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https://github.com/logos-blockchain/logos-blockchain-specs.git
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09c9b7e4ec
* Implement generator polynomial and rs encoding * Implement encode/decode+test using fft. Non-working * Use lagrange for interpolation * Remove fft, use evaluations instead * Move and rename kzg and rs test modules * Update docs
89 lines
2.9 KiB
Python
89 lines
2.9 KiB
Python
from itertools import zip_longest
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from typing import List, Sequence, Self
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from sympy import ntt, intt
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class Polynomial[T]:
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def __init__(self, coefficients, modulus):
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self.coefficients = coefficients
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self.modulus = modulus
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@classmethod
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def from_evaluations(cls, evalutaions: Sequence[T], modulus) -> Self:
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coefficients = intt(evalutaions, prime=modulus)
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return cls(coefficients, modulus)
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def __repr__(self):
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return "Polynomial({}, modulus={})".format(self.coefficients, self.modulus)
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def __add__(self, other):
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return Polynomial(
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[(a + b) % self.modulus for a, b in zip_longest(self.coefficients, other.coefficients, fillvalue=0)],
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self.modulus
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)
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def __sub__(self, other):
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return Polynomial(
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[(a - b) % self.modulus for a, b in zip_longest(self.coefficients, other.coefficients, fillvalue=0)],
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self.modulus
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)
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def __mul__(self, other):
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result = [0] * (len(self.coefficients) + len(other.coefficients) - 1)
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for i in range(len(self.coefficients)):
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for j in range(len(other.coefficients)):
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result[i + j] = (result[i + j] + self.coefficients[i] * other.coefficients[j]) % self.modulus
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return Polynomial(result, self.modulus)
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def divide(self, other):
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if not isinstance(other, Polynomial):
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raise ValueError("Unsupported type for division.")
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dividend = list(self.coefficients)
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divisor = list(other.coefficients)
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quotient = []
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remainder = dividend
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while len(remainder) >= len(divisor):
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factor = remainder[-1] * pow(divisor[-1], -1, self.modulus) % self.modulus
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quotient.insert(0, factor)
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# Subtract divisor * factor from remainder
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for i in range(len(divisor)):
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remainder[len(remainder) - len(divisor) + i] -= divisor[i] * factor
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remainder[len(remainder) - len(divisor) + i] %= self.modulus
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# Remove leading zeros from remainder
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while remainder and remainder[-1] == 0:
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remainder.pop()
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return Polynomial(quotient, self.modulus), Polynomial(remainder, self.modulus)
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def __truediv__(self, other):
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return self.divide(other)
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def __neg__(self):
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return Polynomial([-1 * c for c in self.coefficients], self.modulus)
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def __len__(self):
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return len(self.coefficients)
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def __iter__(self):
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return iter(self.coefficients)
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def __getitem__(self, item):
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return self.coefficients[item]
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def __eq__(self, other):
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return self.coefficients == other.coefficients and self.modulus == other.modulus
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def eval(self, element):
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return sum(
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(pow(element, i)*x) % self.modulus for i, x in enumerate(self.coefficients)
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) % self.modulus
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def evaluation_form(self) -> List[T]:
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return ntt(self.coefficients, prime=self.modulus)
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