def brent_kung_add(A, B, cin=0):
"""Return symbolic logic for an N-bit Brent-Kung adder."""
if len(A) != len(B):
raise ValueError("expected A and B to be equal length")
N = len(A)
# generate/propagate logic
gs = [A[i] & B[i] for i in range(N)]
ps = [A[i] ^ B[i] for i in range(N)]
# carry tree
for i in range(floor(log(N, 2))):
step = 2**i
for start in range(2**(i + 1) - 1, N, 2**(i + 1)):
gs[start] = gs[start] | ps[start] & gs[start - step]
ps[start] = ps[start] & ps[start - step]
# inverse carry tree
for i in range(floor(log(N, 2)) - 2, -1, -1):
start = 2**(i + 1) - 1
step = 2**i
while start + step < N:
gs[start + step] = gs[start + step] | ps[start + step] & gs[start]
ps[start + step] = ps[start + step] & ps[start]
start += step
# sum logic
ss = [A[0] ^ B[0] ^ cin]
ss += [A[i] ^ B[i] ^ gs[i - 1] for i in range(1, N)]
return farray(ss), farray(gs)
def brent_kung_add(A, B, cin=0):
"""Return symbolic logic for an N-bit Brent-Kung adder."""
if len(A) != len(B):
raise ValueError("expected A and B to be equal length")
N = len(A)
# generate/propagate logic
gs = [A[i] & B[i] for i in range(N)]
ps = [A[i] ^ B[i] for i in range(N)]
# carry tree
for i in range(floor(log(N, 2))):
step = 2**i
for start in range(2**(i+1)-1, N, 2**(i+1)):
gs[start] = gs[start] | ps[start] & gs[start-step]
ps[start] = ps[start] & ps[start-step]
# inverse carry tree
for i in range(floor(log(N, 2))-2, -1, -1):
start = 2**(i+1)-1
step = 2**i
while start + step < N:
gs[start+step] = gs[start+step] | ps[start+step] & gs[start]
ps[start+step] = ps[start+step] & ps[start]
start += step
# sum logic
ss = [A[0] ^ B[0] ^ cin]
ss += [A[i] ^ B[i] ^ gs[i-1] for i in range(1, N)]
return farray(ss), farray(gs)
def __radd__(self, other):
from pyeda.boolalg.bfarray import farray
if isinstance(other, Function):
return farray([other] + [self])
elif isinstance(other, farray):
return farray(list(other.flat) + [self])
else:
raise TypeError("expected Function or farray")
def ripple_carry_add(A, B, cin=0):
"""Return symbolic logic for an N-bit ripple carry adder."""
if len(A) != len(B):
raise ValueError("expected A and B to be equal length")
ss, cs = list(), list()
for i, a in enumerate(A):
c = (cin if i == 0 else cs[i-1])
ss.append(a ^ B[i] ^ c)
cs.append(a & B[i] | a & c | B[i] & c)
return farray(ss), farray(cs)
def ripple_carry_add(A, B, cin=0):
"""Return symbolic logic for an N-bit ripple carry adder."""
if len(A) != len(B):
raise ValueError("expected A and B to be equal length")
ss, cs = list(), list()
for i, a in enumerate(A):
c = (cin if i == 0 else cs[i - 1])
ss.append(a ^ B[i] ^ c)
cs.append(a & B[i] | a & c | B[i] & c)
return farray(ss), farray(cs)
def __add__(self, other):
"""Concatenation operator
The *other* argument may be a Function or an farray.
"""
from pyeda.boolalg.bfarray import farray
if other in {0, 1}:
return farray([self] + [self.box(other)])
elif isinstance(other, Function):
return farray([self] + [other])
elif isinstance(other, farray):
return farray([self] + list(other.flat))
else:
raise TypeError("expected Function or farray")
def __add__(self, other):
"""Concatenation operator
The *other* argument may be a Function or an farray.
