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 aspolyhedron(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(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         islpoint = libisl.isl_set_sample_point(islset)
 174         point = {}
 175         for index, symbol in enumerate(self.symbols):
 176             coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 177                 libisl.isl_dim_set, index)
 178             coordinate = islhelper.isl_val_to_int(coordinate)
 179             point[symbol] = coordinate
 180         if bool(libisl.isl_point_is_void(islpoint)):
 181             point = None
 182         libisl.isl_point_free(islpoint)
 183         return point
 184
 185     def intersection(self, *others):
 186         if len(others) == 0:
 187             return self
 188         symbols = self._xsymbols((self,) + others)
 189         islset1 = self._toislset(self.polyhedra, symbols)
 190         for other in others:
 191             islset2 = other._toislset(other.polyhedra, symbols)
 192             islset1 = libisl.isl_set_intersect(islset1, islset2)
 193         return self._fromislset(islset1, symbols)
 194
 195     def __and__(self, other):
 196         return self.intersection(other)
 197
 198     def union(self, *others):
 199         if len(others) == 0:
 200             return self
 201         symbols = self._xsymbols((self,) + others)
 202         islset1 = self._toislset(self.polyhedra, symbols)
 203         for other in others:
 204             islset2 = other._toislset(other.polyhedra, symbols)
 205             islset1 = libisl.isl_set_union(islset1, islset2)
 206         return self._fromislset(islset1, symbols)
 207
 208     def __or__(self, other):
 209         return self.union(other)
 210
 211     def __add__(self, other):
 212         return self.union(other)
 213
 214     def difference(self, other):
 215         symbols = self._xsymbols([self, other])
 216         islset1 = self._toislset(self.polyhedra, symbols)
 217         islset2 = other._toislset(other.polyhedra, symbols)
 218         islset = libisl.isl_set_subtract(islset1, islset2)
 219         return self._fromislset(islset, symbols)
 220
 221     def __sub__(self, other):
 222         return self.difference(other)
 223
 224     def lexmin(self):
 225         islset = self._toislset(self.polyhedra, self.symbols)
 226         islset = libisl.isl_set_lexmin(islset)
 227         return self._fromislset(islset, self.symbols)
 228
 229     def lexmax(self):
 230         islset = self._toislset(self.polyhedra, self.symbols)
 231         islset = libisl.isl_set_lexmax(islset)
 232         return self._fromislset(islset, self.symbols)
 233
 234     def num_parameters(self):
 235         #could be useful with large, complicated polyhedrons
 236         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 237         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 238         return num
 239
 240     def involves_dims(self, dims):
 241         #could be useful with large, complicated polyhedrons
 242         islset = self._toislset(self.polyhedra, self.symbols)
 243         dims = sorted(dims)
 244         symbols = sorted(list(self.symbols))
 245         n = 0
 246         if len(dims)>0:
 247             for dim in dims:
 248                 if dim in symbols:
 249                     first = symbols.index(dims[0])
 250                     n +=1
 251                 else:
 252                     first = 0
 253         else:
 254             return False
 255         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 256         libisl.isl_set_free(islset)
 257         return value
 258
 259     def vertices(self):
 260         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 261         vertices = libisl.isl_basic_set_compute_vertices(islbset);
 262         vertices = islhelper.isl_vertices_vertices(vertices)
 263         for vertex in vertices:
 264             expr = libisl.isl_vertex_get_expr(vertex);
 265             if islhelper.isl_version < '0.13':
 266                 string = islhelper.isl_set_to_str(expr)
 267             else:
 268                 string = islhelper.isl_multi_aff_to_str(expr)
 269             print(string)
 270
 271     def points(self):
 272         if not self.isbounded():
 273             raise ValueError('domain must be unbounded')
 274         from .polyhedra import Universe, Eq
 275         islset = self._toislset(self.polyhedra, self.symbols)
 276         islpoints = islhelper.isl_set_points(islset)
 277         points = []
 278         for islpoint in islpoints:
 279             point = {}
 280             for index, symbol in enumerate(self.symbols):
 281                 coordinate = libisl.isl_point_get_coordinate_val(islpoint,
 282                     libisl.isl_dim_set, index)
 283                 coordinate = islhelper.isl_val_to_int(coordinate)
 284                 point[symbol] = coordinate
 285             points.append(point)
 286         return points
 287
 288     @classmethod
 289     def _fromislset(cls, islset, symbols):
 290         from .polyhedra import Polyhedron
 291         islset = libisl.isl_set_remove_divs(islset)
 292         islbsets = isl_set_basic_sets(islset)
 293         libisl.isl_set_free(islset)
 294         polyhedra = []
 295         for islbset in islbsets:
 296             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 297             polyhedra.append(polyhedron)
 298         if len(polyhedra) == 0:
 299             from .polyhedra import Empty
 300             return Empty
 301         elif len(polyhedra) == 1:
 302             return polyhedra[0]
 303         else:
 304             self = object().__new__(Domain)
