pystencils/alignedarray.py → src/pystencils/alignedarray.py

 import numpy as np
 
 
-def aligned_empty(shape, byte_alignment=32, dtype=np.float64, byte_offset=0, order='C', align_inner_coordinate=True):
+def aligned_empty(shape, byte_alignment=True, dtype=np.float64, byte_offset=0, order='C', align_inner_coordinate=True):
     """
     Creates an aligned empty numpy array
 
     Args:
         shape: size of the array
         byte_alignment: alignment in bytes, for the start address of the array holds (a % byte_alignment) == 0
+                        By default, use the maximum required by the CPU (or 512 bits if this cannot be detected).
+                        When 'cacheline' is specified, the size of a cache line is used.
         dtype: numpy data type
         byte_offset: offset in bytes for position that should be aligned i.e. (a+byte_offset) % byte_alignment == 0
                     typically used to align first inner cell instead of ghost layer
         order: storage linearization order
         align_inner_coordinate: if True, the start of the innermost coordinate lines are aligned as well
     """
+    if byte_alignment is True or byte_alignment == 'cacheline':
+        from pystencils.backends.simd_instruction_sets import (get_supported_instruction_sets, get_cacheline_size,
+                                                               get_vector_instruction_set)
+
+        instruction_sets = get_supported_instruction_sets()
+        if instruction_sets is None:
+            byte_alignment = 64
+        elif byte_alignment == 'cacheline':
+            cacheline_sizes = [get_cacheline_size(is_name) for is_name in instruction_sets]
+            if all([s is None for s in cacheline_sizes]) or \
+                    max([s for s in cacheline_sizes if s is not None]) > 0x100000:
+                widths = [get_vector_instruction_set(dtype, is_name)['width'] * np.dtype(dtype).itemsize
+                          for is_name in instruction_sets
+                          if type(get_vector_instruction_set(dtype, is_name)['width']) is int]
+                byte_alignment = 64 if all([s is None for s in widths]) else max(widths)
+            else:
+                byte_alignment = max([s for s in cacheline_sizes if s is not None])
+        elif not any([type(get_vector_instruction_set(dtype, is_name)['width']) is int
+                      for is_name in instruction_sets]):
+            byte_alignment = 64
+        else:
+            byte_alignment = max([get_vector_instruction_set(dtype, is_name)['width'] * np.dtype(dtype).itemsize
+                                  for is_name in instruction_sets
+                                  if type(get_vector_instruction_set(dtype, is_name)['width']) is int])
     if (not align_inner_coordinate) or (not hasattr(shape, '__len__')):
         size = np.prod(shape)
         d = np.dtype(dtype)
@@ -51,7 +77,7 @@ def aligned_empty(shape, byte_alignment=32, dtype=np.float64, byte_offset=0, ord
         return tmp
 
 
-def aligned_zeros(shape, byte_alignment=16, dtype=float, byte_offset=0, order='C', align_inner_coordinate=True):
+def aligned_zeros(shape, byte_alignment=True, dtype=np.float64, byte_offset=0, order='C', align_inner_coordinate=True):
     arr = aligned_empty(shape, dtype=dtype, byte_offset=byte_offset,
                         order=order, byte_alignment=byte_alignment, align_inner_coordinate=align_inner_coordinate)
     x = np.zeros((), arr.dtype)
@@ -59,7 +85,7 @@ def aligned_zeros(shape, byte_alignment=16, dtype=float, byte_offset=0, order='C
     return arr
 
 
-def aligned_ones(shape, byte_alignment=16, dtype=float, byte_offset=0, order='C', align_inner_coordinate=True):
+def aligned_ones(shape, byte_alignment=True, dtype=np.float64, byte_offset=0, order='C', align_inner_coordinate=True):
     arr = aligned_empty(shape, dtype=dtype, byte_offset=byte_offset,
                         order=order, byte_alignment=byte_alignment, align_inner_coordinate=align_inner_coordinate)
     x = np.ones((), arr.dtype)

pystencils/assignment.py → src/pystencils/assignment.py

-# -*- coding: utf-8 -*-
+import numpy as np
 import sympy as sp
+from sympy.codegen.ast import Assignment, AugmentedAssignment, AddAugmentedAssignment
 from sympy.printing.latex import LatexPrinter
 
-try:
-    from sympy.codegen.ast import Assignment
-except ImportError:
-    Assignment = None
-import numpy as np
-
-__all__ = ['Assignment', 'assignment_from_stencil']
+__all__ = ['Assignment', 'AugmentedAssignment', 'AddAugmentedAssignment', 'assignment_from_stencil']
 
 
 def print_assignment_latex(printer, expr):
+    binop = f"{expr.binop}=" if isinstance(expr, AugmentedAssignment) else ''
     """sympy cannot print Assignments as Latex. Thus, this function is added to the sympy Latex printer"""
     printed_lhs = printer.doprint(expr.lhs)
     printed_rhs = printer.doprint(expr.rhs)
-    return r"{printed_lhs} \leftarrow {printed_rhs}".format(printed_lhs=printed_lhs, printed_rhs=printed_rhs)
+    return fr"{printed_lhs} \leftarrow_{{{binop}}} {printed_rhs}"
 
 
 def assignment_str(assignment):
-    return r"{lhs} ← {rhs}".format(lhs=assignment.lhs, rhs=assignment.rhs)
+    op = f"{assignment.binop}=" if isinstance(assignment, AugmentedAssignment) else '←'
+    return fr"{assignment.lhs} {op} {assignment.rhs}"
 
 
-if Assignment:
+_old_new = sp.codegen.ast.Assignment.__new__
 
-    Assignment.__str__ = assignment_str
-    LatexPrinter._print_Assignment = print_assignment_latex
 
-else:
-    # back port for older sympy versions that don't have Assignment  yet
+# TODO Typing Part2 add default type, defult_float_type, default_int_type and use sane defaults
+def _Assignment__new__(cls, lhs, rhs, *args, **kwargs):
+    if isinstance(lhs, (list, tuple, sp.Matrix)) and isinstance(rhs, (list, tuple, sp.Matrix)):
+        assert len(lhs) == len(rhs), f'{lhs} and {rhs} must have same length when performing vector assignment!'
+        return tuple(_old_new(cls, a, b, *args, **kwargs) for a, b in zip(lhs, rhs))
+    return _old_new(cls, lhs, rhs, *args, **kwargs)
 
-    class Assignment(sp.Rel):  # pragma: no cover
 
-        rel_op = ':='
-        __slots__ = []
+Assignment.__str__ = assignment_str
+Assignment.__new__ = _Assignment__new__
+LatexPrinter._print_Assignment = print_assignment_latex
 
-        def __new__(cls, lhs, rhs=0, **assumptions):
-            from sympy.matrices.expressions.matexpr import (
-                MatrixElement, MatrixSymbol)
-            lhs = sp.sympify(lhs)
-            rhs = sp.sympify(rhs)
-            # Tuple of things that can be on the lhs of an assignment
-            assignable = (sp.Symbol, MatrixSymbol, MatrixElement, sp.Indexed)
-            if not isinstance(lhs, assignable):
-                raise TypeError("Cannot assign to lhs of type %s." % type(lhs))
-            return sp.Rel.__new__(cls, lhs, rhs, **assumptions)
+AugmentedAssignment.__str__ = assignment_str
+LatexPrinter._print_AugmentedAssignment = print_assignment_latex
 
-        __str__ = assignment_str
-        _print_Assignment = print_assignment_latex
+sp.MutableDenseMatrix.__hash__ = lambda self: hash(tuple(self))
 
 
 def assignment_from_stencil(stencil_array, input_field, output_field,
@@ -73,18 +63,21 @@ def assignment_from_stencil(stencil_array, input_field, output_field,
         ...            [0, 6, 0]]
 
         By default 'visual ordering is used - i.e. the stencil is applied as the nested lists are written down
-        >>> assignment_from_stencil(stencil, f, g, order='visual')
-        Assignment(g_C, 3*f_W + 6*f_S + 4*f_C + 2*f_N + 5*f_E)
+        >>> expected_output = Assignment(g[0, 0], 3*f[-1, 0] + 6*f[0, -1] + 4*f[0, 0] + 2*f[0, 1] + 5*f[1, 0])
+        >>> assignment_from_stencil(stencil, f, g, order='visual') == expected_output
+        True
 
         'numpy' ordering uses the first coordinate of the stencil array for x offset, second for y offset etc.
-        >>> assignment_from_stencil(stencil, f, g, order='numpy')
-        Assignment(g_C, 2*f_W + 3*f_S + 4*f_C + 5*f_N + 6*f_E)
+        >>> expected_output = Assignment(g[0, 0], 2*f[-1, 0] + 3*f[0, -1] + 4*f[0, 0] + 5*f[0, 1] + 6*f[1, 0])
+        >>> assignment_from_stencil(stencil, f, g, order='numpy') == expected_output
+        True
 
         You can also pass field accesses to apply the stencil at an already shifted position:
-        >>> assignment_from_stencil(stencil, f[1, 0], g[2, 0])
-        Assignment(g_2E, 3*f_C + 6*f_SE + 4*f_E + 2*f_NE + 5*f_2E)
+        >>> expected_output = Assignment(g[2, 0], 3*f[0, 0] + 6*f[1, -1] + 4*f[1, 0] + 2*f[1, 1] + 5*f[2, 0])
+        >>> assignment_from_stencil(stencil, f[1, 0], g[2, 0]) == expected_output
+        True
     """
-    from pystencils import Field
+    from pystencils.field import Field
 
     stencil_array = np.array(stencil_array)
     if order == 'visual':

pystencils/astnodes.py → src/pystencils/astnodes.py

+import collections.abc
+import itertools
+import uuid
+from typing import Any, List, Optional, Sequence, Set, Union
+
 import sympy as sp
+
+from pystencils.assignment import Assignment
+from pystencils.enums import Target, Backend
 from pystencils.field import Field
-from pystencils.data_types import TypedSymbol, create_type, cast_func
-from pystencils.kernelparameters import FieldStrideSymbol, FieldPointerSymbol, FieldShapeSymbol
 from pystencils.sympyextensions import fast_subs
-from typing import List, Set, Optional, Union, Any, Sequence
+from pystencils.typing import (create_type, get_next_parent_of_type,
+                               FieldPointerSymbol, FieldShapeSymbol, FieldStrideSymbol, TypedSymbol, CFunction)
 
 NodeOrExpr = Union['Node', sp.Expr]
 
@@ -30,9 +37,13 @@ class Node:
         raise NotImplementedError()
 
     def subs(self, subs_dict) -> None:
-        """Inplace! substitute, similar to sympy's but modifies the AST inplace."""
-        for a in self.args:
-            a.subs(subs_dict)
+        """Inplace! Substitute, similar to sympy's but modifies the AST inplace."""
+        for i, a in enumerate(self.args):
+            result = a.subs(subs_dict)
+            if isinstance(a, sp.Expr):  # sympy expressions' subs is out-of-place
+                self.args[i] = result
+            else:  # all other should be in-place
+                assert result is None
 
     @property
     def func(self):
@@ -99,14 +110,22 @@ class Conditional(Node):
         result = self.true_block.undefined_symbols
         if self.false_block:
             result.update(self.false_block.undefined_symbols)
-        result.update(self.condition_expr.atoms(sp.Symbol))
+        if hasattr(self.condition_expr, 'atoms'):
+            result.update(self.condition_expr.atoms(sp.Symbol))
         return result
 
     def __str__(self):
-        return 'if:({!s}) '.format(self.condition_expr)
+        return self.__repr__()
 
     def __repr__(self):
-        return 'if:({!r}) '.format(self.condition_expr)
+        result = f'if:({self.condition_expr!r}) '
+        if self.true_block:
+            result += f'\n\t{self.true_block}) '
+        if self.false_block:
+            result = 'else: '
+            result += f'\n\t{self.false_block} '
+
+        return result
 
     def replace_by_true_block(self):
         """Replaces the conditional by its True block"""
@@ -118,7 +137,6 @@ class Conditional(Node):
 
 
 class KernelFunction(Node):
-
     class Parameter:
         """Function parameter.
 
@@ -130,6 +148,7 @@ class KernelFunction(Node):
         defined in pystencils.kernelparameters.
         If the parameter is related to one or multiple fields, these fields are referenced in the fields property.
         """
+
         def __init__(self, symbol, fields):
             self.symbol = symbol  # type: TypedSymbol
             self.fields = fields  # type: Sequence[Field]
@@ -157,18 +176,37 @@ class KernelFunction(Node):
         def field_name(self):
             return self.fields[0].name
 
-    def __init__(self, body, ghost_layers=None, function_name="kernel", backend=""):
+    def __init__(self, body, target: Target, backend: Backend, compile_function, ghost_layers,
+                 function_name: str = "kernel",
+                 assignments=None):
         super(KernelFunction, self).__init__()
         self._body = body
         body.parent = self
         self.function_name = function_name
         self._body.parent = self
-        self.compile = None
         self.ghost_layers = ghost_layers
+        self._target = target
+        self._backend = backend
         # these variables are assumed to be global, so no automatic parameter is generated for them
         self.global_variables = set()
-        self.backend = backend
         self.instruction_set = None  # used in `vectorize` function to tell the backend which i.s. (SSE,AVX) to use
+        # function that compiles the node to a Python callable, is set by the backends
+        self._compile_function = compile_function
+        self.assignments = assignments
+        # If nontemporal stores are activated together with the Neon instruction set it results in cacheline zeroing
+        # For cacheline zeroing the information of the field size for each field is needed. Thus, in this case
+        # all field sizes are kernel parameters and not just the common field size used for the loops
+        self.use_all_written_field_sizes = False
+
+    @property
+    def target(self):
+        """See pystencils.Target"""
+        return self._target
+
+    @property
+    def backend(self):
+        """Backend for generating the code: `Backend`"""
+        return self._backend
 
     @property
     def symbols_defined(self):
@@ -189,12 +227,24 @@ class KernelFunction(Node):
 
     @property
     def args(self):
-        return [self._body]
+        return self._body,
 
     @property
-    def fields_accessed(self) -> Set['ResolvedFieldAccess']:
+    def fields_accessed(self) -> Set[Field]:
         """Set of Field instances: fields which are accessed inside this kernel function"""
-        return set(o.field for o in self.atoms(ResolvedFieldAccess))
+        return set(o.field for o in itertools.chain(self.atoms(ResolvedFieldAccess)))
+
+    @property
+    def fields_written(self) -> Set[Field]:
+        assignments = self.atoms(SympyAssignment)
+        return set().union(itertools.chain.from_iterable([f.field for f in a.lhs.free_symbols if hasattr(f, 'field')]
+                                                         for a in assignments))
+
+    @property
+    def fields_read(self) -> Set[Field]:
+        assignments = self.atoms(SympyAssignment)
+        return set().union(itertools.chain.from_iterable([f.field for f in a.rhs.free_symbols if hasattr(f, 'field')]
+                                                         for a in assignments))
 
     def get_parameters(self) -> Sequence['KernelFunction.Parameter']:
         """Returns list of parameters for this function.
@@ -202,6 +252,11 @@ class KernelFunction(Node):
         This function is expensive, cache the result where possible!
         """
         field_map = {f.name: f for f in self.fields_accessed}
+        sizes = set()
+
+        if self.use_all_written_field_sizes:
+            sizes = set().union(*(a.shape[:a.spatial_dimensions] for a in self.fields_written))
+            sizes = filter(lambda s: isinstance(s, FieldShapeSymbol), sizes)
 
         def get_fields(symbol):
             if hasattr(symbol, 'field_name'):
@@ -211,7 +266,13 @@ class KernelFunction(Node):
             return ()
 
         argument_symbols = self._body.undefined_symbols - self.global_variables
+        argument_symbols.update(sizes)
         parameters = [self.Parameter(symbol, get_fields(symbol)) for symbol in argument_symbols]
+        if hasattr(self, 'indexing'):
+            parameters += [self.Parameter(s, []) for s in self.indexing.symbolic_parameters()]
+        # Exclude paramters of type CFunction. These parameters will result in a C function call that will be handled
+        # by including a respective header file in the compute kernel. Hence, it is not a free parameter.
+        parameters = [p for p in parameters if not isinstance(p.symbol, CFunction)]
         parameters.sort(key=lambda p: p.symbol.name)
         return parameters
 
@@ -222,7 +283,12 @@ class KernelFunction(Node):
 
     def __repr__(self):
         params = [p.symbol for p in self.get_parameters()]
-        return '{0} {1}({2})'.format(type(self).__name__, self.function_name, params)
+        return f'{type(self).__name__} {self.function_name}({params})'
+
+    def compile(self, *args, **kwargs):
+        if self._compile_function is None:
+            raise ValueError("No compile-function provided for this KernelFunction node")
+        return self._compile_function(self, *args, **kwargs)
 
 
 class SkipIteration(Node):
@@ -240,46 +306,59 @@ class SkipIteration(Node):
 
 
 class Block(Node):
-    def __init__(self, nodes: List[Node]):
+    def __init__(self, nodes: Union[Node, List[Node]]):
         super(Block, self).__init__()
+        if not isinstance(nodes, list):
+            nodes = [nodes]
         self._nodes = nodes
         self.parent = None
         for n in self._nodes:
-            n.parent = self
+            try:
+                n.parent = self
+            except AttributeError:
+                pass
 
     @property
     def args(self):
         return self._nodes
 
     def subs(self, subs_dict) -> None:
-        new_args = []
-        for a in self.args:
-            if isinstance(a, SympyAssignment) and a.is_declaration and a.rhs in subs_dict.keys():
-                subs_dict[a.lhs] = subs_dict[a.rhs]
-            else:
-                new_args.append(a)
-        self._nodes = new_args
-
         for a in self.args:
             a.subs(subs_dict)
 
-    def insert_front(self, node):
-        node.parent = self
-        self._nodes.insert(0, node)
+    def fast_subs(self, subs_dict, skip=None):
+        self._nodes = [fast_subs(a, subs_dict, skip) for a in self._nodes]
+        return self
 
-    def insert_before(self, new_node, insert_before):
+    def insert_front(self, node, if_not_exists=False):
+        if if_not_exists and len(self._nodes) > 0 and self._nodes[0] == node:
+            return
+        if isinstance(node, collections.abc.Iterable):
+            node = list(node)
+            for n in node:
+                n.parent = self
+
+            self._nodes = node + self._nodes
+        else:
+            node.parent = self
+            self._nodes.insert(0, node)
+
+    def insert_before(self, new_node, insert_before, if_not_exists=False):
         new_node.parent = self
+        assert self._nodes.count(insert_before) == 1
         idx = self._nodes.index(insert_before)
 
-        # move all assignment (definitions to the top)
-        if isinstance(new_node, SympyAssignment) and new_node.is_declaration:
-            while idx > 0:
-                pn = self._nodes[idx - 1]
-                if isinstance(pn, LoopOverCoordinate) or isinstance(pn, Conditional):
-                    idx -= 1
-                else:
-                    break
-        self._nodes.insert(idx, new_node)
+        if not if_not_exists or self._nodes[idx] != new_node:
+            self._nodes.insert(idx, new_node)
+
+    def insert_after(self, new_node, insert_after, if_not_exists=False):
+        new_node.parent = self
+        assert self._nodes.count(insert_after) == 1
+        idx = self._nodes.index(insert_after) + 1
+
+        if not if_not_exists or not (self._nodes[idx - 1] == new_node
+                                     or (idx < len(self._nodes) and self._nodes[idx] == new_node)):
+            self._nodes.insert(idx, new_node)
 
     def append(self, node):
         if isinstance(node, list) or isinstance(node, tuple):
@@ -296,6 +375,7 @@ class Block(Node):
         return tmp
 
     def replace(self, child, replacements):
+        assert self._nodes.count(child) == 1
         idx = self._nodes.index(child)
         del self._nodes[idx]
         if type(replacements) is list:
@@ -310,7 +390,10 @@ class Block(Node):
     def symbols_defined(self):
         result = set()
         for a in self.args:
-            result.update(a.symbols_defined)
+            if isinstance(a, Assignment):
+                result.update(a.free_symbols)
+            else:
+                result.update(a.symbols_defined)
         return result
 
