def OneHot(*xs, simplify=True, conj=True):
"""
Return an expression that means
"exactly one input function is true".
If *simplify* is ``True``, return a simplified expression.
If *conj* is ``True``, return a CNF.
Otherwise, return a DNF.
"""
xs = [Expression.box(x).node for x in xs]
terms = list()
if conj:
for x0, x1 in itertools.combinations(xs, 2):
terms.append(exprnode.or_(exprnode.not_(x0), exprnode.not_(x1)))
terms.append(exprnode.or_(*xs))
y = exprnode.and_(*terms)
else:
for i, xi in enumerate(xs):
zeros = [exprnode.not_(x) for x in xs[:i] + xs[i + 1:]]
terms.append(exprnode.and_(xi, *zeros))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def OneHot(*xs, simplify=True, conj=True):
"""
Return an expression that means
"exactly one input function is true".
If *simplify* is ``True``, return a simplified expression.
If *conj* is ``True``, return a CNF.
Otherwise, return a DNF.
"""
xs = [Expression.box(x).node for x in xs]
terms = list()
if conj:
for x0, x1 in itertools.combinations(xs, 2):
terms.append(exprnode.or_(exprnode.not_(x0),
exprnode.not_(x1)))
terms.append(exprnode.or_(*xs))
y = exprnode.and_(*terms)
else:
for i, xi in enumerate(xs):
zeros = [exprnode.not_(x) for x in xs[:i] + xs[i+1:]]
terms.append(exprnode.and_(xi, *zeros))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def NHot(n, *xs, simplify=True):
"""
Return an expression that means
"exactly N input functions are true".
If *simplify* is ``True``, return a simplified expression.
"""
if not isinstance(n, int):
raise TypeError("expected n to be an int")
if not 0 <= n <= len(xs):
fstr = "expected 0 <= n <= {}, got {}"
raise ValueError(fstr.format(len(xs), n))
xs = [Expression.box(x).node for x in xs]
num = len(xs)
terms = list()
for hot_idxs in itertools.combinations(range(num), n):
hot_idxs = set(hot_idxs)
_xs = [
xs[i] if i in hot_idxs else exprnode.not_(xs[i])
for i in range(num)
]
terms.append(exprnode.and_(*_xs))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def NHot(n, *xs, simplify=True):
"""
Return an expression that means
"exactly N input functions are true".
If *simplify* is ``True``, return a simplified expression.
"""
if not isinstance(n, int):
raise TypeError("expected n to be an int")
if not 0 <= n <= len(xs):
fstr = "expected 0 <= n <= {}, got {}"
raise ValueError(fstr.format(len(xs), n))
xs = [Expression.box(x).node for x in xs]
num = len(xs)
terms = list()
for hot_idxs in itertools.combinations(range(num), n):
hot_idxs = set(hot_idxs)
_xs = [xs[i] if i in hot_idxs else exprnode.not_(xs[i])
for i in range(num)]
terms.append(exprnode.and_(*_xs))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def And(*xs, simplify=True):
"""Expression conjunction (product, AND) operator
If *simplify* is ``True``, return a simplified expression.
"""
xs = [Expression.box(x).node for x in xs]
y = exprnode.and_(*xs)
if simplify:
y = y.simplify()
return _expr(y)
def And(*xs, simplify=True):
"""Expression conjunction (product, AND) operator
If *simplify* is ``True``, return a simplified expression.
"""
xs = [Expression.box(x).node for x in xs]
y = exprnode.and_(*xs)
if simplify:
y = y.simplify()
return _expr(y)
def Nand(*xs, simplify=True):
"""Expression NAND (not AND) operator
If *simplify* is ``True``, return a simplified expression.
"""
xs = [Expression.box(x).node for x in xs]
y = exprnode.not_(exprnode.and_(*xs))
if simplify:
y = y.simplify()
return _expr(y)
def Nand(*xs, simplify=True):
"""Expression NAND (not AND) operator
If *simplify* is ``True``, return a simplified expression.
"""
xs = [Expression.box(x).node for x in xs]
y = exprnode.not_(exprnode.and_(*xs))
if simplify:
y = y.simplify()
return _expr(y)
def OneHot0(*xs, simplify=True, conj=True):
"""
Return an expression that means
"at most one input function is true".
If *simplify* is ``True``, return a simplified expression.
If *conj* is ``True``, return a CNF.
Otherwise, return a DNF.
"""
xs = [Expression.box(x).node for x in xs]
terms = list()
if conj:
for x0, x1 in itertools.combinations(xs, 2):
terms.append(exprnode.or_(exprnode.not_(x0), exprnode.not_(x1)))
y = exprnode.and_(*terms)
else:
for _xs in itertools.combinations(xs, len(xs) - 1):
terms.append(exprnode.and_(*[exprnode.not_(x) for x in _xs]))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def Majority(*xs, simplify=True, conj=False):
"""
Return an expression that means
"the majority of input functions are true".
