class ExactRep(object):
"""Fixed-point representation of arrays with auxilliary bits such
that + - * / ops are all exactly invertible (except for
overflow)."""
def __init__(self, val, from_intrep=False, nbits=64):
self.dtype = nbits_to_dtype[nbits]
self.radix_scale = 2**(nbits / 2)
self.rational_bits = nbits / 4
if from_intrep:
self.intrep = val
else:
self.intrep = self.float_to_intrep(val)
self.aux = InfoBuffer(len(val))
def randomize(self, rs):
self.aux.randomize(rs)
return self
def copy(self):
return deepcopy(self)
def add(self, A):
"""Reversible addition of vector or scalar A."""
self.intrep += self.float_to_intrep(A)
return self
def sub(self, A):
self.add(-A)
return self
def rational_mul(self, n, d):
self.aux.push(self.intrep % d, d) # Store remainder bits externally
self.intrep /= d # Divide by denominator
self.intrep *= n # Multiply by numerator
self.intrep += self.aux.pop(n) # Pack bits into the remainder
def mul(self, a):
n, d = self.float_to_rational(a)
self.rational_mul(n, d)
return self
def div(self, a):
n, d = self.float_to_rational(a)
self.rational_mul(d, n)
return self
def float_to_rational(self, a):
assert np.all(a > 0.0)
d = 2**self.rational_bits / np.fix(a+1).astype(int)
n = np.fix(a * d).astype(int) # TODO: fix case n == 0
return n, d
def float_to_intrep(self, x):
return (x * self.radix_scale).astype(self.dtype)
@property
def val(self):
return self.intrep.astype(np.float64) / self.radix_scale
def __init__(self, val, from_intrep=False, nbits=64):
self.dtype = nbits_to_dtype[nbits]
self.radix_scale = 2**(nbits / 2)
self.rational_bits = nbits / 4
if from_intrep:
self.intrep = val
else:
self.intrep = self.float_to_intrep(val)
self.aux = InfoBuffer(len(val))