/usr/share/pyshared/ffc/quadrature/fraction.py is in python-ffc 1.0.0-1.
This file is owned by root:root, with mode 0o644.
The actual contents of the file can be viewed below.
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145 146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211 212 213 214 215 216 217 218 219 220 221 222 223 224 225 226 227 228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259 260 261 262 263 264 265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309 310 311 312 313 314 315 316 317 318 319 320 321 322 323 324 325 326 327 328 329 330 331 332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353 354 355 356 | "This file implements a class to represent a fraction."
# Copyright (C) 2009-2010 Kristian B. Oelgaard
#
# This file is part of FFC.
#
# FFC is free software: you can redistribute it and/or modify
# it under the terms of the GNU Lesser General Public License as published by
# the Free Software Foundation, either version 3 of the License, or
# (at your option) any later version.
#
# FFC is distributed in the hope that it will be useful,
# but WITHOUT ANY WARRANTY; without even the implied warranty of
# MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
# GNU Lesser General Public License for more details.
#
# You should have received a copy of the GNU Lesser General Public License
# along with FFC. If not, see <http://www.gnu.org/licenses/>.
#
# First added: 2009-07-12
# Last changed: 2010-02-09
# FFC modules.
from ffc.log import error
from ffc.cpp import format
# FFC quadrature modules.
from symbolics import create_float
from symbolics import create_product
from symbolics import create_sum
from symbolics import create_fraction
from expr import Expr
class Fraction(Expr):
__slots__ = ("num", "denom", "_expanded", "_reduced")
def __init__(self, numerator, denominator):
"""Initialise a Fraction object, it derives from Expr and contains
the additional variables:
num - expr, the numerator.
denom - expr, the denominator.
_expanded - object, an expanded object of self, e.g.,
self = 'x*y/x'-> self._expanded = y (a symbol).
_reduced - object, a reduced object of self, e.g.,
self = '(2*x + x*y)/z'-> self._reduced = x*(2 + y)/z (a fraction).
NOTE: self._prec = 4."""
# Check for illegal division.
if denominator.val == 0.0:
error("Division by zero.")
# Initialise all variables.
self.val = numerator.val
self.t = min([numerator.t, denominator.t])
self.num = numerator
self.denom = denominator
self._prec = 4
self._expanded = False
self._reduced = False
# Only try to eliminate scalar values.
# TODO: If we divide by a float, we could add the inverse to the
# numerator as a product, but I don't know if this is efficient
# since it will involve creating a new object.
if denominator._prec == 0 and numerator._prec == 0: # float
self.num = create_float(numerator.val/denominator.val)
# Remove denominator, such that it will be excluded when printing.
self.denom = None
# Handle zero.
if self.val == 0.0:
# Remove denominator, such that it will be excluded when printing
self.denom = None
# Compute the representation now, such that we can use it directly
# in the __eq__ and __ne__ methods (improves performance a bit, but
# only when objects are cached).
if self.denom:
self._repr = "Fraction(%s, %s)" %(self.num._repr, self.denom._repr)
else:
self._repr = "Fraction(%s, %s)" %(self.num._repr, create_float(1)._repr)
# Use repr as hash value.
self._hash = hash(self._repr)
# Print functions.
def __str__(self):
"Simple string representation which will appear in the generated code."
if not self.denom:
return str(self.num)
# Get string for numerator and denominator.
num = str(self.num)
denom = str(self.denom)
# Group numerator if it is a fraction, otherwise it should be handled already.
if self.num._prec == 4: # frac
num = format["grouping"](num)
# Group denominator if it is a fraction or product, or if the value is negative.
# NOTE: This will be removed by the optimisations later before writing any code.
if self.denom._prec in (2, 4) or self.denom.val < 0.0: # prod or frac
denom = format["grouping"](denom)
# return num + format["division"] + denom
return format["div"](num, denom)
# Binary operators.
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 __mul__(self, other):
"Multiplication by other objects."
# NOTE: assuming that we get expanded variables.
# If product will be zero.
if self.val == 0.0 or other.val == 0.0:
return create_float(0)
# Create new expanded numerator and denominator and use '/' to reduce.
if other._prec != 4: # frac
return (self.num*other)/self.denom
# If we have a fraction, create new numerator and denominator and use
# '/' to reduce expression.
return create_product([self.num, other.num]).expand()/create_product([self.denom, other.denom]).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]
# The only thing that we shouldn't need to handle is division by other
# Fractions
if other._prec == 4:
error("Did not expected to divide by fraction.")
# Handle division by FloatValue, Symbol, Product and Sum in the same
# way i.e., multiply other by the donominator and use division
# (__div__ or other) in order to (try to) reduce the expression.
# TODO: Is it better to first try to divide the numerator by other,
# if a Fraction is the return value, then multiply the denominator of
# that value by denominator of self. Otherwise the reduction was
# successful and we just use the denom of self as denominator.
return self.num/(other*self.denom)
# Public functions.
def expand(self):
"Expand the fraction expression."
# If fraction is already expanded, simply return the expansion.
if self._expanded:
return self._expanded
# If we don't have a denominator just return expansion of numerator.
if not self.denom:
return self.num.expand()
# Expand numerator and denominator.
num = self.num.expand()
denom = self.denom.expand()
# TODO: Is it too expensive to call expand in the below?
# If both the numerator and denominator are fractions, create new
# numerator and denominator and use division to possibly reduce the
# expression.
if num._prec == 4 and denom._prec == 4: # frac
new_num = create_product([num.num, denom.denom]).expand()
new_denom = create_product([num.denom, denom.num]).expand()
self._expanded = new_num/new_denom
# If the numerator is a fraction, multiply denominators and use
# division to reduce expression.
elif num._prec == 4: # frac
new_denom = create_product([num.denom, denom]).expand()
self._expanded = num.num/new_denom
# If the denominator is a fraction multiply by the inverse and
# use division to reduce expression.
elif denom._prec == 4: # frac
new_num = create_product([num, denom.denom]).expand()
self._expanded = new_num/denom.num
# Use division to reduce the expression, no need to call expand().
else:
self._expanded = num/denom
return self._expanded
def get_unique_vars(self, var_type):
"Get unique variables (Symbols) as a set."
# Simply get the unique variables from numerator and denominator.
var = self.num.get_unique_vars(var_type)
var.update(self.denom.get_unique_vars(var_type))
return var
def get_var_occurrences(self):
"""Determine the number of minimum number of times all variables occurs
in the expression simply by calling the function on the numerator."""
return self.num.get_var_occurrences()
def ops(self):
"Return number of operations needed to evaluate fraction."
# If we have a denominator, add the operations and +1 for '/'.
if self.denom:
return self.num.ops() + self.denom.ops() + 1
# Else we just return the number of operations for the numerator.
return self.num.ops()
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_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)]
# FFC quadrature modules.
from floatvalue import FloatValue
from symbol import Symbol
from product import Product
from sumobj import Sum
|