     @property
@@ -318,8 +401,12 @@ class Block(Node):
         result = set()
         defined_symbols = set()
         for a in self.args:
-            result.update(a.undefined_symbols)
-            defined_symbols.update(a.symbols_defined)
+            if isinstance(a, Assignment):
+                result.update(a.free_symbols)
+                defined_symbols.update({a.lhs})
+            else:
+                result.update(a.undefined_symbols)
+                defined_symbols.update(a.symbols_defined)
         return result - defined_symbols
 
     def __str__(self):
@@ -342,9 +429,9 @@ class PragmaBlock(Block):
 
 class LoopOverCoordinate(Node):
     LOOP_COUNTER_NAME_PREFIX = "ctr"
-    BlOCK_LOOP_COUNTER_NAME_PREFIX = "_blockctr"
+    BLOCK_LOOP_COUNTER_NAME_PREFIX = "_blockctr"
 
-    def __init__(self, body, coordinate_to_loop_over, start, stop, step=1, is_block_loop=False):
+    def __init__(self, body, coordinate_to_loop_over, start, stop, step=1, is_block_loop=False, custom_loop_ctr=None):
         super(LoopOverCoordinate, self).__init__(parent=None)
         self.body = body
         body.parent = self
@@ -355,11 +442,12 @@ class LoopOverCoordinate(Node):
         self.body.parent = self
         self.prefix_lines = []
         self.is_block_loop = is_block_loop
+        self.custom_loop_ctr = custom_loop_ctr
 
     def new_loop_with_different_body(self, new_body):
         result = LoopOverCoordinate(new_body, self.coordinate_to_loop_over, self.start, self.stop,
-                                    self.step, self.is_block_loop)
-        result.prefix_lines = [l for l in self.prefix_lines]
+                                    self.step, self.is_block_loop, self.custom_loop_ctr)
+        result.prefix_lines = [prefix_line for prefix_line in self.prefix_lines]
         return result
 
     def subs(self, subs_dict):
@@ -371,6 +459,16 @@ class LoopOverCoordinate(Node):
         if hasattr(self.step, "subs"):
             self.step = self.step.subs(subs_dict)
 
+    def fast_subs(self, subs_dict, skip=None):
+        self.body = fast_subs(self.body, subs_dict, skip)
+        if isinstance(self.start, sp.Basic):
+            self.start = fast_subs(self.start, subs_dict, skip)
+        if isinstance(self.stop, sp.Basic):
+            self.stop = fast_subs(self.stop, subs_dict, skip)
+        if isinstance(self.step, sp.Basic):
+            self.step = fast_subs(self.step, subs_dict, skip)
+        return self
+
     @property
     def args(self):
         result = [self.body]
@@ -403,18 +501,21 @@ class LoopOverCoordinate(Node):
 
     @staticmethod
     def get_loop_counter_name(coordinate_to_loop_over):
-        return "%s_%s" % (LoopOverCoordinate.LOOP_COUNTER_NAME_PREFIX, coordinate_to_loop_over)
+        return f"{LoopOverCoordinate.LOOP_COUNTER_NAME_PREFIX}_{coordinate_to_loop_over}"
 
     @staticmethod
     def get_block_loop_counter_name(coordinate_to_loop_over):
-        return "%s_%s" % (LoopOverCoordinate.BlOCK_LOOP_COUNTER_NAME_PREFIX, coordinate_to_loop_over)
+        return f"{LoopOverCoordinate.BLOCK_LOOP_COUNTER_NAME_PREFIX}_{coordinate_to_loop_over}"
 
     @property
     def loop_counter_name(self):
-        if self.is_block_loop:
-            return LoopOverCoordinate.get_block_loop_counter_name(self.coordinate_to_loop_over)
+        if self.custom_loop_ctr:
+            return self.custom_loop_ctr.name
         else:
-            return LoopOverCoordinate.get_loop_counter_name(self.coordinate_to_loop_over)
+            if self.is_block_loop:
+                return LoopOverCoordinate.get_block_loop_counter_name(self.coordinate_to_loop_over)
+            else:
+                return LoopOverCoordinate.get_loop_counter_name(self.coordinate_to_loop_over)
 
     @staticmethod
     def is_loop_counter_symbol(symbol):
@@ -428,22 +529,26 @@ class LoopOverCoordinate(Node):
 
     @staticmethod
     def get_loop_counter_symbol(coordinate_to_loop_over):
-        return TypedSymbol(LoopOverCoordinate.get_loop_counter_name(coordinate_to_loop_over), 'int')
+        return TypedSymbol(LoopOverCoordinate.get_loop_counter_name(coordinate_to_loop_over), 'int', nonnegative=True)
 
     @staticmethod
     def get_block_loop_counter_symbol(coordinate_to_loop_over):
-        return TypedSymbol(LoopOverCoordinate.get_block_loop_counter_name(coordinate_to_loop_over), 'int')
+        return TypedSymbol(LoopOverCoordinate.get_block_loop_counter_name(coordinate_to_loop_over),
+                           'int',
+                           nonnegative=True)
 
     @property
     def loop_counter_symbol(self):
-        if self.is_block_loop:
-            return self.get_block_loop_counter_symbol(self.coordinate_to_loop_over)
+        if self.custom_loop_ctr:
+            return self.custom_loop_ctr
         else:
-            return self.get_loop_counter_symbol(self.coordinate_to_loop_over)
+            if self.is_block_loop:
+                return self.get_block_loop_counter_symbol(self.coordinate_to_loop_over)
+            else:
+                return self.get_loop_counter_symbol(self.coordinate_to_loop_over)
 
     @property
     def is_outermost_loop(self):
-        from pystencils.transformations import get_next_parent_of_type
         return get_next_parent_of_type(self, LoopOverCoordinate) is None
 
     @property
@@ -463,15 +568,17 @@ class LoopOverCoordinate(Node):
 
 
 class SympyAssignment(Node):
-    def __init__(self, lhs_symbol, rhs_expr, is_const=True):
+    def __init__(self, lhs_symbol, rhs_expr, is_const=True, use_auto=False):
         super(SympyAssignment, self).__init__(parent=None)
-        self._lhs_symbol = lhs_symbol
-        self.rhs = rhs_expr
+        self._lhs_symbol = sp.sympify(lhs_symbol)
+        self._rhs = sp.sympify(rhs_expr)
         self._is_const = is_const
         self._is_declaration = self.__is_declaration()
+        self._use_auto = use_auto
 
     def __is_declaration(self):
-        if isinstance(self._lhs_symbol, cast_func):
+        from pystencils.typing import CastFunc
+        if isinstance(self._lhs_symbol, CastFunc):
             return False
         if any(isinstance(self._lhs_symbol, c) for c in (Field.Access, sp.Indexed, TemporaryMemoryAllocation)):
             return False
@@ -481,15 +588,35 @@ class SympyAssignment(Node):
     def lhs(self):
         return self._lhs_symbol
 
+    @property
+    def rhs(self):
+        return self._rhs
+
     @lhs.setter
     def lhs(self, new_value):
         self._lhs_symbol = new_value
         self._is_declaration = self.__is_declaration()
 
+    @rhs.setter
+    def rhs(self, new_rhs_expr):
+        self._rhs = new_rhs_expr
+
     def subs(self, subs_dict):
         self.lhs = fast_subs(self.lhs, subs_dict)
         self.rhs = fast_subs(self.rhs, subs_dict)
 
+    def fast_subs(self, subs_dict, skip=None):
+        self.lhs = fast_subs(self.lhs, subs_dict, skip)
+        self.rhs = fast_subs(self.rhs, subs_dict, skip)
+        return self
+
+    def optimize(self, optimizations):
+        try:
+            from sympy.codegen.rewriting import optimize
+            self.rhs = optimize(self.rhs, optimizations)
+        except Exception:
+            pass
+
     @property
     def args(self):
         return [self._lhs_symbol, self.rhs]
@@ -502,7 +629,7 @@ class SympyAssignment(Node):
 
     @property
     def undefined_symbols(self):
-        result = self.rhs.atoms(sp.Symbol)
+        result = {s for s in self.rhs.free_symbols if not isinstance(s, sp.Indexed)}
         # Add loop counters if there a field accesses
         loop_counters = set()
         for symbol in result:
@@ -510,7 +637,9 @@ class SympyAssignment(Node):
                 for i in range(len(symbol.offsets)):
                     loop_counters.add(LoopOverCoordinate.get_loop_counter_symbol(i))
         result.update(loop_counters)
+        
         result.update(self._lhs_symbol.atoms(sp.Symbol))
+        
         return result
 
     @property
@@ -521,6 +650,10 @@ class SympyAssignment(Node):
     def is_const(self):
         return self._is_const
 
+    @property
+    def use_auto(self):
+        return self._use_auto
+
     def replace(self, child, replacement):
         if child == self.lhs:
             replacement.parent = self
@@ -529,7 +662,7 @@ class SympyAssignment(Node):
             replacement.parent = self
             self.rhs = replacement
         else:
-            raise ValueError('%s is not in args of %s' % (replacement, self.__class__))
+            raise ValueError(f'{replacement} is not in args of {self.__class__}')
 
     def __repr__(self):
         return repr(self.lhs) + " ← " + repr(self.rhs)
@@ -537,13 +670,21 @@ class SympyAssignment(Node):
     def _repr_html_(self):
         printed_lhs = sp.latex(self.lhs)
         printed_rhs = sp.latex(self.rhs)
-        return "${printed_lhs} \\leftarrow {printed_rhs}$".format(printed_lhs=printed_lhs, printed_rhs=printed_rhs)
+        return f"${printed_lhs} \\leftarrow {printed_rhs}$"
+
+    def __hash__(self):
+        return hash((self.lhs, self.rhs))
+
+    def __eq__(self, other):
+        return type(self) is type(other) and (self.lhs, self.rhs) == (other.lhs, other.rhs)
 
 
 class ResolvedFieldAccess(sp.Indexed):
     def __new__(cls, base, linearized_index, field, offsets, idx_coordinate_values):
         if not isinstance(base, sp.IndexedBase):
+            assert isinstance(base, TypedSymbol)
             base = sp.IndexedBase(base, shape=(1,))
+            assert isinstance(base.label, TypedSymbol)
         obj = super(ResolvedFieldAccess, cls).__new__(cls, base, linearized_index)
         obj.field = field
         obj.offsets = offsets
@@ -555,7 +696,7 @@ class ResolvedFieldAccess(sp.Indexed):
                                    self.args[1].subs(old, new),
                                    self.field, self.offsets, self.idx_coordinate_values)
 
-    def fast_subs(self, substitutions):
+    def fast_subs(self, substitutions, skip=None):
         if self in substitutions:
             return substitutions[self]
         return ResolvedFieldAccess(self.args[0].subs(substitutions),
@@ -572,11 +713,14 @@ class ResolvedFieldAccess(sp.Indexed):
 
     def __str__(self):
         top = super(ResolvedFieldAccess, self).__str__()
-        return "%s (%s)" % (top, self.typed_symbol.dtype)
+        return f"{top} ({self.typed_symbol.dtype})"
 
     def __getnewargs__(self):
         return self.base, self.indices[0], self.field, self.offsets, self.idx_coordinate_values
 
+    def __getnewargs_ex__(self):
+        return (self.base, self.indices[0], self.field, self.offsets, self.idx_coordinate_values), {}
+
 
 class TemporaryMemoryAllocation(Node):
     """Node for temporary memory buffer allocation.
@@ -588,6 +732,7 @@ class TemporaryMemoryAllocation(Node):
         size: number of elements to allocate
         align_offset: the align_offset's element is aligned
     """
+
     def __init__(self, typed_symbol: TypedSymbol, size, align_offset):
         super(TemporaryMemoryAllocation, self).__init__(parent=None)
         self.symbol = typed_symbol
@@ -645,3 +790,81 @@ class TemporaryMemoryFree(Node):
 def early_out(condition):
     from pystencils.cpu.vectorization import vec_all
     return Conditional(vec_all(condition), Block([SkipIteration()]))
+
+
+def get_dummy_symbol(dtype='bool'):
+    return TypedSymbol(f'dummy{uuid.uuid4().hex}', create_type(dtype))
+
+
+class SourceCodeComment(Node):
+    def __init__(self, text):
+        self.text = text
+
+    @property
+    def args(self):
+        return []
+
+    @property
+    def symbols_defined(self):
+        return set()
+
+    @property
+    def undefined_symbols(self):
+        return set()
+
+    def __str__(self):
+        return "/* " + self.text + " */"
+
+    def __repr__(self):
+        return self.__str__()
+
+
+class EmptyLine(Node):
+    def __init__(self):
+        pass
+
+    @property
+    def args(self):
+        return []
+
+    @property
+    def symbols_defined(self):
+        return set()
+
+    @property
+    def undefined_symbols(self):
+        return set()
+
+    def __str__(self):
+        return ""
+
+    def __repr__(self):
+        return self.__str__()
+
+
+class ConditionalFieldAccess(sp.Function):
+    """
+    :class:`pystencils.Field.Access` that is only executed if a certain condition is met.
+    Can be used, for instance, for out-of-bound checks.
+    """
+
+    def __new__(cls, field_access, outofbounds_condition, outofbounds_value=0):
+        return sp.Function.__new__(cls, field_access, outofbounds_condition, sp.S(outofbounds_value))
+
+    @property
+    def access(self):
+        return self.args[0]
+
+    @property
+    def outofbounds_condition(self):
+        return self.args[1]
+
+    @property
+    def outofbounds_value(self):
+        return self.args[2]
+
+    def __getnewargs__(self):
+        return self.access, self.outofbounds_condition, self.outofbounds_value
+
+    def __getnewargs_ex__(self):
+        return (self.access, self.outofbounds_condition, self.outofbounds_value), {}

pystencils/backends/__init__.py → src/pystencils/backends/__init__.py

@@ -6,9 +6,3 @@ try:
     __all__.append('print_dot')
 except ImportError:
     pass
-
-try:
-    from .llvm import generate_llvm  # NOQA
-    __all__.append('generate_llvm')
-except ImportError:
-    pass

src/pystencils/backends/arm_instruction_sets.py

+from pystencils.typing import CFunction
+
+
+def get_argument_string(function_shortcut, first=''):
+    args = function_shortcut[function_shortcut.index('[') + 1: -1]
+    arg_string = "("
+    if first:
+        arg_string += first + ', '
+    for arg in args.split(","):
+        arg = arg.strip()
+        if not arg:
+            continue
+        if arg in ('0', '1', '2', '3', '4', '5'):
+            arg_string += "{" + arg + "},"
+        else:
+            arg_string += arg + ","
+    arg_string = arg_string[:-1] + ")"
+    return arg_string
+
+
+def get_vector_instruction_set_arm(data_type='double', instruction_set='neon'):
+    if instruction_set not in ['neon', 'sme'] and not instruction_set.startswith('sve'):
+        raise NotImplementedError(instruction_set)
+    if instruction_set in ['sve', 'sve2', 'sme']:
+        cmp = 'cmp'
+    elif instruction_set.startswith('sve2') and instruction_set not in ('sve256', 'sve2048'):
+        cmp = 'cmp'
+        bitwidth = int(instruction_set[4:])
+    elif instruction_set.startswith('sve'):
+        cmp = 'cmp'
+        bitwidth = int(instruction_set[3:])
+    elif instruction_set == 'neon':
+        cmp = 'c'
+        bitwidth = 128
+
+    base_names = {
+        '+': 'add[0, 1]',
+        '-': 'sub[0, 1]',
+        '*': 'mul[0, 1]',
+        '/': 'div[0, 1]',
+        'sqrt': 'sqrt[0]',
+
+        'loadU': 'ld1[0]',
+        'storeU': 'st1[0, 1]',
+
+        'abs': 'abs[0]',
+        '==': f'{cmp}eq[0, 1]',
+        '!=': f'{cmp}eq[0, 1]',
+        '<=': f'{cmp}le[0, 1]',
+        '<': f'{cmp}lt[0, 1]',
+        '>=': f'{cmp}ge[0, 1]',
+        '>': f'{cmp}gt[0, 1]',
+    }
+
+    bits = {'double': 64,
+            'float': 32,
+            'int': 32}
+
+    result = dict()
+
+    if instruction_set in ['sve', 'sve2', 'sme']:
+        width = 'svcntd()' if data_type == 'double' else 'svcntw()'
+        intwidth = 'svcntw()'
+        result['bytes'] = 'svcntb()'
+    else:
+        width = bitwidth // bits[data_type]
+        intwidth = bitwidth // bits['int']
+        result['bytes'] = bitwidth // 8
+    if instruction_set.startswith('sve') or instruction_set == 'sme':
+        base_names['stream'] = 'stnt1[0, 1]'
+        prefix = 'sv'
+        suffix = f'_f{bits[data_type]}'
+    elif instruction_set == 'neon':
+        prefix = 'v'
+        suffix = f'q_f{bits[data_type]}'
+
+    if instruction_set in ['sve', 'sve2', 'sme']:
+        predicate = f'{prefix}whilelt_b{bits[data_type]}_u64({{loop_counter}}, {{loop_stop}})'
+        int_predicate = f'{prefix}whilelt_b{bits["int"]}_u64({{loop_counter}}, {{loop_stop}})'
+    else:
+        predicate = f'{prefix}whilelt_b{bits[data_type]}(0, {width})'
+        int_predicate = f'{prefix}whilelt_b{bits["int"]}(0, {intwidth})'
+
+    for intrinsic_id, function_shortcut in base_names.items():
+        function_shortcut = function_shortcut.strip()
+        name = function_shortcut[:function_shortcut.index('[')]
+
+        arg_string = get_argument_string(function_shortcut, first=predicate if prefix == 'sv' else '')
+        if prefix == 'sv' and not name.startswith('ld') and not name.startswith('st') and not name.startswith(cmp):
+            undef = '_x'
+        else:
+            undef = ''
+
+        result[intrinsic_id] = prefix + name + suffix + undef + arg_string
+
+    if instruction_set in ['sve', 'sve2', 'sme']:
+        result['width'] = CFunction(width, "int")
+        result['intwidth'] = CFunction(intwidth, "int")
+    else:
+        result['width'] = width
+        result['intwidth'] = intwidth
+
+    if instruction_set.startswith('sve') or instruction_set == 'sme':
+        result['makeVecConst'] = f'svdup_f{bits[data_type]}' + '({0})'
+        result['makeVecConstInt'] = f'svdup_s{bits["int"]}' + '({0})'
+        result['makeVecIndex'] = f'svindex_s{bits["int"]}' + '({0}, {1})'
+
+        if instruction_set != 'sme':
+            vindex = f'svindex_u{bits[data_type]}(0, {{0}})'
+            result['storeS'] = f'svst1_scatter_u{bits[data_type]}index_f{bits[data_type]}({predicate}, {{0}}, ' + \
+                               vindex.format("{2}") + ', {1})'
+            result['loadS'] = f'svld1_gather_u{bits[data_type]}index_f{bits[data_type]}({predicate}, {{0}}, ' + \
+                              vindex.format("{1}") + ')'
+        if instruction_set.startswith('sve2') and instruction_set not in ('sve256', 'sve2048'):
+            result['streamS'] = f'svstnt1_scatter_u{bits[data_type]}offset_f{bits[data_type]}({predicate}, {{0}}, ' + \
+                                vindex.format(f"{{2}}*{bits[data_type]//8}") + ', {1})'
+
+        result['+int'] = f"svadd_s{bits['int']}_x({int_predicate}, " + "{0}, {1})"
+
+        result['float'] = f'svfloat{bits["float"]}_{"s" if instruction_set not in ["sve", "sve2", "sme"] else ""}t'
+        result['double'] = f'svfloat{bits["double"]}_{"s" if instruction_set not in ["sve", "sve2", "sme"] else ""}t'
+        result['int'] = f'svint{bits["int"]}_{"s" if instruction_set not in ["sve", "sve2", "sme"] else ""}t'
+        result['bool'] = f'svbool_{"s" if instruction_set not in ["sve", "sve2", "sme"] else ""}t'
+
+        result['headers'] = ['<arm_sve.h>', '<arm_acle.h>', '"arm_neon_helpers.h"']
+
+        result['&'] = f'svand_b_z({predicate},' + ' {0}, {1})'
+        result['|'] = f'svorr_b_z({predicate},' + ' {0}, {1})'
+        result['blendv'] = f'svsel_f{bits[data_type]}' + '({2}, {1}, {0})'
+        result['any'] = f'svptest_any({predicate}, {{0}})'
+        result['all'] = f'svcntp_b{bits[data_type]}({predicate}, {{0}}) == {width}'
+
+        result['maskStoreU'] = result['storeU'].replace(predicate, '{2}')
+        result['maskStream'] = result['stream'].replace(predicate, '{2}')
+        if instruction_set != 'sme':
+            result['maskStoreS'] = result['storeS'].replace(predicate, '{3}')
+            if instruction_set.startswith('sve2') and instruction_set not in ('sve256', 'sve2048'):
+                result['maskStreamS'] = result['streamS'].replace(predicate, '{3}')
+
+        result['streamFence'] = '__dmb(15)'
+
+        if instruction_set == 'sme':
+            result['function_prefix'] = '__attribute__((arm_locally_streaming))'
+        elif instruction_set not in ['sve', 'sve2', 'sme']:
+            result['compile_flags'] = [f'-msve-vector-bits={bitwidth}']
+    else:
+        result['makeVecConst'] = f'vdupq_n_f{bits[data_type]}' + '({0})'
+        result['makeVec'] = f'makeVec_f{bits[data_type]}' + '(' + ", ".join(['{' + str(i) + '}' for i in
+                                                                             range(width)]) + ')'
+        result['makeVecConstInt'] = f'vdupq_n_s{bits["int"]}' + '({0})'
+        result['makeVecInt'] = f'makeVec_s{bits["int"]}' + '({0}, {1}, {2}, {3})'
+
+        result['+int'] = f"vaddq_s{bits['int']}" + "({0}, {1})"
+
+        result[data_type] = f'float{bits[data_type]}x{width}_t'
+        result['int'] = f'int{bits["int"]}x{intwidth}_t'
+        result['bool'] = f'uint{bits[data_type]}x{width}_t'
+
+        result['headers'] = ['<arm_neon.h>', '"arm_neon_helpers.h"']
+
+        result['!='] = f'vmvnq_u{bits[data_type]}({result["=="]})'
+
+        result['&'] = f'vandq_u{bits[data_type]}' + '({0}, {1})'
+        result['|'] = f'vorrq_u{bits[data_type]}' + '({0}, {1})'
+        result['blendv'] = f'vbslq_f{bits[data_type]}' + '({2}, {1}, {0})'
+        result['any'] = f'vaddlvq_u8(vreinterpretq_u8_u{bits[data_type]}({{0}})) > 0'
+        result['all'] = f'vaddlvq_u8(vreinterpretq_u8_u{bits[data_type]}({{0}})) == 16*0xff'
+
+        # SVE has real nontemporal stores, so we only need to zero cachlines on Neon
+        result['cachelineZero'] = 'cachelineZero((void*) {0})'
+
+    result['cachelineSize'] = 'cachelineSize()'
+
+    return result

pystencils/backends/cbackend.py → src/pystencils/backends/cbackend.py

-import sympy as sp
+import re
 from collections import namedtuple
-from sympy.core import S
+import hashlib
 from typing import Set
-from sympy.printing.ccode import C89CodePrinter
 
