def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero")
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
if other._prec == 4: # frac
error("Did not expected to divide by fraction")
# If fraction will be zero.
if self.val == 0.0:
return self
# NOTE: We expect expanded objects here i.e., Product([FloatValue])
# should not be present.
# Handle types appropriately.
if other._prec == 0: # float
return create_float(self.val / other.val)
# If other is a symbol, return a simple fraction.
elif other._prec == 1: # sym
return create_fraction(self, other)
# Don't handle division by sum.
elif other._prec == 3: # sum
# TODO: Here we could do: 4 / (2*x + 4*y) -> 2/(x + 2*y).
return create_fraction(self, other)
# If other is a product, remove any float value to avoid
# 4 / (2*x), this will return 2/x.
val = 1.0
for v in other.vrs:
if v._prec == 0: # float
val *= v.val
# If we had any floats, create new numerator and only use 'real' variables
# from the product in the denominator.
if val != 1.0:
# Check if we need to create a new denominator.
# TODO: Just use other.vrs[1:] instead.
if len(other.get_vrs()) > 1:
return create_fraction(create_float(self.val / val),
create_product(other.get_vrs()))
# TODO: Because we expect all products to be expanded we shouldn't need
# to check for this case, just use other.vrs[1].
elif len(other.get_vrs()) == 1:
return create_fraction(create_float(self.val / val),
other.vrs[1])
error("No variables left in denominator")
# Nothing left to do.
return create_fraction(self, other)
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero")
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
if other._prec == 4: # frac
error("Did not expected to divide by fraction")
# If fraction will be zero.
if self.val == 0.0:
return self
# NOTE: We expect expanded objects here i.e., Product([FloatValue])
# should not be present.
# Handle types appropriately.
if other._prec == 0: # float
return create_float(self.val/other.val)
# If other is a symbol, return a simple fraction.
elif other._prec == 1: # sym
return create_fraction(self, other)
# Don't handle division by sum.
elif other._prec == 3: # sum
# TODO: Here we could do: 4 / (2*x + 4*y) -> 2/(x + 2*y).
return create_fraction(self, other)
# If other is a product, remove any float value to avoid
# 4 / (2*x), this will return 2/x.
val = 1.0
for v in other.vrs:
if v._prec == 0: # float
val *= v.val
# If we had any floats, create new numerator and only use 'real' variables
# from the product in the denominator.
if val != 1.0:
# Check if we need to create a new denominator.
# TODO: Just use other.vrs[1:] instead.
if len(other.get_vrs()) > 1:
return create_fraction(create_float(self.val/val), create_product(other.get_vrs()))
# TODO: Because we expect all products to be expanded we shouldn't need
# to check for this case, just use other.vrs[1].
elif len(other.get_vrs()) == 1:
return create_fraction(create_float(self.val/val), other.vrs[1])
error("No variables left in denominator")
# Nothing left to do.
return create_fraction(self, other)
def __sub__(self, other):
"Subtract other objects."
# Return a new sum
if other._prec == 4 and self.denom == other.denom: # frac
num = create_sum([self.num, create_product([FloatValue(-1), other.num])]).expand()
return create_fraction(num, self.denom)
return create_sum([self, create_product([FloatValue(-1), other])])
def __add__(self, other):
"Addition by other objects."
# Add two fractions if their denominators are equal by creating
# (expanded) sum of their numerators.
if other._prec == 4 and self.denom == other.denom: # frac
return create_fraction(create_sum([self.num, other.num]).expand(), self.denom)
return create_sum([self, other])
def _group_fractions(expr):
"Group Fractions in a Sum: 2/x + y/x -> (2 + y)/x."
if expr._prec != 3: # sum
return expr
# Loop variables and group those with common denominator.
not_frac = []
fracs = {}
for v in expr.vrs:
if v._prec == 4: # frac
if v.denom in fracs:
fracs[v.denom][1].append(v.num)
fracs[v.denom][0] += 1
else:
fracs[v.denom] = [1, [v.num], v]
continue
not_frac.append(v)
if not fracs:
return expr
# Loop all fractions and create new ones using an appropriate numerator.
for k, v in sorted(fracs.iteritems()):
if v[0] > 1:
# TODO: Is it possible to avoid expanding the Sum?
# I think we have to because x/a + 2*x/a -> 3*x/a.
not_frac.append(create_fraction(create_sum(v[1]).expand(), k))
else:
not_frac.append(v[2])
# Create return value.
if len(not_frac) > 1:
return create_sum(not_frac)
return not_frac[0]
def __add__(self, other):
"Addition by other objects."
