rtt-f030/components/rtgui/utils/perfect_hash/perfect_hash.py

871 lines
28 KiB
Python

#!/usr/bin/env python
"""
Generate a minimal perfect hash function for the keys in a file,
desired hash values may be specified within this file as well.
A given code template is filled with parameters, such that the
output is code which implements the hash function.
Templates can easily be constructed for any programming language.
The code is based on an a program A.M. Kuchling wrote:
http://www.amk.ca/python/code/perfect-hash
The algorithm the program uses is described in the paper
'Optimal algorithms for minimal perfect hashing',
Z. J. Czech, G. Havas and B.S. Majewski.
http://citeseer.ist.psu.edu/122364.html
The algorithm works like this:
1. You have K keys, that you want to perfectly hash against some
desired hash values.
2. Choose a number N larger than K. This is the number of
vertices in a graph G, and also the size of the resulting table G.
3. Pick two random hash functions f1, f2, that return values from 0..N-1.
4. Now, for all keys, you draw an edge between vertices f1(key) and f2(key)
of the graph G, and associate the desired hash value with that edge.
5. Check if G is acyclic, i.e. has no loops; if no, go back to step 2.
6. Assign values to each vertex such that, for each edge, you can add
the values for the two vertices and get the desired (hash) value
for that edge. This task is easy, because the graph is acyclic.
This is done by picking a vertex, and assigning it a value of 0.
Then do a depth-first search, assigning values to new vertices so that
they sum up properly.
7. f1, f2, and vertex values of G now make up a perfect hash function.
For simplicity, the implementation of the algorithm combines steps 5 and 6.
That is, we check for loops in G and assign the vertex values in one procedure.
If this procedure succeeds, G is acyclic and the vertex values are assigned.
If the procedure fails, G is cyclic, and we go back to step 2, replacing G
with a new graph, and thereby discarding the vertex values from the failed
attempt.
"""
__author__ = 'Ilan Schnell <ilanschnell@gmail.com>, 2008 (and AMK 2000)'
__license__ = 'GNU GPL 2'
__version__ = '0.1'
import sys, random, string, cStringIO, StringIO
verbose = False
trails = 5
class Graph:
"""
Implements a graph with 'N' vertices. First, you connect the graph with
edges, which have a desired value associated. Then the vertex values
are assigned, which will fail if the graph is cyclic. The vertex values
are assigned such that the two values corresponding to an edge add up to
the desired edge value (mod N).
Example:
>>> G = Graph(3)
>>> G.assign_vertex_values()
True
Now we make an edge between vertex 0 and 1 with desired edge value 2:
>>> G.connect(0, 1, 2)
Make another edge 1:2 with desired edge value 1:
>>> G.connect(1, 2, 1)
The graph is still acyclic, and assigning values works:
>>> G.assign_vertex_values()
True
>>> G.vertex_values
[0, 2, 2]
What do these values mean?
When you add the values for edge 0:1 you get 0 + 2 = 2, as desired.
For edge 1:2 you add 2 + 2 = 4 = 1 (mod 3), as desired.
Adding edge 0:2 produces a loop, so the graph is no longer acyclic.
Assigning values fails.
>>> G.connect(0, 2, 0)
>>> G.assign_vertex_values()
False
"""
def __init__(self, N):
self.N = N # number of vertices
# maps a vertex number to the list of tuples (vertices, edge value)
# to which it is connected by edges.
self.adjacent = [[] for n in xrange(N)]
def connect(self, vertex1, vertex2, edge_value):
"""
Connect 'vertex1' and 'vertex2' with an edge, with associated
value 'value'
"""
# Add vertices to each other's adjacent list
self.adjacent[vertex1].append( (vertex2, edge_value) )
self.adjacent[vertex2].append( (vertex1, edge_value) )
def assign_vertex_values(self):
"""
Try to assign the vertex values, such that, for each edge, you can
add the values for the two vertices involved and get the desired
value for that edge, i.e. the desired hash key.
This will fail when the graph is cyclic.
This is done by a Depth-First Search of the graph. If the search
finds a vertex that was visited before, there's a loop and False is
returned immediately, i.e. the assignment is terminated.
On success (when the graph is acyclic) True is returned.