-from pystencils.cpu.vectorization import vec_any, vec_all
-from pystencils.fast_approximation import fast_division, fast_sqrt, fast_inv_sqrt
+import numpy as np
+import sympy as sp
+from sympy.core import S
+from sympy.logic.boolalg import BooleanFalse, BooleanTrue
+from sympy.functions.elementary.trigonometric import TrigonometricFunction, InverseTrigonometricFunction
+from sympy.functions.elementary.hyperbolic import HyperbolicFunction
+
+from pystencils.astnodes import KernelFunction, LoopOverCoordinate, Node
+from pystencils.cpu.vectorization import vec_all, vec_any, CachelineSize
+from pystencils.typing import (
+    PointerType, VectorType, CastFunc, create_type, get_type_of_expression,
+    ReinterpretCastFunc, VectorMemoryAccess, BasicType, TypedSymbol, CFunction)
+from pystencils.enums import Backend
+from pystencils.fast_approximation import fast_division, fast_inv_sqrt, fast_sqrt
+from pystencils.functions import DivFunc, AddressOf
+from pystencils.integer_functions import (
+    bit_shift_left, bit_shift_right, bitwise_and, bitwise_or, bitwise_xor,
+    int_div, int_power_of_2, modulo_ceil)
 
 try:
-    from sympy.printing.ccode import C99CodePrinter as CCodePrinter
+    from sympy.printing.c import C99CodePrinter as CCodePrinter  # for sympy versions > 1.6
 except ImportError:
-    from sympy.printing.ccode import CCodePrinter  # for sympy versions < 1.1
-
-from pystencils.integer_functions import bitwise_xor, bit_shift_right, bit_shift_left, bitwise_and, \
-    bitwise_or, modulo_ceil, int_div, int_power_of_2
-from pystencils.astnodes import Node, KernelFunction
-from pystencils.data_types import create_type, PointerType, get_type_of_expression, VectorType, cast_func, \
-    vector_memory_access, reinterpret_cast_func
+    from sympy.printing.ccode import C99CodePrinter as CCodePrinter
 
 __all__ = ['generate_c', 'CustomCodeNode', 'PrintNode', 'get_headers', 'CustomSympyPrinter']
 
 
-KERNCRAFT_NO_TERNARY_MODE = False
+HEADER_REGEX = re.compile(r'^[<"].*[">]$')
 
 
-def generate_c(ast_node: Node, signature_only: bool = False, dialect='c') -> str:
+def generate_c(ast_node: Node,
+               signature_only: bool = False,
+               dialect: Backend = Backend.C,
+               custom_backend=None,
+               with_globals=True) -> str:
     """Prints an abstract syntax tree node as C or CUDA code.
 
-    This function does not need to distinguish between C, C++ or CUDA code, it just prints 'C-like' code as encoded
-    in the abstract syntax tree (AST). The AST is built differently for C or CUDA by calling different create_kernel
-    functions.
+    This function does not need to distinguish for most AST nodes between C, C++ or CUDA code, it just prints 'C-like'
+    code as encoded in the abstract syntax tree (AST). The AST is built differently for C or CUDA by calling different
+    create_kernel functions.
 
     Args:
-        ast_node:
-        signature_only:
-        dialect: 'c' or 'cuda'
+        ast_node: ast representation of kernel
+        signature_only: generate signature without function body
+        dialect: `Backend`: 'C' or 'CUDA'
+        custom_backend: use own custom printer for code generation
+        with_globals: enable usage of global variables
     Returns:
         C-like code for the ast node and its descendants
     """
-    printer = CBackend(signature_only=signature_only,
-                       vector_instruction_set=ast_node.instruction_set,
-                       dialect=dialect)
-    return printer(ast_node)
+    global_declarations = get_global_declarations(ast_node)
+    for d in global_declarations:
+        if hasattr(ast_node, "global_variables"):
+            ast_node.global_variables.update(d.symbols_defined)
+        else:
+            ast_node.global_variables = d.symbols_defined
+    if custom_backend:
+        printer = custom_backend
+    elif dialect == Backend.C:
+        try:
+            # TODO Vectorization Revamp: instruction_set should not be just slapped on ast
+            instruction_set = ast_node.instruction_set
+        except Exception:
+            instruction_set = None
+        printer = CBackend(signature_only=signature_only,
+                           vector_instruction_set=instruction_set)
+    elif dialect == Backend.CUDA:
+        from pystencils.backends.cuda_backend import CudaBackend
+        printer = CudaBackend(signature_only=signature_only)
+    else:
+        raise ValueError(f'Unknown {dialect=}')
+    code = printer(ast_node)
+    if not signature_only and isinstance(ast_node, KernelFunction):
+        if with_globals and global_declarations:
+            code = "\n" + code
+            for declaration in global_declarations:
+                code = printer(declaration) + "\n" + code
+
+    return code
+
+
+def get_global_declarations(ast):
+    global_declarations = []
+
+    def visit_node(sub_ast):
+        nonlocal global_declarations
+        if hasattr(sub_ast, "required_global_declarations"):
+            global_declarations += sub_ast.required_global_declarations
+
+        if hasattr(sub_ast, "args"):
+            for node in sub_ast.args:
+                visit_node(node)
+
+    visit_node(ast)
+
+    return sorted(set(global_declarations), key=str)
 
 
 def get_headers(ast_node: Node) -> Set[str]:
@@ -54,15 +111,22 @@ def get_headers(ast_node: Node) -> Set[str]:
     if hasattr(ast_node, 'headers'):
         headers.update(ast_node.headers)
     for a in ast_node.args:
-        if isinstance(a, Node):
+        if isinstance(a, (sp.Expr, Node)):
             headers.update(get_headers(a))
 
+    for g in get_global_declarations(ast_node):
+        if isinstance(g, Node):
+            headers.update(get_headers(g))
+
+    for h in headers:
+        assert HEADER_REGEX.match(h), f'header /{h}/ does not follow the pattern /"..."/ or /<...>/'
+
     return headers
 
 
 # --------------------------------------- Backend Specific Nodes -------------------------------------------------------
 
-
+# TODO future CustomCodeNode should not be backend specific move it elsewhere
 class CustomCodeNode(Node):
     def __init__(self, code, symbols_read, symbols_defined, parent=None):
         super(CustomCodeNode, self).__init__(parent=parent)
@@ -71,7 +135,7 @@ class CustomCodeNode(Node):
         self._symbols_defined = set(symbols_defined)
         self.headers = []
 
-    def get_code(self, dialect, vector_instruction_set):
+    def get_code(self, dialect, vector_instruction_set, print_arg):
         return self._code
 
     @property
@@ -86,11 +150,17 @@ class CustomCodeNode(Node):
     def undefined_symbols(self):
         return self._symbols_read - self._symbols_defined
 
+    def __eq__(self, other):
+        return type(self) is type(other) and self._code == other._code
+
+    def __hash__(self):
+        return hash(self._code)
+
 
 class PrintNode(CustomCodeNode):
     # noinspection SpellCheckingInspection
     def __init__(self, symbol_to_print):
-        code = '\nstd::cout << "%s  =  " << %s << std::endl; \n' % (symbol_to_print.name, symbol_to_print.name)
+        code = f'\nstd::cout << "{symbol_to_print.name}  =  " << {symbol_to_print.name} << std::endl; \n'
         super(PrintNode, self).__init__(code, symbols_read=[symbol_to_print], symbols_defined=set())
         self.headers.append("<iostream>")
 
@@ -101,12 +171,12 @@ class PrintNode(CustomCodeNode):
 # noinspection PyPep8Naming
 class CBackend:
 
-    def __init__(self, sympy_printer=None, signature_only=False, vector_instruction_set=None, dialect='c'):
+    def __init__(self, sympy_printer=None, signature_only=False, vector_instruction_set=None, dialect=Backend.C):
         if sympy_printer is None:
             if vector_instruction_set is not None:
-                self.sympy_printer = VectorizedCustomSympyPrinter(vector_instruction_set, dialect)
+                self.sympy_printer = VectorizedCustomSympyPrinter(vector_instruction_set)
             else:
-                self.sympy_printer = CustomSympyPrinter(dialect)
+                self.sympy_printer = CustomSympyPrinter()
         else:
             self.sympy_printer = sympy_printer
 
@@ -114,6 +184,8 @@ class CBackend:
         self._indent = "   "
         self._dialect = dialect
         self._signatureOnly = signature_only
+        self._kwargs = {}
+        self.sympy_printer._kwargs = self._kwargs
 
     def __call__(self, node):
         prev_is = VectorType.instruction_set
@@ -123,19 +195,25 @@ class CBackend:
         return result
 
     def _print(self, node):
+        if isinstance(node, str):
+            return node
         for cls in type(node).__mro__:
-            method_name = "_print_" + cls.__name__
+            method_name = f"_print_{cls.__name__}"
             if hasattr(self, method_name):
                 return getattr(self, method_name)(node)
-        raise NotImplementedError("CBackend does not support node of type " + str(type(node)))
+        raise NotImplementedError(f"{self.__class__.__name__} does not support node of type {node.__class__.__name__}")
+
+    def _print_AbstractType(self, node):
+        return str(node)
 
     def _print_KernelFunction(self, node):
-        function_arguments = ["%s %s" % (str(s.symbol.dtype), s.symbol.name) for s in node.get_parameters()]
+        function_arguments = [f"{self._print(s.symbol.dtype)} {s.symbol.name}" for s in node.get_parameters()
+                              if not type(s.symbol) is CFunction]
         launch_bounds = ""
-        if self._dialect == 'cuda':
+        if self._dialect == Backend.CUDA:
             max_threads = node.indexing.max_threads_per_block()
             if max_threads:
-                launch_bounds = "__launch_bounds__({}) ".format(max_threads)
+                launch_bounds = f"__launch_bounds__({max_threads}) "
         func_declaration = "FUNC_PREFIX %svoid %s(%s)" % (launch_bounds, node.function_name,
                                                           ", ".join(function_arguments))
         if self._signatureOnly:
@@ -149,50 +227,166 @@ class CBackend:
         return "{\n%s\n}" % (self._indent + self._indent.join(block_contents.splitlines(True)))
 
     def _print_PragmaBlock(self, node):
-        return "%s\n%s" % (node.pragma_line, self._print_Block(node))
+        return f"{node.pragma_line}\n{self._print_Block(node)}"
 
     def _print_LoopOverCoordinate(self, node):
-        counter_symbol = node.loop_counter_name
-        start = "int %s = %s" % (counter_symbol, self.sympy_printer.doprint(node.start))
-        condition = "%s < %s" % (counter_symbol, self.sympy_printer.doprint(node.stop))
-        update = "%s += %s" % (counter_symbol, self.sympy_printer.doprint(node.step),)
-        loop_str = "for (%s; %s; %s)" % (start, condition, update)
+        counter_name = node.loop_counter_name
+        counter_dtype = node.loop_counter_symbol.dtype.c_name
+        start = f"{counter_dtype} {counter_name} = {self.sympy_printer.doprint(node.start)}"
+        condition = f"{counter_name} < {self.sympy_printer.doprint(node.stop)}"
+        update = f"{counter_name} += {self.sympy_printer.doprint(node.step)}"
+        loop_str = f"for ({start}; {condition}; {update})"
+        self._kwargs['loop_counter'] = counter_name
+        self._kwargs['loop_stop'] = node.stop
 
         prefix = "\n".join(node.prefix_lines)
         if prefix:
             prefix += "\n"
-        return "%s%s\n%s" % (prefix, loop_str, self._print(node.body))
+        return f"{prefix}{loop_str}\n{self._print(node.body)}"
 
     def _print_SympyAssignment(self, node):
+        printed_lhs = self.sympy_printer.doprint(node.lhs)
+        printed_rhs = self.sympy_printer.doprint(node.rhs)
+
         if node.is_declaration:
-            data_type = "const " + str(node.lhs.dtype) + " " if node.is_const else str(node.lhs.dtype) + " "
-            return "%s%s = %s;" % (data_type, self.sympy_printer.doprint(node.lhs),
-                                   self.sympy_printer.doprint(node.rhs))
+            if node.use_auto:
+                data_type = 'auto'
+            else:
+                data_type = self._print(node.lhs.dtype).replace(' const', '')
+                if node.is_const:
+                    data_type = f'const {data_type}'
+            return f"{data_type} {printed_lhs} = {printed_rhs};"
         else:
-            lhs_type = get_type_of_expression(node.lhs)
-            if type(lhs_type) is VectorType and isinstance(node.lhs, cast_func):
-                arg, data_type, aligned, nontemporal = node.lhs.args
+            lhs_type = get_type_of_expression(node.lhs)  # TOOD: this should have been typed
+            printed_mask = ""
+            if type(lhs_type) is VectorType and isinstance(node.lhs, CastFunc):
+                arg, data_type, aligned, nontemporal, mask, stride = node.lhs.args
                 instr = 'storeU'
-                if aligned:
-                    instr = 'stream' if nontemporal else 'storeA'
+                if nontemporal and 'storeA' not in self._vector_instruction_set and \
+                        'stream' in self._vector_instruction_set:
+                    instr = 'stream'
+                elif aligned:
+                    instr = 'stream' if nontemporal and 'stream' in self._vector_instruction_set else 'storeA'
+                if mask != True:  # NOQA
+                    instr = 'maskStream' if nontemporal and 'maskStream' in self._vector_instruction_set else \
+                            'maskStoreA' if aligned else 'maskStoreU'
+                    if instr not in self._vector_instruction_set:
+                        if instr == 'maskStream' and 'stream' in self._vector_instruction_set:
+                            store, load = 'stream', 'loadA'
+                        elif (instr in ('maskStream', 'maskStoreA')) and 'storeA' in self._vector_instruction_set:
+                            store, load = 'storeA', 'loadA'
+                        else:
+                            store, load = 'storeU', 'loadU'
+                        load = load if load in self._vector_instruction_set else 'loadU'
+                        self._vector_instruction_set[instr] = self._vector_instruction_set[store].format(
+                            '{0}', self._vector_instruction_set['blendv'].format(
+                                self._vector_instruction_set[load].format('{0}', **self._kwargs),
+                                '{1}', '{2}', **self._kwargs), **self._kwargs)
+                    printed_mask = self.sympy_printer.doprint(mask)
+                    if data_type.base_type.c_name == 'double':
+                        if self._vector_instruction_set['double'] == '__m256d':
+                            printed_mask = f"_mm256_castpd_si256({printed_mask})"
+                        elif self._vector_instruction_set['double'] == '__m128d':
+                            printed_mask = f"_mm_castpd_si128({printed_mask})"
+                    elif data_type.base_type.c_name == 'float':
+                        if self._vector_instruction_set['float'] == '__m256':
+                            printed_mask = f"_mm256_castps_si256({printed_mask})"
+                        elif self._vector_instruction_set['float'] == '__m128':
+                            printed_mask = f"_mm_castps_si128({printed_mask})"
 
                 rhs_type = get_type_of_expression(node.rhs)
                 if type(rhs_type) is not VectorType:
-                    rhs = cast_func(node.rhs, VectorType(rhs_type))
+                    raise ValueError(f'Cannot vectorize {node.rhs} of type {rhs_type} inside of the pretty printer! '
+                                     f'This should have happen earlier!')
+                    # rhs = CastFunc(node.rhs, VectorType(rhs_type)) # Unknown width
                 else:
                     rhs = node.rhs
 
