Source code for ffc.quadrature.quadraturetransformer
# -*- coding: utf-8 -*-
"QuadratureTransformer for quadrature code generation to translate UFL expressions."
# Copyright (C) 2009-2011 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/>.
#
# Modified by Peter Brune 2009
# Modified by Anders Logg 2009, 2013
# Modified by Lizao Li, 2015, 2016
# UFL common.
from ufl.utils.sorting import sorted_by_key
from ufl.measure import custom_integral_types, point_integral_types
# UFL Classes.
from ufl.classes import IntValue
from ufl.classes import FloatValue
from ufl.classes import Coefficient
from ufl.classes import Operator
# FFC modules.
from ffc.log import error, ffc_assert
from ffc.quadrature.cpp import format
# Utility and optimisation functions for quadraturegenerator.
from ffc.quadrature.quadraturetransformerbase import QuadratureTransformerBase
from ffc.quadrature.quadratureutils import create_permutations
from ffc.quadrature.reduce_operations import operation_count
from ffc.quadrature.symbolics import IP
return next(iter(d))
[docs]class QuadratureTransformer(QuadratureTransformerBase):
"Transform UFL representation to quadrature code."
def __init__(self, *args):
# Initialise base class.
QuadratureTransformerBase.__init__(self, *args)
# -------------------------------------------------------------------------
# Start handling UFL classes.
# -------------------------------------------------------------------------
# -------------------------------------------------------------------------
# AlgebraOperators (algebra.py).
# -------------------------------------------------------------------------
[docs] def sum(self, o, *operands):
# print("Visiting Sum: " + "\noperands: \n" + "\n".join(map(repr, operands)))
# Prefetch formats to speed up code generation.
f_group = format["grouping"]
f_add = format["add"]
f_mult = format["multiply"]
f_float = format["floating point"]
code = {}
# Loop operands that has to be summed and sort according to map (j,k).
for op in operands:
# If entries does already exist we can add the code, otherwise just
# dump them in the element tensor.
for key, val in sorted_by_key(op):
if key in code:
code[key].append(val)
else:
code[key] = [val]
# Add sums and group if necessary.
for key, val in sorted_by_key(code):
# Exclude all zero valued terms from sum
value = [v for v in val if v is not None]
if len(value) > 1:
# NOTE: Since we no longer call expand_indices, the following
# is needed to prevent the code from exploding for forms like
# HyperElasticity
duplications = {}
for val in value:
if val in duplications:
duplications[val] += 1
continue
duplications[val] = 1
# Add a product for each term that has duplicate code
expressions = []
for expr, num_occur in sorted_by_key(duplications):
if num_occur > 1:
# Pre-multiply expression with number of occurrences
expressions.append(f_mult([f_float(num_occur), expr]))
continue
# Just add expression if there is only one
expressions.append(expr)
ffc_assert(expressions, "Where did the expressions go?")
if len(expressions) > 1:
code[key] = f_group(f_add(expressions))
continue
code[key] = expressions[0]
else:
# Check for zero valued sum and delete from code
# This might result in returning an empty dict, but that should
# be interpreted as zero by other handlers.
if not value:
del code[key]
continue
code[key] = value[0]
return code
[docs] def product(self, o, *operands):
# print("Visiting Product with operands: \n" + "\n".join(map(repr,operands)))
# Prefetch formats to speed up code generation.
f_mult = format["multiply"]
permute = []
not_permute = []
# Sort operands in objects that needs permutation and objects that does not.
for op in operands:
# If we get an empty dict, something was zero and so is the product.
if not op:
return {}
if len(op) > 1 or (op and firstkey(op) != ()):
permute.append(op)
elif op and firstkey(op) == ():
not_permute.append(op[()])
# Create permutations.
# print("\npermute: " + repr(permute))
# print("\nnot_permute: " + repr(not_permute))
permutations = create_permutations(permute)
# print("\npermutations: " + repr(permutations))
# Create code.
code = {}
if permutations:
for key, val in sorted(permutations.items()):
# Sort key in order to create a unique key.
l = sorted(key) # noqa: E741
# Loop products, don't multiply by '1' and if we encounter a None the product is zero.
# TODO: Need to find a way to remove and J_inv00 terms that might
# disappear as a consequence of eliminating a zero valued term
value = []
zero = False
for v in val + not_permute:
if v is None:
ffc_assert(tuple(l) not in code, "This key should not be in the code.")