"""
self.vertex_values = self.N * [-1] # -1 means unassigned
visited = self.N * [False]
# Loop over all vertices, taking unvisited ones as roots.
for root in xrange(self.N):
if visited[root]:
continue
# explore tree starting at 'root'
self.vertex_values[root] = 0 # set arbitrarily to zero
# Stack of vertices to visit, a list of tuples (parent, vertex)
tovisit = [ (None, root) ]
while tovisit:
parent, vertex = tovisit.pop()
visited[vertex] = True
# Loop over adjacent vertices, but skip the vertex we arrived
# here from the first time it is encountered.
skip = True
for neighbor, edge_value in self.adjacent[vertex]:
if skip and neighbor == parent:
skip = False
continue
if visited[neighbor]:
# We visited here before, so the graph is cyclic.
return False
tovisit.append( (vertex, neighbor) )
# Set new vertex's value to the desired edge value,
# minus the value of the vertex we came here from.
self.vertex_values[neighbor] = \
( edge_value - self.vertex_values[vertex] ) % self.N
# check if all vertices have a valid value
for vertex in xrange(self.N):
assert self.vertex_values[vertex] >= 0
# We got though, so the graph is acyclic,
# and all values are now assigned.
return True
def generate_hash(kdic, Hash):
"""
Return hash functions f1 and f2, and G for a perfect minimal hash.
Input is dictionary 'kdic' with the keys and desired hash values.
'Hash' is a random hash function generator, that means Hash(N) returns a
returns a random hash function which returns hash values from 0..N-1.
"""
# N is the number of vertices in the graph G
N = 1 if not kdic else (max(kdic.values()) + 1)
if verbose >= 2:
sys.stderr.write('N = %i\n' % N)
trail = 0 # Number of trial graphs so far
while True:
if (trail % trails) == 0: # trails failures, increase N slightly
if trail > 0:
N = max(N+1, int(1.05*N))
if verbose:
sys.stderr.write('\n')
sys.stderr.write('Generating graphs N = %i ' % N)
trail += 1
if verbose:
sys.stderr.write('.')
sys.stderr.flush()
G = Graph(N) # Create graph with N vertices
f1 = Hash(N) # Create 2 random hash functions
f2 = Hash(N)
# Connect vertices given by the values of the two hash functions
# for each key. Associate the desired hash value with each edge.
for key, hashval in kdic.iteritems():
G.connect(f1(key), f2(key), hashval)
# Try to assign the vertex values. This will fail when the graph
# is cyclic. But when the graph is acyclic it will succeed and we
# break out, because we're done.
if G.assign_vertex_values():
break
if verbose:
sys.stderr.write('\nAcyclic graph found after %i trails.\n' % trail)
if verbose >= 2:
sys.stderr.write('N = %i\n' % N)
if verbose:
sys.stderr.write('Checking generated hash function... ')
# Sanity check the result by actually verifying that all the keys
# hash to the right value.
for key, hashval in kdic.iteritems():
assert hashval == ( G.vertex_values[f1(key)] +
G.vertex_values[f2(key)] ) % N
if verbose:
sys.stderr.write('OK\n')
return f1, f2, G.vertex_values
class Hash1:
"""
Random hash function generator.
For simplicity and speed, this doesn't implement any byte-level hashing
scheme. Instead, a random string is generated and prefixing to str(key),
and then Python's hashing function is used.
"""
def __init__(self, N):
self.N = N
self.salt = "".join(random.choice(string.letters + string.digits)
for i in xrange(8))
def __call__(self, key):
return hash(self.salt + str(key)) % self.N
template = """
def perfect_hash(key):
return (G[ hash('$S1' + str(key)) % $NG ] +
G[ hash('$S2' + str(key)) % $NG ]) % $NG
"""
class Hash2:
"""
Random hash function generator.
Simple byte level hashing, each byte is multiplied in sequence to a table
containing random numbers modulo N, and then these products are summed up.
The table with random numbers is dynamically expanded whenever
a key longer than the current table size is encountered.
"""
def __init__(self, N):
self.N = N
self.salt = []
def __call__(self, key):
skey = key
while len(self.salt) < len(skey): # add more salt if necessary
self.salt.append(random.randint(0, self.N-1))
return sum(self.salt[i] * ord(c)
for i, c in enumerate(skey)) % self.N
template = """
S1 = [$S1]
S2 = [$S2]
def hash_f(key, T):
return sum(T[i % $NS] * ord(c) for i, c in enumerate(str(key))) % $NG
def perfect_hash(key):
return (G[hash_f(key, S1)] + G[hash_f(key, S2)]) % $NG
"""
class PerfHash:
"""
This class is designed for creating perfect hash tables at run time,
which should be avoided, in particulat inserting new keys is
prohibitively expensive since a new perfect hash table needs to be
constructed. However, this class can be usefull for testing.