-                return self._vector_instruction_set[instr].format("&" + self.sympy_printer.doprint(node.lhs.args[0]),
-                                                                  self.sympy_printer.doprint(rhs)) + ';'
+                ptr = "&" + self.sympy_printer.doprint(node.lhs.args[0])
+
+                if stride != 1:
+                    instr = ('maskStreamS' if nontemporal and 'maskStreamS' in self._vector_instruction_set else
+                             'maskStoreS') if mask != True else \
+                            ('streamS' if nontemporal and 'streamS' in self._vector_instruction_set else 'storeS')  # NOQA
+                    return self._vector_instruction_set[instr].format(ptr, self.sympy_printer.doprint(rhs),
+                                                                      stride, printed_mask, **self._kwargs) + ';'
+
+                pre_code = ''
+                if nontemporal and 'cachelineZero' in self._vector_instruction_set and mask == True:  # NOQA
+                    first_cond = f"((uintptr_t) {ptr} & {CachelineSize.mask_symbol}) == 0"
+                    offset = sp.Add(*[sp.Symbol(LoopOverCoordinate.get_loop_counter_name(i))
+                                      * node.lhs.args[0].field.spatial_strides[i] for i in
+                                      range(len(node.lhs.args[0].field.spatial_strides))])
+                    if stride == 1:
+                        offset = offset.subs({node.lhs.args[0].field.spatial_strides[0]: 1})
+                    size = sp.Mul(*node.lhs.args[0].field.spatial_shape)
+                    element_size = 8 if data_type.base_type.c_name == 'double' else 4
+                    size_cond = f"({offset} + {CachelineSize.symbol/element_size}) < {size}"
+                    pre_code = f"if ({first_cond} && {size_cond}) " + "{\n\t" + \
+                        self._vector_instruction_set['cachelineZero'].format(ptr, **self._kwargs) + ';\n}\n'
+
+                code = self._vector_instruction_set[instr].format(ptr, self.sympy_printer.doprint(rhs),
+                                                                  printed_mask, **self._kwargs) + ';'
+                flushcond = f"((uintptr_t) {ptr} & {CachelineSize.mask_symbol}) == {CachelineSize.last_symbol}"
+                if nontemporal and 'flushCacheline' in self._vector_instruction_set:
+                    code2 = self._vector_instruction_set['flushCacheline'].format(
+                        ptr, self.sympy_printer.doprint(rhs), **self._kwargs) + ';'
+                    code = f"{code}\nif ({flushcond}) {{\n\t{code2}\n}}"
+                elif aligned and nontemporal and 'storeAAndFlushCacheline' in self._vector_instruction_set:
+                    lhs_hash = hashlib.sha1(self.sympy_printer.doprint(node.lhs).encode('ascii')).hexdigest()[:8]
+                    rhs_hash = hashlib.sha1(self.sympy_printer.doprint(rhs).encode('ascii')).hexdigest()[:8]
+                    tmpvar = f'_tmp_{lhs_hash}_{rhs_hash}'
+                    code = 'const ' + self._print(node.lhs.dtype).replace(' const', '') + ' ' + tmpvar + ' = ' \
+                        + self.sympy_printer.doprint(rhs) + ';'
+                    code1 = self._vector_instruction_set[instr].format(ptr, tmpvar, printed_mask, **self._kwargs) + ';'
+                    maskStore, store, load = 'maskStoreAAndFlushCacheline', 'storeAAndFlushCacheline', 'loadA'
+                    instr2 = maskStore if mask != True else store  # NOQA
+                    if instr2 not in self._vector_instruction_set:
+                        self._vector_instruction_set[maskStore] = self._vector_instruction_set[store].format(
+                            '{0}', self._vector_instruction_set['blendv'].format(
+                                self._vector_instruction_set[load].format('{0}', **self._kwargs),
+                                '{1}', '{2}', **self._kwargs),
+                            **self._kwargs)
+                    code2 = self._vector_instruction_set[instr2].format(ptr, tmpvar, printed_mask, **self._kwargs) + ';'
+                    code += f"\nif ({flushcond}) {{\n\t{code2}\n}} else {{\n\t{code1}\n}}"
+                return pre_code + code
             else:
-                return "%s = %s;" % (self.sympy_printer.doprint(node.lhs), self.sympy_printer.doprint(node.rhs))
+                return f"{printed_lhs} = {printed_rhs};"
+
+    def _print_NontemporalFence(self, _):
+        if 'streamFence' in self._vector_instruction_set:
+            return self._vector_instruction_set['streamFence'] + ';'
+        else:
+            return ''
+
+    def _print_CachelineSize(self, node):
+        if 'cachelineSize' in self._vector_instruction_set:
+            code = f'const size_t {node.symbol} = {self._vector_instruction_set["cachelineSize"]};\n'
+            code += f'const size_t {node.mask_symbol} = {node.symbol} - 1;\n'
+            vectorsize = self._vector_instruction_set['bytes']
+            code += f'const size_t {node.last_symbol} = {node.symbol} - {vectorsize};\n'
+            return code
+        else:
+            return ''
 
     def _print_TemporaryMemoryAllocation(self, node):
-        align = 64
+        if self._vector_instruction_set:
+            align = self._vector_instruction_set['bytes']
+        else:
+            align = node.symbol.dtype.base_type.numpy_dtype.itemsize
+
         np_dtype = node.symbol.dtype.base_type.numpy_dtype
         required_size = np_dtype.itemsize * node.size + align
         size = modulo_ceil(required_size, align)
-        code = "{dtype} {name}=({dtype})aligned_alloc({align}, {size}) + {offset};"
+        code = "#if defined(_MSC_VER)\n"
+        code += "{dtype} {name}=({dtype})_aligned_malloc({size}, {align}) + {offset};\n"
+        code += "#elif __cplusplus >= 201703L || __STDC_VERSION__ >= 201112L\n"
+        code += "{dtype} {name}=({dtype})aligned_alloc({align}, {size}) + {offset};\n"
+        code += "#else\n"
+        code += "{dtype} {name};\n"
+        code += "posix_memalign((void**) &{name}, {align}, {size});\n"
+        code += "{name} += {offset};\n"
+        code += "#endif"
         return code.format(dtype=node.symbol.dtype,
                            name=self.sympy_printer.doprint(node.symbol.name),
                            size=self.sympy_printer.doprint(size),
@@ -200,28 +394,44 @@ class CBackend:
                            align=align)
 
     def _print_TemporaryMemoryFree(self, node):
-        align = 64
-        return "free(%s - %d);" % (self.sympy_printer.doprint(node.symbol.name), node.offset(align))
+        if self._vector_instruction_set:
+            align = self._vector_instruction_set['bytes']
+        else:
+            align = node.symbol.dtype.base_type.numpy_dtype.itemsize
+
+        code = "#if defined(_MSC_VER)\n"
+        code += "_aligned_free(%s - %d);\n" % (self.sympy_printer.doprint(node.symbol.name), node.offset(align))
+        code += "#else\n"
+        code += "free(%s - %d);\n" % (self.sympy_printer.doprint(node.symbol.name), node.offset(align))
+        code += "#endif"
+        return code
 
     def _print_SkipIteration(self, _):
-        if self._dialect == 'cuda':
-            return "return;"
-        else:
-            return "continue;"
+        return "continue;"
 
     def _print_CustomCodeNode(self, node):
-        return node.get_code(self._dialect, self._vector_instruction_set)
+        return node.get_code(self._dialect, self._vector_instruction_set, print_arg=self.sympy_printer._print)
+
+    def _print_SourceCodeComment(self, node):
+        return f"/* {node.text } */"
+
+    def _print_EmptyLine(self, node):
+        return ""
 
     def _print_Conditional(self, node):
+        if type(node.condition_expr) is BooleanTrue:
+            return self._print_Block(node.true_block)
+        elif type(node.condition_expr) is BooleanFalse:
+            return self._print_Block(node.false_block)
         cond_type = get_type_of_expression(node.condition_expr)
         if isinstance(cond_type, VectorType):
             raise ValueError("Problem with Conditional inside vectorized loop - use vec_any or vec_all")
         condition_expr = self.sympy_printer.doprint(node.condition_expr)
         true_block = self._print_Block(node.true_block)
-        result = "if (%s)\n%s " % (condition_expr, true_block)
+        result = f"if ({condition_expr})\n{true_block} "
         if node.false_block:
             false_block = self._print_Block(node.false_block)
-            result += "else " + false_block
+            result += f"else {false_block}"
         return result
 
 
@@ -231,27 +441,33 @@ class CBackend:
 # noinspection PyPep8Naming
 class CustomSympyPrinter(CCodePrinter):
 
-    def __init__(self, dialect):
+    def __init__(self):
         super(CustomSympyPrinter, self).__init__()
-        self._float_type = create_type("float32")
-        self._dialect = dialect
-        if 'Min' in self.known_functions:
-            del self.known_functions['Min']
-        if 'Max' in self.known_functions:
-            del self.known_functions['Max']
 
     def _print_Pow(self, expr):
         """Don't use std::pow function, for small integer exponents, write as multiplication"""
-        if expr.exp.is_integer and expr.exp.is_number and 0 < expr.exp < 8:
-            return "(" + self._print(sp.Mul(*[expr.base] * expr.exp, evaluate=False)) + ")"
-        elif expr.exp.is_integer and expr.exp.is_number and - 8 < expr.exp < 0:
-            return "1 / ({})".format(self._print(sp.Mul(*[expr.base] * (-expr.exp), evaluate=False)))
+        # Ideally the printer has as little logic as possible. Therefore,
+        # powers should be rewritten as `DivFunc`s / unevaluated `Mul`s before
+        # printing. `NodeCollection` offers a convenience function to do just
+        # that. However, `cut_loops` rewrites unevaluated multiplications as
+        # `Pow`s again. Neither `deepcopy` nor `func(*args)` are suited to
+        # rebuild unevaluated expressions. Therefore, as long as we stick with
+        # SymPy, this is the only way to avoid printing `pow`s.
+        exp = expr.exp.expr if isinstance(expr.exp, CastFunc) else expr.exp
+        one_type = expr.base.dtype if hasattr(expr.base, "dtype") else get_type_of_expression(expr.base)
+
+        if exp.is_integer and exp.is_number and (0 < exp <= 8):
+            return f"({self._print(sp.Mul(*[expr.base] * exp, evaluate=False))})"
+        elif exp.is_integer and exp.is_number and (-8 <= exp < 0):
+            return f"{self._typed_number(1, one_type)} / ({self._print(sp.Mul(*([expr.base] * -exp), evaluate=False))})"
         else:
             return super(CustomSympyPrinter, self)._print_Pow(expr)
 
+    # TODO don't print ones in sp.Mul
+
     def _print_Rational(self, expr):
         """Evaluate all rationals i.e. print 0.25 instead of 1.0/4.0"""
-        res = str(expr.evalf().num)
+        res = str(expr.evalf(17))
         return res
 
     def _print_Equality(self, expr):
@@ -263,6 +479,15 @@ class CustomSympyPrinter(CCodePrinter):
         result = super(CustomSympyPrinter, self)._print_Piecewise(expr)
         return result.replace("\n", "")
 
+    def _print_Abs(self, expr):
+        if expr.args[0].is_integer:
+            return f'abs({self._print(expr.args[0])})'
+        else:
+            return f'fabs({self._print(expr.args[0])})'
+
+    def _print_AbstractType(self, node):
+        return str(node)
+
     def _print_Function(self, expr):
         infix_functions = {
             bitwise_xor: '^',
@@ -273,63 +498,113 @@ class CustomSympyPrinter(CCodePrinter):
         }
         if hasattr(expr, 'to_c'):
             return expr.to_c(self._print)
-        if isinstance(expr, reinterpret_cast_func):
+        if isinstance(expr, ReinterpretCastFunc):
             arg, data_type = expr.args
-            return "*((%s)(& %s))" % (PointerType(data_type, restrict=False), self._print(arg))
-        elif isinstance(expr, cast_func):
+            if isinstance(data_type, PointerType):
+                const_str = "const" if data_type.const else ""
+                return f"(({const_str} {self._print(data_type.base_type)} *)(& {self._print(arg)}))"
+            else:
+                return f"*(({self._print(PointerType(data_type, restrict=False))})(& {self._print(arg)}))"
+        elif isinstance(expr, AddressOf):
+            assert len(expr.args) == 1, "address_of must only have one argument"
+            return f"&({self._print(expr.args[0])})"
+        elif isinstance(expr, CastFunc):
+            cast = "(({data_type})({code}))"
             arg, data_type = expr.args
-            if isinstance(arg, sp.Number):
+            if arg.is_Number and not isinstance(arg, (sp.core.numbers.Infinity, sp.core.numbers.NegativeInfinity)):
                 return self._typed_number(arg, data_type)
+            elif isinstance(arg, (InverseTrigonometricFunction, TrigonometricFunction, HyperbolicFunction)) \
+                    and data_type == BasicType('float32'):
+                known = self.known_functions[arg.__class__.__name__.lower()]
+                code = self._print(arg)
+                return code.replace(known, f"{known}f")
+            elif isinstance(arg, (sp.Pow, sp.exp)) and data_type == BasicType('float32'):
+                known = ['sqrt', 'cbrt', 'pow', 'exp']
+                code = self._print(arg)
+                for k in known:
+                    if k in code:
+                        return code.replace(k, f'{k}f')
+                # Powers of small integers are printed as divisions/multiplications.
+                if '/' in code or '*' in code:
+                    return cast.format(data_type=data_type, code=code)
+                raise ValueError(f"{code} doesn't give {known=} function back.")
             else:
-                return "((%s)(%s))" % (data_type, self._print(arg))
+                return cast.format(data_type=data_type, code=self._print(arg))
         elif isinstance(expr, fast_division):
-            if self._dialect == "cuda":
-                return "__fdividef(%s, %s)" % tuple(self._print(a) for a in expr.args)
-            else:
-                return "({})".format(self._print(expr.args[0] / expr.args[1]))
+            raise ValueError("fast_division is only supported for Taget.GPU")
         elif isinstance(expr, fast_sqrt):
-            if self._dialect == "cuda":
-                return "__fsqrt_rn(%s)" % tuple(self._print(a) for a in expr.args)
-            else:
-                return "({})".format(self._print(sp.sqrt(expr.args[0])))
+            raise ValueError("fast_sqrt is only supported for Taget.GPU")
+        elif isinstance(expr, fast_inv_sqrt):
+            raise ValueError("fast_inv_sqrt is only supported for Taget.GPU")
         elif isinstance(expr, vec_any) or isinstance(expr, vec_all):
             return self._print(expr.args[0])
-        elif isinstance(expr, fast_inv_sqrt):
-            if self._dialect == "cuda":
-                return "__frsqrt_rn(%s)" % tuple(self._print(a) for a in expr.args)
+        elif isinstance(expr, sp.Abs):
+            return f"abs({self._print(expr.args[0])})"
+        elif isinstance(expr, sp.Mod):
+            if expr.args[0].is_integer and expr.args[1].is_integer:
+                return f"({self._print(expr.args[0])} % {self._print(expr.args[1])})"
             else:
-                return "({})".format(self._print(1 / sp.sqrt(expr.args[0])))
+                return f"fmod({self._print(expr.args[0])}, {self._print(expr.args[1])})"
         elif expr.func in infix_functions:
-            return "(%s %s %s)" % (self._print(expr.args[0]), infix_functions[expr.func], self._print(expr.args[1]))
+            return f"({self._print(expr.args[0])} {infix_functions[expr.func]} {self._print(expr.args[1])})"
         elif expr.func == int_power_of_2:
-            return "(1 << (%s))" % (self._print(expr.args[0]))
+            return f"(1 << ({self._print(expr.args[0])}))"
         elif expr.func == int_div:
-            return "((%s) / (%s))" % (self._print(expr.args[0]), self._print(expr.args[1]))
+            return f"(({self._print(expr.args[0])}) / ({self._print(expr.args[1])}))"
+        elif expr.func == DivFunc:
+            return f'(({self._print(expr.divisor)}) / ({self._print(expr.dividend)}))'
         else:
-            return super(CustomSympyPrinter, self)._print_Function(expr)
+            name = expr.name if hasattr(expr, 'name') else expr.__class__.__name__
+            arg_str = ', '.join(self._print(a) for a in expr.args)
+            return f'{name}({arg_str})'
 
     def _typed_number(self, number, dtype):
         res = self._print(number)
-        if dtype.is_float():
-            if dtype == self._float_type:
-                if '.' not in res:
-                    res += ".0f"
-                else:
-                    res += "f"
-            return res
+        if dtype.numpy_dtype == np.float32:
+            return res + '.0f' if '.' not in res else res + 'f'
+        elif dtype.numpy_dtype == np.float64:
+            return res + '.0' if '.' not in res else res
+        elif dtype.is_int():
+            tokens = res.split('.')
+            if len(tokens) == 1: 
+                return res
+            elif int(tokens[1]) != 0:
+                raise ValueError(f"Cannot print non-integer number {res} as an integer.")
+            else:
+                return tokens[0]
         else:
             return res
 
-    _print_Max = C89CodePrinter._print_Max
-    _print_Min = C89CodePrinter._print_Min
+    def _print_ConditionalFieldAccess(self, node):
+        return self._print(sp.Piecewise((node.outofbounds_value, node.outofbounds_condition), (node.access, True)))
+
+    def _print_Max(self, expr):
+        def inner_print_max(args):
+            if len(args) == 1:
+                return self._print(args[0])
+            half = len(args) // 2
+            a = inner_print_max(args[:half])
+            b = inner_print_max(args[half:])
+            return f"(({a} > {b}) ? {a} : {b})"
+        return inner_print_max(expr.args)
+
+    def _print_Min(self, expr):
+        def inner_print_min(args):
+            if len(args) == 1:
+                return self._print(args[0])
+            half = len(args) // 2
+            a = inner_print_min(args[:half])
+            b = inner_print_min(args[half:])
+            return f"(({a} < {b}) ? {a} : {b})"
+        return inner_print_min(expr.args)
 
 
 # noinspection PyPep8Naming
 class VectorizedCustomSympyPrinter(CustomSympyPrinter):
     SummandInfo = namedtuple("SummandInfo", ['sign', 'term'])
 
-    def __init__(self, instruction_set, dialect):
-        super(VectorizedCustomSympyPrinter, self).__init__(dialect=dialect)
+    def __init__(self, instruction_set):
+        super(VectorizedCustomSympyPrinter, self).__init__()
         self.instruction_set = instruction_set
 
     def _scalarFallback(self, func_name, expr, *args, **kwargs):
@@ -340,41 +615,113 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
             assert self.instruction_set['width'] == expr_type.width
             return None
 
+    def _print_Abs(self, expr):
+        if isinstance(get_type_of_expression(expr), (VectorType, VectorMemoryAccess)):
+            return self.instruction_set['abs'].format(self._print(expr.args[0]), **self._kwargs)
+        return super()._print_Abs(expr)
+
+    def _typed_vectorized_number(self, expr, data_type):
+        basic_data_type = data_type.base_type
+        number = self._typed_number(expr, basic_data_type)
+        instruction = 'makeVecConst'
+        if basic_data_type.is_bool():
+            instruction = 'makeVecConstBool'
+        # TODO Vectorization Revamp: is int, or sint, or uint (my guess is sint)
+        elif basic_data_type.is_int():
+            instruction = 'makeVecConstInt'
+        return self.instruction_set[instruction].format(number, **self._kwargs)
+
+    def _typed_vectorized_symbol(self, expr, data_type):
+        if not isinstance(expr, TypedSymbol):
+            raise ValueError(f'{expr} is not a TypeSymbol. It is {expr.type=}')
+        basic_data_type = data_type.base_type
+        symbol = self._print(expr)
+        if basic_data_type != expr.dtype:
+            symbol = f'(({basic_data_type})({symbol}))'
+
+        instruction = 'makeVecConst'
+        if basic_data_type.is_bool():
+            instruction = 'makeVecConstBool'
+        # TODO Vectorization Revamp: is int, or sint, or uint (my guess is sint)
+        elif basic_data_type.is_int():
+            instruction = 'makeVecConstInt'
+        return self.instruction_set[instruction].format(symbol, **self._kwargs)
+
+    def _print_CastFunc(self, expr):
+        arg, data_type = expr.args
+        if type(data_type) is VectorType:
+            base_type = data_type.base_type
+            # vector_memory_access is a cast_func itself so it should't be directly inside a cast_func
+            assert not isinstance(arg, VectorMemoryAccess)
+            if isinstance(arg, sp.Tuple):
+                is_boolean = get_type_of_expression(arg[0]) == create_type("bool")
+                is_integer = get_type_of_expression(arg[0]) == create_type("int")
+                printed_args = [self._print(a) for a in arg]
+                instruction = 'makeVecBool' if is_boolean else 'makeVecInt' if is_integer else 'makeVec'
+                if instruction == 'makeVecInt' and 'makeVecIndex' in self.instruction_set:
+                    increments = np.array(arg)[1:] - np.array(arg)[:-1]
+                    if len(set(increments)) == 1:
+                        return self.instruction_set['makeVecIndex'].format(printed_args[0], increments[0],
+                                                                           **self._kwargs)
+                return self.instruction_set[instruction].format(*printed_args, **self._kwargs)
+            else:
+                if arg.is_Number and not isinstance(arg, (sp.core.numbers.Infinity, sp.core.numbers.NegativeInfinity)):
+                    return self._typed_vectorized_number(arg, data_type)
+                elif isinstance(arg, TypedSymbol):
+                    return self._typed_vectorized_symbol(arg, data_type)
+                elif isinstance(arg, (InverseTrigonometricFunction, TrigonometricFunction, HyperbolicFunction)) \
+                        and base_type == BasicType('float32'):
+                    raise NotImplementedError('Vectorizer is not tested for trigonometric functions yet')
+                    # known = self.known_functions[arg.__class__.__name__.lower()]
+                    # code = self._print(arg)
+                    # return code.replace(known, f"{known}f")
+                elif isinstance(arg, sp.Pow):
+                    if base_type == BasicType('float32') or base_type == BasicType('float64'):
+                        return self._print_Pow(arg)
+                    else:
+                        raise NotImplementedError('Integer Pow is not implemented')
+                elif isinstance(arg, sp.UnevaluatedExpr):
+                    return self._print(arg.args[0])
+                else:
+                    raise NotImplementedError('Vectorizer cannot cast between different datatypes')
+                    # to_type = self.instruction_set['suffix'][data_type.base_type.c_name]
+                    # from_type = self.instruction_set['suffix'][get_type_of_expression(arg).base_type.c_name]
+                    # return self.instruction_set['cast'].format(from_type, to_type, self._print(arg))
+        else:
+            return self._scalarFallback('_print_Function', expr)
+            # raise ValueError(f'Non VectorType cast "{data_type}" in vectorized code.')
+
     def _print_Function(self, expr):
-        if isinstance(expr, vector_memory_access):
-            arg, data_type, aligned, _ = expr.args
+        if isinstance(expr, VectorMemoryAccess):
+            arg, data_type, aligned, _, mask, stride = expr.args
+            if stride != 1:
+                return self.instruction_set['loadS'].format(f"& {self._print(arg)}", stride, **self._kwargs)
             instruction = self.instruction_set['loadA'] if aligned else self.instruction_set['loadU']
-            return instruction.format("& " + self._print(arg))
-        elif isinstance(expr, cast_func):
-            arg, data_type = expr.args
-            if type(data_type) is VectorType:
-                return self.instruction_set['makeVec'].format(self._print(arg))
-        elif expr.func == fast_division:
+            return instruction.format(f"& {self._print(arg)}", **self._kwargs)
+        elif expr.func == DivFunc:
             result = self._scalarFallback('_print_Function', expr)
             if not result:
-                result = self.instruction_set['/'].format(self._print(expr.args[0]), self._print(expr.args[1]))
+                result = self.instruction_set['/'].format(self._print(expr.divisor), self._print(expr.dividend),
+                                                          **self._kwargs)
             return result
-        elif expr.func == fast_sqrt:
-            return "({})".format(self._print(sp.sqrt(expr.args[0])))
-        elif expr.func == fast_inv_sqrt:
-            result = self._scalarFallback('_print_Function', expr)
-            if not result:
-                if self.instruction_set['rsqrt']:
-                    return self.instruction_set['rsqrt'].format(self._print(expr.args[0]))
-                else:
-                    return "({})".format(self._print(1 / sp.sqrt(expr.args[0])))
-        elif isinstance(expr, vec_any):
-            expr_type = get_type_of_expression(expr.args[0])
-            if type(expr_type) is not VectorType:
-                return self._print(expr.args[0])
-            else:
-                return self.instruction_set['any'].format(self._print(expr.args[0]))
-        elif isinstance(expr, vec_all):
+        elif isinstance(expr, fast_division):
+            raise ValueError("fast_division is only supported for Taget.GPU")
+        elif isinstance(expr, fast_sqrt):
+            raise ValueError("fast_sqrt is only supported for Taget.GPU")
+        elif isinstance(expr, fast_inv_sqrt):
+            raise ValueError("fast_inv_sqrt is only supported for Taget.GPU")
+        elif isinstance(expr, vec_any) or isinstance(expr, vec_all):
+            instr = 'any' if isinstance(expr, vec_any) else 'all'
             expr_type = get_type_of_expression(expr.args[0])
             if type(expr_type) is not VectorType:
                 return self._print(expr.args[0])
             else:
-                return self.instruction_set['all'].format(self._print(expr.args[0]))
+                if isinstance(expr.args[0], sp.Rel):
+                    op = expr.args[0].rel_op
+                    if (instr, op) in self.instruction_set:
+                        return self.instruction_set[(instr, op)].format(*[self._print(a) for a in expr.args[0].args],
+                                                                        **self._kwargs)
+                return self.instruction_set[instr].format(self._print(expr.args[0]), **self._kwargs)
 
         return super(VectorizedCustomSympyPrinter, self)._print_Function(expr)
 