code[tuple(l)] = None
zero = True
break
elif not v:
print("v: '%s'" % repr(v))
error("should not happen")
elif v == "1":
pass
else:
value.append(v)
if not value:
value = ["1"]
if zero:
code[tuple(l)] = None
else:
code[tuple(l)] = f_mult(value)
else:
# Loop products, don't multiply by '1' and if we encounter a None the product is zero.
# TODO: Need to find a way to remove terms from 'used sets' that might
# disappear as a consequence of eliminating a zero valued term
value = []
for v in not_permute:
if v is None:
code[()] = None
return code
elif not v:
print("v: '%s'" % repr(v))
error("should not happen")
elif v == "1":
pass
else:
value.append(v)
# We did have values, but they might have been all ones.
if value == [] and not_permute != []:
code[()] = f_mult(["1"])
else:
code[()] = f_mult(value)
return code
[docs] def division(self, o, *operands):
# print("Visiting Division with operands: \n" + "\n".join(map(repr,operands)))
# Prefetch formats to speed up code generation.
f_div = format["div"]
f_grouping = format["grouping"]
ffc_assert(len(operands) == 2,
"Expected exactly two operands (numerator and denominator): " + repr(operands))
# Get the code from the operands.
numerator_code, denominator_code = operands
# TODO: Are these safety checks needed? Need to check for None?
ffc_assert(() in denominator_code and len(denominator_code) == 1,
"Only support function type denominator: " + repr(denominator_code))
code = {}
# Get denominator and create new values for the numerator.
denominator = denominator_code[()]
ffc_assert(denominator is not None, "Division by zero!")
for key, val in numerator_code.items():
# If numerator is None the fraction is also None
if val is None:
code[key] = None
# If denominator is '1', just return numerator
elif denominator == "1":
code[key] = val
# Create fraction and add to code
else:
code[key] = f_div(val, f_grouping(denominator))
return code
[docs] def power(self, o):
# print("\n\nVisiting Power: " + repr(o))
# Get base and exponent.
base, expo = o.ufl_operands
# Visit base to get base code.
base_code = self.visit(base)
# TODO: Are these safety checks needed? Need to check for None?
ffc_assert(() in base_code and len(base_code) == 1, "Only support function type base: " + repr(base_code))
# Get the base code.
val = base_code[()]
# Handle different exponents
if isinstance(expo, IntValue):
return {(): format["power"](val, expo.value())}
elif isinstance(expo, FloatValue):
return {(): format["std power"](val, format["floating point"](expo.value()))}
elif isinstance(expo, (Coefficient, Operator)):
exp = self.visit(expo)
return {(): format["std power"](val, exp[()])}
else:
error("power does not support this exponent: " + repr(expo))
[docs] def abs(self, o, *operands):
# print("\n\nVisiting Abs: " + repr(o) + "with operands: " + "\n".join(map(repr,operands)))
# Prefetch formats to speed up code generation.
f_abs = format["absolute value"]
# TODO: Are these safety checks needed? Need to check for None?
ffc_assert(len(operands) == 1 and () in operands[0] and len(operands[0]) == 1,
"Abs expects one operand of function type: " + repr(operands))