If *simplify* is ``True``, return a simplified expression.
If *conj* is ``True``, return a CNF.
Otherwise, return a DNF.
"""
xs = [Expression.box(x).node for x in xs]
if conj:
terms = list()
for _xs in itertools.combinations(xs, (len(xs) + 1) // 2):
terms.append(exprnode.or_(*_xs))
y = exprnode.and_(*terms)
else:
terms = list()
for _xs in itertools.combinations(xs, len(xs) // 2 + 1):
terms.append(exprnode.and_(*_xs))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def Majority(*xs, simplify=True, conj=False):
"""
Return an expression that means
"the majority of input functions are true".
If *simplify* is ``True``, return a simplified expression.
If *conj* is ``True``, return a CNF.
Otherwise, return a DNF.
"""
xs = [Expression.box(x).node for x in xs]
if conj:
terms = list()
for _xs in itertools.combinations(xs, (len(xs) + 1) // 2):
terms.append(exprnode.or_(*_xs))
y = exprnode.and_(*terms)
else:
terms = list()
for _xs in itertools.combinations(xs, len(xs) // 2 + 1):
terms.append(exprnode.and_(*_xs))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def OneHot0(*xs, simplify=True, conj=True):
"""
Return an expression that means
"at most one input function is true".
If *simplify* is ``True``, return a simplified expression.
If *conj* is ``True``, return a CNF.
Otherwise, return a DNF.
"""
xs = [Expression.box(x).node for x in xs]
terms = list()
if conj:
for x0, x1 in itertools.combinations(xs, 2):
terms.append(exprnode.or_(exprnode.not_(x0),
exprnode.not_(x1)))
y = exprnode.and_(*terms)
else:
for _xs in itertools.combinations(xs, len(xs) - 1):
terms.append(exprnode.and_(*[exprnode.not_(x) for x in _xs]))
y = exprnode.or_(*terms)
if simplify:
y = y.simplify()
return _expr(y)
def AchillesHeel(*xs, simplify=True):
r"""
Return the Achille's Heel function, defined as:
:math:`\prod_{i=0}^{n/2-1}{X_{2i} + X_{2i+1}}`.
If *simplify* is ``True``, return a simplified expression.
"""
nargs = len(xs)
if nargs & 1:
fstr = "expected an even number of arguments, got {}"
raise ValueError(fstr.format(nargs))
xs = [Expression.box(x).node for x in xs]
y = exprnode.and_(*[exprnode.or_(xs[2*i], xs[2*i+1])
for i in range(nargs // 2)])
if simplify:
y = y.simplify()
return _expr(y)
def AchillesHeel(*xs, simplify=True):
r"""
Return the Achille's Heel function, defined as:
:math:`\prod_{i=0}^{n/2-1}{X_{2i} + X_{2i+1}}`.
If *simplify* is ``True``, return a simplified expression.
"""
nargs = len(xs)
if nargs & 1:
fstr = "expected an even number of arguments, got {}"
raise ValueError(fstr.format(nargs))
xs = [Expression.box(x).node for x in xs]
y = exprnode.and_(
*[exprnode.or_(xs[2 * i], xs[2 * i + 1]) for i in range(nargs // 2)])
if simplify:
y = y.simplify()
return _expr(y)
def Mux(fs, sel, simplify=True):
"""
Return an expression that multiplexes a sequence of input functions over a
sequence of select functions.
"""
# convert Mux([a, b], x) to Mux([a, b], [x])
if isinstance(sel, Expression):
sel = [sel]
if len(sel) < clog2(len(fs)):
fstr = "expected at least {} select bits, got {}"
raise ValueError(fstr.format(clog2(len(fs)), len(sel)))
it = boolfunc.iter_terms(sel)
y = exprnode.or_(*[exprnode.and_(f.node, *[lit.node for lit in next(it)])
for f in fs])
if simplify:
y = y.simplify()
return _expr(y)
def Mux(fs, sel, simplify=True):
"""
Return an expression that multiplexes a sequence of input functions over a
sequence of select functions.
"""
# convert Mux([a, b], x) to Mux([a, b], [x])
if isinstance(sel, Expression):
sel = [sel]
if len(sel) < clog2(len(fs)):
fstr = "expected at least {} select bits, got {}"
raise ValueError(fstr.format(clog2(len(fs)), len(sel)))
it = boolfunc.iter_terms(sel)
y = exprnode.or_(
*[exprnode.and_(f.node, *[lit.node for lit in next(it)]) for f in fs])
if simplify:
y = y.simplify()
return _expr(y)
def __and__(self, other):
other_node = self.box(other).node
return _expr(exprnode.and_(self.node, other_node))
def __and__(self, other):
other_node = self.box(other).node
return _expr(exprnode.and_(self.node, other_node))