@@ -387,7 +734,7 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
         assert len(arg_strings) > 0
         result = arg_strings[0]
         for item in arg_strings[1:]:
-            result = self.instruction_set['&'].format(result, item)
+            result = self.instruction_set['&'].format(result, item, **self._kwargs)
         return result
 
     def _print_Or(self, expr):
@@ -399,16 +746,31 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
         assert len(arg_strings) > 0
         result = arg_strings[0]
         for item in arg_strings[1:]:
-            result = self.instruction_set['|'].format(result, item)
+            result = self.instruction_set['|'].format(result, item, **self._kwargs)
         return result
 
     def _print_Add(self, expr, order=None):
-        result = self._scalarFallback('_print_Add', expr)
+        try:
+            result = self._scalarFallback('_print_Add', expr)
+        except Exception:
+            result = None
         if result:
             return result
+        args = expr.args
+
+        # special treatment for all-integer args, for loop index arithmetic until we have proper int vectorization
+        suffix = ""
+        if all([(type(e) is CastFunc and str(e.dtype) == self.instruction_set['int']) or isinstance(e, sp.Integer)
+                or (type(e) is TypedSymbol and isinstance(e.dtype, BasicType) and e.dtype.is_int()) for e in args]):
+            dtype = set([e.dtype for e in args if type(e) is CastFunc])
+            assert len(dtype) == 1
+            dtype = dtype.pop()
+            args = [CastFunc(e, dtype) if (isinstance(e, sp.Integer) or isinstance(e, TypedSymbol)) else e
+                    for e in args]
+            suffix = "int"
 
         summands = []
-        for term in expr.args:
+        for term in args:
             if term.func == sp.Mul:
                 sign, t = self._print_Mul(term, inside_add=True)
             else:
@@ -424,30 +786,36 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
         assert len(summands) >= 2
         processed = summands[0].term
         for summand in summands[1:]:
-            func = self.instruction_set['-'] if summand.sign == -1 else self.instruction_set['+']
-            processed = func.format(processed, summand.term)
+            func = self.instruction_set['-' + suffix] if summand.sign == -1 else self.instruction_set['+' + suffix]
+            processed = func.format(processed, summand.term, **self._kwargs)
         return processed
 
     def _print_Pow(self, expr):
-        result = self._scalarFallback('_print_Pow', expr)
+        # Due to loop cutting sp.Mul is evaluated again.
+
+        try:
+            result = self._scalarFallback('_print_Pow', expr)
+        except ValueError:
+            result = None
         if result:
             return result
 
-        one = self.instruction_set['makeVec'].format(1.0)
-
-        if expr.exp.is_integer and expr.exp.is_number and 0 < expr.exp < 8:
-            return "(" + self._print(sp.Mul(*[expr.base] * expr.exp, evaluate=False)) + ")"
-        elif expr.exp == -1:
-            one = self.instruction_set['makeVec'].format(1.0)
-            return self.instruction_set['/'].format(one, self._print(expr.base))
-        elif expr.exp == 0.5:
-            return self.instruction_set['sqrt'].format(self._print(expr.base))
-        elif expr.exp == -0.5:
-            root = self.instruction_set['sqrt'].format(self._print(expr.base))
-            return self.instruction_set['/'].format(one, root)
-        elif expr.exp.is_integer and expr.exp.is_number and - 8 < expr.exp < 0:
-            return self.instruction_set['/'].format(one,
-                                                    self._print(sp.Mul(*[expr.base] * (-expr.exp), evaluate=False)))
+        one = self.instruction_set['makeVecConst'].format(1.0, **self._kwargs)
+        root = self.instruction_set['sqrt'].format(self._print(expr.base), **self._kwargs)
+
+        if isinstance(expr.exp, CastFunc) and expr.exp.args[0].is_number:
+            exp = expr.exp.args[0]
+        else:
+            exp = expr.exp
+
+        # TODO the printer should not have any intelligence like this.
+        # TODO To remove all of these cases the vectoriser needs to be reworked. See loop cutting
+        if exp.is_integer and exp.is_number and 0 < exp < 8:
+            return self._print(sp.Mul(*[expr.base] * exp, evaluate=False))
+        elif exp == 0.5:
+            return root
+        elif exp == -0.5:
+            return self.instruction_set['/'].format(one, root, **self._kwargs)
         else:
             raise ValueError("Generic exponential not supported: " + str(expr))
 
@@ -455,7 +823,10 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
         # noinspection PyProtectedMember
         from sympy.core.mul import _keep_coeff
 
-        result = self._scalarFallback('_print_Mul', expr)
+        if not inside_add:
+            result = self._scalarFallback('_print_Mul', expr)
+        else:
+            result = None
         if result:
             return result
 
@@ -486,19 +857,19 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
 
         result = a_str[0]
         for item in a_str[1:]:
-            result = self.instruction_set['*'].format(result, item)
+            result = self.instruction_set['*'].format(result, item, **self._kwargs)
 
         if len(b) > 0:
             denominator_str = b_str[0]
             for item in b_str[1:]:
-                denominator_str = self.instruction_set['*'].format(denominator_str, item)
-            result = self.instruction_set['/'].format(result, denominator_str)
+                denominator_str = self.instruction_set['*'].format(denominator_str, item, **self._kwargs)
+            result = self.instruction_set['/'].format(result, denominator_str, **self._kwargs)
 
         if inside_add:
             return sign, result
         else:
             if sign < 0:
-                return self.instruction_set['*'].format(self._print(S.NegativeOne), result)
+                return self.instruction_set['*'].format(self._print(S.NegativeOne), result, **self._kwargs)
             else:
                 return result
 
@@ -506,13 +877,13 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
         result = self._scalarFallback('_print_Relational', expr)
         if result:
             return result
-        return self.instruction_set[expr.rel_op].format(self._print(expr.lhs), self._print(expr.rhs))
+        return self.instruction_set[expr.rel_op].format(self._print(expr.lhs), self._print(expr.rhs), **self._kwargs)
 
     def _print_Equality(self, expr):
         result = self._scalarFallback('_print_Equality', expr)
         if result:
             return result
-        return self.instruction_set['=='].format(self._print(expr.lhs), self._print(expr.rhs))
+        return self.instruction_set['=='].format(self._print(expr.lhs), self._print(expr.rhs), **self._kwargs)
 
     def _print_Piecewise(self, expr):
         result = self._scalarFallback('_print_Piecewise', expr)
@@ -530,13 +901,11 @@ class VectorizedCustomSympyPrinter(CustomSympyPrinter):
 
         result = self._print(expr.args[-1][0])
         for true_expr, condition in reversed(expr.args[:-1]):
-            if isinstance(condition, cast_func) and get_type_of_expression(condition.args[0]) == create_type("bool"):
-                if not KERNCRAFT_NO_TERNARY_MODE:
-                    result = "(({}) ? ({}) : ({}))".format(self._print(condition.args[0]), self._print(true_expr),
-                                                           result)
-                else:
-                    print("Warning - skipping ternary op")
+            if isinstance(condition, CastFunc) and get_type_of_expression(condition.args[0]) == create_type("bool"):
+                result = "(({}) ? ({}) : ({}))".format(self._print(condition.args[0]), self._print(true_expr),
+                                                       result, **self._kwargs)
             else:
                 # noinspection SpellCheckingInspection
-                result = self.instruction_set['blendv'].format(result, self._print(true_expr), self._print(condition))
+                result = self.instruction_set['blendv'].format(result, self._print(true_expr), self._print(condition),
+                                                               **self._kwargs)
         return result

src/pystencils/backends/cuda_backend.py

+from pystencils.astnodes import Node
+from pystencils.backends.cbackend import CBackend, CustomSympyPrinter, generate_c
+from pystencils.enums import Backend
+from pystencils.fast_approximation import fast_division, fast_inv_sqrt, fast_sqrt
+
+
+def generate_cuda(ast_node: Node, signature_only: bool = False, custom_backend=None, with_globals=True) -> str:
+    """Prints an abstract syntax tree node as CUDA code.
+
+    Args:
+        ast_node: ast representation of kernel
+        signature_only: generate signature without function body
+        custom_backend: use own custom printer for code generation
+        with_globals: enable usage of global variables
+
+    Returns:
+        CUDA code for the ast node and its descendants
+    """
+    return generate_c(ast_node, signature_only, dialect=Backend.CUDA,
+                      custom_backend=custom_backend, with_globals=with_globals)
+
+
+class CudaBackend(CBackend):
+
+    def __init__(self, sympy_printer=None,
+                 signature_only=False):
+        if not sympy_printer:
+            sympy_printer = CudaSympyPrinter()
+
+        super().__init__(sympy_printer, signature_only, dialect=Backend.CUDA)
+
+    def _print_SharedMemoryAllocation(self, node):
+        dtype = node.symbol.dtype
+        name = self.sympy_printer.doprint(node.symbol.name)
+        num_elements = '*'.join([str(s) for s in node.shared_mem.shape])
+        code = f"__shared__ {dtype} {name}[{num_elements}];"
+        return code
+
+    @staticmethod
+    def _print_ThreadBlockSynchronization(_):
+        return "__synchtreads();"
+
+    def _print_TextureDeclaration(self, node):
+        cond = node.texture.field.dtype.numpy_dtype.itemsize > 4
+        return f'texture<{"fp_tex_" if cond else ""}{str(node.texture.field.dtype)}, ' \
+               f'cudaTextureType{node.texture.field.spacial_dimensions}D, cudaReadModeElementType> {node.texture};'
+
+    def _print_SkipIteration(self, _):
+        return "return;"
+
+
+class CudaSympyPrinter(CustomSympyPrinter):
+    language = "CUDA"
+
+    def __init__(self):
+        super(CudaSympyPrinter, self).__init__()
+
+    def _print_Function(self, expr):
+        if isinstance(expr, fast_division):
+            assert len(expr.args) == 2, f"__fdividef has two arguments, but {len(expr.args)} where given"
+            return f"__fdividef({self._print(expr.args[0])}, {self._print(expr.args[1])})"
+        elif isinstance(expr, fast_sqrt):
+            assert len(expr.args) == 1, f"__fsqrt_rn has one argument, but {len(expr.args)} where given"
+            return f"__fsqrt_rn({self._print(expr.args[0])})"
+        elif isinstance(expr, fast_inv_sqrt):
+            assert len(expr.args) == 1, f"__frsqrt_rn has one argument, but {len(expr.args)} where given"
+            return f"__frsqrt_rn({self._print(expr.args[0])})"
+        return super()._print_Function(expr)

pystencils/backends/dot.py → src/pystencils/backends/dot.py

-from sympy.printing.printer import Printer
-from graphviz import Digraph, lang
 import graphviz
+try:
+    from graphviz import Digraph
+    import graphviz.quoting as quote
+except ImportError:
+    from graphviz import Digraph
+    import graphviz.lang as quote
+from sympy.printing.printer import Printer
 
 
 # noinspection PyPep8Naming
@@ -12,7 +17,7 @@ class DotPrinter(Printer):
         super(DotPrinter, self).__init__()
         self._node_to_str_function = node_to_str_function
         self.dot = Digraph(**kwargs)
-        self.dot.quote_edge = lang.quote
+        self.dot.quote_edge = quote.quote
 
     def _print_KernelFunction(self, func):
         self.dot.node(str(id(func)), style='filled', fillcolor='#a056db', label=self._node_to_str_function(func))
@@ -50,22 +55,20 @@ class DotPrinter(Printer):
 
 
 def __shortened(node):
-    from pystencils.astnodes import LoopOverCoordinate, KernelFunction, SympyAssignment, Block, Conditional
+    from pystencils.astnodes import LoopOverCoordinate, KernelFunction, SympyAssignment, Conditional
     if isinstance(node, LoopOverCoordinate):
         return "Loop over dim %d" % (node.coordinate_to_loop_over,)
     elif isinstance(node, KernelFunction):
         params = node.get_parameters()
         param_names = [p.field_name for p in params if p.is_field_pointer]
         param_names += [p.symbol.name for p in params if not p.is_field_parameter]
-        return "Func: %s (%s)" % (node.function_name, ",".join(param_names))
+        return f"Func: {node.function_name} ({','.join(param_names)})"
     elif isinstance(node, SympyAssignment):
         return repr(node.lhs)
-    elif isinstance(node, Block):
-        return "Block" + str(id(node))
     elif isinstance(node, Conditional):
         return repr(node)
     else:
-        raise NotImplementedError("Cannot handle node type %s" % (type(node),))
+        raise NotImplementedError(f"Cannot handle node type {type(node)}")
 
 
 def print_dot(node, view=False, short=False, **kwargs):

src/pystencils/backends/json.py

+# -*- coding: utf-8 -*-
+#
+# Copyright © 2019 Stephan Seitz <stephan.seitz@fau.de>
+#
+# Distributed under terms of the GPLv3 license.
+
+"""
+
+"""
+import json
+
+from pystencils.astnodes import NodeOrExpr
+from pystencils.backends.cbackend import CustomSympyPrinter, generate_c
+
+try:
+    import yaml
+except ImportError:
+    raise ImportError('yaml not installed')
+
+
+def expr_to_dict(expr_or_node: NodeOrExpr, with_c_code=True, full_class_names=False):
+    """Converts a SymPy expression to a serializable dict (mainly for debugging purposes)
+
+    The dict recursively contains all args of the expression as ``dict``s
+
+    See :func:`.write_json`
+
+    Args:
+        expr_or_node (NodeOrExpr): a SymPy expression or a :class:`pystencils.astnodes.Node`
+        with_c_code (bool, optional): include C representation of the nodes
+        full_class_names (bool, optional): use full class names (type(object) instead of ``type(object).__name__``
+    """
+
+    self = {'str': str(expr_or_node)}
+    if with_c_code:
+        try:
+            self.update({'c': generate_c(expr_or_node)})
+        except Exception:
+            try:
+                self.update({'c': CustomSympyPrinter().doprint(expr_or_node)})
+            except Exception:
+                pass
+    for a in expr_or_node.args:
+        self.update({str(a.__class__ if full_class_names else a.__class__.__name__): expr_to_dict(a)})
+
+    return self
+
+
+def print_json(expr_or_node: NodeOrExpr):
+    """Print debug JSON of an AST to string
+
+    Args:
+        expr_or_node (NodeOrExpr): a SymPy expression or a :class:`pystencils.astnodes.Node`
+
+    Returns:
+        str: JSON representation of AST
+    """
+    expr_or_node_dict = expr_to_dict(expr_or_node)
+    return json.dumps(expr_or_node_dict, indent=4)
+
+
+def write_json(filename: str, expr_or_node: NodeOrExpr):
+    """Writes debug JSON represenation of AST to file
+
+    Args:
+        filename (str): Path for the file to write
+        expr_or_node (NodeOrExpr): a SymPy expression or a :class:`pystencils.astnodes.Node`
+    """
+    expr_or_node_dict = expr_to_dict(expr_or_node)
+    with open(filename, 'w') as f:
+        json.dump(expr_or_node_dict, f, indent=4)
+
+
+def print_yaml(expr_or_node):
+    expr_or_node_dict = expr_to_dict(expr_or_node, full_class_names=False)
+    return yaml.dump(expr_or_node_dict)
+
+
+def write_yaml(filename, expr_or_node):
+    expr_or_node_dict = expr_to_dict(expr_or_node)
+    with open(filename, 'w') as f:
+        yaml.dump(expr_or_node_dict, f)

src/pystencils/backends/ppc_instruction_sets.py

+def get_argument_string(function_shortcut):
+    args = function_shortcut[function_shortcut.index('[') + 1: -1]
+    arg_string = "("
+    for arg in args.split(","):
+        arg = arg.strip()
+        if not arg:
+            continue
+        if arg in ('0', '1', '2', '3', '4', '5'):
+            arg_string += "{" + arg + "},"
+        else:
+            arg_string += arg + ","
+    arg_string = arg_string[:-1] + ")"
+    return arg_string
+
+
+def get_vector_instruction_set_ppc(data_type='double', instruction_set='vsx'):
+    if instruction_set != 'vsx':
+        raise NotImplementedError(instruction_set)
+
+    base_names = {
+        '+': 'add[0, 1]',
+        '-': 'sub[0, 1]',
+        '*': 'mul[0, 1]',
+        '/': 'div[0, 1]',
+        'sqrt': 'sqrt[0]',
+        'rsqrt': 'rsqrte[0]',  # rsqrt is available too, but not on Clang
+
+        'loadU': 'xl[0x0, 0]',
+        'loadA': 'ld[0x0, 0]',
+        'storeU': 'xst[1, 0x0, 0]',
+        'storeA': 'st[1, 0x0, 0]',
+        'storeAAndFlushCacheline': 'stl[1, 0x0, 0]',
+
+        'abs': 'abs[0]',
+        '==': 'cmpeq[0, 1]',
+        '!=': 'cmpne[0, 1]',
+        '<=': 'cmple[0, 1]',
+        '<': 'cmplt[0, 1]',
+        '>=': 'cmpge[0, 1]',
+        '>': 'cmpgt[0, 1]',
+        '&': 'and[0, 1]',
+        '|': 'or[0, 1]',
+        'blendv': 'sel[0, 1, 2]',
+
+        ('any', '=='): 'any_eq[0, 1]',
+        ('any', '!='): 'any_ne[0, 1]',
+        ('any', '<='): 'any_le[0, 1]',
+        ('any', '<'): 'any_lt[0, 1]',
+        ('any', '>='): 'any_ge[0, 1]',
+        ('any', '>'): 'any_gt[0, 1]',
+        ('all', '=='): 'all_eq[0, 1]',
+        ('all', '!='): 'all_ne[0, 1]',
+        ('all', '<='): 'all_le[0, 1]',
+        ('all', '<'): 'all_lt[0, 1]',
+        ('all', '>='): 'all_ge[0, 1]',
+        ('all', '>'): 'all_gt[0, 1]',
+    }
+
+    bits = {'double': 64,
+            'float': 32,
+            'int': 32}
+
+    width = 128 // bits[data_type]
+    intwidth = 128 // bits['int']
+
+    result = dict()
+    result['bytes'] = 16
+
+    for intrinsic_id, function_shortcut in base_names.items():
+        function_shortcut = function_shortcut.strip()
+        name = function_shortcut[:function_shortcut.index('[')]
+
+        arg_string = get_argument_string(function_shortcut)
+
+        result[intrinsic_id] = 'vec_' + name + arg_string
+
+    if data_type == 'double':
+        # Clang and XL C++ are missing these for doubles
+        result['loadA'] = '(__vector double)' + result['loadA'].format('(float*) {0}')
+        result['storeA'] = result['storeA'].format('(float*) {0}', '(__vector float) {1}')
+        result['storeAAndFlushCacheline'] = result['storeAAndFlushCacheline'].format('(float*) {0}',
+                                                                                     '(__vector float) {1}')
+
+    result['+int'] = "vec_add({0}, {1})"
+
+    result['width'] = width
+    result['intwidth'] = intwidth
+    result[data_type] = f'__vector {data_type}'
+    result['int'] = '__vector int'
+    result['bool'] = f'__vector __bool {"long long" if data_type == "double" else "int"}'
+    result['headers'] = ['<altivec.h>', '"ppc_altivec_helpers.h"']
+
+    result['makeVecConst'] = '((' + result[data_type] + '){{' + \
+        ", ".join(['(' + data_type + ') {0}' for _ in range(width)]) + '}})'
+    result['makeVec'] = '((' + result[data_type] + '){{' + \
+        ", ".join(['{' + data_type + '} {' + str(i) + '}' for i in range(width)]) + '}})'
+    result['makeVecConstInt'] = '((' + result['int'] + '){{' + ", ".join(['(int) {0}' for _ in range(intwidth)]) + '}})'
+    result['makeVecInt'] = '((' + result['int'] + '){{(int) {0}, (int) {1}, (int) {2}, (int) {3}}})'
+
+    result['any'] = 'vec_any_ne({0}, ((' + result['bool'] + ') {{' + ", ".join(['0'] * width) + '}}))'
+    result['all'] = 'vec_all_ne({0}, ((' + result['bool'] + ') {{' + ", ".join(['0'] * width) + '}}))'
+
+    result['cachelineSize'] = 'cachelineSize()'
+    result['cachelineZero'] = 'cachelineZero((void*) {0})'
+
+    return result