# Take absolute value of operand.
return {(): f_abs(operands[0][()])}
return {(): f_min(operands[0][()], operands[1][()])}
return {(): f_max(operands[0][()], operands[1][()])}
# -------------------------------------------------------------------------
# Condition, Conditional (conditional.py).
# -------------------------------------------------------------------------
[docs] def not_condition(self, o, *operands):
# This is a Condition but not a BinaryCondition, and the operand will be another Condition
# Get condition expression and do safety checks.
# Might be a bit too strict?
cond, = operands
ffc_assert(len(cond) == 1 and firstkey(cond) == (),
"Condition for NotCondition should only be one function: " + repr(cond))
return {(): format["not"](cond[()])}
[docs] def binary_condition(self, o, *operands):
# Get LHS and RHS expressions and do safety checks.
# Might be a bit too strict?
lhs, rhs = operands
ffc_assert(len(lhs) == 1 and firstkey(lhs) == (),
"LHS of Condition should only be one function: " + repr(lhs))
ffc_assert(len(rhs) == 1 and firstkey(rhs) == (),
"RHS of Condition should only be one function: " + repr(rhs))
# Map names from UFL to cpp.py.
name_map = {"==": "is equal", "!=": "not equal",
"<": "less than", ">": "greater than",
"<=": "less equal", ">=": "greater equal",
"&&": "and", "||": "or"}
# Get values and test for None
l_val = lhs[()]
r_val = rhs[()]
if l_val is None:
l_val = format["float"](0.0)
if r_val is None:
r_val = format["float"](0.0)
return {(): format["grouping"](l_val + format[name_map[o._name]] + r_val)}
[docs] def conditional(self, o, *operands):
# Get condition and return values; and do safety check.
cond, true, false = operands
ffc_assert(len(cond) == 1 and firstkey(cond) == (),
"Condtion should only be one function: " + repr(cond))
ffc_assert(len(true) == 1 and firstkey(true) == (),
"True value of Condtional should only be one function: " + repr(true))
ffc_assert(len(false) == 1 and firstkey(false) == (),
"False value of Condtional should only be one function: " + repr(false))
# Get values and test for None
t_val = true[()]
f_val = false[()]
if t_val is None:
t_val = format["float"](0.0)
if f_val is None:
f_val = format["float"](0.0)
# Create expression for conditional
expr = format["evaluate conditional"](cond[()], t_val, f_val)
num = len(self.conditionals)
name = format["conditional"](num)
if expr not in self.conditionals:
self.conditionals[expr] = (IP, operation_count(expr, format), num)
else:
num = self.conditionals[expr][2]
name = format["conditional"](num)
return {(): name}
# -------------------------------------------------------------------------
# FacetNormal, CellVolume, Circumradius, FacetArea (geometry.py).
# -------------------------------------------------------------------------
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
[docs] def facet_normal(self, o):
# print("Visiting FacetNormal:")
# Get the component
components = self.component()
# Safety check.
ffc_assert(len(components) == 1, "FacetNormal expects 1 component index: " + repr(components))
# Handle 1D as a special case.
# FIXME: KBO: This has to change for mD elements in R^n : m < n
if self.gdim == 1: # FIXME: MSA: UFL uses shape (1,) now, can we remove the special case here then?
normal_component = format["normal component"](self.restriction, "")
else:
normal_component = format["normal component"](self.restriction, components[0])
self.trans_set.add(normal_component)
return {(): normal_component}
error("This object should be implemented by the child class.")
[docs] def cell_volume(self, o):
# FIXME: KBO: This has to change for higher order elements
volume = format["cell volume"](self.restriction)
self.trans_set.add(volume)
return {(): volume}
[docs] def circumradius(self, o):
# FIXME: KBO: This has to change for higher order elements
circumradius = format["circumradius"](self.restriction)
self.trans_set.add(circumradius)
return {(): circumradius}
[docs] def facet_area(self, o):