"""
from pyeda.boolalg.bfarray import farray
if other in {0, 1}:
return farray([self] + [self.box(other)])
elif isinstance(other, Function):
return farray([self] + [other])
elif isinstance(other, farray):
return farray([self] + list(other.flat))
else:
raise TypeError("expected Function or farray")
def __mul__(self, other):
from pyeda.boolalg.bfarray import farray
if type(other) is not int:
raise TypeError("expected multiplier to be an int")
if other < 0:
raise ValueError("expected multiplier to be non-negative")
return farray([self] * other)
def kogge_stone_add(A, B, cin=0):
"""Return symbolic logic for an N-bit Kogge-Stone adder."""
if len(A) != len(B):
raise ValueError("expected A and B to be equal length")
N = len(A)
# generate/propagate logic
gs = [A[i] & B[i] for i in range(N)]
ps = [A[i] ^ B[i] for i in range(N)]
for i in range(clog2(N)):
start = 1 << i
for j in range(start, N):
gs[j] = gs[j] | ps[j] & gs[j-start]
ps[j] = ps[j] & ps[j-start]
# sum logic
ss = [A[0] ^ B[0] ^ cin]
ss += [A[i] ^ B[i] ^ gs[i-1] for i in range(1, N)]
return farray(ss), farray(gs)
def kogge_stone_add(A, B, cin=0):
"""Return symbolic logic for an N-bit Kogge-Stone adder."""
if len(A) != len(B):
raise ValueError("expected A and B to be equal length")
N = len(A)
# generate/propagate logic
gs = [A[i] & B[i] for i in range(N)]
ps = [A[i] ^ B[i] for i in range(N)]
for i in range(clog2(N)):
start = 1 << i
for j in range(start, N):
gs[j] = gs[j] | ps[j] & gs[j - start]
ps[j] = ps[j] & ps[j - start]
# sum logic
ss = [A[0] ^ B[0] ^ cin]
ss += [A[i] ^ B[i] ^ gs[i - 1] for i in range(1, N)]
return farray(ss), farray(gs)
def __mul__(self, num):
"""Repetition operator"""
from pyeda.boolalg.bfarray import farray
if not isinstance(num, int):
raise TypeError("expected multiplier to be an int")
if num < 0:
raise ValueError("expected multiplier to be non-negative")
return farray([self] * num)
def __mul__(self, num):
"""Repetition operator"""
from pyeda.boolalg.bfarray import farray
if type(num) is not int:
raise TypeError("expected multiplier to be an int")
if num < 0:
raise ValueError("expected multiplier to be non-negative")
return farray([self] * num)
def test_degenerate():
xs = farray([])
# These are a bit silly
assert xs.uor() == 0
assert xs.unor() == 1
assert xs.uand() == 1
assert xs.unand() == 0
assert xs.uxor() == 0
assert xs.uxnor() == 1
assert_raises(NotImplementedError, xs.decode)
def __radd__(self, other):
from pyeda.boolalg.bfarray import farray
if other in {0, 1}:
return farray([self.box(other)] + [self])
else:
raise TypeError("expected Function or farray")
def gray2bin(G):
"""Convert a gray-coded vector into a binary-coded vector."""
return farray([G[i:].uxor() for i, _ in enumerate(G)])
def __radd__(self, other):
from pyeda.boolalg.bfarray import farray
if other in {0, 1}:
return farray([self.box(other)] + [self])
else:
raise TypeError("expected Function or farray")
def test_farray():
# expected shape volume to match items
assert_raises(ValueError, farray, [X[0], X[1]], shape=((0, 42), ))
# could not determine ftype parameter
assert_raises(ValueError, farray, [])
# expected ftype to be a type
assert_raises(TypeError, farray, [X[0], X[1]], ftype=42)
# expected ftype to match items
assert_raises(ValueError, farray, [X[0], X[1]], ftype=BinaryDecisionDiagram)
# expected ftype to be a property subclass of Function
assert_raises(TypeError, farray, [], ftype=int)