src/pystencils/backends/riscv_instruction_sets.py

+from pystencils.typing import CFunction
+
+
+def get_argument_string(function_shortcut, last=''):
+    args = function_shortcut[function_shortcut.index('[') + 1: -1]
+    arg_string = "("
+    for arg in args.split(","):
+        arg = arg.strip()
+        if not arg:
+            continue
+        if arg in ('0', '1', '2', '3', '4', '5'):
+            arg_string += "{" + arg + "},"
+        else:
+            arg_string += arg + ","
+    if last:
+        arg_string += last + ','
+    arg_string = arg_string[:-1] + ")"
+    return arg_string
+
+
+def get_vector_instruction_set_riscv(data_type='double', instruction_set='rvv'):
+    assert instruction_set == 'rvv'
+
+    bits = {'double': 64,
+            'float': 32,
+            'int': 32}
+
+    base_names = {
+        '+': 'fadd_vv[0, 1]',
+        '-': 'fsub_vv[0, 1]',
+        '*': 'fmul_vv[0, 1]',
+        '/': 'fdiv_vv[0, 1]',
+        'sqrt': 'fsqrt_v[0]',
+
+        'loadU': f'le{bits[data_type]}_v[0]',
+        'storeU': f'se{bits[data_type]}_v[0, 1]',
+        'maskStoreU': f'se{bits[data_type]}_v[2, 0, 1]',
+        'loadS': f'lse{bits[data_type]}_v[0, 1]',
+        'storeS': f'sse{bits[data_type]}_v[0, 2, 1]',
+        'maskStoreS': f'sse{bits[data_type]}_v[3, 0, 2, 1]',
+
+        'abs': 'fabs_v[0]',
+        '==': 'mfeq_vv[0, 1]',
+        '!=': 'mfne_vv[0, 1]',
+        '<=': 'mfle_vv[0, 1]',
+        '<': 'mflt_vv[0, 1]',
+        '>=': 'mfge_vv[0, 1]',
+        '>': 'mfgt_vv[0, 1]',
+        '&': 'mand_mm[0, 1]',
+        '|': 'mor_mm[0, 1]',
+
+        'blendv': 'merge_vvm[2, 0, 1]',
+        'any': 'cpop_m[0]',
+        'all': 'cpop_m[0]',
+    }
+
+    result = dict()
+
+    width = f'vsetvlmax_e{bits[data_type]}m1()'
+    intwidth = 'vsetvlmax_e{bits["int"]}m1()'
+    result['bytes'] = 'vsetvlmax_e8m1()'
+    prefix = 'v'
+    suffix = f'_f{bits[data_type]}m1'
+
+    vl = '{loop_stop} - {loop_counter}'
+    int_vl = f'({vl})*{bits[data_type]//bits["int"]}'
+
+    for intrinsic_id, function_shortcut in base_names.items():
+        function_shortcut = function_shortcut.strip()
+        name = function_shortcut[:function_shortcut.index('[')]
+        if name.startswith('mf'):
+            suffix2 = suffix + f'_b{bits[data_type]}'
+        elif name.endswith('_mm') or name.endswith('_m'):
+            suffix2 = f'_b{bits[data_type]}'
+        elif intrinsic_id.startswith('mask'):
+            suffix2 = suffix + '_m'
+        else:
+            suffix2 = suffix
+
+        arg_string = get_argument_string(function_shortcut, last=vl)
+
+        result[intrinsic_id] = prefix + name + suffix2 + arg_string
+
+    result['width'] = CFunction(width, "int")
+    result['intwidth'] = CFunction(intwidth, "int")
+
+    result['makeVecConst'] = f'vfmv_v_f_f{bits[data_type]}m1({{0}}, {vl})'
+    result['makeVecConstInt'] = f'vmv_v_x_i{bits["int"]}m1({{0}}, {int_vl})'
+    result['makeVecIndex'] = f'vmacc_vx_i{bits["int"]}m1({result["makeVecConstInt"]}, {{1}}, ' + \
+                             f'vid_v_i{bits["int"]}m1({int_vl}), {int_vl})'
+
+    result['storeS'] = result['storeS'].replace('{2}', f'{{2}}*{bits[data_type]//8}')
+    result['loadS'] = result['loadS'].replace('{1}', f'{{1}}*{bits[data_type]//8}')
+    result['maskStoreS'] = result['maskStoreS'].replace('{2}', f'{{2}}*{bits[data_type]//8}')
+
+    result['+int'] = f"vadd_vv_i{bits['int']}m1({{0}}, {{1}}, {int_vl})"
+
+    result['float'] = f'vfloat{bits["float"]}m1_t'
+    result['double'] = f'vfloat{bits["double"]}m1_t'
+    result['int'] = f'vint{bits["int"]}m1_t'
+    result['bool'] = f'vbool{bits[data_type]}_t'
+
+    result['headers'] = ['<riscv_vector.h>', '"riscv_v_helpers.h"']
+
+    result['any'] += ' > 0x0'
+    result['all'] += f' == vsetvl_e{bits[data_type]}m1({vl})'
+
+    result['cachelineSize'] = 'cachelineSize()'
+    result['cachelineZero'] = 'cachelineZero((void*) {0})'
+
+    return result

src/pystencils/backends/simd_instruction_sets.py

+import os
+import platform
+from ctypes import CDLL, c_int, c_size_t, sizeof, byref
+from warnings import warn
+
+import numpy as np
+
+from pystencils.backends.x86_instruction_sets import get_vector_instruction_set_x86
+from pystencils.backends.arm_instruction_sets import get_vector_instruction_set_arm
+from pystencils.backends.ppc_instruction_sets import get_vector_instruction_set_ppc
+from pystencils.backends.riscv_instruction_sets import get_vector_instruction_set_riscv
+from pystencils.cache import memorycache
+from pystencils.typing import numpy_name_to_c
+
+
+def get_vector_instruction_set(data_type='double', instruction_set='avx'):
+    if data_type == 'float':
+        warn(f"Ambiguous input for data_type: {data_type}. For single precision please use float32. "
+             f"For more information please take numpy.dtype as a reference. This input will not be supported in future "
+             f"releases")
+        data_type = 'float64'
+
+    type_name = numpy_name_to_c(np.dtype(data_type).name)
+
+    if instruction_set in ['neon', 'sme'] or instruction_set.startswith('sve'):
+        return get_vector_instruction_set_arm(type_name, instruction_set)
+    elif instruction_set in ['vsx']:
+        return get_vector_instruction_set_ppc(type_name, instruction_set)
+    elif instruction_set in ['rvv']:
+        return get_vector_instruction_set_riscv(type_name, instruction_set)
+    else:
+        return get_vector_instruction_set_x86(type_name, instruction_set)
+
+
+@memorycache
+def get_supported_instruction_sets():
+    """List of supported instruction sets on current hardware, or None if query failed."""
+    if 'PYSTENCILS_SIMD' in os.environ:
+        return os.environ['PYSTENCILS_SIMD'].split(',')
+    if platform.system() == 'Darwin' and platform.machine() == 'arm64':
+        result = ['neon']
+        libc = CDLL('/usr/lib/libc.dylib')
+        value = c_int(0)
+        size = c_size_t(sizeof(value))
+        status = libc.sysctlbyname(b"hw.optional.arm.FEAT_SME", byref(value), byref(size), None, 0)
+        if status == 0 and value.value == 1:
+            result.insert(0, "sme")
+        return result
+    elif platform.system() == 'Windows' and platform.machine() == 'ARM64':
+        return ['neon']
+    elif platform.system() == 'Linux' and platform.machine() == 'aarch64':
+        result = ['neon']  # Neon is mandatory on 64-bit ARM
+        libc = CDLL('libc.so.6')
+        hwcap = libc.getauxval(16)  # AT_HWCAP
+        hwcap2 = libc.getauxval(26)  # AT_HWCAP2
+        if hwcap & (1 << 22):  # HWCAP_SVE
+            if hwcap2 & (1 << 1):  # HWCAP2_SVE2
+                name = 'sve2'
+            else:
+                name = 'sve'
+            length = 8 * libc.prctl(51, 0, 0, 0, 0)  # PR_SVE_GET_VL
+            if length < 0:
+                raise OSError("SVE length query failed")
+            while length >= 128:
+                result.append(f"{name}{length}")
+                length //= 2
+            result.append(name)
+        if hwcap2 & (1 << 23):  # HWCAP2_SME
+            result.insert(0, "sme")  # prepend to list so it is not automatically chosen as best instruction set
+        return result
+    elif platform.system() == 'Linux' and platform.machine().startswith('riscv'):
+        libc = CDLL('libc.so.6')
+        hwcap = libc.getauxval(16)  # AT_HWCAP
+        hwcap_isa_v = 1 << (ord('V') - ord('A'))  # COMPAT_HWCAP_ISA_V
+        return ['rvv'] if hwcap & hwcap_isa_v else []
+    elif platform.system() == 'Linux' and platform.machine().startswith('ppc64'):
+        libc = CDLL('libc.so.6')
+        hwcap = libc.getauxval(16)  # AT_HWCAP
+        return ['vsx'] if hwcap & 0x00000080 else []  # PPC_FEATURE_HAS_VSX
+    elif platform.machine() in ['x86_64', 'x86', 'AMD64', 'i386']:
+        try:
+            from cpuinfo import get_cpu_info
+        except ImportError:
+            return None
+
+        result = []
+        required_sse_flags = {'sse', 'sse2', 'ssse3', 'sse4_1', 'sse4_2'}
+        required_avx_flags = {'avx', 'avx2'}
+        required_avx512_flags = {'avx512f'}
+        possible_avx512vl_flags = {'avx512vl', 'avx10_1'}
+        flags = set(get_cpu_info()['flags'])
+        if flags.issuperset(required_sse_flags):
+            result.append("sse")
+        if flags.issuperset(required_avx_flags):
+            result.append("avx")
+        if flags.issuperset(required_avx512_flags):
+            result.append("avx512")
+        if not flags.isdisjoint(possible_avx512vl_flags):
+            result.append("avx512vl")
+        return result
+    else:
+        raise NotImplementedError('Instruction set detection for %s on %s is not implemented' %
+                                  (platform.system(), platform.machine()))
+
+
+@memorycache
+def get_cacheline_size(instruction_set):
+    """Get the size (in bytes) of a cache block that can be zeroed without memory access.
+       Usually, this is identical to the cache line size."""
+    
+    instruction_sets = get_vector_instruction_set('double', instruction_set)
+    if 'cachelineSize' not in instruction_sets:
+        return None
+    
+    import pystencils as ps
+    from pystencils.astnodes import SympyAssignment
+    import numpy as np
+    from pystencils.cpu.vectorization import CachelineSize
+    
+    arr = np.zeros((1, 1), dtype=np.float32)
+    f = ps.Field.create_from_numpy_array('f', arr, index_dimensions=0)
+    ass = [CachelineSize(), SympyAssignment(f.center, CachelineSize.symbol)]
+    ast = ps.create_kernel(ass, cpu_vectorize_info={'instruction_set': instruction_set})
+    kernel = ast.compile()
+    kernel(**{f.name: arr, CachelineSize.symbol.name: 0})
+    return int(arr[0, 0])

src/pystencils/backends/x86_instruction_sets.py

+def get_argument_string(intrinsic_id, width, function_shortcut):
+    if intrinsic_id == 'makeVecConst' or intrinsic_id == 'makeVecConstInt':
+        arg_string = f"({','.join(['{0}'] * width)})"
+    elif intrinsic_id == 'makeVec' or intrinsic_id == 'makeVecInt':
+        params = ["{" + str(i) + "}" for i in reversed(range(width))]
+        arg_string = f"({','.join(params)})"
+    elif intrinsic_id == 'makeVecBool':
+        params = [f"(({{{i}}} ? -1.0 : 0.0)" for i in reversed(range(width))]
+        arg_string = f"({','.join(params)})"
+    elif intrinsic_id == 'makeVecConstBool':
+        params = ["(({0}) ? -1.0 : 0.0)" for _ in range(width)]
+        arg_string = f"({','.join(params)})"
+    else:
+        args = function_shortcut[function_shortcut.index('[') + 1: -1]
+        arg_string = "("
+        for arg in args.split(","):
+            arg = arg.strip()
+            if not arg:
+                continue
+            if arg in ('0', '1', '2', '3', '4', '5'):
+                arg_string += "{" + arg + "},"
+            else:
+                arg_string += arg + ","
+        arg_string = arg_string[:-1] + ")"
+    return arg_string
+
+
+def get_vector_instruction_set_x86(data_type='double', instruction_set='avx'):
+    comparisons = {
+        '==': '_CMP_EQ_UQ',
+        '!=': '_CMP_NEQ_UQ',
+        '>=': '_CMP_GE_OQ',
+        '<=': '_CMP_LE_OQ',
+        '<': '_CMP_NGE_UQ',
+        '>': '_CMP_NLE_UQ',
+    }
+    base_names = {
+        '+': 'add[0, 1]',
+        '-': 'sub[0, 1]',
+        '*': 'mul[0, 1]',
+        '/': 'div[0, 1]',
+        '&': 'and[0, 1]',
+        '|': 'or[0, 1]',
+        'blendv': 'blendv[0, 1, 2]',
+
+        'sqrt': 'sqrt[0]',
+
+        'makeVecConst': 'set[]',
+        'makeVec': 'set[]',
+        'makeVecBool': 'set[]',
+        'makeVecConstBool': 'set[]',
+        'makeVecInt': 'set[]',
+        'makeVecConstInt': 'set[]',
+
+        'loadU': 'loadu[0]',
+        'loadA': 'load[0]',
+        'storeU': 'storeu[0,1]',
+        'storeA': 'store[0,1]',
+        'stream': 'stream[0,1]',
+        'maskStoreA': 'mask_store[0, 2, 1]' if instruction_set.startswith('avx512') else 'maskstore[0, 2, 1]',
+        'maskStoreU': 'mask_storeu[0, 2, 1]' if instruction_set.startswith('avx512') else 'maskstore[0, 2, 1]',
+    }
+
+    for comparison_op, constant in comparisons.items():
+        base_names[comparison_op] = f'cmp[0, 1, {constant}]'
+
+    headers = {
+        'avx512': ['<immintrin.h>'],
+        'avx512vl': ['<immintrin.h>'],
+        'avx': ['<immintrin.h>'],
+        'sse': ['<immintrin.h>', '<xmmintrin.h>', '<emmintrin.h>', '<pmmintrin.h>',
+                '<tmmintrin.h>', '<smmintrin.h>', '<nmmintrin.h>']
+    }
+
+    suffix = {
+        'double': 'pd',
+        'float': 'ps',
+        'int': 'epi32'
+    }
+    prefix = {
+        'sse': '_mm',
+        'avx': '_mm256',
+        'avx512vl': '_mm256',
+        'avx512': '_mm512',
+    }
+
+    width = {
+        ("double", "sse"): 2,
+        ("float", "sse"): 4,
+        ("int", "sse"): 4,
+        ("double", "avx"): 4,
+        ("float", "avx"): 8,
+        ("int", "avx"): 8,
+        ("double", "avx512vl"): 4,
+        ("float", "avx512vl"): 8,
+        ("int", "avx512vl"): 8,
+        ("double", "avx512"): 8,
+        ("float", "avx512"): 16,
+        ("int", "avx512"): 16,
+    }
+    result = {
+        'width': width[(data_type, instruction_set)],
+        'intwidth': width[('int', instruction_set)],
+        'bytes': 4 * width[("float", instruction_set)]
+    }
+    pre = prefix[instruction_set]
+    for intrinsic_id, function_shortcut in base_names.items():
+        function_shortcut = function_shortcut.strip()
+        name = function_shortcut[:function_shortcut.index('[')]
+
+        if 'Int' in intrinsic_id:
+            suf = suffix['int']
+            arg_string = get_argument_string(intrinsic_id, result['intwidth'], function_shortcut)
+        else:
+            suf = suffix[data_type]
+            arg_string = get_argument_string(intrinsic_id, result['width'], function_shortcut)
+
+        mask_suffix = '_mask' if instruction_set.startswith('avx512') and intrinsic_id in comparisons.keys() else ''
+        result[intrinsic_id] = pre + "_" + name + "_" + suf + mask_suffix + arg_string
+
+    bit_width = result['width'] * (64 if data_type == 'double' else 32)
+    result['double'] = f"__m{bit_width}d"
+    result['float'] = f"__m{bit_width}"
+    result['int'] = f"__m{bit_width}i"
+    result['bool'] = result[data_type]
+
+    result['headers'] = headers[instruction_set]
+    result['any'] = f"{pre}_movemask_{suf}({{0}}) > 0"
+    result['all'] = f"{pre}_movemask_{suf}({{0}}) == {hex(2**result['width']-1)}"
+
+    setsuf = "x" if bit_width < 512 and bit_width // result['width'] == 64 else ""
+
+    if instruction_set.startswith('avx512'):
+        size = result['width']
+        masksize = max(size, 8)
+        result['&'] = f'_kand_mask{masksize}({{0}}, {{1}})'
+        result['|'] = f'_kor_mask{masksize}({{0}}, {{1}})'
+        result['any'] = f'!_ktestz_mask{masksize}_u8({{0}}, {{0}})'
+        result['all'] = f'_kortestc_mask{masksize}_u8({{0}}, {{0}})'
+        result['blendv'] = f'{pre}_mask_blend_{suf}({{2}}, {{0}}, {{1}})'
+        result['rsqrt'] = f"{pre}_rsqrt14_{suf}({{0}})"
+        result['bool'] = f"__mmask{masksize}"
+
+        params = " | ".join(["({{{i}}} ? {power} : 0)".format(i=i, power=2 ** i) for i in range(8)])
+        result['makeVecBool'] = f"__mmask8(({params}) )"
+        params = " | ".join(["({{0}} ? {power} : 0)".format(power=2 ** i) for i in range(8)])
+        result['makeVecConstBool'] = f"__mmask8(({params}) )"
+
+        vindex = f'{pre}_set_epi{bit_width//size}{setsuf}(' + \
+                 ', '.join([str(i) for i in range(result['width'])][::-1]) + ')'
+        vindex = f'{pre}_mullo_epi{bit_width//size}({vindex}, {pre}_set1_epi{bit_width//size}{setsuf}({{0}}))'
+        scale = bit_width // size // 8
+        result['storeS'] = f'{pre}_i{bit_width//size}scatter_{suf}({{0}}, ' + vindex.format("{2}") + \
+                           f', {{1}}, {scale})'
+        result['maskStoreS'] = f'{pre}_mask_i{bit_width//size}scatter_{suf}({{0}}, {{3}}, ' + vindex.format("{2}") + \
+                               f', {{1}}, {scale})'
+        if bit_width == 512:
+            result['loadS'] = f'{pre}_i{bit_width//size}gather_{suf}(' + vindex.format("{1}") + f', {{0}}, {scale})'
+        else:
+            result['loadS'] = f'{pre}_i{bit_width//size}gather_{suf}({{0}}, ' + vindex.format("{1}") + f', {scale})'
+
+    # abs intrinsic exists in 512 bits, but expands to a sequence. We generate that same sequence for 128 and 256 bits
+    if instruction_set == 'avx512':
+        result['abs'] = f"{pre}_abs_{suf}({{0}})"
+    else:
+        result['abs'] = f"{pre}_castsi{bit_width}_{suf}({pre}_and_si{bit_width}(" + \
+                        f"{pre}_set1_epi{bit_width // result['width']}{setsuf}(0x7" + \
+                        'f' * (bit_width // result['width'] // 4 - 1) + "), " + \
+                        f"{pre}_cast{suf}_si{bit_width}({{0}})))"
+
+    if instruction_set == 'avx' and data_type == 'float':
+        result['rsqrt'] = f"{pre}_rsqrt_{suf}({{0}})"
+
+    result['+int'] = f"{pre}_add_{suffix['int']}({{0}}, {{1}})"
+
+    result['streamFence'] = '_mm_mfence()'
+
+    return result