>>> d = PerfHash({'foo':(429, 'bar'), 42:True, False:'baz'})
>>> d['foo'], d[42], d[False]
((429, 'bar'), True, 'baz')
>>> d[False] = (1, 2)
>>> d[False]
(1, 2)
>>> d.has_key('foo')
True
>>> d.has_key(True)
False
"""
def __init__(self, dic):
self.klst = []
self.objs = []
kdic = {}
for hashval, (key, obj) in enumerate(dic.iteritems()):
self.klst.append(key)
self.objs.append(obj)
kdic[key] = hashval
self.N = len(dic)
self.f1, self.f2, self.G = generate_hash(kdic, Hash1)
def __setitem__(self, newkey, newobj):
dic = {}
for key in self.klst:
dic[key] = self[key]
dic[newkey] = newobj
self.__init__(dic)
def hashval(self, key):
return ( self.G[self.f1(key)] + self.G[self.f2(key)] ) % len(self.G)
def __getitem__(self, key):
h = self.hashval(key)
if h < self.N and key == self.klst[h]:
return self.objs[h]
else:
raise IndexError
def has_key(self, key):
h = self.hashval(key)
return h < self.N and key == self.klst[h]
class Format:
"""
>>> class o:
... pass
>>> o.delimiter = ': '
>>> o.width = 75
>>> o.indent = 4
>>> x = Format( o )
>>> x( range(10) )
'0: 1: 2: 3: 4: 5: 6: 7: 8: 9'
>>> o.delimiter = '; '
>>> x = Format( o )
>>> x( range(5) )
'0; 1; 2; 3; 4'
>>> o.delimiter = ' '
>>> x = Format( o )
>>> x( range(5), quote = True )
'"0" "1" "2" "3" "4"'
>>> x(42)
'42'
>>> x('Hello')
'Hello'
"""
def __init__(self, options):
names = ['width', 'indent', 'delimiter']
for name in names:
setattr(self, name, getattr(options, name))
if verbose >=2:
sys.stderr.write("Format options:\n")
for name in names:
sys.stderr.write(' %s: %r\n' % (name, getattr(self, name)))
def __call__(self, data, quote = False):
if type(data) != type([]):
return str(data)
lendel = len(self.delimiter)
aux = StringIO.StringIO()
pos = 20
for i, elt in enumerate(data):
last = bool(i == len(data)-1)
s = ('"%s"' if quote else '%s') % elt
if pos + len(s) + lendel > self.width:
aux.write('\n' + (self.indent * ' '))
pos = self.indent
aux.write(s)
pos += len(s)
if not last:
aux.write(self.delimiter)
pos += lendel
return aux.getvalue()
def keyDict(keys_hashes):
"""
Checks a list with (key, hashvalue) tupels and returns dictionary.
>>> d = keyDict([(1, 2), (3, 4), (5, 6)])
>>> d[3]
4
"""
K = len(keys_hashes) # number of keys
if verbose >= 2:
sys.stderr.write('K = %i\n' % K)
kdic = dict(keys_hashes)
if len(kdic) < K:
sys.stderr.write('Warning: Input contains duplicate keys\n')
if len(set(kdic.values())) < K:
sys.stderr.write('Warning: Input contains duplicate hash values\n')
return kdic
def generate_code(keys_hashes, template, Hash, options, extra_subs):
"""
Takes a list of key value pairs and inserts the generated parameter
lists into the 'template' strinng. 'Hash' is the random hash function
generator, and the optional keywords are formating options.
The return value is the substituted code template.
"""
f1, f2, G = generate_hash(keyDict(keys_hashes), Hash)
assert f1.N == f2.N == len(G)
assert len(f1.salt) == len(f2.salt)
fmt = Format(options)
return string.Template(template).substitute(
NS = len(f1.salt),
S1 = fmt(f1.salt),
S2 = fmt(f2.salt),
NG = len(G),
G = fmt(G),
NK = len(keys_hashes),
K = fmt([key for key, hashval in keys_hashes], quote = True),
H = fmt([hashval for key, hashval in keys_hashes]),
**extra_subs)
def read_table(filename, options):
"""
Reads keys and desired hash value pairs from a file. If no column
for the hash value is specified, a sequence of hash values is generated,
from 0 to N-1, where N is the number of rows found in the file.
