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         return Polyhedron._fromislbasicset(islbset, self.symbols)
 175
 176     def intersection(self, *others):
 177         if len(others) == 0:
 178             return self
 179         symbols = self._xsymbols((self,) + others)
 180         islset1 = self._toislset(self.polyhedra, symbols)
 181         for other in others:
 182             islset2 = other._toislset(other.polyhedra, symbols)
 183             islset1 = libisl.isl_set_intersect(islset1, islset2)
 184         return self._fromislset(islset1, symbols)
 185
 186     def __and__(self, other):
 187         return self.intersection(other)
 188
 189     def union(self, *others):
 190         if len(others) == 0:
 191             return self
 192         symbols = self._xsymbols((self,) + others)
 193         islset1 = self._toislset(self.polyhedra, symbols)
 194         for other in others:
 195             islset2 = other._toislset(other.polyhedra, symbols)
 196             islset1 = libisl.isl_set_union(islset1, islset2)
 197         return self._fromislset(islset1, symbols)
 198
 199     def __or__(self, other):
 200         return self.union(other)
 201
 202     def __add__(self, other):
 203         return self.union(other)
 204
 205     def difference(self, other):
 206         symbols = self._xsymbols([self, other])
 207         islset1 = self._toislset(self.polyhedra, symbols)
 208         islset2 = other._toislset(other.polyhedra, symbols)
 209         islset = libisl.isl_set_subtract(islset1, islset2)
 210         return self._fromislset(islset, symbols)
 211
 212     def __sub__(self, other):
 213         return self.difference(other)
 214
 215     def lexmin(self):
 216         islset = self._toislset(self.polyhedra, self.symbols)
 217         islset = libisl.isl_set_lexmin(islset)
 218         return self._fromislset(islset, self.symbols)
 219
 220     def lexmax(self):
 221         islset = self._toislset(self.polyhedra, self.symbols)
 222         islset = libisl.isl_set_lexmax(islset)
 223         return self._fromislset(islset, self.symbols)
 224
 225     def num_parameters(self):
 226         #could be useful with large, complicated polyhedrons
 227         islbset = self._toislbasicset(self.equalities, self.inequalities, self.symbols)
 228         num = libisl.isl_basic_set_dim(islbset, libisl.isl_dim_set)
 229         return num
 230
 231     def involves_dims(self, dims):
 232         #could be useful with large, complicated polyhedrons
 233         islset = self._toislset(self.polyhedra, self.symbols)
 234         dims = sorted(dims)
 235         symbols = sorted(list(self.symbols))
 236         n = 0
 237         if len(dims)>0:
 238             for dim in dims:
 239                 if dim in symbols:
 240                     first = symbols.index(dims[0])
 241                     n +=1
 242                 else:
 243                     first = 0
 244         else:
 245             return False
 246         value = bool(libisl.isl_set_involves_dims(islset, libisl.isl_dim_set, first, n))
 247         libisl.isl_set_free(islset)
 248         return value
 249
 250     @classmethod
 251     def _fromislset(cls, islset, symbols):
 252         from .polyhedra import Polyhedron
 253         islset = libisl.isl_set_remove_divs(islset)
 254         islbsets = isl_set_basic_sets(islset)
 255         libisl.isl_set_free(islset)
 256         polyhedra = []
 257         for islbset in islbsets:
 258             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 259             polyhedra.append(polyhedron)
 260         if len(polyhedra) == 0:
 261             from .polyhedra import Empty
 262             return Empty
 263         elif len(polyhedra) == 1:
 264             return polyhedra[0]
 265         else:
 266             self = object().__new__(Domain)
 267             self._polyhedra = tuple(polyhedra)
 268             self._symbols = cls._xsymbols(polyhedra)
 269             self._dimension = len(self._symbols)
 270             return self
 271
 272     def _toislset(cls, polyhedra, symbols):
 273         polyhedron = polyhedra[0]
 274         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 275             polyhedron.inequalities, symbols)
 276         islset1 = libisl.isl_set_from_basic_set(islbset)
 277         for polyhedron in polyhedra[1:]:
 278             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 279                 polyhedron.inequalities, symbols)
 280             islset2 = libisl.isl_set_from_basic_set(islbset)
 281             islset1 = libisl.isl_set_union(islset1, islset2)
 282         return islset1
 283
 284     @classmethod
 285     def _fromast(cls, node):
 286         from .polyhedra import Polyhedron