src/pystencils/bit_masks.py

+import sympy as sp
+# from pystencils.typing import get_type_of_expression
+
+
+# noinspection PyPep8Naming
+class flag_cond(sp.Function):
+    """Evaluates a flag condition on a bit mask, and returns the value of one of two expressions,
+    depending on whether the flag is set. 
+
+    Three argument version:
+    ```
+        flag_cond(flag_bit, mask, expr) = expr if (flag_bit is set in mask) else 0
+    ```
+
+    Four argument version:
+    ```
+        flag_cond(flag_bit, mask, expr_then, expr_else) = expr_then if (flag_bit is set in mask) else expr_else
+    ```
+    """
+
+    nargs = (3, 4)
+
+    def __new__(cls, flag_bit, mask_expression, *expressions):
+
+        # TODO Jan reintroduce checking
+        # flag_dtype = get_type_of_expression(flag_bit)
+        # if not flag_dtype.is_int():
+        #     raise ValueError('Argument flag_bit must be of integer type.')
+        #
+        # mask_dtype = get_type_of_expression(mask_expression)
+        # if not mask_dtype.is_int():
+        #     raise ValueError('Argument mask_expression must be of integer type.')
+
+        return super().__new__(cls, flag_bit, mask_expression, *expressions)
+
+    def to_c(self, print_func):
+        flag_bit = self.args[0]
+        mask = self.args[1]
+
+        then_expression = self.args[2]
+
+        flag_bit_code = print_func(flag_bit)
+        mask_code = print_func(mask)
+        then_code = print_func(then_expression)
+
+        code = f"(({mask_code}) >> ({flag_bit_code}) & 1) * ({then_code})"
+
+        if len(self.args) > 3:
+            else_expression = self.args[3]
+            else_code = print_func(else_expression)
+            code += f" + (({mask_code}) >> ({flag_bit_code}) ^ 1) * ({else_code})"
+
+        return code

pystencils/boundaries/__init__.py → src/pystencils/boundaries/__init__.py

+from pystencils.boundaries.boundaryconditions import Dirichlet, Neumann
 from pystencils.boundaries.boundaryhandling import BoundaryHandling
-from pystencils.boundaries.boundaryconditions import Neumann, Dirichlet
 from pystencils.boundaries.inkernel import add_neumann_boundary
 
 __all__ = ['BoundaryHandling', 'Neumann', 'Dirichlet', 'add_neumann_boundary']

pystencils/boundaries/boundaryconditions.py → src/pystencils/boundaries/boundaryconditions.py

-from typing import List, Tuple, Any
-from pystencils import Assignment
+from typing import Any, List, Tuple
+
+from pystencils.astnodes import SympyAssignment
 from pystencils.boundaries.boundaryhandling import BoundaryOffsetInfo
-from pystencils.data_types import create_type
+from pystencils.typing import create_type
 
 
 class Boundary:
@@ -13,7 +14,7 @@ class Boundary:
     def __init__(self, name=None):
         self._name = name
 
-    def __call__(self, field, direction_symbol, index_field) -> List[Assignment]:
+    def __call__(self, field, direction_symbol, index_field) -> List[SympyAssignment]:
         """Defines the boundary behavior and must therefore be implemented by all boundaries.
 
         Here the boundary is defined as a list of sympy assignments, from which a boundary kernel is generated.
@@ -62,20 +63,20 @@ class Neumann(Boundary):
 
         neighbor = BoundaryOffsetInfo.offset_from_dir(direction_symbol, field.spatial_dimensions)
         if field.index_dimensions == 0:
-            return [Assignment(field.center, field[neighbor])]
+            return [SympyAssignment(field.center, field[neighbor])]
         else:
             from itertools import product
             if not field.has_fixed_index_shape:
                 raise NotImplementedError("Neumann boundary works only for fields with fixed index shape")
             index_iter = product(*(range(i) for i in field.index_shape))
-            return [Assignment(field(*idx), field[neighbor](*idx)) for idx in index_iter]
+            return [SympyAssignment(field(*idx), field[neighbor](*idx)) for idx in index_iter]
 
     def __hash__(self):
         # All boundaries of these class behave equal -> should also be equal
         return hash("Neumann")
 
     def __eq__(self, other):
-        return type(other) == Neumann
+        return type(other) is Neumann
 
 
 class Dirichlet(Boundary):
@@ -83,7 +84,7 @@ class Dirichlet(Boundary):
     inner_or_boundary = False
     single_link = True
 
-    def __init__(self, value, name="Dirchlet"):
+    def __init__(self, value, name=None):
         super().__init__(name)
         self._value = value
 
@@ -102,11 +103,11 @@ class Dirichlet(Boundary):
     def __call__(self, field, direction_symbol, index_field, **kwargs):
 
         if field.index_dimensions == 0:
-            return [Assignment(field, index_field("value") if self.additional_data else self._value)]
+            return [SympyAssignment(field.center, index_field("value") if self.additional_data else self._value)]
         elif field.index_dimensions == 1:
             assert not self.additional_data
             if not field.has_fixed_index_shape:
                 raise NotImplementedError("Field needs fixed index shape")
             assert len(self._value) == field.index_shape[0], "Dirichlet value does not match index shape of field"
-            return [Assignment(field(i), self._value[i]) for i in range(field.index_shape[0])]
+            return [SympyAssignment(field(i), self._value[i]) for i in range(field.index_shape[0])]
         raise NotImplementedError("Dirichlet boundary not implemented for fields with more than one index dimension")

pystencils/boundaries/boundaryhandling.py → src/pystencils/boundaries/boundaryhandling.py

+from functools import lru_cache
+
 import numpy as np
 import sympy as sp
-from pystencils.assignment import Assignment
-from pystencils import Field, TypedSymbol, create_indexed_kernel
+
+from pystencils import create_kernel, CreateKernelConfig, Target
+from pystencils.astnodes import SympyAssignment
 from pystencils.backends.cbackend import CustomCodeNode
-from pystencils.boundaries.createindexlist import numpy_data_type_for_boundary_object, create_boundary_index_array
-from pystencils.cache import memorycache
-from pystencils.data_types import create_type
-from pystencils.kernelparameters import FieldPointerSymbol
+from pystencils.boundaries.createindexlist import (
+    create_boundary_index_array, numpy_data_type_for_boundary_object)
+from pystencils.typing import TypedSymbol, create_type
+from pystencils.gpu.gpu_array_handler import GPUArrayHandler
+from pystencils.field import Field
+from pystencils.typing.typed_sympy import FieldPointerSymbol
+
+try:
+    # noinspection PyPep8Naming
+    import waLBerla as wlb
+    if wlb.cpp_available:
+        from pystencils.datahandling.parallel_datahandling import ParallelDataHandling
+        import cupy.cuda.runtime
+    else:
+        ParallelDataHandling = None
+except ImportError:
+    ParallelDataHandling = None
 
 DEFAULT_FLAG_TYPE = np.uint32
 
@@ -19,11 +35,11 @@ class FlagInterface:
         >>> dh = create_data_handling((4, 5))
         >>> fi = FlagInterface(dh, 'flag_field', np.uint8)
         >>> assert dh.has_data('flag_field')
-        >>> fi.reserve_next_flag()
+        >>> int(fi.reserve_next_flag())
         2
-        >>> fi.reserve_flag(4)
+        >>> int(fi.reserve_flag(4))
         4
-        >>> fi.reserve_next_flag()
+        >>> int(fi.reserve_next_flag())
         8
     """
 
@@ -52,13 +68,13 @@ class FlagInterface:
                 self._used_flags.add(flag)
                 assert self._is_power_of_2(flag)
                 return flag
-        raise ValueError("All available {} flags are reserved".format(self.max_bits))
+        raise ValueError(f"All available {self.max_bits} flags are reserved")
 
     def reserve_flag(self, flag):
         assert self._is_power_of_2(flag)
         flag = self.dtype(flag)
         if flag in self._used_flags:
-            raise ValueError("The flag {flag} is already reserved".format(flag=flag))
+            raise ValueError(f"The flag {flag} is already reserved")
         self._used_flags.add(flag)
         return flag
 
@@ -70,7 +86,7 @@ class FlagInterface:
 class BoundaryHandling:
 
     def __init__(self, data_handling, field_name, stencil, name="boundary_handling", flag_interface=None,
-                 target='cpu', openmp=True):
+                 target: Target = Target.CPU, openmp=True):
         assert data_handling.has_data(field_name)
         assert data_handling.dim == len(stencil[0]), "Dimension of stencil and data handling do not match"
         self._data_handling = data_handling
@@ -84,8 +100,33 @@ class BoundaryHandling:
         fi = flag_interface
         self.flag_interface = fi if fi is not None else FlagInterface(data_handling, name + "Flags")
 
-        gpu = self._target == 'gpu'
-        data_handling.add_custom_class(self._index_array_name, self.IndexFieldBlockData, cpu=True, gpu=gpu)
+        if ParallelDataHandling and isinstance(self.data_handling, ParallelDataHandling):
+            array_handler = GPUArrayHandler(cupy.cuda.runtime.getDevice())
+        else:
+            array_handler = self.data_handling.array_handler
+
+        def to_cpu(gpu_version, cpu_version):
+            gpu_version = gpu_version.boundary_object_to_index_list
+            cpu_version = cpu_version.boundary_object_to_index_list
+            for obj, cpu_arr in cpu_version.items():
+                array_handler.download(gpu_version[obj], cpu_arr)
+
+        def to_gpu(gpu_version, cpu_version):
+            gpu_version = gpu_version.boundary_object_to_index_list
+            cpu_version = cpu_version.boundary_object_to_index_list
+
+            for obj, cpu_arr in cpu_version.items():
+                if obj not in gpu_version or gpu_version[obj].shape != cpu_arr.shape:
+                    gpu_version[obj] = array_handler.empty(cpu_arr.shape, cpu_arr.dtype)
+                    array_handler.upload(gpu_version[obj], cpu_arr)
+                else:
+                    array_handler.upload(gpu_version[obj], cpu_arr)
+
+        class_ = self.IndexFieldBlockData
+        class_.to_cpu = to_cpu
+        class_.to_gpu = to_gpu
+        gpu = self._target in data_handling._GPU_LIKE_TARGETS
+        data_handling.add_custom_class(self._index_array_name, class_, cpu=True, gpu=gpu)
 
     @property
     def data_handling(self):
@@ -201,7 +242,7 @@ class BoundaryHandling:
         if self._dirty:
             self.prepare()
 
-        for b in self._data_handling.iterate(gpu=self._target == 'gpu'):
+        for b in self._data_handling.iterate(gpu=self._target in self._data_handling._GPU_LIKE_TARGETS):
             for b_obj, idx_arr in b[self._index_array_name].boundary_object_to_index_list.items():
                 kwargs[self._field_name] = b[self._field_name]
                 kwargs['indexField'] = idx_arr
@@ -216,7 +257,7 @@ class BoundaryHandling:
         if self._dirty:
             self.prepare()
 
-        for b in self._data_handling.iterate(gpu=self._target == 'gpu'):
+        for b in self._data_handling.iterate(gpu=self._target in self._data_handling._GPU_LIKE_TARGETS):
             for b_obj, idx_arr in b[self._index_array_name].boundary_object_to_index_list.items():
                 arguments = kwargs.copy()
                 arguments[self._field_name] = b[self._field_name]
@@ -233,11 +274,13 @@ class BoundaryHandling:
         """
         Writes a VTK field where each cell with the given boundary is marked with 1, other cells are 0
         This can be used to display the simulation geometry in Paraview
-        :param file_name: vtk filename
-        :param boundaries: boundary object, or special string 'domain' for domain cells or special string 'all' for all
-                         boundary conditions.
-                         can also  be a sequence, to write multiple boundaries to VTK file
-        :param ghost_layers: number of ghost layers to write, or True for all, False for none
+
+        Params:
+            file_name: vtk filename
+            boundaries: boundary object, or special string 'domain' for domain cells or special string 'all' for all
+                      boundary conditions.
+                      can also  be a sequence, to write multiple boundaries to VTK file
+            ghost_layers: number of ghost layers to write, or True for all, False for none
         """
         if boundaries == 'all':
             boundaries = list(self._boundary_object_to_boundary_info.keys()) + ['domain']
@@ -272,7 +315,7 @@ class BoundaryHandling:
 
     def _create_boundary_kernel(self, symbolic_field, symbolic_index_field, boundary_obj):
         return create_boundary_kernel(symbolic_field, symbolic_index_field, self.stencil, boundary_obj,
-                                      target=self._target, openmp=self._openmp)
+                                      target=self._target, cpu_openmp=self._openmp)
 
     def _create_index_fields(self):
         dh = self._data_handling
@@ -299,7 +342,7 @@ class BoundaryHandling:
     def _boundary_data_initialization(self, boundary_obj, boundary_data_setter, **kwargs):
         if boundary_obj.additional_data_init_callback:
             boundary_obj.additional_data_init_callback(boundary_data_setter, **kwargs)
-        if self._target == 'gpu':
+        if self._target in self._data_handling._GPU_LIKE_TARGETS:
             self._data_handling.to_gpu(self._index_array_name)
 
     class BoundaryInfo(object):
@@ -309,7 +352,7 @@ class BoundaryHandling:
             self.kernel = kernel
 
     class IndexFieldBlockData:
-        def __init__(self, *_1, **_2):
+        def __init__(self, *args, **kwargs):
             self.boundary_object_to_index_list = {}
             self.boundary_object_to_data_setter = {}
 
@@ -317,24 +360,6 @@ class BoundaryHandling:
             self.boundary_object_to_index_list.clear()
             self.boundary_object_to_data_setter.clear()
 
-        @staticmethod
-        def to_cpu(gpu_version, cpu_version):
-            gpu_version = gpu_version.boundary_object_to_index_list
-            cpu_version = cpu_version.boundary_object_to_index_list
-            for obj, cpu_arr in cpu_version.items():
-                gpu_version[obj].get(cpu_arr)
-
-        @staticmethod
-        def to_gpu(gpu_version, cpu_version):
-            from pycuda import gpuarray
-            gpu_version = gpu_version.boundary_object_to_index_list
-            cpu_version = cpu_version.boundary_object_to_index_list
-            for obj, cpu_arr in cpu_version.items():
-                if obj not in gpu_version or gpu_version[obj].shape != cpu_arr.shape:
-                    gpu_version[obj] = gpuarray.to_gpu(cpu_arr)
-                else:
-                    gpu_version[obj].set(cpu_arr)
-
 
 class BoundaryDataSetter:
 
@@ -356,26 +381,26 @@ class BoundaryDataSetter:
         assert coord < self.dim
         return self.index_array[self.coord_map[coord]] + self.offset[coord] - self.ghost_layers + 0.5
 
-    @memorycache()
+    @lru_cache()
     def link_offsets(self):
         return self.stencil[self.index_array['dir']]
 
-    @memorycache()
+    @lru_cache()
     def link_positions(self, coord):
         return self.non_boundary_cell_positions(coord) + 0.5 * self.link_offsets()[:, coord]
 
-    @memorycache()
+    @lru_cache()
     def boundary_cell_positions(self, coord):
         return self.non_boundary_cell_positions(coord) + self.link_offsets()[:, coord]
 
     def __setitem__(self, key, value):
         if key not in self.boundary_data_names:
-            raise KeyError("Invalid boundary data name %s. Allowed are %s" % (key, self.boundary_data_names))
+            raise KeyError(f"Invalid boundary data name {key}. Allowed are {self.boundary_data_names}")
         self.index_array[key] = value
 
     def __getitem__(self, item):
         if item not in self.boundary_data_names:
-            raise KeyError("Invalid boundary data name %s. Allowed are %s" % (item, self.boundary_data_names))
+            raise KeyError(f"Invalid boundary data name {item}. Allowed are {self.boundary_data_names}")
         return self.index_array[item]
 
 
@@ -401,29 +426,30 @@ class BoundaryOffsetInfo(CustomCodeNode):
         code = "\n"
         for i in range(dim):
             offset_str = ", ".join([str(d[i]) for d in stencil])
-            code += "const int64_t %s [] = { %s };\n" % (offset_sym[i].name, offset_str)
+            code += "const int32_t %s [] = { %s };\n" % (offset_sym[i].name, offset_str)
 
         inv_dirs = []
         for direction in stencil:
             inverse_dir = tuple([-i for i in direction])
             inv_dirs.append(str(stencil.index(inverse_dir)))
 
-        code += "const int %s [] = { %s };\n" % (self.INV_DIR_SYMBOL.name, ", ".join(inv_dirs))
+        code += "const int32_t %s [] = { %s };\n" % (self.INV_DIR_SYMBOL.name, ", ".join(inv_dirs))
         offset_symbols = BoundaryOffsetInfo._offset_symbols(dim)
         super(BoundaryOffsetInfo, self).__init__(code, symbols_read=set(),
                                                  symbols_defined=set(offset_symbols + [self.INV_DIR_SYMBOL]))
 
     @staticmethod
     def _offset_symbols(dim):
-        return [TypedSymbol("c%s" % (d,), create_type(np.int64)) for d in ['x', 'y', 'z'][:dim]]
+        return [TypedSymbol(f"c{d}", create_type(np.int32)) for d in ['x', 'y', 'z'][:dim]]
 
-    INV_DIR_SYMBOL = TypedSymbol("invdir", "int")
+    INV_DIR_SYMBOL = TypedSymbol("invdir", np.int32)
 
 
-def create_boundary_kernel(field, index_field, stencil, boundary_functor, target='cpu', openmp=True):
+def create_boundary_kernel(field, index_field, stencil, boundary_functor, target=Target.CPU, **kernel_creation_args):
     elements = [BoundaryOffsetInfo(stencil)]
-    index_arr_dtype = index_field.dtype.numpy_dtype
-    dir_symbol = TypedSymbol("dir", index_arr_dtype.fields['dir'][0])
-    elements += [Assignment(dir_symbol, index_field[0]('dir'))]
+    dir_symbol = TypedSymbol("dir", np.int32)
+    elements += [SympyAssignment(dir_symbol, index_field[0]('dir'))]
     elements += boundary_functor(field, direction_symbol=dir_symbol, index_field=index_field)
-    return create_indexed_kernel(elements, [index_field], target=target, cpu_openmp=openmp)
+    config = CreateKernelConfig(index_fields=[index_field], target=target, skip_independence_check=True,
+                                **kernel_creation_args)
+    return create_kernel(elements, config=config)

pystencils/boundaries/createindexlist.py → src/pystencils/boundaries/createindexlist.py