# expected a sequence of Function
assert_raises(TypeError, farray, 42)
assert_raises(TypeError, farray, [1, 2, 3, 4])
# expected uniform dimensions
assert_raises(ValueError, farray, [[a, b], [w, x, y, z], 42])
assert_raises(ValueError, farray, [[a, b], [w, x, y, z]])
# expected uniform types
assert_raises(ValueError, farray, [[a, b], [c, bddvar('d')]])
assert_raises(ValueError, farray, [[a, b], [bddvar('c'), bddvar('d')]])
# _check_shape errors
assert_raises(ValueError, farray, [a, b, c, d], shape=((-1, 3), ))
assert_raises(ValueError, farray, [a, b, c, d], shape=((3, -1), ))
assert_raises(ValueError, farray, [a, b, c, d], shape=((5, 1), ))
assert_raises(TypeError, farray, [a, b, c, d], shape=(('foo', 'bar'), ))
assert_raises(TypeError, farray, [a, b, c, d], shape=42)
temp = farray([[a, b], [c, d]])
assert str(temp) == """\
farray([[a, b],
[c, d]])\
"""
# __str__
Z = exprvars('z', 2, 2, 2)
assert str(Z) == """\
farray([[[z[0,0,0], z[0,0,1]],
[z[0,1,0], z[0,1,1]]],
[[z[1,0,0], z[1,0,1]],
[z[1,1,0], z[1,1,1]]]])\
"""
assert str(farray([], ftype=Expression)) == "farray([])"
# __getitem__
# expected <= M slice dimensions, got N
assert_raises(ValueError, X.__getitem__, (2, 2))
sel = exprvars('s', 2)
assert str(X[sel]) == "Or(And(~s[0], ~s[1], x[0]), And(s[0], ~s[1], x[1]), And(~s[0], s[1], x[2]), And(s[0], s[1], x[3]))"
assert str(X[:2][sel[0]]) == "Or(And(~s[0], x[0]), And(s[0], x[1]))"
# expected clog2(N) bits
assert_raises(ValueError, X.__getitem__, sel[0])
# slice step not supported
assert_raises(ValueError, X.__getitem__, slice(None, None, 2))
# type error
assert_raises(TypeError, X.__getitem__, 'foo')
# norm_index
assert X[-1] is X[3]
assert_raises(IndexError, X.__getitem__, 42)
# norm_indices
assert X[-3:-1]._items == [X[-3], X[-2]]
assert not X[-8:-10]._items
assert not X[-10:-8]._items
assert not X[8:10]._items
assert not X[10:8]._items
assert not X[3:1]._items
# __setitem__
Z = exprzeros(4, 4)
Z[0,0] = X[0]
assert Z._items[0] is X[0]
# expected item to be a Function
assert_raises(TypeError, Z.__setitem__, (0, 0), 42)
Z[0,:] = X[:4]
assert Z._items[0:4] == [X[0], X[1], X[2], X[3]]
# expected item to be an farray
assert_raises(TypeError, Z.__setitem__, (0, slice(None, None, None)), 42)
# expected item.size = ...
assert_raises(ValueError, Z.__setitem__, ..., X[:2])
# slice step not supported
assert_raises(ValueError, X.__setitem__, slice(None, None, 2), 42)
# type error
assert_raises(TypeError, X.__setitem__, 'foo', 42)
# __add__
assert (0 + X)._items[0].is_zero()
assert (X + 0)._items[4].is_zero()
assert (Y[0] + X)._items[0] is Y[0]
assert (X + Y[0])._items[4] is Y[0]
assert (X[:2] + Y[2:])._items == [X[0], X[1], Y[2], Y[3]]
# expected Function or farray
assert_raises(TypeError, X.__add__, 42)
assert_raises(TypeError, X.__radd__, 42)
A = exprvars('a', 2, 5, 6)
B = exprvars('b', 2, 5, 6)
C = exprvars('c', (1, 3), 5, 6)
# regular MDA will retain shape
assert (A+B).shape == ((0, 4), (0, 5), (0, 6))
# irregular MDA will not
assert (A+C).shape == ((0, 4*5*6), )
# regular MDA will retain shape
assert (A*2).shape == ((0, 4), (0, 5), (0, 6))
# irregular MDA will not
assert (C*2).shape == ((0, 4*5*6), )
# __mul__
# expected multiplier to be an int
assert_raises(TypeError, X.__mul__, 'foo')
# expected multiplier to be non-negative
assert_raises(ValueError, X.__mul__, -2)
assert (X[:2] * 2)._items == [X[0], X[1], X[0], X[1]]
assert (2 * X[:2])._items == [X[0], X[1], X[0], X[1]]
