pypol/domains.py

   1 import ast
   2 import functools
   3 import re
   4
   5 from . import islhelper
   6
   7 from .islhelper import mainctx, libisl, isl_set_basic_sets
   8 from .linexprs import Expression, Symbol
   9
  10
  11 __all__ = [
  12     'Domain',
  13     'And', 'Or', 'Not',
  14 ]
  15
  16
  17 @functools.total_ordering
  18 class Domain:
  19
  20     __slots__ = (
  21         '_polyhedra',
  22         '_symbols',
  23         '_dimension',
  24     )
  25
  26     def __new__(cls, *polyhedra):
  27         from .polyhedra import Polyhedron
  28         if len(polyhedra) == 1:
  29             polyhedron = polyhedra[0]
  30             if isinstance(polyhedron, str):
  31                 return cls.fromstring(polyhedron)
  32             elif isinstance(polyhedron, Polyhedron):
  33                 return polyhedron
  34             else:
  35                 raise TypeError('argument must be a string '
  36                     'or a Polyhedron instance')
  37         else:
  38             for polyhedron in polyhedra:
  39                 if not isinstance(polyhedron, Polyhedron):
  40                     raise TypeError('arguments must be Polyhedron instances')
  41             symbols = cls._xsymbols(polyhedra)
  42             islset = cls._toislset(polyhedra, symbols)
  43             return cls._fromislset(islset, symbols)
  44
  45     @classmethod
  46     def _xsymbols(cls, iterator):
  47         """
  48         Return the ordered tuple of symbols present in iterator.
  49         """
  50         symbols = set()
  51         for item in iterator:
  52             symbols.update(item.symbols)
  53         return tuple(sorted(symbols, key=Symbol.sortkey))
  54
  55     @property
  56     def polyhedra(self):
  57         return self._polyhedra
  58
  59     @property
  60     def symbols(self):
  61         return self._symbols
  62
  63     @property
  64     def dimension(self):
  65         return self._dimension
  66
  67     def disjoint(self):
  68         islset = self._toislset(self.polyhedra, self.symbols)
  69         islset = libisl.isl_set_make_disjoint(mainctx, islset)
  70         return self._fromislset(islset, self.symbols)
  71
  72     def isempty(self):
  73         islset = self._toislset(self.polyhedra, self.symbols)
  74         empty = bool(libisl.isl_set_is_empty(islset))
  75         libisl.isl_set_free(islset)
  76         return empty
  77
  78     def __bool__(self):
  79         return not self.isempty()
  80
  81     def isuniverse(self):
  82         islset = self._toislset(self.polyhedra, self.symbols)
  83         universe = bool(libisl.isl_set_plain_is_universe(islset))
  84         libisl.isl_set_free(islset)
  85         return universe
  86
  87     def isbounded(self):
  88         islset = self._toislset(self.polyhedra, self.symbols)
  89         bounded = bool(libisl.isl_set_is_bounded(islset))
  90         libisl.isl_set_free(islset)
  91         return bounded
  92
  93     def __eq__(self, other):
  94         symbols = self._xsymbols([self, other])
  95         islset1 = self._toislset(self.polyhedra, symbols)
  96         islset2 = other._toislset(other.polyhedra, symbols)
  97         equal = bool(libisl.isl_set_is_equal(islset1, islset2))
  98         libisl.isl_set_free(islset1)
  99         libisl.isl_set_free(islset2)
 100         return equal
 101
 102     def isdisjoint(self, other):
 103         symbols = self._xsymbols([self, other])
 104         islset1 = self._toislset(self.polyhedra, symbols)
 105         islset2 = self._toislset(other.polyhedra, symbols)
 106         equal = bool(libisl.isl_set_is_disjoint(islset1, islset2))
 107         libisl.isl_set_free(islset1)
 108         libisl.isl_set_free(islset2)
 109         return equal
 110
 111     def issubset(self, other):
 112         symbols = self._xsymbols([self, other])
 113         islset1 = self._toislset(self.polyhedra, symbols)
 114         islset2 = self._toislset(other.polyhedra, symbols)
 115         equal = bool(libisl.isl_set_is_subset(islset1, islset2))
 116         libisl.isl_set_free(islset1)
 117         libisl.isl_set_free(islset2)
 118         return equal
 119
 120     def __le__(self, other):
 121         return self.issubset(other)
 122
 123     def __lt__(self, other):
 124         symbols = self._xsymbols([self, other])