# FIXME: KBO: This has to change for higher order elements
# NOTE: Omitting restriction because the area of a facet is the same
# on both sides.
# FIXME: Since we use the scale factor, facet area has no meaning
# for cell integrals. (Need check in FFC or UFL).
area = format["facet area"]
self.trans_set.add(area)
return {(): area}
[docs] def min_facet_edge_length(self, o):
# FIXME: this has no meaning for cell integrals. (Need check in FFC or UFL).
tdim = self.tdim
if tdim < 3:
return self.facet_area(o)
edgelen = format["min facet edge length"](self.restriction)
self.trans_set.add(edgelen)
return {(): edgelen}
[docs] def max_facet_edge_length(self, o):
# FIXME: this has no meaning for cell integrals. (Need check in FFC or UFL).
tdim = self.tdim
if tdim < 3:
return self.facet_area(o)
edgelen = format["max facet edge length"](self.restriction)
self.trans_set.add(edgelen)
return {(): edgelen}
error("This object should be implemented by the child class.")
error("This object should be implemented by the child class.")
# -------------------------------------------------------------------------
[docs] def create_argument(self, ufl_argument, derivatives, component, local_comp,
local_offset, ffc_element, transformation, multiindices,
tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
# Prefetch formats to speed up code generation.
f_group = format["grouping"]
f_add = format["add"]
f_mult = format["multiply"]
f_transform = format["transform"]
f_detJ = format["det(J)"]
f_inv = format["inverse"]
# Reset code
code = {}
# Handle affine mappings.
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create mapping and basis name.
# print "component = ", component
mapping, basis = self._create_mapping_basis(component, deriv,
avg, ufl_argument,
ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
# Add transformation
code[mapping].append(self.__apply_transform(basis,
derivatives,
multi, tdim,
gdim))
# Handle non-affine mappings.
else:
ffc_assert(avg is None,
"Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
if transformation in ["covariant piola",
"contravariant piola"]:
for c in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(c + local_offset, deriv, avg, ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = f_transform("JINV", c, local_comp, tdim, gdim, self.restriction)
self.trans_set.add(dxdX)
basis = f_mult([dxdX, basis])
elif transformation == "contravariant piola":
self.trans_set.add(f_detJ(self.restriction))
detJ = f_inv(f_detJ(self.restriction))
dXdx = f_transform("J", local_comp, c, gdim, tdim, self.restriction)
self.trans_set.add(dXdx)
basis = f_mult([detJ, dXdx, basis])
# Add transformation if needed.
code[mapping].append(self.__apply_transform(basis, derivatives, multi, tdim, gdim))
elif transformation == "double covariant piola":
# g_ij = (Jinv)_ki G_kl (Jinv)lj
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
k * tdim + l + local_offset,
deriv, avg, ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
J1 = f_transform("JINV", k, i, tdim, gdim,
self.restriction)
J2 = f_transform("JINV", l, j, tdim, gdim,
self.restriction)
self.trans_set.add(J1)
self.trans_set.add(J2)
basis = f_mult([J1, basis, J2])
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(
basis, derivatives, multi,
tdim, gdim))
elif transformation == "double contravariant piola":
# g_ij = (detJ)^(-2) J_ik G_kl J_jl
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
mapping, basis = self._create_mapping_basis(
k * tdim + l + local_offset,
deriv, avg, ufl_argument, ffc_element)
if mapping not in code:
code[mapping] = []
if basis is not None:
J1 = f_transform("J", i, k, gdim, tdim,
self.restriction)
J2 = f_transform("J", j, l, gdim, tdim,
self.restriction)
self.trans_set.add(J1)
self.trans_set.add(J2)
self.trans_set.add(f_detJ(self.restriction))
invdetJ = f_inv(f_detJ(self.restriction))
basis = f_mult([invdetJ, invdetJ, J1, basis,
J2])
# Add transformation if needed.
code[mapping].append(
self.__apply_transform(
basis, derivatives, multi,
tdim, gdim))
else:
error("Transformation is not supported: " +
repr(transformation))
# Add sums and group if necessary.
for key, val in list(code.items()):
if len(val) > 1:
code[key] = f_group(f_add(val))
elif val:
code[key] = val[0]
else:
# Return a None (zero) because val == []
code[key] = None
return code
[docs] def create_function(self, ufl_function, derivatives, component, local_comp,
local_offset, ffc_element, is_quad_element,
transformation, multiindices, tdim, gdim, avg):
"Create code for basis functions, and update relevant tables of used basis."
ffc_assert(ufl_function in self._function_replace_values, "Expecting ufl_function to have been mapped prior to this call.")
