Implements Loechner Reindexing

doc/misc.rst

@@ -456,6 +456,13 @@ Here's a Bibtex entry for your convenience::
        doi = "{10.1145/2627373.2627387}",
     }
 
+References
+==========
+
+.. [Seghir_2006] Seghir and Loechner, Proceedings of the 2006 International
+    Conference on Compilers, Architecture and Synthesis for Embedded systems,
+    `(DOI) <https://doi.org/10.1145/1176760.1176771>`__
+
 Getting help
 ============
 

doc/ref_transform.rst

@@ -52,6 +52,8 @@ Influencing data access
 
 .. automodule:: loopy.transform.privatize
 
+.. automodule:: loopy.transform.reindexing
+
 Padding Data
 ------------
 

loopy/__init__.py

@@ -105,6 +105,8 @@
 from loopy.transform.buffer import buffer_array
 from loopy.transform.fusion import fuse_kernels
 
+from loopy.transform.reindexing import reindex_using_seghir_loechner_scheme
+
 from loopy.transform.arithmetic import (
         fold_constants,
         collect_common_factors_on_increment)
@@ -233,6 +235,8 @@
 
         "fold_constants", "collect_common_factors_on_increment",
 
+        "reindex_using_seghir_loechner_scheme",
+
         "split_array_axis", "split_array_dim", "split_arg_axis",
         "find_padding_multiple", "add_padding",
 

