:
             return Field(new_name, self.field_type, self._dtype, self._layout, self.shape, self.strides)
         else:
-            return Field.create_generic(new_name, self.spatial_dimensions, self.dtype.numpy_dtype,
-                                        self.index_dimensions, self._layout, self.index_shape, self.field_type)
+            return Field(new_name, self.field_type, self.dtype, self.layout, self.shape, self.strides)
 
     @property
     def spatial_dimensions(self) -> int:
@@ -432,8 +355,8 @@ class Field(AbstractField):
         elif len(index_shape) == 2:
             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.Matrix([[[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])])
+            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")
 
@@ -466,35 +389,13 @@ class Field(AbstractField):
         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 interpolated_access(self,
-                            offset: Tuple,
-                            interpolation_mode='linear',
-                            address_mode='BORDER',
-                            allow_textures=True):
-        """Provides access to field values at non-integer positions
-
-        ``interpolated_access`` is similar to :func:`Field.absolute_access` except that
-        it allows non-integer offsets and automatic handling of out-of-bound accesses.
-
-        :param offset:              Tuple of spatial coordinates (can be floats)
-        :param interpolation_mode:  One of :class:`pystencils.interpolation_astnodes.InterpolationMode`
-        :param address_mode:        How boundaries are handled can be 'border', 'wrap', 'mirror', 'clamp'
-        :param allow_textures:      Allow implementation by texture accesses on GPUs
-        """
-        from pystencils.interpolation_astnodes import Interpolator
-        return Interpolator(self,
-                            interpolation_mode,
-                            address_mode,
-                            allow_textures=allow_textures).at(offset)
-
     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
@@ -510,11 +411,8 @@ class Field(AbstractField):
         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 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}")
 
         prefactor = 1
         neighbor_vec = [0] * len(offset)
@@ -528,8 +426,7 @@ class Field(AbstractField):
             if FieldType.is_staggered_flux(self):
                 prefactor = -1
         if neighbor not in self.staggered_stencil:
-            raise ValueError("{} is not a valid neighbor for the {} stencil".format(offset_orig,
-                                                                                    self.staggered_stencil_name))
+            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))
 
@@ -541,15 +438,13 @@ class Field(AbstractField):
             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("Wrong number of indices: "
-                                 "Got %d, expected %d" % (0, self.index_dimensions - 1))
+                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("Wrong number of indices: "
-                                 "Got %d, expected %d" % (len(index), self.index_dimensions - 1))
+                raise ValueError(f"Wrong number of indices: Got {len(index)}, expected {self.index_dimensions - 1}")
 
             return prefactor * Field.Access(self, offset, (idx, *index))
 
@@ -589,7 +484,7 @@ class Field(AbstractField):
     @property
     def staggered_stencil_name(self):
         assert FieldType.is_staggered(self)
-        return "D%dQ%d" % (self.spatial_dimensions, self.index_shape[0] * 2 + 1)
+        return f"D{self.spatial_dimensions}Q{self.index_shape[0] * 2 + 1}"
 
     def __call__(self, *args, **kwargs):
         center = tuple([0] * self.spatial_dimensions)
@@ -624,15 +519,15 @@ class Field(AbstractField):
         return self.coordinate_transform @ \
             (self.coordinate_origin + pystencils.x_staggered_vector(self.spatial_dimensions))
 
-    def index_to_physical(self, index_coordinates, staggered=False):
+    def index_to_physical(self, index_coordinates: sp.Matrix, staggered=False):
         if staggered:
-            index_coordinates = sp.Matrix([i + 0.5 for i in index_coordinates])
+            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, staggered=False):
+    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
@@ -649,15 +544,11 @@ class Field(AbstractField):
 
         return rtn
 
-    def index_to_staggered_physical_coordinates(self, symbol_vector):
-        symbol_vector += sp.Matrix([0.5] * self.spatial_dimensions)
-        return self.create_physical_coordinates(symbol_vector)
-
     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(TypedSymbol, AbstractField.AbstractAccess):
+    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
@@ -676,6 +567,7 @@ class Field(AbstractField):
             >>> 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)
@@ -710,7 +602,11 @@ class Field(AbstractField):
             if superscript is not None:
                 symbol_name += "^" + superscript
 