 305             self._polyhedra = tuple(polyhedra)
 306             self._symbols = cls._xsymbols(polyhedra)
 307             self._dimension = len(self._symbols)
 308             return self
 309
 310     def _toislset(cls, polyhedra, symbols):
 311         polyhedron = polyhedra[0]
 312         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 313             polyhedron.inequalities, symbols)
 314         islset1 = libisl.isl_set_from_basic_set(islbset)
 315         for polyhedron in polyhedra[1:]:
 316             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 317                 polyhedron.inequalities, symbols)
 318             islset2 = libisl.isl_set_from_basic_set(islbset)
 319             islset1 = libisl.isl_set_union(islset1, islset2)
 320         return islset1
 321
 322     @classmethod
 323     def _fromast(cls, node):
 324         from .polyhedra import Polyhedron
 325         if isinstance(node, ast.Module) and len(node.body) == 1:
 326             return cls._fromast(node.body[0])
 327         elif isinstance(node, ast.Expr):
 328             return cls._fromast(node.value)
 329         elif isinstance(node, ast.UnaryOp):
 330             domain = cls._fromast(node.operand)
 331             if isinstance(node.operand, ast.invert):
 332                 return Not(domain)
 333         elif isinstance(node, ast.BinOp):
 334             domain1 = cls._fromast(node.left)
 335             domain2 = cls._fromast(node.right)
 336             if isinstance(node.op, ast.BitAnd):
 337                 return And(domain1, domain2)
 338             elif isinstance(node.op, ast.BitOr):
 339                 return Or(domain1, domain2)
 340         elif isinstance(node, ast.Compare):
 341             equalities = []
 342             inequalities = []
 343             left = Expression._fromast(node.left)
 344             for i in range(len(node.ops)):
 345                 op = node.ops[i]
 346                 right = Expression._fromast(node.comparators[i])
 347                 if isinstance(op, ast.Lt):
 348                     inequalities.append(right - left - 1)
 349                 elif isinstance(op, ast.LtE):
 350                     inequalities.append(right - left)
 351                 elif isinstance(op, ast.Eq):
 352                     equalities.append(left - right)
 353                 elif isinstance(op, ast.GtE):
 354                     inequalities.append(left - right)
 355                 elif isinstance(op, ast.Gt):
 356                     inequalities.append(left - right - 1)
 357                 else:
 358                     break
 359                 left = right
 360             else:
 361                 return Polyhedron(equalities, inequalities)
 362         raise SyntaxError('invalid syntax')
 363
 364     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 365     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 366     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 367     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 368     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 369     _RE_NUM_VAR = Expression._RE_NUM_VAR
 370     _RE_OPERATORS = re.compile(r'(&|\||~)')
 371
 372     @classmethod
 373     def fromstring(cls, string):
 374         # remove curly brackets
 375         string = cls._RE_BRACES.sub(r'', string)
 376         # replace '=' by '=='
 377         string = cls._RE_EQ.sub(r'\1==\2', string)
 378         # replace 'and', 'or', 'not'
 379         string = cls._RE_AND.sub(r' & ', string)
 380         string = cls._RE_OR.sub(r' | ', string)
 381         string = cls._RE_NOT.sub(r' ~', string)
 382         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 383         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 384         # add parentheses to force precedence
 385         tokens = cls._RE_OPERATORS.split(string)
 386         for i, token in enumerate(tokens):
 387             if i % 2 == 0:
 388                 token = '({})'.format(token)
 389                 tokens[i] = token
 390         string = ''.join(tokens)
 391         tree = ast.parse(string, 'eval')
 392         return cls._fromast(tree)
 393
 394     def __repr__(self):
 395         assert len(self.polyhedra) >= 2
 396         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 397         return 'Or({})'.format(', '.join(strings))
 398
 399     @classmethod
 400     def fromsympy(cls, expr):
 401         import sympy
 402         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 403         funcmap = {
 404             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 405             sympy.Lt: Lt, sympy.Le: Le,
 406             sympy.Eq: Eq, sympy.Ne: Ne,
 407             sympy.Ge: Ge, sympy.Gt: Gt,
 408         }
 409         if expr.func in funcmap:
 410             args = [Domain.fromsympy(arg) for arg in expr.args]
 411             return funcmap[expr.func](*args)
 412         elif isinstance(expr, sympy.Expr):
 413             return Expression.fromsympy(expr)
 414         raise ValueError('non-domain expression: {!r}'.format(expr))
 415
 416     def tosympy(self):
 417         import sympy
 418         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 419         return sympy.Or(*polyhedra)
 420
 421
 422 def And(*domains):
 423     if len(domains) == 0:
 424         from .polyhedra import Universe
 425         return Universe
 426     else:
 427         return domains[0].intersection(*domains[1:])
 428
 429 def Or(*domains):
 430     if len(domains) == 0:
 431         from .polyhedra import Empty
 432         return Empty
 433     else:
 434         return domains[0].union(*domains[1:])
 435
 436 def Not(domain):
 437     return ~domain