# Add two fractions if their denominators are equal by creating
# (expanded) sum of their numerators.
if other._prec == 4 and self.denom == other.denom: # frac
return create_fraction(
create_sum([self.num, other.num]).expand(), self.denom)
return create_sum([self, other])
def __sub__(self, other):
"Subtract other objects."
# Return a new sum
if other._prec == 4 and self.denom == other.denom: # frac
num = create_sum(
[self.num,
create_product([FloatValue(-1), other.num])]).expand()
return create_fraction(num, self.denom)
return create_sum([self, create_product([FloatValue(-1), other])])
def reduce_ops(self):
# Try to reduce operations by reducing the numerator and denominator.
# FIXME: We assume expanded variables here, so any common variables in
# the numerator and denominator are already removed i.e, there is no
# risk of encountering (x + x*y) / x -> x*(1 + y)/x -> (1 + y).
if self._reduced:
return self._reduced
num = self.num.reduce_ops()
# Only return a new Fraction if we still have a denominator.
if self.denom:
self._reduced = create_fraction(num, self.denom.reduce_ops())
else:
self._reduced = num
return self._reduced
def reduce_ops(self):
# Try to reduce operations by reducing the numerator and denominator.
# FIXME: We assume expanded variables here, so any common variables in
# the numerator and denominator are already removed i.e, there is no
# risk of encountering (x + x*y) / x -> x*(1 + y)/x -> (1 + y).
if self._reduced:
return self._reduced
num = self.num.reduce_ops()
# Only return a new Fraction if we still have a denominator.
if self.denom:
self._reduced = create_fraction(num, self.denom.reduce_ops())
else:
self._reduced = num
return self._reduced
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# If fraction will be zero.
if self.val == 0.0:
return create_float(0)
# NOTE: assuming that we get expanded variables.
# If other is a Sum we can only return a fraction.
# TODO: We could check for equal sums if Sum.__eq__ could be trusted.
# As it is now (2*x + y) == (3*x + y), which works for the other things I do.
# NOTE: Expect that other is expanded i.e., x + x -> 2*x which can be handled.
# TODO: Fix (1 + y) / (x + x*y) -> 1 / x
# Will this be handled when reducing operations on a fraction?
if other._prec == 3: # sum
return create_fraction(self, other)
# NOTE: We expect expanded sub-expressions with no nested operators.
# Create list of new products using the '*' operator.
# TODO: Is this efficient?
new_fracs = [v / other for v in self.vrs]
# Remove zero valued terms.
# TODO: Can this still happen?
new_fracs = [v for v in new_fracs if v.val != 0.0]
# Create new sum.
# TODO: No need to call expand here, using the '/' operator should have
# taken care of this.
if not new_fracs:
return create_float(0)
elif len(new_fracs) > 1:
return create_sum(new_fracs)
return new_fracs[0]
def __div__(self, other):
"Division by other objects."
# NOTE: We assume expanded objects.
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# Return 1 if the two symbols are equal.
if self._repr == other._repr:
return create_float(1)
# If other is a Sum we can only return a fraction.
# TODO: Refine this later such that x / (x + x*y) -> 1 / (1 + y)?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# Create numerator and list for denominator.
num = [self]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Need copies, so can't just do denom = other.vrs.
denom += other.vrs
# fraction.
else:
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
error("Did not expected to divide by fraction.")
# Remove one instance of self in numerator and denominator if
# present in denominator i.e., x/(x*y) --> 1/y.
if self in denom:
denom.remove(self)
num.remove(self)
# Loop entries in denominator and move float value to numerator.
for d in denom:
# Add the inverse of a float to the numerator, remove it from
# the denominator and continue.
if d._prec == 0: # float
num.append(create_float(1.0 / other.val))
denom.remove(d)
continue
# Create appropriate return value depending on remaining data.
# Can only be for x / (2*y*z) -> 0.5*x / (y*z).
if len(num) > 1:
num = create_product(num)
# x / (y*z) -> x/(y*z),
elif num:
num = num[0]
# else x / (x*y) -> 1/y.
else:
num = create_float(1)
# If we have a long denominator, create product and fraction.
if len(denom) > 1:
return create_fraction(num, create_product(denom))
# If we do have a denominator, but only one variable don't create a
# product, just return a fraction using the variable as denominator.
elif denom:
return create_fraction(num, denom[0])
# If we don't have any donominator left, return the numerator.
# x / 2.0 -> 0.5*x.
return num.expand()
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# If fraction will be zero.
