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"""Provides functions for unrolling formula intermediate values symvolically."""
from typing import List, Tuple
from astunparse import unparse
from public import public
from sympy import Expr, symbols, Poly
from pyecsca.misc.cache import sympify
from pyecsca.ec.formula.base import Formula
@public
def unroll_formula_expr(formula: Formula) -> List[Tuple[str, Expr]]:
"""
Unroll a given formula symbolically to obtain symbolic expressions for its intermediate values.
:param formula: Formula to unroll.
:return: List of symbolic intermediate values, with associated variable names.
"""
params = {
var: symbols(var)
for var in formula.coordinate_model.curve_model.parameter_names
}
inputs = {
f"{var}{i}": symbols(f"{var}{i}")
for var in formula.coordinate_model.variables
for i in range(1, formula.num_inputs + 1)
}
for coord_assumption in formula.coordinate_model.assumptions:
assumption_string = unparse(coord_assumption).strip()
lhs, rhs = assumption_string.split(" = ")
if lhs in params:
expr = sympify(rhs, evaluate=False)
params[lhs] = expr
for assumption_string in formula.assumptions_str:
lhs, rhs = assumption_string.split(" == ")
if lhs in formula.parameters:
# Handle a symbolic assignment to a new parameter.
expr = sympify(rhs, evaluate=False)
for curve_param, value in params.items():
expr = expr.xreplace({curve_param: value})
params[lhs] = expr
locls = {**params, **inputs}
values: List[Tuple[str, Expr]] = []
for op in formula.code:
result: Expr = op(**locls) # type: ignore
locls[op.result] = result
values.append((op.result, result))
return values
@public
def unroll_formula(formula: Formula) -> List[Tuple[str, Poly]]:
"""
Unroll a given formula symbolically to obtain symbolic expressions (as Polynomials) for its intermediate values.
:param formula: Formula to unroll.
:return: List of symbolic intermediate values, with associated variable names.
"""
values = unroll_formula_expr(formula)
polys = []
for name, result in values:
if result.free_symbols:
gens = list(result.free_symbols)
gens.sort(key=str)
poly = Poly(result, *gens)
polys.append((name, poly))
else:
# TODO: We cannot create a Poly here, because the result does not have free symbols (i.e. it is a constant)
pass
return polys
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