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spigot.py
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spigot.py
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from numpy import divmod
Buffer = tuple[list[int], list[int]]
def spigot_init(digits: int) -> Buffer:
size = 10 * digits // 3 + 1
spigot_list = [2] * size
prov_digits = []
return spigot_list, prov_digits
def radix_multiplication(b: Buffer) -> Buffer:
spigot_list, prov_digits = b
spigot_list = [10 * x for x in spigot_list]
return spigot_list, prov_digits
def norm_per_digit(b: Buffer, position: int) -> tuple[Buffer, int, int, int]:
if not position:
raise Exception("position is 0")
spigot_list = b[0].copy()
prov_digits = b[1].copy()
quot, rem = divmod(spigot_list[position], 2 * position + 1)
spigot_list[position] = rem
carry = quot * position
spigot_list[position - 1] = carry + spigot_list[position - 1]
b = (spigot_list, prov_digits)
return b, quot, rem, carry
def new_digit_gen(b: Buffer) -> tuple[Buffer, int, int]:
spigot_list = b[0].copy()
prov_digits = b[1].copy()
new_dig, rem = divmod(spigot_list[0], 10)
spigot_list[0] = rem
b = (spigot_list, prov_digits)
return b, new_dig, rem
def prov_digits_norm(b: Buffer, new_dig: int) -> Buffer:
spigot_list = b[0].copy()
prov_digits = b[1].copy()
if new_dig == 10:
prov_digits = [(x + 1) % 10 for x in prov_digits] + [0]
else:
prov_digits.append(new_dig)
return spigot_list, prov_digits
def digits_emission(b: Buffer, new_dig: int) -> tuple[Buffer, tuple[int]]:
spigot_list = b[0].copy()
prov_digits = b[1].copy()
if len(prov_digits) <= 1:
return (spigot_list, prov_digits), tuple()
if new_dig == 10:
digits_output = tuple(x for x in prov_digits[:-1])
prov_digits = prov_digits[-1:]
elif new_dig == 9:
digits_output = tuple()
else:
digits_output = tuple(prov_digits[:-1])
prov_digits = prov_digits[-1:]
b = (spigot_list, prov_digits)
return b, digits_output
def adv_by_cycles(b: Buffer, t: int) -> tuple[Buffer, tuple[int]]:
output = []
for _ in range(t):
b = adv_subcycle(b)
b, new_dig, _ = new_digit_gen(b)
b = prov_digits_norm(b, new_dig)
b, new_output = digits_emission(b, new_dig)
output += new_output
return b, output
def adv_subcycle(b: Buffer) -> Buffer:
b = radix_multiplication(b)
for i in range(len(b[0]) - 1, 0, -1):
b, _, _, _ = norm_per_digit(b, i)
return b