-            obj = super(Field.Access, self).__xnew__(self, symbol_name, field.dtype)
+            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:
@@ -734,6 +630,9 @@ class Field(AbstractField):
         def __getnewargs__(self):
             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__)
         # noinspection SpellCheckingInspection
@@ -749,18 +648,18 @@ class Field(AbstractField):
                 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, dtype=self.dtype)
+                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"""
@@ -810,7 +709,8 @@ class Field(AbstractField):
             """
             offset_list = list(self.offsets)
             offset_list[coord_id] += offset
-            return Field.Access(self.field, tuple(offset_list), self.index, dtype=self.dtype)
+            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
@@ -823,6 +723,7 @@ class Field(AbstractField):
             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':
@@ -833,12 +734,14 @@ class Field(AbstractField):
                 >>> f(0).at_index(8)
                 f_C^8
             """
-            return Field.Access(self.field, self.offsets, idx_tuple, dtype=self.dtype)
+            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
@@ -856,7 +759,8 @@ class Field(AbstractField):
 
         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)
@@ -877,15 +781,14 @@ class Field(AbstractField):
 
             if FieldType.is_staggered(self._field):
                 if self.index and self.field.index_dimensions > 1:
-                    return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index[1:]
-                                                 if len(self.index) > 2 else self.index[1])
+                    return f"{{{n}}}_{{{offset_str}}}^{{{self.index[1:] if len(self.index) > 2 else self.index[1]}}}"
                 else:
-                    return "{{%s}_{%s}}" % (n, offset_str)
+                    return f"{{{n}}}_{{{offset_str}}}"
             else:
                 if self.index and self.field.index_dimensions > 0:
-                    return "{{%s}_{%s}^{%s}}" % (n, offset_str, self.index if len(self.index) > 1 else self.index[0])
+                    return f"{{{n}}}_{{{offset_str}}}^{{{self.index if len(self.index) > 1 else self.index[0]}}}"
                 else:
-                    return "{{%s}_{%s}}" % (n, offset_str)
+                    return f"{{{n}}}_{{{offset_str}}}"
 
         def __str__(self):
             n = self._field.latex_name if self._field.latex_name else self._field.name
@@ -908,6 +811,75 @@ class Field(AbstractField):
                     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:
+                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):
     index_dimension_ids = [] if index_dimension_ids is None else index_dimension_ids
     coordinates = list(range(len(strides)))
@@ -968,8 +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):
@@ -978,24 +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)))
-    elif layout_str in ('c', 'numpy', 'AoS'):
+    
+    if layout_str in ('f', 'reverse_numpy'):
+        return tuple(reversed(range(dim)))
+    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)))
@@ -1069,7 +1050,6 @@ def _parse_part1(d):
 
 
 def _parse_description(description):
-
     def parse_part2(d):
         result = type_description_regex.match(d)
         if result:

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.cudajit import make_python_function
-from pystencils.gpucuda.kernelcreation import create_cuda_kernel, created_indexed_cuda_kernel
+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.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.gpucuda.texture_utils import ndarray_to_tex
-from pystencils.include import get_pycuda_include_path, get_pystencils_include_path
-from pystencils.interpolation_astnodes import InterpolatorAccess, TextureCachedField
+from pystencils.include import get_pystencils_include_path
 from pystencils.kernel_wrapper import KernelWrapper
-from pystencils.kernelparameters import FieldPointerSymbol
+from pystencils.typing import BasicType, FieldPointerSymbol
 
 USE_FAST_MATH = True
 
@@ -22,57 +21,49 @@ def get_cubic_interpolation_include_paths():
 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 = ['<cstdint>'] + 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', custom_backend=custom_backend))
-    textures = set(d.interpolator for d in kernel_function_node.atoms(
-        InterpolatorAccess) if isinstance(d.interpolator, TextureCachedField))
+    code += 'extern "C" {\n%s\n}\n' % str(generate_cuda(kernel_function_node, custom_backend=custom_backend))
 