 125         islset1 = self._toislset(self.polyhedra, symbols)
 126         islset2 = self._toislset(other.polyhedra, symbols)
 127         equal = bool(libisl.isl_set_is_strict_subset(islset1, islset2))
 128         libisl.isl_set_free(islset1)
 129         libisl.isl_set_free(islset2)
 130         return equal
 131
 132     def complement(self):
 133         islset = self._toislset(self.polyhedra, self.symbols)
 134         islset = libisl.isl_set_complement(islset)
 135         return self._fromislset(islset, self.symbols)
 136
 137     def __invert__(self):
 138         return self.complement()
 139
 140     def simplify(self):
 141         #does not change anything in any of the examples
 142         #isl seems to do this naturally
 143         islset = self._toislset(self.polyhedra, self.symbols)
 144         islset = libisl.isl_set_remove_redundancies(islset)
 145         return self._fromislset(islset, self.symbols)
 146
 147     def polyhedral_hull(self):
 148         # several types of hull are available
 149         # polyhedral seems to be the more appropriate, to be checked
 150         from .polyhedra import Polyhedron
 151         islset = self._toislset(self.polyhedra, self.symbols)
 152         islbset = libisl.isl_set_polyhedral_hull(islset)
 153         return Polyhedron._fromislbasicset(islbset, self.symbols)
 154
 155     def project_out(self, dims):
 156         # use to remove certain variables
 157         islset = self._toislset(self.polyhedra, self.symbols)
 158         n = 0
 159         for index, symbol in reversed(list(enumerate(self.symbols))):
 160             if symbol in dims:
 161                 n += 1
 162             elif n > 0:
 163                 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index + 1, n)
 164                 n = 0
 165         if n > 0:
 166             islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, 0, n)
 167         dims = [symbol for symbol in self.symbols if symbol not in dims]
 168         return Domain._fromislset(islset, dims)
 169
 170     def sample(self):
 171         from .polyhedra import Polyhedron
 172         islset = self._toislset(self.polyhedra, self.symbols)
 173         islbset = libisl.isl_set_sample(islset)
 174         # next instruction should NOT be required
 175         islbset = libisl.isl_basic_set_finalize(islbset)
 176         return Polyhedron._fromislbasicset(islbset, self.symbols)
 177
 178     def intersection(self, *others):
 179         if len(others) == 0:
 180             return self
 181         symbols = self._xsymbols((self,) + others)
 182         islset1 = self._toislset(self.polyhedra, symbols)
 183         for other in others:
 184             islset2 = other._toislset(other.polyhedra, symbols)
 185             islset1 = libisl.isl_set_intersect(islset1, islset2)
 186         return self._fromislset(islset1, symbols)
 187
 188     def __and__(self, other):
 189         return self.intersection(other)
 190
 191     def union(self, *others):
 192         if len(others) == 0:
 193             return self
 194         symbols = self._xsymbols((self,) + others)
 195         islset1 = self._toislset(self.polyhedra, symbols)
 196         for other in others:
 197             islset2 = other._toislset(other.polyhedra, symbols)
 198             islset1 = libisl.isl_set_union(islset1, islset2)
 199         return self._fromislset(islset1, symbols)
 200
 201     def __or__(self, other):
 202         return self.union(other)
 203
 204     def __add__(self, other):
 205         return self.union(other)
 206
 207     def difference(self, other):
 208         symbols = self._xsymbols([self, other])
 209         islset1 = self._toislset(self.polyhedra, symbols)
 210         islset2 = other._toislset(other.polyhedra, symbols)
 211         islset = libisl.isl_set_subtract(islset1, islset2)
 212         return self._fromislset(islset, symbols)
 213
 214     def __sub__(self, other):
 215         return self.difference(other)
 216
 217     def lexmin(self):
 218         islset = self._toislset(self.polyhedra, self.symbols)
 219         islset = libisl.isl_set_lexmin(islset)
 220         return self._fromislset(islset, self.symbols)
 221
 222     def lexmax(self):
 223         islset = self._toislset(self.polyhedra, self.symbols)
 224         islset = libisl.isl_set_lexmax(islset)
 225         return self._fromislset(islset, self.symbols)
