The concrete example I was working on when I started to miss double
break. This is an implementation of polynomial long division in Galois
field. Almost unmodified.
With outer break, I would't need to use the `running` variable. In fact,
for mathematical clarity, I would like to put a test in the outer loop,
like: `while dividend`. It would make clear what this algorithm is
actually doing.
Sure, it could be refactored, but it would lose the relative simplicity.
For such operations it is sometimes important to remain close to the raw
mathematical notation.
def __divmod__(self, other):
dividend = self.canonical()
try:
divisor = other.canonical()
except AttributeError:
return NotImplemented
if not dividend:
return Field.zero(self.size), Field.zero(self.size)
try:
d = next(iter(divisor)) # leading term of the divisor
except TypeError:
d = self.const(divisor)
do = self.__monomial_order(d)
result = Field.zero(self.size)
running = True
while running: # outer loop, retry the changing `dividend`
for x in dividend: # yield all monomials from this polynomial
if self.__monomial_order(x) < do:
# encountered monomial of too small order, finish
running = False
break # exit outer loop
try:
c = self.__monomial_division(x, d) # may fail
assert c # sanity check
result += c
dividend -= c * divisor
dividend = dividend.canonical()
# if `dividend` nonzero, try again
# if `dividend` is zero, finish
running = bool(dividend)
break
except ArithmeticError:
# monomial division failed, try next one
continue # inner loop
else:
# `dividend` exhausted, finish
running = False
pass
if not hasattr(result, 'operator'):
result = self.const(result)
return result.canonical(), dividend.canonical()
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