-    nvcc_options = ["-w", "-std=c++11", "-Wno-deprecated-gpu-targets"]
+    options = ["-w", "-std=c++11"]
     if USE_FAST_MATH:
-        nvcc_options.append("-use_fast_math")
-
-    # Code for CubicInterpolationCUDA
-    from pystencils.interpolation_astnodes import InterpolationMode
-    from os.path import join, dirname, isdir
-
-    if any(t.interpolation_mode == InterpolationMode.CUBIC_SPLINE for t in textures):
-        assert isdir(join(dirname(__file__), ("CubicInterpolationCUDA", "code")),
-                     "Submodule CubicInterpolationCUDA does not exist.\n"
-                     + "Clone https://github.com/theHamsta/CubicInterpolationCUDA into pystencils.gpucuda")
-        nvcc_options += ["-I" + join(dirname(__file__), "CubicInterpolationCUDA", "code")]
-        nvcc_options += ["-I" + join(dirname(__file__), "CubicInterpolationCUDA", "code", "internal")]
-
-        needed_dims = set(t.field.spatial_dimensions for t in textures
-                          if t.interpolation_mode == InterpolationMode.CUBIC_SPLINE)
-        for i in needed_dims:
-            code = 'extern "C++" {\n#include "cubicTex%iD.cu"\n}\n' % i + code
-
-    mod = SourceModule(code, options=nvcc_options, include_dirs=[
-                       get_pystencils_include_path(), get_pycuda_include_path()])
-    func = mod.get_function(kernel_function_node.function_name)
+        options.append("-use_fast_math")
+    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 = {}
@@ -83,7 +74,10 @@ def make_python_function(kernel_function_node, argument_dict=None, custom_backen
                          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)
@@ -94,17 +88,16 @@ def make_python_function(kernel_function_node, argument_dict=None, custom_backen
             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'])
 
-            # TODO: use texture objects:
-            # https://devblogs.nvidia.com/cuda-pro-tip-kepler-texture-objects-improve-performance-and-flexibility/
-            for tex in textures:
-                tex_ref = mod.get_texref(str(tex))
-                ndarray_to_tex(tex_ref, full_arguments[tex.field.name], tex.address_mode,
-                               tex.filter_mode, tex.use_normalized_coordinates, tex.read_as_integer)
-            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
     ast = kernel_function_node
     parameters = kernel_function_node.get_parameters()
@@ -123,8 +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
@@ -159,22 +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])
@@ -182,9 +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]

pystencils/gpucuda/indexing.py → 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
-from pystencils.data_types import TypedSymbol, create_type
+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.slicing import normalize_slice
 from pystencils.sympyextensions import is_integer_sequence, prod
 
 
@@ -32,23 +33,58 @@ GRID_DIM = [ThreadIndexingSymbol("gridDim." + coord, create_type("int32")) for c
 
 class AbstractIndexing(abc.ABC):
     """
-    Abstract base class for all Indexing classes. An Indexing class defines how a multidimensional
-    field is mapped to CUDA's block and grid system. It calculates indices based on CUDA's thread and block indices
-    and computes the number of blocks and threads a kernel is started with. The Indexing class is created with
-    a pystencils field, a slice to iterate over, and further optional parameters that must have default values.
+    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 CUDA block and thread indices.
+        """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 CUDA's block and thread indices, and block and grid dimensions. """
+        """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.
@@ -88,57 +124,79 @@ class AbstractIndexing(abc.ABC):
 
 
 class BlockIndexing(AbstractIndexing):
-    """Generic indexing scheme that maps sub-blocks of an array to CUDA blocks.
+    """Generic indexing scheme that maps sub-blocks of an array to GPU blocks.
 