 226
 227     def num_parameters(self):
 228         #could be useful with large, complicated polyhedrons
 229         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 230         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 231         return num
 232
 233     def involves_dims(self, dims):
 234         #could be useful with large, complicated polyhedrons
 235         islset = self._toislset(self.polyhedra, self.symbols)
 236         dims = sorted(dims)
 237         symbols = sorted(list(self.symbols))
 238         n = 0
 239         if len(dims)>0:
 240             for dim in dims:
 241                 if dim in symbols:
 242                     first = symbols.index(dims[0])
 243                     n +=1
 244                 else:
 245                     first = 0
 246         else:
 247             return False
 248         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 249         libisl.isl_set_free(islset)
 250         return value
 251
 252     def vertices(self):
 253         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 254         vertices = libisl.isl_basic_set_compute_vertices(islbset);
 255         vertices = islhelper.isl_vertices_vertices(vertices)
 256         for vertex in vertices:
 257             expr = libisl.isl_vertex_get_expr(vertex);
 258             if islhelper.isl_version < '0.13':
 259                 string = islhelper.isl_set_to_str(expr)
 260             else:
 261                 string = islhelper.isl_multi_aff_to_str(expr)
 262             print(string)
 263
 264     def points(self):
 265         if not self.isbounded():
 266             raise ValueError('domain must be unbounded')
 267         from .polyhedra import Universe, Eq
 268         islset = self._toislset(self.polyhedra, self.symbols)
 269         islpoints = islhelper.isl_set_points(islset)
 270         points = []
 271         for islpoint in islpoints:
 272             point = {}
 273             for index, symbol in enumerate(self.symbols):
 274                 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 275                     libisl.isl_dim_set, index)
 276                 coordinate = islhelper.isl_val_to_int(coordinate)
 277                 point[symbol] = coordinate
 278             points.append(point)
 279         return points
 280
 281     @classmethod
 282     def _fromislset(cls, islset, symbols):
 283         from .polyhedra import Polyhedron
 284         islset = libisl.isl_set_remove_divs(islset)
 285         islbsets = isl_set_basic_sets(islset)
 286         libisl.isl_set_free(islset)
 287         polyhedra = []
 288         for islbset in islbsets:
 289             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 290             polyhedra.append(polyhedron)
 291         if len(polyhedra) == 0:
 292             from .polyhedra import Empty
 293             return Empty
 294         elif len(polyhedra) == 1:
 295             return polyhedra[0]
 296         else:
 297             self = object().__new__(Domain)
 298             self._polyhedra = tuple(polyhedra)
 299             self._symbols = cls._xsymbols(polyhedra)
 300             self._dimension = len(self._symbols)
 301             return self
 302
 303     def _toislset(cls, polyhedra, symbols):
 304         polyhedron = polyhedra[0]
 305         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 306             polyhedron.inequalities, symbols)
 307         islset1 = libisl.isl_set_from_basic_set(islbset)
 308         for polyhedron in polyhedra[1:]:
 309             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 310                 polyhedron.inequalities, symbols)
 311             islset2 = libisl.isl_set_from_basic_set(islbset)
 312             islset1 = libisl.isl_set_union(islset1, islset2)
 313         return islset1
 314
 315     @classmethod
 316     def _fromast(cls, node):
 317         from .polyhedra import Polyhedron
 318         if isinstance(node, ast.Module) and len(node.body) == 1:
 319             return cls._fromast(node.body[0])
 320         elif isinstance(node, ast.Expr):
 321             return cls._fromast(node.value)
 322         elif isinstance(node, ast.UnaryOp):
 323             domain = cls._fromast(node.operand)
 324             if isinstance(node.operand, ast.invert):
 325                 return Not(domain)