if self.val == 0.0:
return self.vrs[0]
# If other is a Sum we can only return a fraction.
# NOTE: Expect that other is expanded i.e., x + x -> 2*x which can be handled
# TODO: Fix x / (x + x*y) -> 1 / (1 + y).
# Or should this be handled when reducing a fraction?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# NOTE: assuming that we get expanded variables.
# Copy numerator, and create list for denominator.
num = self.vrs[:]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Get copy.
denom = other.vrs[:]
# fraction.
else:
error("Did not expected to divide by fraction.")
# Loop entries in denominator and remove from numerator (and denominator).
for d in denom[:]:
# Add the inverse of a float to the numerator and continue.
if d._prec == 0: # float
num.append(create_float(1.0 / d.val))
denom.remove(d)
continue
if d in num:
num.remove(d)
denom.remove(d)
# Create appropriate return value depending on remaining data.
if len(num) > 1:
# TODO: Make this more efficient?
# Create product and expand to reduce
# Product([5, 0.2]) == Product([1]) -> Float(1).
num = create_product(num).expand()
elif num:
num = num[0]
# If all variables in the numerator has been eliminated we need to add '1'.
else:
num = create_float(1)
if len(denom) > 1:
return create_fraction(num, create_product(denom))
elif denom:
return create_fraction(num, denom[0])
# If we no longer have a denominater, just return the numerator.
return num
def __div__(self, other):
"Division by other objects."
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# If fraction will be zero.
if self.val == 0.0:
return self.vrs[0]
# If other is a Sum we can only return a fraction.
# NOTE: Expect that other is expanded i.e., x + x -> 2*x which can be handled
# TODO: Fix x / (x + x*y) -> 1 / (1 + y).
# Or should this be handled when reducing a fraction?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# NOTE: assuming that we get expanded variables.
# Copy numerator, and create list for denominator.
num = self.vrs[:]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Get copy.
denom = other.vrs[:]
# fraction.
else:
error("Did not expected to divide by fraction.")
# Loop entries in denominator and remove from numerator (and denominator).
for d in denom[:]:
# Add the inverse of a float to the numerator and continue.
if d._prec == 0: # float
num.append(create_float(1.0/d.val))
denom.remove(d)
continue
if d in num:
num.remove(d)
denom.remove(d)
# Create appropriate return value depending on remaining data.
if len(num) > 1:
# TODO: Make this more efficient?
# Create product and expand to reduce
# Product([5, 0.2]) == Product([1]) -> Float(1).
num = create_product(num).expand()
elif num:
num = num[0]
# If all variables in the numerator has been eliminated we need to add '1'.
else:
num = create_float(1)
if len(denom) > 1:
return create_fraction(num, create_product(denom))
elif denom:
return create_fraction(num, denom[0])
# If we no longer have a denominater, just return the numerator.
return num
def reduce_vartype(self, var_type):
"""Reduce expression with given var_type. It returns a tuple
(found, remain), where 'found' is an expression that only has variables
of type == var_type. If no variables are found, found=(). The 'remain'
part contains the leftover after division by 'found' such that:
self = found*remain."""
# Reduce the numerator by the var type.
# print "self.num._prec: ", self.num._prec
# print "self.num: ", self.num
if self.num._prec == 3:
foo = self.num.reduce_vartype(var_type)
if len(foo) == 1:
num_found, num_remain = foo[0]
# num_found, num_remain = self.num.reduce_vartype(var_type)[0]
else:
# meg: I have only a marginal idea of what I'm doing here!
# print "here: "
new_sum = []
for num_found, num_remain in foo:
if num_found == ():
new_sum.append(create_fraction(num_remain, self.denom))
else:
new_sum.append(
create_fraction(
create_product([num_found, num_remain]),
self.denom))
return create_sum(new_sum).expand().reduce_vartype(var_type)
else:
# num_found, num_remain = self.num.reduce_vartype(var_type)
foo = self.num.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
num_found, num_remain = foo[0]