-import numpy as np
-import itertools
 import warnings
 
+import numpy as np
+
+
 try:
     import pyximport
 
     pyximport.install(language_level=3)
-    from pystencils.boundaries.createindexlistcython import create_boundary_neighbor_index_list_2d, \
-        create_boundary_neighbor_index_list_3d, create_boundary_cell_index_list_2d, create_boundary_cell_index_list_3d
-
     cython_funcs_available = True
-except Exception:
+except ImportError:
     cython_funcs_available = False
-    create_boundary_index_list_2d = None
-    create_boundary_index_list_3d = None
+
+if cython_funcs_available:
+    from pystencils.boundaries.createindexlistcython import (
+        create_boundary_neighbor_index_list_2d,
+        create_boundary_neighbor_index_list_3d,
+        create_boundary_cell_index_list_2d,
+        create_boundary_cell_index_list_3d,
+    )
 
 boundary_index_array_coordinate_names = ["x", "y", "z"]
 direction_member_name = "dir"
+default_index_array_dtype = np.int32
 
 
 def numpy_data_type_for_boundary_object(boundary_object, dim):
     coordinate_names = boundary_index_array_coordinate_names[:dim]
-    return np.dtype([(name, np.int32) for name in coordinate_names]
-                    + [(direction_member_name, np.int32)]
-                    + [(i[0], i[1].numpy_dtype) for i in boundary_object.additional_data], align=True)
-
-
-def _create_boundary_neighbor_index_list_python(flag_field_arr, nr_of_ghost_layers, boundary_mask,
-                                                fluid_mask, stencil, single_link):
-    coordinate_names = boundary_index_array_coordinate_names[:len(flag_field_arr.shape)]
-    index_arr_dtype = np.dtype([(name, np.int32) for name in coordinate_names] + [(direction_member_name, np.int32)])
-
-    result = []
-    gl = nr_of_ghost_layers
-    for cell in itertools.product(*reversed([range(gl, i - gl) for i in flag_field_arr.shape])):
-        cell = cell[::-1]
-        if not flag_field_arr[cell] & fluid_mask:
-            continue
+    return np.dtype(
+        [(name, default_index_array_dtype) for name in coordinate_names]
+        + [(direction_member_name, default_index_array_dtype)]
+        + [(i[0], i[1].numpy_dtype) for i in boundary_object.additional_data],
+        align=True,
+    )
+
+
+def _create_index_list_python(
+    flag_field_arr,
+    boundary_mask,
+    fluid_mask,
+    stencil,
+    single_link,
+    inner_or_boundary=False,
+    nr_of_ghost_layers=None,
+):
+    if inner_or_boundary and nr_of_ghost_layers is None:
+        raise ValueError(
+            "If inner_or_boundary is set True the number of ghost layers "
+            "around the inner domain has to be specified"
+        )
+
+    if nr_of_ghost_layers is None:
+        nr_of_ghost_layers = 0
+
+    coordinate_names = boundary_index_array_coordinate_names[
+        : len(flag_field_arr.shape)
+    ]
+    index_arr_dtype = np.dtype(
+        [(name, default_index_array_dtype) for name in coordinate_names]
+        + [(direction_member_name, default_index_array_dtype)]
+    )
+
+    # boundary cells are extracted via np.where. To ensure continous memory access in the compute kernel these cells
+    # have to be sorted.
+    boundary_cells = np.transpose(np.nonzero(flag_field_arr == boundary_mask))
+    for i in range(len(flag_field_arr.shape)):
+        boundary_cells = boundary_cells[boundary_cells[:, i].argsort(kind="mergesort")]
+
+    # First a set is created to save all fluid cells which are near boundary
+    fluid_cells = set()
+    for cell in boundary_cells:
+        cell = tuple(cell)
         for dir_idx, direction in enumerate(stencil):
-            neighbor_cell = tuple([cell_i + dir_i for cell_i, dir_i in zip(cell, direction)])
-            if flag_field_arr[neighbor_cell] & boundary_mask:
-                result.append(cell + (dir_idx,))
-                if single_link:
-                    continue
-
-    return np.array(result, dtype=index_arr_dtype)
+            neighbor_cell = tuple(
+                [cell_i + dir_i for cell_i, dir_i in zip(cell, direction)]
+            )
+            # prevent out ouf bounds access. If boundary cell is at the border, some stencil directions would be out.
+            if any(
+                not 0 + nr_of_ghost_layers <= e < upper - nr_of_ghost_layers
+                for e, upper in zip(neighbor_cell, flag_field_arr.shape)
+            ):
+                continue
+            if flag_field_arr[neighbor_cell] & fluid_mask:
+                fluid_cells.add(neighbor_cell)
 
+    # then this is set is transformed to a list to make it sortable. This ensures continoous memory access later.
+    fluid_cells = list(fluid_cells)
+    if len(flag_field_arr.shape) == 3:
+        fluid_cells.sort(key=lambda tup: (tup[-1], tup[-2], tup[0]))
+    else:
+        fluid_cells.sort(key=lambda tup: (tup[-1], tup[0]))
 
-def _create_boundary_cell_index_list_python(flag_field_arr, boundary_mask,
-                                            fluid_mask, stencil, single_link):
-    coordinate_names = boundary_index_array_coordinate_names[:len(flag_field_arr.shape)]
-    index_arr_dtype = np.dtype([(name, np.int32) for name in coordinate_names] + [(direction_member_name, np.int32)])
+    cells_to_iterate = fluid_cells if inner_or_boundary else boundary_cells
+    checkmask = boundary_mask if inner_or_boundary else fluid_mask
 
     result = []
-    for cell in itertools.product(*reversed([range(0, i) for i in flag_field_arr.shape])):
-        cell = cell[::-1]
-        if not flag_field_arr[cell] & boundary_mask:
-            continue
+    for cell in cells_to_iterate:
+        cell = tuple(cell)
+        sum_cells = np.zeros(len(cell))
         for dir_idx, direction in enumerate(stencil):
-            neighbor_cell = tuple([cell_i + dir_i for cell_i, dir_i in zip(cell, direction)])
-            if any(not 0 <= e < upper for e, upper in zip(neighbor_cell, flag_field_arr.shape)):
+            neighbor_cell = tuple(
+                [cell_i + dir_i for cell_i, dir_i in zip(cell, direction)]
+            )
+            # prevent out ouf bounds access. If boundary cell is at the border, some stencil directions would be out.
+            if any(
+                not 0 <= e < upper
+                for e, upper in zip(neighbor_cell, flag_field_arr.shape)
+            ):
                 continue
-            if flag_field_arr[neighbor_cell] & fluid_mask:
-                result.append(cell + (dir_idx,))
+            if flag_field_arr[neighbor_cell] & checkmask:
                 if single_link:
-                    break
+                    sum_cells += np.array(direction)
+                else:
+                    result.append(tuple(cell) + (dir_idx,))
+
+        # the discrete normal direction is the one which gives the maximum inner product to the stencil direction
+        if single_link and any(sum_cells != 0):
+            idx = np.argmax(np.inner(sum_cells, stencil))
+            result.append(tuple(cell) + (idx,))
 
     return np.array(result, dtype=index_arr_dtype)
 
 
-def create_boundary_index_list(flag_field, stencil, boundary_mask, fluid_mask,
-                               nr_of_ghost_layers=1, inner_or_boundary=True, single_link=False):
+def create_boundary_index_list(
+    flag_field,
+    stencil,
+    boundary_mask,
+    fluid_mask,
+    nr_of_ghost_layers=1,
+    inner_or_boundary=True,
+    single_link=False,
+):
     """Creates a numpy array storing links (connections) between domain cells and boundary cells.
 
     Args:
@@ -82,15 +141,25 @@ def create_boundary_index_list(flag_field, stencil, boundary_mask, fluid_mask,
         nr_of_ghost_layers: only relevant if neighbors is True
         inner_or_boundary: if true, the result contains the cell coordinates of the domain cells -
                     if false the boundary cells are listed
-        single_link: if true only the first link is reported from this cell
+        single_link: if true only the link in normal direction to this cell is reported
 
     """
     dim = len(flag_field.shape)
     coordinate_names = boundary_index_array_coordinate_names[:dim]
-    index_arr_dtype = np.dtype([(name, np.int32) for name in coordinate_names] + [(direction_member_name, np.int32)])
-
-    stencil = np.array(stencil, dtype=np.int32)
-    args = (flag_field, nr_of_ghost_layers, boundary_mask, fluid_mask, stencil, single_link)
+    index_arr_dtype = np.dtype(
+        [(name, default_index_array_dtype) for name in coordinate_names]
+        + [(direction_member_name, default_index_array_dtype)]
+    )
+
+    stencil = np.array(stencil, dtype=default_index_array_dtype)
+    args = (
+        flag_field,
+        nr_of_ghost_layers,
+        boundary_mask,
+        fluid_mask,
+        stencil,
+        single_link,
+    )
     args_no_gl = (flag_field, boundary_mask, fluid_mask, stencil, single_link)
 
     if cython_funcs_available:
@@ -109,24 +178,42 @@ def create_boundary_index_list(flag_field, stencil, boundary_mask, fluid_mask,
         return np.array(idx_list, dtype=index_arr_dtype)
     else:
         if flag_field.size > 1e6:
-            warnings.warn("Boundary setup may take very long! Consider installing cython to speed it up")
-        if inner_or_boundary:
-            return _create_boundary_neighbor_index_list_python(*args)
-        else:
-            return _create_boundary_cell_index_list_python(*args_no_gl)
-
-
-def create_boundary_index_array(flag_field, stencil, boundary_mask, fluid_mask, boundary_object,
-                                nr_of_ghost_layers=1, inner_or_boundary=True, single_link=False):
-    idx_array = create_boundary_index_list(flag_field, stencil, boundary_mask, fluid_mask,
-                                           nr_of_ghost_layers, inner_or_boundary, single_link)
+            warnings.warn(
+                "Boundary setup may take very long! Consider installing cython to speed it up"
+            )
+        return _create_index_list_python(
+            *args_no_gl,
+            inner_or_boundary=inner_or_boundary,
+            nr_of_ghost_layers=nr_of_ghost_layers,
+        )
+
+
+def create_boundary_index_array(
+    flag_field,
+    stencil,
+    boundary_mask,
+    fluid_mask,
+    boundary_object,
+    nr_of_ghost_layers=1,
+    inner_or_boundary=True,
+    single_link=False,
+):
+    idx_array = create_boundary_index_list(
+        flag_field,
+        stencil,
+        boundary_mask,
+        fluid_mask,
+        nr_of_ghost_layers,
+        inner_or_boundary,
+        single_link,
+    )
     dim = len(flag_field.shape)
 
     if boundary_object.additional_data:
         coordinate_names = boundary_index_array_coordinate_names[:dim]
         index_arr_dtype = numpy_data_type_for_boundary_object(boundary_object, dim)
         extended_idx_field = np.empty(len(idx_array), dtype=index_arr_dtype)
-        for prop in coordinate_names + ['dir']:
+        for prop in coordinate_names + ["dir"]:
             extended_idx_field[prop] = idx_array[prop]
 
         idx_array = extended_idx_field

pystencils/boundaries/createindexlistcython.pyx → src/pystencils/boundaries/createindexlistcython.pyx

-# Workaround for cython bug
-# see https://stackoverflow.com/questions/8024805/cython-compiled-c-extension-importerror-dynamic-module-does-not-define-init-fu
-WORKAROUND = "Something"
+# cython: language_level=3str
 
 import cython
 
@@ -21,20 +19,37 @@ def create_boundary_neighbor_index_list_2d(object[IntegerType, ndim=2] flag_fiel
     cdef int xs, ys, x, y
     cdef int dirIdx, num_directions, dx, dy
 
+    cdef int sum_x, sum_y
+    cdef float dot, maxn
+    cdef int calculated_idx
+
     xs, ys = flag_field.shape
     boundary_index_list = []
     num_directions = stencil.shape[0]
 
     for y in range(nr_of_ghost_layers, ys - nr_of_ghost_layers):
         for x in range(nr_of_ghost_layers, xs - nr_of_ghost_layers):
+            sum_x = 0; sum_y = 0;
             if flag_field[x, y] & fluid_mask:
                 for dirIdx in range(num_directions):
-                    dx = stencil[dirIdx,0]
-                    dy = stencil[dirIdx,1]
+                    dx = stencil[dirIdx,0]; dy = stencil[dirIdx,1]
                     if flag_field[x + dx, y + dy] & boundary_mask:
-                        boundary_index_list.append((x,y, dirIdx))
                         if single_link:
-                            break
+                            sum_x += dx; sum_y += dy;
+                        else:
+                            boundary_index_list.append((x, y, dirIdx))
+
+            dot = 0; maxn = 0; calculated_idx = 0
+            if single_link and (sum_x != 0 or sum_y != 0):
+                for dirIdx in range(num_directions):
+                    dx = stencil[dirIdx, 0]; dy = stencil[dirIdx, 1];
+
+                    dot = dx * sum_x + dy * sum_y
+                    if dot > maxn:
+                        maxn = dot
+                        calculated_idx = dirIdx
+
+                boundary_index_list.append((x, y, calculated_idx))
     return boundary_index_list
 
 
@@ -46,6 +61,10 @@ def create_boundary_neighbor_index_list_3d(object[IntegerType, ndim=3] flag_fiel
     cdef int xs, ys, zs, x, y, z
     cdef int dirIdx, num_directions, dx, dy, dz
 
+    cdef int sum_x, sum_y, sum_z
+    cdef float dot, maxn
+    cdef int calculated_idx
+
     xs, ys, zs = flag_field.shape
     boundary_index_list = []
     num_directions = stencil.shape[0]
@@ -53,15 +72,27 @@ def create_boundary_neighbor_index_list_3d(object[IntegerType, ndim=3] flag_fiel
     for z in range(nr_of_ghost_layers, zs - nr_of_ghost_layers):
         for y in range(nr_of_ghost_layers, ys - nr_of_ghost_layers):
             for x in range(nr_of_ghost_layers, xs - nr_of_ghost_layers):
+                sum_x = 0; sum_y = 0; sum_z = 0
                 if flag_field[x, y, z] & fluid_mask:
                     for dirIdx in range(num_directions):
-                        dx = stencil[dirIdx,0]
-                        dy = stencil[dirIdx,1]
-                        dz = stencil[dirIdx,2]
+                        dx = stencil[dirIdx,0]; dy = stencil[dirIdx,1]; dz = stencil[dirIdx,2]
                         if flag_field[x + dx, y + dy, z + dz] & boundary_mask:
-                            boundary_index_list.append((x,y,z, dirIdx))
                             if single_link:
-                                break
+                                sum_x += dx; sum_y += dy; sum_z += dz
+                            else:
+                                boundary_index_list.append((x, y, z, dirIdx))
+
+                dot = 0; maxn = 0; calculated_idx = 0
+                if single_link and (sum_x != 0 or sum_y != 0 or sum_z != 0):
+                    for dirIdx in range(num_directions):
+                        dx = stencil[dirIdx, 0]; dy = stencil[dirIdx, 1]; dz = stencil[dirIdx, 2]
+
+                        dot = dx * sum_x + dy * sum_y + dz * sum_z
+                        if dot > maxn:
+                            maxn = dot
+                            calculated_idx = dirIdx
+
+                    boundary_index_list.append((x, y, z, calculated_idx))
     return boundary_index_list
 
 
@@ -74,21 +105,39 @@ def create_boundary_cell_index_list_2d(object[IntegerType, ndim=2] flag_field,
     cdef int xs, ys, x, y
     cdef int dirIdx, num_directions, dx, dy
 
+    cdef int sum_x, sum_y
+    cdef float dot, maxn
+    cdef int calculated_idx
+
     xs, ys = flag_field.shape
     boundary_index_list = []
     num_directions = stencil.shape[0]
 
     for y in range(0, ys):
         for x in range(0, xs):
+            sum_x = 0; sum_y = 0;
             if flag_field[x, y] & boundary_mask:
                 for dirIdx in range(num_directions):
-                    dx = stencil[dirIdx,0]
-                    dy = stencil[dirIdx,1]
+                    dx = stencil[dirIdx,0]; dy = stencil[dirIdx,1]
                     if 0 <= x + dx < xs and 0 <= y + dy < ys:
                         if flag_field[x + dx, y + dy] & fluid_mask:
-                            boundary_index_list.append((x,y, dirIdx))
                             if single_link:
-                                break
+                                sum_x += dx; sum_y += dy
+                            else:
+                                boundary_index_list.append((x, y, dirIdx))
+
+            dot = 0; maxn = 0; calculated_idx = 0
+            if single_link and (sum_x != 0 or sum_y != 0):
+                for dirIdx in range(num_directions):
+                    dx = stencil[dirIdx, 0]; dy = stencil[dirIdx, 1]
+
+                    dot = dx * sum_x + dy * sum_y
+                    if dot > maxn:
+                        maxn = dot
+                        calculated_idx = dirIdx
+
+                boundary_index_list.append((x, y, calculated_idx))
+
     return boundary_index_list
 
 
@@ -100,6 +149,10 @@ def create_boundary_cell_index_list_3d(object[IntegerType, ndim=3] flag_field,
     cdef int xs, ys, zs, x, y, z
     cdef int dirIdx, num_directions, dx, dy, dz
 
+    cdef int sum_x, sum_y, sum_z
+    cdef float dot, maxn
+    cdef int calculated_idx
+
     xs, ys, zs = flag_field.shape
     boundary_index_list = []
     num_directions = stencil.shape[0]
@@ -107,14 +160,27 @@ def create_boundary_cell_index_list_3d(object[IntegerType, ndim=3] flag_field,
     for z in range(0, zs):
         for y in range(0, ys):
             for x in range(0, xs):
+                sum_x = 0; sum_y = 0; sum_z = 0
                 if flag_field[x, y, z] & boundary_mask:
                     for dirIdx in range(num_directions):
-                        dx = stencil[dirIdx,0]
-                        dy = stencil[dirIdx,1]
-                        dz = stencil[dirIdx,2]
+                        dx = stencil[dirIdx, 0]; dy = stencil[dirIdx, 1]; dz = stencil[dirIdx, 2]
                         if 0 <= x + dx < xs and 0 <= y + dy < ys and 0 <= z + dz < zs:
                             if flag_field[x + dx, y + dy, z + dz] & fluid_mask:
-                                boundary_index_list.append((x,y,z, dirIdx))
                                 if single_link:
-                                    break
+                                    sum_x += dx; sum_y += dy; sum_z += dz
+                                else:
+                                    boundary_index_list.append((x, y, z, dirIdx))
+
+                dot = 0; maxn = 0; calculated_idx=0
+                if single_link and (sum_x != 0 or sum_y !=0 or sum_z !=0):
+                    for dirIdx in range(num_directions):
+                        dx = stencil[dirIdx, 0]; dy = stencil[dirIdx, 1]; dz = stencil[dirIdx, 2]
+
+                        dot = dx*sum_x + dy*sum_y + dz*sum_z
+                        if dot > maxn:
+                            maxn = dot
+                            calculated_idx = dirIdx
+
+                    boundary_index_list.append((x, y, z, calculated_idx))
+
     return boundary_index_list
\ No newline at end of file

pystencils/boundaries/inkernel.py → src/pystencils/boundaries/inkernel.py

 import sympy as sp
-from pystencils import Field, TypedSymbol
-from pystencils.integer_functions import bitwise_and
+
 from pystencils.boundaries.boundaryhandling import DEFAULT_FLAG_TYPE
-from pystencils.data_types import create_type
+from pystencils.typing import TypedSymbol, create_type
+from pystencils.field import Field
+from pystencils.integer_functions import bitwise_and
 
 
 def add_neumann_boundary(eqs, fields, flag_field, boundary_flag="neumann_flag", inverse_flag=False):
     """
     Replaces all neighbor accesses by flag field guarded accesses.
     If flag in neighboring cell is set, the center value is used instead
-    :param eqs: list of equations containing field accesses to direct neighbors
-    :param fields: fields for which the Neumann boundary should be applied
-    :param flag_field: integer field marking boundary cells
-    :param boundary_flag: if flag field has value 'boundary_flag' (no bit operations yet)
-                          the cell is assumed to be boundary
-    :param inverse_flag: if true, boundary cells are where flag field has not the value of boundary_flag
-    :return: list of equations with guarded field accesses
+
+    Args:
+        eqs: list of equations containing field accesses to direct neighbors
+        fields: fields for which the Neumann boundary should be applied
+        flag_field: integer field marking boundary cells
+        boundary_flag: if flag field has value 'boundary_flag' (no bit operations yet)
+                       the cell is assumed to be boundary
+        inverse_flag: if true, boundary cells are where flag field has not the value of boundary_flag
+
+    Returns:
+        list of equations with guarded field accesses
     """
     if not hasattr(fields, "__len__"):
         fields = [fields]