def _rand_der(self):
r"""
Produces a random derangement of `[1, 2, \ldots, n]`.
This is an
implementation of the algorithm described by Martinez et. al. in
[MPP2008]_.
EXAMPLES::
sage: D = Derangements(4)
sage: d = D._rand_der()
sage: d in D
True
"""
n = len(self._set)
A = list(range(1, n + 1))
mark = [x < 0 for x in A]
i, u = n, n
while u >= 2:
if not (mark[i - 1]):
while True:
j = randrange(1, i)
if not (mark[j - 1]):
A[i - 1], A[j - 1] = A[j - 1], A[i - 1]
break
p = random()
if p < (u - 1) * self._count_der(u - 2) // self._count_der(u):
mark[j - 1] = True
u -= 1
u -= 1
i -= 1
return A
def random_element(self):
r"""
Produces all derangements of a positive integer, a list, or
a string. The list or string may contain repeated elements.
If an integer `n` is given, then a random
derangements of `[1, 2, 3, \ldots, n]` is returned
For an integer, or a list or string with all elements
distinct, the value is obtained by an algorithm described in
[MPP2008]_. For a list or string with repeated elements the
derangement is formed by choosing an element at random from the list of
all possible derangements.
OUTPUT:
A single list or string containing a derangement, or an
empty list if there are no derangements.
EXAMPLES::
sage: D = Derangements(4)
sage: D.random_element() # random
[2, 3, 4, 1]
sage: D = Derangements(['A','AT','CAT','CATS','CARTS','CARETS'])
sage: D.random_element() # random
['AT', 'CARTS', 'A', 'CAT', 'CARETS', 'CATS']
sage: D = Derangements('UNCOPYRIGHTABLE')
sage: D.random_element() # random
['C', 'U', 'I', 'H', 'O', 'G', 'N', 'B', 'E', 'L', 'A', 'R', 'P', 'Y', 'T']
sage: D = Derangements([1,1,1,1,2,2,2,2,3,3,3,3])
sage: D.random_element() # random
[3, 2, 2, 3, 1, 3, 1, 3, 2, 1, 1, 2]
sage: D = Derangements('ESSENCES')
sage: D.random_element() # random
['N', 'E', 'E', 'C', 'S', 'S', 'S', 'E']
sage: D = Derangements([1,1,2,2,2])
sage: D.random_element()
[]
TESTS:
Check that index error discovered in :trac:`29974` is fixed::
sage: D = Derangements([1,1,2,2])
sage: _ = [D.random_element() for _ in range(20)]
"""
if self.__multi:
L = list(self)
if len(L) == 0:
return self.element_class(self, [])
i = randrange(len(L))
return L[i]
temp = self._rand_der()
return self.element_class(self, [self._set[ii - 1] for ii in temp])
def _fork_test_func(iterator=None): """ Test function for `fork()`. See `fork_test()` and others. """ if not iterator: import itertools iterator = itertools.count() x = None for i in iterator: m = matrix(QQ, 100, [randrange(-100,100) for i in range(100*100)]) x = m.kernel() print x return x
def test_irred(p, i1, i2, number=0, repeat=3):
K = GF(p)
P = FFDesc(p, irred(K, i1).list())
Q = FFDesc(p, irred(K, i2).list())
R = P.compositum(Q)
context = globals()
context.update(locals())
# must be done only once to avoid (dis)counting caching
tcomp = sage_timeit('P.compositum(Q)', context, number=1, repeat=1, seconds=True)
a = FFElt(P, [randrange(p) for i in range(i1)])
b = FFElt(Q, [randrange(p) for i in range(i2)])
c = FFElt(R, [randrange(p) for i in range(i1*i2)])
context = globals()
context.update(locals())
tembed_pre = sage_timeit('a.embed(b,R)', context, number=1, repeat=1, seconds=True)
tembed = sage_timeit('a.embed(b,R)', context, number=number, repeat=repeat, seconds=True)
# Burn R's precomputed polynomials
ab = a.embed(b,R)
ab.project(P,b)
ab = a.embed(b, R)
d = a.embed(b, R)
context = globals()
context.update(locals())