loopy/transform/reindexing.py

@@ -0,0 +1,320 @@
+"""
+.. currentmodule:: loopy
+
+.. autofunction:: reindex_using_seghir_loechner_scheme
+"""
+
+__copyright__ = "Copyright (C) 2022 Kaushik Kulkarni"
+
+__license__ = """
+Permission is hereby granted, free of charge, to any person obtaining a copy
+of this software and associated documentation files (the "Software"), to deal
+in the Software without restriction, including without limitation the rights
+to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
+copies of the Software, and to permit persons to whom the Software is
+furnished to do so, subject to the following conditions:
+
+The above copyright notice and this permission notice shall be included in
+all copies or substantial portions of the Software.
+
+THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
+AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
+THE SOFTWARE.
+"""
+
+
+import islpy as isl
+from typing import Union, Sequence, Iterable, Tuple, List
+from loopy.kernel import LoopKernel
+from loopy.diagnostic import LoopyError
+from loopy.symbolic import CombineMapper
+from loopy.kernel.instruction import (MultiAssignmentBase,
+                                      CInstruction, BarrierInstruction)
+from loopy.symbolic import RuleAwareIdentityMapper
+
+
+ISLMapT = Union[isl.BasicMap, isl.Map]
+ISLSetT = Union[isl.BasicSet, isl.Set]
+
+
+def make_dim_names_primed(isl_map: ISLMapT, dts: Iterable[isl.dim_type]) -> ISLMapT:
+    """
+    Returns a copy of *isl_map* with dims of types *dts* having their names
+    suffixed with an apostrophe (``'``).
+
+    .. testsetup::
+
+        >>> import islpy as isl
+        >>> from loopy.transform.reindexing import make_dim_names_primed
+
+    .. doctest::
+
+        >>> amap = isl.Map("{[i]->[j=2i]}")
+        >>> make_dim_names_primed(amap, [isl.dim_type.in_, isl.dim_type.out])
+        Map("{ [i'] -> [j' = 2i'] }")
+    """
+    for dt in dts:
+        for idim in range(isl_map.dim(dt)):
+            old_name = isl_map.get_dim_name(dt, idim)
+            new_name = f"{old_name}'"
+            isl_map = isl_map.set_dim_name(dt, idim, new_name)
+
+    return isl_map
+
+
+def _get_seghir_loechner_reindexing_from_range(access_range: ISLSetT
+                                               ) -> Tuple[isl.PwQPolynomial,
+                                                          isl.PwQPolynomial]:
+    """
+    Returns ``(reindex_map, new_shape)``, where,
+
+    * ``reindex_map`` is a quasi-polynomial of the form ``[i1, .., in] -> {f(i1,
+      .., in)}`` representing that an array indexed via the subscripts
+      ``[i1, ..,in]`` should be re-indexed into a 1-dimensional array as
+      ``f(i1, .., in)``.
+    * ``new_shape`` is a quasi-polynomial corresponding to the shape of the
+      re-indexed 1-dimensional array.
+    """
+
+    # {{{ create amap: an ISL map which is an identity map from access_map's range
+
+    amap = isl.BasicMap.identity(
+        access_range
+        .space
+        .add_dims(isl.dim_type.in_, access_range.dim(isl.dim_type.out)))
+
+    # set amap's dim names
+    for idim in range(amap.dim(isl.dim_type.in_)):
+        amap = amap.set_dim_name(isl.dim_type.in_, idim,
+                                 f"_lpy_in_{idim}")
+        amap = amap.set_dim_name(isl.dim_type.out, idim,
+                                 f"_lpy_out_{idim}")
+
+    amap = amap.intersect_domain(access_range)
+
+    # }}}
+
+    n_in = amap.dim(isl.dim_type.out)
+    n_out = amap.dim(isl.dim_type.out)
+
+    amap_lexmin = amap.lexmin()
+    primed_amap_lexmin = make_dim_names_primed(amap_lexmin, [isl.dim_type.in_,
+                                                             isl.dim_type.out])
+
+    lex_lt_map = isl.Map.lex_lt_map(primed_amap_lexmin, amap_lexmin)
+
+    # make the lexmin map parametric in terms of it's previous access expressions.
+    lex_lt_set = (lex_lt_map
+                  .move_dims(isl.dim_type.param, 0, isl.dim_type.out, 0, n_in)
+                  .domain())
+
+    # {{{ initialize amap_to_count
+
+    amap_to_count = make_dim_names_primed(amap, [isl.dim_type.in_])
+    amap_to_count = amap_to_count.insert_dims(isl.dim_type.param, 0, n_in)
+
+    for idim in range(n_in):
+        amap_to_count = amap_to_count.set_dim_name(
+            isl.dim_type.param, idim,
+            amap.get_dim_name(isl.dim_type.in_, idim))
+
+    amap_to_count = amap_to_count.intersect_domain(lex_lt_set)
+
+    # }}}
+
+    result = amap_to_count.range().card()
+
+    # {{{ simplify 'result' by gisting with 'access_range'
+
+    aligned_access_range = access_range.move_dims(isl.dim_type.param, 0,
+                                                  isl.dim_type.set, 0, n_out)
+
+    for idim in range(result.dim(isl.dim_type.param)):
+        aligned_access_range = (
+            aligned_access_range
+            .set_dim_name(isl.dim_type.param, idim,
+                          result.space.get_dim_name(isl.dim_type.param,
+                                                    idim)))
+
+    result = result.gist_params(aligned_access_range.params())
+
+    # }}}
+
+    return result, access_range.card()
+
+
+class _IndexCollector(CombineMapper):
+    """
+    A mapper that collects all instances of
+    :class:`pymbolic.primitives.Subscript` accessing :attr:`var_name`.
+    """
+    def __init__(self, var_name):
+        super().__init__()
+        self.var_name = var_name
+
+    def combine(self, values):
+        from functools import reduce
+        return reduce(frozenset.union, values, frozenset())
+
+    def map_subscript(self, expr):
+        if expr.aggregate.name == self.var_name:
+            return frozenset([expr]) | super().map_subscript(expr)
+        else:
+            return super().map_subscript(expr)
