Improve hash functions in linexprs
[linpy.git] / 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))
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 if isinstance(symbols, str):
158 symbols = symbols.replace(',', ' ').split()
159 else:
160 symbols = list(symbols)
161 for i, symbol in enumerate(symbols):
162 if isinstance(symbol, Symbol):
163 symbols[i] = symbol.name
164 elif not isinstance(symbol, str):
165 raise TypeError('symbols must be strings or Symbol instances')
166 islset = self._toislset(self.polyhedra, self.symbols)
167 # the trick is to walk symbols in reverse order, to avoid index updates
168 for index, symbol in reversed(list(enumerate(self.symbols))):
169 if symbol in symbols:
170 islset = libisl.isl_set_project_out(islset, libisl.isl_dim_set, index, 1)
171 # remaining symbols
172 symbols = [symbol for symbol in self.symbols if symbol not in symbols]
173 return Domain._fromislset(islset, symbols)
174
175 def sample(self):
176 from .polyhedra import Polyhedron
177 islset = self._toislset(self.polyhedra, self.symbols)
178 islbset = libisl.isl_set_sample(islset)
179 return Polyhedron._fromislbasicset(islbset, self.symbols)
180
181 def intersection(self, *others):
182 if len(others) == 0:
183 return self
184 symbols = self._xsymbols((self,) + others)
185 islset1 = self._toislset(self.polyhedra, symbols)
186 for other in others:
187 islset2 = other._toislset(other.polyhedra, symbols)
188 islset1 = libisl.isl_set_intersect(islset1, islset2)
189 return self._fromislset(islset1, symbols)
190
191 def __and__(self, other):
192 return self.intersection(other)
193
194 def union(self, *others):
195 if len(others) == 0:
196 return self
197 symbols = self._xsymbols((self,) + others)
198 islset1 = self._toislset(self.polyhedra, symbols)
199 for other in others:
200 islset2 = other._toislset(other.polyhedra, symbols)
201 islset1 = libisl.isl_set_union(islset1, islset2)
202 return self._fromislset(islset1, symbols)
203
204 def __or__(self, other):
205 return self.union(other)
206
207 def __add__(self, other):
208 return self.union(other)
209
210 def difference(self, other):
211 symbols = self._xsymbols([self, other])
212 islset1 = self._toislset(self.polyhedra, symbols)
213 islset2 = other._toislset(other.polyhedra, symbols)
214 islset = libisl.isl_set_subtract(islset1, islset2)
215 return self._fromislset(islset, symbols)
216
217 def __sub__(self, other):
218 return self.difference(other)
219
220 def lexmin(self):
221 islset = self._toislset(self.polyhedra, self.symbols)
222 islset = libisl.isl_set_lexmin(islset)
223 return self._fromislset(islset, self.symbols)
224
225 def lexmax(self):
226 islset = self._toislset(self.polyhedra, self.symbols)
227 islset = libisl.isl_set_lexmax(islset)
228 return self._fromislset(islset, self.symbols)
229
230 @classmethod
231 def _fromislset(cls, islset, symbols):
232 from .polyhedra import Polyhedron
233 islset = libisl.isl_set_remove_divs(islset)
234 islbsets = isl_set_basic_sets(islset)
235 libisl.isl_set_free(islset)
236 polyhedra = []
237 for islbset in islbsets:
238 polyhedron = Polyhedron._fromislbasicset(islbset, symbols)
239 polyhedra.append(polyhedron)
240 if len(polyhedra) == 0:
241 from .polyhedra import Empty
242 return Empty
243 elif len(polyhedra) == 1:
244 return polyhedra[0]
245 else:
246 self = object().__new__(Domain)
247 self._polyhedra = tuple(polyhedra)
248 self._symbols = cls._xsymbols(polyhedra)
249 self._dimension = len(self._symbols)
250 return self
251
252 @classmethod
253 def _toislset(cls, polyhedra, symbols):
254 polyhedron = polyhedra[0]
