Enumeration.py source code [clang_source_code/utils/ABITest/Enumeration.py]

1	"""Utilities for enumeration of finite and countably infinite sets.
2	"""
3	from __future__ import absolute_import, division, print_function
4	###
5	# Countable iteration
6
7	# Simplifies some calculations
8	class Aleph0(int):
9	_singleton = None
10	def __new__(type):
11	if type._singleton is None:
12	type._singleton = int.__new__(type)
13	return type._singleton
14	def __repr__(self): return '<aleph0>'
15	def __str__(self): return 'inf'
16
17	def __cmp__(self, b):
18	return 1
19
20	def __sub__(self, b):
21	raise ValueError("Cannot subtract aleph0")
22	__rsub__ = __sub__
23
24	def __add__(self, b):
25	return self
26	__radd__ = __add__
27
28	def __mul__(self, b):
29	if b == 0: return b
30	return self
31	__rmul__ = __mul__
32
33	def __floordiv__(self, b):
34	if b == 0: raise ZeroDivisionError
35	return self
36	__rfloordiv__ = __floordiv__
37	__truediv__ = __floordiv__
38	__rtuediv__ = __floordiv__
39	__div__ = __floordiv__
40	__rdiv__ = __floordiv__
41
42	def __pow__(self, b):
43	if b == 0: return 1
44	return self
45	aleph0 = Aleph0()
46
47	def base(line):
48	return line*(line+1)//2
49
50	def pairToN(pair):
51	x,y = pair
52	line,index = x+y,y
53	return base(line)+index
54
55	def getNthPairInfo(N):
56	# Avoid various singularities
57	if N==0:
58	return (0,0)
59
60	# Gallop to find bounds for line
61	line = 1
62	next = 2
63	while base(next)<=N:
64	line = next
65	next = line << 1
66
67	# Binary search for starting line
68	lo = line
69	hi = line<<1
70	while lo + 1 != hi:
71	#assert base(lo) <= N < base(hi)
72	mid = (lo + hi)>>1
73	if base(mid)<=N:
74	lo = mid
75	else:
76	hi = mid
77
78	line = lo
79	return line, N - base(line)
80
81	def getNthPair(N):
82	line,index = getNthPairInfo(N)
83	return (line - index, index)
84
85	def getNthPairBounded(N,W=aleph0,H=aleph0,useDivmod=False):
86	"""getNthPairBounded(N, W, H) -> (x, y)
87
88	Return the N-th pair such that 0 <= x < W and 0 <= y < H."""
89
90	if W <= 0 or H <= 0:
91	raise ValueError("Invalid bounds")
92	elif N >= W*H:
93	raise ValueError("Invalid input (out of bounds)")
94
95	# Simple case...
96	if W is aleph0 and H is aleph0:
97	return getNthPair(N)
98
99	# Otherwise simplify by assuming W < H
100	if H < W:
101	x,y = getNthPairBounded(N,H,W,useDivmod=useDivmod)
102	return y,x
103
104	if useDivmod:
105	return N%W,N//W
106	else:
107	# Conceptually we want to slide a diagonal line across a
108	# rectangle. This gives more interesting results for large
109	# bounds than using divmod.
110
111	# If in lower left, just return as usual
112	cornerSize = base(W)
113	if N < cornerSize:
114	return getNthPair(N)
115
116	# Otherwise if in upper right, subtract from corner
117	if H is not aleph0:
118	M = W*H - N - 1
119	if M < cornerSize:
120	x,y = getNthPair(M)
121	return (W-1-x,H-1-y)
122
123	# Otherwise, compile line and index from number of times we
124	# wrap.
125	N = N - cornerSize
126	index,offset = N%W,N//W
127	# p = (W-1, 1+offset) + (-1,1)*index
128	return (W-1-index, 1+offset+index)
129	def getNthPairBoundedChecked(N,W=aleph0,H=aleph0,useDivmod=False,GNP=getNthPairBounded):
130	x,y = GNP(N,W,H,useDivmod)
131	assert 0 <= x < W and 0 <= y < H
132	return x,y
133
134	def getNthNTuple(N, W, H=aleph0, useLeftToRight=False):
135	"""getNthNTuple(N, W, H) -> (x_0, x_1, ..., x_W)
136
137	Return the N-th W-tuple, where for 0 <= x_i < H."""
138
139	if useLeftToRight:
140	elts = [None]*W
141	for i in range(W):
142	elts[i],N = getNthPairBounded(N, H)
143	return tuple(elts)
144	else:
145	if W==0:
146	return ()
147	elif W==1:
148	return (N,)
149	elif W==2:
150	return getNthPairBounded(N, H, H)
151	else:
152	LW,RW = W//2, W - (W//2)
153	L,R = getNthPairBounded(N, HLW, HRW)
154	return (getNthNTuple(L,LW,H=H,useLeftToRight=useLeftToRight) +
155	getNthNTuple(R,RW,H=H,useLeftToRight=useLeftToRight))
156	def getNthNTupleChecked(N, W, H=aleph0, useLeftToRight=False, GNT=getNthNTuple):
157	t = GNT(N,W,H,useLeftToRight)
158	assert len(t) == W
159	for i in t:
160	assert i < H
161	return t
162
163	def getNthTuple(N, maxSize=aleph0, maxElement=aleph0, useDivmod=False, useLeftToRight=False):
164	"""getNthTuple(N, maxSize, maxElement) -> x
165
166	Return the N-th tuple where len(x) < maxSize and for y in x, 0 <=
167	y < maxElement."""
