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, symbols):
 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 symbols:
 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         symbols = [symbol for symbol in self.symbols if symbol not in symbols]
 168         return Domain._fromislset(islset, symbols)
 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     @classmethod
 226     def _fromislset(cls, islset, symbols):
 227         from .polyhedra import Polyhedron
 228         islset = libisl.isl_set_remove_divs(islset)
 229         islbsets = isl_set_basic_sets(islset)
 230         libisl.isl_set_free(islset)
 231         polyhedra = []
 232         for islbset in islbsets:
 233             polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
 234             polyhedra.append(polyhedron)
 235         if len(polyhedra) == 0:
 236             from .polyhedra import Empty
 237             return Empty
 238         elif len(polyhedra) == 1:
 239             return polyhedra[0]
 240         else:
 241             self = object().__new__(Domain)
 242             self._polyhedra = tuple(polyhedra)
 243             self._symbols = cls._xsymbols(polyhedra)
 244             self._dimension = len(self._symbols)
 245             return self
 246
 247     def _toislset(cls, polyhedra, symbols):
 248         polyhedron = polyhedra[0]
 249         islbset = polyhedron._toislbasicset(polyhedron.equalities,
 250             polyhedron.inequalities, symbols)
 251         islset1 = libisl.isl_set_from_basic_set(islbset)
 252         for polyhedron in polyhedra[1:]:
 253             islbset = polyhedron._toislbasicset(polyhedron.equalities,
 254                 polyhedron.inequalities, symbols)
 255             islset2 = libisl.isl_set_from_basic_set(islbset)
 256             islset1 = libisl.isl_set_union(islset1, islset2)
 257         return islset1
 258
 259     @classmethod
 260     def _fromast(cls, node):
 261         from .polyhedra import Polyhedron
 262         if isinstance(node, ast.Module) and len(node.body) == 1:
 263             return cls._fromast(node.body[0])
 264         elif isinstance(node, ast.Expr):
 265             return cls._fromast(node.value)
 266         elif isinstance(node, ast.UnaryOp):
 267             domain = cls._fromast(node.operand)
 268             if isinstance(node.operand, ast.invert):
 269                 return Not(domain)
 270         elif isinstance(node, ast.BinOp):
 271             domain1 = cls._fromast(node.left)
 272             domain2 = cls._fromast(node.right)
 273             if isinstance(node.op, ast.BitAnd):
 274                 return And(domain1, domain2)
 275             elif isinstance(node.op, ast.BitOr):
 276                 return Or(domain1, domain2)
 277         elif isinstance(node, ast.Compare):
 278             equalities = []
 279             inequalities = []
 280             left = Expression._fromast(node.left)
 281             for i in range(len(node.ops)):
 282                 op = node.ops[i]
 283                 right = Expression._fromast(node.comparators[i])
 284                 if isinstance(op, ast.Lt):
 285                     inequalities.append(right - left - 1)
 286                 elif isinstance(op, ast.LtE):
 287                     inequalities.append(right - left)
 288                 elif isinstance(op, ast.Eq):
 289                     equalities.append(left - right)
 290                 elif isinstance(op, ast.GtE):
 291                     inequalities.append(left - right)
 292                 elif isinstance(op, ast.Gt):
 293                     inequalities.append(left - right - 1)
 294                 else:
 295                     break
 296                 left = right
 297             else:
 298                 return Polyhedron(equalities, inequalities)
 299         raise SyntaxError('invalid syntax')
 300
 301     _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
 302     _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
 303     _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
 304     _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
 305     _RE_NOT = re.compile(r'\bnot\b|!|¬')
 306     _RE_NUM_VAR = Expression._RE_NUM_VAR
 307     _RE_OPERATORS = re.compile(r'(&|\||~)')
 308
 309     @classmethod
 310     def fromstring(cls, string):
 311         # remove curly brackets
 312         string = cls._RE_BRACES.sub(r'', string)
 313         # replace '=' by '=='
 314         string = cls._RE_EQ.sub(r'\1==\2', string)
 315         # replace 'and', 'or', 'not'
 316         string = cls._RE_AND.sub(r' & ', string)
 317         string = cls._RE_OR.sub(r' | ', string)
 318         string = cls._RE_NOT.sub(r' ~', string)
 319         # add implicit multiplication operators, e.g. '5x' -> '5*x'
 320         string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
 321         # add parentheses to force precedence
 322         tokens = cls._RE_OPERATORS.split(string)
 323         for i, token in enumerate(tokens):
 324             if i % 2 == 0:
 325                 token = '({})'.format(token)
 326                 tokens[i] = token
 327         string = ''.join(tokens)
 328         tree = ast.parse(string, 'eval')
 329         return cls._fromast(tree)
 330
 331     def __repr__(self):
 332         assert len(self.polyhedra) >= 2
 333         strings = [repr(polyhedron) for polyhedron in self.polyhedra]
 334         return 'Or({})'.format(', '.join(strings))
 335
 336     @classmethod
 337     def fromsympy(cls, expr):
 338         import sympy
 339         from .polyhedra import Lt, Le, Eq, Ne, Ge, Gt
 340         funcmap = {
 341             sympy.And: And, sympy.Or: Or, sympy.Not: Not,
 342             sympy.Lt: Lt, sympy.Le: Le,
 343             sympy.Eq: Eq, sympy.Ne: Ne,
 344             sympy.Ge: Ge, sympy.Gt: Gt,
 345         }
 346         if expr.func in funcmap:
 347             args = [Domain.fromsympy(arg) for arg in expr.args]
 348             return funcmap[expr.func](*args)
 349         elif isinstance(expr, sympy.Expr):
 350             return Expression.fromsympy(expr)
 351         raise ValueError('non-domain expression: {!r}'.format(expr))
 352
 353     def tosympy(self):
 354         import sympy
 355         polyhedra = [polyhedron.tosympy() for polyhedron in polyhedra]
 356         return sympy.Or(*polyhedra)
 357
 358
 359 def And(*domains):
 360     if len(domains) == 0:
 361         from .polyhedra import Universe
 362         return Universe
 363     else:
 364         return domains[0].intersection(*domains[1:])
 365
 366 def Or(*domains):
 367     if len(domains) == 0:
 368         from .polyhedra import Empty
 369         return Empty
 370     else:
 371         return domains[0].union(*domains[1:])
 372
 373 def Not(domain):
 374     return ~domain