     Args:
-        field: pystencils field (common to all Indexing classes)
-        iteration_slice: slice that defines rectangular subarea which is iterated over
+        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 cuda variable 'blockDim' is used
+        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, field, iteration_slice,
-                 block_size=(16, 16, 1), permute_block_size_dependent_on_layout=True, compile_time_block_size=False,
-                 maximum_block_size=(1024, 1024, 64)):
-        if field.spatial_dimensions > 3:
-            raise NotImplementedError("This indexing scheme supports at most 3 spatial dimensions")
+    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:
-            block_size = self.permute_block_size_according_to_layout(block_size, field.layout)
+        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 pycuda.driver as cuda
-            # noinspection PyUnresolvedReferences
-            import pycuda.autoinit  # NOQA
-            da = cuda.device_attribute
-            device = cuda.Context.get_device()
-            maximum_block_size = tuple(device.get_attribute(a)
-                                       for a in (da.MAX_BLOCK_DIM_X, da.MAX_BLOCK_DIM_Y, da.MAX_BLOCK_DIM_Z))
+            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._iterationSlice = normalize_slice(iteration_slice, field.spatial_shape)
-        self._dim = field.spatial_dimensions
-        self._symbolic_shape = [e if isinstance(e, sp.Basic) else None for e in field.spatial_shape]
         self._compile_time_block_size = compile_time_block_size
+        self._device_number = device_number
 
     @property
-    def coordinates(self):
-        offsets = _get_start_from_slice(self._iterationSlice)
+    def cuda_indices(self):
         block_size = self._block_size if self._compile_time_block_size else BLOCK_DIM
-        coordinates = [block_index * bs + thread_idx + off
-                       for block_index, bs, thread_idx, off in zip(BLOCK_IDX, block_size, THREAD_IDX, offsets)]
+        indices = [block_index * bs + thread_idx
+                   for block_index, bs, thread_idx in zip(BLOCK_IDX, block_size, THREAD_IDX)]
+
+        return indices[:self._dim]
 
-        return coordinates[: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):
-        substitution_dict = {sym: value for sym, value in zip(self._symbolic_shape, arr_shape) if sym is not None}
+        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]]
 
-        widths = [end - start for start, end in zip(_get_start_from_slice(self._iterationSlice),
-                                                    _get_end_from_slice(self._iterationSlice, arr_shape))]
-        widths = sp.Matrix(widths).subs(substitution_dict)
         extend_bs = (1,) * (3 - len(self._block_size))
         block_size = self._block_size + extend_bs
         if not self._compile_time_block_size:
@@ -147,7 +205,8 @@ class BlockIndexing(AbstractIndexing):
             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]))
-            block_size = tuple(adapted_block_size) + extend_bs
+            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))
@@ -158,42 +217,59 @@ class BlockIndexing(AbstractIndexing):
 
     def guard(self, kernel_content, arr_shape):
         arr_shape = arr_shape[:self._dim]
-        conditions = [c < end
-                      for c, end in zip(self.coordinates, _get_end_from_slice(self._iterationSlice, arr_shape))]
+        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)])
 
-    @staticmethod
-    def limit_block_size_by_register_restriction(block_size, required_registers_per_thread, device=None):
-        """Shrinks the block_size if there are too many registers used per multiprocessor.
+    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 pycuda function.
-        :returns smaller block_size if too many registers are used.
+        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 pycuda.driver as cuda
-        # noinspection PyUnresolvedReferences
-        import pycuda.autoinit  # NOQA
-
-        da = cuda.device_attribute
-        if device is None:
-            device = cuda.Context.get_device()
-        available_registers_per_mp = device.get_attribute(da.MAX_REGISTERS_PER_MULTIPROCESSOR)
+        import cupy as cp
 
-        block = block_size
+        # 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:
-            num_threads = 1
-            for t in block:
-                num_threads *= t
-            required_registers_per_mt = num_threads * required_registers_per_thread
-            if required_registers_per_mt <= available_registers_per_mp:
-                return block
+            required_registers = math.prod(result) * required_registers_per_thread
+            if required_registers <= max_registers_per_block:
+                return result
             else:
-                largest_grid_entry_idx = max(range(len(block)), key=lambda e: block[e])
-                assert block[largest_grid_entry_idx] >= 2
-                block[largest_grid_entry_idx] //= 2
+                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):
@@ -222,42 +298,48 @@ class BlockIndexing(AbstractIndexing):
 
 class LineIndexing(AbstractIndexing):
     """
-    Indexing scheme that assigns the innermost 'line' i.e. the elements which are adjacent in memory to a 1D CUDA block.
+    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 CUDA block (which depends on device).
+    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, field, iteration_slice):
-        available_indices = [THREAD_IDX[0]] + BLOCK_IDX
-        if field.spatial_dimensions > 4:
+    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")
 