 326         elif isinstance(node, ast.BinOp):
 327             domain1 = cls._fromast(node.left)
 328             domain2 = cls._fromast(node.right)
 329             if isinstance(node.op, ast.BitAnd):
 330                 return And(domain1, domain2)
 331             elif isinstance(node.op, ast.BitOr):
 332                 return Or(domain1, domain2)
 333         elif isinstance(node, ast.Compare):
 334             equalities = []
 335             inequalities = []
 336             left = Expression._fromast(node.left)
 337             for i in range(len(node.ops)):
 338                 op = node.ops[i]
 339                 right = Expression._fromast(node.comparators[i])
 340                 if isinstance(op, ast.Lt):
 341                     inequalities.append(right - left - 1)
 342                 elif isinstance(op, ast.LtE):
 343                     inequalities.append(right - left)
 344                 elif isinstance(op, ast.Eq):
 345                     equalities.append(left - right)
 346                 elif isinstance(op, ast.GtE):
 347                     inequalities.append(left - right)
 348                 elif isinstance(op, ast.Gt):
 349                     inequalities.append(left - right - 1)
 350                 else:
 351                     break
 352                 left = right
 353             else:
 354                 return Polyhedron(equalities, inequalities)
 355         raise SyntaxError('invalid syntax')
 356
 357     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 358     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 359     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 360     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 361     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 362     _RE_NUM_VAR = Expression._RE_NUM_VAR
 363     _RE_OPERATORS = re.compile(r'(&|\||~)')
 364
 365     @classmethod
 366     def fromstring(cls, string):
 367         # remove curly brackets
 368         string = cls._RE_BRACES.sub(r'', string)
 369         # replace '=' by '=='
 370         string = cls._RE_EQ.sub(r'\1==\2', string)
 371         # replace 'and', 'or', 'not'
 372         string = cls._RE_AND.sub(r' & ', string)
 373         string = cls._RE_OR.sub(r' | ', string)
 374         string = cls._RE_NOT.sub(r' ~', string)
 375         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 376         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 377         # add parentheses to force precedence
 378         tokens = cls._RE_OPERATORS.split(string)
 379         for i, token in enumerate(tokens):
 380             if i % 2 == 0:
 381                 token = '({})'.format(token)
 382                 tokens[i] = token
 383         string = ''.join(tokens)
 384         tree = ast.parse(string, 'eval')
 385         return cls._fromast(tree)
 386
 387     def __repr__(self):
 388         assert len(self.polyhedra) >= 2
 389         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 390         return 'Or({})'.format(', '.join(strings))
 391
 392     @classmethod
 393     def fromsympy(cls, expr):
 394         import sympy
 395         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 396         funcmap = {
 397             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 398             sympy.Lt: Lt, sympy.Le: Le,
 399             sympy.Eq: Eq, sympy.Ne: Ne,
 400             sympy.Ge: Ge, sympy.Gt: Gt,
 401         }
 402         if expr.func in funcmap:
 403             args = [Domain.fromsympy(arg) for arg in expr.args]
 404             return funcmap[expr.func](*args)
 405         elif isinstance(expr, sympy.Expr):
 406             return Expression.fromsympy(expr)
 407         raise ValueError('non-domain expression: {!r}'.format(expr))
 408
 409     def tosympy(self):
 410         import sympy
 411         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 412         return sympy.Or(*polyhedra)
 413
 414
 415 def And(*domains):
 416     if len(domains) == 0:
 417         from .polyhedra import Universe
 418         return Universe
 419     else:
 420         return domains[0].intersection(*domains[1:])
 421
 422 def Or(*domains):
 423     if len(domains) == 0:
 424         from .polyhedra import Empty
 425         return Empty
 426     else:
 427         return domains[0].union(*domains[1:])
 428
 429 def Not(domain):
 430     return ~domain