255 islbset = polyhedron._toislbasicset(polyhedron.equalities,
256 polyhedron.inequalities, symbols)
257 islset1 = libisl.isl_set_from_basic_set(islbset)
258 for polyhedron in polyhedra[1:]:
259 islbset = polyhedron._toislbasicset(polyhedron.equalities,
260 polyhedron.inequalities, symbols)
261 islset2 = libisl.isl_set_from_basic_set(islbset)
262 islset1 = libisl.isl_set_union(islset1, islset2)
263 return islset1
264
265 @classmethod
266 def _fromast(cls, node):
267 from .polyhedra import Polyhedron
268 if isinstance(node, ast.Module) and len(node.body) == 1:
269 return cls._fromast(node.body[0])
270 elif isinstance(node, ast.Expr):
271 return cls._fromast(node.value)
272 elif isinstance(node, ast.UnaryOp):
273 domain = cls._fromast(node.operand)
274 if isinstance(node.operand, ast.invert):
275 return Not(domain)
276 elif isinstance(node, ast.BinOp):
277 domain1 = cls._fromast(node.left)
278 domain2 = cls._fromast(node.right)
279 if isinstance(node.op, ast.BitAnd):
280 return And(domain1, domain2)
281 elif isinstance(node.op, ast.BitOr):
282 return Or(domain1, domain2)
283 elif isinstance(node, ast.Compare):
284 equalities = []
285 inequalities = []
286 left = Expression._fromast(node.left)
287 for i in range(len(node.ops)):
288 op = node.ops[i]
289 right = Expression._fromast(node.comparators[i])
290 if isinstance(op, ast.Lt):
291 inequalities.append(right - left - 1)
292 elif isinstance(op, ast.LtE):
293 inequalities.append(right - left)
294 elif isinstance(op, ast.Eq):
295 equalities.append(left - right)
296 elif isinstance(op, ast.GtE):
297 inequalities.append(left - right)
298 elif isinstance(op, ast.Gt):
299 inequalities.append(left - right - 1)
300 else:
301 break
302 left = right
303 else:
304 return Polyhedron(equalities, inequalities)
305 raise SyntaxError('invalid syntax')
306
307 _RE_BRACES = re.compile(r'^\{\s*|\s*\}$')
308 _RE_EQ = re.compile(r'([^<=>])=([^<=>])')
309 _RE_AND = re.compile(r'\band\b|,|&&|/\\|∧|∩')
310 _RE_OR = re.compile(r'\bor\b|;|\|\||\\/|∨|∪')
311 _RE_NOT = re.compile(r'\bnot\b|!|¬')
312 _RE_NUM_VAR = Expression._RE_NUM_VAR
313 _RE_OPERATORS = re.compile(r'(&|\||~)')
314
315 @classmethod
316 def fromstring(cls, string):
317 # remove curly brackets
318 string = cls._RE_BRACES.sub(r'', string)
319 # replace '=' by '=='
320 string = cls._RE_EQ.sub(r'\1==\2', string)
321 # replace 'and', 'or', 'not'
322 string = cls._RE_AND.sub(r' & ', string)
323 string = cls._RE_OR.sub(r' | ', string)
324 string = cls._RE_NOT.sub(r' ~', string)
325 # add implicit multiplication operators, e.g. '5x' -> '5*x'
326 string = cls._RE_NUM_VAR.sub(r'\1*\2', string)
327 # add parentheses to force precedence
328 tokens = cls._RE_OPERATORS.split(string)
329 for i, token in enumerate(tokens):
330 if i % 2 == 0:
331 token = '({})'.format(token)
332 tokens[i] = token
333 string = ''.join(tokens)
334 tree = ast.parse(string, 'eval')
335 return cls._fromast(tree)
336
337 def __repr__(self):
338 assert len(self.polyhedra) >= 2
339 strings = [repr(polyhedron) for polyhedron in self.polyhedra]
340 return 'Or({})'.format(', '.join(strings))
341
342 @classmethod
343 def fromsympy(cls, expr):
344 raise NotImplementedError
345
346 def tosympy(self):
347 raise NotImplementedError
348
349 def And(*domains):
350 if len(domains) == 0:
351 from .polyhedra import Universe
352 return Universe
353 else:
354 return domains[0].intersection(*domains[1:])
355
356 def Or(*domains):
357 if len(domains) == 0:
358 from .polyhedra import Empty
359 return Empty
360 else:
361 return domains[0].union(*domains[1:])
362
363 def Not(domain):
364 return ~domain