-        coordinates = available_indices[:field.spatial_dimensions]
+    @property
+    def cuda_indices(self):
+        available_indices = [THREAD_IDX[0]] + BLOCK_IDX
+        coordinates = available_indices[:self.dim]
 
-        fastest_coordinate = field.layout[-1]
+        fastest_coordinate = self.data_layout[-1]
         coordinates[0], coordinates[fastest_coordinate] = coordinates[fastest_coordinate], coordinates[0]
 
-        self._coordinates = coordinates
-        self._iterationSlice = normalize_slice(iteration_slice, field.spatial_shape)
-        self._symbolicShape = [e if isinstance(e, sp.Basic) else None for e in field.spatial_shape]
+        return coordinates
 
     @property
     def coordinates(self):
-        return [i + offset for i, offset in zip(self._coordinates, _get_start_from_slice(self._iterationSlice))]
+        return [i + o.start for i, o in zip(self.cuda_indices, self._iteration_space)]
 
-    def call_parameters(self, arr_shape):
-        substitution_dict = {sym: value for sym, value in zip(self._symbolicShape, arr_shape) if sym is not None}
+    def get_loop_ctr_assignments(self, loop_counter_symbols):
+        return _loop_ctr_assignments(loop_counter_symbols, self.coordinates, self._iteration_space)
 
-        widths = [end - start for start, end in zip(_get_start_from_slice(self._iterationSlice),
-                                                    _get_end_from_slice(self._iterationSlice, arr_shape))]
-        widths = sp.Matrix(widths).subs(substitution_dict)
+    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._coordinates:
+            if cuda_idx not in self.cuda_indices:
                 return 1
             else:
-                idx = self._coordinates.index(cuda_idx)
+                idx = self.cuda_indices.index(cuda_idx)
                 return widths[idx]
 
         return {'block': tuple([get_shape_of_cuda_idx(idx) for idx in THREAD_IDX]),
@@ -272,30 +354,66 @@ class LineIndexing(AbstractIndexing):
     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_start_from_slice(iteration_slice):
+def _get_numeric_iteration_slice(iteration_slice, arr_shape):
     res = []
-    for slice_component in iteration_slice:
-        if type(slice_component) is slice:
-            res.append(slice_component.start if slice_component.start is not None else 0)
-        else:
-            assert isinstance(slice_component, int)
-            res.append(slice_component)
+    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_end_from_slice(iteration_slice, arr_shape):
-    iter_slice = normalize_slice(iteration_slice, arr_shape)
-    res = []
-    for slice_component in iter_slice:
-        if type(slice_component) is slice:
-            res.append(slice_component.stop)
+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:
-            assert isinstance(slice_component, int)
-            res.append(slice_component + 1)
-    return res
+            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):

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

+import sympy as sp
+
 from pystencils.astnodes import Block, KernelFunction, LoopOverCoordinate, SympyAssignment
-from pystencils.data_types import BasicType, StructType, TypedSymbol
+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.gpucuda.cudajit import make_python_function
-from pystencils.gpucuda.indexing import BlockIndexing
+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 (
-    add_types, get_base_buffer_index, get_common_shape, implement_interpolations,
-    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,
-                       use_textures_for_interpolation=True):
-    assert assignments, "Assignments must not be empty!"
-    fields_read, fields_written, assignments = add_types(assignments, type_info, not skip_independence_check)
+    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: 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])
 
-    buffers = set([f for f in all_fields if FieldType.is_buffer(f) or FieldType.is_custom(f)])
+    buffers = set([f for f in all_fields if FieldType.is_buffer(f)])
     fields_without_buffers = all_fields - buffers
 