"""
if verbose >= 2:
sys.stderr.write("Reading table from file `%s' to extract keys.\n" %
filename)
try:
f = file(filename)
except IOError :
exit("Error: Could not open `%s' for reading." % filename)
keys_hashes = []
hashval = -1
if verbose >= 2:
sys.stderr.write("Reader options:\n")
for name in ['comment', 'splitby', 'keycol', 'hashcol']:
sys.stderr.write(' %s: %r\n' %
(name, getattr(options, name)))
for n, line in enumerate(f):
line = line.strip()
if not line or line.startswith(options.comment):
continue
if line.count(options.comment): # strip content after comment
line = line.split(options.comment)[0].strip()
row = [col.strip() for col in line.split(options.splitby)]
try:
key = row[options.keycol-1]
except IndexError :
exit("%s:%i: Error: Cannot read key, not enough columns." %
(filename, n+1))
if options.hashcol:
try:
val = row[options.hashcol-1]
except IndexError :
exit("%s:%i: Error: Cannot read hash value, not enough columns."
% (filename, n+1))
try:
hashval = int(val)
except ValueError :
exit("%s:%i: Error: Cannot convert `%s' to int." %
(filename, n+1, row[options.hashcol-1]))
else:
hashval += 1
keys_hashes.append( (key, hashval) )
f.close()
if not keys_hashes:
exit("Error: no keys found in file `%s'." % filename)
return keys_hashes
def print_keys_hashes(keys_hashes):
fmt = '%-20s %10s'
head = fmt % ('Key', 'Hash value')
sys.stderr.write('\n' + head + '\n')
sys.stderr.write(len(head)*'-' + '\n')
for tup in keys_hashes:
sys.stderr.write(fmt % tup + '\n')
sys.stderr.write('\n')
def read_template(filename):
if verbose >= 2:
sys.stderr.write("Reading template from file `%s'.\n" % filename)
try:
f = file(filename)
except IOError :
fatal_error("Error: Could not open `%s' for reading." % filename)
return f.read()
def builtin_template(Hash):
return """\
# =======================================================================
# ================= Python code for perfect hash function ===============
# =======================================================================
G = [$G]
""" + Hash.template + """
# ============================ Sanity check =============================
K = [$K]
H = [$H]
assert len(K) == len(H) == $NK
for k, h in zip(K, H):
assert perfect_hash(k) == h
"""
def print_code(code, name, width = 78):
def center(s):
v = (width - len(s))/2
return '='*v + s + '='*v
sys.stderr.write(center(' BEGIN %s ' % name) + '\n')
sys.stderr.write(code + '\n')
sys.stderr.write(center(' END %s ' % name) + '\n')
def self_test(options):
import doctest
global verbose
print 'Starting self tests ...'
def random_word():
return ''.join(random.choice(string.letters + string.digits)
for i in xrange(random.randint(1, 20)))
def flush_dot():
sys.stdout.write('.')
sys.stdout.flush()
def run(K, Hash):
flush_dot()
keys = [chr(65+i) for i in xrange(K)]
hashes = range(K)
random.shuffle(keys)
random.shuffle(hashes)
code = generate_code(zip(keys, hashes),
builtin_template(Hash),
Hash,
options)
exec(code) in {}
verbose = False
for Hash in [Hash1, Hash2]:
for K in xrange(0, 27):
run(K, Hash)
print
verbose = options.verbose
N = 250
for Hash in [Hash1, Hash2]:
if verbose:
print 'Generating approximately %i key/hash pairs ...' % N
kh = {}
for i in xrange(N):
kh[random_word()] = i
if verbose:
print 'Generating code for %i key/hash pairs ...' % len(kh)
code = generate_code(kh.items(),
builtin_template(Hash),
Hash,
options)
if verbose:
print 'Executing code ...'
flush_dot()
exec(code) in {}
flush_dot()
d = PerfHash(dict([(100-i, i*i) for i in xrange(500)]))
for i in xrange(500):
assert d[100-i] == i*i
flush_dot()
d[None] = True
assert d[None] == True
if verbose:
print 'Running doctest ...'
verbose = False
failure_count, test_count = doctest.testmod(report = True, verbose = False)
print
if failure_count:
sys.stderr.write('FAILED\n')
sys.exit(2)
else:
sys.stderr.write('%i tests passed.\n' % test_count)
sys.stderr.write('OK\n')
sys.exit(0)
if __name__ == '__main__':
from optparse import OptionParser
usage = "usage: %prog [options] KEYS_FILE [TMPL_FILE]"
description = """\
Generates code for perfect hash functions from
a file with keywords and a code template.
If no template file is provided, a small built-in Python template
is processed and the output code is written to stdout.