# offsets
Z = exprzeros((1, 5), (17, 21))
assert Z.offsets == (1, 17)
# reshape
assert Z.reshape(4, 4).shape == ((0, 4), (0, 4))
# expected shape with equal volume
assert_raises(ValueError, Z.reshape, 42, 42)
# restrict
assert str(X.vrestrict({X: '0101'})) == "farray([0, 1, 0, 1])"
# compose
assert X.compose({X[0]: Y[0]})._items[0] == Y[0]
# to_uint / to_int
assert uint2exprs(42).to_uint() == 42
assert uint2exprs(42, 8).to_uint() == 42
# expected all functions to be a constant (0 or 1) form
assert_raises(ValueError, X.to_uint)
# expected num >= 0
assert_raises(ValueError, uint2exprs, -1)
# overflow
assert_raises(ValueError, uint2exprs, 42, 2)
assert_raises(ValueError, int2exprs, 42, 2)
assert int2exprs(-42).to_int() == -42
assert int2exprs(-42, 8).to_int() == -42
assert int2exprs(42).to_int() == 42
assert int2exprs(42, 8).to_int() == 42
# zext, sext
assert X.zext(1)[4].is_zero()
assert X.sext(1)[4] is X[3]
# __invert__, __or__, __and__, __xor__
assert str(~X) == "farray([~x[0], ~x[1], ~x[2], ~x[3]])"
assert str(X | Y) == "farray([Or(x[0], y[0]), Or(x[1], y[1]), Or(x[2], y[2]), Or(x[3], y[3])])"
assert str(X & Y) == "farray([And(x[0], y[0]), And(x[1], y[1]), And(x[2], y[2]), And(x[3], y[3])])"
assert str(X ^ Y) == "farray([Xor(x[0], y[0]), Xor(x[1], y[1]), Xor(x[2], y[2]), Xor(x[3], y[3])])"
# _op_shape
# expected farray input
assert_raises(TypeError, X.__or__, 42)
Z = exprvars('z', 2, 2)
assert str(X | Z) == "farray([Or(x[0], z[0,0]), Or(x[1], z[0,1]), Or(x[2], z[1,0]), Or(x[3], z[1,1])])"
Z = exprvars('z', 2, 3)
# expected operand sizes to match
assert_raises(ValueError, X.__or__, Z)
# lsh, rsh
assert str(X.lsh(0)) == "(farray([x[0], x[1], x[2], x[3]]), farray([]))"
assert str(X << 0) == "farray([x[0], x[1], x[2], x[3]])"
assert str(X.lsh(2)) == "(farray([0, 0, x[0], x[1]]), farray([x[2], x[3]]))"
assert str(X << 2) == "farray([0, 0, x[0], x[1]])"
assert str(X << (2, Y[:2])) == "farray([y[0], y[1], x[0], x[1]])"
assert str(X.rsh(0)) == "(farray([x[0], x[1], x[2], x[3]]), farray([]))"
assert str(X >> 0) == "farray([x[0], x[1], x[2], x[3]])"
assert str(X.rsh(2)) == "(farray([x[2], x[3], 0, 0]), farray([x[0], x[1]]))"
assert str(X >> 2) == "farray([x[2], x[3], 0, 0])"
assert str(X >> (2, Y[:2])) == "farray([x[2], x[3], y[0], y[1]])"
assert_raises(TypeError, X.__lshift__, 'foo')
assert_raises(ValueError, X.__lshift__, -1)
assert_raises(ValueError, X.__lshift__, (2, Y))
assert_raises(TypeError, X.__rshift__, 'foo')
assert_raises(ValueError, X.__rshift__, -1)
assert_raises(ValueError, X.__rshift__, (2, Y))
# arsh
assert str(X.arsh(0)) == "(farray([x[0], x[1], x[2], x[3]]), farray([]))"
assert str(X.arsh(2)) == "(farray([x[2], x[3], x[3], x[3]]), farray([x[0], x[1]]))"
assert_raises(ValueError, X.arsh, -1)
# unary ops
assert str(X.uor()) == "Or(x[0], x[1], x[2], x[3])"
assert str(X.unor()) == "Not(Or(x[0], x[1], x[2], x[3]))"
assert str(X.uand()) == "And(x[0], x[1], x[2], x[3])"
assert str(X.unand()) == "Not(And(x[0], x[1], x[2], x[3]))"
assert str(X.uxor()) == "Xor(x[0], x[1], x[2], x[3])"
assert str(X.uxnor()) == "Not(Xor(x[0], x[1], x[2], x[3]))"
# decode
assert str(farray([], ftype=Expression).decode()) == "farray([1])"
assert str(X[:2].decode()) == "farray([And(~x[0], ~x[1]), And(x[0], ~x[1]), And(~x[0], x[1]), And(x[0], x[1])])"
def gray2bin(G):
"""Convert a gray-coded vector into a binary-coded vector."""
return farray([G[i:].uxor() for i, _ in enumerate(G)])