     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
@@ -49,41 +63,51 @@ def create_cuda_kernel(assignments,
                 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
-
-    block = Block(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 = indexing.guard(block, common_shape)
     unify_shape_symbols(block, common_shape=common_shape, fields=fields_without_buffers)
 
     ast = KernelFunction(block,
-                         'gpu',
-                         'gpucuda',
+                         Target.GPU,
+                         Backend.CUDA,
                          make_python_function,
                          ghost_layers,
                          function_name,
                          assignments=assignments)
     ast.global_variables.update(indexing.index_variables)
 
-    implement_interpolations(ast, implement_by_texture_accesses=use_textures_for_interpolation)
-
-    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)
@@ -102,34 +126,41 @@ def create_cuda_kernel(assignments,
     return ast
 
 
-def created_indexed_cuda_kernel(assignments,
-                                index_fields,
-                                function_name="kernel",
-                                type_info=None,
-                                coordinate_names=('x', 'y', 'z'),
-                                indexing_creator=BlockIndexing,
-                                use_textures_for_interpolation=True):
-    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(f"Index {name} not found in any of the passed index fields")
 
@@ -138,17 +169,19 @@ def created_indexed_cuda_kernel(assignments,
     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, 'gpu', 'gpucuda', make_python_function,
+    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)
 
-    implement_interpolations(ast, implement_by_texture_accesses=use_textures_for_interpolation)
-
     coord_mapping = indexing.coordinates
     base_pointer_spec = [['spatialInner0']]
     base_pointer_info = {f.name: parse_base_pointer_info(base_pointer_spec, [2, 1, 0],

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

 import numpy as np
 from itertools import product
 
-import pystencils.gpucuda
-import pystencils.opencl
+from pystencils import CreateKernelConfig, create_kernel
+from pystencils.gpu import make_python_function
 from pystencils import Assignment, Field
-from pystencils.gpucuda.kernelcreation import create_cuda_kernel
+from pystencils.enums import Target
 from pystencils.slicing import get_periodic_boundary_src_dst_slices, normalize_slice
 
 
@@ -26,24 +26,21 @@ def create_copy_kernel(domain_size, from_slice, to_slice, index_dimensions=0, in
         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)
+    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, target='gpu', opencl_queue=None, opencl_ctx=None):
-    assert target in ['gpu', 'opencl']
+                                  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 = []
 
     for src_slice, dst_slice in src_dst_slice_tuples:
         ast = create_copy_kernel(domain_size, src_slice, dst_slice, index_dimensions, index_dim_shape, dtype)
-        if target == 'gpu':
-            kernels.append(pystencils.gpucuda.make_python_function(ast))
-        else:
-            ast._target = 'opencl'
-            ast._backend = 'opencl'
-            kernels.append(pystencils.opencl.make_python_function(ast, opencl_queue, opencl_ctx))
+        kernels.append(make_python_function(ast))
 
     def functor(pdfs, **_):
         for kernel in kernels:

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

-from os.path import dirname, join, realpath
+from os.path import dirname, realpath
 
 
 def get_pystencils_include_path():
     return dirname(realpath(__file__))
-
-
-def get_pycuda_include_path():
-    import pycuda
-    return join(dirname(realpath(pycuda.__file__)), 'cuda')

