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381 lines
11 KiB
381 lines
11 KiB
# ===================================================================
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#
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# Copyright (c) 2014, Legrandin <helderijs@gmail.com>
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# All rights reserved.
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#
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# Redistribution and use in source and binary forms, with or without
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# modification, are permitted provided that the following conditions
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# are met:
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#
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# 1. Redistributions of source code must retain the above copyright
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# notice, this list of conditions and the following disclaimer.
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# 2. Redistributions in binary form must reproduce the above copyright
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# notice, this list of conditions and the following disclaimer in
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# the documentation and/or other materials provided with the
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# distribution.
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#
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# THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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# "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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# LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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# FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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# COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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# INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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# BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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# LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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# CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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# LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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# ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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# POSSIBILITY OF SUCH DAMAGE.
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# ===================================================================
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from ._IntegerBase import IntegerBase
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from Crypto.Util.number import long_to_bytes, bytes_to_long
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class IntegerNative(IntegerBase):
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"""A class to model a natural integer (including zero)"""
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def __init__(self, value):
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if isinstance(value, float):
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raise ValueError("A floating point type is not a natural number")
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try:
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self._value = value._value
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except AttributeError:
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self._value = value
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# Conversions
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def __int__(self):
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return self._value
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def __str__(self):
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return str(int(self))
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def __repr__(self):
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return "Integer(%s)" % str(self)
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# Only Python 2.x
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def __hex__(self):
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return hex(self._value)
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# Only Python 3.x
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def __index__(self):
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return int(self._value)
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def to_bytes(self, block_size=0):
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if self._value < 0:
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raise ValueError("Conversion only valid for non-negative numbers")
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result = long_to_bytes(self._value, block_size)
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if len(result) > block_size > 0:
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raise ValueError("Value too large to encode")
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return result
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@classmethod
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def from_bytes(cls, byte_string):
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return cls(bytes_to_long(byte_string))
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# Relations
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def __eq__(self, term):
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if term is None:
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return False
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return self._value == int(term)
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def __ne__(self, term):
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return not self.__eq__(term)
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def __lt__(self, term):
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return self._value < int(term)
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def __le__(self, term):
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return self.__lt__(term) or self.__eq__(term)
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def __gt__(self, term):
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return not self.__le__(term)
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def __ge__(self, term):
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return not self.__lt__(term)
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def __nonzero__(self):
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return self._value != 0
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__bool__ = __nonzero__
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def is_negative(self):
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return self._value < 0
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# Arithmetic operations
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def __add__(self, term):
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try:
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return self.__class__(self._value + int(term))
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except (ValueError, AttributeError, TypeError):
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return NotImplemented
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def __sub__(self, term):
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try:
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return self.__class__(self._value - int(term))
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except (ValueError, AttributeError, TypeError):
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return NotImplemented
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def __mul__(self, factor):
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try:
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return self.__class__(self._value * int(factor))
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except (ValueError, AttributeError, TypeError):
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return NotImplemented
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def __floordiv__(self, divisor):
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return self.__class__(self._value // int(divisor))
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def __mod__(self, divisor):
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divisor_value = int(divisor)
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if divisor_value < 0:
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raise ValueError("Modulus must be positive")
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return self.__class__(self._value % divisor_value)
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def inplace_pow(self, exponent, modulus=None):
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exp_value = int(exponent)
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if exp_value < 0:
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raise ValueError("Exponent must not be negative")
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if modulus is not None:
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mod_value = int(modulus)
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if mod_value < 0:
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raise ValueError("Modulus must be positive")
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if mod_value == 0:
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raise ZeroDivisionError("Modulus cannot be zero")
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else:
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mod_value = None
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self._value = pow(self._value, exp_value, mod_value)
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return self
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def __pow__(self, exponent, modulus=None):
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result = self.__class__(self)
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return result.inplace_pow(exponent, modulus)
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def __abs__(self):
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return abs(self._value)
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def sqrt(self, modulus=None):
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value = self._value
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if modulus is None:
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if value < 0:
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raise ValueError("Square root of negative value")
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# http://stackoverflow.com/questions/15390807/integer-square-root-in-python
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x = value
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y = (x + 1) // 2
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while y < x:
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x = y
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y = (x + value // x) // 2
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result = x
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else:
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if modulus <= 0:
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raise ValueError("Modulus must be positive")
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result = self._tonelli_shanks(self % modulus, modulus)
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return self.__class__(result)
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def __iadd__(self, term):
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self._value += int(term)
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return self
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def __isub__(self, term):
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self._value -= int(term)