 287         if isinstance(node, ast.Module) and len(node.body) == 1:
 288             return cls._fromast(node.body[0])
 289         elif isinstance(node, ast.Expr):
 290             return cls._fromast(node.value)
 291         elif isinstance(node, ast.UnaryOp):
 292             domain = cls._fromast(node.operand)
 293             if isinstance(node.operand, ast.invert):
 294                 return Not(domain)
 295         elif isinstance(node, ast.BinOp):
 296             domain1 = cls._fromast(node.left)
 297             domain2 = cls._fromast(node.right)
 298             if isinstance(node.op, ast.BitAnd):
 299                 return And(domain1, domain2)
 300             elif isinstance(node.op, ast.BitOr):
 301                 return Or(domain1, domain2)
 302         elif isinstance(node, ast.Compare):
 303             equalities = []
 304             inequalities = []
 305             left = Expression._fromast(node.left)
 306             for i in range(len(node.ops)):
 307                 op = node.ops[i]
 308                 right = Expression._fromast(node.comparators[i])
 309                 if isinstance(op, ast.Lt):
 310                     inequalities.append(right - left - 1)
 311                 elif isinstance(op, ast.LtE):
 312                     inequalities.append(right - left)
 313                 elif isinstance(op, ast.Eq):
 314                     equalities.append(left - right)
 315                 elif isinstance(op, ast.GtE):
 316                     inequalities.append(left - right)
 317                 elif isinstance(op, ast.Gt):
 318                     inequalities.append(left - right - 1)
 319                 else:
 320                     break
 321                 left = right
 322             else:
 323                 return Polyhedron(equalities, inequalities)
 324         raise SyntaxError('invalid syntax')
 325
 326     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 327     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 328     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 329     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 330     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 331     _RE_NUM_VAR = Expression._RE_NUM_VAR
 332     _RE_OPERATORS = re.compile(r'(&|\||~)')
 333
 334     @classmethod
 335     def fromstring(cls, string):
 336         # remove curly brackets
 337         string = cls._RE_BRACES.sub(r'', string)
 338         # replace '=' by '=='
 339         string = cls._RE_EQ.sub(r'\1==\2', string)
 340         # replace 'and', 'or', 'not'
 341         string = cls._RE_AND.sub(r' & ', string)
 342         string = cls._RE_OR.sub(r' | ', string)
 343         string = cls._RE_NOT.sub(r' ~', string)
 344         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 345         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 346         # add parentheses to force precedence
 347         tokens = cls._RE_OPERATORS.split(string)
 348         for i, token in enumerate(tokens):
 349             if i % 2 == 0:
 350                 token = '({})'.format(token)
 351                 tokens[i] = token
 352         string = ''.join(tokens)
 353         tree = ast.parse(string, 'eval')
 354         return cls._fromast(tree)
 355
 356     def __repr__(self):
 357         assert len(self.polyhedra) >= 2
 358         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 359         return 'Or({})'.format(', '.join(strings))
 360
 361     @classmethod
 362     def fromsympy(cls, expr):
 363         import sympy
 364         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 365         funcmap = {
 366             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 367             sympy.Lt: Lt, sympy.Le: Le,
 368             sympy.Eq: Eq, sympy.Ne: Ne,
 369             sympy.Ge: Ge, sympy.Gt: Gt,
 370         }
 371         if expr.func in funcmap:
 372             args = [Domain.fromsympy(arg) for arg in expr.args]
 373             return funcmap[expr.func](*args)
 374         elif isinstance(expr, sympy.Expr):
 375             return Expression.fromsympy(expr)
 376         raise ValueError('non-domain expression: {!r}'.format(expr))
 377
 378     def tosympy(self):
 379         import sympy
 380         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 381         return sympy.Or(*polyhedra)
 382
 383
 384 def And(*domains):
 385     if len(domains) == 0:
 386         from .polyhedra import Universe
 387         return Universe
 388     else:
 389         return domains[0].intersection(*domains[1:])
 390
 391 def Or(*domains):
 392     if len(domains) == 0:
 393         from .polyhedra import Empty
 394         return Empty
 395     else:
 396         return domains[0].union(*domains[1:])
 397
 398 def Not(domain):
 399     return ~domain