# # TODO: Remove this test later, expansion should have taken care of
# # no denominator.
# if not self.denom:
# error("This fraction should have been expanded.")
# If the denominator is not a Sum things are straightforward.
denom_found = None
denom_remain = None
# print "self.denom: ", self.denom
# print "self.denom._prec: ", self.denom._prec
if self.denom._prec != 3: # sum
# denom_found, denom_remain = self.denom.reduce_vartype(var_type)
foo = self.denom.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
denom_found, denom_remain = foo[0]
# If we have a Sum in the denominator, all terms must be reduced by
# the same terms to make sense
else:
remain = []
for m in self.denom.vrs:
# d_found, d_remain = m.reduce_vartype(var_type)
foo = m.reduce_vartype(var_type)
d_found, d_remain = foo[0]
# If we've found a denom, but the new found is different from
# the one already found, terminate loop since it wouldn't make
# sense to reduce the fraction.
# TODO: handle I0/((I0 + I1)/(G0 + G1) + (I1 + I2)/(G1 + G2))
# better than just skipping.
# if len(foo) != 1:
# raise RuntimeError("This case is not handled")
if len(foo) != 1 or (denom_found is not None
and repr(d_found) != repr(denom_found)):
# If the denominator of the entire sum has a type which is
# lower than or equal to the vartype that we are currently
# reducing for, we have to move it outside the expression
# as well.
# TODO: This is quite application specific, but I don't see
# how we can do it differently at the moment.
if self.denom.t <= var_type:
if not num_found:
num_found = create_float(1)
return [(create_fraction(num_found,
self.denom), num_remain)]
else:
# The remainder is always a fraction
return [(num_found,
create_fraction(num_remain, self.denom))]
# Update denom found and add remainder.
denom_found = d_found
remain.append(d_remain)
# There is always a non-const remainder if denominator was a sum.
denom_remain = create_sum(remain)
# print "den f: ", denom_found
# print "den r: ", denom_remain
# If we have found a common denominator, but no found numerator,
# create a constant.
# TODO: Add more checks to avoid expansion.
found = None
# There is always a remainder.
remain = create_fraction(num_remain, denom_remain).expand()
# print "remain: ", repr(remain)
if num_found:
if denom_found:
found = create_fraction(num_found, denom_found)
else:
found = num_found
else:
if denom_found:
found = create_fraction(create_float(1), denom_found)
else:
found = ()
# print "found: ", found
# print len((found, remain))
return [(found, remain)]
def reduce_var(self, var):
"Reduce the fraction by another variable through division of numerator."
# We assume that this function is only called by reduce_ops, such that
# we just need to consider the numerator.
return create_fraction(self.num / var, self.denom)
def reduce_var(self, var):
"Reduce the fraction by another variable through division of numerator."
# We assume that this function is only called by reduce_ops, such that
# we just need to consider the numerator.
return create_fraction(self.num/var, self.denom)
def reduce_vartype(self, var_type):
"""Reduce expression with given var_type. It returns a tuple
(found, remain), where 'found' is an expression that only has variables
of type == var_type. If no variables are found, found=(). The 'remain'
part contains the leftover after division by 'found' such that:
self = found*remain."""
# Reduce the numerator by the var type.
# print "self.num._prec: ", self.num._prec
# print "self.num: ", self.num
if self.num._prec == 3:
foo = self.num.reduce_vartype(var_type)
if len(foo) == 1:
num_found, num_remain = foo[0]
# num_found, num_remain = self.num.reduce_vartype(var_type)[0]
else:
# meg: I have only a marginal idea of what I'm doing here!
# print "here: "
new_sum = []
for num_found, num_remain in foo:
if num_found == ():
new_sum.append(create_fraction(num_remain, self.denom))
else:
new_sum.append(create_fraction(create_product([num_found, num_remain]), self.denom))
return create_sum(new_sum).expand().reduce_vartype(var_type)
else:
# num_found, num_remain = self.num.reduce_vartype(var_type)
foo = self.num.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
num_found, num_remain = foo[0]