tproject_pre = sage_timeit('ab.project(P,b)', context, number=1, repeat=1, seconds=True)
tproject = sage_timeit('ab.project(P,b)', context, number=number, repeat=repeat, seconds=True)
tmono2dual = (sage_timeit('c.embed(P, P)', context, number=1, repeat=1, seconds=True) -
sage_timeit('c.embed(P, P)', context, number=1, repeat=1, seconds=True))
tmul = sage_timeit('c*c', context, number=number, repeat=repeat, seconds=True)
ttmul = sage_timeit('c*d', context, number=number, repeat=repeat, seconds=True)
tiso = sage_timeit('c.eltseq_dual_python(P,Q)', context, number=number, repeat=repeat, seconds=True)
tbsgs = sage_timeit('c.eltseq_dual_BSGS(P,Q)', context, number=number, repeat=repeat, seconds=True)
tmatrix = sage_timeit('c.eltseq_dual_matrix(P,Q)', context, number=number, repeat=repeat, seconds=True)
return tcomp, tembed_pre, tembed, tproject_pre, tproject, tmono2dual, tmul, ttmul, tiso, tbsgs, tmatrix
def __init__(self, dp, entity):
TB_sequential.__init__(self, dp, entity)
op_count = 10
self.add_port("x: in std_logic_vector")
self.add_port("y: in std_logic_vector")
self.add_port("z: out std_logic_vector")
# Build signal
self.add_signal(
"signal x_sti: std_logic_vector(c_N-1 downto 0) := (others=>'0')"
)
self.add_signal(
"signal y_sti: std_logic_vector (c_K-1 downto 0) := (others=>'0')"
)
self.add_signal("signal z_obs: Fp_element := c_FP_ZERO")
# Build port map
self.add_port_map("x => x_sti")
self.add_port_map("y => y_sti")
self.add_port_map("z => z_obs")
# Build function parameters
self.add_func_param("x : std_logic_vector(c_N-1 downto 0)")
self.add_func_param("y : std_logic_vector(c_K-1 downto 0)")
self.add_func_param("z : Fp_element")
# Build signal driving
self.add_drive("x_sti <= x;")
self.add_drive("y_sti <= y;")
# Build compare
self.add_compare("if (z_obs /= z) then")
self.add_compare(" logger.log_error( LF &")
self.add_compare(
" \"Error: transaction number \" & integer'image(op_count) & \" on\" & \"<BR>\" & LF &"
)
self.add_compare(
" \"x : \" & to_hstring(x_sti) & \"<BR>\" & LF &")
self.add_compare(
" \"y : \" & to_hstring(y_sti) & \"<BR>\" & LF &")
self.add_compare(
" \"yield : \" & to_string(z_obs) & \"<BR>\" & LF &")
self.add_compare(
" \"should be: \" & to_string(z) & \"<BR>\" & LF &")
self.add_compare(
" \"took \" & integer'image(cycle) & \" cycles\"")
self.add_compare(" );")
self.add_compare("else")
self.add_compare(" logger.log_note( LF &")
self.add_compare(
" \"Transaction number \" & integer'image(op_count) & \" on\" & \"<BR>\" & LF &"
)
self.add_compare(
" \"x : \" & to_hstring(x_sti) & \"<BR>\" & LF &")
self.add_compare(
" \"y : \" & to_hstring(y_sti) & \"<BR>\" & LF &")
self.add_compare(
" \"yield : \" & to_string(z_obs) & \"<BR>\" & LF &")
self.add_compare(
" \"took \" & integer'image(cycle) & \" cycles\"")
self.add_compare(" );")
self.add_compare("end if;")
self.add_action("-- Testbench actions")
self.add_action("")
self.add_action("-- " + str(op_count) + " reduction of random " +
str(2 * dp.p.nbits()) + " bits elements")
for i in range(op_count):
x = randrange(2**(2 * dp.p.nbits()) - 1)
z = mod(x, dp.p)
self.add_action("func(" + str(2 * dp.p.nbits()) + "X\"" +
Integer(x).str(base=16) + "\", -- x_sti")
self.add_action(" " + str(dp.p.nbits()) + "X\"" +
Integer(dp.p).str(base=16) +
"\", -- y_sti (modulus)")
self.add_action(" " + str(dp.p.nbits()) + "X\"" +
Integer(z).str(base=16) + "\"); -- z_ref")
self.add_action("")
self.add_action("-- Testbench actions end")