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
+

src/pystencils/include/arm_neon_helpers.h

+/*
+Copyright 2021-2023, 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.
+*/
+
+#if defined(_MSC_VER)
+#define __ARM_NEON
+#endif
+
+#ifdef __ARM_NEON
+#include <arm_neon.h>
+#endif
+
+#if defined(__ARM_FEATURE_SVE) && defined(__ARM_FEATURE_SVE_BITS) && __ARM_FEATURE_SVE_BITS > 0
+#include <arm_sve.h>
+
+typedef svbool_t svbool_st __attribute__((arm_sve_vector_bits(__ARM_FEATURE_SVE_BITS)));
+typedef svfloat32_t svfloat32_st __attribute__((arm_sve_vector_bits(__ARM_FEATURE_SVE_BITS)));
+typedef svfloat64_t svfloat64_st __attribute__((arm_sve_vector_bits(__ARM_FEATURE_SVE_BITS)));
+typedef svint32_t svint32_st __attribute__((arm_sve_vector_bits(__ARM_FEATURE_SVE_BITS)));
+#endif
+
+#ifdef __ARM_NEON
+inline float32x4_t makeVec_f32(float a, float b, float c, float d)
+{
+    alignas(16) float data[4] = {a, b, c, d};
+    return vld1q_f32(data);
+}
+
+inline float64x2_t makeVec_f64(double a, double b)
+{
+    alignas(16) double data[2] = {a, b};
+    return vld1q_f64(data);
+}
+
+inline int32x4_t makeVec_s32(int a, int b, int c, int d)
+{
+    alignas(16) int data[4] = {a, b, c, d};
+    return vld1q_s32(data);
+}
+#endif
+
+inline void cachelineZero(void * p) {
+#if !defined(_MSC_VER) || defined(__clang__)
+	__asm__ volatile("dc zva, %0"::"r"(p):"memory");
+#endif
+}
+
+inline size_t _cachelineSize() {
+#if !defined(_MSC_VER) || defined(__clang__)
+	// check that dc zva is permitted
+	uint64_t dczid;
+	__asm__ volatile ("mrs %0, dczid_el0" : "=r"(dczid));
+	if ((dczid & (1 << 4)) != 0) {
+		return SIZE_MAX;
+	}
+
+	// allocate and fill with ones
+	const size_t max_size = 0x100000;
+	uint8_t data[2*max_size];
+	for (size_t i = 0; i < 2*max_size; ++i) {
+		data[i] = 0xff;
+	}
+	
+	// find alignment offset
+	size_t offset = max_size - ((uintptr_t) data) % max_size;
+
+	// zero a cacheline
+	cachelineZero((void*) (data + offset));
+
+	// make sure that at least one byte was zeroed
+	if (data[offset] != 0) {
+		return SIZE_MAX;
+	}
+
+	// make sure that nothing was zeroed before the pointer
+	if (data[offset-1] == 0) {
+		return SIZE_MAX;
+	}
+
+	// find the last byte that was zeroed
+	for (size_t size = 1; size < max_size; ++size) {
+		if (data[offset + size] != 0) {
+			return size;
+		}
+	}
+#endif
+	
+	// too much was zeroed
+	return SIZE_MAX;
+}
+
+inline size_t cachelineSize() {
+	static size_t size = _cachelineSize();
+	return size;
+}

src/pystencils/include/gpu_defines.h

+/*
+Copyright 2023, Markus Holzer.
+Copyright 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.
+*/
+
+#pragma once
+
+#define POS_INFINITY __int_as_float(0x7f800000)
+#define INFINITY POS_INFINITY
+#define NEG_INFINITY __int_as_float(0xff800000)
+
+#ifdef __HIPCC_RTC__
+typedef __hip_uint8_t uint8_t;
+typedef __hip_int8_t int8_t;
+typedef __hip_uint16_t uint16_t;
+typedef __hip_int16_t int16_t;
+#endif

src/pystencils/include/half_precision.h

+/*
+Copyright 2023, Markus Holzer.
+
+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.
+*/
+
+
+/// Half precision support. Experimental. Use carefully.
+///
+/// This feature is experimental, since it strictly depends on the underlying architecture and compiler support.
+/// On x86 architectures, what you can expect is that the data format is supported natively only for storage and
+/// interchange. Arithmetic operations will likely involve casting to fp32 (C++ float) and truncation to fp16.
+/// Only bandwidth bound code may therefore benefit. None of this is guaranteed, and may change in the future.
+
+/// Clang version must be 15 or higher for x86 half precision support.
+/// GCC version must be 12 or higher for x86 half precision support.
+/// Also support seems to require SSE, so ensure that respective instruction sets are enabled.
+/// See
+///   https://clang.llvm.org/docs/LanguageExtensions.html#half-precision-floating-point
+///   https://gcc.gnu.org/onlinedocs/gcc/Half-Precision.html
+/// for more information.
+
+#pragma once
+using half    = _Float16;