# # TODO: Remove this test later, expansion should have taken care of
# # no denominator.
# if not self.denom:
# error("This fraction should have been expanded.")
# If the denominator is not a Sum things are straightforward.
denom_found = None
denom_remain = None
# print "self.denom: ", self.denom
# print "self.denom._prec: ", self.denom._prec
if self.denom._prec != 3: # sum
# denom_found, denom_remain = self.denom.reduce_vartype(var_type)
foo = self.denom.reduce_vartype(var_type)
if len(foo) != 1:
raise RuntimeError("This case is not handled")
denom_found, denom_remain = foo[0]
# If we have a Sum in the denominator, all terms must be reduced by
# the same terms to make sense
else:
remain = []
for m in self.denom.vrs:
# d_found, d_remain = m.reduce_vartype(var_type)
foo = m.reduce_vartype(var_type)
d_found, d_remain = foo[0]
# If we've found a denom, but the new found is different from
# the one already found, terminate loop since it wouldn't make
# sense to reduce the fraction.
# TODO: handle I0/((I0 + I1)/(G0 + G1) + (I1 + I2)/(G1 + G2))
# better than just skipping.
# if len(foo) != 1:
# raise RuntimeError("This case is not handled")
if len(foo) != 1 or (denom_found is not None and repr(d_found) != repr(denom_found)):
# If the denominator of the entire sum has a type which is
# lower than or equal to the vartype that we are currently
# reducing for, we have to move it outside the expression
# as well.
# TODO: This is quite application specific, but I don't see
# how we can do it differently at the moment.
if self.denom.t <= var_type:
if not num_found:
num_found = create_float(1)
return [(create_fraction(num_found, self.denom), num_remain)]
else:
# The remainder is always a fraction
return [(num_found, create_fraction(num_remain, self.denom))]
# Update denom found and add remainder.
denom_found = d_found
remain.append(d_remain)
# There is always a non-const remainder if denominator was a sum.
denom_remain = create_sum(remain)
# print "den f: ", denom_found
# print "den r: ", denom_remain
# If we have found a common denominator, but no found numerator,
# create a constant.
# TODO: Add more checks to avoid expansion.
found = None
# There is always a remainder.
remain = create_fraction(num_remain, denom_remain).expand()
# print "remain: ", repr(remain)
if num_found:
if denom_found:
found = create_fraction(num_found, denom_found)
else:
found = num_found
else:
if denom_found:
found = create_fraction(create_float(1), denom_found)
else:
found = ()
# print "found: ", found
# print len((found, remain))
return [(found, remain)]
def __div__(self, other):
"Division by other objects."
# NOTE: We assume expanded objects.
# If division is illegal (this should definitely not happen).
if other.val == 0.0:
error("Division by zero.")
# Return 1 if the two symbols are equal.
if self._repr == other._repr:
return create_float(1)
# If other is a Sum we can only return a fraction.
# TODO: Refine this later such that x / (x + x*y) -> 1 / (1 + y)?
if other._prec == 3: # sum
return create_fraction(self, other)
# Handle division by FloatValue, Symbol, Product and Fraction.
# Create numerator and list for denominator.
num = [self]
denom = []
# Add floatvalue, symbol and products to the list of denominators.
if other._prec in (0, 1): # float or sym
denom = [other]
elif other._prec == 2: # prod
# Need copies, so can't just do denom = other.vrs.
denom += other.vrs
# fraction.
else:
# TODO: Should we also support division by fraction for generality?
# It should not be needed by this module.
error("Did not expected to divide by fraction.")
# Remove one instance of self in numerator and denominator if
# present in denominator i.e., x/(x*y) --> 1/y.
if self in denom:
denom.remove(self)
num.remove(self)
# Loop entries in denominator and move float value to numerator.
for d in denom:
# Add the inverse of a float to the numerator, remove it from
# the denominator and continue.
if d._prec == 0: # float
num.append(create_float(1.0/other.val))
denom.remove(d)
continue
# Create appropriate return value depending on remaining data.
# Can only be for x / (2*y*z) -> 0.5*x / (y*z).
if len(num) > 1:
num = create_product(num)
# x / (y*z) -> x/(y*z),
elif num:
num = num[0]
# else x / (x*y) -> 1/y.
else:
num = create_float(1)
# If we have a long denominator, create product and fraction.
if len(denom) > 1:
return create_fraction(num, create_product(denom))
# If we do have a denominator, but only one variable don't create a
# product, just return a fraction using the variable as denominator.
elif denom:
return create_fraction(num, denom[0])
# If we don't have any donominator left, return the numerator.
# x / 2.0 -> 0.5*x.
return num.expand()