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sby/docs/examples/indinv/example.py
Claire Xenia Wolf 4a07e026dd Add inductive invariants example
Signed-off-by: Claire Xenia Wolf <claire@clairexen.net>
2021-12-17 15:42:04 +01:00

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2.6 KiB
Python

from collections import defaultdict
import inspect
N = 32
f = lambda x: (2*x-1) ^ (x&7)
table = [f(i) & (N-1) for i in range(N)]
rtable = [table.count(i) for i in range(N)]
def getPath(v):
if table[v] is None:
return [v]
bak = table[v]
table[v] = None
r = [v] + getPath(bak)
table[v] = bak
return r
def getPaths():
visited = set()
paths = list()
for i in range(N):
if rtable[i] == 0:
paths.append(getPath(i))
for path in paths:
for i in path:
visited.add(i)
for i in range(N):
if i not in visited:
paths.append(getPath(i))
for j in paths[-1]:
visited.add(j)
return paths
pathsByLidx = defaultdict(set)
loopsByIdx = dict()
loopsByLidx = dict()
for path in getPaths():
i = path.index(path[-1])+1
head, loop, lidx = tuple(path[:i]), tuple(path[i:]), max(path[i:])
pathsByLidx[lidx].add((head, loop))
print()
print("The %d-bit function f(x) produces %d loops:" % (N.bit_length()-1, len(pathsByLidx)))
print(" ", inspect.getsource(f).strip())
for lidx, paths in pathsByLidx.items():
loop = None
for path in paths:
for i in path[0] + path[1]:
loopsByIdx[i] = lidx
if loop is None or path[1][0] > loop[0]:
loop = path[1]
loopsByLidx[lidx] = loop
print()
print("%d-Element Loop:" % len(loop))
print(" ", " ->- ".join(["%2d" % i for i in loop + (loop[0],)]))
lines = []
lastPath = []
for path in sorted([tuple(reversed(p[0])) for p in paths]):
line = ""
for i in range(len(path)):
if i < len(lastPath) and lastPath[i] == path[i]:
line += " %s " % (" " if i == 0 else "| ")
else:
line += " %s %2d" % (" " if i == 0 else "`<-" if len(lastPath) else "-<-", path[i])
lastPath = []
lastPath = path
lines.append(line)
for i in range(len(lines)-1, -1, -1):
line, nextline = list(lines[i]), "" if i == len(lines)-1 else lines[i+1]
if len(nextline) < len(line): nextline = nextline.ljust(len(line))
for k in range(len(line)):
if line[k] == "|" and nextline[k] in " -":
line[k] = " "
lines[i] = "".join(line)
print("%d Lead-Ins:" % len(lines))
for line in lines:
print(line)
print()
print("Loop Membership:")
for lidx in pathsByLidx:
print("%18s |" % (loopsByLidx[lidx],), end="")
for i in range(N):
print("*" if loopsByIdx[i] == lidx else ".", end="")
print("|")
print()