168
169	# All zero sized tuples are isomorphic, don't ya know.
170	if N == 0:
171	return ()
172	N -= 1
173	if maxElement is not aleph0:
174	if maxSize is aleph0:
175	raise NotImplementedError('Max element size without max size unhandled')
176	bounds = [maxElement**i for i in range(1, maxSize+1)]
177	S,M = getNthPairVariableBounds(N, bounds)
178	else:
179	S,M = getNthPairBounded(N, maxSize, useDivmod=useDivmod)
180	return getNthNTuple(M, S+1, maxElement, useLeftToRight=useLeftToRight)
181	def getNthTupleChecked(N, maxSize=aleph0, maxElement=aleph0,
182	useDivmod=False, useLeftToRight=False, GNT=getNthTuple):
183	# FIXME: maxsize is inclusive
184	t = GNT(N,maxSize,maxElement,useDivmod,useLeftToRight)
185	assert len(t) <= maxSize
186	for i in t:
187	assert i < maxElement
188	return t
189
190	def getNthPairVariableBounds(N, bounds):
191	"""getNthPairVariableBounds(N, bounds) -> (x, y)
192
193	Given a finite list of bounds (which may be finite or aleph0),
194	return the N-th pair such that 0 <= x < len(bounds) and 0 <= y <
195	bounds[x]."""
196
197	if not bounds:
198	raise ValueError("Invalid bounds")
199	if not (0 <= N < sum(bounds)):
200	raise ValueError("Invalid input (out of bounds)")
201
202	level = 0
203	active = list(range(len(bounds)))
204	active.sort(key=lambda i: bounds[i])
205	prevLevel = 0
206	for i,index in enumerate(active):
207	level = bounds[index]
208	W = len(active) - i
209	if level is aleph0:
210	H = aleph0
211	else:
212	H = level - prevLevel
213	levelSize = W*H
214	if N<levelSize: # Found the level
215	idelta,delta = getNthPairBounded(N, W, H)
216	return active[i+idelta],prevLevel+delta
217	else:
218	N -= levelSize
219	prevLevel = level
220	else:
221	raise RuntimError("Unexpected loop completion")
222
223	def getNthPairVariableBoundsChecked(N, bounds, GNVP=getNthPairVariableBounds):
224	x,y = GNVP(N,bounds)
225	assert 0 <= x < len(bounds) and 0 <= y < bounds[x]
226	return (x,y)
227
228	###
229
230	def testPairs():
231	W = 3
232	H = 6
233	a = [[' ' for x in range(10)] for y in range(10)]
234	b = [[' ' for x in range(10)] for y in range(10)]
235	for i in range(min(W*H,40)):
236	x,y = getNthPairBounded(i,W,H)
237	x2,y2 = getNthPairBounded(i,W,H,useDivmod=True)
238	print(i,(x,y),(x2,y2))
239	a[y][x] = '%2d'%i
240	b[y2][x2] = '%2d'%i
241
242	print('-- a --')
243	for ln in a[::-1]:
244	if ''.join(ln).strip():
245	print(' '.join(ln))
246	print('-- b --')
247	for ln in b[::-1]:
248	if ''.join(ln).strip():
249	print(' '.join(ln))
250
251	def testPairsVB():
252	bounds = [2,2,4,aleph0,5,aleph0]
253	a = [[' ' for x in range(15)] for y in range(15)]
254	b = [[' ' for x in range(15)] for y in range(15)]
255	for i in range(min(sum(bounds),40)):
256	x,y = getNthPairVariableBounds(i, bounds)
257	print(i,(x,y))
258	a[y][x] = '%2d'%i
259
260	print('-- a --')
261	for ln in a[::-1]:
262	if ''.join(ln).strip():
263	print(' '.join(ln))
264
265	###
266
267	# Toggle to use checked versions of enumeration routines.
268	if False:
269	getNthPairVariableBounds = getNthPairVariableBoundsChecked
270	getNthPairBounded = getNthPairBoundedChecked
271	getNthNTuple = getNthNTupleChecked
272	getNthTuple = getNthTupleChecked
273
274	if __name__ == '__main__':
275	testPairs()
276
277	testPairsVB()
278
279

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