"""
parser = OptionParser(usage = usage,
description = description,
prog = sys.argv[0],
version = "%prog 0.1")
parser.add_option("--delimiter",
action = "store",
default = ", ",
help = "Delimiter for list items used in output, "
"the default delimiter is '%default'",
metavar = "STR")
parser.add_option("--indent",
action = "store",
default = 2,
type = "int",
help = "Make INT spaces at the beginning of a "
"new line when generated list is wrapped. "
"Default is %default",
metavar = "INT")
parser.add_option("--width",
action = "store",
default = 76,
type = "int",
help = "Maximal width of generated list when "
"wrapped. Default width is %default",
metavar = "INT")
parser.add_option("--comment",
action = "store",
default = "#",
help = "STR is the character, or sequence of "
"characters, which marks the beginning "
"of a comment (which runs till "
"the end of the line), in the input "
"KEYS_FILE. "
"Default is '%default'",
metavar = "STR")
parser.add_option("--splitby",
action = "store",
default = ",",
help = "STR is the character by which the columns "
"in the input KEYS_FILE are split. "
"Default is '%default'",
metavar = "STR")
parser.add_option("--keycol",
action = "store",
default = 1,
type = "int",
help = "Specifies the column INT in the input "
"KEYS_FILE which contains the keys. "
"Default is %default, i.e. the first column.",
metavar = "INT")
parser.add_option("--hashcol",
action = "store",
default = 0,
type = "int",
help = "Specifies the column INT in the input "
"KEYS_FILE which contains the desired "
"hash values. "
"By default the hash values are given by the "
"sequence 0..N-1.",
metavar = "INT")
parser.add_option("--trails",
action = "store",
default = 5,
type = "int",
help = "Specifies the number of trails before "
"N is increased. A small INT will give "
"compute faster, but the array G will be "
"large. A large INT will take longer to "
"compute but G will be smaller. "
"Default is %default",
metavar = "INT")
parser.add_option("--hft",
action = "store",
default = 2,
type = "int",
help = "Hash function type INT (see documentation), "
"The default is %default",
metavar = "INT")
parser.add_option("-e", "--execute",
action = "store_true",
help = "Execute the generated code within "
"the Python interpreter.")
parser.add_option("-o", "--output",
action = "store",
help = "Specify output FILE explicitly. "
"`-o std' means standard output. "
"`-o no' means no output. "
"By default, the file name is obtained "
"from the name of the template file by "
"substituting `tmpl' to `code'.",
metavar = "FILE")
parser.add_option("--test",
action = "store_true",
help = "Perform self test")
parser.add_option("-v", "--verbose",
action = "count",
help = "Be verbose, "
"use -vv to be even more verbose")
options, args = parser.parse_args()
print type(options), '\n', repr(options)
if options.trails > 0:
trails = options.trails
else:
parser.error("trails before increasing N has to be larger than zero")
verbose = options.verbose
if options.test:
self_test(options)
if len(args) not in (1, 2):
parser.error("incorrect number of arguments")
if len(args) == 2 and not args[1].count('tmpl'):
parser.error("template filename does not contain 'tmpl'")
if options.hft == 1:
Hash = Hash1
elif options.hft == 2:
Hash = Hash2
else:
parser.error("Hash function %i not implemented.")
# --------------------- end parsing and checking --------------
# ---------------- keys_file
keys_file = args[0]
if verbose:
sys.stderr.write("keys_file = %r\n" % keys_file)
# ---------------- keys_hashes
keys_hashes = read_table(keys_file, options)
if verbose >= 3:
print_keys_hashes(keys_hashes)
# ---------------- tmpl_file
if len(args) == 2:
tmpl_file = args[1]
else:
tmpl_file = None
if verbose:
sys.stderr.write("tmpl_file = %r\n" % tmpl_file)
# ---------------- template
if tmpl_file:
template = read_template(tmpl_file)
else:
template = builtin_template(Hash)
if verbose >= 3:
print_code(template, 'TEMPLATE')
# ---------------- outname
if options.output:
outname = options.output
else:
if tmpl_file:
if tmpl_file.count('tmpl'):
outname = tmpl_file.replace('tmpl', 'code')
else:
exit("Hmm, template filename does not contain 'tmpl'")
else:
outname = 'std'
if verbose:
sys.stderr.write("outname = %r\n" % outname)
# ---------------- outstream
if outname == 'std':
outstream = sys.stdout
elif outname == 'no':
outstream = None
else:
try:
outstream = open(outname, 'w')
except IOError :
exit("Error: Could not open `%s' for writing." % outname)
# ---------------- generated code
code = generate_code(keys_hashes, template, Hash, options)
if verbose >= 3:
print_code(code, 'GENERATED CODE')
# ---------------- execute code
if options.execute or template == builtin_template(Hash):
if verbose:
sys.stderr.write('Executing code...\n')
exec(code)
# ---------------- write code to output stream
if outstream:
outstream.write(code)
if not outname == 'std':
outstream.close()