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return self
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def __imul__(self, term):
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self._value *= int(term)
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return self
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def __imod__(self, term):
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modulus = int(term)
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if modulus == 0:
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raise ZeroDivisionError("Division by zero")
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if modulus < 0:
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raise ValueError("Modulus must be positive")
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self._value %= modulus
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return self
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# Boolean/bit operations
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def __and__(self, term):
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return self.__class__(self._value & int(term))
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def __or__(self, term):
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return self.__class__(self._value | int(term))
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def __rshift__(self, pos):
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try:
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return self.__class__(self._value >> int(pos))
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except OverflowError:
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if self._value >= 0:
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return 0
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else:
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return -1
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def __irshift__(self, pos):
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try:
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self._value >>= int(pos)
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except OverflowError:
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if self._value >= 0:
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return 0
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else:
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return -1
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return self
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def __lshift__(self, pos):
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try:
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return self.__class__(self._value << int(pos))
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except OverflowError:
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raise ValueError("Incorrect shift count")
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def __ilshift__(self, pos):
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try:
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self._value <<= int(pos)
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except OverflowError:
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raise ValueError("Incorrect shift count")
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return self
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def get_bit(self, n):
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if self._value < 0:
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raise ValueError("no bit representation for negative values")
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try:
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try:
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result = (self._value >> n._value) & 1
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if n._value < 0:
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raise ValueError("negative bit count")
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except AttributeError:
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result = (self._value >> n) & 1
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if n < 0:
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raise ValueError("negative bit count")
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except OverflowError:
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result = 0
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return result
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# Extra
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def is_odd(self):
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return (self._value & 1) == 1
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def is_even(self):
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return (self._value & 1) == 0
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def size_in_bits(self):
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if self._value < 0:
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raise ValueError("Conversion only valid for non-negative numbers")
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if self._value == 0:
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return 1
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bit_size = 0
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tmp = self._value
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while tmp:
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tmp >>= 1
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bit_size += 1
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return bit_size
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def size_in_bytes(self):
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return (self.size_in_bits() - 1) // 8 + 1
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def is_perfect_square(self):
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if self._value < 0:
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return False
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if self._value in (0, 1):
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return True
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x = self._value // 2
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square_x = x ** 2
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while square_x > self._value:
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x = (square_x + self._value) // (2 * x)
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square_x = x ** 2
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return self._value == x ** 2
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def fail_if_divisible_by(self, small_prime):
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if (self._value % int(small_prime)) == 0:
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raise ValueError("Value is composite")
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def multiply_accumulate(self, a, b):
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self._value += int(a) * int(b)
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return self
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def set(self, source):
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self._value = int(source)
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def inplace_inverse(self, modulus):
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modulus = int(modulus)
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if modulus == 0:
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raise ZeroDivisionError("Modulus cannot be zero")
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if modulus < 0:
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raise ValueError("Modulus cannot be negative")
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r_p, r_n = self._value, modulus
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s_p, s_n = 1, 0
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while r_n > 0:
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q = r_p // r_n
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r_p, r_n = r_n, r_p - q * r_n
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s_p, s_n = s_n, s_p - q * s_n
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if r_p != 1:
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raise ValueError("No inverse value can be computed" + str(r_p))
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while s_p < 0:
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s_p += modulus
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self._value = s_p
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return self
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def inverse(self, modulus):
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result = self.__class__(self)
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result.inplace_inverse(modulus)
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return result
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def gcd(self, term):
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r_p, r_n = abs(self._value), abs(int(term))
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while r_n > 0:
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q = r_p // r_n
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r_p, r_n = r_n, r_p - q * r_n
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return self.__class__(r_p)
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def lcm(self, term):
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term = int(term)
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if self._value == 0 or term == 0:
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return self.__class__(0)
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return self.__class__(abs((self._value * term) // self.gcd(term)._value))
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@staticmethod
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def jacobi_symbol(a, n):
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a = int(a)
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n = int(n)
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if n <= 0:
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raise ValueError("n must be a positive integer")
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if (n & 1) == 0:
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raise ValueError("n must be even for the Jacobi symbol")
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# Step 1
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a = a % n
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# Step 2
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if a == 1 or n == 1:
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return 1
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# Step 3
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if a == 0:
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return 0
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# Step 4
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e = 0
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a1 = a
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while (a1 & 1) == 0:
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a1 >>= 1
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e += 1
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# Step 5
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if (e & 1) == 0:
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s = 1
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elif n % 8 in (1, 7):
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s = 1
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else:
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s = -1
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# Step 6
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if n % 4 == 3 and a1 % 4 == 3:
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s = -s
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# Step 7
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n1 = n % a1
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# Step 8
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return s * IntegerNative.jacobi_symbol(n1, a1)
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