# Prefetch formats to speed up code generation.
f_mult = format["multiply"]
f_transform = format["transform"]
f_detJ = format["det(J)"]
f_inv = format["inverse"]
# Reset code
code = []
# Handle affine mappings.
if transformation == "affine":
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
# Create function name.
function_name = self._create_function_name(component, deriv, avg, is_quad_element, ufl_function, ffc_element)
if function_name:
# Add transformation if needed.
code.append(self.__apply_transform(function_name, derivatives, multi, tdim, gdim))
# Handle non-affine mappings.
else:
ffc_assert(avg is None, "Taking average is not supported for non-affine mappings.")
# Loop derivatives and get multi indices.
for multi in multiindices:
deriv = [multi.count(i) for i in range(tdim)]
if not any(deriv):
deriv = []
if transformation in ["covariant piola", "contravariant piola"]:
# Vectors
for c in range(tdim):
function_name = self._create_function_name(c + local_offset, deriv, avg, is_quad_element, ufl_function, ffc_element)
if function_name:
# Multiply basis by appropriate transform.
if transformation == "covariant piola":
dxdX = f_transform("JINV", c, local_comp, tdim, gdim, self.restriction)
self.trans_set.add(dxdX)
function_name = f_mult([dxdX, function_name])
elif transformation == "contravariant piola":
self.trans_set.add(f_detJ(self.restriction))
detJ = f_inv(f_detJ(self.restriction))
dXdx = f_transform("J", local_comp, c, gdim, tdim, self.restriction)
self.trans_set.add(dXdx)
function_name = f_mult([detJ, dXdx, function_name])
else:
error("Transformation is not supported: ", repr(transformation))
# Add transformation if needed.
code.append(self.__apply_transform(function_name, derivatives, multi, tdim, gdim))
elif transformation == "double covariant piola":
# g_ij = (Jinv)_ki G_kl (Jinv)lj
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
function_name = self._create_function_name(k * tdim + l + local_offset, deriv, avg, is_quad_element, ufl_function, ffc_element)
J1 = f_transform("JINV", k, i, tdim, gdim, self.restriction)
J2 = f_transform("JINV", l, j, tdim, gdim, self.restriction)
self.trans_set.add(J1)
self.trans_set.add(J2)
function_name = f_mult([J1, function_name, J2])
# Add transformation if needed.
code.append(self.__apply_transform(function_name, derivatives, multi, tdim, gdim))
elif transformation == "double contravariant piola":
# g_ij = (detJ)^(-2) J_ik G_kl J_jl
i = local_comp // tdim
j = local_comp % tdim
for k in range(tdim):
for l in range(tdim):
# Create mapping and basis name.
function_name = self._create_function_name(
k * tdim + l + local_offset,
deriv, avg, is_quad_element,
ufl_function, ffc_element)
J1 = f_transform("J", i, k, tdim, gdim,
self.restriction)
J2 = f_transform("J", j, l, tdim, gdim,
self.restriction)
invdetJ = f_inv(f_detJ(self.restriction))
self.trans_set.add(J1)
self.trans_set.add(J2)
function_name = f_mult([invdetJ, invdetJ, J1,
function_name, J2])
# Add transformation if needed.
code.append(self.__apply_transform(function_name,
derivatives,
multi, tdim,
gdim))
else:
error("Transformation is not supported: " + repr(transformation))
if not code:
return None
elif len(code) > 1:
code = format["grouping"](format["add"](code))
else:
code = code[0]
return code
# -------------------------------------------------------------------------
# Helper functions for Argument and Coefficient
# -------------------------------------------------------------------------
def __apply_transform(self, function, derivatives, multi, tdim, gdim): # XXX UFLACS REUSE
"Apply transformation (from derivatives) to basis or function."
