def adjust_ret_list(retlist):
retlist[0].cdf_low="0.0"
retlist[-1].cdf_up="1.0"
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
min_value=gmpy2.exp10(-digits_for_input_cdf)
current=min_value
for pbox in retlist:
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
if gmpy2.is_zero(gmpy2.mpfr(pbox.cdf_low)) or gmpy2.mpfr(pbox.cdf_low)<current:
pbox.cdf_low=round_number_down_to_digits(current, digits_for_input_cdf)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundUp, precision=mpfr_proxy_precision) as ctx:
current=current+min_value
if gmpy2.is_zero(gmpy2.mpfr(pbox.cdf_up)) or gmpy2.mpfr(pbox.cdf_up)<current:
pbox.cdf_up=round_number_down_to_digits(current, digits_for_input_cdf)
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
current=gmpy2.sub(gmpy2.mpfr("1.0"), min_value)
for pbox in retlist[::-1]:
with gmpy2.local_context(gmpy2.context(), round=gmpy2.RoundDown, precision=mpfr_proxy_precision) as ctx:
if gmpy2.mpfr(pbox.cdf_up)==gmpy2.mpfr("1.0") or gmpy2.mpfr(pbox.cdf_up)>current:
pbox.cdf_up=round_number_up_to_digits(current, digits_for_input_cdf)
current=gmpy2.sub(current, min_value)
if gmpy2.mpfr(pbox.cdf_low)==gmpy2.mpfr("1.0") or gmpy2.mpfr(pbox.cdf_low)>current:
pbox.cdf_low=round_number_up_to_digits(current, digits_for_input_cdf)
retlist[0].cdf_low = "0.0"
retlist[-1].cdf_up = "1.0"
return retlist
def check_interval_is_zero(interval):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
left = mpfr(interval.lower)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
right = mpfr(interval.upper)
if gmpy2.is_zero(left) and gmpy2.is_zero(right):
return True
return False
def check_zero_is_in_interval(interval):
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
left = mpfr(interval.lower)
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
right = mpfr(interval.upper)
if gmpy2.is_zero(left) and interval.include_lower:
return True
if gmpy2.is_zero(right) and interval.include_upper:
return True
if left < mpfr("0.0") < right:
return True
return False
def ll(n):
two = mpz(2)
s = two * two
div = two**n - 1
for i in prange(2, n):
s = powmod(s, two, div)
s -= 2
if (not is_zero(s)):
raise Exception("Not Prime")
def clean_affine_operation(self):
keys = []
for key in self.coefficients:
value = self.coefficients[key]
remove = [False, False]
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
if gmpy2.is_zero(mpfr(value.lower)):
remove[0] = True
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
if gmpy2.is_zero(mpfr(value.upper)):
remove[1] = True
if remove[0] and remove[1]:
keys.append(key)
for delete in keys:
del self.coefficients[delete]
self.update_interval()
return self
def lucas_lehmer(n):
if n == 2:
return True
if not mp.is_prime(n):
return False
two = mp.mpz(2)
m = two**n - 1
s = two * two
for i in range(2, n):
sqr = s * s
s = (sqr & m) + (sqr >> n)
if s >= m:
s -= m
s -= two
return mp.is_zero(s)
def lucas_lehmer(n):
if n == 2:
return True
if not mp.is_prime(n):
return False
two = mp.mpz(2)
m = two**n - 1
s = two*two
for i in range(2, n):
sqr = s*s
s = (sqr & m) + (sqr >> n)
if s >= m:
s -= m
s -= two
return mp.is_zero(s)
def mpfr_to_mpf(f):
ctx = gmpy2.get_context()
p = ctx.precision
# emax = ctx.emax - 1
# emax = (2 ** (w - 1)) - 1
# emax + 1 = 2 ** (w - 1)
# ln2(emax + 1) = w - 1
# w = ln(emax + 1) + 1
# w = ln(ctx.emax) + 1
w = log2(ctx.emax) + 1
assert w.is_integer()
w = int(w)
# w = k - p
# k = w + p
k = w + p
eb = k - p
sb = p
rv = MPF(eb, sb)
if gmpy2.is_nan(f):
rv.set_nan()
elif gmpy2.is_infinite(f):
if gmpy2.sign(f) > 0:
rv.set_infinite(0)
else:
rv.set_infinite(1)
elif gmpy2.is_zero(f):
if str(f) == "-0.0":
rv.set_zero(1)
elif str(f) == "0.0":
rv.set_zero(0)
else:
assert False
else:
a, b = f.as_integer_ratio()
rv.from_rational(RM_RNE, Rational(int(a), int(b)))
assert mpf_to_mpfr(rv) == f
return rv
def fp_is_zero(self) -> Bit:
return Bit(gmpy2.is_zero(self._value))
def multiplication(self, interval):
reset_default_precision()
tmp_res_left = []
tmp_res_right = []
zero_is_included = self.check_zero_is_in_interval(
) or interval.check_zero_is_in_interval()
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundDown,
precision=mpfr_proxy_precision) as ctx:
tmp_res_left.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.lower)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.upper)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.lower)))
tmp_res_left.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.upper)))
min_index = [
i for i, value in enumerate(tmp_res_left)
if value == min(tmp_res_left)
]
with gmpy2.local_context(gmpy2.context(),
round=gmpy2.RoundUp,
precision=mpfr_proxy_precision) as ctx:
tmp_res_right.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.lower)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.lower), mpfr(interval.upper)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.lower)))
tmp_res_right.append(
gmpy2.mul(mpfr(self.upper), mpfr(interval.upper)))
max_index = [
i for i, value in enumerate(tmp_res_right)
if value == max(tmp_res_right)
]
tmp_bounds = [
self.include_lower * interval.include_lower,
self.include_lower * interval.include_upper,
self.include_upper * interval.include_lower,
self.include_upper * interval.include_upper
]
res_inc_left = any([tmp_bounds[index] for index in min_index])
res_inc_right = any([tmp_bounds[index] for index in max_index])
min_value = tmp_res_left[min_index[0]]
max_value = tmp_res_right[max_index[0]]
if gmpy2.is_zero(min_value) and zero_is_included:
res_inc_left = True
if gmpy2.is_zero(max_value) and zero_is_included:
res_inc_right = True
res_left = round_number_down_to_digits(min_value, self.digits)
res_right = round_number_up_to_digits(max_value, self.digits)
return Interval(res_left, res_right, res_inc_left, res_inc_right,
self.digits)