+
+    def map_constant(self, expr):
+        return frozenset()
+
+    map_variable = map_constant
+    map_function_symbol = map_constant
+    map_tagged_variable = map_constant
+    map_type_cast = map_constant
+    map_nan = map_constant
+
+
+def _union_access_ranges(access_ranges: Sequence[ISLSetT]):
+    result = access_ranges[0]
+
+    for access_range in access_ranges[1:]:
+        assert result.dim(isl.dim_type.out) == access_range.dim(isl.dim_type.out)
+        result, accesss_range = isl.align_two(result, access_range)
+        result = result | access_range
+
+    return result
+
+
+class ReindexingApplier(RuleAwareIdentityMapper):
+    def __init__(self, rule_mapping_context,
+                 var_to_reindex,
+                 reindexed_var_name,
+                 new_index_expr,
+                 index_names):
+
+        super().__init__(rule_mapping_context)
+
+        self.var_to_reindex = var_to_reindex
+        self.reindexed_var_name = reindexed_var_name
+        self.new_index_expr = new_index_expr
+        self.index_names = index_names
+
+    def map_subscript(self, expr, expn_state):
+        if expr.aggregate.name != self.var_to_reindex:
+            return super().map_subscript(expr, expn_state)
+
+        from loopy.symbolic import SubstitutionMapper
+        from pymbolic.mapper.substitutor import make_subst_func
+        from pymbolic.primitives import Subscript, Variable
+
+        rec_indices = tuple(self.rec(idx, expn_state) for idx in expr.index_tuple)
+
+        assert len(self.index_names) == len(rec_indices)
+        subst_func = make_subst_func({idx_name: rec_idx
+                                      for idx_name, rec_idx in zip(self.index_names,
+                                                                   rec_indices)})
+
+        return SubstitutionMapper(subst_func)(
+            Subscript(Variable(self.reindexed_var_name),
+                      self.new_index_expr)
+        )
+
+
+def reindex_using_seghir_loechner_scheme(kernel: LoopKernel, var_name: str):
+    """
+    Returns a kernel with expressions of the form ``var_name[i1, .., in]``
+    replaced with ``var_name_reindexed[f(i1, .., in)]`` where ``f`` is a
+    quasi-polynomial as outlined in [Seghir_2006]_.
+    """
+    from loopy.transform.subst import expand_subst
+    from loopy.symbolic import (get_access_map, pw_qpolynomial_to_expr,
+                                qpolynomial_to_expr, SubstitutionRuleMappingContext)
+
+    if var_name not in kernel.temporary_variables:
+        raise LoopyError(f"'{var_name}' not in temporary variable in kernel"
+                         f" '{kernel.name}'.")
+
+    # {{{ compute the access_range of *var_name* in *kernel*
+
+    subst_kernel = expand_subst(kernel)
+    vng = kernel.get_var_name_generator()
+    new_var_name = vng(var_name+"_reindexed")
+
+    access_ranges: List[ISLSetT] = []
+
+    for insn in subst_kernel.instructions:
+        domain = subst_kernel.get_inames_domain(insn.within_inames)
+        if isinstance(insn, MultiAssignmentBase):
+            access_exprs = _IndexCollector(var_name)((insn.assignees,
+                                                      insn.expression,
+                                                      tuple(insn.predicates)))
+        elif isinstance(insn, (CInstruction, BarrierInstruction)):
+            access_exprs = _IndexCollector(var_name)(insn.predicates)
+        else:
+            raise NotImplementedError(type(insn))
+
+        for access_expr in access_exprs:
+            access_ranges.append(get_access_map(domain,
+                                                access_expr.index_tuple,
+                                                assumptions=kernel.assumptions)
+                                 .range())
+
+    del subst_kernel
+
+    # }}}
+
+    subst, new_shape = _get_seghir_loechner_reindexing_from_range(
+        _union_access_ranges(access_ranges))
+
+    # {{{  update kernel.temporary_variables
+
+    new_shape = new_shape.drop_unused_params()
+
+    if new_shape.dim(isl.dim_type.param) != 0:
+        raise NotImplementedError("Temporaries with parametric shapes not yet"
+                                  " supported.")
+
+    (_, shape_qpoly), = new_shape.get_pieces()
+
+    new_temps = kernel.temporary_variables.copy()
+    new_temps[new_var_name] = new_temps.pop(var_name).copy(
+        name=new_var_name,
+        shape=qpolynomial_to_expr(shape_qpoly),
+        strides=None,
+        dim_tags=None,
+        dim_names=None,
+    )
+
+    # }}}
+
+    # {{{ perform the substitution i.e. reindex the accesses
+
+    subst_expr = pw_qpolynomial_to_expr(subst)
+    subst_dim_names = tuple(
+        subst.space.get_dim_name(isl.dim_type.param, idim)
+        for idim in range(len(kernel.temporary_variables[var_name].shape)))
+    assert not (set(subst_dim_names) & kernel.all_variable_names())
+
+    kernel = kernel.copy(temporary_variables=new_temps)
+    rule_mapping_context = SubstitutionRuleMappingContext(kernel.substitutions,
+                                                          vng)
+    reindexing_mapper = ReindexingApplier(rule_mapping_context,
+                                          var_name, new_var_name,
+                                          subst_expr, subst_dim_names)
+
+    def _does_access_var_name(kernel, insn, *args):
+        return var_name in insn.dependency_names()
+
+    kernel = reindexing_mapper.map_kernel(kernel,
+                                          within=_does_access_var_name,
+                                          map_args=False,
+                                          map_tvs=False)
+    kernel = rule_mapping_context.finish_kernel(kernel)
+
+    # }}}
+
+    return kernel
+
+# vim: fdm=marker