f_transform = format["transform"]
# Add transformation if needed.
transforms = []
if self.integral_type in custom_integral_types:
for i, direction in enumerate(derivatives):
# Custom integrals to not need transforms, so in place
# of the transform, we insert an identity matrix
ref = multi[i]
if ref != direction:
transforms.append(0)
else:
for i, direction in enumerate(derivatives):
ref = multi[i]
t = f_transform("JINV", ref, direction, tdim, gdim, self.restriction)
self.trans_set.add(t)
transforms.append(t)
# Only multiply by basis if it is present.
if function:
prods = transforms + [function]
else:
prods = transforms
return format["multiply"](prods)
# -------------------------------------------------------------------------
# Helper functions for transformation of UFL objects in base class
# -------------------------------------------------------------------------
def _create_symbol(self, symbol, domain):
return {(): symbol}
def _create_product(self, symbols):
return format["multiply"](symbols)
def _format_scalar_value(self, value):
# print("format_scalar_value: %d" % value)
if value is None:
return {(): None}
# TODO: Handle value < 0 better such that we don't have + -2 in the code.
return {(): format["floating point"](value)}
def _math_function(self, operands, format_function):
# TODO: Are these safety checks needed?
ffc_assert(len(operands) == 1 and () in operands[0] and len(operands[0]) == 1,
"MathFunctions expect one operand of function type: " + repr(operands))
# Use format function on value of operand.
new_operand = {}
operand = operands[0]
for key, val in operand.items():
new_operand[key] = format_function(val)
return new_operand
def _atan_2_function(self, operands, format_function):
x1, x2 = operands
x1, x2 = sorted(x1.values())[0], sorted(x2.values())[0]
if x1 is None:
x1 = format["floating point"](0.0)
if x2 is None:
x2 = format["floating point"](0.0)
return {(): format_function(x1, x2)}
def _bessel_function(self, operands, format_function):
# TODO: Are these safety checks needed?
ffc_assert(len(operands) == 2,
"BesselFunctions expect two operands of function type: " + repr(operands))
nu, x = operands
ffc_assert(len(nu) == 1 and () in nu,
"Expecting one operand of function type as first argument to BesselFunction : " + repr(nu))
ffc_assert(len(x) == 1 and () in x,
"Expecting one operand of function type as second argument to BesselFunction : " + repr(x))
nu = nu[()]
x = x[()]
if nu is None:
nu = format["floating point"](0.0)
if x is None:
x = format["floating point"](0.0)
# Use format function on arguments.
# NOTE: Order of nu and x is reversed compared to the UFL and C++
# function calls because of how Symbol treats exponents.
# this will change once quadrature optimisations has been cleaned up.
return {(): format_function(x, nu)}
# -------------------------------------------------------------------------
# Helper functions for code_generation()
# -------------------------------------------------------------------------
def _count_operations(self, expression):
return operation_count(expression, format)
def _create_entry_data(self, val, integral_type):
# Multiply value by weight and determinant
# Create weight and scale factor.
weight = format["weight"](self.points)
if self.points is None or self.points > 1:
weight += format["component"]("", format["integration points"])
# Update sets of used variables.
if integral_type in (point_integral_types + custom_integral_types):
trans_set = set()
value = format["mul"]([val, weight])
else:
f_scale_factor = format["scale factor"]
trans_set = set([f_scale_factor])
value = format["mul"]([val, weight, f_scale_factor])
trans_set.update(self.trans_set)
used_points = set([self.points])
ops = self._count_operations(value)
used_psi_tables = set([v for k, v in self.psi_tables_map.items()])
return (value, ops, [trans_set, used_points, used_psi_tables])